Answer:
The maximum height that the stone reaches is of 26 feet.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
y = -2x2 + 8x + 5
Quadratic function with [tex]a = -2, b = 8, c = 5[/tex]
What is the maximum height that the stone reaches?
y value of the vertex. So
[tex]\Delta = 8^2-4(-2)(5) = 64 + 40 = 104[/tex]
[tex]y_{v} = -\frac{104}{4(-2)} = 26[/tex]
The maximum height that the stone reaches is of 26 feet.
Please help
Honestly cant understand
Which of the following best describes the graph of the polynomial function
below?
Answer:
Step-by-step explanation:
The given curve crosses the x-axis in two places, (-2, 0) and (0, 0), which are the zeros. This parabolic curve opens up and has its vertex (minimum) at (-1, -1).
Answer: The graph has two zeros.
Step-by-step explanation:
The given graph is the graph of parabola open upward. In the graph of parabola, we will have two solutions since the highest degree of the function is 2.
y = ax^2 + bx + c, where a, b, c are real number and a ≠ 0.
You can see the height degree of the function is 2.
Therefore, there should be two zeros of the function.
According to the given graph of parabola has two zeros at x = -2 and x = 0.
The graph cross the x-axis at x = -2 and x = 0.
Hence, the graph has two zeros.
Answer is A. The graph has two zeros
Andres went out to a restaurant for dinner. His total bill before tax and tip was $27.30. He was charged an additional 9% tax and he also paid a 15% tip on the original bill.
Answer:
$25.66
Step-by-step explanation:
Given data
Total Bill before tax and tip= $27.30
Tax= 9%
Tip= 15%
Let us find the tax
=9/100*27.30
=0.09*27.30
=$2.457
Let us find the tip
=15/100*27.30
=0.15*27.30
=$4.095
Therefore his bill after tax and tip is
=27.30+2.457-4.095
=$25.66
The equation of the line of best fit of a scatter plot is y = −8x + 3. What is the the y-intercept?
A. −8
B. −3
C. 3
D. 8
Answer:
C. 3
Step-by-step explanation:
The y intercept will always be the 'b' in the formula
y= mx+b
since your formula is y = -8x +3, and 3 is in the place of "b", your y intercept will be 3
Answer:
C.3
Step-by-step explanation:
In the equation of y = -8x +3 you can find the y - intercept by looking at number which replaces b which is a positve three. Meaning that your y - intercept would be answer choice C which is positive three.
Select all expressions that at equivalent to the expression 3x + 5. A. 9x − (−5 + 6x) B. 9x − (5 − 6x) C. 9x − (6x + 5) D. 9x − (6x − 5) E. 9x − (−6x + 5)
Answer:
A. 9x − (−5 + 6x)
D. 9x − (6x − 5)
Step-by-step explanation:
Select all expressions that at equivalent to the expression 3x + 5.
To get our answer, we have to solve each option
A. 9x − (−5 + 6x)
= 9x + 5 - 6x
= 9x - 6x + 5
= 3x + 5
Option A is correct
B. 9x − (5 − 6x)
= 9x - 5 + 6x
= 9x + 6x - 5
= 15x - 5
Option B is wrong
C. 9x − (6x + 5)
9x - 6x - 5
= 3x - 5
Option C is wrong
D. 9x − (6x − 5)
= 9x - 6x + 5
= 3x + 5
Option D is correct
E. 9x − (−6x + 5)
= 9x + 6x - 5
= 15x - 5
Therefore, Option A and D are the correct options with the right expressions
A certain type of bacteria is growing at an exponential rate that is modeled by the equation y=aekt, where t represents the number of hours. There are 100 bacteria initially, and 500 bacteria five hours later.
Answer:
meow meow
Step-by-step explanation:
Pleaseeeeeeee help me
Answer:
The answer is "The discriminant is positive"
Step-by-step explanation:
When the discriminant is positive there is two real solutions.
When the discriminant is equal to 0, there is one real solution.
When the discriminant is negative, there is no real number solutions.
I don’t know where to start
Answer:
Either 90 degrees clockwise or 90 degrees counterclockwise
Step-by-step explanation:
Answer:
First the image would need to be reflexed over y = 2
Then the x values would need to be increased by 6
(x+6, y)
Step-by-step explanation:
Which graph represents an exponential function?
On a coordinate plane, a curve decreases rapidly and then levels out.
On a coordinate plane, a curve decreases, changes directions, and then decreases again.
Answer:
A
Step-by-step explanation:
A
ally and bo share 60$ how much money does bo get
Answer:
If Ally and Bo share evenly, Bo will get 30$, so will Ally. The half of 60 is 30.
explain fully please
Answer:
whats the question..........
evaluate the function for x = -8.
f(x) = -2x - 12
Answer:
4
Step-by-step explanation:
f(-8)=-2(-8)-12
f(-8)=16-12
=4
the volume of this triangular prism is ….. cubic inches. please someone help, will give brainliest asap ❤️❤️❤️❤️❤️
Answer:
576'' squared
Step-by-step explanation:
Which values of a, b, and c correctly represent the answer in simplest form?
3
- 2
b
32
O a=38, b= 14, C = 1
O a=1,5=14, C= 38
O a=1,b=7.C= 19
O a= 19, b=7,C= 1
Answer:
The answer for this is a=1,b=7,c=19.
A mechanic has a set fee for working on someone's automobile and charges by the hour for making repairs. The total cost of her services (yes she
female mechanic), is c(t) = 100t + 90. Which statement(s) about this function is true?
1. The one time fee for working on the car is $90.
II. The mechanic charges $100 per hour.
III. The number of hours the job takes is represented byt
a. I and III
b. I, II, and III
c. I and II
d. ll and III
Solve 2x-5/x-2 ≤ 1
please answer fast
Answer:
x<=-3
Step-by-step explanation:
2x-5/x-2 <= 1
Multiply both sides by x-2
2x-5<=x-2 (anything times 1 is that number.)
add 5 to both sides
2x<=x-3
subtract x from both sides
x<=-3
Answer:
Step-by-step explanation:
[tex]\frac{2x-5}{x-2} \leq 1\\case ~1. both ~numerator~and~denominator \geq 0\\x\neq 2\\2x-5\leq x-2\\x\leq 3\\so~0\leq x<2U2<x\leq 3\\case~2.\\both~numerator~and~denominator<0\\2x-5\geq x-2\\x>3\\which~is~rejected~as~it~gives~both~2x-5~and ~x-2>0[/tex]
Pls help I’ll give crown
Answer:
B
Step-by-step explanation:
because area of prism = L×W×H
so
[tex] \frac{3}{4} \times \frac{5}{2} \times \frac{5}{4} [/tex]
answer is 75/32
hope this make sense:)
Answer:
Hi there uwu The answer is 75/32, also explained by the other answerer!
Step-by-step explanation:
Help!! Please also explain how you got your answer
Answer:
y = -½x + 4
Step-by-step explanation:
the line passes point of y-intercept (0, 4) ,
and another point (6, 1)
the slope = (1-4)/(6-0) = (-3)/6 = -½
so the Equation is y = -½x + 4
simplify 2⁴
please help me with this question
Answer:
16
Step-by-step explanation:
2^4= 2x2x2x2 = 16
Answer:
16
Step-by-step explanation:
Raise 2 to the power of 4.
4x2x2= 16
You're rasing 2 two times so...
4x2x2= 16
helpppppppppppppppppppppppppppppppppp!!!!!!!!!
a) Write down the exact value of tan 60' b) Find the value of h in this triangle, h= c) Write down the exact area of this triangle, h 60° 43
Step-by-step explanation:
maybe this can help you with your problem
a) The exact value of tan 60 degree is [tex]\sqrt{3}[/tex].
b) The value of h in the given triangle is √3.
c) The area of the given triangle is 24[tex]\sqrt{3}[/tex].
What is tangent of an angle?The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
What is the value of tan 60 degrees?The value of tan 60 degree is [tex]\sqrt{3}[/tex].
What is the formula for area of a triangle?[tex]Area = \frac{1}{2}bh[/tex]
Where,
b is the base of the triangle.
h is the height of the triangle.
a) Since, the value of tan60 degree is [tex]\sqrt{3}[/tex].
Hence, the exact value of tan 60 degree is [tex]\sqrt{3}[/tex].
b). According to the given question, we have a right angled triangle in which
The length of the adjacent side w.r.t angle 60 degrees is [tex]4\sqrt{3}[/tex].
And, the length of the opposite side w.r.t angle 60 degrees is h.
Therefore, the value of h in the given triangle is given by
[tex]tan60 = \frac{h}{4\sqrt{3} }[/tex]
⇒[tex]\sqrt{3} =\frac{h}{4\sqrt{3} }[/tex] (because tan60=√3)
⇒[tex]h=4\sqrt{3} \sqrt{3}[/tex]
⇒[tex]h = 12[/tex]
Hence, the value of h in the given triangle is √3.
c) For the given triangle
Length of base = 4[tex]\sqrt{3}[/tex] unit.
And, the height of the given triangle is 12 unit.
The area of the given triangle is given by
[tex]Area = \frac{1}{2} (4\sqrt{3} )(12)[/tex]
⇒[tex]Area =24\sqrt{3}[/tex]
Hence, the area of the given triangle is 24[tex]\sqrt{3}[/tex].
Learn more about tangent of an angle and area of a triangle here:
https://brainly.com/question/15110994
#SPJ2
determine tan(t) if cos(t) = -12/13 and sin(t)
Determine tan(t) if cos(t) = -12/13 and sin(t) = 5/13
Answer:tan(t) = [tex]\frac{-5}{12}[/tex]
Step-by-step explanation:Method 1:
The sketch of the trigonometry is attached to this response.
Since cos(t) is negative and sin(t) is positive, then t should be in the second quadrant as shown in the sketch. A triangle is formed.
We know that, in a given triangle, the cosine of a given angle is the ratio of the adjacent side to the hypotenuse side.
i.e
cos (t) = adjacent / hypotenuse = - 12 / 13
Where;
adjacent = -12 [the adjacent side is in the -x direction]
hypotenuse = 13
Also, the sine of a given angle is the ratio of the opposite side to the hypotenuse side.
sin (t) = opposite / hypotenuse
Where;
opposite = 5
hypotenuse = 13
These sides - opposite, adjacent and hypotenuse - are labelled in the sketch.
From this triangle and the labels, the tangent can be found.
We know that the tangent of a given angle is the ratio of the opposite side to the hypotenuse side. i.e
tan (t) = opposite / adjacent
Where;
opposite = 5
adjacent = -12
Therefore,
tan (t) = [tex]\frac{-5}{12}[/tex]
Method 2:
The tangent of an angle is the ratio of the sine of that angle to the cosine of that angle. i.e
tan(t) = sin(t) / cos (t) ---------------(i)
sin(t) = 5 / 13
cos(t) = -12 / 13
Substitute for sin(t) and cos (t) in equation (i)
tan(t) = [5 / 13] / [-12 / 13]
tan(t) = [5 / 13] x [-13 / 12]
tan(t) = [tex]\frac{5}{13} * \frac{-13}{12}[/tex]
tan(t) = [tex]\frac{-5}{12}[/tex]
Pls help me with this it's urgent!
Answer:
function is the correct answer
Answer:
an = a1 + (n - 1 ) d (Function)
Step-by-step explanation:
This is the formula that will be used when we find the general (or nth) term of an arithmetic sequence. So it is function
A baker uses 20 cups of flour to make 4 loves of bread. Use this to solve the question in the picture!
Answer:
60 cups of flour
Step-by-step explanation:
Since it takes 20 cups of flour for 4 loves of bread this means we're going to need to multiply 20x3=60
(6n-25) + (3n + 20) = 180
Answer:
n = 185/9
Step-by-step explanation:
(6n-25) + (3n + 20) = 180
Combine like terms
9n -5 = 180
Add 5 to each side
9n - 5 +5 = 180+5
9n = 185
Divide each side by 9
9n/9 = 185/9
n = 185/9
Can anybody help me with this one ??
if the angles (4x+4) and 6x-4 are supplement Ary angles find value of x plzz helppp
Angles (4x + 4°) and (6x - 4°) are supplementary.
That is :
[tex](4x + 4°) + (6x - 4°) = 180°[/tex]Solution :[tex]\hookrightarrow \: 4x + 4 \degree + 6x -4 \degree = 180 \degree[/tex]
[tex]\hookrightarrow10x = 180 \degree[/tex]
[tex]\hookrightarrow x = 18 \degree[/tex]
__________________________
[tex] \mathrm{✌TeeNForeveR✌}[/tex]
In order to simulate conditions near roads treated with road salt, scientists raised wood frog tadpoles in a high concentration of salt, and tadpole survival was measured. The survival rates for 5 replicates were 32, 37, 41, 45, and 50 percent. The sample mean for these values is 41 percent, and the sample variance is 48.5 percent squared. Determine the standard error of the sample mean for this data set.
Answer:
[tex]SE_{\bar x} = 0.311[/tex]
Step-by-step explanation:
Given
[tex]n=5[/tex]
[tex]\bar x = 41\%[/tex]
[tex]\sigma^2= 48.5\%[/tex] --- variance
Required
The standard error of the sample mean
This is calculated as:
[tex]SE_{\bar x} = \frac{\sigma}{\sqrt n}[/tex]
This can be rewritten as:
[tex]SE_{\bar x} = \frac{\sqrt{\sigma^2}}{\sqrt n}[/tex]
So, we have:
[tex]SE_{\bar x} = \frac{\sqrt{48.5\%}}{\sqrt 5}[/tex]
Rewrite as:
[tex]SE_{\bar x} = \sqrt{\frac{48.5\%}{5}}[/tex]
[tex]SE_{\bar x} = \sqrt{0.097}[/tex]
[tex]SE_{\bar x} = 0.311[/tex]
did I choose the right graph?
Answer:
Step-by-step explanation:
The - tells you that it is upside down. So that much of your choice is correct for certain.
The 1/8 squishes the graph something fierce. So of those graphs given, the one you chose is most likely correct. But you are right to be a little miffed at the question. You should never have to choose an answer with only a picture to guide you. If you have a graphing calculator, try y = -1/8 x^2 which is a good candidate for all the graphs.
What are the zeros of the polynomial function y = (x - 3)(2x + 1)(x - 1)? A. 1/2, 1, 3 B. -1, 1, 3 C. -1/2, 1, 3 D. -3, 1/2, -1
Answer:
x=3 x = -1/2 x=1
Step-by-step explanation:
y = (x - 3)(2x + 1)(x - 1)
Set the function equal to zero
0 = (x - 3)(2x + 1)(x - 1)
Using the zero product property
x-3 =0 2x+1 =0 x-1 =0
x=3 2x = -1 x=1
x=3 x = -1/2 x=1