A librarian is rearranging the bookshelves and notices that the pair of bookends on the shelf are not the same size. The librarian then notices that the bookends create similar triangles.


Two triangular book ends. The right angles are shown. The bottom right angle of the triangle are marked congruent to each other. The larger bookshelf has a height of 10 inches and a diagonal height of 12 inches. The smaller bookshelf has a height of 6 inches and a diagonal height labeled x.

What is the length of the diagonal, x, created by the smaller bookend?


27.2 in.



7.2 in.



20 in.



5 in.

Answer: $54.40

Step-by-step explanation: 37.5%-5.5% = 32% off $80-32% = $54.40

Answer: D

You get the same answer from doing both!

Answer:

a

Step-by-step explanation:

Antonio’s total lifetime cost will be $11680.99 after calculating all loans

Given that

Loan Amount ($)

5,894$

5,258$

Interest Rate (%)

6.9%

7.5%

Now for the loan amount 5,894$ at 6.9% interest, the amount will be

[tex]A=P(1+\dfrac{r}{h} )^{n\times t}[/tex]

[tex]A=5894(1+\dfrac{0.069}{12} )^{12\times 10}[/tex]

[tex]A=5894\times(1.00575)x^{120} =11727.76[/tex]

Now for the loan amount 5.258$ at 7.5% interest, the amount will be

[tex]A=5258(1+\dfrac{0.075}{12} )^{12\times 10}[/tex]

[tex]A=5258\times2.1120=111105.23[/tex]

So the total lifetime cost will be

[tex]=11727.76-5894+111105.23-5258=11680.99[/tex]

Thus Antonio’s total lifetime cost will be $11680.99 after calculating all loans

To know more about Compound interest follow

https://brainly.com/question/24924853

Answer:

a. $16,246.80

Step-by-step explanation:

EDGE

Answer:

angle 2 is 85

Step-by-step explanation:

since its facing the 85

Answer:

Answer:1 is 95°

2 is 85°

3 is 95°

Step-by-step explanations

opposite angles are equal so 2 is 85° 95°Step-by-step explanation:directly opposite angles are equal so 2 is 85angles on a straight line add up to 180°

Answer:1 is 95°2 is 85°3 is 95°Step-by-step explanation:directly opposite angles are equal so 2 is 85angles on a straight line add up to 180° so 3 is 180-85=95°

Answer:1 is 95°2 is 85°3 is 95°Step-by-step explanation:directly opposite angles are equal so 2 is 85angles on a straight line add up to 180° so 3 is 180-85=95°then 3 is directly opposite to 1 so both are 95

Answer:1 is 95°2 is 85°3 is 95°Step-by-step explanation:directly opposite angles are equal so 2 is 85angles on a straight line add up to 180° so 3 is 180-85=95°then 3 is directly opposite to 1 so both are 95 I hope you're helped?

Answer:

A. multiplied by

Step-by-step explanation:

For example, sub n = 2

8(2) = 16

Hello.

The correct word is "multiplied by"

Eight multiplied by a number n equals 8n.

Remember that

[tex]\bigstar[/tex] We always write the number next to the variable.

[tex]\bigstar[/tex] We write the number and the variable together.

Can we write 8×n? Sure! However, we usually write it as

8n

Therefore, the correct answer is "[tex]\mathrm{multiplied\:by}[/tex]"

I hope it helps.

Have a great day.

[tex]\boxed{imperturbability}[/tex]

Step-by-step explanation:

X = 3

-14x=-42

-3/5 + x=12/5

X-5=-2

X/4=6/8

X= -3

-6+x=-9

X/3=9

Answer:

girls = 61

boys = 73

Step-by-step explanation:

Let x = number of girls

Let y = number of boys

Given the difference between the number of the girls and the number of the boys in the outdoors club is 12:

⇒ y - x = 12

Given there are 4 times the number of the girls decreased by 25 equals 3 times the number of the boys:

⇒ 4x - 25 = 3y

Rearrange x - y = 12 to make y the subject:

⇒ y = 12 + x

Substitute x = 12 + y into 4x - 25 = 3y and solve for y:

⇒ 4x- 25 = 3(12 + x)

⇒ 4x- 25 = 36 + 3x

⇒ x = 61

Now we have found the value of x, substitute this into y = 12 + x and solve for y:

⇒ y = 12 + 61

⇒ y = 73

Answer:

it is a pattern. 8: add 1. 9: multiply m by 3 to get n

The investment of the kelly at the end of 8 years is $7393.78.

