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2 years ago

8

Darnell's car used 8 gallons of gasoline to travel 340 miles. After a mechanic worked on the car , it used 7 gallons of gasoline

to travel 350 miles. If the price of gasoline was approximately $4.00 per gallon , how much less to the nearest cent per mile , did it cost to run the car after the mechanic worked on it ?

1 answer:

NeTakaya2 years ago

5 0

After the mechanic it cost $1.88 cheaper to run the car

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( 2/3 x+2− 1/6 x+4)∙ 1/5 ÷ 1/5

UNO [17]

(2/3x + 2 - 1/6x + 4) • 1/5 ÷ 1/5
(1/2x + 6) • 1
1/2x + 6

5 0

2 years ago

Read 2 more answers

For questions 1 - 2, use the distributive property to find the product of the binomials.

igor_vitrenko [27]

Answer:

1). 2x^2-3x+20

2). 4x^2-14x+6

Step-by-step explanation:

1. (x-4)(2x+5)

FOIL:

(x)(2x)+5(x)-8(x)+(4)(5)

2x^2+5x-8x+20

=2x^2-3x+20

2. (4x-2)(x-3)

FOIL:

(4x)(x)-(3)(4x)-2(x)-2(-3)

4x^2-12x-2x+6

=4x^2-14x+6

5 0

2 years ago

Two collinear points on a line are given in the table below:

katrin [286]

Answer:

$(4,3)$ and $(7,2)$ do not lie on the line

Step-by-step explanation:

Given

$(0,0)\ and\ (2,1)$

Required

Determine which points that are not on the line

First, we need to determine the slope (m) of the line:

$m = \frac{y_2 - y_1}{x_2- x_1}$

Where

$(x_1,y_1) = (0,0)$

$(x_2,y_2) = (2,1)$

So;

$m = \frac{y_2 - y_1}{x_2- x_1}$

$m = \frac{1 - 0}{2-0}$

$m = \frac{1}{2}$

Next, we determine the line equation using:

$y - y_1 = m(x -x_1)$

Where

$m = \frac{1}{2}$

$(x_1,y_1) = (0,0)$

$y - y_1 = m(x -x_1)$ becomes

$y - 0 = \frac{1}{2}(x - 0)$

$y = \frac{1}{2}x$

To determine which point is on the line, we simply plug in the values of x to in the equation check.

For $(4,2)$

$x = 4$ and $y =2$

Substitute 4 for x and 2 for y in $y = \frac{1}{2}x$

$2 = \frac{1}{2} * 4$

$2 = \frac{4}{2}$

$2=2$

<em>This point is on the graph</em>

<em></em>

For $(4,3)$

$x = 4$ and $y = 3$

Substitute 4 for x and 3 for y in $y = \frac{1}{2}x$

$3 = \frac{1}{2} * 4$

$3 = \frac{4}{2}$

$3 \neq 2$

<em>This point is not on the graph</em>

<em></em>

For $(7,2)$

$x = 7$ and $y = 2$

Substitute 7 for x and 2 for y in $y = \frac{1}{2}x$

$2 = \frac{1}{2} * 7$

$2 = \frac{7}{2}$

$2 \neq 3.5$

<em></em>

<em>This point is not on the graph</em>

<em></em>

<em></em> $(\frac{4}{8},\frac{2}{8})$ <em></em>

<em></em> $x = \frac{4}{8}$ and<em> </em> $y = \frac{2}{8}$ <em></em>

<em>Substitute </em> $\frac{4}{8}$ <em> for x and </em> $\frac{2}{8}$ <em> for y in </em> $y = \frac{1}{2}x$ <em></em>

<em></em> $\frac{2}{8} = \frac{1}{2} * \frac{4}{8}$ <em></em>

<em></em> $\frac{2}{8} = \frac{1 * 4}{8 * 2}$ <em></em>

<em></em> $\frac{2}{8} = \frac{4}{16}$ <em></em>

<em></em> $\frac{1}{4} = \frac{1}{4}$ <em></em>

<em></em>

<em>This point is on the graph</em>

3 0

2 years ago

The sum of the ages of Kristen and Ben is 32. Four years ago Kristen was twice as old as Ben. How old are they both now?

Elan Coil [88]

Let us say that:

K = age of Kristen

B = age of Ben

From the problem, we make the equations:

eqtn 1: K + B = 32

eqtn 2: (K – 4) = 2 (B – 4)

Simplifying eqtn 2:

K – 4 = 2 B – 8

K = 2 B – 4

Plugging in this to eqtn 2:

(2 B – 4) + B = 32

3 B – 4 = 32

3 B = 36

B = 12

From eqtn 2:

K = 2 B – 4 = 2 (12) – 4 = 20

So Kristen is 20 while Ben is 12.

5 0

3 years ago

Given ; 2(10-13x)+9x=-34x+60

rewona [7]

Try comparing your solution with the following:

Solution:

$2(10-13x)+9x=-34x+60\\(20-26x)+9x=-34x+60\\20-26x+9x=-34x+60\\20-17x=-34x+60\\20-60=-34x+17x\\-40=-17x\\x=\frac{40}{17}$

Answer:

$x=\frac{40}{17}$

Check:

$2[10-13(\frac{40}{17})]+9(\frac{40}{17})=-34(\frac{40}{17})+60\\-20=-20$

<em>Hope this was helpful.</em>

3 0

2 years ago