Can anyone please help me answer this question?
Find the limit of p(x)= (x^4 - x^3 - 1)/ x^2 (x + 1) as x approaches -3

Answers

Answer 1

Answer:

Step-by-step explanation:To find the limit of p(x) as x approaches -3, we can first simplify the expression by factoring the numerator:

p(x) = (x^4 - x^3 - 1) / x^2(x + 1)

= [(x - 1)(x^3 + x^2 - x - 1)] / [x^2(x + 1)]

Now, when x approaches -3, the denominator of the fraction becomes zero, which means we have an indeterminate form of the type 0/0. To evaluate the limit, we can use L'Hopital's rule, which states that if we have an indeterminate form of the type 0/0 or infinity/infinity, we can take the derivative of the numerator and denominator separately and then evaluate the limit again.

Taking the derivative of the numerator and denominator, we get:

p'(x) = [(3x^2 - 2x - 1)(x^2 + 2x) - 2(x - 1)(2x + 1)] / [x^3(x + 1)^2]

Now, plugging in x = -3 into the derivative, we get:

p'(-3) = [(3(-3)^2 - 2(-3) - 1)((-3)^2 + 2(-3)) - 2((-3) - 1)(2(-3) + 1)] / [(-3)^3((-3) + 1)^2]

= [28 - 44] / [(-3)^3(-2)^2]

= -16 / 108

= -4 / 27

Since the derivative is defined and nonzero at x = -3, we can conclude that the original limit exists and is equal to the limit of the derivative, which is:

lim x->-3 p(x) = lim x->-3 [(x - 1)(x^3 + x^2 - x - 1)] / [x^2(x + 1)]

= p'(-3)

= -4 / 27

Therefore, the limit of p(x) as x approaches -3 is equal to -4/27.

Answer 2

Answer:

[tex]\lim_{x \to -3}p(x) =-\dfrac{107}{18}[/tex]

Step-by-step explanation:

Given the function [tex]p(x)=\dfrac{x^4-x^3-1}{x^2(x+1)}[/tex]

Let's give the expressions in the numerator and denominator their own function names so they are easy to refer to:

n, for numerator: [tex]n(x)=x^4-x^3-1[/tex]

d, for denominator:  [tex]d(x)=x^2(x+1)[/tex]

So [tex]p(x)=\dfrac{n(x)}{d(x)}[/tex]

Now, we want the limit of p(x) as x goes to -3.

[tex]\lim_{x \to -3}p(x) =\lim_{x \to -3}\dfrac{n(x)}{d(x)}[/tex]

For limits of quotients, it is important to analyze the numerator and the denominator.

Take a moment to observe that inputting -3 into the denominator is defined and does not equal zero:  [tex]d(-3)=(-3)^2((-3)+1)=-18\ne0[/tex]

Also, observe that inputting -3 into the numerator is defined:  [tex]n(-3)=(-3)^4-(-3)^3-1=81+27-1=107[/tex]

Importantly, both functions n & d are polynomials, which are functions that are continuous over [tex]\mathbb{R}[/tex].

Since both functions n & d are continuous, both n & d are defined at [tex]x=-3[/tex], and [tex]d(-3)\ne0[/tex], then the limit of the quotient is the quotient of the limits:

[tex]\lim_{x \to -3}\dfrac{n(x)}{d(x)}=\dfrac{ \lim_{x \to -3}n(x)}{ \lim_{x \to -3}d(x)}[/tex]

From here, again, since n & d are continuous over [tex]\mathbb{R}[/tex] and defined at the limit, [tex]\lim_{x \to -3}n(x)}=n(-3)[/tex] and [tex]\lim_{x \to -3}d(x)}=d(-3)[/tex].

Therefore,

[tex]\lim_{x \to -3}p(x) =\lim_{x \to -3}\dfrac{n(x)}{d(x)}=\dfrac{ \lim_{x \to -3}n(x)}{ \lim_{x \to -3}d(x)}=\dfrac{n(-3)}{d(-3)}=\dfrac{107}{-18}=-\dfrac{107}{18}[/tex]


Related Questions

Malaika has a number of candies. She can give out 12 to each of her friends and have 3 left over. or she can give 9 out to each of her friends and have 12 left over. How many friends can receive candy?

Answers

If she can give out 12 to each of her friends and have 3 left over. or she can give 9 out to each of her friends and have 12 left over, Malaika has 3 friends who can receive candies.

Let's suppose Malaika has "c" candies, and "f" is the number of friends she has.

According to the problem statement, we have two equations:

c = 12f + 3

c = 9f + 12

To solve for "f", we can set the two equations equal to each other:

12f + 3 = 9f + 12

Simplifying the equation, we get:

3f = 9

Dividing both sides by 3, we get:

f = 3

We can verify our solution by plugging "f=3" back into one of the original equations:

c = 12f + 3

c = 12(3) + 3

c = 39

So, Malaika has 39 candies in total. We can also check the other equation to make sure it is true:

c = 9f + 12

c = 9(3) + 12

c = 39

Both equations are true, so our solution of "f=3" is correct.

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Solve For X
Solve For Y

Answers

Using the properties of a parallelogram, the values of x and y are:

x = 9; y = 22.

How to Find x and y in the Parallelogram?

Since the opposite sides are parallel and equal to each other in the parallelogram above, therefore, Opposite angles are equal (or congruent) while the consecutive angles are supplementary to each other.

Therefore, we have:

6y = 180 - 48

6y = 132

Divide both sides by 6:

6y/6 = 132/6

y = 22

(5x + 3) + 6y = 180

5x + 3 + 6(22) = 180

5x + 135 = 180

5x = 180 - 135

5x = 45

x = 9

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Solve for x. −−9x+5<17 AND13x+25<−1

Answers

Answer: x<4/3

Step-by-step explanation: 17-5=12/9

Solve for x. Round to the nearest tenth, if necessary.

Answers

Answer:

Step-by-step explanation:

You are looking for the tangent ratio, which is opposite side over adjacent side.  Using the tangent ratio of an angle of 37°.

tan37° = x/89

.75355405 = x/89

.75355405 · 89 = x/89 · 89/1

67.06 = x

rounded to 67.1

Answer:

67.1? that's what I got lol

the price of a shirt was $25, but it is now on sale for $20. what is the percent decrease in price?

Answers

The percent decrease in price is 20%.

To calculate the percent decrease, you can use the following formula:

(Original Price - New Price) / Original Price x 100%

Plugging in the numbers, we get:

($25 - $20) / $25 x 100% = 20%

Therefore, the percent decrease in price is 20%

:)

-5-4-3-2
y
5
3
+ do
Mark this and return
23
Which equation represents a circle with the same
radius as the circle shown but with a center at (-1, 1)?
(x-1)2 + (y + 1)² = 16
(x-1)² + (y + 1)² = 4
(x + 1)² + (y-1)² = 4
O(x + 1)² + (y-1)² = 16
Save and Exit
Next
Submis

Answers

The equation that represents the circle is (x + 1)² + (y - 1)² = 16

Writing the equation that represents a circle

The equation of a circle with center (h,k) and radius r is:

(x - h)² + (y - k)² = r²

To find the equation of the circle with center (-1,1) and radius 4, we need to shift the center of the circle to (-1,1).

We can do this by replacing x with (x - (-1)) = (x + 1) and y with (y - 1) in the equation of the original circle. This gives:

(x + 1)² + (y - 1)² = 16

This equation represents a circle with center (-1,1) and radius 4.

Therefore, the correct option is (O) (x + 1)² + (y - 1)² = 16.

The other options do not have the correct center or radius to describe the circle.

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bao mom is picking him up from the ice rink she is at home which is located at the origin (0,0) how many total units is the ice rink away from the origin explain

Answers

The total units of length for the ice rink away from the origin is 14.42 units.

How to determine the distance between the coordinates for each points?

In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

Note: Ice rink is located at point (12, 8).

By substituting the given end points into the distance formula, we have the following;

Distance = √[(12 - 0)² + (8 - 0)²]

Distance = √[(12)² + (8)²]

Distance = √[144 + 64]

Distance = √208

Distance = 14.42 units.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

PLS HELP ME OUT! A sporting event has a promotion in which the first 1,000 fans to enter the arena receive either a blue cap or a red cap. A random number generator is used to simulate the color of a cap given to a person where indicates a blue cap and indicates a red cap. Ten simulations, each consisting of ten random numbers, are conducted, and the results
are shown in the following table:
Based on the simulations, what is the probability that ten hats given to ten people will consist of more blue caps than red caps? a. 0.20
b. 0.40 c. 0.60 d. 0.80

Answers

The probability that ten hats given to ten people will consist of more blue caps than red caps is given as follows:

a. 0.2.

Here, we have to calculate a probability:

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The outcomes in which there are more blue than red caps are those in which the number of zeros is greater than the number of ones, hence the number of desired outcomes is of:

2. (simulation number 7 and simulation number 10).

Hence the probability is of:

p = 2/10

p = 0.2.

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Solve. Show the system of equations used and your work in solving the system.
A phone store sells Android phones for $400 and iOS phones for $650 each. This
week they sold a total of 110 phones and earned $54,000. How many Android and
how many iOS phones did they sell?

Answers

Let's assume that the number of Android phones sold is x and the number of iOS phones sold is y. Then we can write two equations based on the given information:

x + y = 110    (equation 1)

400x + 650y = 54000   (equation 2)

To solve for x and y, we can use any method of solving systems of equations. Here, we will use the substitution method:

From equation 1, we can solve for x in terms of y: x = 110 - y

Substitute x = 110 - y into equation 2 and solve for y:

400(110 - y) + 650y = 54000

44000 - 400y + 650y = 54000

250y = 10000

y = 40

Substitute y = 40 into equation 1 and solve for x:

x + 40 = 110

x = 70

Therefore, the phone store sold 70 Android phones and 40 iOS phones.

area of traingle is what if square root 6 in height iand base is square root 24

Answers

The area of the triangle that has height of √6 and a base of √24 is calculated as: 6 square units.

How to Find the Area of a Triangle?

The area of a triangle = 1/2 * b * h, where:

h is the height of the triangle, and

b is the base length of the triangle.

Given the following:

Height of triangle = √6

Base length of the triangle = √24

Plug in the values:

Area of triangle = 1/2 * √24 * √6

= (√24 * √6) / 2

= √144 / 2

= 12/2

Area of triangle = 6 square units.

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ACTIVITY 2: Solve the following problems completely.

Answers

1) The amount is php 340,060

2) The rate is 13%

3) The amount is  php 137,622

What is the compound interest?

Compound interest is commonly used in many types of financial products, such as savings accounts, CDs, and loans.

1)

[tex]A = P(1 + r/n)^nt\\A = 80000( 1 + 0.16)^9.75\\A = php 340,060[/tex]

2)

[tex]12300 = 9750(1 + r)^2\\12300/9750 = (1 + r)^21.26 = (1 + r)^2\\ln 1.26 = 2 ln1 + r\\ln 1.26/2 = ln1 + r\\0.12 = ln1 + r\\e^{0.12} = 1 + r\\r = e^{0.12} - 1\\r = 0.13\\r = 13%[/tex]

3)

[tex]A = 50000(1 + 0.15/2)^2 * 7\\A = php 137,622[/tex]

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Suppose that the functions f and g are defined as follows.
Find f.g and f+ g. Then, give their domains using interval notation.

Answers

Using interval notation, the domain of f.g and f+g is [1/4, ∞).

Given, f(x)= 1/ (5x² + 3) and [tex]g(x) = \sqrt{4x-1}[/tex]

To find f.g, we substitute g(x) into f(x) and simplify:

f.g(x) = f(g(x))

[tex]=f(\sqrt{4x-1})[/tex]

[tex]=\frac{1}{5(\sqrt{4x-1})^2 +3}[/tex]

= 1/(5(4x-1)+3)

= 1 / (20x - 2)

To find f+g, we add the functions f(x) and g(x):

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

= [tex]\frac{1}{5x^2+3}+\sqrt{4x-1}[/tex]

The domain of f.g and f+g is the intersection of the domains of f(x) and g(x).

The domain of f(x) is all real numbers except for the values of x that make the denominator zero, i.e., 5x² + 3 = 0. This equation has no real solutions, so the domain of f(x) is all real numbers.

The domain of g(x) is the set of all real numbers that make the argument of the square root non-negative, i.e., 4x - 1 ≥ 0. Solving this inequality, we get x ≥ 1/4.

Therefore, the domain of f.g and f+g is x ≥ 1/4.

Using interval notation, the domain of f.g and f+g is [1/4, ∞).

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If the median of a data set is 13 and the mean is 13, which of the following is most likely?

Select the correct answer below:

a. The data are skewed to the left.

b. The data are skewed to the right.

c. The data are symmetrical.

Answers

Answer:

C

Step-by-step explanation:

if the mean and median are the same, the graph will be symmetrical

Suppose the function f(t) = e^t describes the growth of a colony of bacteria, where t is hours. find the number of bacteria present at 5 hours
a) 59.598
b) 148.413
c) 8.155
d) 79. 432

Answers

The number of bacteria present at 5 hours is (b) 148.413

How can the number of bacteria present be described?

From the question, we were given,

f(t) = eᵗ

Then  f(t) = number of bacterials present at a particular time t.

f(5) = number of bacterial present at 5 hours

So, we have

f(5) = e⁵

f(5) = 148.413

Then this can be written in the whole number as 148  which implies that the second option is correct because using f(t) = eᵗ to describes the growth of a colony of bacteria will provide us with the answer

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A local supermarket offers a pack of 12 sodas for $3.48 on sale, and the local discount warehouse offers the soda in a 36-can case for $11.52. Which is the better value?

Answers

If local supermarket offers a pack of 12 sodas for $3.48 on sale, and the local discount warehouse offers the soda in a 36-can case for $11.52, In terms of price per soda, the supermarket pack is the better value.

To determine which is the better value between the supermarket pack of 12 sodas for $3.48 and the discount warehouse 36-can case for $11.52, we need to calculate the price per soda for each option.

For the supermarket pack, the price per soda can be found by dividing the total cost by the number of sodas in the pack:

Price per soda = $3.48 / 12 = $0.29

For the discount warehouse case, the price per soda can be found by dividing the total cost by the number of sodas in the case:

Price per soda = $11.52 / 36 = $0.32

From these calculations, we can see that the price per soda is lower for the supermarket pack at $0.29 compared to $0.32 for the discount warehouse case. Therefore, in terms of price per soda, the supermarket pack is the better value.

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Find the terms: a=_1=8, r=0.7

Answers

The formula of the nth term of the sequence is f(n) = 8 *0.7r^(n - 1)

Finding the terms of the sequence:

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

a=_1=8, r=0.7

Express properly

So, we have

First term, a = 8

Common ratio, r = 0.7

The above definition is of a geometric sequence that has a first term of 8 and a common ratio of 0.7

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

f(n) = a * r^(n - 1)

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

f(n) = 8 *0.7r^(n - 1)

Hence, the nth term of the sequence is f(n) = 8 *0.7r^(n - 1)

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Bandar Industries manufactures sporting equipment. One of the company’s products is a football helmet that requires special plastic. During the quarter ending June 30, the company manufactured 3,500 helmets, using 2,485 kilograms of plastic. The plastic cost the company $16,401.



According to the standard cost card, each helmet should require 0.66 kilograms of plastic, at a cost of $7.00 per kilogram.



