Answer:
[tex]\huge\boxed{\text{1. } h(t) = -5(t-3)^2 + 45}[/tex]
[tex]\huge\boxed{\text{2. 3 seconds}}[/tex]
Step-by-step explanation:
If we're looking for the point at with the ball reaches its highest point, we want to find the graph's vertex. In order to get the equation into a form with the vertex in it, we need to convert the equation into vertex form. This is an equation in the form [tex]y=a(x-h)^2 + k[/tex], h being the x value of the vertex, and k being the y value of the vertex.
In order to convert our equation, [tex]-5t^2+30t[/tex] into vertex form, we can algebraically manipulate it to get it into the form we want.
[tex]-5t^2 +30t[/tex] [tex]-5 \cdot t^2 + 30t[/tex] (Separate the -5 from the t^2)[tex]-5(t^2-6t+0)[/tex] (Factor out a -5)[tex]-5(t^2 -6t + (-3)^2 - (-3)^2 + 0)[/tex] (Completing the Square)[tex]-5((t-3)^2 - (-3)^2 + 0)[/tex] (Binomial Formula)[tex]-5((t-3)^2 - 9)[/tex] (Simplify)[tex]-5(t-3)^2 + 45[/tex] (Factor the -5 back in)Therefore, our equation with the vertex in it is [tex]-5(t-3)^2 + 45[/tex]. To find the vertex, we can examine the equation to find the values of h and k in the formula [tex]y=a(x-h)^2 + k[/tex] (where the vertex coordinates are (h, k)).
It seems that h is 3 and k is 45. Therefore, the coordinate of the vertex is (3, 45). Since it asks for how many seconds after being hit does the ball reach its highest point, we would take the x value since x represents seconds. This is 3. Therefore, the ball reaches its highest point after 3 seconds.
Hope this helped!
Andrea earns $32.25 a day. After 9 days , about how much will she have earned?
ESTIMATE
8+3(p-9)
Pleaseeee helppp
Answer:
3p - 19
Step-by-step explanation:
8 + 3(p - 9)
Distribute;
8 + 3p - 27
Collect like terms;
-19 + 3p
3p-19 by using addition and the distributive property
Hello! :)
Please help me solve this + explain your answer :)
I will indeed give you Brainlst <3
If the radius of a circle is 5 inches, what is the diameter of that circle? Show
your work and label your answer.
Answer:
If the radius of a circle is 5 inches, the diameter is 10.
Step-by-step explanation:
This is because to find the diameter of a circle sing the radius is to multiply it by two. 5x2=10
So the diameter is 10. If you want to find the radius just reciprocate the process, divide the diameter by 2 and yo will get the radius.
I really hope this helped you out. Make sure to give my answer brainliest. Have a radiant day or night ! :D
Which of the following is not equivalent to x-y+z?
y-X+Y-Z
x+Z- y
z+x-y
Z- y + x
Answer:
the first one
Step-by-step explanation:
look at the signs and then whatever one has the values with the wrong sign, is not the same
+x -y +z (what they need to be)
+y -x -z (not the same)
+x +z -y (the same)
+z +x -y (the same)
+z -y +x (the same)
i hope this helped :)
Solve for x.
-1+4x5= 3
Answer:
[tex]x = 0.2 \: or \: \frac{1}{5} [/tex]
Step-by-step explanation:
[tex] - 1 + 4x.5 = 3[/tex]
[tex] = > 20x - 1 = 3[/tex]
[tex] = > 20x = 3 + 1 = 4[/tex]
[tex] = > x = \frac{4}{20} = \frac{1}{5} = 0.2[/tex]
--6x = 48 (solving equations)
Find the value of x in the triangle shown below 9 12
Use the scale factor to find the area of the enlarged figure. Explain your steps.
A small rectangle has a length of 8 and width of 4. A large rectangle has a length of 25.6 and width of a.
9514 1404 393
Answer:
327.68 units^2
Step-by-step explanation:
The area of the small figure is ...
area = length · width
area = (8)(4) = 32 . . . . square units
The scale factor is ...
scale factor = large length / small length = 25.6/8 = 3.2
The area of the larger rectangle will be the small rectangle area multiplied by the square of the scale factor:
(32 units^2)(3.2^2) = 327.68 units^2
_____
Additional comment
We note the width is half the length, so we could figure the larger rectangle's width at 25.6/2 = 12.8 units. Then its area would be
length · width = (25.6 units)(12.8 units) = 327.68 units^2
This seems easier to me, but is not the method required by the problem statement.
Answer:
The scale factor of the enlargement is 3.2. Square the scale factor to get 10.24. Find the area of the original figure, which is 32. Multiply 32 and 10.24 to get the area of the enlarged figure, which is 327.68.
