Answer:
a) The maximum height of the ball is 272.25 feet
b) The balls take 8 seconds to hit the ground.
Step-by-step explanation:
a) You know that the quadratic function h(t)=−16*t²+124*t+32 models the ball's height about the ground, h(t), in feet, t seconds after it was thrown.
Being a quadratic function of the form:
f (x) = a*x² + b*x + c
The vertex of a quadratic or parabola equation is the highest or lowest point on the graph corresponding to that function. When a> 0, the vertex of the parabola is at the bottom of it and indicates the minimum of the function. When a <0 the vertex is at the top and indicates the maximum of the function.
The value of x at the vertex is calculated by the expression:
[tex]x=\frac{-b}{2*a}[/tex]
The value of y at the vertex is calculated by substituting the value of x at the vertex into the quadratic function.
In this case, being a=-16, b=124 and c=32 you get that the maximum time is:
[tex]x=\frac{-124}{2*(-16)}=3.875[/tex]
Then a maximum height of:
h(3.875)=−16*(3.875)²+124*3.875+32
h(3.875)= 272.25
The maximum height of the ball is 272.25 feet
b) When the ball hits the ground the height is zero. So h (t) = 0:
0=−16*t²+124*t+32
Applying the resolvent:
[tex]\frac{-b+-\sqrt{b^{2} -4*a*c} }{2*a} =\frac{-124+-\sqrt{124^{2} -4*(-16)*32} }{2*(-16)}[/tex]
you get:
[tex]\frac{-124+\sqrt{124^{2} -4*(-16)*32} }{2*(-16)} =-0.25[/tex]
[tex]\frac{-124-\sqrt{124^{2} -4*(-16)*32} }{2*(-16)} =8[/tex]
Since the time cannot be negative, the balls take 8 seconds to hit the ground.
Write an equation of the line that passes through (2,-4) and is perpendicular to the line
y = -2x + 5 in slope intercept form
Answer:
y = (1/2)x - 5
Step-by-step explanation:
The slope of the line y = -2x + 5 is -2. The slope of any straight line perpendicular to this line is therefore the negative reciprocal of -2, which comes out to +1/2.
Using this fact, and the point (2, -4), we write out the slope-intercept form y = mx + b, and substitute the appropriate values:
-4 = (1/2)(2) + b
Then:
-4 = 1 + b, which yields b = -5
Thus, the desired equation is y = (1/2)x - 5
Clue: I am 0.02 units away from -3.8. Where am I?
Answer:
-3.82
Step-by-step explanation:
You are going up the line of negative numbers so you have to add o.o2 to 3.8 (3.80).
Doug took 93 minutes to answer 31 questions. Click on the equation that can be used to determine the number of questions, q, that Doug answered per minute. How many questions did Doug answer per minute?
what is the sum of all interior angles of a parallelogram
What is the domain of f(x)?
What is the domain of g(x)?
Step-by-step explanation:
Domain is the range of x-values for the function to be defined.
Domain of f(x) = [2,9]
Domain of g(x) = [2,9]
Can someone explain how to work this out?
Step-by-step explanation:
2.
(13y)° and (8x+y)° are supplementary angles on a straight line therefore:
13y+8x+y=180°
14y+8x=180°——equation 1
Again,
(13y)° and (20x+3y)° are corresponding angles therefore are equal so:
13y=20x+3y
13y-3y-20x=0
10y-20x=0——equation 2
Now we find the value of x and y using the system of equations
Thus,we solve :
14y+8x=180°
10y-20x=0
Solving them,x=5 and y=10
3.We use the same approach for this
3(x+y)° and 5x are corresponding angles and are equal therefore:
3x+3y=5x
3x-5x+3y=0
-2x+3y=0——equation 1
Again,(5x)° and (4x-9)° are supplementary angles on a straight line so:
5x+4x-9=180
9x-9=180°
9x=180+9
9x=189°
x=21
Plug in the value of x into equation 1 for y
-2x+3y=0
-2(21)+3y=0
-42+3y=0
3y=42
y=42/3=14
So x is 21 and y is 14
Complete the proof.....
Answer:
Step-by-step explanation:
From the given attachment to the question, the following can be deduced.
1. M is the midpoint of GH, given that M is the definition of midpoint.
2. GM ≅ MH, given that x = 2. So that,
GM = 5x = 5(2)
= 10
MH = 3x + 4 = 3(2) + 4
= 10
Thus, GM ≅ MH
3. GM = MH is the definition of congruence. This implies that they are similar.
4. 5x = 3x + 4, by substitution property of equality.
Since, x = 2 then;
5(2) = 3(2) + 4
10 - 10
5. 2x = 4, given that x = 2.
6. GH = GM + MH, by division property of equality.
January 19 national popcorn day. A bag of popcorn has the average of 450 kennels if 4%% of the kernels dont pop how manu pieces of popcorn will the bag make
Answer:
The bag will make 432 pieces of popcorn.
Step-by-step explanation:
From the information given, you know that the bag has an average of 450 kernels and that 4% don't pop. So, with this information you can find the pieces of popcorn that the bag will made by calculating 4% of the average number of kernels in a bag and subtracting the result from that amount:
450*4%=18
450-18=432
According to this, the answer is that the bag will make 432 pieces of popcorn.
Given the equation, y=2x+5 evaluate when x=2.
5
9
0
7
also no need to rush you can wait to answer as long as you want but i probely only have 1o or 20 mins before parents catch me on a site im not suppose to be on lol
Alyssa used a can of paint that was 5/6 full to touch paint her house. When she was done, the bucket was 11/30 full. What fraction of the can did she use?
Answer:
7 / 15
Step-by-step explanation:
Fraction before painting = 5/6
Fraction left after painting = 11/30
Fracrion used = difference of the fraction before painting and fraction left after painting
Fraction used = 5/6 - 11/30
Lowest common factor of 6 and 30 = 30
5/6 - 11/30 = (25 - 11) / 30 = 14/ 30
Fraction used = 14/30 = 7/15
Find the sum
1/2 (w-6)+ 1/4(w+12)
2x + 9 > 21
solve the inequality
Answer:
x>6
Step-by-step explanation:
2x + 9 > 21
2x > 21-9
2x>12 dividing by 2
x>12/2
x>6
hope this helps
Answer:
x > 6
X has to be smaller than 6
what is the volume of this cube?
Answer:
1
Step-by-step explanation:
The volume of this cube is 1 cu.cm , Option B is the correct answer.
What is a cube ?A cube is a three dimensional shape having 6 square faces , all the faces are of equal length , breadth and height.
The volume of the cube is given by side * side * side
Let side = a
Then volume of the cube = a³
In the given figure all the side of the cube is given as 1 cm.
Therefore to determine the value of the volume , we will substitute in the equation
V = (1)³
Volume = 1 cu.cm
Therefore , the volume of this cube is 1 cu.cm, Option B is the correct answer.
To know more about Cube
https://brainly.com/question/14075440
#SPJ2
Nadeen bought a magazine for $7.50 and two sandwiches that cost the same price. She spent a total of $20. How much did each sandwich cost?
Answer:
Each sandwich cost $6.25
Step-by-step explanation:
Subtract the price of magazine then divide the remaining amount with 2 since the price of sandwiches same
(20 - 7.5) ÷ 2 = 6.25
Lindsay Skyler and Valerie are sisters Lindsey is 8 years older than Skyler Skyler is 5 years older than Valley who is 16 years old how old is Lindsay
Answer:
valley is 16
skyler is 21
lindsay is 29
hope this helps!
OH MY GOSH PLEASE IM ABOUT TO CRY HELP ASAPP
Answer:
All systems have 2 real solutions.
Explanation: there are X and Y unknowns.
The density of a substance is 3.4 g cm-3. Its relative density relative to another substance is 2.0. what is the density of the second substance?
Answer: The density of the second substance = [tex]1.7\text{ g cm}^{-3}[/tex]
Step-by-step explanation:
[tex]\text{Relative density }=\dfrac{\text{Density of substance}}{\text{Density of reference}}[/tex]
Given: Density of a substance is [tex]3.4 \text{ g cm}^{-3}[/tex] .
Its relative density relation to another substance = 2.0
Substitute all values in the formula , we get
[tex]2=\dfrac{3.4}{\text{Density of reference}}\\\\\Rightarrow\ {\text{Density of reference}=\dfrac{3.4}{2}\\\\\Rightarrow\ {\text{Density of reference}=1.7 \text{ g cm}^{-3}[/tex]
Hence, the density of the second substance = [tex]1.7\text{ g cm}^{-3}[/tex]
plsss need help!!! will give brainliest !!!
the x values in the table for f(x) were multiplied by -1 to create the table for g(x).what is the relationship between the graphs of the two functions.
Answer:
The relationship between the graphs of the two functions is "They are reflections of each other across the y-axis" ⇒ B
Step-by-step explanation:
If the function f(x) reflected across the x-axis, then the new function g(x) = - f(x), which means the signs of the y-coordinates of the points on f(x) are opposite in g(x)If the function f(x) reflected across the y-axis, then the new function g(x) = f(-x), which means the signs of the x-coordinates of the points on f(x) are opposite in g(x)∵ The points on f(x) are (-2, -31), (-1, 0), (1, 2), (2, 33)
∵ The points on g(x) are (2, 3), (1, 0), (-1, 2), (-2, 33)
∵ All x-coordinates on f(x) multiplied by -1 to get the x-coordinates of g(x)
→ By using the 2nd rule above
∴ g(x) is the image of f(x) after reflection across the y-axis
∴ The relationship between the graphs of the two functions is
"They are reflections of each other across the y-axis"
A yathc is anchored 90 feet offshore from the base of a lighthouse. The angle of elevation from the boat to the top of the lighthouse is 26 degrees. What is nearest to the hieght of the lighthouse
Answer:
44 ftStep-by-step explanation:
The set up will give a right angled triangle where;
Base of the triangle = 90 ft (distance of the offshore from the base of the house)
theta = 26 degrees (angle of elevation)
Height of the house will be the opposite side = x
Using the TOA trig identity;
tan 26 = opp/hyp
tan 26 x/90
x = 90tan 26
x = 90(0.4877)
x = 43.89 ft
Hence the nearest height of the house is 44ft
11. In the diagrams below the rows of green tiles are surrounded by white tiles
Find a formula for the number of white tiles which would be needed to
surround a row of n green tiles.
Hii please help!!! Show work
Step-by-step explanation:
There are 12 white tiles surrounding 3 green tiles, and 16 white tiles surrounding 5 green tiles.
Common difference = (16-12)/(5-3) = 2.
Hence number of white tiles = 2n + 6.
Please help! if abcd is dilated by a factor of 3, the coordinate of b would be
Answer:
(-6, 6)
Step-by-step explanation:
The coordinates of B to start with is
(-2, 2)
To dilate this by a factor of 3....
-2 * 3 = -6
2 * 3 = 6
The new coordinates of B' would be
(-6, 6)
A few things to know:
- The number 3 is called a "scale factor"
- Dilation means we are multiplying all the (X, Y)'s by the scale factor
- If the scale factor is greater than 1, the size of the shape overall increases
- If the scale factor is less than 1, the size of the shape overall decreases
- If the scale factor is negative, the shape size stays the same. The shape just rotates 180 degrees and moves to the opposite quadrant.
Answer:
-9,-1
Step-by-step explanation:
this is for A
I was looking for it so here you go
you multiply your x and Y by 2
hope this helps :))
15 3/8 + 7 5/6 =
Helppp what’s the. Answer
Answer:
Exact Form:
557/24
Decimal Form:
23.208¯3
Mixed Number Form:
23 5/24
Step-by-step explanation:
Convert the mixed numbers to improper fractions, then find the LCD and combine.
The ratio of boys to girls in a choir is 3 to 7 there are 35 girls in the choir how many members are in the choir
Answer:
50
Step-by-step explanation:
35/7= 5
5*10=50
Answer:
50 people in the choir
Step-by-step explanation:
we can solve for x, assuming x is the value in which 1 is on the ratio. 7x=35, so the value of x would be 5. Next, we must multiply x by 3 since that is what the ratio states. If we do this, we will get 5*3, or 15. Therefore, there are 15 boys in the choir. Last, we have to add 15+35 to get the total number of people in the choir. There are 50 people in the choir.
Hope this helps! :)
(Also i know my explanation is rly bad just ignore it)
48 ounces of liquid detergent
for $6.19
Find the unit rate
Answer:
Step-by-step explanation:
48/6.19=7.7544
Round that answer so it’s 7.75
Unit rate is $7.75 per ounce
Does Anyone Know This
Answer:
1 g-h
2 g^2-h
3 gh
4 g+h
5 h-g
6 g+h^2
Step-by-step explanation:
Help me classify the triangles by its sides and measuring its angles :)
Answer:
Triangle 1: Isosceles obtuse
Triangle 2: Right scalene
Step-by-step explanation:
Isosceles triangles have two congruent sides and two congruent angles. Triangle one fits this description because the double markers on sides AC and AB indicate that the two sides are congruent.
Obtuse triangles have an angle that is larger than 90 degrees. Triangle one fits this description as indicated by angle A. If it were a right angle, it would have a square symbol (as shown in triangle 2). The other two angles are obviously smaller, and they would be acute angles.
Right triangles have an angle that is exactly 90 degrees. Right triangles will have a square to indicate that it has this measurement.
Scalene triangles have three different measurements for its sides and its angles.
please help meee i dont know what i have to do
How do you find the y intercept of a graph
Answer:
Make x equal 0 in the equation of the graph (the equation in the form of y=mx+b)
Step-by-step explanation:
Then, solve the equation for y.
-x+4=x+6
Show full work
Answer:
x=-1
Step-by-step explanation:
Step 1: Subtract x from both sides.
−x+4−x=x+6−x
−2x+4=6
Step 2: Subtract 4 from both sides.
−2x+4−4=6−4
−2x=2
Step 3: Divide both sides by -2.
−2x/−2= 2/−2
x=−1
Hope this helped :)
The town of Apple Valley, California is at an elevation of 2,900 feet above sea level. Death Valley, California has an elevation of 282 feet below sea level. What is the difference in elevation of the two towns?
Answer:
The difference in elevation of the two towns is 3182 feet.
Step-by-step explanation:
Let's treat the elevation of sea level as 0 feet. That way, we can calculate the elevation of the two spots by using it as a measuring parameter.
Apple Valley is 2,900 feet above sea level. Hence, its elevation is (0 + 2,900) feet, which is 2,900 feet.
Death Valley is 282 feet below sea level. Hence, its elevation is (0 - 282) feet, which is -282 feet.
Hence, to calculate the difference, we subtract the elevation of Death Valley from that of Apple Valley, getting [2900 - (-282)] feet, which equals to (2900 + 282) feet which is 3182 feet.
Therefore, the difference in elevation of the two towns is 3182 feet.
Hope this helped!
