C'A'LM'. Parallelogram C'A'L'M' has an area of 485.64 square feet. What is the

scale factor for the area of the pre-image to get the image?

The **scale** factor for the area of the pre-image to get the image is 2.

Suppose a figure (pre image) is **dilated **(dilated image) by scale factor of k. So, if a **side **of the figure is of length L units, and that of its similar figure is of M units, then:

L = k × M

where 'k' will be called as scale factor.

The linear things grow linearly like length, height etc.

The quantities which are squares or multiple of linear things twice grow by square of scale factor. Thus, we need to multiply or divide by k² to get each other **corresponding **quantity from their similar **figures**' quantities.

So area of first figure = k² × area of second figure

Given that **Parallelogram **CALM is multiplied by a scale factor to create Parallelogram C'A'LM'. Parallelogram C'A'L'M' has an area of 485.64 square feet. Also, the area of the parallelogram CALM is 121.41 square feet.

Therefore, we can write,

Final Area / Initial Area = (Scale Factor)²

485.64 square feet / 121.41 square feet = (**Scale **Factor)²

4 = (Scale Factor)²

(Scale Factor) = √4

Scale Factor = 2

Hence, Scale Factor = 2

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The complete question is:

The area of **Parallelogram **CALM is 121.41 square feet. Parallelogram CALM is multiplied by a scale factor to create Parallelogram C'A'LM'. Parallelogram C'A'L'M' has an area of 485.64 square feet. What is the scale factor for the area of the pre-image to get the image?

34 on april 18, 1775, paul revere set off on his midnight ride from charlestown to lexington. if he had ridden straight to lexington without stopping, he would have traveled 11 miles in 26 minutes. in such a ride, what would the average speed of his horse have b

The **average** speed of Paul **Revere's** horse, assuming he rode straight to Lexington without stopping, would have been approximately 25.4 miles per hour.

To find the average speed of Paul **Revere's** horse, we can use the formula:

average speed = total distance / total time

In this case, the total **distance **is 11 miles, and the total time is 26 minutes, or 0.4333 hours (since there are 60 minutes in an hour).

So, the average speed of Paul Revere's horse would be:

average speed = 11 miles / 0.4333 hours

average speed ≈ 25.4 miles per hour

Therefore, the average **speed** of Paul Revere's horse, to the nearest tenth of a mile per hour, would have been 25.4 miles per hour.

Using the formula for **average** speed, we can calculate that Paul Revere's horse would have had to travel at an average speed of approximately 25.4 miles per hour to cover the 11-mile distance in 26 minutes. This assumes that he rode straight through without stopping.

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The complete question is:

On April 18, 1775, Paul Revere set off on his midnight ride from Charlestown to Lexington. If he had ridden straight to Lexington without stopping, he would have traveled 11 miles in 26 minutes. In such a ride, what would the average speed of his horse have been, to the nearest tenth of a mile per hour?

how many ways can patricia choose 3 pizza toppings from a menu of 10 toppings if each topping can only be chosen once?

**Step-by-step explanation:**

the equation we use here is [items to choose from] to the power of [required items]; in this case, we get [tex]10^{3}[/tex].

Feb 10, 9:11:47 AM

10. Find the value of X.

The **solution **of x in the **rhombus **is 3

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

The **rhombus**

Also, we have

LN = 14

AN = x + 4

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

LN = 2 * AN

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

2 * (x + 4) = 14

Evaluate the **expression**

x + 4 = 7

**Subtract **4 from both sides

so, we have the following representation

x = 3

Hence, the solution is 3

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Pls help thank you will mark the Brainliest

**Option d)** [tex]y= 30.5(0.7)^x[/tex] is the **function** that best models the number of game **systems** sold in millions x years since 2015.

In mathematics, a **function** is a rule that associates each element in one set (called the domain) with a unique element in another set (called the range). The rule specifies how the **input values** (the elements of the domain) are transformed into **output** **values** (the elements of the range).

