A ball is thrown upward in the air. The height h, in feet, of the ball t seconds
after being thrown can be determined by the equation
h=-16t² + 40t + 4
How long does it take for the ball to hit the ground? Round to one decimal
place.

Check the picture below.

so hmmm if Lydia is correct, then there's one angle in the triangle that is 90°, hmmm well, looking at the picture, we can pretty much forget about angle Z or Y, they're both acute, hmm how about angle X? is it 90°?

well, if angle X is indeed a right-angle, the lines XZ and XY are perpendicular, but are they?  if that's so then the slopes of XZ and XY are  negative reciprocal of each other, let's check

[tex]X(\stackrel{x_1}{0}~,~\stackrel{y_1}{-4})\qquad Z(\stackrel{x_2}{2}~,~\stackrel{y_2}{-6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-6}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{0}}} \implies \cfrac{-6 +4}{2 +0}\implies -1[/tex]

now, the negative reciprocal of that will be

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{-1\implies \cfrac{-1}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-1}\implies 1}}[/tex]

well, let's see if XY has a slope is 1 then

[tex]X(\stackrel{x_1}{0}~,~\stackrel{y_1}{-4})\qquad Y(\stackrel{x_2}{2}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{0}}} \implies \cfrac{-3 +4}{2 +0}\implies \cfrac{1}{2}[/tex]

OMG!!! Lydia needs to go get a nice Latte with cinnamon and to recheck her triangle.

Answer:

2

Step-by-step explanation:

[tex]~~~~~~15=6y+5-8y\\\\\implies 15-5=-2y\\\\\implies 10 = -2y\\\\\implies -\dfrac{10}2 = y\\\\\implies -5 = y\\\\\implies y = -5[/tex]

Answer:

y=−5

Step-by-step explanation:

15=6y+5−8y

⟹15−5=−2y

⟹10=−2y

⟹−210=y

⟹−5=y

⟹y=−5

Answer:

Yes

Step-by-step explanation:

At the age of 22 Alex will have twice the age of His brother who is 11 years old

Answer:

8

Step-by-step explanation:

Answer:  [tex]-6\sqrt{2}+2\sqrt{3}-\sqrt{6}+9[/tex]

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

Explanation

Let:

[tex]x = \sqrt{2}\\\\y = \sqrt{6}-\sqrt{3}\\\\[/tex]

We can then say:

[tex](\sqrt{2}-\sqrt{3}+\sqrt{6})(\sqrt{6}-\sqrt{3})\\\\(\sqrt{2}+\sqrt{6}-\sqrt{3})(\sqrt{6}-\sqrt{3})\\\\(x+y)(y)\\\\xy+y^2\\\\2\sqrt{3}-\sqrt{6}+9-6\sqrt{2}\\\\-6\sqrt{2}+2\sqrt{3}-\sqrt{6}+9\\\\[/tex]

Check out the screenshot below for the scratch work on how I computed the [tex]xy[/tex] and [tex]y^2[/tex] terms.

A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. The integer values that satisfy the given diagram are 0, 1, 2, and, 3.

A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. It’s not a ruler, so the space between each number doesn’t matter, but the numbers included on the line determine how it’s meant to be used.

Given a solid dot at 3, while an open dot at -1, also, there is a line from -1 to 3. Therefore, the integer values that satisfy the given diagram are 0, 1, 2, and, 3.

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Considering the area of the hole, it is found that there is a 4.9% probability of hitting a ball into the circular hole.

The area of a circle of radius r is given by:

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

In this problem, the hole has a diameter of 1 ft, hence it is radius is of r = 1 ft/2 = 0.5 ft, and it's area is given by:

[tex]A = \pi \times (0.5)^2 = 0.7854 \text{ft}^2[/tex]

Hence the probability is given by:

p = 0.7854/16 = 0.049 = 4.9%

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Answer:

[tex]8 \times(2+15)[/tex]

Step-by-step explanation:

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to write "8 times the sum of 2 and 15" as an algebraic expression.

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

So, we add 2 and 15:

[tex]\mathtt{2+15}[/tex]

Now we multiply 8 times this expression:

[tex]\mathtt{8\times(2+15)}[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

#StudyWithBrainly

~Just a smiley person helping fellow students :)

Answer:

y=3x+5

Step-by-step explanation:

See attached image

Answer:

D.) y = 3x + 5

Step-by-step explanation:

The general structure for an equation in slope-intercept form is:

y = mx + b

In this form, "m" is the slope and "b" is the y-intercept.

To convert the given equation into slope-intercept form, you need to do some expanding and rearranging.

y - 2 = 3(x + 1)                       <----- Given equation

y - 2 = 3x + 3                        <----- Multiply 3 by every term in the parentheses

y = 3x + 5                            <----- Add 2 to both sides

Volume is a three-dimensional scalar quantity. The expression that could also be used to determine the volume of this prism is 11(9)(4).

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

The volume of a right rectangular prism can be found by using the product of 9(4)(11). The expression that could also be used to determine the volume of this prism is 11(9)(4).

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Answer:

11(9)(4)

Step-by-step explanation:

Hope this helps!!!!

Answer:

3:36PM

Step-by-step explanation:

Leon starts at 12PM with 12 gallons of gas, and after 2 hours he has used 5 gallons of gas. This means that every 2 hours he uses 5 gallons of gas.

Next we will find at what point Leon will stop to get gas. Since he will stop when the tank is at [tex]\frac{1}{4}[/tex] capacity, we can use the equation:

[tex]\frac{1}{4} * 12 = \boxed{3}[/tex]

This shows [tex]\frac{1}{4}[/tex] of his tank's capacity ([tex]12[/tex]) is equal to [tex]3[/tex] gallons. This means he will stop for gas when [tex]3[/tex] gallons are remaining.

Now we need to find how many gallons of gas he uses, but as a unit rate. (This will allow us to find what time Leon will stop to get gas.) To find the unit rate, we will need to find how many gallons of gas he uses per hour.

[tex]\frac{\mbox{5 gallons}}{\mbox{2 hours}} = \frac{\mbox{2.5 gallons}}{\mbox{1 hours}}[/tex]

This is a simple proportion, and now we know he uses [tex]2.5[/tex] gallons of gas per hour.

Now we can how many hours of gas Leon has left.

He has [tex]7[/tex] gallons of gas left at 2PM, so we can divide to find how many hours left of gas he has.

[tex]\frac{7-3}{2.5} = 1.6[/tex]

The [tex]7-3[/tex] is because Leon doesn't stop when his tank is empty, he stops [tex]3[/tex] gallons earlier. We are dividing by [tex]2.5[/tex] because that is how much gas he uses per hour, meaning the result of this division ([tex]1.6[/tex]) is how many hours he has left.

Now we can solve for what time Leon will stop to get gas.

12PM + [tex]2[/tex] hours of driving + the remaining [tex]1.6[/tex] hours = 3:36PM

([tex]1.6[/tex] hours is equal to 1 hour and 36 minutes)

Therefore, Leon will stop for gas at 3:36PM

In the given image, [tex]a_{23}[/tex] is 5. The correct option is the first option 5

From the question, we are to determine which entry in the given matrix represents [tex]a_{23}[/tex]

NOTE: For any entry denoted as [tex]a_{mn}[/tex], it represents the entry in the m-th row and n-th column.

Thus,  

 [tex]a_{23}[/tex] represents the entry in the 2nd row and 3rd column.

In the given image, the entry in the 2nd row and 3rd column is 5.

Hence, in the given image, [tex]a_{23}[/tex] is 5. The correct option is the first option 5

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Answer:

3/16 of the whole pie

Step-by-step explanation:

Lexi had 3/4 of an apple pie. She gave 1/4 of it to Julie. That means what Julie receives is the product of the whole and the portion.

