an object falls from a height, h m, varies directly as the square of its time, t s on planet Q. given that the object falls from the height of 5 m in 2 s, calculate the time taken in seconds, for the object to fall from a height of 45 m on the planet.​

Area = length x width

Fill in the given information

20 = 2 x width

Solve for width by dividing both sides by 2

Width =20/2

Width = 10 feet

Answer:

It is 10 feet wide

Step-by-step explanation:

The area of a rectangle is:

A = Length x width

So if we have the area, finding the width means diving the area by the given length.

In this case, the area of the rectangle is 20 square feet and the length is 2 feet:

20/2 = 10

Therefore the missing width is 10 feet

Answer:

y = -x - 6

Step-by-step explanation:

Parallel lines have same slope

y = -x + 9   {y = mx  + c}

m = -1  

(x₁, y₁) = (7 , -13)

Equation: y - y₁ = m(x -x₁)

y - [-13] = -1(x -7)

y+ 13 = -x + 7

    y = - x + 7 - 13

y = -x - 6

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Explanation:

Choice B has the GCF x we can factor out like so

10x^4-5x^3+70x^2+3x = x(10x^3-5x^2+70x+3)

Showing that choice B is not prime. If a polynomial can be factored, then we consider it not prime. It's analogous to saying a number like 15 isn't prime because 15 = 3*5, ie 15 can be factored into something that doesn't involve 1 as a factor.

In contrast, we consider 7 prime because even though 7 = 1*7, there aren't any other ways to write this integer as a factorization if we don't involve 1.

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Choice C is a similar story. This time we can factor out 3

3x^2 + 18y = 3(x^2 + 6y)

So we can rule this out as well.

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Choice D is a bit tricky, but we can use the difference of cubes factoring rule

a^3 - b^3 = (a-b)(a^2+ab+b^2)

where in this case a = x and b = 3y^2

Note how b^3 = (3y^2)^3 = 3^3*(y^2)^3 = 27y^(2*3) = 27y^6

All of this means choice D can be factored and it's not prime either.

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We've ruled out choices B through D. The answer must be choice A.

If you let w = x^2, then w^2 = x^4

The polynomial w^2+20w-100 is prime because setting it equal to zero and solving for w leads to irrational solutions. I'm assuming your teacher wants you to factor over the rational numbers.

Because w^2+20w-100 can't be factored over the rational numbers, neither can x^4+20x^2-100. This confirms that choice A is prime.

When a pair of parallel lines is intersected by a transversal, then

Interior opposite angles are equal.

So, (3x + 4)° = 115°

=> 3x + 4 = 115

=> 3x = 115 - 4

=> 3x = 111

=> x = 111/3

=> x = 37

Answer:

37

Step-by-step explanation:

So, if you got two parallel line, which are crossed by another line, the conterminal angles are gonna be as big as each other.

what we get outta this explanation is

3X+4=115===> 3X=111===> X=37

Answer:

The last one is the answer

Answer: For each hour that Michelle drove, she travelled an additional 50 miles.

Step-by-step explanation:

Test each option to see its accuracy

Calculate the slope:

[tex](x_{1}, y_{1}) = (7, 0)\\(x_{2}, y_{2}) = (0, 350)\\ \\\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{350-0}{0-7} =\frac{350}{-7} =-50[/tex]

This means that Michelle drove 50 miles per hour.

The other three options are wrong because if you bring in:

into your function- y = -50x + 350, you would not get the stated miles.

Answer:

B

Step-by-step explanation:

It is shifted 15 units up. Think of how you're solving for y, and by adding 15 to the equation, y increases by 15. If y increases by 15 the graph shifts up by 15. Hope that helps.

Given:

The dotted boundary line passes through the points (-3,-8), (1,-2) and (9,10).

Above line is shaded.

To find:

The inequality for the given graph.

Solution:

Consider any two points on the line. Let the two points are (1,-2) and (9,10). So, the equation of the line is:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-(-2)=\dfrac{10-(-2)}{9-1}(x-1)[/tex]

[tex]y+2=\dfrac{10+2}{8}(x-1)[/tex]

[tex]y+2=\dfrac{12}{8}(x-1)[/tex]

[tex]y+2=\dfrac{3}{2}(x-1)[/tex]

Multiply both sides by 2.

[tex]2(y+2)=3(x-1)[/tex]

[tex]2y+4=3x-3[/tex]

[tex]2y-3x=-3-4[/tex]

[tex]-3x+2y=-7[/tex]

Above line is shaded and the boundary line is a dotted line. So, the sign of inequality must be >.

[tex]-3x+2y>-7[/tex]

This inequality is not in the equations. So, multiply both sides by -1 and change the inequality sign.

[tex](-3x+2y)(-1)<-7(-1)[/tex]

[tex]3x-2y<7[/tex]

Therefore, the correct option is D.

Refer to the picture in the question for reference.

A statement-reason format is used to solve this problem. Statements are in normal print, reasons are bolded.

Statement                                                       Reason                                

1. AD = AE                                                        Given

  <B = <C

2. <A = <A                                                        Reflexive Property

3. ΔABE = ΔACD                                             Angle - Angle - Side

The given information refers to the information that is given with the problem.

The reflexive property states that if two polygons share a part (a side or an angle), then this part called in one of the polygons is congruent to itself in the other polygon.

Finally, the (angle-angle-side) congruence theorem states that if two triangles have two congruent angles and a congruent side between them, then the triangles as a whole are congruent to each other.

Answer:

slope= difference in y ÷difference in x

=y-y1÷x-x1

=-3-(-1)÷-3-1

=-3+1÷-3-1

=-2÷-4

=1/2

Step-by-step explanation:

hope this is helpful

Y2 -Y1 ÷ X2-X1

-1 - 1 ÷ -3 - -3= 0.5 or 1/2

9514 1404 393

Answer:

  -2/3

Step-by-step explanation:

  2^a = 0.5 = 2^-1   ⇒   a = -1

  5^b = 125 = 5^3   ⇒   b = 3

Then the expression a^b  +b^a is ...

  a^b +b^a = (-1)^3 +3^(-1) = -1 +1/3 = -2/3

Answer:

0.75

Step-by-step explanation:

Given the table :

Number of sodas 24

28

32

36

Total Cost ($)

18

21

24

27

The rate of change :

Rate of change = Rise / Run

Rise = y2 - y1 ; Run = x2 - x1

From the table :

Take number of sodas as X - axis

Total cost as Y - axis

Taking the points :

(24, 18) ;(36, 27)

x1 = 24 ; x2 = 36

y1 = 18 ; y2 = 27

Rise = (y2 - y1) = (27 - 18) = 9

Run = (x2 - x1) = (36 - 24) = 12

Rate of change = 9 / 12 = 0.75

Answer:

B. b = 3a + 2

Step-by-step explanation:

We can write the equation in slope-intercept form as b = ma + c, where,

m = slope/rate of change

c = y-intercept/initial value

✔️Find m using any two given pair of values, say (2, 8) and (4, 14):

Rate of change (m) = change in b/change in a

m = (14 - 8)/(4 - 2)

m = 6/2

m = 3

✔️Find c by substituting (a, b) = (2, 8) and m = 3 into b = ma + c. Thus:

8 = 3(2) + c

8 = 6 + c

8 - 6 = c

2 = c

c = 2

✔️Write the equation by substituting m = 3 and c = 2 into b = ma + c. Thus:

b = 3a + 2

Answer : - 4 + 3 = - 1

- 2 + 3 = 1

By half gives - 1/2 and 1/2

So midpoint (-1/2, 1/2)

Answer:

C the line that divides the design into two similar parts

The line of symmetry divides the design into two similar parts.

"The line of symmetry can be defined as the axis or imaginary line that passes through the center of the shape or object and divides it into identical halves. "

A line divides a design into two parts.

If the line is described as the line of symmetry, then the two parts that are divided by this line are similar parts.

Learn more about line of symmetry here: https://brainly.com/question/1389470

#SPJ2

Answer:

Step-by-step explanation:

We see a graph going down as x-value increases.

It is not increasing (line shod go up) or constant (horizontal) graph..

Correct choice is B

Answer:

The graph decreases everywhere.

Step-by-step explanation:

As we view the graph, in the x - axis from 0 to 9 the line has came down (decreased). So, we can say that the graph decreases everywhere.

Answer:

2x-y-1=0

Step-by-step explanation:

.

We have that

x - 3y = 12 and -x + y = 4

We add the 2 equations together

x - 3y + (-x + y) = 16

-> -2y = 16

-> y = -8 (1)

We plug y = -8 into -x + y =4

-> -x - 8 = 4

-> -x = 12

-> x = - 12 (2)

From (1) and (2) we could conclude that the answer is B

Answer:

12,-2

Step-by-step explanation:

Answer:

7:24 pm

Step-by-step explanation:

speed = distance/time

time * speed = distance

time = distance/speed

time = (195 miles)/(50 miles/hour)

time = 3.9 hours

The trip will take 3.9 hours.

3 hours + 0.9 hours = 3 hours + 0.9 hours * 60 minutes/hour =

= 3 hours + 54 minutes

The trip will take 3 hours and 54 minutes.

3:30 pm + 3:54 = 6:84 pm = 7:24 pm

Answer: 7:24 pm

Answer:

Triangle A is rotated 90° clockwise with the origin as the center of rotation to create a new figure. ... Triangle A is rotated 90° clockwise with the origin as the center of rotation to create a new figure.

Answer:

Triangle A is rotated 90° clockwise with the origin as the center of rotation to create a new figure. Which rule describes rotating 90° clockwise? Triangle A is rotated 90° clockwise with the origin as the center of rotation to create a new figure

Answer:

A

Step-by-step explanation:

A and B are the only answer choices that give you imaginary number outputs

But because the function in the answer choices is a negation of the original function they give different outputs, thus a different range

Therefore A is the correct answer

BRAINLIEST PLEASEEEEEEEE

Answer:

it is the first answer... has the same domain as  the function

Step-by-step explanation:

Answer:

Step-by-step explanation:

(3,9)

Answer:

m∠B =  

✔ 101

°

m∠C =  

✔ 79

°

m∠D =  

✔ 101

°

Step-by-step explanation:

Answer:

The answer above is right!

The correct answers are:

First box: option C. 101

Second box: option B. 79

Third box: option C. 101

Step-by-step explanation:

Just got it right on edge - Hope it helps :)

Brainliest would be greatly appreciated :D

Answer:

Domain = ( -∞ , ∞ )

Range = ( ∞ , ∞ )

Step-by-step explanation:

A function is given to us and we need to find the domain and range of the given function .

The function :-

[tex]\rm \implies y = \dfrac{1}{4}x - 6 [/tex]

Definitions :-

In this case, there is no real number that makes the expression undefined. Therefore the domain will be :-

Domain :-

[tex]\rm Domain = ( -\infty , \infty ) [/tex]

or

[tex]\rm Domain = \{ x | x \in \mathbb{R} \}[/tex]

Range :-

[tex]\rm Range = ( -\infty , \infty ) [/tex]

or

[tex]\rm Range = \{ y | y \in \mathbb{R}\} [/tex]

Answer:

Create a table or a graph of the function. The domain represents all input values and the range represents all output values. The domain and range contain all real numbers.

Step-by-step explanation:

Answer:

41

Step-by-step explanation:

Answer:

760

Step-by-step explanation:

25%= 190

100 = 25 × 4

100% (total number of people) = 190 × 4 = 760