It is given that

The principle P= $5000

rate of interest R=4.9%

The rate is compounded monthly so

[tex]CI=P(1+\dfrac{R}{12}^{12t} )[/tex]

By putting the value

[tex]CI= 5000\times (1+\dfrac{0.049}{12}^{12\times8} )[/tex]

[tex]CI=7393.78[/tex]

Thus the investment of the kelly at the end of 8 years is $7393.78.

To know more about Compound interest follow

https://brainly.com/question/24924853

Answer:

13

Step-by-step explanation:

For this problem, work backwards to determine what the starting number was. Take 3.5 and multiply it by 3 to get 10.5, then subtract 4 to get 6.5. Finally, multiply 6.5 by 2 to get the starting number, which is 13. To check your work, you can always take 13 and perform the operations to make sure you end up with 3.5.

Hopefully this helps- let me know if you have any questions!

Answer: 73.9

Step-by-step explanation:

Answer:

Julie has 5 bunnies. She looses 2. How many bunnies does she have now?

Answer: 3 bunnies left

RIP BUNNIES!!

If you wanted a harder one, then please, be more specific.

Answer:

(69/40 , 7/11)

Step-by-step explanation:

multiply the bottom equation by 2

-4x + 8y = 12

4x+3y=-5

cancel out both 4x

8y+3y=11y

12+ -5 = 7

11y=7

divide both sides by 11

y=7/11

substitute that in for y

4x + 3(7/11) = -5

4x + 21/11 = -5

4x = -69/10

x= 69/40

Answer:

5mn(2m + 6n + 1)

Step-by-step explanation:

Look at the coefficients (the numbers): 10, 30, 5

The greatest common factor of 10, 30, and 5 is 5.

Now look at the variable parts of the three terms.

Start with the variable m.

There is m², m, and m.

The GCF of m², m, and m is m.

Now look at the variable n.

There is n, n², n.

The GCF on n, n², and n is n.

The GCF for the entire polynomial is 5mn.

Now we factor out 5mn from all terms.

To factor out 5mn, you divide each term by the GCF, 5mn.

10m²n + 30mn² + 5mn = 5mn(2m + 6n + 1)

Answer:

4 maybe??...

Step-by-step explanation:

I really dunno P-P

Answer:

see image

Step-by-step explanation:

Supplementary means the angles add up to 180°.

Add the given angles and set equal to 180°

To solve, combine like terms, add 10, divide by two to get x all by itself.

Replace x with 95 to find the measures of Angles A, C, D.

Use the supplementary definition a second time to find the measure of Angle B.

see image.

Answer:

194

Step-by-step explanation:

you would do 340 divided by 2 and that gets you 170 then you would subtract 24 from Rita and that is 146 so Rita drove 146 miles. then for Joel you add 170 +24 = 194. So Joel drove 194 miles.

The expression that is equivalent to m(n(x)) is [tex]25x^{2} +90x+84[/tex].

It is given that

[tex]m(x) = x^{2} +3\\n(x) = 5x+9[/tex]

If there are two functions f(x) and g(x), f(g(x)) will be obtained by replacing x by g(x) into f(x).

So, [tex]m (n(x))= (5x+9)^2+ 3[/tex]

[tex]m (n(x))= 25x^{2} +81+90x +3[/tex]

[tex]m (n(x))= 25x^{2} +90x+84[/tex]

Therefore, the expression that is equivalent to m(n(x)) is [tex]25x^{2} +90x+84[/tex].

To get more about functions visit:

https://brainly.com/question/26613452

Answer:

b

Step-by-step explanation:

Answer:

the answer is x=6

Step-by-step explanation:

A perfect square is an expression that factors into two other expressions that are identical.  The equation that represents this model is (2x)²=4x².

A perfect square is an expression that factors into two other expressions that are identical. A monomial is a single phrase made up of a product of constants, variables, and their positive integer powers. As a result, a perfect square monomial is a monomial that factors into two monomials that are identical.

As given to us that the first row consists of tile 2x², and the second row also consists of tile 2x². Thus, the expression can be written as,

[tex]2x^2+2x^2\\\\=(2x)^2=4x^2[/tex]

Hence, the equation that represents this model is (2x)²=4x².

Learn more about Perfect square Monomial:

https://brainly.com/question/13647939

Answer:

A

Step-by-step explanation:

2022

The area of shaded region is 32 square units.

"The area can be defined as the space occupied by a flat shape or the surface of an object.  The area of a figure is the number of unit squares that cover the surface of a closed figure. The area is measured in square units such as square centimeters, square feet, square inches, etc."  

To find the area of the shaded region

1. Find the area of the biggest square ([tex]A_{1}[/tex])

Formula for area of a square

[tex]A_{1}[/tex] = side × side

⇒[tex]A_{1}[/tex] = 10×10

⇒[tex]A_{1}[/tex] = 100 square units.

