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3 years ago

14

5) Consider the sequence of steps to solve the equation: 2(x − 4) + 5x = 9x − 10 Given ⇒ 2(x − 4) + 6x = 9x − 10 Step 1 ⇒ 2x − 8

+ 6x = 9x − 10 Step 2 ⇒ 2x + 6x − 8 = 9x − 10 Step 3 ⇒ 8x − 8 = 9x − 10 Step 4 ⇒ 8x − 8x − 8 = 9x − 8x − 10 Step 5 ⇒ 0 − 8 = x − 10 Step 6 ⇒ −8 = x − 10 Step 7 ⇒ −8 + 10 = x − 10 + 10 Step 8 ⇒ 2 = x + 0 Step 9 ⇒ 2 = x Which step in solving this equation is justified by the Addition Property of Equality?

2 answers:

sasho [114]3 years ago

8 0

Answer: Step 7 is the answer.

vlada-n [284]3 years ago

5 0

<span>The answer to this question is Step 7.
Step 7 ⇒ −8 + 10 = x − 10 + 10
This is where 10 is being added to both sides. It is not Step 4 as that uses the Subtraction Property of Equality (which can be proved true by taking the addition of a negative number).
</span>

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If there are approximately 1.8 million cars in Vancouver and if each car travels an average of 17,500 kilometres in a year, how

Goryan [66]

Rates are used to measure a quantity over another.

<em>The 1.8 million cars use </em> $1.85 \times 10^{10}$ <em> liters each year</em>

Given

$Cars = 1.8\ million$

$d = 17500km$ --- distance

$r = 40miles/gallon$

First, we calculate the number (n) of gallons used by each car

$r = \frac{d}{n}$

Solve for n

$n = \frac{d}{r}$

So, we have:

$n = \frac{17500km}{40miles/gallon}$

$n = \frac{17500km}{40miles}gallon$

Convert miles to kilometers

$n = \frac{17500km}{40km \times 1.60934}gallon$

$n = \frac{17500km}{64.3738km}gallon$

$n = 271.85\ gallon$

The number of gallons (N), used by all the cars is:

$N = n \times cars$

$N = 271.85 \times 1.8\ million$

$N = 489330000$

Convert to liters

$N = 489330000 \times 3.78541L$

$N = 1852314675.3L$

In scientific notation to 2 decimal places, we have:

$N = 1.85 \times 10^{10}L$

<em>Hence, the number of liters used is </em> $1.85 \times 10^{10}$ <em />

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3 years ago

How would I solve this?

lutik1710 [3]

Answer:

It is rotated by 72 degrees.

Step-by-step explanation:

Since it is a regular polygon,

when u connect all the corners of it to the middle of the polygon, they will meet at a point i.e, CENTER.

The sum of the angles subtended by all the sided at the center will be 360 degrees.

As there are 60 sides, the angle subtended by each side at the center will be 6 degrees.

Because,

$\frac{360}{60} = 6$

As the polygon rotates every minute and it is rotated for 12 minutes,

$12*6 = 72$

( For every minute, it will be rotated by 6 degrees.

so, for 12 minutes it should be rotated by 12 times 6 ( 12*6) = 72 degrees)

So, after 12 minutes it will be rotated by 72 degrees.

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3 years ago

Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.

Oduvanchick [21]

Answer:

go up 1 from 9x and left 2

Step-by-step explanation:

-1/2 is the slope of the line

up means pos

right means pos

down means neg

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3 years ago

Solve the following system of equations. What is one x-value of a solution? f(x)=x^(2)+7x-24 g(x)=-3x-40

Yuki888 [10]

One x- value of the solution is : -2 or -8

<h3>What is an equation?</h3>

An Equation is an algebraic statement that shows that two quantities are equal.

Analysis:

for one x-value of a solution, f(x) = g(x)

$x^{2}$ + 7x -24 = -3x - 40

$x^{2}$ +7x +3x -24 +40 = 0

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x(x+8) +2(x+8) = 0

(x+2)(x+8) = 0

x = -2 or -8

In conclusion, the values of x are -2 or -8

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2 years ago

How long does a car traveling at 70 mph take to travel 88 miles, in hours

dybincka [34]

So,

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The time it will take for the car to go another 18 miles will be 18 divided by 70.
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Simplify.
$\frac{2*3*3}{2*5*7}$
$\frac{3*3}{5*7}$
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Divide.
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So a car traveling at 70 mph will take approximately 1.25714 hours or 1.26 hours to travel 88 miles.

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3 years ago