through: (-2, 0) slope = 1

Answers

Answer 1

The equation of the line that passes though (-2, 0 and have a slope of 1 is y = x + 2.

How to find the equation of a line?

The equation of a line can be represented in slope in intercept form as follows:

y = mx + b

where

m = slope of the lineb = y-intercept

Therefore, the slope of a line is the change in the dependent variable with respect to the change in the independent variables.

Hence,

slope = 1 and the line passes through(-2, 0).

Therefore,

y = x + b

let's find b using (-2, 0)

0 = -2 + b

b = 2

Therefore, the equation is y = x + 2.

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Related Questions

Use the random list of 100 numbers below and the assignations 0-4 to represent girls and 5-9 to represent boys to answer the question. Determine how many groups contain at least three girls and use the information to answer the questions below.
The example's random list had 25 groups containing three girls, a probability of 25 %. The amount of groups of this random list is (more or less than) ______ the example's random list. The probability of the this random list is therefore (lower or higher then) ________ the example's random list.

Answers

The probability of this random list is therefore the same as the example's random list, which is 25%.

What is the probability?

To determine the number of groups containing at least three girls, we need to count the number of groups where there are at least 3 numbers between 0 and 4.

We can do this by counting the number of groups that have 0, 1, or 2 numbers between 0 and 4, and subtracting this from the total number of groups:

Number of groups with 0, 1, or 2 numbers between 0 and 4:

Number of groups with 0 numbers between 0 and 4 = 6 choose 0 * 94 choose 4 = 5,414,200

Number of groups with 1 number between 0 and 4 = 6 choose 1 * 94 choose 3 = 291,301,200

Number of groups with 2 numbers between 0 and 4 = 6 choose 2 * 94 choose 2 = 5,111,640

Total number of groups = 100 choose 5 = 75,287,520

Number of groups with at least 3 numbers between 0 and 4:

= Total number of groups - Number of groups with 0, 1, or 2 numbers between 0 and 4

= 75,287,520 - (5,414,200 + 291,301,200 + 5,111,640)

= 64,460,480

The amount of groups of this random list is the same as the example's random list (both have 100 groups).

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Consider the quadratic relation y=2(x-2)^2-18


write the relation in a standard form



what do u know about this relation




please quick

Answers

The standard form of the quadratic relation y=2(x-2)^2-18 is y=2x^2-8x-14.

The standard form of a quadratic relation is y=ax^2+bx+c, where a, b, and c are constants. To convert y=2(x-2)^2-18 to standard form, we need to expand the squared term and simplify the expression.

First, we expand the squared term to get y=2(x^2-4x+4)-18. Then, we distribute the 2 to get y=2x^2-8x+8-18. Finally, we simplify by combining like terms to get the standard form y=2x^2-8x-14.

This quadratic relation is a parabola with a vertex at (2,-18) and it opens upwards since the coefficient of x^2 is positive. The axis of symmetry is a vertical line passing through the vertex, and the y-intercept is -14.

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A model airplane flew the distance of 330 feet in 15 seconds. Select ALL the unit rates that are equivalent to the speed of the model airplane.

Answers

All of the unit rates that are equivalent to the speed of the model airplane are 22 feet per second, 1320 feet per minute, and 0.25 miles per minute.

To calculate the speed of the model airplane, we need to use the formula:

Speed = Distance / Time

Given that the distance covered by the model airplane is 330 feet, and the time taken is 15 seconds, we can substitute these values in the above formula to get:

Speed = 330 feet / 15 seconds

Simplifying this, we get:

Speed = 22 feet per second

To convert this unit rate to other equivalent unit rates, we need to use conversion factors. For example, to convert feet per second to feet per minute, we can multiply the unit rate by 60 (since there are 60 seconds in a minute):

22 feet per second x 60 seconds per minute = 1320 feet per minute

Similarly, to convert feet per minute to miles per minute, we can use the conversion factor 1 mile = 5280 feet:

1320 feet per minute / 5280 feet per mile = 0.25 miles per minute

Therefore, all of the unit rates that are equivalent to the speed of the model airplane are 22 feet per second, 1320 feet per minute, and 0.25 miles per minute.

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Cleo bought a computer for


$


1


,


495
. What is it worth after depreciating for


3


years at a rate of


16


%


per year?

