Identify an equation in standard form for ellipse with its center at the origin, a vertex at (3, 0), and a focus at (1, 0). Below are the options for the answer. HELP ASAP!!!

Answers

Answer 1

The equation in standard form of the eclipse is expressed as:

D. x²/9 + y²/8 = 1.

How to Write the Equation of an Eclipse in Standard Form?

The standard form equation for an ellipse with center at the origin, a vertex at (a, 0), and a focus at (c, 0) is:

x²/a² + y²/b² = 1, where c² = a² - b².

In this case, the center is at the origin, a vertex is at (3, 0), and a focus is at (1, 0).

Since the center is at the origin, we know that a vertex is located a distance of a units to the right and left of the center, so a = 3.

Since the focus is located a distance of c units to the right and left of the center, we know that c = 1.

Using c² = a² - b², we can solve for b²:

1² = 3² - b²

b² = 8

So the equation in standard form is:

x²/9 + y²/8 = 1.

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Related Questions

A large department store found that it averages 362 customers per hour. Assume that the standard deviation is 29.6 and a random sample of 40 hours was used to determine the average. Which statements about this situation are true?

Answers

The 99% confidence interval of the population mean is (352.32, 371.68).

To find the 99% confidence interval of the population mean, we need to use the following formula:

CI = x; ± zα/2 * (σ/√n)

where:

x' = sample mean (362)

zα/2 = z-score for 99% confidence level (2.576)

σ = population standard deviation (29.6)

n = sample size (40)

Substituting the values, we get:

CI = 362 ± 2.576 * (29.6/√40)

CI = 362 ± 9.68

This means that if we take many random samples of 40 hours from the population, we can be 99% confident that the true population mean of the number of customers per hour falls between 352.32 and 371.68.

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Complete question is:

How do you write 9.6 × 103 in standard form?

Answers

your answer is 1,248 this bro

An agency wanted to study annual-sales distribution of 500 cottage industries of the same standard. Since the industries are located in different regions, it will be expensive to collect data from all 500 industries. Thus, the study is to be based on the sales of 75 industries which are selected to represent the whole. a) The agency summarized the collected data in tabular form, displayed it in graph and further found the average annual sales to be 36 thousand birr. What type of statistical technique is used here? b) The average sale of the 500 cottage industries is estimated to be 36 thousand birr based on the sample average. What type of statistical technique is used here?

Answers

The type of statistical technique used here is inferential

We are given that;

Annual-sales distribution of cottage industries of the same standard=500

Number of industries=500

Now,

a) The type of statistical technique used here is descriptive statistics, which involves summarizing, organizing, and presenting data in a meaningful way. Descriptive statistics can use tables, graphs, and numerical measures such as mean, median, mode, range, standard deviation, etc. to describe the main features and patterns of a data set.

b) The type of statistical technique used here is inferential statistics, which involves drawing conclusions or making predictions about a population based on a sample. Inferential statistics can use methods such as estimation, hypothesis testing, confidence intervals, regression analysis, etc. to make inferences about the population parameters from the sample statistics.

Therefore, by statistics the answer will be inferential.

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Suppose that the function h is defined as follows.

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For the given function h(x) the points can be plotted on,

(-1,-1)(0,0)(1,1)(2,2)

The given function h(x) is having four conditions and each condition can be clearly discussed below:

Given that for the first condition, the x-axis is ranging from -1 [tex]\leq[/tex] x < 0, the y-axis point is present exactly at -1. Similarly, for the second condition, the x-axis is ranging from 0 [tex]\leq[/tex] x < 1, and the y-axis point is present at 0. For the third condition, the x-axis is ranging from 1 [tex]\leq[/tex] x < 2, and the y-axis point is at 1.Finally, for the fourth condition, the x-axis is ranging from 2 [tex]\leq[/tex] x < 3, and the y-axis point is at 2.

From, the above analysis we plotted the graph and attaching below.

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A metallurgist made two purchases. The first purchase, which cost $1224, included 48 kilograms of an iron alloy and 40 kilograms of a lead alloy. The second purchase, at the same price, cost $507 and included 24 kilograms of the iron alloy and 13 kilograms of the lead alloy. Find the cost per kilogram of the iron and lead alloys. What is the cost of the iron alloy and the lead alloy?

Answers

Let's start by finding the cost per kilogram of each alloy.
For the first purchase:
- 48 kilograms of iron alloy and 40 kilograms of lead alloy cost $1224.
- Let x be the cost per kilogram of the iron alloy and y be the cost per kilogram of the lead alloy.
- We can write a system of two equations to represent the cost of the alloys:
```
48x + 40y = 1224
x + y = ?
```
We don't know the total cost per kilogram of both alloys combined, so we'll use a variable to represent it: `x + y = z`.
For the second purchase:
- 24 kilograms of iron alloy and 13 kilograms of lead alloy cost $507.
- We can use the total cost per kilogram of both alloys combined to find the cost of each alloy. We know that the total cost per kilogram is the same for both purchases, so we can write:
```
24x + 13y = 507
```
Now we can solve the system of equations:
```
48x + 40y = 1224
24x + 13y = 507
```
Multiplying the second equation by 2 to get the same number of x's as the first equation:
```
48x + 26y = 1014
48x + 40y = 1224
```
Subtracting the first equation from the second:
```
14y = 210
y = 15
```
Substituting y into the first equation:
```
48x + 40(15) = 1224
48x = 624
x = 13
```
So the cost per kilogram of the iron alloy is $13 and the cost per kilogram of the lead alloy is $15.
To find the cost of each alloy:
- For the first purchase, the cost of the 48 kilograms of iron alloy is 48 x $13 = $624, and the cost of the 40 kilograms of lead alloy is 40 x $15 = $600.
- For the second purchase, the cost of the 24 kilograms of iron alloy is 24 x $13 = $312, and the cost of the 13 kilograms of lead alloy is 13 x $15 = $195.
So the total cost of the iron alloy is $624 + $312 = $936, and the total cost of the lead alloy is
!

I would be rally thankful if you help

Answers

The matrix after the row operation is given as follows:

[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]

The row operation is given as follows:

Division by 7 = multiplication by 1/7, as the element at the desired position is of 7.

How to do the row operation?

The matrix in the context of this problem is defined as follows:

[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]

We want to have element 1 into row 1 and column 1, that is, the element of 7 at row 1 and column 1 of the matrix must assume a value of -1.

An example of a valid row operation is the multiplication of the row by a constant, and as the element has a value of 7, the constant to obtain a value of 1 is:

7/k = 1

k = 7.

Dividing every element of the first row by 7, the resulting matrix is then given as follows:

[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]

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Please help me this is so hard and i really dont get this. if you help me with both parts ill give you 60 points

Answers

1) We can rewrite the function in vertex form to find the time when the ball hits the ground. To do this, we need to complete the square.

h(t) = -5t^2 + 40t

h(t) = -5(t^2 - 8t)

h(t) = -5(t^2 - 8t + 16) + 80 (adding and subtracting 16 inside the parentheses to complete the square)

h(t) = -5(t - 4)^2 + 80 (factoring and simplifying)

So, the function in vertex form is h(t) = -5(t - 4)^2 + 80.

2) To find when the ball hits the ground, we need to find when h(t) = 0, since h(t) represents the height of the ball above the ground.

0 = -5(t - 4)^2 + 80 (substituting h(t) = 0)

5(t - 4)^2 = 80

(t - 4)^2 = 16

t - 4 = ±4

t = 4 ± 4

So, the ball hits the ground at t = 0 or t = 8 seconds after launch. However, we can discard the t = 0 solution because that represents the time when the ball is launched, and we are looking for when it hits the ground. Therefore, the ball hits the ground at t = 8 seconds after launch.

Express all real numbers greater than 2 in interval notation

Answers

The interval-notation for "all real-numbers" greater than 2 is (2, ∞).

The "Interval-Notation" is a way of expressing a set of real numbers using brackets to show which numbers are included in the set. In the case of all real numbers greater than 2, we can write this as:

(2, ∞)

The open-bracket "(" indicate that the number 2 is not included in the set, while the symbol "∞" represents all real numbers greater than 2.

This notation is used to express an open interval, meaning that the endpoints (in this case, 2 and infinity) are not included in the set.

Therefore, the required interval-notation is (2, ∞).