A function can be represented using **various** **notations**, such as f(x), where f is the name of the function and x is the input value, or y = f(x), where y is the **output** value and x is the input value. The function can be defined explicitly, as in[tex]f(x) = x^2,[/tex] or implicitly, as in the equation of a circle, [tex]x^2 + y^2 = r^2[/tex], where y is a **function** of x.

To determine which **function** best models the number of game systems sold, we need to observe the trend in the **data**.

We can see that the number of game systems sold is decreasing as time goes on, which means the **function** should be **decreasing** as well.

Option a) [tex]y=21.35(0.7)^x[/tex] is an exponential function with a base less than 1, which means it would also be **decreasing**. However, it starts with a higher initial value than the data suggests.

Option b) [tex]y= 30.5(21.35)^x[/tex] is an exponential function with a base greater than 1, which means it would be **increasing**. This function does **not** **match** the trend in the data.

Option c) [tex]y= 30.5(1.3)^x[/tex] is an **exponential** **function** with a base greater than 1, which means it would be increasing. This function also does **not** **match** the trend in the data.

Option d) [tex]y= 30.5(0.7)^x[/tex]is an **exponential** **function** with a base less than 1, which means it would be decreasing. Additionally, this function passes through all three data points, and it has a starting value that matches the first data point. Therefore, **option d) **is the function that best models the number of game systems sold in **millions** x years since 2015.

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A grain silo has a cylindrical shape. Its diameter is 17 , and its height is 38. What is the volume of the silo?

The **volume** of the **silo** of cylinder shape containing grain is 8625.24 cubic units.

The volume of the **cylindrical shaped** grain silo will be calculated by the formula -

Volume = πr²h, where r represents radius and h represents height of the cylinder.

Now, as we know **radius** is half of the diameter. So, radius = 17/2

Performing division on Right Hand Side of the equation

Radius of the cylinder = 8.5

Keep the values in formula to find the value of volume of silo

Volume = π × 8.5² × 38

Taking square and performing multiplication on Right Hand Side of the equation

Volume = 8625.24 cubic units

Hence, the volume is 8625.24 cubic units.

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Please need help with this math problem

**Answer:**

maximum value = 135

**Step-by-step explanation:**

the maximum value is situated at the right end of the whisker.

each division on the number line is 5 units

so maximum value = 125 + 2 units = 125 + 10 = 135

which equation can be used to represent "three minus the difference of a number and one equals one-half of the difference of three times the same numb

The **equation** can be used to represent "three minus the difference of a number and one equals one-half of the difference of three times the same number" is** **3 – (n – 1) = 1/2(3n – 4)

Let the number be n.

Gven: "three minus the difference of a number and one equals one-half of the difference of three times the same number and four"

So,

The expression "three minus the difference of a number and one" represent the equation is;

3 – (n – 1)

Also,

The expression "one-half of the difference of three times the same number and four" represent the equation is;

1/2(3n – 4)

Hence,

**Complete expression represents the equation is**

3 – (n – 1) = 1/2(3n – 4)

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(1 – n) – 3 = (4 – 3n)

3 – (1 – n) = (4 – 3n)

(n – 1) – 3 = (3n – 4)

3 – (n – 1) = (3n – 4)

the following frequency table represents the number of drinks someone has in a week for 40 people. what is the 70th percentile of the data?

Answer:

Step-by-step explanation:

Simplify the expression below:

14^2 - 24 / 3(2)

--------------------- (divided by)

|-3 + 2(6)|

**Answer:**

I got 20 when calculating this

Mrs. Harris has a piece of lumber that is 11 5/8 inches wide she plans to split the width of the lumber into three equal pieces how wide will each piece be

The size of **width **of each **lumber **piece will be 3.875 inches.

Logic is the arrangement of all those concepts, whereas **algebra **is the study of **abstract concepts**.

Making something a little **less complicated **while both making it easier to attain or **understand **is the concept of clarity.

Mrs. Harris intends to **divide **the breadth of a piece of timber that is 11 ⁵/₈ inches broad into **three equal **pieces.

Convert the **mixed fraction **number to a decimal number. Then we have

11 ⁵/₈ = 11 + ⁵/₈

11 ⁵/₈ = 11.625 inches

The width of **each lumber **piece is given as,

⇒ 11.625 / 3

⇒ 3.875 inches

The size of **width **of each **lumber **piece will be 3.875 inches.

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A prize is divided in the ratio 7:5. One share is £122 more than the other what is the total amount?

a = amount given to the 1st share, ratio of 5.

a + 122 = amount given to the 2nd share, ratio of 7.

T = total amount

so the total amount is really "T", and we'll be splitting that into a 7 : 5 ratio, that is, we'll be dividing "T" by (7 + 5) and distribute accordingly.

[tex]\stackrel{\textit{total split by 7 + 5}}{\cfrac{T}{7+5}\implies \cfrac{T}{12}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{we know the 1st share is}}{a= 5\cdot \cfrac{T}{12}}\implies a=\cfrac{5T}{12} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{we know the 2nd share is}}{a+122= 7\cdot \cfrac{T}{12}}\implies a+122=\cfrac{7T}{12}\implies \stackrel{\textit{substituting from above}}{\left( \cfrac{5T}{12} \right)+122=\cfrac{7T}{12}} \\\\\\ 122=\cfrac{7T}{12}-\cfrac{5T}{12}\implies 122=\cfrac{2T}{12}\implies 122=\cfrac{T}{6}\implies \boxed{732=T}[/tex]

PLEASE THIS IS REALLY ARGENT

Two simultaneous equations are given below, where p and q are constants.

3x-py = 4

4x-3y + q = 0

The solution to these equations is x = 1, y = 2.

Find the value of p and q.

To find the values of p and q, we can use the given solution of x = 1 and y = 2.

Substituting these values into the first equation, we get:

3x - py = 4

3 * 1 - p * 2 = 4

3 - 2p = 4

-2p = 1

p = -1/2

Substituting these values into the second equation, we get:

4x - 3y + q = 0

4 * 1 - 3 * 2 + q = 0

4 - 6 + q = 0

-2 + q = 0

q = 2

So the solution to the system of equations is x = 1, y = 2, p = -1/2, and q = 2.

Substituting these values into the first equation, we get:

3x - py = 4

3 * 1 - p * 2 = 4

3 - 2p = 4

-2p = 1

p = -1/2

Substituting these values into the second equation, we get:

4x - 3y + q = 0

4 * 1 - 3 * 2 + q = 0

4 - 6 + q = 0

-2 + q = 0

q = 2

So the solution to the system of equations is x = 1, y = 2, p = -1/2, and q = 2.

12. Solve the problem.

According to a college survey, 22% of all students work full time. Find the mean for the

number of students who work full time in samples of size 16.

00.2

03.5

04.0

02.8

The **mean **for the number of students who work full-time in

samples of size 16 are 3.5.

What is the expected value?We understand The expected value, also known as the expected **average **in the field of probability theory, is a generalization of the weighted average.

Given, 22% of all students work full-time, per a college poll.

Now, If we choose a sample of 16 students the **mean **number of students working full-time is,

= 16(22/100)

= 16×0.22

= 3.5.

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A recipe calls for 6 cups of flour to make 24 pancakes. How many pancakes

can be made with a single cup of flour?

On the double number line below, fill in the given values, then use

multiplication or division to find the missing value:

cups of flour

pancakes

4 pancakes 24/6=4 so 4 is the answe

What is the area of this compound figure?

**Answer:**

**199 cm²**

**Step-by-step explanation:**

in the picture

A candle burns 2 inches per hour. After burning for 2 hours, the candle was 5 inches

long. If one the candle has been burning for 240 minutes, how long is the candle?

Write an equation that models the situation.

The **length** of the **candle** that has been **burning** for the total of 240 minutes would be = **9 inches**.

The **rate** at which a **candle burns **= 2 in/ 2 hours

That is,

2 in = 2 hour; 2 inches = 120 minutes

X in = 240 minutes

Make X the subject of **formula**;

X = 2×240/120

X= 480/120

X = 4+5

X = 9 inches

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Someone help me with this equation please!!

The given statement is** transitive property**.

Transitive property is also called** transitive property of equality **when we have two equal values and either of this value is equal to third value.

DE≅XY AND [tex]\hat{DE}$$\approx\hat{XY} and \hat{XY}$$\approx$$\YZ, then\hat{DE}$$\approx$$\hat{YZ}[/tex]

This is a** transitive property**.

Here we have three values, initially first two values are equal and second & third values are equal.

Which gives any one of the value of first and second equals third value.

This is the transitive property.

Hence, the given statement is** transitive property.**

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a bag of 15 scrabble tiles contains three each of the letters a, c, e, h, and n. if you pick six letters one at a time, what is the chance that you spell c-h-a-n-c-e?

A bag of 15 scrabble tiles contains three each of the **letters **a, c, e, h, and n. The chance of spelling "**chance**" is approximately 0.0108 or about 1.08%.

First, we need to count the number of **ways **to choose two "c"s, two "e"s, and one each of "h" and "n" from the 15 tiles in the bag. To do this, we use the combination **formula**:

C(n, r) = n! / (r! * (n - r)!)

where n is the total number of **items **and r is the number of items we want to choose. For example, to choose two "c"s from three, we can calculate:

C(3, 2) = 3! / (2! * (3 - 2)!) = 3

We can use this formula to **calculate **the number of ways to choose two "c"s, two "e"s, and one each of "h" and "n":

C(3, 2) * C(3, 2) * C(3, 1) * C(3, 1) = 54

Therefore, there are 54 ways to choose the required letters out of the 15 tiles in the bag.

Next, we need to count the total number of ways to choose 6 tiles from the 15 in the bag. We can again use the **combination **formula:

C(15, 6) = 15! / (6! * (15 - 6)!) = 5005

Therefore, there are 5005 ways to choose any 6 tiles from the bag.

Finally, we can calculate the probability of spelling "**chance**" by dividing the number of ways to choose the required letters by the total number of ways to choose 6 tiles:

54 / 5005 ≈ 0.0108 or about 1.08%

So the probability of spelling "chance" when picking six tiles one at a time from the bag is approximately 0.0108 or about 1.08%.

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A coin is flipped 14 times and lands on heads 8 times. The theoretical probability that the next coin flip will be heads is 50%.

what’s the question?

SOLVING EQUATIONS Solve the equation. Check your solution.

50. y+4-1 = 18

52. v-7= 9+12

St 53.5+44=2+r

51. m+ 18+ 23 = 71

54. 22 +15=d-17

The **solution** of the **equation** are as follows:

y = 15

v = 28

r = 95.5

m = 30

d = 54

How to solve equation?In mathematics, an **equation** is a formula that expresses the equality of two expressions, by connecting them with the equals sign =. The equation can be solved by finding the value of the variables.

A** variable** is a number represented with letter in an equation.

Therefore, let's solve the equation.

y + 4 - 1 = 18

y = 18 - 4 + 1

y = 15

v - 7 = 9 + 12

v = 12 + 9 + 7

v = 28

53.5 + 44 = 2 + r

r = 53.5 + 44 - 2

r = 95.5

m + 18 + 23 = 71

m = 71 - 18 - 23

m = 30

22 + 15 = d - 17

d = 22 + 15 + 17

d = 54

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HELP will give BRAINLYST

For a function to have an inverse, it must be a bijective function, meaning that it must be both injective (one-to-one) and surjective (onto). In other words, every element in the range of the function must correspond to exactly one element in the domain, and vice versa.

In this case, the restricted domain would be all real numbers, because the function f(x) = x^2 + 6x - 9 is defined for all x in the real numbers and the range of the function is also the real numbers. Thus, the function is both injective and surjective, and it has an inverse.

Note that the inverse of f(x) = x^2 + 6x - 9 is not a simple expression like the original function, but it can be found by interchanging the variables and solving for y, as long as y = f(x).

In this case, the restricted domain would be all real numbers, because the function f(x) = x^2 + 6x - 9 is defined for all x in the real numbers and the range of the function is also the real numbers. Thus, the function is both injective and surjective, and it has an inverse.

Note that the inverse of f(x) = x^2 + 6x - 9 is not a simple expression like the original function, but it can be found by interchanging the variables and solving for y, as long as y = f(x).

Groundhog Day predictions have a 39% accuracy. How baby times should we expect to be correct over the next 38 years? *PLEASE HELP*

It would be **expected **to be correct **approximately **14.82 times over the next 38 years, based on the 39% accuracy of Groundhog Day predictions.

The **expected value**, also known as the mathematical expectation, is a key concept in **probability theory **and **statistics**.

Here,

Groundhog Day predictions have a 39% accuracy, so on average, 39% of the predictions made on Groundhog Day are correct.

To find the **expected number **of correct **predictions **over the next 38 years, we can multiply the accuracy of the predictions (39%) by the number of predictions made (38),

39% * 38 = 14.82

So, we would expect to be correct approximately 14.82 times over the next 38 years, based on the 39% accuracy of Groundhog Day predictions.

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What is x and y equal to?

-10x + 4y = -14

7x + 5y = 2

**Answer: x =1, y = -1**

**Step-by-step explanation:**

-10x+4y=-14

7x+5y=2

Let's eliminate y.

5(-10x+4y= -14)

4(7x + 5y=2)

[ I multiplied the first equation by the coefficient of y in the second equation and did the same in the second equation].

=> -50x+20y =-70

28x+20y = 8

Notice how the coefficients of y are the same. We can subtract the 2 equations to eliminate y.

Thus,

-78x = -78 ( y has been eliminated)

∴ x=-78/-78 =1.

Put the value of x in any equation to find y.

7x + 5y =2

=> 7(1) + 5y =2

7+5y=2

5y = 2-7

5y = -5

y = -1.

Hope this helps :)

in the country of united states of heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 56.6 inches, and standard deviation of 6.5 inches. a) what is the probability that a randomly chosen child has a height of less than 40.65 inches? answer

The **probability **that a randomly chosen child has a **height **of less than 68.15 inches is 0.9162, the probability that a **randomly **chosen child has a height of more than 54.4 inches is 0.6255.

Simply put, **probability **is the liability that commodity will do. When we do not know how an event will turn out, we can bandy the liability or liability of several issues. **Statistics** is the study of events that follow a probability distribution.

a) We need to find p(x<68.15)

**Standardize **x to z, we have, z = (68.15-μ)/σ

=(68.15-57)/8.1

=1.38

Reading from **standard **normal tables,

p(z<1.38) =0.9162.

Therefore, the probability that a **randomly **chosen child has a height of less than 68.15 inches is 0.9162.

b) We need to find p(x>54.4)

**Standardize **x to z, we have, z = (54.4-μ)/σ

=(54.4-57)/8.1

=-0.32

**Reading **from standard normal tables,

p(z>-0.32) = 0.6255

Therefore, the **probability **that a randomly chosen child has a height of more than 54.4 inches is 0.6255.

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HELP ME PLEASE ASAP! I NEED TO PASS THIS CLASS BY MONDAY!

The length of the two sides of the given **right triangle** is 5√2

A **triangle **with an angle right angle is called a **right triangle**.

Given that, a **right triangle**, with an **acute angle** of 45° and the length of **hypotenuse** is 10 units,

We need to find the **length **of two sides u and v,

The sum of a **triangle **is 180°, and if one angle is 90° and the other is 45° therefore, the third is also 45°

Now, we know that, sides opposite to equal angles are equal,

Therefore, v = u,

Now, using the **Pythagoras theorem**,

10² = v²+u²

v² + v² = 100

2v² = 100

v² = 50

v = 5√2

u = 5√2

Hence, the length of the two sides of the given **right triangle** is 5√2

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(SAT Prep) Find the value of x

PLS ASAP

The **value of x** is given as follows:

x = 155º.

How to obtain the value of x?For the triangle at the **left**, considering that the sum of the measures of the internal angles of a triangle is of 180º, the angle measures are given as follows:

For the triangle at the **right**, considering the ray formed at the top, the measures are given as follows:

An angle is supplementary with it's external angle, meaning that the sum of their measures is of 180º, hence the **value of x** is obtained as follows:

x = 180 - 25

x = 155º.

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f(x) = -x² + 5 and g(x) = -2x+2, find all values of x for which f(x) = g(x).

**Answer: **Since the square root of a negative number is not a real number, there are no real solutions to this equation, and therefore no values of x for which f(x) = g(x).

**Step-by-step explanation:**

To find all values of x for which f(x) = g(x), we can set the two functions equal to each other and solve for x:

-x² + 5 = -2x + 2

Expanding the right-hand side:

-x² + 5 = -2x + 2

-x² + 2x + 3 = 0

Solving for x using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = 2, and c = 3

x = (-2 ± √(2² - 4(1)(3))) / 2(1)

x = (-2 ± √(4 - 12)) / 2

x = (-2 ± √(-8)) / 2

Since the square root of a negative number is not a real number, there are no real solutions to this equation, and therefore no values of x for which f(x) = g(x).

Write the linear equation given slope is -1/3 and the point (-9,-1)

The **Linear Equation** for the line with slope as -1/3 and the point (-9,-1) is y = (-1/3)x - 4 .

We use the **point slope form** of a linear equation to write the equation of a line with its slope and a point on the line.

The point-slope form is ⇒ y - y₁ = m(x - x₁) ;

Where m is = **slope **of line, and (x₁, y₁) is a point on line.

The Slope (m) of line is = -1/3 and **point **on line** **(x₁, y₁) is = (-9, -1),

Now , we substitute these values ;

we get ;

⇒ y - (-1) = (-1/3)(x - (-9)) ;

⇒ y + 1 = (-1/3)(x + 9) ;

Simplifying further ,

we get ;

⇒ y + 1 = (-1/3)x - 9/3 ;

Subtracting 1 from both sides, we get:

⇒ y = (-1/3)x - 4

Therefore, the **equation **of the line is y = (-1/3)x - 4 .

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what is the number of ways to choose two toppings for a pizza, one topping from a group of 5 kinds of meats and the other topping from a group of 7 kinds of vegetables?

There are **35 ways** to choose two toppings for a pizza, one topping from a group of 5 kinds of meats and the other topping from a group of 7 kinds of vegetables.

The **multiplication rule of counting **in **Permutation and Combinations** states that if there are n ways to perform one task and m ways to perform a second task, then there are n x m ways to perform both tasks in **sequence**.

The number of ways to choose a meat topping from 5 kinds of meats = 5.

The number of ways to choose a vegetable topping from 7 kinds of vegetables = 7.

Using the multiplication rule, the **number of ways** to choose one meat topping and one vegetable topping is = 5 x 7 = 35 ways.

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Find b and then solve the equation

2x^2+bx-10=0 if one of its roots is 5

well, since we know that one root is 5, that is a factor of it is (x-5), so hmmm by the **remainder theorem** we also know that if we plug "5" as our argument in our f(x), that is, if we do f(5), it must result to 0. so f(5) = 0, if that's so then

[tex]2x^2+bx-10=f(x)\implies 2(5)^2+b(5)-10=f(5) \\\\\\ 2(5)^2+b(5)-10=0\implies 50+5b-10=0\implies 5b=-40 \\\\\\ b=\cfrac{-40}{5}\implies \boxed{b=-8} \\\\[-0.35em] ~\dotfill\\\\ 2x^2-8x-10=0\implies 2(x^2-4x-5)=0\implies 2\stackrel{ {\Large \begin{array}{llll} x=-1 \end{array}} }{(x+1)}(x-5)=0[/tex]

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