The trampoline is 10 units off the ground.
The maximum height of the acrobat is 18 units, and it takes 1 second to reach this height.
We have,
To find the height of the trampoline off the ground, we need to determine the value of f(x) when x is equal to zero.
This is because at the moment the acrobat jumps (x=0), the height of the acrobat is the height of the trampoline.
Given the function f(x) = -8x² + 16x + 10, we substitute x=0 into the function:
f(0) = -8(0)² + 16(0) + 10
f(0) = 0 + 0 + 10
f(0) = 10
Now,
To find the maximum height of the acrobat and the time it takes to reach this height, we can observe that the function f(x) is in the form of a quadratic equation in the form of ax² + bx + c, where a = -8, b = 16, and c = 10.
The maximum height of the acrobat occurs at the vertex of the quadratic function.
The x-coordinate of the vertex is given by:
x = -b / (2a)
Substituting the values, we have:
x = -16 / (2 * -8)
x = -16 / -16
x = 1
The time it takes to reach the maximum height is 1 second.
To find the maximum height, substitute the value of x back into the function:
f(1) = -8(1)² + 16(1) + 10
f(1) = -8 + 16 + 10
f(1) = 18
Therefore,
The trampoline is 10 units off the ground.
The maximum height of the acrobat is 18 units, and it takes 1 second to reach this height.
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Answer the question below
Answer:
d
Step-by-step explanation:
What is the slope of this line?
PLEASE HELP 22 POINTS!
Select the correct answer.
f(x) and g(x) are inverse functions. What is g(f(-4)) equal to?
A.
4
B.
-4
C.
x
D.
1
E.
-1
Answer:
The answer is B -4
Step-by-step explanation:
An inverse function is a function that will “undo” anything that the original function does. For example, if a function takes a to b, then the inverse must take b to a.
Answer:
-4
Step-by-step explanation:
The inverse of a function and the function counteract each other. The are opposites. It is like adding and subtracting the same thing. You end up where you started
Since f(x) and g(x) are inverses
f(g(x) = x
g(f(-4)) = -4
What is the base of the expression 9 Superscript 12? 3 9 12 21
Answer:
9
....................
Answer:
9
Step-by-step explanation:
heeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
A 25ft ladder is leaning up against a
wall. If the ladder makes a 63° with
the ground, how far is the base of the
ladder from the wall?
Step-by-step explanation:
A
C H
Cos(23)×25 = 23.0126
The distance of the base of the ladder from the wall is 23.01 ft
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
We are solving from how far the base of the ladder from the wall and we are representing it as x.
Based on the type of triangle, we are going to use Trigonometry ratios.
We are going to use the cos ratio.
Let opposite be x, base be 25 and theta (angle) be 23.
Cos(23) = x/ 25
Make x the subject;
x = Cos(23)×25
x = 23.0126 ft
Therefore the distance is 23.01 ft
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Help help plizzzzz!!! Due today!!!!
Answer:
FIll in the first box comepletely, and the first line of the second box.
Step-by-step explanation:
5/4 is 1 1/4, so it's one whole, and one fourth of a whole. Hope this helps!
Answer:
20/4
Step-by-step explanation:
Multiply diagonally
[tex]\frac{5}{4} = \frac{1}{4}= \frac{20}{4}[/tex]
That's how I learned it others might do it a different way but I hope this helps Good luck.
please help asappp!!! i need serious help with this pleaseee. whoever finishes it first and completes it and show how you got it will get brainliest.
Answer:
Think of even square roots close to 27: the closest is 25 which has a square root of 5. Now think of the number with an even square root after 25: 36 which has a square root of 6. Since 27 is between 25 and 36, the square root of 27 would be between 5 and 6.
Evaluate
b−(−18)+cb-\left(-\dfrac{1}{8}\right)+c
b−(−
8
1
)+c
b, minus, left parenthesis, minus, start fraction, 1, divided by, 8, end fraction, right parenthesis, plus, c
where
b=2b = 2
b=2
b, equals, 2
and
c=−74c = -\dfrac{7}{4}
c=−
4
7
c, equals, minus, start fraction, 7, divided by, 4, end fraction
.
Answer:
3/8
Step-by-step explanation:
We want to evaluate
b - (-1/8) + c
where b = 2 and c = -7/4
First, replace b and c values into the expression
2 - (-1/8) + (-7/4)
Then, eliminate the parenthesis
2 + 1/8 - 7/4
Finally, express all terms as fractions with the same denominator, and perform the addition and subtraction
2*8/8 + 1/8 - 7/4 * 2/2
16/8 + 1/8 - 14/8
(16 + 1 - 14)/8
3/8
Answer:
the answer is 3/8
Step-by-step explanation:
solve the inequality below. Use the drop-down menus to describe the solution and its graph -7x+13>41
｡☆✼★ ━━━━━━━━━━━━━━ ☾
-7x + 13 > 41
- 13
-7x > 28
/ -7
x < -4
Have A Nice Day ❤
Stay Brainly! ヅ
- Ally ✧
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What is the are of the figure?
Answer:
14CM times 32CM
Step-by-step explanation:
448 Cm
CAN SOMEONE HELP ME WITH THESE PLEASE ASAP
Help
Will mark as brainliest
Answer:
C
Step-by-step explanation:
Given
3a - 2a × 4a + 6a
According to order of operations.
Multiplication is performed before addition/ subtraction, thus
= 3a - 8a² + 6a ← collect like terms
= (3a + 6a) - 8a²
= 9a - 8a² → C
what is the range of possible sizes of side x 3.2 5.5
Answer:
i know one can be nine
Please please help me it’s due at 9:00
Answer:
If lines are tangent to the circle that means that they are equal lengths.
14x - 7 = 7x +49
14x - 7x = 49 + 7
7x = 56
x =56/7
x = 8
Step-by-step explanation:
X-16=42 what does x equal and how did you get your answer.
So the right answer is 58.
look at the attached picture
Hope it will help you
Good luck on your assignment
Answer:
58
Step-by-step explanation:
Add 16 to both sides
x-16=42
x-16+16 = 42+16
-16 and 16 cancel out
x = 58
Find the circumference of a pizza if the diameter is 10 inches
Answer:
Pizza Comparison (old version)
Diameter (in) Area (sq in) Diameter (cm)
10 79 25.4
12 113 30.5
14 154 35.6
16 201 40.6
Step-by-step explanation:
These are the exact dimensions
Which of the following expressions is equivalent to -9?
Answer:
-63 / 7
Step-by-step explanation:
Type the correct answer in each box. Use numerals instead of words. Consider this quadratic equation. x2 + 2x + 7 = 21 The number of positive solutions to this equation is _______ . The approximate value of the greatest solution to the equation, rounded to the nearest hundredth, is _______ .
Answer:
-1 ± 3i√6
Step-by-step explanation:
Please write this quadratic equation as follows: x^2 + 2x + 7 = 21. The " ^ " indicates exponentiation.
The coefficients of this quadratic are 1, 2, 7.
Thus, the "discriminant" b^2 - 4(a)(c) is (2)^2 - 4(1)(7), or 4 - 28, or -24.
Because the discriminant is negative, this quadratic has two different complex roots:
-b ± √[ discriminant ] -2 ± 2i√6
x = --------------------------------- = ----------------- = -1 ± 3i√6
2a 2
Select all the correct answers.
will mark brainliest for correct answer
pls take ur time
Answer:
I think it's B, C, E
Answer:
true b c e
false a d f
Step-by-step explanation:
no explanation
1.25 = 0.75 + r
What is r ?
r = 0.5
Step-by-step explanation:
[tex]1.25=0.75+5[/tex]
We can subtract 0.75 from both sides. The 0.75 will then cancel out.
[tex]0.5=r[/tex]
r = 0.5
Answer:
r = 0.5
Step-by-step explanation:
1.25= 0.75 + r
r = 1.25- 0.75
r = 0.5
plz solve -8 ( x - 3 ) - 4x = 48
Answer:
x = -2
Step-by-step explanation:
-8 ( x - 3 ) - 4x = 48
Distribute
-8x +24 -4x = 48
Combine like terms
-12x +24 = 48
Subtract 24 from each side
-12x+24-24 = 48-24
-12x = 24
Divide each side by -12
-12x/-12 = 24/-12
x = -2
Answer:
X= -2
Step-by-step explanation:
First, you need to distribute -8 into (x-3) ---> -8(x-3)-4x=48
-8x + 24 -4x= 48
Get numbers with variables on its own side--> -24 -24
-8x - 4x = 24
Combine -8x and -4x -----> -8x-4x = -12x -12x = 24
Divide ----------------------------------> -12 -12
24÷ -12 = -2
If 12% is always withheld from dan’s wages, how much would be taken out if he earned $220
Answer:
$26.40
Step-by-step explanation:
multiply 220 by 0.12 to get 12 percent of the total amount
the question is what is the surface area of the three dimensional figure the choices are
1.184ft²
2.180ft²
3.150ft²
4.125ft²
Answer:
im not sure about this one but i think its 2. 180ft squared
Step-by-step explanation:
Answer:
It is 2 180ft
Step-by-step explanation:
How to write 5(2x+1)(x+1) in standard form explain....?
1.So the problem "y=2x+5" is in standard form and no modification is necessary. For a parabolic equation, the standard form is y = a(x - h)^2 + k, from which direction (polarity of "a") and axis of symmetry (value of "h"), etc.
2.Ax + By + C = 0 or Ax + By = C.
Answer:
[tex]=10x^2+15x+5[/tex]
Step-by-step explanation:
[tex]5\left(2x+1\right)\left(x+1\right)\\\mathrm{Expand}\:\left(2x+1\right)\left(x+1\right):\quad 2x^2+3x+1\\\mathrm{Apply\:FOIL\:method}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd\\a=2x,\:b=1,\:c=x,\:d=1\\=2xx+2x\cdot \:1+1\cdot \:x+1\cdot \:\\=2xx+2\cdot \:1\cdot \:x+1\cdot \:x+1\cdot \:1\\\mathrm{Simplify}\:2xx+2\cdot \:1\cdot \:x+1\cdot \:x+1\cdot \:1:\quad 2x^2+3x+1\\2xx+2\cdot \:1\cdot \:x+1\cdot \:x+1\cdot \:1\\2xx=2x^2\\2\cdot \:1\cdot \:x=2x\\1\cdot \:x=x\\1\cdot \:1=1\\=2x^2+2x+x+1[/tex]
[tex]\mathrm{Add\:similar\:elements:}\:2x+x=3x\\=2x^2+3x+1\\=5\left(2x^2+3x+1\right)\\\mathrm{Expand}\:5\left(2x^2+3x+1\right):\quad 10x^2+15x+5\\5\left(2x^2+3x+1\right)\\\mathrm{Distribute\:parentheses}\\=5\cdot \:2x^2+5\cdot \:3x+5\cdot \:1\\\mathrm{Simplify}\:5\cdot \:2x^2+5\cdot \:3x+5\cdot \:1:\quad 10x^2+15x+5\\5\cdot \:2x^2+5\cdot \:3x+5\cdot \:1\\\mathrm{Multiply\:the\:numbers:}\:5\cdot \:2=10\\=10x^2+5\cdot \:3x+5\cdot \:1\\\mathrm{Multiply\:the\:numbers:}\:5\cdot \:3=15[/tex]
[tex]=10x^2+15x+5\cdot \:1\\\mathrm{Multiply\:the\:numbers:}\:5\cdot \:1=5\\=10x^2+15x+5\\[/tex]
Multiply
[tex]\frac{\sqrt{2} }{6}cis(\frac{3\pi }{5} )[/tex]
by
[tex]\frac{\sqrt{6} }{4} cis(\frac{2\pi }{3} )[/tex]
Use the distance formula and/or the Pythagorean Theorem to find the area of the triangle.
A) 8.4 square units
B) 20.5 square units
C) 41 square units
D) 60.5 square units
What the extreme point on the parabola
Answer:
Directrix
Step-by-step explanation:
8,9,10,11,11,14,18,28,28,29,40,41,41,44,45,47,55 which histogram represents data
Answer:
did this b4
Step-by-step explanation:
I used bars of width 10. There are 3 values from 0-9; 4 values from 10-19; 3 values from 20-29; 0 values from 30-39; 6 values from 40-49; and 1 value from 50-59.
please mark as brainliest
Answer:
The histogram representing the set data will be given as follows:
8, 9, 10, 11, 11, 14, 18, 28, 28, 29, 40, 41, 41, 44, 45, 47, 55
the data will be as shown in the attached data:
Help! Check the pic below to see the options and question.
Answer:
Kinda sad because
Step-by-step explanation:
No one responded in 2 yrs ;(
:)
Select all that apply.
If 2x2-6x=0, then
2x = 0
OX-6 = 0
a
X-3 = 0
x + 1 = 0
Answer:
2x =0 x-3 =0
Step-by-step explanation:
2x^2-6x=0
Factor out 2x
2x( x-3) = 0
Using the zero product property
2x =0 x-3 =0
Answer:
x = 3
x = 0
Step-by-step explanation:
The correct answer is
x = 3
x = 0.
Steps below.
Pulling out like terms
Theory - Roots of a product
Solving a Single Variable Equation
Two answers were found
Hope this helps.