2. Find the area of the unshaded region ([tex]A_{2}[/tex])

[tex]A_{2}[/tex] = X(biggest square)+ 2.Y(smallest square)

⇒[tex]A_{2}[/tex] = [tex](6[/tex]×[tex]6)[/tex] + [tex]2(4[/tex]×[tex]4)[/tex]

⇒[tex]A_{2} =36+2.(16)[/tex]

⇒[tex]A_{2}=68[/tex] square units

3. Find the difference of [tex]A_{1}[/tex] and [tex]A_{2}[/tex]

Area of the shaded part = [tex]A_{1}[/tex] - [tex]A_{2}[/tex]

= 100-68

= 32 square units.

Hence, The area of shaded region is 32 square units.

Learn more about area of square here

https://brainly.in/question/7636962

#SPJ2

Answer:

Your given polynomial has only one real root which is x= -4

Step-by-step explanation:

find any zero of the polynomial.

x-a divides the polynomial where a is a zero of polynomial:

So x+4 divides [tex]2x^{3} +2x^{2} -19x+20[/tex]

If we factor out a two, we can use the quadratic formula.

2(x^2-3x+2.5) so we have x = (-(-3)+/-(9-4*1*2.5)^(1/2))/2*1)=(3+i) or (3-i)/2 .

Final answer:

[tex]2x^{3} +2x^{2} -19x+20=0[/tex]

then x=-4, (3+i)/2, or (3-i)/2

Graph attached

Zeros are the x intercepts

Answer: See below

Step-by-step explanation:

[tex]\begin{bmatrix}y=x^2-20x+73\\ y=-3x+3\end{bmatrix}[/tex]

[tex]\mathrm{Subtract\:the\:equations:}[/tex]

[tex]y=x^2-20x+73[/tex]

[tex]-[/tex]

[tex]\underline{y=-3x+3}[/tex]

[tex]y-y=x^2-20x+73-\left(-3x+3\right)[/tex]

[tex]\mathrm{Simplify:}[/tex]

[tex]0=x^2-17x+70[/tex]

[tex]x^2-17x+70=0[/tex]

[tex]\mathrm{Solve\:with\:the\:quadratic\:formula}[/tex] [tex]\mathrm{for\:}\ a=1,\:b=-17,\:c=70:[/tex]

[tex]x_{1,\:2}=\frac{-\left(-17\right)\pm \sqrt{\left(-17\right)^2-4\cdot \:1\cdot \:70}}{2\cdot \:1}[/tex]

[tex]x_{1,\:2}=\frac{-\left(-17\right)\pm \:3}{2\cdot \:1}[/tex]

[tex]\mathrm{Separate\:the\:solutions:}[/tex]

[tex]x_1=\frac{-\left(-17\right)+3}{2\cdot \:1},\:x_2=\frac{-\left(-17\right)-3}{2\cdot \:1}[/tex]

[tex]\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}[/tex]

[tex]x=10,\:x=7[/tex]

[tex]\mathrm{Plug\:the\:solutions\:}x=10,\:x=7\mathrm{\:into\:}y=x^2-20x+73:[/tex]

[tex]\mathrm{For\:}y=x^2-20x+73\mathrm{,\:subsitute\:}x\mathrm{\:with\:}10[/tex]

[tex]y=10^2-20\cdot \:10+73[/tex]

[tex]y=10^2-200+73[/tex]

[tex]y=100-127[/tex]

[tex]y=-27[/tex]

[tex]\mathrm{For\:}y=x^2-20x+73\mathrm{,\:subsitute\:}x\mathrm{\:with\:}7[/tex]

[tex]y=7^2-20\cdot \:7+73[/tex]

[tex]y=7^2-140+73[/tex]

[tex]y=49-67[/tex]

[tex]y=-18[/tex]

[tex]\mathrm{Therefore,\:the\:final\:solutions\:for\:}y=x^2-20x+73,\:y=-3x+3\mathrm{\:are\:}:[/tex]

[tex]\begin{pmatrix}x=10,\:&y=-27\\ x=7,\:&y=-18\end{pmatrix}[/tex]

Answer:

bbbbb

Step-by-step explanation:

Answer: 15

Step-by-step explanation:

We know that the scale factor of the dilation is the ratio of similtude, and that the ratio of similitude is equal to the ratio of the perimeters. So, the new perimeter is 30(0.5)=15.

Step-by-step explanation:

= a_(n-1) x 1.5

1.5a_(n-1)

Answer:

$1556.25

Step-by-step explanation:

Answer:

a way to not find the answer is to do anything but divide 9 by 16

Step-by-step explanation:

hope this helps, brainliest appreciated :)