Required:

1. What is the standard quantity of kilograms of plastic (SQ) that is allowed to make 3,500 helmets?

2. What is the standard materials cost allowed (SQ × SP) to make 3,500 helmets?

3. What is the materials spending variance?

4. What is the materials price variance and the materials quantity variance

Answers

1. The standard quantity of plastic allowed to make 3,500 helmets is 2,310 kilograms.

2. The standard materials cost allowed to make 3,500 helmets is $16,170.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

1. The standard quantity of kilograms of plastic (SQ) allowed to make 3,500 helmets can be calculated as:

SQ = Standard quantity per unit × Actual output

= 0.66 kg/helmet × 3,500 helmets

= 2,310 kg

Therefore, the standard quantity of plastic allowed to make 3,500 helmets is 2,310 kilograms.

2. The standard materials cost allowed (SQ × SP) to make 3,500 helmets can be calculated as:

Standard materials cost allowed = Standard price × Standard quantity allowed

= $7.00/kg × 2,310 kg

= $16,170

Therefore, the standard materials cost allowed to make 3,500 helmets is $16,170.

3. The materials spending variance can be calculated as the difference between the actual cost incurred and the standard cost allowed:

Materials spending variance = Actual materials cost - Standard materials cost allowed

= $16,401 - $16,170

= $231 (Favorable)

Therefore, the materials spending variance is $231 (Favorable).

4. The materials price variance and the materials quantity variance can be calculated as follows:

Materials price variance = (Actual price - Standard price) × Actual quantity

= ($16,401/2,485 kg - $7.00/kg) × 2,485 kg

= $9,141.77 (Unfavorable)

Materials quantity variance = (Actual quantity - Standard quantity allowed) × Standard price

= (2,485 kg - 2,310 kg) × $7.00/kg

= $1,225 (Unfavorable)

Therefore, the materials price variance is $9,141.77 (Unfavorable) and the materials quantity variance is $1,225 (Unfavorable).

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write two different equations with variables and draw a diagram to solve the situation. For cleaning the attic Kristin was given $18. now she has $50. how much money did she have before

Answers

Once again, we get the same answer: Kristin had $32 before receiving the $18 for cleaning the attic. we solve this by forming equation and solving it

what is equation ?

An equation is a mathematical statement that shows that two expressions are equal. It usually consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to solve problems in various fields, including mathematics, physics, engineering

In the given question,

Let's use "x" to represent the amount of money Kristin had before receiving the $18 for cleaning the attic. We can set up the following equation:

x + 18 = 50

This equation represents the total amount of money Kristin has now, which is $50, after receiving the $18 for cleaning the attic. To solve for "x", we can subtract 18 from both sides of the equation:

x + 18 - 18 = 50 - 18

x = 32

Therefore, Kristin had $32 before receiving the $18 for cleaning the attic.

Alternatively, we can also use a diagram to represent the situation. We can draw a rectangle to represent the total amount of money Kristin has now, which is $50. We can then divide the rectangle into two parts: one part representing the $18 she received for cleaning the attic, and the other part representing the amount of money she had before. We can label this unknown amount as "x", and set up the following equation:

x + 18 = 50

This equation is the same as the one we set up earlier. To solve for "x", we can again subtract 18 from both sides of the equation:

x + 18 - 18 = 50 - 18

x = 32

Once again, we get the same answer: Kristin had $32 before receiving the $18 for cleaning the attic.

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Simplify. (x-6)^3Write your answer without using negative exponents.

Answers

Answer:

x^3-18x^2+108x-216

There is a formula for this simplification, and you can write the answer directly if you remember the formula.

Who can help me with this?

Answers

The original price of this car is equal to $6,600.

What is a percentage?

In Mathematics, a percentage can be defined as any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.

Assuming the original price is represented by the variable x, we have the following:

12.5/100 × x = x - 5,775

0.125x = x - 5,775

5,775 = (x - 0.125x)

5,775 = 0.875x

x = 5,775/0.875

x = $6,600.

In conclusion, we can logically deduce that the percentage Pat Bain paid is 87.5%.

