A driver runs over a nail, puncturing the tire without causing a leak. The position of the nail in the tire, with relation to the ground, while the car is moving at a constant speed is shown in the table.
Time (s) Approximate height of the nail off the ground (inches)
0 0
0.01 2.1
0.02 7.6
0.03 14.9
0.04 21.5
0.05 25.5
0.06 25.5
0.07 21.5

Which key features of the function representing the nail’s travel can be used to determine the amount of time it takes for the nail to reach the same orientation it had when it entered the tire?

A. period
B. minimum
C. maximum
D. amplitude

Lines that are parrellell presume to have the same slope.

So if we just calculate the slope of a function or a line we should be good.

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

Now put in the data from the coordinates of the points [tex]A(3,-1)\wedge B(1,7)[/tex]

[tex]s=\dfrac{7-(-1)}{1-3}=\dfrac{8}{-2}=\underline{-4}[/tex]

The form of a function now looks like: [tex]

f(x)\vee y=-4x+n[/tex]

From here we are no longer required to calculate anything more. Leave n alone.

The solutions are the equations of the form above.

That would mean:

[tex]

y=-4x \\

y=-4x+8 \\

y+1=-4(x+1) \\

y-6=-4(x-3)

[/tex]

Hope this helps.

Answer:

-6x - 6x² + 2x³

Step-by-step explanation:

Match each like-term to end up with the above answer.

I hope this helps.

Answer:

W+100=M

Explanation:

So the problem says there will always be 100 more men than woman. So that would mean you just have to add the amount of women and 100 to find the number of men. For example, if there are 3 women, there will be 103 men.

Hope this helps ;)

Certainly! To create an algebraic equation representing the given situation, we can use the information that there are 100 more men than women at the school.

Let's use the variables:
- \( W \) to represent the number of women
- \( M \) to represent the number of men

The key piece of information that we have is that the number of men is 100 more than the number of women. We can write this relationship with an equation:

\[ M = W + 100 \]

This equation states that if you take the number of women (\( W \)) and add 100 to it, you will get the number of men (\( M \)). It directly translates the information given into an algebraic equation, showing the relationship between the number of women and the number of men in the school.

Answer:

The answer would be 18.

Step-by-step explanation

If 20% of a number is 12, then 30% of that same number would be 18. This means that the number would be 60 (6×2=12, 6×3=18). Hope this helps you to understand your math problem better!

Answer:

D

Step-by-step explanation:

by definition, the square root of an negative number is known as an imaginary number. i.e Not a real number

[tex]\sqrt{-2}[/tex] = [tex]\sqrt{2}[/tex][tex]\sqrt{-1}[/tex] = [tex]\sqrt{2}[/tex]i (imaginary number)

The [tex]\sqrt{-2}[/tex] is not a real number.

The following information should be considered with respect to the real number:

Therefore, the first three options are considered to be the real number.

Thus we can conclude that the [tex]\sqrt{-2}[/tex] is not a real number.

Learn more: brainly.com/question/17429689

Answer: 4 feet and 2 feet

Step-by-step explanation: The only factor of 8 that is an even integer is 4 and 2. So the answer is 4 feet and 2 feet.

Answer:

Step-by-step explanation:

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have the points (12, 6) and (12, -9). Substitute:

[tex]d=\sqrt{(12-12)^2+(-9-6)^2}=\sqrt{0^2+(-15)^2}=\sqrt{225}=15[/tex]

[tex]\text{Hey there!}[/tex]

[tex]\text{The formula is:}\bf{\frac{y_2-y_1}{x_2-x_1}}[/tex] [tex]\text{ or you can say}\rightarrow[/tex] [tex]\frac{Rise}{Run}[/tex]

[tex]\text{y}_2=-9\\\\\text{y}_1=6\\\\\text{x}_2=12\\\\\text{x}_1=12[/tex]

[tex]\text{Now, that we know what our points are we could solve this equation}[/tex]

[tex]\frac{-9-6}{12-12}[/tex]

[tex]\text{-9 - 6 = -15}[/tex]

[tex]\text{12 - 12 = 0}[/tex]

[tex]\bf{= \ \frac{-15}{0}}[/tex]

[tex]\boxed{\boxed{\bf{Answer: \ \frac{-15}{0}}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

$8.40

Step-by-step explanation:

To find the unit rate, take the total cost and divide by the number of times that you went

84/10

8.4

The unit rate (or cost per visit) is $8.40

Answer:

2/5 and 8/9  (answers can vary)

Step-by-step explanation:

The lcm of 5 and 9 is 45 so that works for our denominators.

So 2/5 and 8/9 (the answers are many)

Answer:

1/45 and 8/90

Step-by-step explanation:

Between these two fractions, the lowest shared denominator is 45.

Answer:

Length=87 ft

Width=77 ft

Step-by-step explanation:

Let

L ----> the length of rectangular movie screen

W ----> the width of rectangular movie screen

we know that

The area is equal to

[tex]A=LW[/tex]

[tex]A=6,699\ ft^{2}[/tex]

so

[tex]6,699=LW[/tex] ----> equation A

[tex]L=W+10[/tex] ----> equation B

substitute equation B in equation A

[tex]6,699=(W+10)W\\ \\W^{2} +10W-6,699=0[/tex]

Solve the quadratic equation by graphing

The solution is [tex]W=77\ ft[/tex]

see the attached figure

Find the value of L

[tex]L=77+10=87\ ft[/tex]

Answer:

14 dish soaps

Step-by-step explanation:

Johnny has 19 bottles of dish soap and he gives 5 to Jeina

19 - 5 = 14

Answer:

14

Step-by-step explanation:

Johnny has 19 bottles of dish soap and he gives 5 to Jeina  

19 - 5 = 14

Answer:

20% decrease.

Step-by-step explanation:

difference over original

50.97-40.78= 10.19

diff/orig=sales tax

10.19 / 50.97= 19.99..

19.99 is approximately 20.

Answer:

[tex]\large\boxed{x<-3\ or\ x>6}[/tex]

Step-by-step explanation:

[tex]x+7<4\qquad\text{subtract 7 from both sides}\\\\x+7-7<4-7\\\\x<-3\\\\7-x<1\qquad\text{subtract 7 from both sides}\\\\7-7-x<1-7\\\\-x<-6\qquad\text{change the signs}\\\\x>6[/tex]

Step-by-step explanation:

all work is pictured and shown

Answer:

Yes, they are.

Step-by-step explanation:

Remember that a triangle is only a right triangle if its sides meet this mathematical requirement:

(leg)² + (leg)² = (hypotenuse)²

The hypotenuse of a right triangle is the longest side, while the legs are the two shorter sides. We can't say exactly where √34 is, but since √25 = 5 and √36 = 6, we know it must be at least bigger than 5, making it the triangle's longest side.

Using √34 as the "hypotenuse" and 3 and 5 as the "legs" of our triangle makes the equation 3² + 5² = (√34)², and simplifying gets us

9 + 25 = 34

34 = 34

The requirement's been met, so yes, this is a right triangle.

Answer:

[8, inifinity sign)

Step-by-step explanation:

(2)/1 x -1/2 (greater than or equal to sign) 4(2), You need to get rid of the fraction so times 2 on both sides.

So the fraction cancels out and your answer is x (greater than or equal to) 8

The open side of the sign always is facing the bigger number so like this > so x is positive.

Since i can't show the number line i'll try to explain it if it's a greater than sign its a closed dot on the 8 going right. The 8 is in a bracket and the infinity is with a parenthesis. like this [8, infinity sign)

My teacher may have taught me different but it should be about the same.

Hope my answer has helped you and if not i'm sorry.

Answer:

So there are 35 quarters and 21 nickels.

Step-by-step explanation:

So I guess that is all we have is quarters and nickels.

Quarters are worth .25

Nickels are worth .05

Let x represent the number of quarters

Let y represent the number of nickels

x+y=56

.25x+.05y=9.8

We are going to solve this system.

I'm going to use substitution. I will solve the first equation for y and then plug that into the second equation.

y=56-x  

.25x+.05(56-x)=9.8

.25x+2.8-.05x=9.8

.20x+2.8=9.8

.2x          = 7

 x=7/(.2) or 7*5=35

y=56-x

y=56-35=21

So there are 35 quarters and 21 nickels.

Answer:

A) n + q = 56

B) .05n + .25q = 9.80

We multiply A) by -.25

A) -.25n -.25q = -14  then add it to equation B)

B) .05n + .25q = 9.80

-.2n = -4.20

nickels = 4.20 / .20 = 21

quarters = 35

Step-by-step explanation:

Answer:

C. 4 root 2

Step-by-step explanation:

Total amount of angles = 45° + 45° = 90°

sin90 * 4 root 2 = 5.656854

Answer:

4

Step-by-step explanation:

You will either use cos or sin solve this problem

1. set up the problem like this

x/sin 45   x     4 root 2/sin 90

2. cross multiply (it will be useful to use calculator or if you know unit circle then you're good)

sin 90 = 1 and sin 45 = .7071067812 (don't really need to know this)

1x = (sin 45 x 4 root 2)

3. Solve for x like normal

1x = 4

1x/1 = 4/1

x = 4

Answer: 2x^3+4x+4 would be the answer.

Step-by-step explanation: x^2 can only be combines with another variable with the same exponent. Then you just multiply the whole equation by 2. Hope this helps!

Answer:

poooooooooooooooooop

Step-by-step explanation:

Answer:

200.96 inch²

Step-by-step explanation:

formula for a circle: (pi) x r²

pi= 3.14

3.14 x 8²

=200.96 inch²

For this case we have by definition, that the area of a circle is given by:

[tex]A = \pi * r ^ 2[/tex]

Where:

A: It is the radius of the circle

They tell us as data that the radius is 8 inches.

Substituting we have:

[tex]A = \pi * (8) ^ 2\\A = \pi * 64\\A = (3.14) (64)\\A = 200.96[/tex]

Thus, the area of the circle is [tex]200.96 \ in ^ 2[/tex]

Answer:

[tex]200.96 \ in ^ 2[/tex]

To find the equation of a line perpendicular to 5x - 2y = -6 and passing through (5, -4), first determine the slope of the given line and then find the negative reciprocal of that slope. Using point-slope form with the new slope and the given point, the equation is y = - (2/5)x - 2.

To find the equation of the line that is perpendicular to the given line 5x - 2y = -6 and passes through the point (5, -4), follow these steps:

Step 1: Find the slope of the given line

Rewrite the given line in slope-intercept form (y = mx + b):

5x - 2y = -6
-2y = -5x - 6
y = (5/2)x + 3

The slope (m) of the given line is 5/2.

Step 2: Find the slope of the perpendicular line

The slope of the line perpendicular to another is the negative reciprocal. Thus, the slope of the perpendicular line is -2/5.

Step 3: Use the point-slope form

Using the point (5, -4) and the slope -2/5 in the point-slope form (y - y1 = m(x - x1)):

y - (-4) = - (2/5)(x - 5)
y + 4 = - (2/5)x + 2
y = - (2/5)x - 2

Therefore, the equation of the line that is perpendicular to 5x - 2y = -6 and passes through the point (5, -4) is y = - (2/5)x - 2.

Answer:

That would be B.  Graph A.

Step-by-step explanation:

The  graph y < 2x - 1 is a dotted line which rises to the right with  a slope of 2 and passes through y = -1  and is shaded below the line. The graph y > -2 x +  2 rises to the left and passes through y = 2 and is shaded above the line.

Answer:

He is not correct because he made a sign error.

Step-by-step explanation:

-2 |8-x| - 6 = -12

-2 |8-x| = -12 + 6

-2 |8-x| = - 6

2 |8-x| = 6

|8-x| = 3

2 possible solutions:

8-x = 3 ----> x = 5

or

8-x = -3  ----> x = 11

Comparing the answer choices, we can see that Johan got the sign of x = 11 wrong.

Hence the correct answer is:

He is not correct because he made a sign error.

Answer: Just did it on ed, answer is "He is not correct because he made a sign error."

Step-by-step explanation:

Answer:

The height of the cylinder is 4x units

Step-by-step explanation:

see the attached document

Answer:

The answer is 1,3, and 6 Hope this helps

Step-by-step explanation:

Answer:

5.2% increase

Step-by-step explanation:

In 2015 the total population was 750.

In 2016 the total population was 17% more than in 2015, so 750 x 1.17 = 877.

In 2017 the total population was 10% less than in 2016, so 877 x 0.9 = 789.

Compared to 2015, the population in 2017 was 789/750 = 1.052 or 5.2% greater.

In one step:

((750 x 1.17) x 0.9) / 750 = 5.2%

In this question, we're going to need to find the population in 2017, while using the given information.

Lets gather the information we should know from the question.

Key information:

2015 -- Population of 750

Increased by 17% in the next year

Decreased by 10% the next year

With the information above, we can solve the problem.

We know that our starting population for crickets is 750, and it increases by 17% for the next year (2016), so we would multiply 750 by 1.17

[tex]750*1.17=877.5[/tex]

Our population in 2016 is 877.5.

Now, we know that he population in 2016 decreased by 10% going into 2017. We would need to find how much of 877.5 is 10%, and then subtract.

[tex]877.5*.10=87.75\\\\877.5-87.75=789.75[/tex]

When you're done solving, you should get 789.75

This means that the population of crickets in 2017 is 789.75.

Now, we know that we started with 750 crickets, now we have 789.5 crickets.

We would divide 789.5 by 750.

[tex]789.5\div750=1.053[/tex]

We would move the decimal place two times to the right, giving us 5.3.

This means that the population increased by 5.3% from 2015 to 2017.

Answer:

[tex]GT=10\ units[/tex]  and [tex]TA=6\ units[/tex]

Step-by-step explanation:

we know that

In the diagram

Triangles GRT and GEA are similar by AA Similarity Postulate

Remember that

If two figures are similar, then the ratio of its corresponding sides is proportional

so

[tex]\frac{GR}{GE}=\frac{GT}{GA}[/tex]

we have

[tex]GR=5\ units[/tex]

[tex]GE=5+3=8\ units[/tex]

[tex]GT=16-x\ units[/tex]

[tex]GA=16\ units[/tex]

substitute

[tex]\frac{5}{8}=\frac{16-x}{16}\\ \\5*16=8*(16-x)\\ \\80=128-8x\\ \\8x=128-80\\ \\x=48/8\\ \\x=6\ units[/tex]

therefore

[tex]GT=16-x=16-6=10\ units[/tex]

[tex]TA=x=6\ units[/tex]

Answer:

Step-by-step explanation:

Take home pay = 10*h + 50       I assume the 50 is a flat rate.

Savings = 1/10 of the take home pay.

Savings = (10*h + 50)/10

Answer:

(5e)^4

Step-by-step explanation:

Step-by-step explanation:

to add or subtract in this case you have to the same common denominator. but what ever you do to the denominator you have to do to the numerator. top = numerator and bottom = denominator.

Answer:

[tex]-x+19/6[/tex]

Step-by-step explanation: