piecewise functions. please help it’s for a test. please write the tables! i will give out brainliest!!

Answer:

A) f(t) = 4(t − 1)^2 + 3; the minimum height of the roller coaster is 3 meters from the ground

Step-by-step explanation:

f(t) = 4t^2 − 8t + 7

Factor out 4 from the first two terms

f(t) = 4(t^2 − 2t) + 7

Complete the square

(-2/2)^2 =1  But there is a 4 out front so we add 4 and then subtract 4 to balance

f(t) = 4( t^2 -2t+1) -4 +7

f(t) = 4( t-1)^2 +3

The vertex is (1,3)

This is the minimum since a>0

The minimun is y =3 and occurs at t =1

Answer:

The above answer is correct.

Step-by-step explanation:

These angles are corresponding angles, and we know that corresponding angles are equal when a transversal intersects two parallel lines.

So,

8x - 12 = 6x + 8

=> 8x - 6x = 8 + 12

=> 2x = 20

=> x = 20/2

=> x = 10

So, the value of x is 10.

please mark this answer as brainlist

Answer:

525 in³

Step-by-step explanation:

Use the direct variation equation, y = kx.

Substitute y with v (volume) and substitute x with l (length) to represent this situation:

y = kx

v = kl

Plug in 35 as l and 15 as k, then solve for v (the volume):

v = kl

v = 15(35)

v = 525

So, the volume of the box is 525 in³

9514 1404 393

Answer:

  138.77

Step-by-step explanation:

Your scientific or graphing calculator will have exponential functions for bases 10 and e. On the calculator shown in the first attachment, they are shifted (2nd) functions on the log and ln keys. Consult your calculator manual for the use of these functions.

The value can be found using Desmos, the Go.ogle calculator, or any spreadsheet by typing 10^2.1423 as input. (In a spreadsheet, that will need to be =10^2.1423.) The result using the Go.ogle calculator is shown in the second attachment.

You can also use the y^x key or the ^ key (shown to the left of the log key in the first attachment). Again, you would calculate 10^2.1423.

__

We have assumed your log is to the base 10. If it is base e (a natural logarithm), then you use the e^x key instead. Desmos, and most spreadsheets, will make use of the EXP( ) function for the purpose of computing e^( ). You can type e^2.1423 into the Go.ogle calculator.

_____

Additional comment

There are also printed logarithm tables available that you can use to look up the number whose log is 0.1423. You may have to do some interpolation of table values. You should get a value of 1.3877 as the antilog. The characteristic of 2 tells you this value is multiplied by 10^2 = 100 to get the final antilog value.

The logarithm 2.1423 has a "characteristic" (integer part) of 2, and a "mantissa" (fractional part) of 0.1423.

Answer:

With new regime is 183,750Rs

Step-by-step explanation:

I. 75,000 * 13 [12 months + 1 month bonus] = 975,000

II. Ms.Gurung tax rate will be ₹37500 + 15%

III. Perform ratio x/975,000 = 15/100 [15% is 15/100] = 146,250

IIII. ₹37500 + 146,250 = 183,750Rs

It depends on how tax rate will costs, could be more or less.

Answer

15x^4+2x^3+8x^2-15

Answer:

15^4+2^3−8^2−22−15

Step-by-step explanation:

(3^2−2−3)(5^2+4+5)

Distribute:

3(5^2+4+5) ⋅ ^2−2(5^2+4+5) − 3(5^2+4+5)

15^4+12^3+15^2 − 2(52+4+5) − 3(52+4+5)

15^4+12^3+15^2 − 10^3−8^2−10 − 3(52+4+5)

15^4+12^3+15^2 − 10^3−8^2−10 − 15^2−12−15

Combine like terms:

15^4+12^3−10^3+15^2−8^2−15^2−10−12−15

15^4+2^3+15^2−8^2−15^2−10−12−15

15^4+2^3−8^2−10−12−15

15^4+2^3−8^2−22−15

15^4+2^3−8^2−22−15

hope it helps :)

please mark brainliest!

Answer:

16p - 2

Step-by-step explanation:

Answer:

20p - 2

Step-by-step explanation:

To find a perimeter, you take the values of each side and add them together.

[tex](p-8)+(9p-7)+(p-8)+(9p-7)[/tex]

[tex]p+9p+9p+p-8+7-8+7[/tex]

[tex]20p-8+7-8+7[/tex]

[tex]20p-2[/tex]

Answer:

-86

Step-by-step explanation:

-102-

98 so the answer is -86

Answer:

could you explain your question better please

Making r the subject of formula, we have; [tex]r = \frac{V}{\pi h^{2} } \; + \;\frac{h}{3}[/tex]

In Mathematics, making a variable the subject of formula simply means making the particular variable to be equal to all the other variable contained in an algebraic expression or mathematical equation. Thus, the subject of a formula is typically on the left-hand side of a mathematical equation while the other variables on the right-side.

Given the mathematical expression;

[tex]V = \pi h^{2}(r \; - \;\frac{h}{3} )[/tex]

To make "r" subject of formula​;

First of all, we would divide both sides by [tex]\pi h^{2}[/tex]

[tex]\frac{V}{\pi h^{2} } = r \; - \;\frac{h}{3}[/tex]

Next, we would rearrange the equation;

[tex]r = \frac{V}{\pi h^{2} } \; + \;\frac{h}{3}[/tex]

For more on subject of formula visit: https://brainly.com/question/17148850

Answer:

75

Step-by-step explanation:

Answer:

Step-by-step explanation:

Supplementary angles add up to 180°.

The angle x, supplementary with 105°:

Answer:

Step-by-step explanation:

Use Pythagorean's Theorem:

[tex]c^2=15^2+8^2[/tex] and

[tex]c^2=225+64[/tex] and

[tex]c^2=289[/tex] so

c = 17

Answer:

lines 1 and 3

Step-by-step explanation:

y = 2 is a horizontal line parallel to the x- axis

x = - 4 is a vertical line parallel to the y- axis

Then these 2 lines are perpendicular to each other

y = 15x - 3 ( in the form y = mx + c ) with m = 15

y + 1 = - 5(x + 2) ( in the form y - b = m(x - a) with m = - 5

For the lines to be perpendicular the product of their slopes = - 1

However

15 × - 5 = - 75 ≠ - 1

The 2 lines 1 and 3 are perpendicular

Answer:

[tex]a = \frac{1}{2} \\ b = - 3 \\ c = - 2[/tex]

Step-by-step explanation:

The explanation is in the picture!

Answer:

x = 6

Step-by-step explanation:

s = 6

t = 4

x = 4 + s - t

Substituting s and t in equation,

x = 4 + 6 - 4

x = 6

Answer:

6

Step-by-step explanation:

s=6

t=4

x= 4+6-4

x=10-4

x=6

Therefore; the final result is 6

Answer:

sinΘ = opposite/ hypotenuse

sin (37)= CV/55

55 sin (37) = CV

CV=33.1

OAmalOHopeO

Step-by-step explanation:

the number in which 4 has the highest value is

6748.9251

Answer:

6834.2590

Step-by-step explanation:

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Answer:

Step-by-step explanation:

I discounted the 2-m ramp. If we are supposed to be looking for the length of time the ride is above 38 m from the ground, that translates to 36 m from the very bottom of the circle that is the Ferris wheel (where the wheel would meet the "ground"). I first found the circumference of the circle:

C = 48(3.1415) so

C = 150.792 m

I enclosed this circle (the Ferris wheel is a circle) in a square and then split the square in 4 parts. Each square has a quarter of the circle in it. If you divide the circumference by 4, that means that the arc length of each quarter circle is a length of 37.698 m. But that doesn't put us 36 m above the ground, that only puts us 24 m above the ground (remember the diameter of the circle is 48, so half of that is 24, the side length of each of the 4 squares). What that means to us (so far, and we are not at the answer yet) is that when the height off the ground is 24 m, a car that starts at the bottom of the ride has traveled 37.698 m around the circle. Traveling in an arc around the outside of the circle is NOT the same thing as a height off the ground. Going around a circle takes longer because of the curve. In other words, if the car has traveled 37.698 m around the outside of the circle, it is NOT 37.698 m above the ground...it's only 24 m above the ground. Hence, the reason I enclosed the circle in a square so we have both the circle's curve {arc length} and height above the ground {side of the square}). As the car travels farther along the outside of the circle it gets higher off the ground. If one quarter of the circle is 24 m above the ground, we need to figure out how much farther around the circle we need to go so we are 36 m above the ground. The height difference is 36 - 24 = 12m. we need now to find how long the arc length of the circle is that translates to another 12 m (the difference between the 24 we found and the 36 total). Using right triangle trig I found that arc length to be 12.566. The total arc length on the circle that translates to 36 m above the ground is 50.26437 m.

Going back to the beginning of the problem, the circumference of the circle is 150.792, and it makes one complete revolution in 5 minutes. That means that a car will travel 30.1584 m in 1 minute. Since this is the case, we can use proportions to solve for how long it takes to get 36 m above the ground:

[tex]\frac{m}{min}:\frac{30.1584m}{1min}=\frac{50.26437m}{xmin}[/tex] and cross multiply:

30.1584x = 50.26437 so

x = 1.6667 minutes, the time it takes to reach a height of 36 m. BUT this is not what the question is asking. The question is asking how long it's HIGHER than that 36 m. Let's think.