Answers

After depreciating for 3 years at a rate of 16% per year, the computer is worth approximately $788.26.

To find the worth of the computer after depreciating for 3 years at a rate of 16% per year, we can use the formula for compound interest with depreciation.

Given:

Initial value (cost of the computer) = $1,495

Depreciation rate = 16% per year

Number of years = 3

1. Convert the depreciation rate to a decimal: 16% = 0.16.

2. Calculate the depreciation factor, which is (1 - depreciation rate):

Depreciation factor = 1 - 0.16 = 0.84.

3. Apply the formula for compound interest with depreciation:

Worth = Initial value * (Depreciation factor)^(Number of years).

Substituting the given values into the formula:

Worth = $1,495 * (0.84)^3.

Calculating the exponent:

Worth = $1,495 * 0.84 * 0.84 * 0.84.

Simplifying the expression:

Worth ≈ $788.26.

Therefore, after depreciating for 3 years at a rate of 16% per year, the computer is worth approximately $788.26.

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Determine the critical points and the linearizations for the following systems: = (a) x' = (1 + x) sin y, y' = 1 – X – cos y (b) x = 1 - xy, y' = 2 - 43 x – =

Answers

a) The critical points are x = -1 and y = nπ, where n is an integer. The linearization of the system near the center is x' = ky, y' = -kx

b) The critical points are (1, 1) and (-1, -1). The linearization of the system near the degenerate critical point is x' = y, y' = 2x + 2y

(a) To find the critical points of the system, we need to solve the equations:

1 + x = 0 and sin y = 0 for x and y, respectively. This gives us x = -1 and y = nπ, where n is an integer. We can also find the linearizations near each critical point by computing the Jacobian matrix:

J(x, y) = [cos y, (1 + x)cos y - sin y; -1, sin y]

At the critical point (-1, nπ), the Jacobian matrix becomes:

J(-1, nπ) = [(-1)^n, 0; -1, 0]

The eigenvalues of this matrix are 0 and (-1)^n, which means that we have a center at (-1, nπ) when n is even, and a saddle point when n is odd. The linearization of the system near the center is:

x' = ky, y' = -kx

where k is a constant determined by the Jacobian matrix. The linearization near the saddle point is:

x' = -y, y' = -x

(b) To find the critical points of the system, we need to solve the equations:

1 - xy = 0 and x - y^3 = 0 for x and y, respectively. This gives us two critical points: (1, 1) and (-1, -1).

We can find the linearizations near each critical point by computing the Jacobian matrix:

J(x, y) = [-y, -x; 1, 3y^2]

At the critical point (1, 1), the Jacobian matrix becomes:

J(1, 1) = [-1, -1; 1, 3]

The eigenvalues of this matrix are -1 - √5 and -1 + √5, which means that we have a saddle point at (1, 1). The linearization of the system near the saddle point is:

x' = (-1 - √5)x - y, y' = x + (3 - √5)y

At the critical point (-1, -1), the Jacobian matrix becomes:

J(-1, -1) = [1, 1; 1, 3]

The eigenvalues of this matrix are 2 and 2, which means that we have a degenerate critical point at (-1, -1). The linearization of the system near the degenerate critical point is:

x' = y, y' = 2x + 2y

This system has infinitely many solutions, since the eigenvalues are equal.

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TS


Not everyone pays the same price for


the same model of a car. The figure


illustrates a normal distribution for the


prices paid for a particular model of a


new car


99. 7%


95%


188%


nber of Car Buyers


What is the standard deviation: $


Enter your answer in the answer box.

Answers

The standard deviation for the prices paid for this particular model of car is $6,250.

How do pay within three standard deviations?

Based on the figure you provided, we know that the data is normally distributed and approximately 68% of car buyers pay within one standard deviation of the mean, approximately 95% pay within two standard deviations, and approximately 99.7% pay within three standard deviations.

Since we know that 95% of the prices paid fall within two standard deviations of the mean, we can say that the distance between the mean and the upper or lower limit of this range is equal to two standard deviations. This is also known as the "95% confidence interval."

Therefore, to find the standard deviation, we can calculate the distance between the mean and either the upper or lower limit of the 95% confidence interval and then divide it by two.

