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kumpel [21]
3 years ago
9

8(2x – 14) + 13 = 4x – 27

Mathematics
1 answer:
Juliette [100K]3 years ago
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
You might be interested in
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.

<em>This shows direct variation</em>

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

4x+10=30

Step 2: Subtract 10 from both sides.

4x+10−10=30−10

4x=20

Step 3: Divide both sides by 4.

4x

4

=

20

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.<br> 1 3/8
Mnenie [13.5K]

3/2

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

  1. 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
  2. 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).
  3. After multiplying, we'll add are product with the numerator (3) for the process. 8+3= 12
  4. 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
  5. 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.
  6. 4 can be divide by both number so: 12/4= 3 and 8/4=2
  7. Now 3 is are simplify numerator and 2 is are simplify denominator.

8 0
3 years ago
Can someone please help me??
dmitriy555 [2]

Answer:

I is clear that, the linear equation 5x+12=5x-7 has no solution.

Step-by-step explanation:

<u>Checking the first option:</u>

\frac{2}{3}\left(9x+6\right)=6x+4

6x+4=6x+4

\mathrm{Subtract\:}4\mathrm{\:from\:both\:sides}

6x+4-4=6x+4-4

6x=6x

\mathrm{Subtract\:}6x\mathrm{\:from\:both\:sides}

6x-6x=6x-6x

0=0

\mathrm{Both\:sides\:are\:equal}

\mathrm{True\:for\:all}\:x

<u>Checking the 2nd option:</u>

5x+12=5x-7

\mathrm{Subtract\:}5x\mathrm{\:from\:both\:sides}

5x+12-5x=5x-7-5x

\mathrm{Simplify}

12=-7

\mathrm{The\:sides\:are\:not\:equal}

\mathrm{No\:Solution}

<u>Checking the 3rd option:</u>

4x+7=3x+7

\mathrm{Subtract\:}7\mathrm{\:from\:both\:sides}

4x+7-7=3x+7-7

\mathrm{Simplify}

4x=3x

\mathrm{Subtract\:}3x\mathrm{\:from\:both\:sides}

4x-3x=3x-3x

\mathrm{Simplify}

x=0

<u>Checking the 4th option:</u>

-3\left(2x-5\right)=15-6x

\mathrm{Subtract\:}15\mathrm{\:from\:both\:sides}

-6x+15-15=15-6x-15

\mathrm{Simplify}\

-6x=-6x

\mathrm{Add\:}6x\mathrm{\:to\:both\:sides}

-6x+6x=-6x+6x

\mathrm{Simplify}

\mathrm{Both\:sides\:are\:equal}

\mathrm{True\:for\:all}\:x

Result:

Therefore, from the above calculations it is clear that, the linear equation

5x+12=5x-7 has no solution.

4 0
3 years ago
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