A truck driver earns $51.20 driving an 80-mile route. The driver’s next route is 120 miles long and is billed at the same rate.
How much does the driver earn on this next route?

Using the relation between velocity, distance and time, it is found that:

Velocity is distance divided by time, that is:

[tex]v = \frac{d}{t}[/tex]

In opposite directions, the relative velocity is [tex]v = v_1 + v_2[/tex], and the 64 km are run in 4 hours, hence:

[tex]v_1 + v_2 = \frac{64}{4}[/tex]

[tex]v_1 + v_2 = 16[/tex]

[tex]v_1 = 16 - v_2[/tex]

In the same direction, the relative velocity is [tex]v = v_1 - v_2[/tex], and the 64 km are run in 16 hours, hence:

[tex]v_1 - v_2 = \frac{64}{16}[/tex]

[tex]v_1 - v_2 = 4[/tex]

Since [tex]v_1 = 16 - v_2[/tex]:

[tex]16 - v_2 - v_2 = 4[/tex]

2v2 = 12.

v2 = 6.

v1 = 16 - 6 = 10 km/h.

Hence:

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Answer:

McKinley, Logan, Pico de Orizaba

Step-by-step explanation:

Answer:

Male

Step-by-step explanation:

There are 28 males and 26 professors so you are more likely to choose a male rather than professor of any other gender!

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Since it's a Trapezoid with its non - parallel sides equal to one another,

[tex]\qquad \sf  \dashrightarrow \:\angle A + \angle P = 180[/tex]

[ By forming co - interior angle pair ]

[tex]\qquad \sf  \dashrightarrow \:\angle A +100 = 180[/tex]

[tex]\qquad \sf  \dashrightarrow \:\angle A = 180 - 100[/tex]

[tex]\qquad \sf  \dashrightarrow \:\angle A = 80 [/tex]

Now, similarly,

[tex]\qquad \sf  \dashrightarrow \:\angle A + \angle R = 180[/tex]

[tex]\qquad \sf  \dashrightarrow \: \angle R + 80 = 180[/tex]

[tex]\qquad \sf  \dashrightarrow \: \angle R = 100[/tex]

Similarly,

[tex]\qquad \sf  \dashrightarrow \angle K + \angle R = 180[/tex]

[tex]\qquad \sf  \dashrightarrow \angle K + 100 = 180[/tex]

[tex]\qquad \sf  \dashrightarrow \angle K = 80[/tex]

Consecutive angles are supplementary

Opposite angles are equal

Opposite angles are equal again

Answer:

A circle of radius = 10 or diameter = 20 or circumference = 62.83 inches has an area of: 2.02709 × 10 -7 square kilometers (km²) 0.202709 square meters (m²) 2027.09 square centimeters (cm²)

Step-by-step explanation:

The volume of 3 of shipping containers 267.75 cubic yards.

We need to find the volume of one shipping container and then multiply it by 3 to find the volume of three shipping containers.
Find the volume of one shipping container.
Volume = Base Area × Height
Volume = 25.5 square yards × 3.5 yards
Calculate the volume.
Volume = 89.25 cubic yards
Find the volume of three shipping containers.
Total Volume = Volume × Number of Containers
Total Volume = 89.25 cubic yards × 3
Calculate the total volume.
Total Volume = 267.75 cubic yards.

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Answer:

Step-by-step explanation:

Given equation,

⇒ 5x - 6 = 3x - 8

Subtracting 3x from both sides :

⇒ 5x – 6 – 3x = 3x – 8 – 3x

⇒ 2x – 6 = – 8

Adding 6 to both sides we get :

⇒ 2x – 6 + 6 = – 8 + 6

⇒ 2x = – 2

Dividing both sides by 2 we get :

⇒ 2x/2 = – 2/2

⇒ x = – 1

Therefore,

Answer:

[tex]\sf \boxed{\bold{x=-1}}[/tex]

Solving Stepwise:

[tex]\dashrightarrow \sf 5x-6=3x-8[/tex]

add 6 on both sides

[tex]\dashrightarrow \sf 5x-6+6=3x-8+6[/tex]

simplify

[tex]\dashrightarrow \sf 5x=3x-2[/tex]

subtract both sides by 3x

[tex]\dashrightarrow \sf 5x-3x=3x-2-3x[/tex]

simplify

[tex]\dashrightarrow \sf 2x=-2[/tex]

divide both sides by 2

[tex]\dashrightarrow \sf \dfrac{2x}{2} =\dfrac{-2}{2}[/tex]

simplify

[tex]\dashrightarrow \sf x =-1[/tex]

Check for the answer:

insert x = -1

[tex]\hookrightarrow \sf 5(-1)-6=3(-1)-8[/tex]

[tex]\hookrightarrow \sf -5-6=-3-8[/tex]

[tex]\hookrightarrow \sf -11=-11[/tex]

Answer:

B. 8.75

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Find Θ from the problem by using arcos. Find that Θ=64.158....

plug this into cos(Θ) and find that cos(Θ)= [tex]\frac{\sqrt{19} }{10}[/tex] or 0.43589. A is the only answer choice with this so it must be correct.

is there any answer choices

Answer:

Step-by-step explanation:

Answer A represents an exponential equation; see below for a demo.

In Answer A we have (1, 3), (2, 3²), (3,3³)

For the given function g(x)=xpower of 2-6x-16, the statement which is true, is the zeros are -2 and 8 because the factor of g are (x+2) and (x-8).

A quadratic function is the function in which the unknown variable is one and the highest power of the unknown variable is two.

The standard form of the quadratic function is,

[tex]f(x)=ax^2+bx+c[/tex]

Here,(a,b, c) is the real numbers and (x) is the variable.

The quadratic function given in the problem is,

[tex]g(x)=x^2-6x+16[/tex]

Factorized it with split the middle term method,

[tex]g(x)=x^2-6x-16\\g(x)=x^2-8x+2x-16\\g(x)=x(x-8)+2(x-8)\\g(x)=(x-8)(x+2)[/tex]

Equate the factors of the function, to find the zeros,

[tex]x-8=0;x=8\\x+2=0;x=-2[/tex]

Hence, for the given function g(x)=xpower of 2-6x-16, the statement which is true, is the zeros are -2 and 8 because the factor of g are (x+2) and (x-8).

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Answer:

They are not equivalent.

Step-by-step explanation:

5(3a+2)=15a+10

15a+10≠15a+2

Answer:

not equivalent.

Step-by-step explanation:

5(3a+2). multiply the 5 into the parenthesis, so multiply it by both numbers.

15a+10≠15a+2

if you wanted to go further, since 15a is equivalent, just take it out.

10≠2

Answer:

x=1 it is not inverse

Answer:

Attached image

Step-by-step explanation:

Convert 3/4 to 6/8, then count out the points on the line for each number to plot it.

Answer:

There are 8 tick marks, so......

2.75 would go on the 6th tick mark between 2 and 3

1.625 would go on the fifth mark between 1 and 2

For clarification, I have graphed it out below!

Hope this helps!

Answer:

A. 9.0 seconds

Step-by-step explanation:

Answer:

x=4/5

Step-by-step explanation:

Add 18 to both sides and simplify

Zeros are

Write in factor form and solve

Points given (-2,16)

Solve for n

On solving we get

So the function is

Answer:

-4x³ - 28x²- 48x

Explanation:

→ so equation: a(x+4)(x+3)(x+0)

→ substitute these points to find a

so the graphed cubic equation:

from Chicago to Atlanta is 700 miles, so in plain-vanilla shipping costs for that will be $240 per every 100 lbs.

if we're shipping 2,000 lbs, hmmm that's 2000/100 = 20, so 100 lbs 20 times, so our plain-vanillla cost will be 20 * 240 = 4800 bucks.

Now, we're Da Bomb, and hell, why not, let's ship it on a 3-5 day, but that has a Premium of an extra 20%, hmmm that means our cost using 3-5 days service is 4800 + 20%.

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{20\% of 4800}}{\left( \cfrac{20}{100} \right)4800}\implies 960~\hfill \underset{final~cost}{\stackrel{4800~~ + ~~960}{5760}}[/tex]

Answer:

y=51, z and x= 129

Step-by-step explanation:

its complicated, but try to think of it as 51 and x/z are complementary angles, meaining they are on the same line, which means they equal 180, which makes this easier to solve meaning all you have to do is subtract 180-51=129.

Answer:

67°

Step-by-step explanation:

Ignore the 2500m for now.

To find angle x, we know that the sum of the degrees in a triangle is 180. We see that under the 2500m there is a square, indicating that the angle is 90 degrees.
So we can do 180-23-90 = 67.

Therefore, the angle measure of ∠x is 67°

[tex]1000000000 \times 43000000 = 43000000000000000[/tex]

Answer:

76 in^2

Step-by-step explanation:

2 rectangles on the sides: 64 in^2

8x4 = 32

32x2 = 64

rectangle in the middle: 12 in^2

4x3 = 12

altogether area: 76 in^2

64+12 = 76

Answer: About 10.2857 years

=============================================================

Explanation:

For the rule of 72, we divide the number 72 over the interest rate without the percent sign. We do not convert to decimal form. Simply erase the percent sign.

For example, if the interest rate was 6%, then we estimate it would take 72/6 = 12 years for the amount to double.

In this case of a 7% interest rate, the doubling time is roughly 72/7 = 10.2857 years.

-------------

Extra Notes:

Answer:

-5

Step-by-step explanation:

formula of slope is

[tex] \frac{y2 - y1}{x2 - x1} [/tex]

y2 is the second y value

y1 is the first y value so you get

[tex] \frac{6 - 11}{14 - 13} [/tex]

that leaves you with -5 /1 which can be written as -5

-5

The slope is rise over run. In other words, it is the change in y divided by the change in x.

Slope Formula

The formula for slope is [tex]\frac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex]. This will give the the difference in y-values divided by the difference in x-values. To find the slope, plug in the values.

Final Slope

The y-value decreases by 5 as the x-value increases by 1. This means that the slope must be -5/1. This can be rewritten as -5.

Answer:

Larger number = 25

Smaller number = 14

Step 1. Establish variables and system of equations

Larger number = x

Smaller number = y

&

x + y = 39

y + 11 = x

Step 2. Isolate a variable in ONE equation

x + y = 39

y = 39 - x

Step 3. Substitute that into the OTHER equation to find x

y + 11 = x

(39 - x) + 11 = x

50 - x = x

50 = 2x

25 = x

Step 4. Substitute that into the OTHER equation to find y

x + y = 39

(25) + y = 39

y = 14

Answer:

C. Equally likely

Step-by-step explanation:

1/2=0.5=50% probability