Last year, the school library had a total of x books. Over the summer, the library acquired another 40 books and now has a total of 1,795 books. Which equation could be used to find x, the number of books the library had last year?

Answer:

The required polynomial is:

[tex]f\left(x\right)=x^3+8x^2+19x+12[/tex]

Step-by-step explanation:

Given the zeros

-4, -1, -3

Zeros can be written as:

x = -4, x = -1, x = -3

Finding the factors

x = -4

x +4 = 0

x = -1

x + 1 = 0

x = -3

x + 3 = 0

Thus, the factor are:

(x+4) (x+1) (x+3)

The original function can be computed by multiplying the factors

[tex]\left(x+4\right)\left(x+1\right)\left(x+3\right)=0[/tex]

as

[tex]\left(x+4\right)\left(x+1\right)=x^2+5x+4[/tex]

so the expression becomes

[tex]\left(x^2+5x+4\right)\left(x+3\right)=0[/tex]

Distribute parentheses

[tex]x^2x+x^2\cdot \:3+5xx+5x\cdot \:3+4x+4\cdot \:3=0[/tex]

[tex]x^2x+3x^2+5xx+5\cdot \:\:3x+4x+4\cdot \:\:3=0[/tex]

[tex]x^3+3x^2+5x^2+15x+4x+12=0[/tex]

Add similar elements: [tex]3x^2+5x^2=8x^2[/tex]

[tex]x^3+8x^2+15x+4x+12 = 0[/tex]

Add similar elements: [tex]15x+4x=19x[/tex]

[tex]x^3+8x^2+19x+12=0[/tex]

Thus, the required polynomial is:

[tex]f\left(x\right)=x^3+8x^2+19x+12[/tex]

Note: your answer choices are a little ambiguous, but I have explained the entire procedure. Hopefully, it will clear your concept.

Answer:

$72.76 Us Dollars

Step-by-step explanation:

1st I found out what 20% off of $85 was and it was $68 US Dollars then I had to add 7% of $68 US Dollars and it came out to $72.76

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Answer:

Jill earns $57,000

Step-by-step explanation:

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Answer:

All you have to do is replace the X with the number on the table

Step-by-step explanation:

so the first number is -3 so 3×-3+2

that equals -7 so put -7 as the first number under y. can continue like that

Answer:

1. -7, -4, -1, 2, 5, 8, 11

2. 5, 3, 1, -1, -3, -5, -7

3. -7, -6, -5, -4, -3, -2, -1

4. 13, 10, 7, 4, 1, -2, 5

Step-by-step explanation:

The expression equivalent to 4^-5 • 3^-5  is 12^-5

Equivalent expressions are simply known as expressions with the same solution but different arrangement.

Given the index expressions;

4^-5 • 3^-5

Using the exponent rule, the two values are have different bases but the same exponent and thus, we multiply the bases and leave the exponents the same way.

This can be written as;

4(3) ^ -5

expand the bracket

12^-5

Thus, the expression equivalent to 4^-5 • 3^-5  is 12^-5

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Answer:

Slope is -2/3

Step-by-step explanation:

Change slope to slope form

Y=-2/3x+1

Slopes gonna be the same if they’re parallel

A reasonable estimate for how long the job will take if she has her two sons help if they each work at approximately the same rate as Astrid is  5.75 hours.

Outside of her cabin, Astrid is painting. She is aware that if she works alone, the task will take her 23 hours to finish. If her two boys labor at roughly the same rate as Astrid, a fair estimate of how long the job will take with their assistance is

Astrid is painting the outside of her cabin = 23 hours

Astrid has her two sons help if they each work at approximately the same rate as Astrid is 23/2 = 11.5

Then 11.5/2 = 5.75 hours.

The work is calculated using the work formula. Let's review what work means before learning the formula. When we apply a force to an item and the object is moved, we say that work has been done. The work done becomes zero if there is no displacement in the direction of the force. Calculating the amount of labor required to move an object is done using the work formula.

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Outside of her cabin, Astrid is painting. If her two boys labor at roughly the same rate as Astrid, a fair estimate of 5.75 hours long the job will take with their assistance is.

Given that,

Outside of her cabin, Astrid is painting. She is aware that if she works alone, the task will take her 23 hours to finish.

We have to find If her two boys labor at roughly the same rate as Astrid, a fair estimate of how long the job will take with their assistance is.

