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3 years ago

8(2x – 14) + 13 = 4x – 27

1 answer:

3 0

8 (2x - 14) + 13 = 4x -27

distribute 8 through the parentheses

16x - 112 + 13 = 4x - 27

combine like terms

16x - 99 = 4x -27

subtract 4x from each side

12x - 99 = -27

add 99 to each side

12x = 72

divide each side by 12

x = 6

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4) The quantities x and y are in proportion x 4 30 8 __b__ a) b) c) y 6 45 __a__ 15 Find the value of a and b. Find the constant

Ivan

Question:

The quantities x and y are in proportion

x y

4 6

30 45

8 b

a 15

(a) Find the values of a and b.

(b) Find the constant of variation. Is it direct variation or inverse variation?

Answer:

$a = 10$ and $b = 12$

Constant of variation is 1.5

Direct Variation

Step-by-step explanation:

Solving (a): The values of a and b

First, we determine the equation that relates x and y

From the table, we have:

$(x_1,y_1) = (4,6)$

$(x_2,y_2) = (30,45)$

The slope (m) is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{45 - 6}{30 -4}$

$m = \frac{39}{26}$

$m = 1.5$

The equation is then calculated using:

$y - y_1 = m(x - x_1)$

This gives:

$y - 6 = 1.5(x - 4)$

$y - 6 = 1.5x - 6$

$y = 1.5x$

Solving for the value of b

From the table: x = 8, y = b

Substitute these values in $y = 1.5x$

$b = 1.5 * 8$

$b = 12$

Solving for the value of a

From the table: x = a, y = 15

Substitute these values in $y = 1.5x$

$15 = 1.5 * a$

Solve for a

$a = \frac{15}{1.5}$

$a = 10$

Solving (b): The constant of variation.

This has been solved in (a) above as:

$m = 1.5$

Direct or Inverse?

From the given table, we notice that y increases as x increases and y decreases as x decreases.

This shows direct variation

3 0

2 years ago

If 25% of all students in the 7th grade have pets, and there are 40 students with pets, how many total students are there in the

VashaNatasha [74]

Answer:

there would be 160 as if 25% of the student body is 40 then you would multiply it by 4 to get to 100% of the student body thus giving you 160.

Step-by-step explanation:

4 0

3 years ago

The length of a rectangle is 5 cm longer than its width.

blondinia [14]

Equation To write :2 {x+ ( x+5) }=30

Let's solve your equation step-by-step.

2(x+x+5)=30

Step 1: Simplify both sides of the equation.

2(x+x+5)=30

(2)(x)+(2)(x)+(2)(5)=30(Distribute)

2x+2x+10=30

(2x+2x)+(10)=30(Combine Like Terms)

4x+10=30

Step 2: Subtract 10 from both sides.

4x+10−10=30−10

4x=20

Step 3: Divide both sides by 4.

x=5

So... x+5=10.

Area =5x10=50 cm squared.

4 0

3 years ago

Read 2 more answers

Write each decimal as a fraction or mixed number in simplest form. 1 3/8

Mnenie [13.5K]

3/2

Step One: 1 3/8, transform the number into a improper fraction:

To have a mixed number in to a improper fraction, you need to use addition and multiplication. For 1 3/8, We first multiply the denominator (8, also know to be the bottom number of the fraction) to the whole number (1). 8x1= 8
NOTE: The original denominator (8) will be use for are improper, again playing as the denominator, we only multiply the denominator for the numerator (which is the top number of a fraction).
After multiplying, we'll add are product with the numerator (3) for the process. 8+3= 12
Now we have both numerator and denominator for 1 3/8, we can create the improper fraction. 12 as the numerator and 8 as the denominator. 12/8
We still need to simplify the number. To that, we need the biggest whole number, or rather I call it the lowest number, that can be divide both in 12 and 8.
4 can be divide by both number so: 12/4= 3 and 8/4=2
Now 3 is are simplify numerator and 2 is are simplify denominator.