Step-by-step explanation:
This is the sample response but I would use the other pearsons answer because it is NOT the sample response.
Have a great day!
A rectangle has a length of 3x + 7 and a width of 2x. If the perimeter of the
rectangle is 94 units, what is the length of the rectangle.
Answer:
The length of the rectangle is 31.
Step-by-step explanation:
We have that the length (L) and width (W) are:
[tex] L = 3x + 7 [/tex]
[tex] W = 2x [/tex]
The perimeter of the rectangle is given by:
[tex] P = 2W + 2L [/tex]
[tex] 94 = 2(2x + 3x + 7) [/tex]
[tex] 94 = 10x + 14 [/tex]
[tex] x = 8 [/tex]
Now, we can calculate the length of the rectangle:
[tex] L = 3x + 7 = 3*8 + 7 = 31 [/tex]
Therefore, the length of the rectangle is 31 units.
I hope it helps you!
Ed spent 25% of his savings on lunch, which cost $5.25. How much did he have in savings before lunch?
Step-by-step explanation:
I think 21 dollars is the answer
A store pays $13 for a bicycle helmet and marks up the price by 40% what is the amount of the mark-up?
Answer:
Step-by-step explanation:
the amount of mark up is
13*(40/100)=5.20
Write an equivalent expression 2x + 10
Answer: 2 (x+5)
Step-by-step explanation:
Answer:
x+5
Step-by-step explanation:
In which direction must the graph of f(x) = |x| be shifted to produce the graph of g(x) = |x − 3|?
A.
left
B.
down
C.
up
D.
right
Answer:
In which direction must the graph of f(x) = |x| be shifted to produce the graph of g(x) = |x − 3|?
A. left
B. down
C. up
✓D. right
Right is the right answer.
Answer:
Down
Step-by-step explanation:
I took the test and got it right
What is measure p angles has 5 sides
Answer:
[tex]\huge\boxed{m\angle P = 94\textdegree}[/tex]
Step-by-step explanation:
In order to answer this question, we need to note a couple of things about the angle relationships in a pentagon.
A) The sum of the measures in a pentagon will be 540° (We know this because the angle sum formula tells us that an n sided polygon angles will have a sum of [tex](n-2) \cdot 180[/tex] - 180 * 3 = 540).B) Equations can represent angle measures, added together will help us determine their value.Since we know the sum of all of the angles will be 540, we can create an addition statement to find out the value of x.
[tex]132 + (4x-10) + (5x-11) + 128 + (4x+2)=540[/tex]
Let's solve for x.
Combine the angles we already know:[tex]132 + 128 =260[/tex] Combine like terms: [tex]260 + 13x - 19=540[/tex] Add 19 to both sides, subtract 260 from both sides: [tex]13x =299[/tex] Divide both sides by 13: [tex]x = 23[/tex]Now that we know the value of x, we can substitute it into the expression for point P ([tex]4x+2[/tex]) to find it's value.
[tex]4 \cdot 23 + 2[/tex] [tex]92+ 2[/tex] [tex]94[/tex]Therefore, the angle of measure P is 94°.
Hope this helped!
Can y’all plz help me
Answer:
D. 10
Step-by-step explanation:
Assuming that <COA is a right angle, we can say that the two given angles are complementary
complementary angles are angles that add up to 90 degrees
this means we can create this equation: 3x + 46 + 14 = 90
so subtract 46 and 14 from 90: 3x = 30
divide both sides by 3: x = 10
Answer:
I think that it is letter D
Step-by-step explanation:
sorry if im wrong. but i hope this helps! :)
Which fraction is equal to 30%?
A.
30
100
B.
100
300
C.
100
30
D.
3.0
100
Answer:
A. 30/100
Step-by-step explanation:
All you have to do is divide the numerator by the denominator and then multiply that result with 100 like so:
(Numerator/Denominator)*100
When you enter 30/100 into the above formula, you get (30/100)*100 which calculates to:
30%
Good Luck!
Answer:
1. 30/100
Step-by-step explanation:
Convert fraction (ratio) 30 / 100 Answer: 30%
What is the value of 9(4x - 4) when x = 5
Answer:
144
Step-by-step explanation:
plug in 5 where you see the x.
that gives us 9(4(5)-4)
multiply the 4 and the 5 first to get 9(20-4)
and by PEMDAS, we solve the parentheses first so now we have 9(16)
so now just multiply 9x16 to get 144
Step-by-step explanation:
9((4×5)-4)
9(20-4)
9(16)
144
4 x 6 + 29 divided by 5 - 4
Answer:
25.8
Step-by-step explanation:
pls mark this as brainliest! thx hope this helped. :)
Answer:
The answer would be 25.8 or you can do 258
Step-by-step explanation:
3.2 - 5.1n - 3n + 5= n +8.2 can someone tell me what goes in the blank
what is the y-intercept of the following equation
A ladder 5 m long, leaning against a vertical wall makes
an angle of 65° with the ground. How far up the wall is
the top of the ladder?
