Answer:
The maximum height of the ball is 380.25 feet in the air.
Step-by-step explanation:
The quadratic function:
[tex]h(t)=-16t^2+132t+108[/tex]
Models the ball's height h(t), in feet, above the ground t seconds after it was thrown.
We want to determine the maximum height of the ball.
Note that this is a quadratic function. Therefore, the maximum or minimum value will always occur at its vertex point.
Since our leading coefficient is leading, we have a maximum point. So to find the maximum height, we will find the vertex. The vertex of a quadratic equation is given by:
[tex]\displaystyle \left(-\frac{b}{2a},f\left(\frac{b}{2a}\right)\right)[/tex]
In this case, a = -16, b = 132, and c = 108. Find the t-coordinate of the vertex:
[tex]\displaystyle t=-\frac{132}{2(-16)}=-\frac{132}{-32}=\frac{33}{8}=4.125[/tex]
So, the maximum height occurs after 4.125 seconds of the ball being thrown.
To find the maximum height, substitute this value back into the equation. Thus:
[tex]h(4.125)=-16(4.125)^2+132(4.125)+108=380.25\text{ feet}[/tex]
The maximum height of the ball is 380.25 feet in the air.
simplify (3x+2)(3x-2)
Answer:
9 (*2) − 4
Step-by-step explanation:
the *2 is the square unit
help put the work plzzzz
Solve by using common denominators 2/1 divide 1/4
Answer:
8
Step-by-step explanation:
That'd be "2/1 divided by 1/4" and if we use common denominators we get:
2 8
----- = ----- divided by 1/4 comes out to 8/1, or just 8
1 4
Which of the following pairs of functions are inverses of each other?
Answer:
THE ANSWER IS B
Step-by-step explanation:
IT JUST MAKES SENSE TO CHOOSE B
The option D pairs of functions are inverses of each other.
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
To find the inverse of a function, write the function f(x) as a function of x and then solve for x as a function of f(x).
For option A,
f(x) = 2 + ∛x
To solve for x,
∛x = f(x) - 2
x = (f(x) - 2)³
That is also the inverse So,
g(x) = (x -2)³ "Not correct"
For Option B,
f(x) = x/6 + 8
To solve for x,
x/6 = f(x) -8
x = 6f(x) - 6 *8
That is also the inverse So,
g(x) = 6x - 6 *8 "Not correct"
For Option C,
f(x) = 7/x - 9
To solve for x,
7/x = f(x) +9
x = [tex]\frac{7}{f(x) +9}[/tex]
That is also the inverse So,
g(x) = [tex]\frac{7}{x +9}[/tex] "Not correct"
For Option D,
f(x) = 5x - 11
To solve for x,
5x= f(x) + 11
x = (f(x) + 11)/5
That is also the inverse So,
g(x) =(x + 11)/5 "correct"
Thus, the option D pairs of functions are inverses of each other.
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Given that Triangle KLM is congruent to Triangle RQP, what is the measurement of Angle L? Write only the numerical answer. You do not have to include degrees.
Answer:
Did you ever get the answer?
Step-by-step explanation:
i need help on these questions i don't know about these
Answer:
Step-by-step explanation:
1) Polynomial
2) the 1st choice is correct... the exponents are in descending order
Answer: question one is option 2 and question 2 is option 1
Step-by-step explanation:
How many sides does a polygon have if the sum of the interior angles is 900∘?
Answer:
7 slides
Step-by-step explanation:
Sum of exterior angles of any polygon is always 360∘, it can never be 900∘. Hence, there cannot be any polygon like this.
It appears that by error the word "exterior" has been mentioned. In case sum of interior angles is 900∘,
total sum of all the angles is 900∘+360∘=1260∘.
But sum of each pair of interior and exterior angles add up to 180∘
we have 1260∘180∘=7 such pairs
and hence polygon has 7 sides.
Answer:
It's a heptagon, so 7 sides
Step-by-step explanation:
The difference of two numbers is 8. If the sum of the smaller number and the square of the larger number is 148, what is the larger number?
A farmer has 500 acres of arable land on which he wants to plant potatoes and corn. The farmer has $40,000 available for planting and $30,000 for fertilizer. Planting 1 acre of potatoes costs $90, and planting 1 acre of corn costs $50. Fertilizer costs $30 for 1 acre of potatoes and $80 for 1 acre of corn. (a) Find a system of inequalities that describes the number of acres of each crop that the farmer can plant with the available resources. (Let x and y be the numbers of acres of potatoes and corn, respectively.)
Answer:
90x+ 50 y ≤ $40,000------ A
30x+ 80y ≤ $ 30,000------- B
x + y ≤ 500 --- C
Step-by-step explanation:
Let x and y be the numbers of acres of potatoes and corn, respectively.
Then according to the given conditions
90x+ 50 y ≤ $40,000------ A
30x+ 80y ≤ $ 30,000------- B
x + y ≤ 500 --- C
where both x and y equal to or greater than zero and cannot take a value less than zero.
x + y ≤ 500 --- C
gives us an idea that the total arable land is less or equal to 500 acres.
90x+ 50 y ≤ $40,000------ A
tells us that the total cost of planting potatoes and corn is less or equal to $ 40,000
30x+ 80y ≤ $ 30,000------- B
tells us that the total cost of fertilizers for potatoes and corn is less or equal to $ 30,000
In each of these x and y cannot have negative values or less than zero.
Can someone help please :)
Answer:
x = 5
Step-by-step explanation:
These triangles are similar, so they are in proportion to each other. Because of this we can say [tex]\frac{2.5}{3.5}[/tex] (the lengths of the vertical sides) = [tex]\frac{x}{7}[/tex] (the lengths of the hypotenuses). If we solve by cross-multiplying the numbers and then dividing we get x = 5.
Marc is filling 1-cup containers with juice.
He has 5 gallons of juice. How many 1-cup
containers can he fill? (1 gallon = 16 cups)
Answer:
80
Step-by-step explanation:
5*16 = 80
Hence, the Marc has the number of cups are [tex]80[/tex].
What is the equation?
An equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.
The most basic and common algebraic equations in math consist of one or more variables.
Here given that,
Marc is filling one-cup containers with juice. He has five gallons of juice.
As we know,
[tex]1gallon=16cups[/tex]
So, it would be [tex]5(16)=80[/tex].
Hence, the Marc has the number of cups are [tex]80[/tex].
To know more about the equation
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hello my friend is from 7th grade she need help with her math 5200 at 49% for 3years??
Answer:
At the end you will have 12,844$ and you have earned 7644$
Step-by-step explanation:
49% 49 times the money 5,200$ = 254,800 divided by 100 = 2548 in 1 year.
Times 2548 by 3 and get 7644$ ( Interest Earned ) add that by original money and get 12,844$ (Money In Total)
Please help!!!!!!!!!
Nov. 1 Loaned $52,200 cash to C. Bohr on a 12-month, 7% note. Dec. 11 Sold goods to K. R. Pine, Inc., receiving a $1,800, 90-day, 8% note. Dec. 16 Received a $4,800, 180-day, 10% note to settle an open account from A. Murdock. Dec. 31 Accrued interest revenue on all notes receivable.
Answer:
Dr Notes Receivable $52,200
Cr Cash $52,200
Dec. 11
Dr Notes Receivable $1,800
Cr Cash $1,800
Dec. 16
Dr Notes Receivable $4,800
Cr Accounts Receivable $4,800
Dec. 31
Dr Interest Receivable $637
Cr Interest Revenue $637
Step-by-step explanation:
Preparation of the journal entries
Nov 1
Dr Notes Receivable $52,200
Cr Cash $52,200
Dec. 11
Dr Notes Receivable $1,800
Cr Cash $1,800
Dec. 16
Dr Notes Receivable $4,800
Cr Accounts Receivable $4,800
Dec. 31
Dr Interest Receivable $637
Cr Interest Revenue $637
($609+$8+$20)
Working:.
Interest Revenue
Note that 1 Nov to Dec 31st will give us 2 months
=$52,200 x 0.07 x 2/12 =$609
Note that Dec 11 to Dec 31st will give us 20 days
=$1,800 x 0.08 x 20/360 =$8
Note that Dec 16 to Dec 31st will give us 15 days
=$4,800 x 0.10 x 15/360=$20
Pls help me!!!! Im stuck!!!
Answer:
has no solution.
Step-by-step explanation:
you can see that the two equations are almost identical except for the fact that one is multiplied by 7, but it isnt completely multiplied correctly so there would be no solutions.
Answer:
infinite solutions
Step-by-step explanation:
you can solve this by the elimination method. take the rover a equation and multiply it by -7 and then combine the equations. when you do this, you can see that either side equals 0 which means that there are infinite solutions.
-7(y= 1.5x - 6) which equals the equation below
-7y= -10.5x-42 then combine the other equation
7y=10.5x+42 and that equals
0=0
Help plssssss! Thnx!
Answer:
$55.48
Step-by-step explanation:
nice to help you.hope it helps
A school sells chips and candy bars for a fundraiser.
· Each bag of chips sells for 75 cents.
· Each candy bar sells for $1.25
• The school sold fifty more bags of chips than candy bars
• The school made a total of $437.50
How many bags of chips did the school sell?
Answer: 21
Step-by-step explanation: 21 + 21 = 21
Find the value of x
Answer:
1
Step-by-step explanation:
As per circle theorem rule, ∠GDE is twice than ∠GFE
10x +94 = 2 × (x+51)
10x + 94 = 2x + 102
8x = 8
x = 1
∠GDE= 10x+94° = 104°
∠GFE= x + 51° = 52°
find the diffrence of the following sequence : -7,-9,-11
Answer:
-2
Step-by-step explanation:
you're subtracting 2 from each to get the next number, so the answer is -2
hope this helps, have a wonderful day :))
Solve for x -(-2x+1)=9-14x
Answer:
x = 5/8
Step-by-step explanation:
Last one
What is the volume, in cubic centimeters, of the cylinder?
A 602.88
B 150.72
C 50.24
D 301.44
Answer:
A
Step-by-step explanation:
The base of your cylinder has a radius of 4 cm, its area is 16 × 3.14, or 50,24 square centimeters. If that same cylinder is 12 cm tall, its volume is 50,24 × 12 = 602,88 cubic centimeters.
Hope this helps
Kind Regards
Farah Syed
Will give brainlyest!! the measures of the angles of the triangle are 50, 30 and 95 degrees.
What is the measure of the largest exterior angle of the triangle
Answer:
145 degrees
Step-by-step explanation:
The largest exterior angle would be the one with the smallest interior angle, which is 35 And exterior and interior angles is always 180.
180 - 35 = 145 degrees
I need the brainliest
Answer:
145 degrees
Step-by-step explanation:
I don't want the brainleist.
find the circumference of the circle. circle radius is 8cm
Answer:
50.24
Step-by-step explanation:
you multiply 8 x 2 to get 16
then you multiply 16 x 3.14 to get 50.24
Solve m+18+23=71
PLZZZZZ I NEED THE ANSER PLZZZ
Answer:
m + 18 + 23 = 71
m + 41 = 71
m = 71 - 41
m = 30
Answer:
30
Step-by-step explanation:
m+18+23=71
m+41=71
m=71-41
m=30
Item 14
Find the missing dimension. Use the scale factor 1 : 12.
Answer:
3.84m
Step-by-step explanation:
If the scale for this Water tower is 1 : 12 then this means that for every 1cm of the model, the actual water tower has 12cm. Therefore, in order to find the actual depth of the water tower we first need to multiply the depth of the model by 12.
32cm * 12 = 384cm
1 cm is equal to 0.01 m , therefore we now have to multiply the depth of the actual water tower which is in cm by 0.01 to get the actual depth in meters
384 * 0.01 = 3.84m
PLEASE HELP AND HURRY!!!!!
A square playground is covered with pebbles, except for two equal size triangular portions that have grass. How many square feet do the pebbles cover?
7ft
14ft
Answer:28\2
Step-by-step explanation:
7+7=14
7+7=14
14+14=28
Triangle A=1\2bh
So 28\2
The pebbles cover an area of 147 sq ft. We can use the Pythagorean theorem to find the solution.
What is Pythagoras theorem?
The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.
Now, Let's call the length of the third side of the triangle "x".
Since the two triangles are equal in size, and they share two sides with the square, we can use the Pythagorean theorem to find x.
a² + b² = c²
7² + 7² = c²
49 + 49 = c²
98 = c²
c = √(98)
c = 7 √(2)
So, each triangle has a base of 7 ft and a height of 7 √(2) ft.
And, Area of each triangle = (base × height) / 2
= (7 × 7√(2)) / 2
= 24.5 ft²
Since, there are two triangles,
Hence, the total area of the grass is,
⇒ 24.5 sq ft × 2 = 49 sq ft
Hence, The square has an area of,
⇒ 14ft × 14ft = 196 sq ft
So, The pebbles cover an area of,
⇒ 196 sq ft - 49 sq ft = 147 sq ft.
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I need to know the answer to this question? 9(p−4)=−18
Answer:
p = 2
Step-by-step explanation:
Solve the equation:
Distributive property: 9p - 36 = -18
Isolate the variable: 9p = 18
Divide: p = 2
Can I have Brainliest?
u/9+11 at u = -18 can u please show steps?
Answer:
u = -261
Step-by-step explanation:
Subtract 11 from both sides:
u/9 + 11= -8
u/9 + 11 - 11 = -18 -11
u/9 = -18 - 11
u/9 = -29
u/9 9 = -29 9
u= - 29 9
u = -261
hope i helped
What are the solutions to this equation?
16x2 + 9 = 25
Answer:
x = 1, -1
Step-by-step explanation:
Answer: 16x2 + 9 = 25 A. x = -4 and x = 4 B. x = 0 and x = 4 C.
Step-by-step explanation:
What is the smallest perfect square
Answer:
Answer: 0 is smallest perfect square but if Any number that can be written as a POSITIVE integer to the power of 2. then 1 is the smallest perfect square number.
Step-by-step explanation:
Answer:
Answer: 0 is smallest perfect square but if Any number that can be written as a POSITIVE integer to the power of 2. then 1 is the smallest perfect square number.
Step-by-step explanation: