Amira is solving the equation x2 – 6x = 1. Which value must be added to both sides of the equation to make the left side a perfect-square trinomial?
–9
8
9
36

The side lengths 10.5 cm, 20.8 cm, and 23.3 cm create a right scalene triangle.

Answer:

She'll need 8143 cubic inches of foam and 1,809.6  square inches of fabric.

Step-by-step explanation:

Assuming you want to know how much foam and fabric she will need...

First the foam... so we need to determine the volume of that footstool.  The Volume of a cylinder is given by:

V = π * r² * h

So, we plug in the numbers:

V = π * 12² * 18 = π * 144 * 18

V = 2,592 π  = 8143 cubic inches.

Now for the fabric... we'll assume Maria wants to cover the side of the stool and the top, but not the bottom.

The side of the stool is basically a rectangle of width of 18 inches and a length of the circumference of the base of the stool.  The circumference is given by: C = 2 π * r of course, so C = 24π = 75.14 inches.

So the lateral surface of the cylinder is:

LS = 18 * 75.14 = 1,357.2 sq inches.

Then we need to calculate the area of the top... which is easy:

A = π * r²  = π * 12²  = 144 π = 452.4 sq inches

So, to cover the lateral side of the footstool and its top, she needs to use:

TA = 1,357.2 + 452.4 = 1,809.6 sq inches of fabric.

Answer:

The fabric needed = 2260.8 square inches

Step-by-step explanation:

Points to remember

Surface area of cylinder = 2πr(r + h)

It is given that,

Maria want to make a footstool in the shape of a cylinder.

radius of cylinder = 12 in and height = 18 in

To find the surface area

Here r = 12 in and h = 18 in

Surface area = 2πr( r + h)

 = 2 * 3.14 * 12 (12 + 18)

 = 2260.8 square inches

Answer:

System #2:

3x - y = 4---->6x - 2y = 8

Answer: the answer is 18

Step-by-step explanation:

[tex]\bf 12+9\times \cfrac{4}{2}\div (2+1)\implies \stackrel{\mathbb{P~E~M~D~A~S}}{12+9\times \cfrac{4}{2}\div (\stackrel{\downarrow }{3})}\implies 12+9\times \stackrel{\downarrow }{2}\div(3) \\\\\\ 12+\stackrel{\downarrow }{18}\div (3)\implies 12+\stackrel{\downarrow }{6}\implies 18[/tex]

So this equation is in slope intercept form:

y = mx + b

m is slope

b is y-intercept

This means that for this equation the slope is 6/5 and the y-intercept is (0 , 1)

Look at image below for the graph

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

White: 2/5

Dark: 3/5

Step-by-step explanation:

There are 5 sections and there are 2 white spots and 3 dark spots.

So, 2 out of the 5 sections are white which is 2/5 and 3 out of the 5 sections is dark which is 3/5.

Answer:

Step-by-step explanation:

Given : The total number of sections = 5

The number of white sections = 2

The number of dark sections =3

Now, the probability that the spinner lands on a white section is given by :-

[tex]\text{P(white)}=\dfrac{\text{Number of white sections}}{\text{total sections}}\\\\=\dfrac{2}{5}[/tex]

Now, the probability that the spinner lands on a dark section is given by :-

[tex]\text{P(dark)}=\dfrac{\text{Number of dark sections}}{\text{total sections}}\\\\=\dfrac{3}{5}[/tex]

Answer:

B.[tex]14in^{2}[/tex]

Step-by-step explanation:

Solve this by using one of two methods.

Split up into different shapes:

This method uses the sum of the areas of a rectangle and two triangles to find the area of the parallelogram:

[tex]A=(b*h)_{rectangle} +2*(0.5*b*h)_{triangle} \\A=(5*2)+2(0.5*2*2)\\A=10+4\\A=14in^{2}[/tex]

Use Parallelogram formula:

This formula is the same as the formula for a rectangle where you multiply the base by the height.

[tex]A=b*h\\A=(5+2)*2\\A=14in^{2}[/tex]

Answer: The answer is 14 in2

Answer:

the answer would be y=2x+4

Step-by-step explanation:

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{6}{ h},\stackrel{-3}{ k})\qquad \qquad radius=\stackrel{5}{ r}\\[2em] [x-6]^2+[y-(-3)]^2=5^2\implies (x-6)^2+(y+3)^2=25[/tex]

Answer:

Step-by-step explanation:

The x value for the center is part of the x^2 part of the equation.

The y value for the center is part of the y^2 part of the equation.

The radius is squared.

(x - 6)^2 + (y + 3)^2 = 5^2  

Notice the sign change for the center. When you move horizontally the sign of the center changes sign in the circle's equation.

The graph is included to show you that.

Answer:

92

Step-by-step explanation:

You need to divide the total number of souvenir paperweights divded by how much the box holds.

You will get 91.923 however you cant have only part of a box so you have to round up to 92.

The volume of the cylindrical aquarium to the nearest whole number is [tex]\(\boxed{26694}\)[/tex] cubic feet.

The volume [tex]V[/tex] of a cylinder can be calculated using the formula:

[tex]\[ V = \pi r^2 h \][/tex]

 where [tex]r[/tex] is the radius of the cylinder's base and [tex]h[/tex] is the height of the cylinder.

 Given:

- Radius [tex]\( r = 18.8 \)[/tex] feet

- Height [tex]\( h = 24 \)[/tex] feet

- [tex]\( \pi \approx 3.14[/tex]

Now, let's calculate the volume:

[tex]\[ V = 3.14 \times (18.8 \text{ feet})^2 \times 24 \text{ feet} \][/tex]

[tex]\[ V = 3.14 \times 18.8^2 \times 24 \][/tex]

[tex]\[ V = 3.14 \times 353.44 \times 24 \][/tex]

[tex]\[ V = 3.14 \times 8482.56 \][/tex]

[tex]\[ V \approx 26694.1216[/tex]

To the nearest whole number, the volume of the aquarium is approximately:

[tex]\[ V \approx 26694 \] cubic feet.[/tex]

Therefore, the volume of the cylindrical aquarium to the nearest whole number is [tex]\(\boxed{26694}\)[/tex] cubic feet.

P means permutation, so using the permutation formula:

8P4 = 8! / (8-4)!

= (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (4 x 3 x 2 x 1)

= 8 x 7 x 6 x 5

= 1680

The answer is C.

Answer:

C

Step-by-step explanation:

Its C

Answer:

C

Step-by-step explanation:

ANSWER

1 bell shape

2 to find probability when sampling

EXPLANATION

1 In a normal distribution, the mode,mean and median are equal.

As a result, the distribution is neither skewed to the right or left.

The shape of the normal distribution looks like a bell.

That is why it is also called the bell curve.

2. The area under the normal curve is 1.

The line of symmetry of the bell shaped distribution divides it into two halves with area 0.5 each.

The normal curve is therefore used to find the probabilities of a sample distributions.

Answer:7

Step-by-step explanation:

In the first store, you pay 12.5+1.5x per x movies

In the second store, you pay 3.5x per x movies

The first store offers a better deal when:

12.5 + 1.5x > 3.5x

12.5 > 2x

6.25 > x

Which means if you rent minimum 7 movies in month, you should go to the first store

Answer:

Step-by-step explanation:

We know that the first store charges $12.50 per month, which is a initial condition, and charges additionally $1.50 per movie, which is variable, this represents the ratio of change, so this can be expressed as

[tex]\$12.50 + \$1.50x[/tex]

Where [tex]x[/tex] represents movies.

Now, the second store doesn't charge and membership fee, just it charges a cost per movie which is $3.50.

Then, to solve the minimum number of movies needed to Plan A be the best choice, we just have to solve the following inequality

[tex]\$12.50 + \$1.50x> \$3.50[/tex]

Which expresses the case where Plan A is a better choice, solving for [tex]x[/tex], we have

[tex]\$12.50 + \$1.50x> \$3.50x\\\$1.50x - \$3.50x >-\$12.50\\(-1)(-2x)>(-12.50)(-1)\\2x<12.50\\x<\frac{12.50}{2}\\ x<6.25[/tex]

Which means that the minimum number of movies is 7, which is the next whole number after 6.

Answer:

68.7

Step-by-step explanation:

We need only estimate (approximate) the value of f(x) at x = 5:

f(x)=6.87(2.5)(x – 1)   →   f(5)=6.87(2.5)(5 – 1).

Note that 2.5(4) = 10, so now we have (exactly) f(5)=6.87(10), which, in turn, is

equal to 68.7.

Answer:

The answer is D, 30.4

Step-by-step explanation:

Because the two parallelograms are similar, the relationship between the sides of them are directly proportional.

So:

[tex]\frac{9}{8} =\frac{x}{27}[/tex]

Cross multiply

8x = 243

÷8 both sides

x = 30.375 ≈ 30.4

The answer is D, 30.4

ANSWER

D. 30.4

EXPLANATION

The two parallelograms are similar, therefore the corresponding sides must be in the same proportion:

[tex] \frac{x}{9} = \frac{27}{8} [/tex]

Multiply both sides of the equation by 8. This implies that,

[tex]x = \frac{27}{8} \times 9[/tex]

[tex]x = 30.375[/tex]

Rounding to the nearest tenth gives us:

[tex]x = 30.4 \: units[/tex]

18/25= 21/x

18x=525

525/18 = 29.16

29.4

Answer:

About 1 dollar.

Step-by-step explanation:

First we must establish the possible values that 96 cents can be rounded to.

We know that 96 cents is more than nothing, or 0. We also know that a dollar is 100 cents. This means 96 cents is in between 0 and 1 dollar. We just have to determine whether 96 is closer to 100 cents or 0 cents.

To do this find the difference between 96 and each value.

100-96 = 4

96-0 =96

The difference between 96 and 100 is smaller, so the values are closer and 96 should be rounded to a dollar.

Answer:

84.78

Step-by-step explanation:

Final answer:

To determine the cost of silver needed for a solid sphere with a radius of 1.5 cm, the volume is calculated first, and then multiplied by the cost per cubic centimeter of silver, resulting in a total cost of $84.78.

Explanation:

The problem requires calculating the cost of the silver needed to manufacture a solid sphere. To find the cost, we first need to calculate the volume of the sphere using the formula V = (4/3)πr³, where V is the volume and r is the radius. Then, we multiply the volume by the cost per cubic centimeter of silver to get the total cost.

Given the radius r = 1.5 cm and the cost of silver = $6.00/cm³, we can plug these values into the formula:

Therefore, the silver required to make one solid sphere would cost $84.78.

There is no solution to Kamal's equation because -24 ≠ 7

How to solve the problem

The equations are given as

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

ii. 3x-24=3x+7

iii. -24=7

We have to expand the first equation

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

this would produce the second equation

3 * x - 3 * 8 = 3x + 7

we have

ii. 3x-24=3x+7

from here we have to take like terms on put them on same side

3x - 3x = 7 + 24

0 = 31

or from 3x-24=3x+7

the 3x is eliminated

-24 = 7

But we know that -24 ≠ 7. Hence no solution.

Find the area of the shaded figure.

40192 mm²

the area of the circle inside

= phi × r × r

= 3,14 × 40 mm × 40 mm

= 314/100 × 40 mm × 40 mm

= 5024 mm²

large circle area

= phi × r × r

= 3,14 × 120 mm × 120 mm

= 314/100 × 120 mm × 120 mm

= 45216 mm²

broad shaded

= 45216 mm² - 5024 mm²

= 40192 mm²

The area of the shaded figure is 10053.08 [tex]mm^2[/tex].

To find the area of the shaded region, we can use the following steps:

Calculate the area of the larger circle.

Calculate the area of the smaller circle.

Subtract the area of the smaller circle from the area of the larger circle.