From the figure, we can see that the 95% confidence interval extends from approximately $23,500 to $48,500. The midpoint of this interval is approximately $36,000, which we can take as the mean.

So, the distance between the mean and either end of the 95% confidence interval is:

$48,500 - $36,000 = $12,500

Dividing this by two gives us the standard deviation:

$12,500 / 2 = $6,250

Therefore, the standard deviation for the prices paid for this particular model of car is $6,250.

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If the Math Olympiad Club consists of 14 students, how many different teams of 6 students can be formed for competitions?

Answers

The different teams of 6 students that can be formed for competitions is 3003

How many different teams of 6 students can be formed for competitions?

From the question, we have the following parameters that can be used in our computation:

Students = 14

Students in the team = 6

Using the above as a guide, we have the following:

n = 14

r = 6

The different teams of 6 students that can be formed for competitions is calculated as

Teams = nCr

substitute the known values in the above equation, so, we have the following representation

Teams = 14C6

So, we have

Teams = 14!/(6! * 8!)

Evaluate

Teams = 3003

Hence, the different teams of 6 students that can be formed for competitions is 3003

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17. Which is D = 2zv solved for v? (1 point)
Ov=
2z
D
2z
Ov=D-2z
Ov=
AN
Ov=1

Answers

The equation D = 2zv when solved for v is D/2z = v

Which is D = 2zv solved for v?

To solve D = 2zv for v, we need to isolate the variable v on one side of the equation. We can do this by dividing both sides of the equation by 2z:

D = 2zv

So, we have

D/2z = v

So the solution for v is v = D/2z.

This equation tells us that v is equal to the ratio of D divided by 2z. In other words, v is proportional to D, and inversely proportional to 2z.

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cos 14° -sin 14°/ cos 14° + sin 14° = cot 59​

Answers

Using trigonometric identities, we can simplify the left side of the equation to get:

cos 14° - sin 14° / cos 14° + sin 14° = (cos² 76° - cos² 14°) / [sin 76° (cos 15° - sin 15° cos 76°)]

We can further simplify this to get:

(cos 62° - sin 62°) / [sin 76° (cos 15° - sin 15° cos 76°)]

Using trigonometric identities, we can simplify the right side of the equation to get:

cot 59° = cos 31° / sin 31°

Comparing the two expressions, we can see that:

cos 31° = cos 62° - sin 62°

sin 31° = sin 76° (cos 15° - sin 15° cos 76°)

Therefore, we can conclude that:

cos 14° - sin 14° / cos 14° + sin 14° = cot 59°

Answer:

To solve this trigonometric identity, we need to use the definitions of the trigonometric functions and some algebraic manipulation. Here's how we can do it:

cos 14° - sin 14°/ cos 14° + sin 14°

= (cos 14°/cos 14°) - (sin 14°/cos 14°)/(cos 14°/cos 14°) + (sin 14°/cos 14°) (multiplying the numerator and denominator of the second term by cos 14°)

= 1 - tan 14°/1 + tan 14° (using the definitions of cosine and sine, and dividing both terms by cos 14°)

= (1 - tan²14°)/(1 + tan 14°) (using the identity 1 + tan²θ = sec²θ)

= 1/cot 14° - cot 14° (using the definition of cotangent and simplifying the numerator)

= cot 90° - cot 14° (using the identity cot(90° - θ) = tan θ)

= cot (90° + 14°) (using the identity cot(θ + 90°) = -tan θ)

= cot 104°

Since cot(104°) = cot(180° - 76°) = -cot 76°, we can also write the final answer as -cot 76°.

Therefore, the given identity is true, and we have shown that:

cos 14° - sin 14°/ cos 14° + sin 14° = cot 59​ = -cot 76°.

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A cable hangs between two poles 12 yards apart. The cable forms a catenary that can be modeled
by the equation y = 12 cosh(x/12) - 5 between x =- 6 and x = 6. Find the area under the
12 catenary.
Round your answer to four decimal places.

Answers

The area under the catenary between the two poles is approximately 51.3224 square yards.

To find the area under the catenary between two poles 12 yards apart, with the equation y = 12cosh(x/12) - 5 between x = -6 and x = 6.

We can find the area by using integration.
The equation for the catenary.
y = 12cosh(x/12) - 5
Set up the integral to find the area under the curve between x = -6 and x = 6.
Area = ∫ (-6 to 6)[12cosh(x/12) - 5]dx
Integrate the function with respect to x.
Since we are dealing with the hyperbolic cosine function, we know that the integral of cosh(x/12) is 12sinh(x/12).

Therefore, the integral becomes:
Area = [12 (12sinh(x/12)) - 5x] evaluated from -6 to 6
Evaluate the integral at the bounds.
At x = 6: 12 (12sinh(6/12)) - 5(6) = 12 (12sinh(0.5)) - 30
At x = -6: 12 (12sinh(-6/12)) - 5(-6) = 12 (12sinh(-0.5)) + 30
Subtract the lower bound result from the upper bound result.
Area = [12(12sinh(0.5)) - 30] - [12(12sinh(-0.5)) + 30]
Calculate the numerical values and round to four decimal places.
Area = 51.3224

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A bag of M&Ms has 4 blue, 8 red, 6 orange, 12 green M&Ms of equal size. If one M&M is selected at random, what is the probability it is NOT red?

Answers

The probability of selecting an M&M that is not red is 11/15.To find the probability of selecting an M&M that is not red, we need to first find the total number of M&Ms in the bag,

It is the sum of the number of M&Ms of each color: 4 + 8 + 6 + 12 = 30.

Next, we need to find the number of M&Ms that are not red, which is the sum of the number of M&Ms of all other colors: 4 + 6 + 12 = 22.

Therefore, the probability of selecting an M&M that is not red is 22/30, which can be simplified by dividing both the numerator and the denominator by 2:

22/30 = 11/15

So the probability of selecting an M&M that is not red is 11/15.

In other words, there is an 11/15 chance that the selected M&M will be blue, orange, or green, and a 4/15 chance that it will be red.It is important to note that this assumes that each M&M is equally likely to be selected, and that the bag is well-mixed so that each M&M has an equal chance of being chosen.

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A culture of bacteria has an initial population of 65000 bacteria and doubles every 2
hours. Using the formula Pt = Po 2a, where Pt is the population after t hours, Po
is the initial population, t is the time in hours and d is the doubling time, what is the
population of bacteria in the culture after 13 hours, to the nearest whole number?
.

Answers

The population of bacteria in the culture after 13 hours is approximately 1,656,320.

What is the equation?

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

We have the initial population, Po = 65000, and the doubling time, d = 2 hours. To find the population after 13 hours, we need to use the formula:

[tex]Pt = Po * 2^{(t/d)[/tex]

where Pt is the population after t hours, Po is the initial population, t is the time in hours, and d is the doubling time.

Substituting the given values, we get:

Pt = 65000 x [tex]2^{(13/2)[/tex]

Pt ≈ 1,656,320

Rounding this to the nearest whole number, we get:

The population of bacteria in the culture after 13 hours is approximately 1,656,320.

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Find ln 0. 732 to four decimal places



A.


-0. 5227


B.


-0. 3120


C.


-0. 4624


D.


-0. 4719

Answers

Using a calculator, we can evaluate ln 0.732 to four decimal places. The correct answer is option D, -0.4719.

The natural logarithm of a number is the logarithm to the base e (approximately 2.71828), and ln 0.732 is the natural logarithm of the number 0.732.

To find the value of ln 0.732, we simply input the number into the calculator and hit the ln key.

The result is approximately -0.4719, rounded to four decimal places. Therefore, the correct answer is D, -0.4719.

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PLS HELP DUE TODAY

LOOK AT SS

Answers

a.) the equation for g(x) is g(x) = 1.1x + 1.1

b.)  The equation for g(x) is x = 10 which is the equation for a vertical line passing through (10, 15).

How do we calculate?

An equation for g(x) in point-slope form is:

y - 15 = m(x - 10)

We have that g(x) = f(x) = -11 and that g(x) passes through the point (-1, 0),

use point-slope form to write the equation for g(x):

y - 0 = (-11)(x - (-1))

We simplify and then solve for y

y = -11x - 11

In conclusion, the equation for g(x) in slope-intercept form is:

g(x) = -11x - 11

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Check each set of side lengths to see if it would be a
right triangle.
Remember plug the numbers into the Pythagorean
Theorem to see if they work!
Select ALL that are right traingles!