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find the margin of error given the values of C, stigma, and n.
c= 0.95, stigma=3.4, n=100

E=?

Answers

The margin of error is E = 0.67.

To find the margin of error

We can use the formula:

E = z* (σ / sqrt(n))

Where

E is the margin of errorz* is the z-score corresponding to the desired level of confidence Cσ is the population standard deviation (also known as the population parameter) n is the sample size

In this case, we are given that C = 0.95, σ = 3.4, and n = 100. We can use a standard normal distribution table to find the z-score that corresponds to a 95% confidence level, which is approximately 1.96.

Substituting the values:

E = 1.96 * (3.4 / sqrt(100))

E = 1.96 * 0.34

E = 0.6664

Rounding to two decimal places, the margin of error is approximately 0.67.

Therefore, the margin of error is E = 0.67.

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Which expression is equivalent to 6^2/7 ?

Answers

Answer: A

Step-by-step explanation:

well i did alll of them and got A

Solution to augmented matrix? Never seen a problem like this one. How do I solve it?

Answers

The row of zeros at the bottom immediately lets us conclude "infinitely many solutions". This system is consistent and dependent. This is because we have 0x+0y+0z = 0 aka 0 = 0 which is always true for any choice of x, y, and z.

The second row of values lead to the equation 0x+0y+1z = 6, aka z = 6

The first row says: 1x+6y+0z = 1 which is the same as x+6y = 1

Let's say we isolate x

x+6y = 1

x+6y-6y = 1-6y

x = 1-6y

Then we have these three values or expressions

x = 1-6yy = any real numberz = 6

All of the infinitely many solutions are of the form (x,y,z) = (1-6y, y, 6)

A lot of textbooks will use a parameter such as t, so we could write it as (1-6t, t, 6).

The choice of the letter for the parameter does not matter. I think t is most popular because it represents time. Each (x,y,z) point could represent a particle's location at any given time.

If t = 0, then we have (1, 0, 6)If t = 1, then we have (-5, 1, 6)If t = 2, then we have (-11, 2, 6)If t = 3, then we have (-17, 3, 6)

and so on.

=============================

Conclusion:

There are infinitely many solutions of the form (x,y,z) = (1-6t, t, 6) where t is any real number.

This system is consistent and dependent.

PLEASE HELP ME WITH THIS IM SO CONFUSED

Answers

The probability of hitting the shaded region is 0.755 or 75.5%.

What is the probability of hitting the shaded region?

To find the probability of hitting the shaded region, we need to find the area of the shaded region and divide it by the area of the entire square.

Let's label the side length of the small square as x.

Then, we know that the diagonal of the small square is 7, so we can use the Pythagorean theorem to solve for x:

x^2 + x^2 = 7^2

2x^2 = 49

x^2 = 24.5

So the area of each white square is x^2 = 24.5 square units.

Let's label the side length of the large square as y.

Then, we know that the diagonal of the large square is 20, so we can use the Pythagorean theorem to solve for y:

y^2 + y^2 = 20^2

2y^2 = 400

y^2 = 200

So the area of the large square is y^2 = 200 square units.

Now, we can find the area of the shaded region by subtracting the area of the two white squares from the area of the large square:

Area of shaded region = Area of large square - 2 * Area of white square

= 200 - 2(24.5)

= 151

Therefore, the probability of hitting the shaded region is:

Probability = Area of shaded region / Area of entire square

Probability = 151 / 200

Probability = 0.755 or 75.5% (rounded to one decimal place)

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Someone help i really need help with this

Answers

Answer:

35 pages per minute

Step-by-step explanation:

175/5= 35

Check

35 x 5 = 175

175/35= 5

If the third and fourth term of an arithmetic sequence are -1 and -4, what are the first and second terms?

Answers

Answer: 5 and 2

Step-by-step explanation:

In an arithmetic sequence, the difference between consecutive terms is constant. Since the third and fourth terms are -1 and -4, the common difference is -4 - (-1) = -3. Therefore, the second term is -1 - (-3) = 2 and the first term is 2 - (-3) = 5. So the first and second terms of the sequence are 5 and 2 respectively.

Find the approximate area of the shaded region below, consisting of a right triangle with a circle cut out of it. Use 3.14 as an
approximation for pi.

O 1.254 square meters
O 312 square meters
O2, 822 square meters
O 314 square meters

Answers

Answer:

(a) 1.254 square meters

Step-by-step explanation:

We are given a figure, consisting of a right triangle with a circle cut out of it.

To Calculate : area of the shaded region below,

First Let's find the Area of the right triangle:

Area(triangle) = 1/2 × Base × Height

= 1/2 × 56 × 56

= 1/2 × 3136

= 3136/2

= 1568 m².

Now, We are diameter of the circle = 20 m

Radius of the circle = 20/2 = 10 m

Area of circle = πr²

Acc. to question we have to use 3.14 as an

approximation for pi.

Area (circle) = 3.14 × 10 × 10

Area (circle) = 3.14 × 100

Area (circle) = 314 m²

Area of shaded region = Area of triangle - Area of circle =

= 1568 m² - 314 m²

= 1.254 square meters

Therefore, The approximate area of the shaded region is 1.254 square meters.

Option (a) is the required answer

which has the greatest rate? y = -x , y = 3/4x +1, y = 1/2x +2, y = x

Answers

The function that has the greatest rate of change is y = x

Which function has the greatest rate of change?

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

y = -x ,

y = 3/4x +1,

y = 1/2x +2,

y = x

A linear function is represented as

y = mx + c

Where

rate of change = m

So, we have

y = -x , rate = -1

y = 3/4x +1, rate = 3/4

y = 1/2x +2, rate = 1/2

y = x, rate = 1

This means that the function with the highest rate is y = x

Read more about linear relation at

https://brainly.com/question/30318449

#SPJ1

Beth has three as much money as Dennis. Dennis has $20 more than Will. If all of them had a total of $1260, how much money does Beth have?

Answers

Let's use variables to represent the amounts of money each person has:

- Let x be the amount of money that Will has.
- Then, Dennis has $20 more than Will, so Dennis has x + $20.
- Beth has three times as much money as Dennis, so Beth has 3(x + $20).

We know that the total amount of money that all three have is $1260, so we can write an equation:

x + (x + $20) + 3(x + $20) = $1260

Simplifying and solving for x:

x + x + $20 + 3x + $60 = $1260
5x + $80 = $1260
5x = $1180
x = $236

So Will has $236, Dennis has x + $20 = $256 + $20 = $276, and Beth has 3(x + $20) = 3($256) = $768.

Therefore, Beth has $768.

Answer:

Beth has $752

Step-by-step explanation:

First we lay out what we know:

Beth: 3x+20

Will: x

Dennis: x+20

Next we write the equation:

3x+20+20+x+x=1260

Then we add any numbers that can be added to each other:

5x+40=1260

Then we solve,

We first minus 40 from both sides of the equation,

5x+40=1260

-40 -40

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

5x=. 1220

Last we divide 1220 by 5,

5x=1220

÷5. ÷ 5

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

x=244

Now that we know that x is 244 we fill in the blanks,

Beth: 732+20

Will: 244

Dennis: 244+20

Then we just solve the equations,

Beth: 732+20=752

Will: 244

Dennis: 244+20=264

That's it,

if you want to check your work you can add them all up and if they equal 1260 it's correct.

752+244+264=1260

Your welcome, have a good day/night.

S=4lw +2wh s=92 l=9 w=2

Answers

Answer:

h=5

Step-by-step explanation:

Substituting in 92 for s,
92=4lw+2wh
Substituting in 9 for l,
92=4(9)(w)+2wh

Substituting 2 for w,

92=4(9)(2)+2(2)(h)

Simplifying by multiplying terms

92=72+4h

Subtract 72 on both sides

20=4h

Divide by 4 on both sides

5=h

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