A ball is released from rest and falls 125 meters in 5 seconds. What was the magnitude of its acceleration?

The equation of the linear graph is expressed in slope intercept form as; y = 20x

The equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept (which is the point where the line crosses the y-axis)

From the graph given we can see that the line crosses the y-axis at 0. Thus; c = 0

Now, we can pick two coordinates to find the slope;

Slope = (y2 - y1)/(x2 - x1)

Slope = (40 - 20)/(2 - 1)

Slope = 20

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Answer:

x = 300°

Step-by-step explanation:

If m and n are parallel, then m∠4x is equal to 120, since they are congruent angles.

Solve for x:

4x = 1200

Divide both sides by four

x = 300

Answer:

x = -5/6

Step-by-step explanation:

First, set the equation (6x + 5) * 86 equal to 0. The equation is now (6x + 5) * 86 = 0. Next, simplify (6x + 5) * 86 by multplying 86 to 6x and 5. This will turn the equation into 516x + 430 = 0. Next, subtract 430 from both sides, cancelling out the 430 on the left side. After that, get the x value by itself by dividing 516 on both sides, cancelling out the 516 on the left side. Now, x = -430/516. From here, find the common factor of both the numerator and denominator; this turns out to be 86. Since 86 is the common factor, divide the numerator and denominator by 86 and you get x = -5/6.

The expression equivalent to (3x²z⁻³)² is 9x⁴z⁻⁶.

For the given question;

The expression is given as;

= (3x²z⁻³)²

Squaring each term individually.

= (3)²(x²)²(z⁻³)²

As the property of the index, the power will be multiplied.

= 9x⁴z⁻⁶.

Thus, the expression equivalent obtained for the given expression (3x²z⁻³)² is 9x⁴z⁻⁶.

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The student that is correct with regards to the prime factorization of 956 is student B.

A factor is a number that divides another number without leaving any remainder. For example, 10 is a factor of 100. A prime number is a number that is perfectly divisible by 1 and that number only.

For example, a prime number is 7. A prime factor is the factor of a number that is a prime number. For example, a prime factor of 28 is 2.

In order to determine the prime factorization of a number, express the number as its prime factors.

Prime factors of 92 = 2 x 2 x 2 x 2 x 2 x 3

Thus, it is only student B that is correct. 5 is not a factor of 96.

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Answer: The answer is C. You start off by first thinking about your slope equation, being y=Mx+b. Remember b equals your y- intercept. In this case one of your y-intercepts is positive 1 and the other is positive 2. Now you have the “b” part of the equation. Looking for slope or your “mx” part of the equation is next. All this is going to be is the rise over the run from your y intercept. How much did you rise and how much did you run to get to the next point. Both of these slopes are going up therefore both slopes will be positives. For the first one it rises 2 and runs 1 to get to the next point, however you do not need to write the one at the bottom of the 2 and can leave it as “2x+1”, because it is shaded below the red line the inequality will be less than or equal to

. The blue slope rises 1 and runs 2, it is written as

and because it is shaded above the blue one it will be greater than or equal to

.

Step-by-step explanation:

Considering the linear functions on the graph, the inequality that matches the situation is:

B. y ≥ x/2 + 2

   y ≤ 2x + 1

A linear function is modeled by:

y = mx + b, In which: m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

here, we have,

The lower bound of the interval is a linear function with

y-intercept of b = 2,

that also passes through (2,3), hence the slope is:

m = (3 - 2)/(2 - 0)

   = 1/2.

Hence the inequality is:

y ≥ x/2 + 2

The upper bound of the interval is a linear function with y-intercept of b = 1, that also passes through (2,5), hence the slope is:

m = (5 - 1)/(2 - 0) = 2.

Hence the inequality is:

y ≤ 2x + 1

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Answer: 21 quarters and 2 nickels.

Step-by-step explanation: $0.25(one quarter) x 21 = $5.25. $0.05(one nickel) x 2 = $0.10. $5.25 + $0.10= $5.35.

Answer:

I'm guessing the whole question is: "A car drives 283.5 miles in 4.5 hours. Assuming that the distance traveled directly with the time traveled, how far will the car travel in 7 hours?"

Step-by-step explanation:

If so, here's the answer:

441 miles will be traveled in 7 hours

You could find the speed in mph

To do that, divide 283.5 by 4.5 which gives us 63

because [tex]\frac{283.5 miles}{4.5 hours}[/tex] divide to get the 4.5 hours into 1 hour so, [tex]\frac{283.5/4.5}{1}[/tex]

63 mph times 7 hours = 441

Answer:

19.5/3=6.5 centimeters

Step-by-step explanation:

The scale of drawing of Bonnie's drawing is 5 inches : 6 yards.

She measured a city and made a scale drawing.

The neighbourhood park is 115 inches long in the drawing. The actual park is 138 yards long.

Therefore, the scale of the drawing can be calculated as follows:

Hence,

115 inches = 138 yards

5 inches = ?

cross multiply

scale of the drawing = 5 × 138 / 115

scale of the drawing = 690 / 115

Therefore,

scale of the drawing is 5 inches : 6 yards

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Answer:

y = -3(x + 2)^2 + 10.

Step-by-step explanation:

y = –3x2 – 12x – 2

Divide first 2 terms by -3:

y = -3(x^2 + 4x) - 2            Now complete the square on x^2 + 4x:-

y = -3(x^2 + 4x + 4 - 4) - 2

y = -3[(x + 2)^2 - 4] - 2

y = -3(x + 2)^2 + 12 - 2

y = -3(x + 2)^2 + 10.

1800 lawns were mowed. 800 driveways were shoveled.

A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2. In the above example, the variable x exists. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

Given Data

Let mowed grass be x

Let shoveled snow be y

Last year you mowed grass and shoveled snow for 12 houses

x + y = 12

y = 12 -x

You earned $225 for each lawn you mowed and $200 for each house you shoveled for a total of $2600.

225x + 200y = 2600

Equating value of y

225x + 200(12-x) = 2600

225x + 2400 - 200x = 2600

225x - 200x = 2600 - 2400

25x = 200

x = 8

For value of y,

y= 12 -x

y = 12 - 8

y = 4

Lawn mowed = 225(8)

Lawn mowed = 1800

Shoveled snow = 200(4)

Shoveled snow = 800

1800 lawns were mowed. 800 driveways were shoveled.

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Probability when a student is selected at random to be the captain. Probability the captain has a blue shirt is unlikely. Probability the captain has a red shirt is impossible. Probability the captain has a blue or white shirt is likely certain.

The total number of students is 15.

4 students are wearing blue shirt.

11 students are wearing white shirt.

10 students are wearing yellow shirt.

Only any one student can be captain.

The total outcomes are 25.

Probability that the student has blue shirt B is,

Total favorable outcomes = 4

P(B) = 1/25.

Probability that the student has red shirt R is,

Total favorable outcomes = 0

P(B) = 0/25.

P(B) = 0

Probability that the student has blue or white shirt B and W is,

Total favorable outcomes = 15

P(B&W) = 15/25.

P(B&W) = 3/5.

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The rule to describe the transformation, dilation by a scale factor of 4 with center of dilation at the  origin is (x,y)→(4x,4y) and the coordinates of rectangle Q'R'S'T' is are Q'(-32,20) , R'(-32,28) , S'(-20,28) , T'(-20,20) .

In the question ,

a rectangle QRST with coordinates Q(-8,5), R(-8,7), S(-5,7), and T(-5,5) is given ,

and to dilate the rectangle by a scale factor of 4 with center of dilation at the origin , we multiply coordinates of the original shape with the dilation factor

so the rule to describe the dilation will be

(x,y)→(4x,4y)

Using this rule to find the new coordinates of the rectangle Q'R'S'T' .

When Q = (-8,5)

Q' = (4*(-8),4*5)

Q' = (-32,20)

When R = (-8,7)

R' = (4*(-8),4*7)

R' = (-32,28)

When S = (-5,7)

S' = (4*(-5),4*7)

S' = (-20,28)

When T= (-5,5)

T'  = (4*(-5),4*5)

T' = (-20,20)

So the coordinates of the rectangle Q'R'S'T' is Q' = (-32,20) , R' = (-32,28) , S' = (-20,28) , T' = (-20,20) .

Therefore , the rule to describe the transformation, dilation by a sale factor of 4 with center of dilation at the origin is (x,y)→(4x,4y) and the coordinates of rectangle Q'R'S'T' are Q'(-32,20) , R'(-32,28) , S'(-20,28) , T'(-20,20) .

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Answer: the slope is 1

Step-by-step explanation:

The directed number suggested by the following will be:

A 14 degrees below zero = -14°

B altitude 200 metres = +200

It should be noted that the directed number simply means the numbers that had both size and direction. It should be noted that the direction can either be positive or negative.

A measurement of altitude or height is the distance between a location or item and a reference datum, typically in the vertical or "up" direction. Although the term "altitude" is frequently used to refer to a location's height above sea level, the term "elevation" is frequently preferred in the context of geography. The term "depth" often refers to vertical distance measurements taken in the "down" direction. Globally, the research team discovered that the pace of temperature change frequently quickens as altitude increases.

Therefore, the directed number suggested by 14 degrees below zero will be negative 14 and this will be -14°

Also, altitude 200 metres will be positive 200 and this will be +200

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Step-by-step explanation:

850÷100=17/2=8.5

8.5×24=204

850-204=646

646÷100=6.46

6.46×13=83.98 1st

646-83.98=562.02

562.02÷100=5.6202 2nd

5.6202×13=73.0626

562.02-73.0626=488.9574

488.9574÷100=4.889574 3rd

4.889574×13=63.564462

4.889574×13=63.564462

488.9574-63.564462=425.392938

425.392938÷100=4.25392938 4th

4.25392938×13=55.30108194

425.392938-55.30108194=370.0918561

370.0918561÷100=3.700918561 5th

3.700918561×13=48.11194129

370.0918561-48.11194129=321.9799148

321.9799148÷100=3.219799148 6th

3.219799148×13=41.85738893

321.9799148-41.85738893=280.1225259

280.1225259÷100=2.801225259 7th

2.801225259×13=36.41592836

280.1225259-36.41592836=243.7065975

I spent waaaaay to much time typing this

answer out I swear if it is incorrect I am done

£243.71

Answer:

the relation in the table is a function

the relation in the set of points is not a function

Step-by-step explanation:

the definition of a function is that one input (x) can only have one output (y). In the set of points, the input 4 appears twice, which means it is not a function.

The expected number of points as a function of a and b is C = b+a.

In this questions what we are been asked is for the expected value C, to solve the problem we need to recognize the random variables and their respective probability.

x1 = roll a 1 -> P1 = 1/6

x2 = roll a 2 -> P2 = 1/6

x3 = roll a 6 -> P3 = 1/6

x4 = roll a 1, 4 or 5 -> P4 = 1/2

E = P1*x1 + P2*x2 + P3*x2 + P4*x4

x1 is equal to zero (no points and the game stop), x2 is equal to C+b (win a points, affecting the expected value), x3 is equal to C-a (win b points, affecting the expected value) and x4 is equal B (no points are lost and the game continues, therefore the expected value is not affected)

C = 1/6*0 + 1/6*(C+b) + 1/6*(C-a) + 1/2*(C)

1/6*C = 1/6*b + 1/6a

Solving for C

C = b+a

Conclusion: If you get a "2, 4 or 5, this means the game will be unaffected (in terms of points), you need to pay special attention to x1 and x2 (all with the same probability)  that are the results that are going to affect your game.  

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The Distance between line ℓ and the point j (-5,-1) is 8units.

The distance between a point PP and a line LL is the shortest distance between PP and LL; it is the minimum length required to move from point PP to a point on LL. In fact, this path of minimum length can be shown to be a line segment perpendicular to LL. The distance d can then be defined as the length of the line segment that has PP as an endpoint and is perpendicular to LL.

We know that the distance d between a point (x1,y1) and a line having equation in form of ax+by+c=0 can be expressed as,

[tex]d = \frac{|ax1+by1+c|}{\sqrt{(a^2+b^2)} }[/tex]

So, we have given that equation of line

y = 7

y-7=0

Point j = (-5,-1)

So, Distance between point j and line = d

d = [tex]\frac{|0(-5)+1(-1)-7|}{\sqrt{(0^2+1^2)} }[/tex]

d = [tex]\frac{8}{\sqrt{1} }[/tex]

d = 8 units

Therefore, The point j is at a distance of 8 units from the line ℓ.

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The mean number of people per day visiting in August will be equal to option (D) 180.

Mean number of students in July = 160

20 more people visited the people each day in the month of August.

As, there is a constant increase in the number of who are visiting the museum in August each day that is 20 people, the mean will also increase by the same number that is 20 and will be:

Mean number of people per day visiting in August = 160 + 20

Mean number of people per day visiting in August = 180

Therefore, we get that, the mean number of people per day visiting in August will be equal to option (D) 180.

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d. Using the Standard Form, identify the x - intercept of the graph and explain

how the x-intercept relates to the number of hot dogs and sodas sol

Maybe sorry if i got it wrong

The value of the inequality expression given as –3(2x – 5) < 5(2 – x) are x < 5 and number line (4)

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

The inequality expression is given as

–3(2x – 5) < 5(2 – x)

Open the brackets

So, we have

-6x + 15 > 10 - 5x

Collect the like terms

So, we have

5x -6x > 10- 15

Evaluate the like terms

So, we have

-x > -5

This gives

x < 5

When represented on a number line, it can be represented as the number line in option (4)

Hence, the equivalents of the inequality are x < 5 and number line (4)

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The correct answer to the task 0.80 divided by 50 given above is 0.016

When we are trying to find the number of times a number can be obtained in another number, we use the term "division" to describe the mathematical expression. The division can be represented as ÷

For instance, the division of 0.80 by 50 is represented and solved below:

0.80 ÷ 50 = 0.016

It can also be represented like this:

0.80 / 50 = 0.016.

Another example of division of numbers is:

8/4 = 2

10 ÷ 2 = 5

So therefore, from the explanation given above we can confirm that when 0.80 ÷ 50, the answer is 0.016.

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WS bisects angle BWV, m ∠BWS = 36° , then the measure of angle

m ∠BWV is equal to 72°.

As given in the question,

Measure of given angle :

m ∠BWS =36°   ____(1)

let 'x' be the measure of angle BWV

WS bisects angle BWV.

⇒ m ∠BWS= m ∠SWV

⇒ m ∠SWV=36° ____(2)

Also , m ∠BWV is equal to the sum of the measure of ∠ BWS and ∠SWV.

⇒ m ∠BWV =m ∠BWS + m ∠SWV

Substitute the value of m∠ BWS and m ∠SWV from (1) and (2),

⇒ m ∠BWV=36° + 36°

⇒m ∠BWV=72°

Therefore, WS bisects angle BWV, m ∠BWS=36° , then the measure of angle m ∠BWV is equal to 72°.

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Answer: True

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Answer:

use v for the value

Step-by-step explanation:

Answer:

Here are all 3 number combinations that you can multiply to get 300: 300 × 1 × 1 = 300 150 × 2 × 1 = 300 150 × 1 × 2 = 300 100 × 3 × 1 = 300: