1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
zysi [14]
1 year ago
7

Solve the equation. Then check your solution.4- 3/5(3a+4)=7A. -7.4B. -6C. 3D. -3

Mathematics
1 answer:
Evgesh-ka [11]1 year ago
5 0
Answer: a = -3

Explanations:

The given equation is:

4\text{ - }\frac{3}{5}(3a+4)\text{ = 7}

This can be re-written as:

4-\frac{3(3a+4)}{5}=7

Collect like terms:

\begin{gathered} -\frac{3(3a+4)}{5}=\text{ 7 - 4} \\ -\frac{3(3a+4)}{5}=\text{ 3} \end{gathered}

Cross multiply:

\begin{gathered} -3(3a+4)\text{ = 3}\times5 \\ -3(3a+4)=\text{ 15} \\ \text{Expand the bracket} \\ -9a\text{ - 12 = 15} \\ \text{Collect like terms} \\ -9a\text{ = 15 + 12} \\ -9a\text{ = 27} \\ \text{Divide both sides by -9} \\ \frac{-9a}{-9}=\frac{27}{-9} \\ a\text{ = -3} \end{gathered}

To verify if the solution is correct, substitute a = -3 into the question given. If the Right Hand Side equals the Left Hand Side, then the solution is correct.

\begin{gathered} 4-\frac{3(3a+4)}{5}=\text{ 7} \\ \text{Substitute a = }-3 \\ 4\text{ - }\frac{3(3(-3)+4)}{5}\text{ = 7} \\ 4\text{ - }\frac{3(-9+4)}{5}\text{ = 7} \\ 4\text{ - }\frac{3(-5)}{5}\text{ = 7} \\ 4\text{ - }\frac{-15}{5}=\text{ 7} \\ 4-(-3)=7 \\ 4+3=7 \\ 7=7 \end{gathered}

Since the Left Hand Side = Right Hand Side = 7, the solution a = -3 is correct

You might be interested in
Help me solve these please
Burka [1]
<span>______________________________________________________</span>
7y-1=-1+9(y-9)

Add 1 on both sides.
7y=9(y-9)
Distribute.
7y=9y-81
Subtract 7y and add 81 on both sides.
2y=81
y=40.5
______________________________________________________

<span>4c+3=-12+c-1
</span>Subtract 3 on both sides.
4c=-12-1-3+c
Subtract c on both sides.
3c=-16
c=-16/3
______________________________________________________
<span>-(k+1)-10=-5k+3
</span>Add 10 on both sides.
-(k+1)=-5k+13
Distribute.
-k-1=-5k+13
Add 1 and add 5k on both sides.
4k=14
k=4/14
______________________________________________________
-w-10=-9-2(w-8)
Distribute.
-w-10=-9-2w+16
Simplify.
-w-10=-2w+7
Add 2w and 10 on both sides.
w=17
______________________________________________________
-2(n-3)-5=-5n+1
Distribute.
-2n+6-5=-5n+1
Simplify.
-2n+1=-5n+1
Add 5n and subtract 1 on both sides.
3n=0
n=0
______________________________________________________

To make sure you got the right answer, you can check your work by plugging the result back into the question and seeing if both sides become equal. If both sides are equal, then the result is correct.
______________________________________________________
4 0
3 years ago
Johns family has $12 to spend after buying tickets to the Aquarium. Parking costs $3 an hour.
TEA [102]

Answer:

4 hours

Step-by-step explanation:

4 x 3 =12 or 12÷3 = 4

7 0
3 years ago
Enter the value of b when the expression 14.1x - b is equivalent 4.7(3x-3.5)?
3241004551 [841]

Answer:

I believe it is: B= 16.45

4 0
3 years ago
What are the coordinates of point f?<br> A) (7,5)<br> B) (7,-5)<br> C) (-5,7)<br> D) (5,-7)
aliina [53]
Ahh, point F.  I know where point F is.  Its right over there on the graph.

No, im kidding.

Please provide a graph
5 0
3 years ago
A new sample of 225 employed adults is chosen. Find the probability that less than 7.1% of the individuals in this sample hold m
arsen [322]

Answer:

The probability that less than 7.1% of the individuals in this sample hold multiple jobs is 0.0043.

Step-by-step explanation:

Let <em>X</em> = number of individuals in the United States who held multiple jobs.

The probability that an individual holds multiple jobs is, <em>p</em> = 0.13.

The sample of employed individuals selected is of size, <em>n</em> = 225.

An individual holding multiple jobs is independent of the others.

The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 225 and <em>p</em> = 0.13.

But since the sample size is too large Normal approximation to Binomial can be used to define the distribution of proportion <em>p</em>.

Conditions of Normal approximation to Binomial are:

  • np ≥ 10
  • n (1 - p) ≥ 10

Check the conditions as follows:

np=225\times 0.13=29.25>10\\n(1-p)=225\times (1-0.13)=195.75>10

The distribution of the proportion of individuals who hold multiple jobs is,

p\sim N(p, \frac{p(1-p)}{n})

Compute the probability that less than 7.1% of the individuals in this sample hold multiple jobs as follows:

P(p

*Use a <em>z</em>-table.

Thus, the probability that less than 7.1% of the individuals in this sample hold multiple jobs is 0.0043.

7 0
3 years ago
Other questions:
  • Peter is giving marbles to some children at a carnival. He has 5 red marbles, 4 blue marbles, and 3 yellow marbles. If Peter sel
    14·1 answer
  • At the 2012 London Olympics, Michael Phelps won the gold medal in the men's 100-meter butterfly.
    5·1 answer
  • In a recent study, researchers found that 31 out of 150 boys aged 7-13 were overweight or obese. On the basis of this study can
    11·1 answer
  • Out of 1200 people polled, 30% do not like radio, and 10% of the people who do not like radio also do not like music. How many p
    7·2 answers
  • Complete the statements about the graph.
    8·1 answer
  • 13 is one third of a number m
    6·1 answer
  • Please help!! I'm really confused
    9·2 answers
  • The capacity of a cylindrical water tank is 539 litres. If its height is 1.4 meter then find the radius of the base.​
    9·1 answer
  • A square has a perimeter of 12 yd. What is the length of each side?
    5·1 answer
  • f(x)=(x+3)(x-4) and g(x)=1/3(x+3)(x-4). the graphs of each are shown here. Which graph represents which polynomial function? exp
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!