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Yuri [45]
3 years ago
7

ac%7B5%7D%7B4%7D" id="TexFormula1" title="\frac{1}{2}x +\frac{1}{4} = \frac{1}{3}x + \frac{5}{4}" alt="\frac{1}{2}x +\frac{1}{4} = \frac{1}{3}x + \frac{5}{4}" align="absmiddle" class="latex-formula">
Select the appropriate response
A)x=8
B)x=6
C)x = 10
D)x = 11
Mathematics
1 answer:
ycow [4]3 years ago
7 0

Answer:

B)x=6

Step-by-step explanation:

Given the equation \frac{1}{2}x+\frac{1}{4}=\frac{1}{3}x+\frac{5}{4}

-We first group the like terms on the same side of the equal side;

\frac{1}{2}x-\frac{1}{3}x=\frac{5}{4}-\frac{1}{4}\\\\\\\\\frac{1}{6}x=1

#Multiply both sides by 6 to remove denominator;

6\times \frac{1}{6}x=1\times6\\\\x=6

Hence, x=6

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Andres bought a pair of shoes for $80 and 1 shirt for $20. The sales tax is 5%. How much did Andres pay for all the items includ
Savatey [412]

Answer: $21

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6 0
3 years ago
Read 2 more answers
Which ordered pair is a solution to the system of equations?
iren2701 [21]

(- 2, - 3) is a solution to the given system of equations.

Answer: Option D

<u>Step-by-step explanation:</u>

Given equation are not presented in proper format. So, let assume the given system of are as below,

         2 x - y = -1

         2 x -4 y = 8

Now, subtract the second equation from the first, we get

          (2 x - y) -(2 x - 4 y) = -1 -8

          3 y = -9  

           y = -3 (obtained this when divide by 3)

Substituting y = - 3 into the first equation, we get

          2 x - (-3) = - 1

          2 x = - 1 + 3

          x = - 2 (obtained when divide by 2)

Now, the answer is (x, y) = (- 2, - 3)

3 0
4 years ago
The Boy Scouts self popcorn Ethan sold 9 small
NARA [144]

Answer:

The cost of 1 small bag of popcorn = $2.95

The cost of 1 large bag of popcorn   = $4.75

Step-by-step explanation:

Here, let us assume the cost of 1 small bag of popcorn = $ m

And,  the cost of 1 large bag of popcorn = $ n

So, the cost of 9 small bag = 9 x ( cost of 1 small bag)  = 9 x (m) = 9 m

and  the cost of 2 large bag = 2 x ( cost of 1 large bag)  = 2 x (n) = 2 n

Also, cost of 9 small + 2 large bag of popcorn sold by  Ethan for   $ 36.05 .

⇒ Total cost of 9 small + 2 large bag of popcorn =  9 m + 2 n

⇒ 9  m +  2 n =  $ 36.05  ..........  (1)

Also, the cost of 5 small bag = 5 x ( cost of 1 small bag)  = 5 m

and  the cost of 7 large bag = 7 x ( cost of 1 large bag)  = 7 n

Also, cost of 5 small + 7 large bag of popcorn sold by  Jack for   $ 48 .

⇒ Total cost of 5 small + 7 large bag of popcorn =  5 m + 7 n

⇒ 5 m +  7 n =  $ 48 ..........  (2)

Now, solving (1) and (2) for the values of m and n , we get

9  m +  2 n =   36.05

5 m +  7 n =  48

Multiply (1) with (-7) and (2) by 2 , add both equation we get:

-63 m - 14 n  + 10 m + 14 n =  -252.35 + 96

or, - 53 m = -156.35

or, m =   2.95

Now, put the value of m in (1), we get:  5 ( 2.95) + 7 n =  48

or, n =  33.25 /7 = 4.75

Hence the cost of 1 small bag of popcorn = $2.95

The cost of 1 large bag  = $4.75

6 0
3 years ago
Read 2 more answers
An office supply store sells 12 rolls of tape for $29.88. At that rate, which proportion could be used to solve for c, the cost
kobusy [5.1K]

Answer:

$89.64

Step-by-step explanation:

First, you want to find your unit rate.

To do that, simply just divide what you know (cost/amount):

29.88/12

= 2.49

This means that one role of tape costs $2.49.

Now that we know that, you can simply just solve for value "c":

c = 2.49(36)

c = 89.64

8 0
3 years ago
The topic is piecewise functions, can someone help? i’m a little confused :)
AleksAgata [21]

Given:

The piecewise function is:

f(x)=\begin{cases}x+5&x

To find:

The values of f(-4),f(-2),f(0),f(3).

Solution:

For x, the function is

f(x)=x+5

For x\geq -2, the function is

f(x)=x^2+2x+3

a) The value of f(-4) is:

f(-4)=-4+5

f(-4)=1

b) The value of f(-2) is:

f(-2)=(-2)^2+2(-2)+3

f(-2)=4-4+3

f(-2)=3

c) The value of f(0) is:

f(0)=(0)^2+2(0)+3

f(0)=0-0+3

f(0)=3

d) The value of f(3) is:

f(3)=(3)^2+2(3)+3

f(3)=9+6+3

f(3)=18

Therefore, the required values are f(-4)=1,f(-2)=3,f(0)=3,f(3)=18.

8 0
3 years ago
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