It takes the diver 5 s to reach the water.
Quadratic equationsThese are mathematical equations in which the highest power of the unknown is 2 and in factored form are written as f(x) = (x -a)(x - b)
Since the Olympic divers height in feet above the water can be modeled by the function f(x) = -2(x-5)(x+1), where x is the time in seconds after he begins the dive.
The diver reaches the top of the water when f(x) = 0.
So, equating f(x) to zero, we have
f(x) = 0
-2(x-5)(x+1) = 0
Dividing through by -2, we have
(x-5)(x+1) = 0
So, (x - 5) = 0 or (x + 1) = 0
x = 5 or x = -1
Since time cannot be negative, x = 5 s.
So, it takes the diver 5 s to reach the water.
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Answer:
[tex]a^-^7[/tex]
Step-by-step explanation:
[tex]\frac{a^{-13}}{a^{-6}}[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}[/tex]
[tex]=a^{-13-\left(-6\right)}[/tex]
[tex]\mathrm{Apply\:rule}\:-\left(-a\right)=a[/tex]
[tex]=a^{-13+6}[/tex]
[tex]\mathrm{Add/Subtract\:the\:numbers:}\:-13+6=-7[/tex]
[tex]=a^{-7}[/tex]
Answer [tex]=a^{-7}[/tex]
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You worked
44 hours. 40
regular hours a
$8.50 and 4
overtime hours. What would be your gross pay?
Answer:
$391.00
Step-by-step explanation:
Typically, regular work hours are paid at the rate given ($8.50), and overtime is "time and a half", or 1.5 times the regular pay.
We will get paid 40 hours at $8.50, and 4 four hours at 1.5x$8.50:
[tex]40(8.5)+4(1.5)(8.5)\\340+51\\391[/tex]
You will get paid $391.00 in gross pay, before taxes :)
Is my answer correct?
Answer: yes there are just delete the last one and replace it with the sixth one start from the start also does this happen to be K12 7th grade?
Step-by-step explanation:
4 cases of Sprite are on sale for $12.
What is the cost per case?
At this rate, how many cases can you purchase for $48?
Answer
One case of sprite costs 3 dollars, All four cases are $12. You can buy 16 cases of sprite with 48 dollars.
Step-by-step explanation:
How to get the cost for 1 case:
You have 4 cases of sprite which all four combined costs $12. You divide 12 by 4 and get 3.
How to get the amount of cases of sprite you can buy with $48:
divide 48 by 3 and you get 16. Why 3? Because 3 is the amount per case and 16 x 3 is 48. Thank me later!
Answer:
It costs $3 per case of Sprite
With 48 dollars, you could buy 16 cases.
Step-by-step explanation:
12/4 = 3 12 dollars divided buy 4 dollars each equals 3 dollars per case
48/3 = 16 48 dollars divided by 3 dollars per case equals 16 cases of sprite
What is the quotient? X^2-11x+24/(x-8)(x+2)
Answer:
D
Step-by-step explanation:
[tex]\frac{x^2-11x+24}{(x-8)(x+2)}[/tex] ← factorise the numerator
= [tex]\frac{(x-8)(x-3)}{(x-8)(x+2)}[/tex] ← cancel the common factor (x - 8) on numerator/ denominator
= [tex]\frac{x-3}{x+2}[/tex]
The quotient of the given division problem is D. (x - 3) / (x + 2).
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
Given expression is,
(x² - 11x + 24) / (x - 8)(x + 2)
We have to first factor the numerator.
x² - 11x + 24 can be factored as (x - 8) (x - 3).
This is done using the factorization method.
Now the expression becomes,
(x² - 11x + 24) / (x - 8)(x + 2) = (x - 8) (x - 3) / (x - 8)(x + 2)
= (x - 3) / (x + 2)
Hence the quotient is option D.
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Y= x + 6
y= -x+2
solve each system of equations by substitution
Answer:
x= -2
y=4
Step-by-step explanation:
Since we have an equation set equal to y, we can plug it in for either value of y.
I will be using y= x+6 in this case.
Plug in x+6 for the other equation, so instead of y=-x+2 it will now be that x+6 = -x+2
Now add x to both sides, and that will remove the x on the left side leaving us with 2x+6 = 2
Now, subtract 6 from both sides to get 2x isolated, and you will get 2x= -4
Divide both sides by 2 to get x= -2
Not plug x= -2 in back for the top (or bottom) equation and get that y=4
Hope this helps and isn't too complicated!
please help. please help.
Answer:
A. $3960
B. r=40x^2+400x+3000
C. $200
Step-by-step explanation:
A. Total Revenue (R) is equal to price per dive (P) multiplied by number of customers (C). We can write . R=PC
Per price increase is $20. So four price increase is $20x4=80. Hence, price per dive is 100+80=$180.
Also per price increase, 2 customers are reduced from 30. For 4 price increases, 4x2=8 customers are reduced. Hence, total customers is 30-8=22
So Total Revenue is: R= 180 x 22= 3960
B. Each price increase is 20. So x price increase is 20x. Hence, new price per dive would be equal to the sum of 100 and 20x.
Also per price increase, customers decrease by 2. So per x price increases, the customer decrease is 2x. Hence, new number of customers is the difference of 30 and 2x.
Therefor we can write the quadratic equation for total revenue as the new price times the new number of customers.
R= (100+2x)(30-2x) = -40x^2+400x+3000
C. We are looking for the point (x) at which the equation modeled in part (B) gives a maximum value of revenue (y).
That means, the greatest revenue is achieved after 5 price increases. Each price increase was 20, so 5 price increase would be 5 x 20= 100. So the price that gives the greatest revenue is 100+100 = 200
Rebecca is calculating her expected expenses for her week long trip to Thailand. Her plane ticket costs 22,885 baht, her lodging costs 15,307 baht, and she has set aside 29,071 baht for food and spending money. What is Rebecca’s total expense? a. 128,071 baht b. 67,263 baht c. 21,493 baht d. 9,121 baht.
Answer:
The answer is B because you add up the 3 expenses
Step-by-step explanation:
Add the three expenses
The total expected expense of Rebecca for her week long trip to Thailand is given by: Option B: 67,263 baht
How to calculate total expense?Total expense shows the overall expense for the thing we're expending for. We add all the expenses to get the total expense.
For this case, we're given that:
Cost of plane tickets = 22,885 bahtCost of lodging = 15,307Cost for food and other expenses = 29,071So, total expected expense is sum of all these expenses.
Total expected expense = 22885 + 15307 + 29071 = 67263 baht
Thus, the total expected expense of Rebecca for her week long trip to Thailand is given by: Option B: 67,263 baht
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true or false are these lines are intersecting
Answer: True.
Step-by-step explanation: Lines that don't intersect are parallel lines, and those are not parallel. Parallel lines look like the image below. The point of intersection in your image is where K is.
Hope this helps! :)
7(g + 2h)
What is an equivalent expression
Answer:
7g+14h
Step-by-step explanation:
hope it helped you
Answer:
7g + 14h
Step-by-step explanation:
What is an equivalent expression?
7(g + 2h)
7(g) + 7(2h) <== multipe both terms by 7
7g + 14h
Hope this helps!
Jade wants to buy a $200,000 term life insurance policy. she is 34 years old. using the premium table, what is her annual premium for a 10 year policy? a 5-column table with 6 rows titled annual life insurance premium (per 1,000 dollars of face value). column 1 is labeled age with entries 30, 31, 32, 33, 34, 35. column 2 is labeled 5-year term male with entries 3.98, 4.08, 4.19, 4.30, 4.42, 4.54. column 3 is labeled 5 year term female with entries 3.66, 3.76, 3.87, 3.98, 4.10, 4.22. column 4 is labeled 10-year term male with entries 6.06, 6.13, 6.30, 6.38, 6.45, 6.53. column 5 is labeled female with entries 5.72, 5.79, 5.85, 5.93, 6.01, 6.09. a. $1,290 b. $1,202 c. $6,010 d. $820
Premium rates are often referred to as premium per fixed face value. Jade's annual premium for a 10-year policy of $200,000 is $1,202.
How to calculate the total annual premium for $x?
When it's given that the annual premium is $p per $y face value, then we can calculate the annual premium for $1 face value and then use it to calculate the annual premium for $x. Therefore using proportions, we can write,
$y face value : $p annual premium
[tex]\text{\$1 face value} : \$\dfrac{P}{y}\ \rm annual\ premium[/tex]
[tex]\text{\$x face value} : \$\dfrac{P\times x}{y}\ \rm annual\ premium[/tex]
In the given case, from the tables, we see that for age 34, and 10-year life insurance for the female gender, there is an annual premium of 6.01 per $1000 face value.
Therefore, we will get the value of p = 6.01, and y = 1000.
As mentioned that Jade wants to buy Life insurance for $200,000, therefore, x = $200,000
Putting it in the above-derived formula, we get:
[tex]\text{\$x face value} : \$\dfrac{P\times x}{y}\ \rm annual\ premium[/tex]
[tex]\text{\$200,000 face value} : \$\dfrac{6.01\times 200,000}{1,000}\ \rm annual\ premium = \$1,202\ \rm annual\ premium[/tex]
Hence, Jade's annual premium for a 10-year policy of $200,000 is $1,202.
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Answer:
b 1,202 on edge 2022
Step-by-step explanation:
Please help ASAP
Dave is 8 years younger than 4 times Julia's age. If Dave is 16, how old is Julia?
6 years
24 years
32 years
O
56 years
Step-by-step explanation:
Age of dave = y
Age of Julia = x
y = 4x - 8
if y = 16
then
4x - 8 = 16
4x = 16 + 8
4x = 24
x = 24/4
x = 6
Julia is 6 years old
Answer:
Julia is 6 years old.
Step-by-step explanation:
Dave + 8 = 4 Julia
16 + 8 = 4 Julia
24 = 4 Julia
6 = Julia
Julia is 6 years old
Which could be the area of one lateral face of the triangular prism? A triangular prism. The rectangular sides are 8 feet by 2. 5 feet, 8 feet by 6 feet, and 8 feet by 6. 5 feet. The triangular sides have a base of 2. 5 feet and height of 6 feet. [Not drawn to scale] 7. 5 ft2 15 ft2 20 ft2 39 ft2.
The area of one lateral face of the triangular prism could be 20 ft².
What is a prism?a prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy of the first base, and n other faces, necessarily all parallelograms, joining corresponding sides of the two bases.
Since the base of the prism is triangular so there will be three lateral faces.
Dimensions of rectangular lateral faces are:
1)8 feet by 2.5 feet
2)8 feet by 6 feet
3) 8 feet by 6. 5 feet
Area of the lateral face with dimension 8 feet by 2.5 feet = 8*2.5 =20 ft²
Area of the lateral face with dimension 8 feet by 6 feet = 8*6 =48 ft²
Area of the lateral face with dimension 8 feet by 6.5 feet = 8*6.5 =51 ft²
Therefore, the area of one lateral face of the triangular prism could be 20 ft².
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Phoebe spent $12.87 at the bookstore. She paid with a $20 bill. How much is her change?
Answer:
7.28 in change
Step-by-step explanation:
When she used 20 bucks it gave her 7.28 cents.
poiuytredfghjkl........
Answer:
yes you are correct
Step-by-step explanation:
not sure what you mean but yea
Gabe's math class starts at 12:15 P.M. and lasts for 1 hour and 30 minutes. After math class, Gabe has recess for 15 minutes. What time does Gabe's recess end?
please help n explain ily
Answer:
Ends at 2:00
Step-by-step explanation:
12:15 + 1:30 = 13:45.
13:45 + 00:15 = 14:00
14 - 12 = 2
Recess ends at 2:00
Answer:
2p
Step-by-step explanation:
ok so 12:15 + 1 hour = 1:15pm
1:15pm + 30 minutes = 1:45pm
so that's the time that class ends at.
now Gabe has recess for 15 minutes.
so 1:45pm + 15 minutes = 2pm
Gabe's recess finishes at 2pm
hope that helps : )
Which expression is equivalent to –12 – 40?
Which expression has a value of 13? (2 points)
a
(20 ÷ 4) − 4 + 3 x 2
b
(18 ÷ 2) + 6 ÷ 6 + 3
c
(16 ÷ 4) + 3 x 4 − 1
d
(10 ÷ 2) − 3 + 4 x 2
Answer:
it is option B that is correct
Step-by-step explanation:
use BODMAS
B- Brackets
O-order
D-division
M-multiplication
Addition
Subtraction
Solve the system using linear combination.
41
S 5x + 3y
Зх бу
9
We want to eliminate the variable y. What number should we multiply times the first
equation, so that when we add the two equations, we can eliminate the variable y?
Answer:
Delta does not have a relative extreme in the equation, so it is variable y It can not be true
Step-by-step explanation:
[tex]s = 5x + 3y[/tex]
There is an answer
The rest of the equation that has no substituted delta is not true, so the prime variables have relative extremes.
Kelly has some money. She spends $17.50 on clothes,
She has $6.21 left. Which model represents this?
a $17.50 -6.21 =n
b. n - 17.50 = 6.21
c. n + 17.50 = 6.21
d. n + 6.21 = 17.50
Explain.
Answer:
b
Step-by-step explanation:
because we dont know what she started with.
Answer:
b) I guess
Step-by-step explanation:
she has n. she spends $17.50 (-). she has $6.21 left
n - 17.50 =$6.21
n-17.50=$6.21
Write an expression for the area of square 4 by combining the areas of the four triangles and the two squares.
The area of Square 4 is a2+2ab+b2
The area of Square 5 is 2ab+c2
Setting them equal to one another (a2+2ab+b2=2ab+c2) and simplifying yields that a2+b2=c2 (note that 2ab is what they have in common), which is Pythagoras' theorem.
if x=2 and y=-3 solve each of the question
a) 3x+y^2=
b) 3x^2+5y^2=
c)2x+y
d)5y+x^2=
Answer:
A) 15
B) 57
C) 7
D) 19
Step-by-step explanation:
a) 3x+y^2=
Insert the values
3(2) + 3^2
6+9 (3^2 = 3 x 3 = 9)
= 15
b) 3x^2+5y^2=
Insert the values
3(2)^2 + 5(3)^2
3(2^2 = 2 x 2 = 4) + 5(3^2 = 3 x 3 = 9)
3(4) + 5(9)
12+ 45
= 57
c) 2x+y
insert the values
2(2) + 3
4 + 3
= 7
d) 5y+x^2=
Insert the values
5(3)+ 2^2
15 + (2^2 = 2x2 = 4)
15+4
= 19
Paisley is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 22 meters from the building. The angle of elevation from her eyes to the roof (point A) is 29°, and the angle of elevation from her eyes to the top of the antenna (point B) is 42°. If her eyes are 1.74 meters from the ground, find the height of the antenna (the distance from point A to point B). Round your answer to the nearest meter if necessary.
Using the tangent ratio, the height of the antenna, to the nearest meter, is AB = 8 m.
What is the Tangent Ratio?Tangent ratio is expressed as: tan ∅ = opposite/adjacent (TOA).
The information given has been sketched in the diagram attached below.
Find AC using the tangent ratio. Thus, we would have:
tan 29 = AC/CD
Substitute
tan 29 = AC/22
AC = tan 29 × 22 = 12.2 m.
Find BC using the tangent ratio:
tan 42 = BC/DC
Substitute
tan 42 = BC/22
BC = tan 42 × 22 = 19.8 m.
The height of the antenna, AB = BC - AC = 19.8 - 12.2 ≈ 8 m.
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==========================================================
Explanation:
The full circle has a circumference of
C = 2*pi*r
C = 2*3.14*4
C = 25.12
Divide this by four because we only want a quarter circle (and not the whole thing). Imagine cutting a pizza into four equal slices, and we only focus on one slice.
The curved portion of the slice is roughly 25.12/4 = 6.28 units long.
Add on the two straight line portions of the quarter circle to get 6.28+4+4 = 14.28
The straight line portions are the radius.
The answer of 14.28 is approximate because pi = 3.14 is approximate.
If Sam has 120 dollars to spent what will he use it on, 20 apples that cost $6 or 50 pears that cost $3 dollars
Answer:
50 pears = 3 dollars
Step-by-step explanation:
he would want to save as much as possible
is this correct or no if not what the answer
Answer:
A.
While D is partially correct, A is the way to go, because samples are easier to collect than whole populations. The internet quotes, "It is a much quicker process and is more time efficient." This proves the theory why A is the correct answer.
What type of number is -91i?
Choose all answers that apply:
real
imaginary
complex
Answer:
complex
Step-by-step explanation:
Jory's motorcycle travels at a constant rate of 18 miles in 45 minutes. What is the rate, in miles per hour,
that Jory is traveling?
A. 13
B. 18
C. 24
D. 26
please give explanation
Answer:
C. 24
Step-by-step explanation:
We should find how many miles Jory travels in 15 minutes first.
45 ÷ 15 = 3
18÷3=6
6 miles in 15 minutes
every hour has 60 minutes
60 ÷ 15 = 4
multiply 6 by 4 to find miles per hour
6×4=24
You ask 179 of your classmates how they feel about the school year being made longer. Complete the two-way frequency table to show the results of the survey. Use pencil and paper. Combine the very unhappy and unhappy categories into one category called dislike and combine the happy and very happy categories into one category called like. Complete a new two-way frequency table.
Answer:
The answer are in the file
Write a function rule for the relationship between the amount of plant food remaining, f), and the number of days that have passed, Type the correct answer in the box 0 B 2 ve CSC Eco 109 f(x) =
Answer: f(x) = 72-12x
Step-by-step explanation: Hope it helps