The area of a circle is calculated by multiplying the radius squared by pi. The radius of the larger circle is 60 mm, so the area of the larger circle is:

[tex]A_l[/tex] = [tex]\pi[/tex] * [tex](60 mm)^2[/tex]

= 11309.72 [tex]mm^2[/tex]

The radius of the smaller circle is 20 mm, so the area of the smaller circle is:

[tex]A_s[/tex] = [tex]\pi[/tex] * [tex](20 mm)^2[/tex]

= 1256.64 [tex]mm^2[/tex]

The area of the shaded figure is calculated by subtracting the area of the smaller circle from the area of the larger circle:

A = [tex]A_l[/tex] - [tex]A_s[/tex]

= 11309.72 [tex]mm^2[/tex] - 1256.64 [tex]mm^2[/tex]

= 10053.08 [tex]mm^2[/tex]

Therefore, the area of the shaded figure is 10053.08 [tex]mm^2[/tex].

To learn more about area here:

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Answer:

sin(81)

Step-by-step explanation:

Since the sine of something is the ratio of the opposite side to the hypotenuse, to get the same ratio in cosine, you take the complement of the angle. So the answer is sin(90 - 9) or sin(81).

The expression in terms of cosine cos 81°. The expression is obtained by the trigonometric rules.

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

The given expression is;

sin9°

The expression in terms of cosine.

sin 9°= sin(90-81°)

sin 9°= cos 81°

Hence,the expression in terms of cosine cos 81°.

To learn more about the trigonometry, refer to the link;

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Answer:

The answer is actually C. here's proof:

It also makes sense since 2.5 is very unlikely, so the change is significant.

Answer: $40.80

Explanation: 60*.68=40.8

Answer:

Sale price = $40.80

Step-by-step explanation:

The original price = $60

After mark down of 32% is applied,

The selling price becomes 100% - 32% = 68%

The selling price = 68% of $60 = [tex]\frac{68}{100}[/tex] × $60 = $40.80

Answer:

∠A ≅ ∠A'  and CB ~ C'B'

Step-by-step explanation:

In a dilation, you get a SIMILAR figure. It will have the same shape, but a different size.

Similar figures have the same angle measures but the side lengths will change.

Any of the answers with congruent (≅) angles are correct:

∠A ≅ ∠A'

Any of the answers with SIMILAR (~) side lengths are correct:

CB ~ C'B'

Answer:

∠A ≅ ∠A'  and CB ~ C'B'

Step-by-step explanation:

let's firstly convert the mixed fractions to improper fractions and proceed from there.

[tex]\bf \stackrel{mixed}{8\frac{2}{3}}\implies \cfrac{8\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{26}{3}}~\hfill \stackrel{mixed}{7\frac{x}{3}}\implies \cfrac{7\cdot 3+x}{3}\implies \stackrel{improper}{\cfrac{21+x}{3}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \cfrac{26}{3}=\cfrac{21+x}{3}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3\left( \cfrac{26}{3} \right)=3\left( \cfrac{21+x}{3} \right)}\implies 26=21+x\implies \boxed{5=x} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 8\frac{2}{3}=7\frac{5}{3}~\hfill[/tex]

7 5/3 if that’s what your asking

8 2/3 is equal to 7 5/3

I believe the Surface Area is 37 inches^2 and the Volume is 15 inches^2

Answer:1.) 6/52

Step-by-step explanation:

The answer provides step-by-step solutions to a set of 10 different probability questions based on a standard deck of 52 playing cards. Each solution follows the same basic principle of dividing the number of ways the desired outcome can occur by the number of total possible outcomes.

The probability calculations, based on a 52-card deck, are as follows:

Remember that probabilities are calculated as the desired outcome divided by the total possible outcomes.

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Answer:

10 ounces of water

Step-by-step explanation:

16=8/5

z=1

16*1=16

8/5*z=8/5z

16=8/5z

16/1.6z=10

z = 10

Answer:

10 ounces of water

Step-by-step explanation: