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n200080 [17]
2 years ago
12

Part A: Solve the equation 5(x + 2) = 6x + 3x − 14, and show your work. (5 points)

Mathematics
1 answer:
Cerrena [4.2K]2 years ago
8 0

Answer:

x = 6

Step-by-step explanation:

Step 1 - Expand brackets via distributive property:

5(x + 2) = 6x + 3x - 14\\5(x) + 5(2) = 6x + 3x - 14\\5x + 10 = 6x + 3x - 14

Step 2 - Combine like terms:

5x + 10 = 6x + 3x - 14\\5x + 10 = 9x - 14

Step 3 - Use the addition property of equality to isolate the 9x:

5x + 10 = 9x - 14\\5x + 10 + 14 = 9x - 14 + 14\\5x + 24 = 9x

Step 4 - Use the subtraction property of equality to move the 5x over and isolate the 24:

5x + 24 = 9x\\5x + 24 - 5x = 9x - 5x\\24 = 4x

Step 5 - Use the division property of equality to simplify:

4x = 24\\\\\frac{4x}{4} = \frac{24}{4}\\\\x = 6

Hope this helps!

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a grocer stacks apples in a pyramid-like stack whose rectangular base is 7 apples by 5 apples. each apple above the first level
g100num [7]

The arrangement of the apples in the stack is in a sequence that can be

used to find the number of apples in each row and in the stack.

Correct response:

  • The number of apples in the stack are <u>85 apples</u>

<h3>How to find the sum of a sequence</h3>

The given parameters are;

Dimensions of apples in the rectangular base = 7 apples by 5 apples

Number of apples on which each apple above rests = 4 apples

Required:

The number of apples in the stack.

Solution:

The dimensions, length and width of the apples in each row decreases

by 1 compared to the row on which the apple rests, as follows;

In the base, the dimension = 7 by 5

In the row directly above, the dimension = (7 - 1) by (5 - 1)

The number of apples sequence continues and is completed by a singles row of apples at the top, from which gives;

Number of apples in the stack = 7 × 5 + 6 × 4 + 5 × 3 + 4 × 2 + 3 × 1 = 85

  • The number of apples in the tack = <u>85 apples</u>

Learn more about sequence and series here:

brainly.com/question/13043887

4 0
2 years ago
Paul's car will go 49 kilometers on 7 tanks. Paul wants to know how fuel efficient the car is. Please help by computing the rati
alisha [4.7K]

Answer:

7 : 1

Step-by-step explanation:

Paul's car goes 40 kilometers on 7 tanks.

Distance    :     Tanks

     49        :         7

Fuel efficiency means the distance traveled by the car in one tank.

Therefore, we will reduce the ratio by dividing both sides by 7.

Distance    :     Tanks

    \frac{49}{7}           :         \frac{7}{7}

    7            :         1

Therefore, car's fuel efficiency is 7 kilometers in one tank or the ratio between Distance traveled and fuel tanks is 7 : 1.  

8 0
3 years ago
ANSWER PLSSS!! Brian puts $2000 in the bank. He leaves it there for 2 years. The bank uses an interest rate of 4%. How much mone
irinina [24]

Answer:

the answer is $1920

Step-by-step explanation:

4% of $2000 is $80 so if they take 4% its just $2000 - $80 = $1920

Hope this helped! <3

3 0
3 years ago
In the fraction 35/10 what is the product that lies between
RUDIKE [14]
The result of the fraction is 3.5

we can calculate this like this:
\frac{35}{10} = \frac{5*7}{2*5} = \frac{7}{5}=3.5

I think that the question is asking between which two natural numbers the result lies, and the result is 3 and 4: it's bigger than 3 and smaller than 4

 
8 0
3 years ago
A direct relationship occurs when
amid [387]
A direct relationship requires a change in the same direction of both variables, answer c.
4 0
3 years ago
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