8TH GRADE MATH ¯\_(ツ)_/¯

What is the fractional equivalent of the repeating decimal n = 0.1515.... ?

Answer the questions to find out.

1. How many repeating digits does the number represented by n have?

2. You need to multiply n by a power of 10 to help you find the fraction. Decide on the power of 10 to multiply by, and tell how you identified that number.

3. Write an equation where the left side is your power of 10 time n and the right side is the result of multiplying 0.1515... by that power.

4. Write the original equation, n = 0.1515... underneath your equation from question 3. Then subtract the equations. Show your work!

5. Write n as a fraction in simplest form. Show your work!​

Answer:

Apply the distributive property.

4

x

+

4

⋅

−

3

−

2

(

x

−

1

)

>

0

Multiply

4

by

−

3

.

4

x

−

12

−

2

(

x

−

1

)

>

0

Apply the distributive property.

4

x

−

12

−

2

x

−

2

⋅

−

1

>

0

Multiply

−

2

by

−

1

.

4

x

−

12

−

2

x

+

2

>

0

Given:- 4(x - 3) - 2(x - 1) > 0.

Solving It:-

4(x - 3) - 2(x - 1) > 0

4x - 12 - 2x + 2 > 0

2x -10 > 0

2x > 10

x > 10/2

x > 5

Answer:

A=29.12ft^2

Step-by-step explanation:

first, find the area of the triangle and semicircle separately, then add them together to find the total area of the figure:

area of a triangle: 1/2bh

1/2(6)(8)=24ft^2

area of a circle: πr^2

(**we're using 3.14 instead of pi, and it's a semicircle)

1/2(3.14)(4)^2

1/2(3.14)(16)

1/2(50.24)

25.12ft^2

total area of the figure:

24+25.12=29.12ft^2

Answer: 49.12 ft²

Step-by-step explanation:

This figure is composed of

First, find the area of the half-circle.

The area of a full circle is π · r², but since it's only half a circle, we divide that by half, resulting in (π · r²)/2

Therefore, the area of the half-circle is:

(3.14 · 4²)/2 = (3.14 · 16)/2 = 50.24/2 = 25.12 ft²

Second, find the area of the right triangle.

The area of a triangle = ½bh.

Therefore, the area of the triangle is:

½ · 6 · 8 = ½ · 48 = 24 ft²

Add the two areas together:

24 + 25.12 = 49.12 ft²

Answer:

-23/9  or -2 5/9

Step-by-step explanation:

w+(-x) - 2/3

Let w = -5/9  and x = 4/3

-5/9+(- 4/3) - 2/3

Get a common denominator of 9

-5/9 - 4/3 *3/3 - 2/3 *3/3

-5/9 - 12/9 - 6/9

-23/9

-2 5/9

Answer:

-2 5/9

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

The first five multiples of 5 are 5, 10, 15, 20, and 25. The sum of the first five multiples of 5 is 75.

Answer:

119?

Step-by-step explanation:

Answer:

Hello,

answer B

2

Step-by-step explanation:

[tex]\dfrac{2}{x} -\dfrac{x}{x+5} =\dfrac{10}{x^2+5x} \\\\we\ suppose\ x\neq 0\ and\ x\neq -5\\\\\text{Reducing to the same denominator}\\\dfrac{2(x+5)-x^2}{x(x+5)} =\dfrac{10}{x^2+5x} \\\\Simplify\ by\ x^2+5x\\\\2x+10-x^2=10\\\\-x^2+2x=0\\\\-x(x-2)=0\\\\roots\ are\ 2 \ and\ 0\ (to\ be\ excluded)\\\\Root=2\\[/tex]

Answer:

5

Step-by-step explanation:

The Fundamental theorem of Algebra states that a polynomial of degree n has n roots, some may be complex.

11[tex]x^{5}[/tex] + 5x - 3 = 0 ← is a polynomial of degree 5

Thus the equation will have 5 roots

Answer:

cannot be determined

Step-by-step explanation:

We do not know if any of the angles are equal and are only given two sides.

We cannot determine if the two triangles are similar

Answer: 1:3

Step-by-step explanation:

The odds are 2/6 because you’re given 2 choices from the 6 side die you can then simplify that fraction to 1:3

Answer:

second x -1,-3,-5 y 1 3 5 for proportional relation

Answer:

32 = <4

Step-by-step explanation:

The exterior angle of a  triangle is equal to the sum of the opposite interior angles

15+17 = <4

32 = <4

==================================================

Explanation:

The ratio of boys to girls is 3 to 5, which means,

b/g = 3/5

12/g = 3/5 ... plug in b = 12

12*5 = g*3 ... cross multiply

60 = 3g

3g = 60

g = 60/3 .... divide both sides by 3

g = 20 is the number of girls

b+g = 12+20 = 32 total students in the chess club.

Step-by-step explanation:

[tex]x + 3y = 7 \\ 2x + 4y = 8 \\ x = 7 - 3y \\ 2(7 - 3y) + 4y = 8 \\ 14 - 6y + 4y = 8 \\ 14 - 2y = 8 \\ - 2y = - 6 \\ y = 3 \\ x = 7 - 3(3) \\ x = 7 - 9 \\ x = - 2[/tex]

Answer:

2x+3y=7x4

x+4y=8x3

8x+12y=27

3x+12y=24

8x-3x =5x

+12y-+12y=0

27-24=3

5x/5 3/5x

answer = x = 3/5

y=1.85

Answer:

H^2 = P^2 + B^2

H^2 = ( 3 root 2 )^2 + ( 3 root 2)^2

H^2 = 18 + 18

H^2 = 36

H = 6

Hence , option A is correct

hope that helps ✌

The answer is

w + c ≤ 32

w < 11

w - the number of acres of wheat

c - the number of acres of corn

Johanna will plant up to 32 acres on her farm with wheat and corn:

w + c ≤ 32

Fewer than 11 acres will be planted with wheat:

w < 11

The two inequalities are:

w + c ≤ 32

w < 11

Answer:

5 up and 2 to the right

Step-by-step explanation:

The center will be at the same spot as circle D, dilate by 3, then the dilation maps circle C into circle D.

Answer:

61

Step-by-step explanation:

45/3 = 15

2*8 = 16

15+16-12+42 = 61

Answer:

15 + 16 + 30

and that is in total 61

Step-by-step explanation:

45/3 = 15

2×8 = 16

-12 + 42 = 30

you simplify an expression by calculating the part expressions, to be left only with the main terms and main operations.

Answer:

5 cm

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

let h be the hypotenuse , then

h² = 3² + 4² = 9 + 16 = 25 ( take the square root of both sides )

h = [tex]\sqrt{25}[/tex] = 5

9514 1404 393

Answer:

  5.7·10^-3

Step-by-step explanation:

The expanded scale shows point P lies 7/10 of the way between 5 and 6 times 10^-3. Its value is 5.7·10^-3.

Answer:

sqrt(24)

Step-by-step explanation:

The number is slightly less than 5

We know that 5^2 =25

sqrt(25) = 5

so the number has to be less that sqrt(25)

The only number less than sqrt(25) is sqrt(24) and sqrt(20)

sqrt(20) is too far away to be slightly less than 5 so it must be sqrt(24)

Answer:

d talking into microphone

Answer:

35.54

Step-by-step explanation:

use inverse tan

soh cah toa

we have both opposite and adjacent so we are using tangent

[tex]tan^{-1} (\frac{5}{7} )[/tex]

put that into a calculator and it would give you approximately 35.54 degrees

Answer:

i can help you i know this answer

Answer:

a polygon has 3 or more sides

Answer:

The Tasty Beans Coffee House being planned for the corner of SE 12th and Main will ruin a perfectly nice neighborhood. Besides the fact that Tasty Beans already has coffee shops all over the city, it will pull business away from local coffee houses that have been here for decades. In addition, there is already a parking problem on that street, and the new business will just add to the congestion. They're planning a drive-up window, too, and that will mean a steady stream of traffic in a very high-volume area. Ask anyone walking down the street, and they'll tell you this is a bad idea. I speak for my whole neighborhood when I say, "Go away, Tasty Beans!"

Step-by-step explanation:

Answer:

x=15

Step-by-step explanation:

The first triangle

90+2x+4x=180

90+6x=180

6x=90

x=15

Answer:

17 lb I guess 8 don't think the question is full

Step-by-step explanation:

the question is half

Answer:

[tex]\text{1) }\\\text{Circumference: }24\pi \text{ m}},\\\text{Length of bolded arc: }18\pi \text{ m}\\\\\text{3)}\\\text{Circumference. }4\pi \text{ mi},\\\text{Length of bolded arc: } \frac{3\pi}{2}\text{ mi}[/tex]

Step-by-step explanation:

The circumference of a circle with radius [tex]r[/tex] is given by [tex]C=2\pi r[/tex]. The length of an arc is makes up part of this circumference, and is directly proportion to the central angle of the arc. Since there are 360 degrees in a circle, the length of an arc with central angle [tex]\theta^{\circ}[/tex] is equal to [tex]2\pi r\cdot \frac{\theta}{360}[/tex].

Formulas at a glance:

Question 1:

The radius of the circle is 12 m. Therefore, the circumference is:

[tex]C=2\pi r,\\C=2(\pi)(12)=\boxed{24\pi\text{ m}}[/tex]

The measure of the central angle of the bolded arc is 270 degrees. Therefore, the measure of the bolded arc is equal to:

[tex]\ell_{arc}=24\pi \cdot \frac{270}{360},\\\\\ell_{arc}=24\pi \cdot \frac{3}{4},\\\\\ell_{arc}=\boxed{18\pi\text{ m}}[/tex]

Question 2:

In the circle shown, the radius is marked as 2 miles. Substituting [tex]r=2[/tex] into our circumference formula, we get:

[tex]C=2(\pi)(2),\\C=\boxed{4\pi\text{ mi}}[/tex]

The measure of the central angle of the bolded arc is 135 degrees. Its length must then be:

[tex]\ell_{arc}=4\pi \cdot \frac{135}{360},\\\ell_{arc}=1.5\pi=\boxed{\frac{3\pi}{2}\text{ mi}}[/tex]

Answer:

UV = 10

HG = 25

Step-by-step explanation:

UV = (11+9)/2 = 20/2 = 10

HG = (28+22)/2 = 50/2 = 25

Answer:

Below in bold.

Step-by-step explanation:

First problem:

The length of the mid segment is the mean of the 2 outer segments.

So it is (11+9)/2

= 20/2

= 10.

Second problem:

As above, it is (22+28) / 2

= 50/2

= 25.