What is the equation of the line that passes through point (4, 12) and has a y-intercept of —2?

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]

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: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:

the answer would be y=2x+4

Step-by-step explanation:

Answer:

<CDH = 110°

Step-by-step explanation:

Given <1 = 70°

Because BF ║ CD so <1 = <3 = 70° (corresponding angles are equal)

<CDH = 180° - <3

<CDH = 180° - 70°

<CDH = 110°

Answer:

125

Step-by-step explanation:

We are given that <1=70. Using that, we know that <5 also equals 70 because of the definition of vertical angles, we then can find <2 also by subtracting 70 from 180 and dividing it by 2 to get 55. <4=<2 and <6=<5, so using substitution we can get m<CDH=125

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

ANSWER

7.8cm

EXPLANATION

Given an acute angle of the right triangle to be 40°, the two sides of the triangles involve are the opposite side and the hypotenuse.

The trigonometric ratio that, involves opposite side and the hypotenuse is the sine ratio.

[tex] \sin(40 \degree) = \frac{opposite}{hypotenuse} [/tex]

[tex] \sin(40 \degree) = \frac{5}{hypotenuse} [/tex]

hypotenuse =5÷sin(40°)

hypotenuse=7.77cm

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: 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]

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.

Angles:

A=76 degrees

C=90 degrees

B=180-(90+76)=180-166

=14 degrees

Answer:

It’s c (B=14,b=3.2,c=13.4)

Step-by-step explanation:

edge

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.

Answer:

C

Step-by-step explanation:

Answer:

200.96 ft²

Step-by-step explanation:

The question is on surface area of a closed cylinder

Formulae= SA=2 ×pi× r² + 2×pi×r×h

Where pi=3.14

SA= 2×3.14×2² + 2×3.14×2×14

SA=25.12+175.84

SA=200.96 ft²

18/25= 21/x

18x=525

525/18 = 29.16

29.4

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.

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.

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:

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

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:

V=94.5 cm^3

Explanation:

Volume of a Prism: (B)H

B=Base Formula

H=Height of Prism

H=12

Triangle Base Formula: 1/2bh

b=3.5

h=4.5

Substitute Variables in formula:

V=[1/2(3.5)(4.5)](12)

Solve:

V=(7.875)(12)

V=94.5 cm^3

Answer:

Pretty sure it's 140.87 cm

Step-by-step explanation:

Multiply 3 1/2 by 4 1/4

Divide by two which is 7.43

Multiply 3 1/2 by 12

Now add 42+42+42+7.43+7.43

OR

126+14.87  

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

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:

System #2:

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

Answer:

x= 8/3 and x= -8/3

Step-by-step explanation:

Remember the difference of two squares method

a²- b²= (a+b) (a-b)

Given;

9x²-64=0

We notice 9 and 64 are in square form thus can be written as

(3x-8) (3x+8)....................................applying the difference in squares method to simplify

Solving for x

(3x-8) (3x+8) =0

3x-8=0

3x=8

x= 8/3

or

3x+8=0

x= -8/3

Answer:

8/3 and -8/3

Step-by-step explanation:

Answer:

123

Step-by-step explanation:

In a parallelogram, both pairs of opposite angles are congruent. Also, both pairs of opposite sides are parallel, meaning there are consecutive interior angles. Consecutive interior angles equal 180, so simply subtract 57 from 180 to find your missing angles.

Answer:

The perimeter of the equilateral triangle, P = 24 units

Step-by-step explanation:

All sides of an equilateral triangle are equal. The height of the equilateral triangle is given by :

[tex]h=\dfrac{\sqrt{3} }{2}\times a[/tex]

a is the side of triangle

If the height of an equilateral triangle is, [tex]h=4\sqrt{3}[/tex]

Equation (1) becomes,

[tex]a=\dfrac{2h}{\sqrt{3} }[/tex]

Put h in above formula. So,

[tex]a=\dfrac{2\times 4\sqrt{3}}{\sqrt{3} }[/tex]

a = 8

So, the side of triangle is 8. The sum of all sides is called perimeter of any figure. So,

[tex]P=8\times 3[/tex]

P = 24 units

So, the perimeter of the equilateral triangle is 24 units. Hence, this is the required solution.

Final answer:

To find the perimeter of the equilateral triangle with a height of 4√3, we determine the side length using the relationship between the height and side length of the triangle, and then multiply by three to get a perimeter of 24 units.

Explanation:

The height of an equilateral triangle is given as 4√3. To find the perimeter, we need to determine the length of a side of the triangle. In an equilateral triangle, the height (h) creates a right-angled triangle where the height is opposite to a 60° angle, and the half of a side of the triangle (half-base) is adjacent to it. The relationship is given by the equation h = (a√3)/2, where a is the side length of the equilateral triangle. By substituting the height with 4√3, we get:

4√3 = (a√3)/2 → a = 8

Since all sides of an equilateral triangle are equal, the perimeter is three times the side length, which means the perimeter P = 3 × 8 = 24 units.

Answer:

x+1, y-9

Step-by-step explanation:

Answer:

(x, y) ----> (x +1, y - 9)

Step-by-step explanation:

A square on a coordinate plane is translated 9 units down and 1 unit to the right.

Let's (x, y) is coordinate plane.

Here x represents the horizontal move and y represents the vertical move.

It is translated 9 units down and 1 unit right.

(x, y) ----> (x +1, y - 9)

Translation (x, y )---> (x+1, y-9)

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]