The amount of money earned varies directly as the number of hours worked. After working 14 hours, Joe earned $119. How
much would Joe earn for working 20 hours?

[tex] \: \Large \mathbb{SOLUTION:}[/tex]

[tex] \: \: \rm{ \bigg( - \frac{5}{3} \bigg) {}^{2} } \\ [/tex]

[tex] \: \: \text{Determine the sign for exponential or radical expreasions}[/tex]

[tex] \: \: \rm{ \bigg( \frac{5}{3} \bigg) {}^{2} } \\ [/tex]

[tex] \: \: \text{Calculate the power}[/tex]

[tex] \: \: \rm \boxed{ \frac{25}{9} } \\ [/tex]

[tex] \frac{25}{9} \\ [/tex]

Determine the sign

[tex]( -\frac{5}{3} ) {}^{2} [/tex]

[tex]( \frac{5}{3} ) {}^{2} [/tex]

[tex] \frac{5 {}^{2} }{3 {}^{2} } \\ [/tex]

[tex] \frac{25}{3 {}^{2} } \\ [/tex]

[tex] \frac{25}{9} \\ [/tex]

The height of the tree is 21 feet if manny stands 512 feet tall, and his shadow is 414 feet long. The tree's shadow extends 17 feet in length.

A ratio is defined as a relationship between two quantities, it is expressed as one divided by the other

The length of Manny's shadow, which is 414 feet long, is 512 feet.

The tree's shadow extends 17 feet.

Here, we'll assume that the height is x.

According to the data given, the calculation is as follows:

414 : 512 = 17 : x

⇒ 414 / 512 = 17 / x

⇒ (414)x = (512)(17)

⇒ x = (512)(17)/(414)

⇒ x =21.02

⇒ x = 21 feet

Therefore, the height of the tree is 21 feet if manny stands 512 feet tall, and his shadow is 414 feet long. The tree's shadow extends 17 feet in length.

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Your question is incomplete, probably the complete question is:

One triangle shown is formed by the tree, its shadow, and a line of sight from the ground to the top of the tree. The other is formed by Manny, his shadow, and a line of sight from the ground to the top of his head. Manny is 512 feet tall, and his shadow is 414 feet long. The shadow of the tree is 17 feet long. How can you determine the height of the tree?

Answer:

This is not a function

Step-by-step explanation:

Assuming that the line in question is parallel with the y axis, by using the line test we can see that the line is not a function. The line test is where you draw straight lines going vertically over the graph and if the lines touch the figure in question more than once that means it's not a function.

This can also be proved by imagining there are 2 different points on the line in question. Since the line is straight vertically that means that the points will share the same x value for different y values, which makes it not a function

Answer:

This is not a function.

Step-by-step explanation:

The questioned parallel line within the y-axis does not meet the requirements to be a function. The line test, as the other person stated, is a test where lines are drawn over the points to determine if the graph / model is, or is not a function. Doing so in this process, if the lines touch the same point more than once, that means the graph is not a function.

Answer: The cost of one small box of oranges is $6, while the cost of one large box of oranges is $11.

Step-by-step explanation:

First, set x for the cost of one small box of oranges in dollars, and y for the cost of one large box of oranges in dollars.

Hence, the equations will be:

[tex]13x+5y=133[/tex]

[tex]10x+8y=148[/tex]

Then solve for the equations using the method of elimination. In order to eliminate one of the variables, you need to make the coefficients the same. So, we can multiply the first equation by 8 and the second equation by 5. That would make the equations:

[tex]104x+40y=1064[/tex]

[tex]50x+40y=740[/tex]

Then you can eliminate the y by subtracting.

[tex]54x = 324[/tex]

Then divide by 54 on both sides.

[tex]x=6[/tex]

Now that x is solved, solve for y by substituting for x.

[tex]13(6) + 5y = 133[/tex]

[tex]5y+78=133[/tex]

[tex]5y=55[/tex]

[tex]y=11[/tex]

So, x=6 and y=11.

Answer:

3:5.7

Step-by-step explanation:

please Mark me as

Answer:

its not a accurate questions

cant be answered

Step-by-step explanation:

The gradient of the line y = x/3 - 4 is; 1/3

Slope is defined as the gradient of a graph at any point

We are given the equation of the line as;

y = x/3 - 4

Now, the formula for equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Thus, from the given equation, we can tell that the gradient which is the slope is 1/3.

Thus, we conclude that the gradient of the line y = x/3 - 4 is; 1/3

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Answer:

A Cartesian Plane is a plane in Geometry which is an flat surface of infinite size. It has two number lines that intersect at right angles at their zeros. One number line is horizontal, and the other number line is vertical. The point of intersection is the zero of each line. In the horizontal line, the numbers increase to the right. In the vertical line, the numbers increase up. The horizontal line is called the x axis. The vertical line is called the y axis. The center of the Cartesian Plane is the intersection of the two axes, the two number lines, and is called the origin. Points on the Cartesian Plane are described with two numbers in parentheses separated by a comma. The position of the point in the Cartesian Plane is given by the first number, called the x-coordinate, telling us the number of units to the right (positive) or left (negative) of the origin and by the second number, called the y-coordinate, telling us the number of units up (positive) or down (negative) from the origin.

The linear regression equation for the data is given by:

y = 1.08x + 2.76.

To find the equation, we need to insert the points (x,y) in the calculator.

For this problem, the points (x,y) are given as follows:

(1, 3.58), (2, 5.18), (3, 6.24), (4, 7.97), (5, 7.09), (6, 8.31), (7, 11.33).

Inserting these points into a calculator, the linear regression equation for the data is given by:

y = 1.08x + 2.76.

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Answer:

b= p-(a+c)

Step-by-step explanation:

Step-by-step explanation:

5.|12 - r| > 15

|12 - r| > 15/5

|12 - r| > 3

12 - r < -3 or 12 - r > 3

-r < -3 - 12 or -r > 3 - 12

-r < -15 or -r > -9

r > 15 or r < 9

APY for Kevin's account = 1.67%

The interest on a loan or deposit that is computed based on both the original principle and the accumulated interest from prior periods is known as compound interest (also known as compounding interest). Compared to simple interest, which is computed just on the principal amount, it will cause a sum to increase more quickly.

The frequency of compounding determines the pace at which compound interest accumulates. The compound interest increases with the number of compounding periods.

APY = [tex](1 + \frac{r}{n})^{n} - 1[/tex]  =   [tex](1 + \frac{1.667}{365})^{365} - 1[/tex]  =  1.0167 - 1 = 0.0167

APY = 1.67%

Therefore, APY for Kevin's account = 1.67%

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Answer:

$2000 was invested at 5% and $5000 was invested at 8%.

Step-by-step explanation:

Assuming the interest is simple interest.

Simple Interest Formula

I = Prt

where:

Given:

Create two equations from the given information:

[tex]\textsf{Equation 1}: \quad \sf P_1+P_2=7000[/tex]

[tex]\textsf{Equation 2}: \quad \sf P_1r_1t+P_2r_2t=I\implies 0.05P_1+0.08P_2=500[/tex]

Rewrite Equation 1 to make P₁ the subject:

[tex]\implies \sf P_1=7000-P_2[/tex]

Substitute this into Equation 2 and solve for P₂:

[tex]\implies \sf 0.05(7000-P_2)+0.08P_2=500[/tex]

[tex]\implies \sf 350-0.05P_2+0.08P_2=500[/tex]

[tex]\implies \sf 0.03P_2=150[/tex]

[tex]\implies \sf P_2=\dfrac{150}{0.03}[/tex]

[tex]\implies \sf P_2=5000[/tex]

Substitute the found value of P₂ into Equation 1 and solve for P₁:

[tex]\implies \sf P_1+5000=7000[/tex]

[tex]\implies \sf P_1=7000-5000[/tex]

[tex]\implies \sf P_1 = 2000[/tex]

$2000 was invested at 5% and $5000 was invested at 8%.

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Answer:

3-11-(-6)

the answer will be

-2

Answer:

x = 1/9

Step-by-step explanation:

8x¹ - x +4 can be also written as 7x + 4 or 7x = -4

And 3x + 5 can be written as 3x = -5

So,

7x = -4

-(3x = -5)

4x = 1

x = 1/9

Step-by-step explanation:

we get the points with extreme values as the 0 points of the first derivative of the function.

h'(t) = 592 - 32/7 t = 0

592 = 32/7 t

4144 = 32t

t = 129.5 seconds

so, it will reach its max. height after 129.5 seconds.

The time that the ball reaches its maximum height is 129.5 seconds.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The height above the lunar surface (in feet) after ‘t’ seconds is given by the formula;

⇒ h =592t - 16/7t²

Now,

We have to find the derivative of above formula and equate to zero for the maximum time as;

⇒ h =592t - 16/7t²

⇒ h' =592 - 16/7 × 2t = 0

⇒ 592 - 32/7 t = 0

⇒ 32/7 t = 592

⇒ 32t = 592 × 7

⇒ 32t = 4,144

⇒ t = 4,144/32

⇒ t = 129.5 seconds.

Thus, The time that the ball reaches its maximum height is 129.5 seconds.

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Answer:

if 3 equal 8 , then 600 will be 1600.

Answer:

There is no special hypothesis that you can come up with. You could, of course, hypothesize that they are special numbers

Step-by-step explanation:

The value of the expression is 0 without calculation.