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

Solving :

Therefore, the equation is :

⇒ 3/4 × 1/4

⇒ 3/16 of the whole pie

Answer:

16

Step-by-step explanation:

the range is the amount of numbers between the highest and lowest number in a set.  if the lowest number is 3, and the range is thirteen, and the number must be a positice, the highest number in the range is 16.

A function assigns the value of each element of one set to the other specific element of another set. The correct option is D.

A function assigns the value of each element of one set to the other specific element of another set.

The time at which the ball will hit the ground is,

h(t) = −16t² + 10t + 6

0 = -16t² + 10t + 6

8t² - 8t + 3t - 3= 0

8t(t-1)+3(t-1) = 0

(8t+3)(t-1)=0

t = -0.375, 1

Hence, the ball hit the ground at 1 second, while the function in intercept form can be written as h(t) = (−8t − 3)(2t − 2).

Thus, the correct option is D.

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Answer:

The answer above is correct, a teacher confirmed it, and the quiz marked it as correct.

Step-by-step explanation:

Answer:

both

Step-by-step explanation:

that's the answer to the question

Answer:

-x²-2

Step-by-step explanation:

x² = the curve faces upwards

but

-x² the curve faces downwards.

also

the downward curve touches -2 on the y axis.

therefore gx = -x²-2

Answer:

8 cubic cm

Step-by-step explanation:

6 * ( L square ) = 24

L= 2

then

v= l cube

= 2*2*2

=8

Answer:

9

Step-by-step explanation:

Answer:

4 large folders     ( and 8 small folders....with $ 1 left over)

Step-by-step explanation:

x = small    y = large folders

x+y >= 12      x >= 12-y

3x + 5y <= 45

3 (12-y) + 5y <=45

36 -3y + 5y <= 45

    y <= 4.5               you cannot buy .5 of a large folder, so 4 large folders

A beam measuring 2 meters can support 172 kilograms

The variation is a direct variation.

So, we have:

w = kl

Where k is the constant of variation.

When l = 5, w = 430.

This means that:

430 = 5k

Divide both sides by 5

k = 86

So, we have:

w = 86l

When l = 2, we have:

w = 86 * 2

Evaluate

w = 172

Hence, a beam measuring 2 meters can support 172 kilograms

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Answer:

Step-by-step explanation:

1) Angle 1 and angle 2 are complementary angles. If angle 1 measures (3x + 2), what is the measure of angle 2? 3x+2 + y = 90

2) Angle A and angle b are supplementary angles. Angle A measures (2m – 10) degrees and angle b measures (m + 25) degrees. Find the measure of angle A and angle b.

3) Three angles are supplementary angles. If one angle measures 25 degrees, the second angle measures m + 15. The third angle measures 2m degrees. What is the value of m?

Answer:

No answer. There is no table. The answer for it is probably the frequency which is 8 for the 6 values of dice.

Step-by-step explanation:

50/6 = 8.33333....

So for the numbers 1,2,3,4,5,6 it is 8 times.

which means each number will have the frequency of 8.

This is the most answer that I could get. Since, there was no picture to support this answer. DO NOT PUT THIS AS YOUR REAL ANSWER BECAUSE IT MAY BE WRONG.

Problem 1

Ignore the smaller circle for now. We'll be focusing on the portion on the right.

It's a partial circle with central angle theta = 150 degrees and radius r = 24 inches. The 24 inches also happens to be the slant height of the cone when we form the 3D figure.

Let's compute the arc length based on those inputs.

L = arc length

L = (theta/360)*2*pi*r

L = (150/360)*2*pi*24

L = 20pi

This is the distance along the green curve of this portion.

Now imagine we rolled up that partial circle on the right. We'd form the curved slanted roof of the cone. The green curve wraps around to help match up with the circular base. The 20pi calculated earlier is the circumference of this circular base. Use this to find r.

C = 2pi*r

20pi = 2pi*r

r = (20pi)/(2pi)

r = 10

-------------------------

So far we found that this cone has:

Now compute the height (h) perpendicular to the base

[tex]h^2+r^2 = s^2\\\\h = \sqrt{s^2-r^2}\\\\h = \sqrt{24^2-10^2}\\\\h = \sqrt{476}[/tex]

-------------------------

We can now compute the volume

[tex]V = (1/3)*\pi*r^2*h\\\\V = (1/3)*\pi*10^2\sqrt{476}\\\\V \approx 2284.7153\\\\[/tex]

The units of which are cubic inches.

The surface area is of this cone is:

[tex]SA = \pi*r*s + \pi*r^2\\\\SA = \pi*10*24 + \pi*10^2\\\\SA \approx 1068.1415\\\\[/tex]

The units are in square inches.

For each case, I used the calculator's stored value of pi to get the most accuracy possible. Round the decimal values however you need to, or however your teacher instructs.

-------------------------

Answers:

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

Problem 2

Use the pythagorean theorem to find the slant height

[tex]h^2+r^2 = s^2\\\\s = \sqrt{h^2+r^2}\\\\s = \sqrt{15^2+8^2}\\\\s = \sqrt{289}\\\\s = 17\\\\[/tex]

This slant height will act as the radius of the partial circle that results when forming the net of the unrolled cone.

The process used in the previous problem was to use the slant height and central angle to find the circumference of the base.

We'll follow that process in reverse to use the circumference and slant height to find the central angle.

But first, we need to find the circumference of the base.

C = 2*pi*r

C = 2*pi*8

C = 16pi

This is the arc length similar to the green arc shown in the previous problem (the figure on the right side of that diagram)

This means we'll plug in L = 16pi and r = 17 (not to be confused with the previous radius of 8 inches) to determine theta

L = (theta/360)*2*pi*r

16pi = (theta/360)*2*pi*17

16pi = theta*(34pi/360)

theta = 16pi*(360/(34pi))

theta = 169.4118 degrees approximately

This is the central angle of the unrolled net. The diagram is basically the same as the previous drawing, where we have a circle on the left to represent the base of the cone. The other portion forms the roof of the cone.

-------------------------

Let's compute the volume (V) and surface area (SA)

[tex]V = (1/3)*\pi*r^2*h\\\\V = (1/3)*\pi*8^2*15\\\\V \approx 1005.3096\\\\[/tex]

and,

[tex]SA = \pi*r*s + \pi*r^2\\\\SA = \pi*8*17 + \pi*8^2\\\\SA \approx 628.3185[/tex]

-------------------------

Answers:

Answer:

20 is.the net force act in object

Answer:

  (b)  $6,769

Step-by-step explanation:

The value in the account can be found by using the compound interest formula:

  A = P(1 +r/n)^(nt)

where P is the principal invested, r is the annual rate, n is the number of times per year interest is compounded, and t is the number of years.

__

Using the given values in the formula, we have ...

  P = 5600, r = 0.019, n = 4, t = 10

  A = 5600(1 +0.019/4)^(4·10) = 5600×1.00475^40 ≈ 6768.752

The amount in the account at the end of 10 years was about $6,769.

_____

Additional comment

Any number of spreadsheets, calculators, or apps can find the future value (FV) for you. The attachment shows the use of a TI-84 calculator work-alike.

The attached image represents the interval 2 < x ≤ 9 on the number line

The interval is given as:

2 < x ≤ 9

The above interval means that:

In inequality, the < symbol uses an open circle, while the ≤ uses a closed circle

Next, we highlight the interval using the above rules (see attachment)

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Answer

100

Step-by-step explanation:

bxh is the formula for area of the triangle (base_

so 5x4=20

20x5 (height) = 100

Answer:

80 cm

Step-by-step explanation:

formula

b x h x .5

b= the area of the base