The car starts at the bottom of the ride, gets to a height of 36 m, keeps going around the circle to its max height of 48 m, then eventually comes back down and keeps going til it's back on the ground. That means that there is a portion at the top of the wheel that is above 36 m. If it goes 50.2647 m around the circle til it's at 36 m, then when it passes the max height and drops back to 36 m, it's 50.2647 m around the other side of the circle. We just found that to travel that 50.2647 m, it took the car 1.6667 minutes. We travel this distance twice (once meeting the height going up and then again coming down) so that takes up 3.3334 minutes.

5 minutes - 3.3334 minutes leaves us off 36 m above the ground for 1.6664213 minutes.

Answer:

[tex]x = - 8[/tex]

Step-by-step explanation:

First,Step write the given equation.

[tex] \frac{x}{2} + 7 = 3[/tex]

In Algebra, we learn how to solve for a missing term called a variable. We must use inverse operations to undo terms to isolate our variable. Inverse operations means that we do the opposite of the given.

For example, say we have a equation

[tex]x + 2 = 3[/tex]

We would subtract 2 from both sides. E.g( remember the golden rule of algebra). What we do to one side, we do the other. This applies when we solving for a variable.

This means that

[tex]x = 1[/tex]

And if we substitute 1 in for x, it is indeed true.

[tex]1 + 2 = 3 = 3[/tex]

Now, back to the question.

[tex] \frac{x}{2} + 7 = 3[/tex]

First, we subtract 7 from both sides to get rid of the 7 on the left side. Also remeber to undo terms that aren't included in the variable when solving these problems.

So now we got

[tex] \frac{x}{2} = - 4[/tex]

Then we multiply 2 by both sides since that the opposite of division.

[tex] \frac{x}{2} \times 2 = x = -4 \times 2 = - 8[/tex]

So this means that

[tex]x = - 8[/tex]

If we plug this in, this is true.

[tex] \frac{ - 8}{2} + 7 = 3[/tex]

Answer:

-24

Step-by-step explanation:

4(x+2−5x)

Combine like terms

4(2 -4x)

Distribute

8 -16x

Let x=2

8 - 16(2)

8 - 32

-24

how to evaluate 4(x+2−5x) when x=2

4(x + 2 - 5x)

Putting the value of x we get

4(2 + 2 - 5 × 2)

According to BODMAS multiplication comes first then addition

So 5 × 2 will be solved after that we will simplify 2 added with 2

4(2 + 2 - 10)

4(4 - 10)

4(-6)

- 24

Henceforth, the required answer is -24

Answer:

sqrt(3) + sqrt(7)

Step-by-step explanation:

3*sqrt(7) / sqrt(21) = 3/sqrt(3)

If you rationalize the denominator, you get 3*sqrt(3)/3. The threes cancel

You are left with sqrt(3)

7sqrt(3)/sqrt(21) = 7 / sqrt(7)

If you rationalize the denominator, you get

7  sqrt(7)/ 7 = sqrt(7)

The 7s have been canceled out

The answer is

sqrt(3) + sqrt(7)

Answer:

A

Step-by-step explanation:

the brigde means anything in between

Answer:

Q1 = 87 ;

Q2 = 102 ;

Q3 = 115 ;

IQR = 28

OUTLIER = None

Step-by-step explanation:

Given the data:

111, 68, 93, 88, 74, 152, 119, 87, 88, 105, 84, 102, 151, 115, 112

Ordered data : 68, 74, 84, 87, 88, 88, 93, 102, 105, 111, 112, 115, 119, 151, 152

Sample size, n = 15

The first quartile, Q1 = 1/4(n+1)th term

Q1 = 1/4(15+1)th term

Q1 = 1/4(16) = 4th term

Q1 = 87

The Median , Q2 = 1/2(n+1)th term

Q2 = 1/2(15+1)th term

Q2 = 1/2(16) = 8th term

Q2 = 102

The third quartile, Q3 = 3/4(n+1)th term

Q3 = 1/4(15+1)th term

Q3 = 3/4(16) = 12th term

Q3 = 115

The interquartile range, IQR = Q3 - Q1

IQR = (115 - 87) = 28

Q1 = 87 ;

Q2 = 102 ;

Q3 = 115 ;

IQR = 28

OUTLIER = None

Answer:

n = √108

Step-by-step explanation:

Use similar triangles or the right triangle altitude theorem.

18/n = n/6

n^2 = 18 * 6

n^2 = 108

n = √108

Answer:

B. 24 sqrt 10

Step-by-step explanation:

Hope this helped.

Answer:

11√5

Step-by-step explanation:

just putting the question with the symbols here so its easier to find for others

Which choice is equivalent to the expression below? 3√5+8√5

A. 24√5
B. 24√10
C. 11√10
D. 11√5