Astrid is spent 23 hours painting the outside of her cabin.

If each son works at roughly the same rate as Astrid, which is 23/2 = 11.5 she asks her two sons to assist.

Then 11.5/2 = 5.75 hours.

Therefore, If her two boys labor at roughly the same rate as Astrid, a fair estimate of 5.75 hours long the job will take with their assistance is.

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Answer:

(X+1)+93=3x ( exterior angle of triangle is equal to sum of interior angle)

94=2x

X=94/2

X=47

also X+1=48

3*47=141

now,

Step-by-step explanation:

93+48+X=180 ( angle of triangle)

141+X=180

X=180-141

X=39

angleFGH=39

Answer:

G.

Step-by-step explanation:

The line A has the constant of proportionality between x and y as 5.

In mathematics, we use the constant of proportionality to determine the type of proportionality, whether direct or indirect.

For, the data given in the question;

Given lines A, B, and C Obtaining the equation for the line yields the proportionality constant.

1) Line A intersects (0,0) and (1, 5). Line A's equation is given by:

y - y₁ = [(y₂ - y₁)/(x₂ - x₁)]×(x - x₁)

Substitute the values;

y - 0 = [(5 - 0)/(1 - 0)]×(x - 0)

y = 5x

y/x = 5

The proportionality constant between y and x is 5.

2) Line B traverses (0,0) and (3, 5). Line A's equation is given by:

y - y₁ = [(y₂ - y₁)/(x₂ - x₁)]×(x - x₁)

Substitute the values;

y - 0 = [(5 - 0)/(3 - 0)]×(x - 0)

y = 5x/3

y/x = 5/3

The proportionality constant between y and x is 5/3.

3) Line C intersects (0,0) and (3, 2). Line A's equation is given by:

y - y₁ = [(y₂ - y₁)/(x₂ - x₁)]×(x - x₁)

Substitute the values;

y - 0 = [(3 - 0)/(2 - 0)]×(x - 0)

y = 3x/2

y/x = 3/2

The proportionality constant between y and x is 2/3.

Therefore, the constant of proportionality between x and y as 5 shown by line A.

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The correct question is -

Lines A, B, and C show proportional relationships.

Which line has a constant of proportionality between y and x of 5?

Answer: 1 and 3 dont 2 and 4 do have a line of symmetry

Step-by-step explanation:

Graphs 1, 3 function are not line symmetry and 2 and 4 have line symmetry.  

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The line of symmetry is an imaginary line that runs through the centre of a line or shape creating two perfectly halves.

To check a function to be symmetrical about the origin we need to replace y with minus y and x with minus x and the function must be equal to original function.

In the given graphs, 1 and 3 are not symmetrical and 2 and 4 are symmetrical.

Hence graphs 1, 3 function are not line symmetry and 2 and 4 have line symmetry.

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Using sampling concepts, one sample of 5 high schools in the city of Chicago is given by:

Brooks,  Hyde Park, Young Womens, Marshall, Noble - UIC.

The problem is incomplete, but researching it on a search engine, it gives us a list of 15 high schools in Chicago, and asks us to take a sample of 5.

Hence, from the concepts of sample and populations, the sample of 5 means that we have to select 5 schools from the 15 listed, hence one possible option is given by:

Brooks,  Hyde Park, Young Womens, Marshall, Noble - UIC.

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Answer:

The answer of 5 ⅔ ÷ 4 ⅔= 1 3/14

Answer:

188.5

Step-by-step explanation:

in order to find the circumference you need to know the radius which is half of the diameter. the picture shows the formula used.

Answer:

f(x)=-0.25x+4.75

Step-by-step explanation:

-0.25x+4.75

-0.25(-1)+4.75=5

-0.25(3)+4.75=4

Hope this helps!

The volume of the rectangular prism will increase by 33% if the width, length, and height are each increased by 10%.

Every three-dimensional object occupies some space. This space is measured in terms of its volume. Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

The formula for the volume of a rectangular prism is:

V = l x w x h

where

“l” is the base length

“w” is the base width

“h” is the height of the prism

If the width, length, and height are each increased by 10%, the equation will now become:

[tex]V_{2}= 1.10 l * 1.10 w*1.10h[/tex]

[tex]V_{2}= 1.331* l*w*h[/tex]            V = l*w*h

[tex]V_{2}= 1.331* V[/tex]

Hence, if the width, length, and height are each increased by 10%, the volume of the rectangular prism will increase by 33%.

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Answer: Average rate of change = 2

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Answer:

i think its 96% ???

Step-by-step explanation:

Answer:

all angles are 60 degrees

Step-by-step explanation:

since all sides are equal, all angles will be equal so its a equilateral triangle

all angles in a equilateral triangle are 60 as 180/3 is 60

so all angles equal 2x

2x = 60

x = 60/2 = 30

Answer:

e= 2

W= 15

m= 9

Step-by-step explanation:

for e: yout multiply 5 x 7 to get 35 so 2 x 7 = 14

for W: 20/10 = 2 so divide 30/2 to get 15

for m: 11 x 2 = 22 so do 18 divided 2 to get 9

Answer:

E = 2

W = 15

M = 9

Step-by-step explanation:

You just have to make the denominator / numerator the same.

[tex]\frac{E}{5}[/tex] = [tex]\frac{14}{35}[/tex]

Multiply the first fraction by 7 so that their denominators are both 35.

[tex]\frac{7E}{35}[/tex] = [tex]\frac{14}{35}[/tex]

7E = 14

E = 14 ÷ 7

E = 2

[tex]\frac{20}{30}[/tex] = [tex]\frac{10}{W}[/tex]

Multiply the second fraction by 2 so that their numerators are both 20.

[tex]\frac{20}{30}[/tex] = [tex]\frac{20}{2W}[/tex]

2W = 30

W = 30 ÷ 2

W = 15

[tex]\frac{M}{11}[/tex] = [tex]\frac{18}{22}[/tex]

Multiply the first fraction by 2 so that their denominators are both 22.

[tex]\frac{2M}{22}[/tex] = [tex]\frac{18}{22}[/tex]

2M = 18

M = 18 ÷ 2

M = 9

Answer:

y=2x-1

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

it is a 3:5

Step-by-step explanation:

Answer:

Since these are right triangles, the unmarked sides can be determined to be congruent because of the Pythagorean theorem. Once the third set of congruent sides is determined, the SSS or SAS theorem can be used to prove triangle congruency. 

Step-by-step explanation:

sorry I know this is late but i just took the assignment and this was the answer

Answer:

they are right triangles so they are congruent

Step-by-step explanation:

got it right on edge

e = -2

that should be the correct answer

Answer:

e = 2

Step-by-step explanation:

We need to know about the relation between roots of a quadratic equation for solving the question. The quadratic equation with roots 3/4 and 1/2 is [tex]8x^{2} -10x+3=0[/tex]

Quadratic equation is an equation with the highest order of variable being 2. Roots of a quadratic equation are the values that satisfy the equation.Since quadratic equation has the highest order as 2, the equation has two roots. Roots of a quadratic equation can be real and unique, real and equal or imaginary. The roots of a quadratic equation can be used to get the quadratic equation itself.

Let there be a quadratic equation:

[tex]ax^{2} +bx+c=0\\x^{2} +\frac{b}{a} x+\frac{c}{a} =0[/tex]

Let the roots of the quadratic equation be α and β, then

α+β=-b/a

αβ=c/a

In this question we know the two roots are 3/4 and 1/2. So we can derive the quadratic equation from them

[tex]\frac{3}{4} +\frac{1}{2} =\frac{-b}{a} \\\frac{-b}{a} =\frac{5}{4}[/tex]

[tex]\frac{3}{4}[/tex]×[tex]\frac{1}{2} =\frac{c}{a}[/tex]

[tex]\frac{c}{a} =\frac{3}{8}[/tex]

The quadratic equation is:

[tex]x^{2} -\frac{5}{4} x+\frac{3}{8} =0\\8x^{2} -10x+3=0[/tex]

Therefore we found the quadratic equation with roots 3/4 and 1/2 to be [tex]8x^{2} -10x+3=0[/tex]

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Answer:

The acceleration of the car will be 400 m/s².

Step-by-step explanation:

The acceleration of the car can be found using Newton second law:

[tex] F = ma [/tex]

Where:

F: is the net force = 200 N

m: is the mass = 500 g

a: is the acceleration =?

Then, the acceleration will be:

[tex] a = \frac{F}{m} = \frac{200 N}{500 g*\frac{1 kg}{1000 g}} = 400 m/s^{2} [/tex]  

Therefore, the acceleration of the car will be 400 m/s².

I hope it helps you!