Simplifying Fractions
 Simplify each fraction to its lowest terms.


1) 9 =
18

8) 4 =
16


15)

21 =
63



2) 8 =
10

9) 18 =
36

16)

30 =
84



6
3) =
8

6
10) =
42

50
17) =
125



4) 5 =
20

13
11) =
39

72
18) =
108



18
5) =
24

21
12) =
28

49
19) =
112



6
6) =
9

12
7) =
15


63
13) =
77

36
14) =
40





4

240
20) =
320

120
21) =
150

Answer:

x = 14 and y = 10

Step-by-step explanation:

TRANSLATING WORDS INTO EQUATIONS:

Let the two numbers be x and y  

"The sum of two numbers is 24" translate as x + y = 24  

"Their difference is 4" translates as x-y=4

Those two equations make up the system of linear equations

SOLVING BY ELIMINATION:

Adding the two equations, we get

x + y + x - y = 24 + 4

2x = 28

x = 28 / 2

x = 14

substituting that into x + y = 24 we get

14 + y = 24

y = 24 - 14

y = 10

hope it helps :)

Answer:

y = 5/3x - 4

Step-by-step explanation:

(6, 6)

m = 5/3

Slope-intercept:

y - y1 = m(x - x1)

y - 6 = 5/3(x - 6)

y - 6 = 5/3x - 10

y = 5/3x - 10 + 6

y = 5/3x - 4

Answer:

A 21/4

Step-by-step explanation:

When forming a perfect square trinomial you need to "complete the square".

All of the steps to completing the square when solving an equation:

1.  The leading coefficient must be 1.  

2.  Divide b by 2.

3.  Square (b/2)

4.  Add (b/2)^2 to both sides to keep the polynomial balanced.

5.  You can now write the perfect square trinomial and solve.

x^2 - 3x  

-3/2

(-3/2)^2 = 9/4 = 2 1/4

Answer: D

Step-by-step explanation:

5x + 4x = 180°

Angles on a straight line add to 180°

Answer:

if you rearrange to complete the square, you get (x^2-4)^2 +4

and seeing as anything squared will always be positive or zero, the lowest possible value for (x^2-4)^2 is 0, when x = 4

and 0 + 4 = 4, which is greater than 0, so positive

Step-by-step explanation:

We have x^2-8x+20 is always positive.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

x^2-8x+20

=x^2-2.x.4+16+4

if you rearrange to complete the square,

you get (x^2-4)^2 +4

and seeing as anything squared will always be positive or zero,

the lowest possible value for (x^2-4)^2 is 0, when x = 4

and 0 + 4 = 4, which is greater than 0,

so, positive.

To learn more on equation click:

brainly.com/question/24169758

#SPJ2

Answer:

13,564.8

Step-by-step explanation:

The ratio of the volumes of similar solids is the cube of the scale factor.

Scale factor:

red solid : blue solid = 12/10 = 6/5

Ratio of volumes:

volume red solid : volume blue solid = (6/5)^3

volume of red solid = 7850 ft^3 * (6/5)^3 = 13,564.8 ft^3

Answer: V = 13,564.8 ft^3

Answer:

(2,5)

Step-by-step explanation:

Answer: the answer is 6

Step-by-step explanation: You can use polynomial long division or synthetic division.

Answer:

x=0,x=1/4

Step-by-step explanation:

2x=8(x^2)

Subtract 8(x^2) from both sides

2x-8x^2=8x^2-8x^2

Simplify

2x-8x^2=0

Factor 2x-8x^2;

2x-8x^2

=-8xx+2x

Rewrite 8 as 2*4

=-2*4xx+2x

Factor out common term -2x

=-2x(4x-1)

-2x(4x-1)=0

x=0 or 4x-1=0

Solve 4x-1=0;x=1/4

4x-1=0

Add 1 to both sides

4x-1+1=0+1

Simplify

4x=1

Divide both sides by 4

4x/4=1/4

Simplify

x=1/4

The solutions to the quadratic equation are;

x=0,x=1/4

Hope this helped!!!!

Answer:

12

Step-by-step explanation:

A sequence is given and we need to find the term when it will become -24 . The given sequence is,

9 , 6 , 3 ,0 , . . . . .

Here Common Difference can be calculated by subtracting consecutive terms . So the Common Difference is 6-9 = -3 . Here the nth term is (-24) .Now using the formula to find nth term .

⇒ T_n = a + (n-1)d

⇒ (-24) = 9 + (n-1)(-3)

⇒ -24-9 = (n-1)(-3)

⇒ (n-1) = -33/-3

⇒ n-1 = 11

⇒ n = 11 + 1

⇒ n = 12

Answer:

r= 275

Step-by-step explanation:

Let's write an equation with the given information.

44= r% ×16

Rewrite the percentage as a fraction:

[tex]44 = \frac{r}{100} \times 16[/tex]

Divide both sides by 16:

[tex] \frac{r}{100} = 44 \div 16[/tex]

[tex] \frac{r}{100} = 2.75[/tex]

Multiply both sides by 100:

r= 2.75(100)

r= 275

1. Even

2. Odd

3. Even

4. Odd

5. Odd

6. Even

7. Odd

8. Odd

9. Even

10. Even

Answer:

B

Step-by-step explanation:

I hope this helps you :)

Answer:

thx for the points

Step-by-step explanation:

Answer:

2r

Step-by-step explanation:

You suppose that the radius of a larger circle = r

so diameter = r*2 = 2r

aint really sure tho

Answer:

2R

Step-by-step explanation:

The formula to find the diameter states the relationship between the diameter and the radius. The diameter is made up of two segments that are each a radius. Therefore, the formula is: Diameter = 2 * the measurement of the radius. You can abbreviate this formula as d=2r.

Answer:

12

Step-by-step explanation:

hello :

√24 ×√6 = √(24×6) =√144 = √12² = 12

Answer:

root 144 or 12

Step-by-step explanation:

24 by 6 is 144 so root 144 becomes 12

Step-by-step explanation:

According to the base of similarity, then

12÷6=8÷x

12x=48

=4

6+4=

10

Answer:

24 miles

Step-by-step explanation:

if J (Jeremy) ran 16 less than K(Kacie) and J ran 8 miles add 8 and 16 together which is 24 to get the answer.

hope this helped

Answer:

24 miles

Step-by-step explanation:

let what Kacie ran be x miles

x-16=8, 16 being the difference of what they ran, 8 being how many miles jeremey ran

that makes x=24 because 16+8=24

Answer:

2xm+3=34

Step-by-step explanation:

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Answer:

2,000 m (2 Liters) = 100 plants

Step-by-step explanation:

2,000 milliliters make up 2 liters.

200 liters are being poured.

2,000/200 = 10

10 plants are being watered each time.

200 m = 10 plants

400 m = 20 plants

600 m = 30 plants

800 m = 40 plants

1,000 m = 50 plants

1,200 m = 60 plants

1,400 m = 70 plants

1,600 m = 80 plants

1,800 m = 90 plants

2,000 m = 100 plants

Let me know if this helps!

Answer:

3.84 in³

Step-by-step explanation:

V=l*w*h

[tex]5.97*1.34*.48\\=3.839904[/tex]

≈3.84

Answer:3.84 in³

Step-by-step explanation:

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