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how large a sample should be taken if the population mean is to be estimated with 98 percent confidence to within $100? The population has a standard deviation of $800.

Answers

A sample of at least 433 individuals would need to be taken to estimate the population mean with 98% confidence to within $100.

Understanding Population Estimate

To estimate the sample size needed to estimate the population mean with 98% confidence to within $100, we can use the formula:

n = (z * σ / E)²

where:

n = sample size

z = z-score for the desired level of confidence (98% in this case), which can be found using a standard normal distribution table or calculator. For 98% confidence, the z-score is approximately 2.33.

σ = population standard deviation ($800 in this case)

E = margin of error ($100 in this case)

Plugging in the values, we get:

n = (2.33 * 800 / 100)²

n ≈ 432.64

Rounding up to the nearest whole number, we get a sample size of 433. Therefore, a sample of at least 433 individuals would need to be taken to estimate the population mean with 98% confidence to within $100.

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40% of the fish are carp and 60% of the fish are bass. What’s the probability that the next three fish I catch are all carp?

Answers

Answer:

0.064 or 6.4%

----------------------------

The probability of catching a carp is 40% since 40% of the fish are carp.

We assume the fish is replaced each time so the probability of three carps is:

P = 0.4³ = 0.064 or 6.4%

Help pleaseee

Expand the logarithm as much as possible

logy^10

Answers

The expanded form of log y^10 is either 10 log y or 10 ln y

Expanding the logarithm

Assuming that the base of the logarithm is not specified, we can use the change of base formula to expand the logarithm:

log y^10 = log (y^10) / log (base)

Using base 10:

log y^10 = log (y^10) / log 10

= 10 log y / 1

= 10 log y

Using natural logarithm:

log y^10 = log (y^10) / log e

= 10 log y / 1

= 10 ln y

Therefore, the expanded form of log y^10 is either 10 log y or 10 ln y, depending on the base used.

Answers

The value of b when the graph of function f(x) = a*bˣ passes through (2,54) and (5,16), is given by, b = 2/3.

Given the function of the graph is,

f(x) = a*bˣ

It is given that the graph of the function passes through the points with coordinates (2, 54) and (5, 16). So this points must satisfy the given function.

Substituting the point (2, 54) in the given function we get,

f(2) = 54

a*b² = 54 ..................... (i)

Substituting the point (5, 16) in the given function we get,

f(5) = 16

a*b⁵ = 16 ..................... (ii)

So dividing equation (ii) by equation (i) we get,

(a*b⁵)/(a*b²) = 16/54

b³ = 8/27

b³ = (2/3)³

b = 2/3

Hence the value of b is 2/3.

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Apply the repeated nearest neighbor algorithm to the graph above. Starting at which vertex or vertices produces the circuit of lowest cost?

Answers

The vertices that produces the circuit of lowest cost is A and D. So, the correct answer is A) and D).

To apply the repeated nearest neighbor algorithm, we need to start at a vertex and repeatedly choose the nearest neighbor until all vertices have been visited. Then, we return to the starting vertex to complete the circuit.

Starting at vertex A, we can follow the path A-DE-BE-C-AD-BC-E-A. The total cost of this circuit is 3 + 1 + 13 + 7 + 6 + 5 + 3 = 38. Starting at vertex B, we can follow the path B-E-DE-BC-AD-C-A-B. The total cost of this circuit is 1 + 3 + 7 + 6 + 5 + 15 + 10 = 47.

Starting at vertex C, we can follow the path C-BC-AD-DE-E-B-CA-C. The total cost of this circuit is 5 + 6 + 1 + 13 + 3 + 15 = 43. Starting at vertex D, we can follow the path D-AD-BC-C-E-DE-BD-DA. The total cost of this circuit is 6 + 5 + 7 + 3 + 10 + 11 = 42.

Starting at vertex E, we can follow the path E-DE-BE-C-BC-AD-CA-E. The total cost of this circuit is 1 + 13 + 7 + 5 + 6 + 15 = 47. Therefore, the circuits with the lowest cost are those starting at vertex A and vertex D, both with a total cost of 38 and 42 respectively. So, the correct option is A) and D).

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100 Points! Algebra question. Only looking for an answer to B. Please show as much work as possible. Thank you! Photo attached.

Answers

The quotient of functions f(x) and g(x) is given as follows:

(f/g)(x) = (x + 4)/(x - 3).

How to obtain the quotient function?

The quotient function of f(x) and g(x) is given by the division of function f(x) by function g(x), as follows:

(f/g)(x) = f(x)/g(x)

The functions for this problem are given as follows:

f(x) = x² + 7x + 12.g(x) = x² - 9.

The functions can be factored as follows:

f(x) = (x + 4)(x + 3) -> according to it's roots.f(x) = (x + 3)(x - 3) -> subtraction of perfect squares.

The term (x + 3) is common to both numerator and denominator, hence it is simplified and the quotient function is given as follows:

(f/g)(x) = (x + 4)/(x - 3).

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Joey wants to buy a $3,000 vehicle with 20 percent down for three years at 12 percent interest. What will his monthly payment be?
Monthly Payment per $1,000 Finance
A. $72.82
B. $89.67
C. $79.70
D. $119.56

Answers

Joey’s monthly payment is solved to be

C. $79.70

How to find the monthly payment

20% down 600 to calculate the monthly payment on a 3 000 car we would pay 2 400.

the interest rate is 12% per annum which equates to 1% per month the term of the loan is three years which equates to 36 months we can use a formula to calculate the monthly payments

[tex]Monthly salary = (P * r * (1 + r)^n) / ((1 + r)^n - 1) .[/tex]

where

P is the principal (premium),

r is the monthly interest rate, and

n is the number of months.

Plug in the prices and we have:

[tex]Monthly salary = (2400 * 0.01 * (1 + 0.01)^{36} ) / ((1 + 0.01)^{36} - 1)[/tex]

= $79.65 per square foot

So Joey’s monthly payment would be $79.65.

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Maggie spent $16 on rock climbing. This included a $6 charge for climbing shoes and a $2.50 charge per hour she climbed. If h represents the number of hours she climbed for, write an equation that can be solved to find the number of hours she spent rock climbing.

Answers

Answer:

16 = 6+2.5h

Step-by-step explanation:

The total cost is 16 dollars. She spends 6 dollars for shoes and 2.50 per hour.

16 = 6+2.5h

To solve, subtract 6 from each side

16-6 = 6+2.5h-6

10 = 2.5h

Divide each side by 2.5

10/2.5 = 2.5h/2.5

4 =h

She can climb for 4 hours.

I need help, I’m struggling with 3 and 4 can someone help me

Answers

Answer:

3 and 4 ==> see work below

[tex]5. \quad\quad f^{-1}(x) = x^{1/7}[/tex]

[tex]6. \quad\quad f^{-1}(x) = -\left(\dfrac{5x}{2}\right)^{1/3}$}\\\text{We can also write this as $-\sqrt[3]{\frac{5x}{2}}$ }\\[/tex]

Step-by-step explanation:

Definition of inverse functions

If f and g are inverse functions, then f(x) = y if and only if g(y) = x

Or, in other words
If f(g(x)) = (g(f(x)) = x
then f and g are inverse functions

We have f(x) = x + 4 and g(x) = x - 4

To find f(g(x)), substitute g(x) = x - 4 wherever there is an x term in f(x)

f(g(x)) = g(x) + 4

= x - 4 + 4 = x

g(f(x)) = f(x) - 4

= x + 4 - 4 =x

Hence f(x) and g(x) are inverse functions

[tex]f(x) = \dfrac{1}{4}x^3\\\\g(x) = (4x)^{1/3}[/tex]

[tex]\\\begin{aligned}f(g(x)) &= \dfrac{1}{4} (g(x))^3\\\\\end{aligned}[/tex]

[tex]\begin{aligned}(g(x))^3 &= \left((4x)^{1/3} \right)^3 \\& = (4x)^{\frac{1}{3} \cdot 3}\\& = 4x\end{aligned}[/tex]

Therefore

[tex]\\\begin{aligned}f(g(x)) &= \dfrac{1}{4} (g(x))^3\\&= \dfrac{1}{4} \cdot 4x\\&= x\\\end{aligned}[/tex]

[tex]\begin{aligned}g\left(f(x)\right) & = \left(4f(x)\right)^{1/3}\\&= \left(4 \cdot \dfrac{1}{4}x^3\right)^{1/3}\\& = \left(x^3\right)^{1/3}\\& =x& \end{aligned}[/tex]

So f(x) and g(x) are inverse functions

[tex]\text{Given $f(x) = x^7 $ we are asked to find inverse $f^{-1}(x)$}[/tex]

[tex]\rm{Let \: y = f(x) = x^7}\\[/tex]

Interchange x and y:
[tex]x = y^7[/tex]

Solve for y:
[tex]y = x^{1/7}[/tex]

The right hand side is the inverse function of f(x)

[tex]f^{-1}(x) = x^{1/7}[/tex]

Q6
[tex]\rm{Given \;f(x) = -\dfrac{2}{5}x^3 \:find\:the\:inverse,\;f^{-1}(x)}[/tex]

Using the same procedure as for Q5

[tex]y=-\dfrac{2}{5}x^3\\\\x=-\dfrac{2}{5}y^3\\\\\text{Solve for y}\\[/tex]

[tex]y^3=-\dfrac{5x}{2}[/tex]

[tex]y=-\left(\dfrac{5x}{2}\right)^{1/3}\\\\\\\text{Inverse of $f(x)$ is $f^{-1}(x) = -\left(\dfrac{5x}{2}\right)^{1/3}$}\\\text{We can also write this as $-\sqrt[3]{\frac{5x}{2}}$ }\\[/tex]

PQRSTU is plotted on a coordinate plane with vertices p(-1,0) Q(-1,3) R(1,4) S(2,5) T(4,4) and U(4,0) what is the hexagons area

Answers

To find the area of the hexagon, we can split it into two triangles and a rectangle, and then add up the areas of each shape.

First, we can find the length and width of the rectangle by finding the distance between points R and T, and between points Q and U, respectively.

Length of the rectangle RT = sqrt((4-1)^2 + (4-5)^2) = sqrt(10)

Width of the rectangle QU = sqrt((4-(-1))^2 + (0-3)^2) = sqrt(50)

The area of the rectangle is then:

Area of rectangle = Length x Width = sqrt(10) x sqrt(50) = 10sqrt(2)

To find the area of the two triangles, we can use the formula for the area of a triangle:

Area of triangle = 1/2 x Base x Height

Triangle 1 has base PQ, which has length 3, and height 1, which is the distance between PQ and RS. The area of triangle 1 is:

Area of triangle 1 = 1/2 x 3 x 1 = 3/2

Triangle 2 has base RS, which has length sqrt((4-1)^2 + (5-4)^2) = sqrt(10), and height 1, which is the distance between PQ and RS. The area of triangle 2 is:

Area of triangle 2 = 1/2 x sqrt(10) x 1 = sqrt(10)/2

Therefore, the total area of the hexagon is:

Area of hexagon = Area of rectangle + Area of triangle 1 + Area of triangle 2
= 10sqrt(2) + 3/2 + sqrt(10)/2
= 10sqrt(2) + (3+sqrt(10))/2

So the area of the hexagon is approximately 19.55 square units.

I have part (a) answered, I just need part (b) if anyone could help with that please?

Answers

(a) The two dots on the graph at 53 represent two different samples of size 40 that both had a range of 53.

(b) No, the simulation does not provide evidence that the sample range is a biased estimator of the population.

What is range?

Range is a statistical measure that refers to the difference between the highest and lowest values in a set of data. In other words, it is the distance between the largest and smallest values in a dataset.

According to given information:

(a) The two dots on the graph at 53 represent two different samples of size 40 that both had a range of 53.

(b) No, the simulation does not provide evidence that the sample range is a biased estimator of the population. A biased estimator systematically overestimates or underestimates the population parameter of interest. The fact that the distribution of sample ranges is approximately symmetric and centered around the true population range suggests that the sample range is an unbiased estimator of the population range. However, the variability of the sample range is quite large, which means that a single sample range may not be a very precise estimate of the population range.

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20x^2-7x-6=0 by factoring

Answers

Answer:

x = -2/5

x = 3/4

Step-by-step explanation:

Factoring:

20x²-7x-6=0

20x²+8x - 15x - 6 = 0

4x * (5x + 2) - 3 * (5x + 2) = 0

(5x + 2) * (4x - 3) = 0

Cases:

5x + 2 = 0

4x - 3 = 0

x = -2/5

x = 3/4

Answer:

20x^2 -x(15-8)-6=0 here 6×20=120an by subtracting 15-8 we got seven where the 15×8 is also 120

Step-by-step explanation:

now,

20x^2 -15x+8x -6 =0 (here -×-is equal to +thus we write +8)

5x(4x-3) +2(4x-3)=0

(5x+2) (4x-3)=0

Either 5x=-2

X=-2/5

4x=3

X=3/4

A rectangle has length (3x-8) and width (2x-7) cm as shown below... Write down and simplify an expression for the perimeter of the rectangle. (3x-8) (2x-7)

Answers

The simplified expression for the perimeter of the rectangle is 10x-30

What is perimeter of a rectangle?

The perimeter of a shape is the addition of all the sides of the shape. If l is the length and w is the width, then the perimeter of a rectangle can be expressed as ;

p = 2(l+w)

The length is 3x-8 and the breadth is 2x-7

therefore the perimeter = 2( l+w)

= 2( 3x-8+2x-7)

= 2( 5x-15)

= 10x-30

therefore, the simplified expression for the perimeter of the rectangle is 10x-30

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Evaluate each expression using the values given in the table.

Answers

Answer:

a) f(g(1)) = f(0) = 5

b) f(g(2)) = f(-3) = 8

c) g(f(2)) = g(3) = -8

d) g(f(3)) = g(2) = -3

e) g(g(1)) = g(0) = 2

f) f(f(3)) = f(2) = 3

Find the perimeter of each figure

Answers

Answer: 53 ft

Step-by-step explanation:

The perimeter of a polygon is the sum of all sides. In this example, the sides are 4 ft, 20 ft, 18 ft, and 11 ft, so the perimeter is

4+20+18+11=53 ft

Let u = - 3i + 2j, v = 3i - 3j and w = - 3j

Find the specified scalar or vector.

5u(3v - 4w)

Answers

If u = - 3i + 2i, v = 2i - 2j and w = - 4j, 5u(3v - 4w) is a scalar quantity with a value of 440.

To evaluate the expression 5u(3v - 4w), we need to first perform the scalar multiplication and then the vector subtraction. We can start by computing the scalar multiplication of 3v - 4w:

3v - 4w = 3(2i - 2j) - 4(-4j) = 6i + 14j

Next, we can perform the scalar multiplication of u and the vector 6i + 14j:

5u(3v - 4w) = 5(-3i + 2j)(6i + 14j)

Expanding the product, we get:

5(-18i² + 36ij + 42ij - 28j²)

Since i² = j² = -1, we can simplify this expression as:

5(18 + 70) = 440

Therefore, 5u(3v - 4w) is a scalar quantity with a value of 440.

The key concept used in this problem is the distributive property of scalar multiplication over vector addition and subtraction. This property allows us to simplify expressions that involve scalar multiplication and vector operations by distributing the scalar to each component of the vector.

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Simplify 5(x+3) -9x+4... Can somebody please help me??

Answers

Answer:

-4x+19

Step-by-step explanation:

Otherwise known as option B :D

Answer is B so -4x + 19

please help for this question

Answers

Translating the shape S by the vector ( -1 , - 3 ) would lead to S ' with vertices of ( 1, -2 ), ( 1, -1 ), ( 3, -2 ), and (3, 1).

How to translate the figure ?

Given that the translation vector is negative, this means that you would have to subtract the corresponding values of the vector from the x and y coordinates of each vertex.

The vertices of the new shape S' would be :

Vertex 1: (2 , 1 ) + ( -1, -3 ) = ( 2 - 1 , 1 - 3 ) = ( 1, -2 )

Vertex 2: ( 2, 2 ) + ( -1, -3 ) = ( 2 - 1, 2 - 3 ) = ( 1, - 1 )

Vertex 3: ( 4, 1 ) + (-1 , -3 ) = ( 4 - 1 , 1 - 3) = (3 , -2)

Vertex 4: ( 4, 4 ) + (- 1, -3 ) = (4 - 1, 4 - 3 ) = (3 , 1 )

In conclusion, the translated vertices would be ( 1, -2 ), ( 1, -1 ), ( 3, -2 ), and (3, 1).

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In its second year of operation, a local Internet provider’s profits were $170,500. If this amount was 576% of the company’s first-year profits, find the first- year profits (to the nearest hundred dollars).

Answers

Proportionately, if $170,500 profits in the second year of operation represent 576% of the company's first-year profits, the first-year profits will be $29,600.

What is a proportion?

A proportion describes two ratios equated to each other.

Proportion is a fractional value that compares one value or quantity to another.

The profits for the second year of operation = $170,500

Let the profits for the first year of operation = x

Proportionately, if $170,500 is 576% of x, x = $29,600 ($170,500 ÷ 576%)

Using equations, 5.76x = $170,500

x = $29,600 ($170,500 ÷ 5.76)

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Can someone help me please

Chapter 13/14. The Civil War. Watch the Hari Jones TED talk. Then, answer the following questions in 7-10 sentences. Then, respond to two different classmates' posts by asking a question or challenging their assertions (respectfully). Try to make sure everyone has a response to their post. Finally, respond to the question or assertion your classmate(s) replied to you. Responses are meant to acknowledge what the other student has communicated, and either expand on their ideas, or push back on them, then offer positive feedback. Consider using the following template: "Hi _____. I was interested in ______ about your post because _______. Also/However, ______. I think ______ because _____. Do you think/feel _____/? I feel _____. "

In serving in the military, what contributions did African Americans make to the Union war effort?

What kinds of discrimination did they face? What kind of heroism did they exhibit, and when?

Write a reaction to Dr/ Jones' TED talk. What did you know/not know? What surprised/amazed/angered/made you proud/saddened/made you happy?

Answers

Hi Annie. I was interested in engaging you about your post because of my differing view. However, I think I am open to changing my views because I am not dogmatic. Do you think I am too pliable?

How did African Americans contribute?

Throughout the Civil War, African Americans assumed crucial roles in the Union war effort. From enlisting as soldiers to acting as laborers and even spies, their contributions left an indelible impact on history.

Despite being subjected to rampant discrimination and racism from both Confederacy and Union forces, these individuals exhibited incredible heroism and bravery.

Excelling in dangerous missions that often led them to become prisoners of war, they persevered as they fought for the freedoms of themselves and others.

Hari Jones' TED talk shines a much-needed light on this overlooked aspect of history, revealing not only the extensive involvement of African American soldiers but also the pivotal role played by women in areas such as nursing, cooking, and espionage.

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A vehicle use 2 gallons of gasoline to travel 18 1⁄2 miles. At this rate, how many miles can 2 3 the vehicle travel per gallon of gasoline?

Answers

If a vehicle uses 2 gallons of gasoline to travel 18¹/₂ miles, at this rate, the vehicle can travel 9¹/₄ miles per gallon of gasoline.

What is the rate?

The rate refers to the average speed of the vehicle.

The rate also describes the unit rate or the rate expressed as a percentage or in terms of speed.

The number of gallons of gasoline used to travel 18¹/₂ miles = 2 gallons

The total distance traveled using two gallons of gasoline = 18¹/₂ miles

The average distance traveled per gallon of gasoline = 9¹/₄ miles (18¹/₂ ÷ 2)

Thus, on the average, the vehicle can travel 9¹/₄ miles miles per gallon of gasoline.

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Correct Question:

A vehicle uses 2 gallons of gasoline to travel 18 1⁄2 miles. At this rate, how many miles can the vehicle travel per gallon of gasoline?

what’s the numbers that correspond to the corret number of solutions

Answers

The number of solutions for the given system of linear equations is: Infinitely many solutions.

Calculating the number of solutions

To determine the number of solutions for the given system of linear equations:

3x - y = 4

6x - 2y = 8

We can use the algebraic method of solving the system of equations by substitution or elimination.

Let's use the algebraic method to determine the number of solutions:

3x - y = 4 (1)

6x - 2y = 8 (2)

We can simplify equation (2) by dividing both sides by 2:

3x - y = 4 (1)

3x - y = 4 (2')

Equations (1) and (2') are equivalent, which means that they represent the same line.

Therefore, the two equations represent the same line, and we have infinitely many solutions.