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scoundrel [369]
2 years ago
6

Maya is solving the equation 2(1+7x)=72. She lists an explanation for each step as shown. Which is the missing explanation for M

aya's first step after writing the given equation?
Mathematics
1 answer:
Alborosie2 years ago
4 0

Answer:

x = 5

Step-by-step explanation:

The given equation is :

2(1+7x)=72

Use the distributive property to the LHS.

2(1)+2(7x) = 72

2+14x = 72

Subtract 2 from both sides.

2+14x-2 = 72-2

14x = 70

x = 70/14

x = 5

So, the answer of the given equation is x = 5.

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Solve the system by substitution.<br> y = -4x<br> 23 - 5y = 44
spin [16.1K]
<h3><u>Explanation</u></h3>
  • Given the system of equations.

\begin{cases} y =  - 4x \\ 23 - 5y = 44 \end{cases}

  • Substitute y = -4x in the second equation.

23 - 5( - 4x) = 44 \\ 23 + 20x = 44 \\ 20x = 44 - 23 \\ 20x = 21 \\ x =  \frac{21}{20}

  • Substitute the value of x in any given equations. I will substitute the value of x in the first equation.

y =  - 4x \Longrightarrow y =  - 4( \frac{21}{20} ) \\ y =   \cancel{ - 4}( \frac{21}{ \cancel{20}} ) \Longrightarrow y =  -  \frac{21}{5}  \\ y =  -  \frac{21}{5}

  • Answer Check by substituting both values in two equations.

<u>First</u><u> </u><u>Equation</u>

y =  - 4x \Longrightarrow  -  \frac{21}{5}  =  - 4( \frac{21}{20} ) \\  -  \frac{21}{5}  =   \cancel{ - 4}( \frac{21}{ \cancel{20}} ) \\  -  \frac{21}{5}  =  -  \frac{21}{5}  \:  \:   \: \checkmark

<u>Second</u><u> </u><u>Equation</u>

23 - 5y = 44 \\ 23 - 5( -  \frac{21}{5} ) = 44 \\23 -  \cancel{5}( -  \frac{21}{ \cancel{5}} ) = 44 \\ 23 + 21 = 44 \\ 44 = 44 \:  \:  \:  \:  \checkmark

Both equations are true for the value of x and value of y.

<h3><u>Answer</u></h3>

<u>\begin{cases} x =  \frac{21}{20}  \\ y =  -  \frac{21}{5}  \end{cases}</u>

<u>Coordinate</u><u> </u><u>Point</u><u> </u><u>form</u>

<u>( \frac{21}{20} , -  \frac{21}{5} )</u>

5 0
2 years ago
Can someone plz help me
ANEK [815]

Answer:

D)

Step-by-step explanation:

8 0
2 years ago
A student finished 8 of her homework problems in class. If the ratio of problems she finished to problems she still had left was
nirvana33 [79]

Answer:

10

Step-by-step explanation:

8/4*5=10

5 0
2 years ago
Find the LCM of the numbers 12, 17 using the prime factorization
Makovka662 [10]

LCM of 12 and 17 = 204

Hope this helps!

3 0
3 years ago
Dream borrowed $500 at an interest rate of 8%. At the end of the loan period, she had to pay back $530. How long was the loan fo
Aliun [14]

Answer:

The loan was for 9 months only

Step-by-step explanation:

In this question, we are concerned with calculating the time taken for a loan om an interest to be paid back

To calculate this, we use the simple interest formula

Mathematically;

I = PRT/100

where P is the principal which is the amount borrowed and that is $500 according to the question

R is the rate which is 8% according to the question

Interest can be calculated by subtracting the principal from the  amount paid back = 530-500 = 30$

We now plug these values into the equation

30 = (500 × 8× T)/100

100 × 30 = 4000T

T = 3000/4000

T = 0.75 (same as 0.75 × 12 months = 9 months)

5 0
2 years ago
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