X=
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Answer:

Step-by-step explanation:

(4x + 50)° = 150°

4x = 150° - 50°

4x = 100°

x = 100° / 4 = 25°

Answer:

4x3+6x6=48

Step-by-step explanation:

PEMDAS

4x3=12

6x6=36

12+36=48

therefore, the answer is 48

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

Answer:

The answer is 43

Step-by-step explanation:

Remember that the sum of the angles of all triangles is 180 degrees.

80+57+x=180

137+x=180

x=43

Answer:

It would be MOP is adjacent

Step-by-step explanation:

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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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°

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

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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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

[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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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.

Answer:

x = 2.64

Step-by-step explanation:

Do the distributive property first.

0.9(x + 1.4)

0.9(x) + 0.9(1.4)

0.9x + 1.26 - 2.3 + 0.1x = 1.6

Simplify the left side by adding like terms. I'm going rewrite the equation and group the like terms together.

0.9x + 0.1x + 1.26 - 2.3 = 1.6

1x - 1.04 = 1.6

1x is the same as x, so I am going to remove the 1. Solve for x.

x - 1.04 + 1.04 = 1.6 +1.04

x = 2.64

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

Answer:

125 inches squared

Step-by-step explanation:

A=lw

A=(5)(25)

A=125

The smallest and greatest number that rounds to 380 when rounding to the nearest ten are 375 and 384 respectively.

Adjusting a number's digits so that it produces an approximation of a result is known as rounding.

The given number is 380.

When rounding a number to the nearest ten, pay attention to the last digit; if it is less than five, round down; if it is five or more, round up.

Therefore, the smallest number that rounds to 380 when rounding to the nearest ten is 375.

Similarly, the greatest number that rounds to 380 when rounding to the nearest ten is 384.

Hence, the smallest and greatest number that rounds to 380 when rounding to the nearest ten are 375 and 384 respectively.

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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:  [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]

Y'=33.67+0.54*X' .

For married couples in their early 20s, the regression equation and the prediction of a husband's height. In statistics, a regression equation is used to determine whether or not there is a link between two sets of data.

In statistics, a regression equation is used to determine whether or not there is a link between two sets of data. For instance, you might discover that a child grows roughly 3 inches a year if you measure their height each year. A regression equation can be used to model the three-inch growth tendency.

Detailed explanation:

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test of 250 questions

40% of the fist 125 are ok, this means that 125(0.4) = 50 questions of the first 125 are ok

If jassi needs 60% of the 250 ok, that is 250(0.6) = 150

If of the first half she already has 50 questions ok, and needs 150, she needs to have 100 questions our of the second 125

If she needs 100 out of 125, this percent is 100/125 = 0.8, this means 80%

Answer:

Jassi needs 80% of the second 125 questions to be ok

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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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)

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

Step-by-step explanation: hope this helps

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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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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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.