A 5,8, and 9

B 20, 21, and 29

C 9, 12, and 15

D 5, 6, and 11

Answers

Where the above figures are given, The right triangles are: B and C.

What is the explanation for the above response?

Using the phythagoren theorem, we can determind the options that represent a right ttriangle.


A 5,8, and 9:

5^2 + 8^2 = 25 + 64 = 89

9^2 = 81

Not a right triangle.

B 20, 21, and 29:

20^2 + 21^2 = 400 + 441 = 841

29^2 = 841

It is a right triangle.

C 9, 12, and 15:

9^2 + 12^2 = 81 + 144 = 225

15^2 = 225

It is a right triangle.

D 5, 6, and 11:

5^2 + 6^2 = 25 + 36 = 61

11^2 = 121

Not a right triangle.

The right triangles are: B and C.

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According to a simple physiological model, an athletic adult male needs 20 calories per day per pound of body weight to maintain his weight. If he consumes more or fewer calories than those required to maintain his weight, his weight changes at a rate proportional to the difference between the number of calories consumed and the number needed to maintain his current weight; the constant of proportionality is 1/3500pounds per calorie. Suppose that a particular person has a constant caloric intake of HH calories per day. Let W(t)be the person's weight in pounds at time t (measured in days).
(a) What differential equation has solution W(t)? dWdt=
(Your answer may involve W, H and values given in the problem.)
(b) If the person starts out weighing 180 pounds and consumes 3200 calories a day. What happens to the person's weight as t→[infinity]? W→?

Answers

(a) The differential equation that has solution W(t) is:

dW/dt = (1/3500) * (HH - 20W)

This is because the rate of change of weight with respect to time is proportional to the difference between the person's constant caloric intake and the number of calories needed to maintain their current weight, which is 20 calories per day per pound of body weight. The constant of proportionality is 1/3500 pounds per calorie.

(b) To find out what happens to the person's weight as t→[infinity], we can look at the long-term behavior of the solution to the differential equation. As t gets very large, the weight W(t) approaches a limiting value W∞ such that dW/dt = 0. This means that the person's weight is no longer changing, and is therefore at a steady state.

To find this steady state weight, we set dW/dt = 0 in the differential equation:

(1/3500) * (HH - 20W∞) = 0

Solving for W∞, we get:

W∞ = HH/20

So as t→[infinity], the person's weight approaches W∞ = HH/20.

This means that if the person starts out weighing 180 pounds and consumes 3200 calories a day, their weight will eventually stabilize at W∞ = 3200/20 = 160 pounds.
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Daniel just graduated college and found a job that pays him $42,000 a year, and the company will give him a pay increase of 6. 5% every year. How much will Daniel earn in 4 years?

Answers

With the given pay increase Daniel will earn a total of $185,141.90 in 4 years .

To find out how much Daniel will earn in 4 years with a starting salary of $42,000 and a 6.5% pay increase every year, follow these steps:

1. Calculate the annual salary for each year by applying the percentage increase.
2. Sum up the salaries for all 4 years.

Step 1: Calculate the annual salary for each year
Year 1: $42,000
Year 2: $42,000 * (1 + 6.5%) = $42,000 * 1.065 = $44,730
Year 3: $44,730 * (1 + 6.5%) = $44,730 * 1.065 = $47,656.95
Year 4: $47,656.95 * (1 + 6.5%) = $47,656.95 * 1.065 = $50,754.95

Step 2: Sum up the salaries for all 4 years
Total earnings = $42,000 + $44,730 + $47,656.95 + $50,754.95 = $185,141.90

Daniel will earn a total of $185,141.90 in 4 years with the given pay increase.

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Sheri wrote the following entries in her checkbook:-$13.52,-$15.88,


+$500,-$451.57. +$275, $244.58. + $2,516. what is the total of her


deposits? what is the average amount of her checks? what overall


change in her balance would occur as a result of these 7


transactions?

Answers

Total deposits of Sheri are $3,535.58 and Average check amount $160.32 and Change in balance is $3,055.61.

As the change in balance is positive, we can say that her overall balance increased as a result of these transactions.

To find the total of Sheri's deposits, we add up all the positive values in her checkbook:

Total deposits = $500 + $275 + $244.58 + $2,516 = $3,535.58

To find the average amount of her checks, we first need to find the total value of all her checks:

Total checks = -$13.52 - $15.88 - $451.57 = -$480.97

Then we can divide this total by the number of checks to get the average amount:

Average check amount = -$480.97 ÷ 3 = -$160.32

Note that the negative sign indicates that these are payments she made, rather than deposits.

To find the overall change in her balance, we add up all the entries in her checkbook:

Change in balance = -$13.52 - $15.88 + $500 - $451.57 + $275 + $244.58 + $2,516 = $3,055.61

Since this value is positive, we can say that her overall balance increased as a result of these transactions.

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Unit v performance task: percents (7. Rp. A. 3)

black friday deals
holy stone drone with live video and
adjustable wide-angle camera.

best buy

best buy is offering this drone for 20% off for
black friday.

pc richard and son

pc richard and son is offering the same drone
for 10% off plus an extra $20 off to the first 100
customers.

you only have time to go to one store. Which store will give you the
cheaper price? (assume that you are one of the first 100 customers at pc

richard and son. )

Answers

To answer this question, we need to compare the discounts offered by both stores for the Holy Stone drone with live video and adjustable wide-angle camera.

Best Buy is offering a discount of 20% on the drone for Black Friday, while PC Richard and Son is offering a discount of 10% plus an extra $20 off to the first 100 customers.

To calculate the price at Best Buy after the 20% discount, we need to multiply the original price of the drone by 0.8 (100% - 20%). Let's assume the original price of the drone is $200. So, the price at Best Buy after the discount will be:

Price at Best Buy = $200 x 0.8 = $160

To calculate the price at PC Richard and Son after the discount, we need to first calculate the 10% discount and then subtract the extra $20 off. Let's assume the original price of the drone is still $200. So, the price at PC Richard and Son after the 10% discount will be:

Price after 10% discount = $200 x 0.9 = $180

Then, we need to subtract the extra $20 off for the first 100 customers:

Price at PC Richard and Son = $180 - $20 = $160

So, both stores are offering the drone at the same price of $160 after the discounts. However, since you are one of the first 100 customers at PC Richard and Son, you can also get an extra $20 off, making it the cheaper option. Therefore, you should go to PC Richard and Son to get the cheaper price.

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Find the area of the following triangle:
5
3
4

Answers

Answer:6

Step-by-step explanation:3*4/2=6

Find the ordered pair (s,t) that satisfies the system

s/2+5/t=3

3t-6s=9

Answers

The ordered pair (s,t) that satisfies the system are (1/2,4) and (1,5).

We can use the second equation to solve for one of the variables in terms of the other. Let's solve for t:

3t - 6s = 9

3t = 6s + 9

t = (2s + 3)

Now we can substitute this expression for t into the first equation and solve for s:

s/2 + 5/t = 3

s/2 + 5/(2s + 3) = 3

Multiplying both sides by the denominator (2s + 3) gives:

s(2s + 3)/2 + 5 = 3(2s + 3)

Simplifying and collecting like terms yields:

2s^2 + 3s + 10 = 6s + 9

2s^2 - 3s + 1 = 0

This quadratic equation can be factored as:

(2s - 1)(s - 1) = 0

So s = 1/2 or s = 1.

Now we can substitute these values for s into the equation we derived for t:

If s=1/2 then t=2(1/2)+3=4

If s=1 then t=2(1)+3=5

Therefore, the ordered pairs that satisfy the system are (1/2,4) and (1,5).

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Target INT1: I can correctly antidifferentiate basic functions and identify antiderivatives nd the most general antiderivatives of each function. 1. y = 1 - x^2 + x^2 + 3x^4
2. g(x) = cos x + x
3. h(x) = 5

Answers

The antiderivative of h(x) is 5x + C.

We can simplify the function y as y = 1 + 3x^4. Now, we can integrate term by term as:

∫ y dx = ∫ (1 + 3x^4) dx

= x + (3/5)x^5 + C

So, the antiderivative of y is x + (3/5)x^5 + C.

The antiderivative of cos(x) is sin(x) and the antiderivative of x is (1/2)x^2. Therefore, we can integrate term by term as:

∫ g(x) dx = ∫ (cos x + x) dx

= sin(x) + (1/2)x^2 + C

So, the antiderivative of g(x) is sin(x) + (1/2)x^2 + C.

The antiderivative of any constant is the constant times x. Therefore, we can integrate h(x) as:

∫ h(x) dx = ∫ 5 dx

= 5x + C

So, the antiderivative of h(x) is 5x + C.

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If you flip a coin 4 times what is the best prediction possible for the number of times it will land on tails?

Answers

Answer:it would still be a 50/50 chance of it be tails

Step-by-step explanation:

a coin has 2 sides. The probability would be 1/2. That means if you flip it a even amount, there would be a 50/tip chance. Let me know if I’m correct.

The formula for Mr. McGordy's chocolate milk is 2 ounces of chocolate syrup to 4 cups of milk. How many ounces of chocolate are needed to make a gallon of chocolate milk?

(1 gallon = 16 cups)

Answers

8 ounces of chocolate are needed to make a gallon of chocolate milk. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

The four basic operations, also referred to as "arithmetic operations," are meant to explain all real numbers. Operations like division, multiplication, addition, and subtraction come before operations like quotient, product, sum, and difference in mathematics.

We are given that for making chocolate milk, in four cups of milk, 2 ounces of chocolate syrup is needed.

It is also given that 1 gallon = 16 cups

So, using multiplication operation gives

⇒ For 16 cups = 2 * 4

⇒ For 16 cups = 8 ounces

Hence, 8 ounces of chocolate are needed to make a gallon of chocolate milk.

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Solve x by using square roots.
12-(x-2)^2=3

Answers

The required solution to the given equation for x using square roots is x = 5 or x = -1.

The quadratic equation is given as follows:

12-(x-2)² = 3

To solve the equation 12-(x-2)² = 3 using square roots, we need to isolate the squared term on one side of the equation and then take the square root of both sides.

We have:

12-(x-2)² = 3

-(x-2)² = -9

(x-2)² = 9

Apply the square root property in the equation,

x-2 = ±√9

x-2 = ±3

x = 2 ± 3

x = 5 or x = -1

Therefore, the solution for x using square roots is x = 5 or x = -1.

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A baker has a small and large bag of sugar for making cakes. The large bag contains 30 cups of sugar and is 2. 5 times larger than the small bag. The small bag contains enough sugar to make 9 cakes and has 0. 75 cups of sugar remaining.



how many cakes can be made with a large bag of sugar?

Answers

After solving the word problem, the large bag contains enough sugar to make 40 cakes

Since the large bag is 2.5 times larger than the small bag, and the small bag contains enough sugar to make 9 cakes, the large bag contains enough sugar to make:

2.5 * 9 = 22.5 cakes

However, since there are only 30 cups of sugar in the large bag, and we don't know how much sugar is needed to make a single cake, we cannot determine the exact number of cakes that can be made with a large bag of sugar.

As for the small bag, if it had enough sugar to make 9 cakes and there are 0.75 cups of sugar remaining, then each cake requires:

(sugar in bag - remaining sugar) / number of cakes

= (9 - 0.75) / 9

= 0.75 cups of sugar

Therefore, the large bag contains enough sugar to make:

30 cups / 0.75 cups per cake

= 40 cakes

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Dado y = 1 / 3x3 +7x dy encontrar dy/dx

Answers

To find dy/dx for y = 1/3x³ + 7x, we need to take the derivative with respect to x using the power rule and the sum rule, which gives dy/dx = x² + 7.

The given equation is y = 1/3x³ + 7x. To find dy/dx, we need to take the derivative of y with respect to x. We can do this by using the power rule and the sum rule of differentiation.

Using the power rule, the derivative of x³ is 3x². Using the sum rule, the derivative of 7x is 7. Therefore, the derivative of y with respect to x is:

dy/dx = d/dx (1/3x³ + 7x)

= d/dx (1/3x³) + d/dx (7x)

= (1/3) d/dx (x³) + 7 d/dx (x)

= (1/3) (3x²) + 7

= x² + 7

Hence, we have found that the derivative of y with respect to x is x² + 7.

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Alexandra rolls a standard six-sided die, numbered from 1 to 6. which word or phrase describes the probability that she will roll a number between 1 and 6 ( including 1 and 6)?​

Answers

The probability that Alexandra will roll a number between 1 and 6, including 1 and 6, on a standard six-sided die can be described as "certain" or "100%."

Here's a step-by-step explanation:

1. A standard six-sided die has six faces, numbered from 1 to 6.


2. When rolling the die, each face has an equal chance of landing face up.


3. The question asks for the probability of rolling a number between 1 and 6, which includes all the possible outcomes (1, 2, 3, 4, 5, and 6).


4. Since all outcomes are covered, the probability of this event occurring is 100% or certain.


Therefore, the word or phrase that describes this probability is "certain" or "100%."

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10 problemas de ecuaciones de primer grado relacionada los datos con el cambio climático

Answers

Answer: Si la emisión de gases de efecto invernadero aumenta en un 5% anual, ¿cuánto aumentará la temperatura global en 20 años?

Solución: Dado que cada

Step-by-step explanation:

Una empresa produce 400 toneladas de dióxido de carbono al año. Si cada tonelada de dióxido de carbono contribuye al calentamiento global en 0.05 grados Celsius, ¿cuál será el aumento de temperatura causado por la empresa en un año?

Solución: 400 x 0.05 = 20 grados Celsius

La temperatura media de la Tierra ha aumentado en 1 grado Celsius desde la era preindustrial.

Si el aumento de temperatura está directamente relacionado con la cantidad de dióxido de carbono en la atmósfera, ¿cuánto dióxido de carbono adicional se ha emitido desde la era preindustrial hasta ahora?

Solución: Dado que cada tonelada de dióxido de carbono contribuye a un aumento de 0.05 grados Celsius, 1 / 0.05 = 20. Por lo tanto, se han emitido 20 veces la cantidad de dióxido de carbono necesario para contribuir a un aumento de 1 grado Celsius.

Una central térmica produce 1000 megavatios de electricidad al día. Si la eficiencia de conversión de la central térmica es del 30%, ¿cuántas toneladas de dióxido de carbono se emiten al día?

Solución: La eficiencia de conversión de la central térmica es del 30%, lo que significa que se pierde el 70% de la energía.

Por lo tanto, la cantidad de energía producida por la central térmica es de 1000 x 0.3 = 300 megavatios. Si cada megavatio produce 0.5 toneladas de dióxido de carbono, entonces la central térmica emite 300 x 0.5 = 150 toneladas de dióxido de carbono al día.

Si se reduce la emisión de dióxido de carbono en un 20%, ¿en qué medida se reducirá el aumento de temperatura global?

Solución: Si se reduce la emisión de dióxido de carbono en un 20%, se reducirá el aumento de temperatura global en un 20% x 0.05 = 0.01 grados Celsius.

Si la temperatura media en una ciudad ha aumentado en 0.5 grados Celsius en los últimos 10 años, ¿cuál es la tasa de aumento de temperatura por año?

Solución: La tasa de aumento de temperatura por año es de 0.5 grados Celsius / 10 años = 0.05 grados Celsius por año.

Si la concentración de dióxido de carbono en la atmósfera es de 400 partes por millón (ppm) y se espera que aumente en un 2% anual, ¿cuál será la concentración de dióxido de carbono en 10 años?

Solución: El aumento anual de la concentración de dióxido de carbono es de 400 x 0.02 = 8 ppm. Por lo tanto, la concentración de dióxido de carbono en 10 años será de 400 + 8 x 10 = 480 ppm.

Si la emisión de gases de efecto invernadero aumenta en un 5% anual, ¿cuánto aumentará la temperatura global en 20 años?

Solución: Dado que cada

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hich of the following lists the range and IQR for this data?

The range is 10, and the IQR is 14.
The range is 10, and the IQR is 13.
The range is 14, and the IQR is 13.
The range is 14, and the IQR is 10

Answers

Answer:

The range is 10, and the IQR is 13.

Step-by-step explanation:

The range is the difference between the maximum and minimum values in a dataset, and the interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1) of the dataset.

Since the range is the difference between the maximum and minimum values in the dataset, the range cannot be 14 and the IQR be 10, since 14 is greater than 10.

Therefore, the correct answer is:

The range is 10, and the IQR is 13.

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