We have to find the exact value of

sin 26° - cos 26°

From the trigonometric function we know that:

cos (90°-Ф) = sinФ and,

sin(90° -Ф) = cosФ

By this, we have an expression that,

=sin 26° - cos 64°

=sin 26° - cos (90° - 26)

=sin 26° - sin 26°

=0

Therefore the value of sin 26° - cos 64° =0.

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Answer:750

Step-by-step explanation:

multiply the numbers

1250-250x2

1250-500

subract the two numbers and you will get

750

Drone nerds will get 15 Mavic air 2's for $23196.192 after offering a chain discount of 6/4/3.

Chain discount is the series of discounts that are offered from the list price of an object when bought from a store.

A general example of a 10/5 chain discount denotes that there will be a series of discounts on the list price. First a discount of 10% is awarded on the list price then a further 5% on the reduced price.

The List price of the drones is $26500.

Chain discount=6/4/3

So the first discount received is 6% on the $26500.

Price after the first discount=26500- 6%of 26500

Simplifying we get

[tex]=26500-.06\times26500\\=24910[/tex]

The price after the first discount is $24910

Now we will apply the 4% discount on $24910

Price after second discount=24910-4% of 24910

=$23913.60

Now we apply the third discount

Price after third discount is=23913.60-3%of 23913.60

=$23196.192

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The Distance between city C and city D is 5405 miles.

Given that Distance from city a to city b is 3003 miles less than the Distance fron city c to city d, the total of these two Distance is 7807 miles and asked to find Distance between  city C and city D.

Given that,

(d-c)-(b-a)=3,003 miles { (Distance between city D and city C)-(Distance between city A and city B)} Let's assume it as equation A

(d-c)+(b-a)=7,807 miles { (Distance between city D and city C)+(Distance between city A and city B)} Let's assume it as equation B

Add equation A and B

2(d-c)=10,810

(d-c)=5,405

Hence,Distance between city D and city C is 5,405

Therefore,The Distance between city C and city D is 5405 miles.

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The equation  equivalent to -2m - 5m - 8 = 3 + (-7) + m is

-7m - 8 = m - 4. Option E

This is further explained below.

Generally,   the equations equivalence is  mathematically given as

-2m - 5m - 8 = 3 + (-7) + m

Therefore

-7m - 8 = 3 + (-7) + m

When we write the equation such that the variable appears on the right-hand side first, we get the following:

-7m - 8 = m - 4

In conclusion, The equation  equivalent to -2m - 5m - 8 = 3 + (-7) + m is

-7m - 8 = m - 4.

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Answer:

Asking yourself how much you'd be willing to spend if someone else offered you a similar product.

The dimensions of the rectangular garden are 29 feet by 23 feet .

A rectangle is a quadrilateral with parallel opposite sides and equal angles. There are a lot of rectangular objects all around us. Any rectangular form's two defining characteristics are its length and width. A rectangle's longer and shorter sides are its width and length, respectively.

The area of a rectangle is given by length × width

Now the given area of the rectangle is 667 ft² .

Let the width of the rectangle is x ft. Therefore length = x + 6

Now area of the rectangle is x (x+6) = x² + 6 x

Therefore x² + 6 x = 667

or,  x² + 6 x - 667  = 0

or, (x-23)(x+29) = 0

Either x = 23 or x = -29(not possible)

Hence the width is 23 feet.

Length = 23 + 6 = 29 feet

Therefore the dimensions of the rectangle are 29 feet by 23 feet .

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Step-by-step explanation:

f(x) = 2x

g(x) = -8x + 2

h(x) = x² + x + 3

= f(g(6))

= 2x

= 2.(-8x + 2)

= 2.(-8.6 + 2)

= 2.(-48 + 2)

= 2.(-46)

= -92

= g(h(-4))

= -8x + 2

= -8.(x² + x + 3) + 2

= -8.((-4)² + (-4) + 3) + 2

= -8.(16 - 1) + 2

= -8.15 + 2

= -120 + 2

= -118

= g(f(x))

= -8x + 2

= -8.(2x) + 2

= -16x + 2

Answer:

(-2[tex]x^{2}[/tex]+3x+1)

Step-by-step explanation:

f(x) = -2x² + 4  g(x) = 3x - 3 find f (4) + g(-6).

f(x)+g(x)

(-2[tex]x^{2}[/tex]+4) +(3x-3)

(-2[tex]x^{2}[/tex]+3x+4-3)

(-2[tex]x^{2}[/tex]+3x+1)

The solution to the system of equation is (2, 7)

Given the  system of equation expressed as:

3x – y = -1  * 2

x – 2y = -12 * 1

________________

6x – 2y = -2

x – 2y = -12

Subtract to have;

6x-x = -2-(-12)

5x = 10

x = 2

Substitute x = 2 into 2 to have:

2 - 2y = -12

-2y = -14

y = 7

Hence the solution to the system of equation is (2, 7)

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Answer: 300

Step-by-step explanation: