Answer:
The ball was thrown from a height of [tex]3\; {\rm ft}[/tex].
Step-by-step explanation:
The expression for the height of this ball, [tex]h(t) = -16\, t^{2} + 40\, t + 3[/tex], represents a parabola (with respect to time [tex]t[/tex].)
In this expression, "[tex]3[/tex]" represents the [tex]y[/tex]-intercept of the parabola- the output of the parabola when the input is [tex]t = 0[/tex]. The reason is that when [tex]t = 0\![/tex], terms of this parabola that include [tex]t[/tex] ([tex](-16\, t^{2})[/tex] and [tex]40\, t[/tex]) would evaluate to [tex]0[/tex]:
[tex]\begin{aligned}h(0) &= -16\times 0^{2} + 40\times 0 + 3 = 3\end{aligned}[/tex].
In the case of this ball, the term "[tex]3[/tex]" means that height of this ball is [tex]3\; {\rm ft}[/tex] when [tex]t = 0[/tex] (right when the ball was thrown.) Thus, the ball was thrown from a height of [tex]3\; {\rm ft}[/tex].
given f (x)=x-4/x^2+13x+36 which of the following is true
The function [tex]f(x) =\frac{x - 4}{x^2 + 13x + 36}[/tex] is a rational function
The simplified expression of the function [tex]f(x) =\frac{x - 4}{x^2 + 13x + 36}[/tex] is [tex]f(x) =\frac{x - 4}{(x + 9)(x + 4)}[/tex]
How to simplify the function?The function expression is given as:
f(x) =x - 4/x^2 + 13x + 36
Rewrite properly as:
[tex]f(x) =\frac{x - 4}{x^2 + 13x + 36}[/tex]
Expand the denominator
[tex]f(x) =\frac{x - 4}{x^2 + 4x + 9x + 36}[/tex]
Factorize the denominator
[tex]f(x) =\frac{x - 4}{x(x + 4) + 9(x + 4)}[/tex]
Factor out x + 9
[tex]f(x) =\frac{x - 4}{(x + 9)(x + 4)}[/tex]
Hence, the simplified expression of the function [tex]f(x) =\frac{x - 4}{x^2 + 13x + 36}[/tex] is
[tex]f(x) =\frac{x - 4}{(x + 9)(x + 4)}[/tex]
Read more about rational functions at:
https://brainly.com/question/1851758
Answer: f(x) is increasing for all x > -4
Proof of validity is shown below.
Giving out brainliest!! Help?
Answer:
(8/3,11/3) is the centroid of the given triangle
pls do mention in comment if u need full solution
Answer:
(8/3, 11/3)
Step-by-step explanation:
Formula of the centroid
(x, y) = [(x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3]Points
(-2, 3)(6, 7)(4, 1)Solving :
Centroid = [(6 + 4 - 2)/3, (3 + 7 + 1)/3]Centroid = (8/3, 11/3)can someone help me out with khan?
Hello can someone help me out please
Answer:
The answers are: 35 hot dogs & 52 sodas.
Image is attached. Will give brainliest.
Answer:
outside the circle
sorry if I'm wrong
find the mean of the following data set 5,17,19,24,10,17,21,6,22,5,9
Answer:
the answer to that question is 14.09
Find an equation for the line that passes through the points (-1,-4) and (5,-2)
Linear equations are typically organized in slope-intercept form:
[tex]y=mx+b[/tex]
m = the slope of the lineb = the y-intercept (the value of y when the line crosses the y-axis)To determine a linear equation in slope-intercept form:
Find the slopePlug the slope into y=mx+bFind the y-interceptPlug the y-intercept into y=mx+bSolving the QuestionWe're given:
The line passes through the points (-1,-4) and (5,-2)First, find the slope of the line (m):
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex] where two points that fall on the line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
⇒ Plug in the given points (-1,-4) and (5,-2):
[tex]m=\dfrac{-2-(-4)}{5-(-1)}\\\\m=\dfrac{-2+4}{5+1}\\\\m=\dfrac{2}{6}\\\\m=\dfrac{1}{3}[/tex]
⇒ Therefore, the slope of the line is [tex]\dfrac{1}{3}[/tex]. Plug this into y=mx+b:
[tex]y=\dfrac{1}{3}x+b[/tex]
Now, determine the y-intercept (b):
[tex]y=\dfrac{1}{3}x+b[/tex]
⇒ Plug in one of the points and solve for b:
[tex]-4=\dfrac{1}{3}(-1)+b\\\\-4=-\dfrac{1}{3}+b\\\\-4+\dfrac{1}{3}=b\\\\b=-\dfrac{11}{3}[/tex]
⇒ Therefore, the y-intercept is [tex]-\dfrac{11}{3}[/tex]. Plug this back into our original equation:
[tex]y=\dfrac{1}{3}x-\dfrac{11}{3}[/tex]
Answer[tex]y=\dfrac{1}{3}x-\dfrac{11}{3}[/tex]
The speed of the jet Alyssa flew on from Boston to London was 480
mph. On her return flight, the speed of the jet was 600 mph with a tail
wind. What was Alyssa's average speed on the round trip? Round your
answer to one decimal place.