Step-by-step explanation:
Given:length of ladder =5 m
Angle formed = 65°
Let h be the Height of the top of the ladder from the ground
Required:Height of the top of the ladder from the ground
Equation:SOH-CAH-TOA
Since the hypotenuse side is given and what we are to solve is the opposite side, use SOH
[tex]sinθ\:=\: \frac{opposite}{hypotenuse}[/tex]
[tex]sin(65°)\:=\: \frac{opposite}{5\: m}[/tex]
[tex]opposite\:=\:(5 \:m )\:sin(65°)[/tex]
[tex]opposite\:=\:4.53 \:m[/tex]
Final Answer:The height of the top of the ladder from the ground is 4.53 mPlease refer to the photo for the illustration
Graph 16x−4y=2.Please answer I will make you the brainlist and rate you 5 stars if good.And report if bad.
Answer:
First one is the graph second one is the equation
Step-by-step explanation:
Hope this helps :)
Answer:
Step-by-step explanation:
as graphed
Write a linear model for the amount of boxes, b, as a function of the number of hours since they opened, h. Use your model to predict the number of boxes in stock at the end of an 8 hour shift.
Question:
A company produces boxes of DVDs at a rate of 52 boxes per hour they begin to produce boxes when they first opened for the day and after 3 hours have 400 boxes in stock.
- How many boxes were in stock when they opened?
- Write a linear model for the amount of boxes, b, as a function of the number of hours since they opened, h.
- Use your model to predict the number of boxes in stock at the end of an 8 hour shift.
Answer:
1. [tex]Initial = 244[/tex]
2. [tex]b = 244 + 52h[/tex]
3. 660 boxes
Step-by-step explanation:
Given
[tex]Rate = 52\ per\ hour[/tex]
[tex]Total\ boxes\ in\ 3\ hours = 400[/tex]
Solving (a): Initial Number of boxes
First, we calculate the number of boxes made in 3 hours
[tex]Boxes = Rate * Hours[/tex]
[tex]Boxes = 52 * 3[/tex]
[tex]Boxes = 156[/tex]
If they had 400 boxes at the 3rd hour.
Then, the number of boxes when they opened is:
[tex]Initial = 400 - 156[/tex]
[tex]Initial = 244[/tex]
Solving (b): Linear function
[tex]b = boxes[/tex]
[tex]h = hours[/tex]
Since, we have the rate and the initial number of boxes.
The linear function is:
[tex]Boxes = Initial + Rate * Hours[/tex]
i.e.
[tex]b = 244 + 52 * h[/tex]
[tex]b = 244 + 52h[/tex]
Solving (c): Boxes at the end of the 8th hour
We have:
[tex]b = 244 + 52h[/tex]
In this case:
[tex]h = 8[/tex]
Substitute 8 for h
[tex]b = 244 + 52 * 8[/tex]
[tex]b = 244 + 416[/tex]
[tex]b = 660[/tex]
Hence, there are 660 boxes at the end of the 8th hour
What’s is 9 divided by 3/10
Answer:
30
Step-by-step explanation:
9/(3/10)=9*(10/3)=30
Please help me again!!!!!!!!
Answer:
I agree with Mo.
Step-by-step explanation:
Considering Mo's chart;
0 Tth Hth Thth
1 2 1 = 0.121
Considering Annie's chart;
0 Tth Hth Thth
0 12 1 = 0.0121
From the results obtained from Mo and Annie's chart, only Mo's chart show a grid of of 0.121.
Thus, I agree with Mo.
What is the value of q?
52 589
9
which expression is equivalent to 15+8x+3+2x
Answer:
10x + 18
Step-by-step explanation:
First, we need to add like terms. Like terms are terms that are alike. For instance 8x and 2x are like terms. 15 and 3 are also like terms.
So, we have to add 8x plus 2x and 15 plus 3. That’s comes out to 10x plus 18.
Therefore, this expression is equivalent to 10x + 18.
pls help a.s.a.p!!!!!
Answer:
The correct answers are A and E
Step-by-step explanation:
Nada is making square coasters with sides of 3 inches. On each coaster is a circular design. What is the radius of the largest circle that fits on one of the coasters?
Answer:
1.5
Step-by-step explanation:
diameter is half the length of the circle so if it is 1.5 the full length will be 3 inches which is the full length of the coaster
