teresa earned 425 dollars for working 25 hours last week what is her hourly rate

Answer:

125 inches squared

Step-by-step explanation:

A=lw

A=(5)(25)

A=125

First let's find the length of AC using the Pythagorean theorem in the right triangle with legs of 5 and 12:

So the diagonal of the rectangle is 13 units. Now, since the area of a triangle is calculated as the product of a base and the corresponding height, we can use the legs as base and height or we can use the segment AC and the corresponding height, and the result is the same, so we have:

So the distance from B or D to the diagonal AC is 60/13 units.

Given:

given expression is

Find:

The main objective is to evaluate the expression.

Explanation:

we will use BoDMAS formula for evaluating the expression.

Conclusion:

Therefore, correct option is C.16

Answer:

The time take for the journey can be calculated by dividing the total distance by the distance travelled in an hour.

Which is 2171 (Total distance) / 520 (Distance travelled in a hour)

[tex]2171/520 = 4.175[/tex]

Which can be rounded of to 4.2

It takes 4.2 hours for the flight between Los Angeles and Toronto

Answer:

Step-by-step explanation:

(4x + 50)° = 150°

4x = 150° - 50°

4x = 100°

x = 100° / 4 = 25°

Problem

Kyle just graduated from college and got his first job, he has $45,000 in student loan debt, wants to buy a new car, and is considering opening up a retirement account. He has a disposable income of $300/month, what would you recommend he do with this money? Why?

Solution

For this case the best option would be put the $45000 in a bank with a compound interest

And with the earnings each month of 300$ he can put the half of this into the account and the remain to spend on other things

Part (a)

distance = rate*time

rate = distance/time

rate = 84/4

rate = 21

Answer: 21 mph

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

Part (b)

distance = rate*time

distance = 21*7

distance = 147

Answer: 147 miles

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

Part (c)

distance = rate*time

time = distance/rate

time = 57/21

time = 2.71428571428571

time = 2.714

Answer: Approximately 2.714 hours

Answer;

A.21:1

B:147 Miles

C.2.7 hours or 182 minutes

Answer:  [tex]132000 \le f(t) \le 264000[/tex]

Explanation:

The domain is [tex]3 \le t \le 6[/tex] to represent the time values between 3 and 6 hours, including the endpoints. This represents the set of possible inputs to the function.

The function f(t) = 44000t is an increasing function. This means the smallest range value corresponds to the smallest domain value.

Plug in t = 3 to find that:

f(t) = 44000t

f(3) = 44000*3

f(3) = 132000

This says he mows 132,000 sq ft of lawn in 3 hours.

Now plug in the largest domain value to find the largest range value

f(t) = 44000t

f(6) = 44000*6

f(6) = 264000

He mows 264,000 sq ft of lawn in 6 hours.

The range is the set of f(t) values between 132,000 and 264,000

We can write that as [tex]132000 \le f(t) \le 264000[/tex]

The unit rate for the cereal is  104 calories per cup and there are 416 calories in 4 cups

From the question, the given parameters are

Calories = 78 calories

Size of cups = 3/4-cup

The unit rate of the calories per cup is calculated as

Unit rate = Number of Calories/Size of cup

Substitute the known values in the above equation

So, we have the following equation

Unit rate = 78/(3/4)

Evaluate the quotient

So, we have the following equation

Unit rate = 104

So, the unit rate is 104 calories per cup

For four cups of cereal, we have

Calories = 104 x 4

Evaluate

Calories = 416

So, the number of calories is 416 calories

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Answer:

It would be MOP is adjacent

Step-by-step explanation:

Given three side lengths form an acute obtuse or a right triangle 17, 21, & 28

Check Right triangle

Not a Right triangle

An obtuse triangle is a triangle with one obtuse angle and two acute angles. Since a triangle's angles must sum to 180° in Euclidean geometry.

Not an Obtuse triangle

Hence it is acute angle because all angles are less than 90°

Answer:

y = -5x + 6

Step-by-step explanation:

Looking at the graph it looks that the slope of the line is -5

and the y intercept is (0, 6)

So the slope intercept form is y = -5x + 6

this should be correct hope this helps

Step 1

Write the slope, y-intercept form of the equation of a line.

For part A. One way to know if there is a correlation between the data is to graph the data set, like this

Then, as can you see the data presents a positive linear correlation.

For part B. You can take the coordinates of two points and find the slope of the line using the formula

If you take

Now, using the slope formula, you can find the equation of the line in its slope-intercept form

Therefore, the function that best fits the data is

For part C. The slope of the plot is 10 and indicates that for every hour students spend time studying, they get 10 more points on the science test.

The y-intercept of the plot is 57 and indicates that if students study 0 hours for the science test, they will obtain 57 points as a grade.

Answer:{(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}

Step-by-step explanation: hope this helps

The midpoint between the given figures are -2.5 and 5.5 respectively.

A midpoint is defined as that particular point that divides two separate figures into two equal halves or the centre of two endpoints on a number line.

That is;

point a + point b/2

The figures given are :

Point a = -3

Point b = -2

= -3 + -2/ 2

= -5/2

= -2.5

For points 4 and 7 ;

= 4 + 7 / 2

= 11/2

= 5.5

Therefore, the middle or midpoint of -3 and -2 is -2.5 and the midpoint for 4 and 7 is 5.5.

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The minutes it take Mai to complete 4 laps of the track would be 6 minutes 24 seconds.

Speed can be calculated as the ratio of distance traveled to the time taken.

Speed = distance /time

Also, Time = distance/ speed

In this case, the distance is 4 laps of 400 meters, so;

4 x 400=1600 meters

Speed = 250 per minute

Now,

Time =1600 meters /250 meter per minute

= 6,40 minutes is the same 6 minutes 24 seconds

Hence, the minutes it take Mai to complete 4 laps of the track would be 6 minutes 24 seconds.

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Given:

1. The sum of X and 96 equals half of X.

To determine the algebraic equation, we note that the sum of x and 96 would be:

x+96

Next, half of x must be like this:

x/2

Then, the phrase equals means we set x+96 equals to x/2.

Therefore, the answer is:

Yes, 4x² - 20x + 25 = (2x+5)² is a perfect square trinomial.

What is perfect square trinomial?

A trinomial that may be expressed as the square of a binomial is referred to as a perfect square trinomial. Remember that the square of the first term, twice the product of the first two terms, and the square of the final term are the results of squaring a binomial.

The perfect squared trinomials are always in the form:

[tex]a^2 +- 2ab + b^2 = (a+-b)^2[/tex]

The given equation can also be written as:

(2x)² - 2(2x)(5) + 5² = (2x+5)²

This equation is similar to the ideal equation for perfect square trinomial.

Here, a = 2x, b = 5

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Complete Question

Is the given trinomial, 4x² - 20x + 25 = (2x+5)² , a perfect square trinomial?

In the absence of ATC restriction on climb or descent, and aircraft are within 1,000 feet of assigned altitude. pilots should attempt to both climb and descend at a rate of between 500 fpm and 15000 fpm. (Option A)

An Air Traffic Controller (ATC) clearance refers to an authorization by ATC for the purpose of preventing known aircraft collision. The rate of climb or descend expected by ATV is when an aircraft is within 1000 feet of assigned altitude, descend, or climb at an optimum rate consistent with the operating characteristics of the aircraft to 1,000 feet above or below the assigned altitude, and then attempt to descend or climb at a rate of between 500 and 1,500 fpm until the assigned altitude is reached.

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The rate of change of angle of elevation between the radar station and airplane is

                       [tex]\displaystyle \frac{-10}{109} \left(\frac{rad}{min}\right)[/tex]

The airplane is flying at the speed of 200 mph

The airplane is at an altitude of 3 miles over the radar station

The distance travelled by the airplane after 3 mins

      distance = speed x time

                     = 200 mi/hr x 3 min

Since the speed is hour let us convert it to mins

                     = 200 x 3 x 1/60

                     = 600 / 60

                    = 10 miles

So , let us assume that the airplane is exactly at the top of the radar station at an altitude of 3 miles

Then the elevation angle of the between radar station and airplane can be find by

                              tan θ = O / A
where O is the opposite side to the angle of elevation

          A is the adjacent side to the angle of elevation.

But we need the find the rate of change of angle of elevation , so let us differentiate on both side with respect to time

                                [tex]\displaystyle sec^{2}\theta\frac{ d\theta }{dt} = \frac{A \frac{dO}{dt} - O \frac{dA}{dt} }{A^{2}}[/tex]

                                        [tex]\displaystyle \frac{ d\theta }{dt} = \frac{A \frac{dO}{dt} - O \frac{dA}{dt} }{sec^{2}\theta A^{2}}[/tex]

                                       [tex]\displaystyle \frac{d\theta}{dt} = \frac{10 (0) - 3 (200 mi/hr)}{sec^{2}(10)^{2}}[/tex]

The altitude is gonna be a constant , thus the derivative of altitude will be zero whereas , the the distance travelled by airplane is changing with respect to time.

                                   [tex]\displaystyle \frac{d\theta}{dt} = \frac{10 (0) - 3 (200 mi/hr)}{\frac{109}{100}(10)^{2}}[/tex]

We had found the value of sec²θ = (hyp/adj)²

                                    [tex]\displaystyle \frac{d\theta}{dt} = \frac{-600}{109} \frac{rad}{hr}[/tex]

Now , let us convert in terms of rad/min

                                   [tex]\displaystyle \frac{d\theta}{dt} = \frac{-600}{109} \left(\frac{1}{60}\right)[/tex]

                                  [tex]\displaystyle \frac{d\theta}{dt} = \frac{-10}{109} \left(\frac{rad}{min}\right)[/tex]    

Therefore , the rate of change of angle of elevation is -10/109 (rad/min)    

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Answer:

4x3+6x6=48

Step-by-step explanation:

PEMDAS

4x3=12

6x6=36

12+36=48

therefore, the answer is 48

The eqations are 149=19/9 (10) +b and 130=19/9(1)+b

Given that,

As part of her work, Loren found the solution to the equation 10 = start fraction 19 over 9 end fraction (149) b for b and the points are  (1, 130) and (10, 149)

Finding the slope of a line that goes through two locations for Loren is as follows: m=y2-y1/x2-x1

=149-130/10-1

=19/9 

m=19/9

There are two ways to solve for b in the equation y=mx+b for the location (1,130), where y=130, x=1, and m=19/9, and for the position (10,149), where 149=19/9 (10) +b.

Therefore, the equation of a trend line that passes through the points (1, 130) and (10, 149) are 149=19/9 (10) +b ,130=19/9(1)+b

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Answer:

Step-by-step explanation:

A perpendicular line will have a sope that is the negative inverse of the reference line.  The reference line is y = -3 + 4, with a slope of -3.  The negative inverse would be -(-1/3) or (1/3).

The new line will take the form of y = (1/3)x + b, where b is the y-intercept (the value of y when x=0).  We want the new line to go through point (-3,-7).  We;ll need a value of b that will make that happen.  To find b, enter the given data point and solve for b:

y = (1/3)x + b for (-3,-7).

-7 = (1/3)(-3) + b

-7 = -1 + b

b = -6

The new equation is y = (1/3)x - 6

See the attached graph.

We know that the point-slope formula is given by:

y − y₁=m(x − x₁)

where the terms: m, y₁ and x₁ are numbers.

Given that the line passes through a given points we have that:

m is the slope of the line

y₁ is the y value of that given point

x₁ is the x value of that given point

We want to find the slope m, having that

(x₁, y₁) = (-18, -2)

(x₂, y₂) = (9, 10)

The slope is always a rate of change. It is:

m = Δy/Δx,

where Δ means "change"

Step 1: finding the change of each term x and y

Δy = change of y = y₂ - y₁

Δy = 10 - (-2) = 12

Δx = change of x = x₂ - x₁

Δx = 9 - (-18) = 27

Step 2: dividing the found quantities

Then

m = Δy/Δx = 12/27

m = 4/9

Step 3: replacing in the equation

Using the equation, we have that

y − y₁ = m(x − x₁)

replacing m:

y − y₁= 4/9(x − x₁)

For the first point: (-18, -2)

We have that (x₁, y₁) = (-18, -2)

since the equation is

y − y₁ = 4/9(x − x₁)

replacing each term for each number of the given coordinate

y − (-2) = 4/9(x − (-18))

y + 2 = 4/9(x + 18)

Equation: y + 2 = 4/9(x + 18)

For the second point: (9, 10)

We have that (x₂, y₂) = (9, 10)

since the equation is

y − y₂ = 4/9(x − x₂)

replacing each term for each number of the given coordinate

y − (10) = 4/9(x − (9))

y - 10 = 4/9(x - 9)

Equation: y - 10 = 4/9(x - 9)

Based on the amount you have received in grants, and the amount the boss wants to increase it to, the increase the new amount represents over the previous amount is $15,000 or 33.3%.

Your boss wants to increase the grants to $60,000 from the current amount of $45,000.

This means that the new amount will represent an increase over the previous amount by:
= 60,000 - 45,000

= $15,000

In percentage terms this is:
= Increase over previous amount / Previous amount x 100%

= 15,000 / 45,000 x 100%

= 33.3%

In conclusion, the difference between the grants applied for in the past 5 years and the amount the boss is asking for, gives the increase of $15,000.

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[tex]f^{-1} (x) = \sqrt{65.5 - 0.0625x }\\[/tex] is the inverse function and it means the time in seconds it will take the ball to attain a certain height in feet.

Given:

[tex]f(x) = 1048 - 16x^{2}[/tex]

Since the function f(x) is the height (h), we can write the function as :

[tex]h = 1048 - 16x^{2}[/tex]

We will make x the subject:

[tex]16x^{2} = 1048 - h[/tex]

[tex]x^{2} = \frac{1048 - h}{16}[/tex]

[tex]x = \sqrt{\frac{1048 - h}{16} }[/tex]

[tex]x = \sqrt{65.5 - 0.0625h }[/tex]

Since:

[tex]x = f^{-1} (h) = \sqrt{65.5 - 0.0625h }[/tex]

Thus:

[tex]f^{-1} (x) = \sqrt{65.5 - 0.0625x }\\[/tex]

Therefore, the inverse function is  [tex]f^{-1} (x) = \sqrt{65.5 - 0.0625x }\\[/tex] and it is a function describing the amount of time (in seconds) it takes for the ball to reach a height of h feet.

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