Answer:
540 Mies per hour
Step-by-step explanation:
add 600 and 480 then divide by 2
Alyssa's average speed on the round trip is 540 Mies per hour.
We have given,
The speed of the jet Alyssa flew on from Boston to London was 480
mph.
On her return flight, the speed of the jet was 600 mph with a tail
wind.
What is the average speed?[tex]average speed=\frac{a+b}{2}[/tex]
a=inital speed
b=final speed
add 600 and 480 then divide by 2
That can be given by
[tex]=\frac{600+480}{2}\\\\=\frac{1080}{2}\\\\=540[/tex]
Alyssa's average speed on the round trip is 540mph.
To learn more about the average speed visit:
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A right triangle has side lengths 3, 4, and 5 as shown below.
Use these lengths to flnd sinX, tanX, and cosX.
Answer:
See below
Step-by-step explanation:
Remember S-O-H-C-A-H-T-O-A
Sin = Opp / Hyp
Cos = Adjacent / Hyp
Tan =Opp / Adj
You didn't say WHICH angle is X , so you will have to finish this !
The dimensions of a rectangular prism are 26 inches by 10 inches by 8 inches. What is the surface area, in square inches, of the prism?
The surface area of this rectangular prism of dimensions 26 inches by 10 inches by 8 inches is 1096 square inches.
What is the surface area of this rectangular prism?A rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.
The surface area of this rectangular prism = 2( lb + bh + hl)
The dimensions of a rectangular prism are 26 inches by 10 inches by 8 inches.
The surface area of this rectangular prism = 2( lb + bh + hl)
= 2( 26 x 10 + 10 x 8 + 26 x 8)
= 2(260 + 80 + 208)
= 2 x 548
= 1096
Thus, The surface area of this rectangular prism is 1096 square inches.
Learn more about the area;
https://brainly.com/question/6754997
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Write the pair of fractions as a pair of fractions with a common denominator.
1/3 and 3/8
Help help help math math math
Answer:
Equation of straight line is y=Mx+X
or, y-7=-1/5x(x-(-1)
Hence y-7=-1/5x(x-(-1) is the required equation.
Answer:
ok i heres the answer
Step-by-step explanation:
there you go have a nice day
please help me with this one
Answer:
36 km^2
Step-by-step explanation:
We will use the way to find the area of trapezoids which is b+b/2 *h and that is 3+5/2 * 9 so 8/2 is 4 and 4*9=36
URGENT! In ABC. what is the value of r?
Answer:
16.2
Step-by-step explanation:
By geometric mean theorem:
[tex] {9}^{2} = 5(x) \\ \\ \implies \: 81 = 5x \\ \\ \implies \: x= \frac{81}{5} \\ \\ \implies \: x=16.2[/tex]
HELP ME OUT PLS!!!!!!!!
The total cost for one year at the state university is $22,500. A student has the following help in covering the costs of school. . • An academic scholarship for $10,000. • Other scholarships and grants for $4,400. Parents pay $1,800, . What is the amount that the student will need to save every month in order to pay off the remaining costs in 10 months?
A) $630
B) $525
C) $1,200
D) $1,440
so her University costs are $22,500
however she gets some help because
◉ academic scholarship pays 10,000 off of that
◉ other scholarships pay 4,400 off of that
◉ and her parents pay 1800 off of that
what's left? well, what's left is 22500 - 10000 - 4400 - 1800 = 6300 bucks.
so for the next 10 months she needs to cover 6300 bucks of her expenses, now 6300 spread over 10 months is 630 a pop.
What’s 9+10 equal to???
Answer:
19
Step-by-step explanation:
9+10=19
11+8=19
Hope it Helps
Find the mean absolute deviation for each data set.
1. The number of kittens in 10 litters: 4, 5, 5, 6, 6, 7, 8, 8, 8, and 9
Med
Answer:
The mean is 6. When you add all the numbers you get 66 and then youre suppose to divide 66 by 10 in order to get the mean which is 6.
Step-by-step explanation:
4 + 5 + 5 + 6 + 6 + 7 + 8 + 8 + 8 + 9 = 66
66 ÷ 10 = 6
Use the quadratic formula to solve the equation 9 x 2 + 30 x + 50 = 0 .
Answer:
I did how you told us to do it and I came up with 98 im not sure if that the right answer but I try to help
The original blueprint of a concrete patio has a scale of 2 inches =3 feet
Victoria want to make a new blueprint of the patio with a length of 16.8 inches
Scale of the new blueprint: 2 inches = 2.5 feet (or 4 inches = 5 feet)
Width of the new blueprint: 14.4 inches
Whoever gets the Question right and first gets 15 points
(275x523)+19x34/3=?
Answer:
144040.3333
Step-by-step explanation:
275*523 = 143825
19x34/3 = 215.3333333
so add them up to get 144040.3333
Answer:
144040.333333
Step-by-step explanation:
start with parenthesis (275x523)
This would get you, 143825.
Next, you would do, (19x34/3)
That would get you, 215.333333333.
Finally, you would add the two numbers together and get a product of 144040.333333.
Which proportion could you use to convert 5 gallons to quarts?
Convert.
5gallons=
quarts
helps pls with this math problems . I’ll give Brainly
The entrance fee is d dollars, and the meal ticket is $4 less than the entrance fee -> Each meal ticket is d - 4
So, the total amount that the friends pay is 5(d-4)
PLEASE ANSWER ASAP WILL MARK BRAINLIEST
Answer:
the first one is the answer
3.5 is the number in parentheses!
Show all work
Explain♥️
[tex]\begin{cases} f(x)=x^2\\ g(x)=x-3 \end{cases}\qquad \qquad (g\circ f)(x)\implies g(~~ f(x)~~) \\\\[-0.35em] ~\dotfill\\\\ f(3.5)=(3.5)^2\implies f(3.5)=12.25 \\\\\\ g(~~ f(3.5)~~)\implies g(~~ 12.25~~)=(12.25)-3\implies \stackrel{(g\circ f)(3.5)}{g(~~ 12.25~~)}=9.25[/tex]
Find the perimeter of the figure below. Notice that one side length is not given.
Assume that all intersecting sides meet at right angles.
Be sure to include the correct unit in your answer.
Answer:
52 cm
Step-by-step explanation:
The only tricky part is getting the not measured side. However, you have a portion of it. 16-11=5, and that is the missing side. Then just add everything together.
write each of the following expressions without using absolute value
|y-x| if y>x
Answer:
y can only be greater than x if x has a variable less than y so the answers is ly- lx
Step-by-step explanation:
∠A and \angle B∠B are complementary angles. If m\angle A=(x+10)^{\circ}∠A=(x+10)
∘
and m\angle B=(3x+28)^{\circ}∠B=(3x+28)
∘
, then find the measure of \angle B∠B.
Answer:
67
Step-by-step explanation:
Complementary angles add to 90 degrees
<A + <B = 90
x+10 + 3x+28 = 90
Combine like terms
4x+38 =90
Subtract 38 from each side
4x+38-38 = 90-38
4x = 52
Divide by 4
4x/4 = 52/4
x = 13
We want to find <B
<B = 3x+28
= 3(13) +28
= 39+28
=67
The polynomial of degree 3 , P ( x ) , has a root of multiplicity 2 at x = 1 and a root of multiplicity 1 at x = − 2 . The y -intercept is y = − 0.2 .
Answer:
The polynomial of degree 3 ,P(x), has a root of multiplicity 2 at x=1 and a root of multiplicity 1 at x=−1. The y-intercept is y=−0.2
what is the answer to this?
Answer:
the answer is c
Step-by-step explanation:
its c i dont know what the words say tho i need to read what it say first.
Compute the flux of the vector field F = xy, 5yz, 6zx through the portion of the plane 3x + 2y + z = 6 in the first octant with the downward orientation.
The plane has intercepts
y = z = 0 ⇒ 3x = 6 ⇒ x = 2
x = z = 0 ⇒ 2y = 6 ⇒ y = 3
x = y = 0 ⇒ z = 6
and thus passes through the points (2, 0, 0), (0, 3, 0), and (0, 0, 6).
Parameterize the portion of the plane (call it P) by the vector function,
[tex]\vec r(s,t) = \left\langle 2(1-s)(1-t), 3s(1-t), 6t \right\rangle[/tex]
where 0 ≤ s ≤ 1 and 0 ≤ t ≤ 1.
Compute the normal vector to P :
[tex]\vec n = \dfrac{\partial \vec r}{\partial t} \times \dfrac{\partial \vec r}{\partial s} = -\left\langle 18-18t, 12-12t, 6-6t \right\rangle[/tex]
Then the flux of F through P is given by the surface integral,
[tex]\displaystyle \iint_P \vec F \cdot d\vec S = \int_0^1 \int_0^1 \left\langle 6s(1-s)(1-t)^2, 90st(1-t), 72t(1-s)(1-t) \right\rangle \cdot \vec n \, ds \, dt \\\\ = - \int_0^1 \int_0^1 \left(108(t-1)^3 s^2 + 108(t-1)^2(5t+1) s + 432t(t-1)^2\right) \, ds \, dt \\\\ = - \int_0^1 18(t-1)^2(41t+1) \, dt \\\\ = \boxed{-\frac{135}2}[/tex]