9514 1404 393
Answer:
19.6 in²
Step-by-step explanation:
The area in terms of the diameter is given by ...
A = (π/4)d²
A = π/4(5 in)² = 25π/4 in² ≈ 19.6 in²
A t-shirt is launched into the stands at a game. The equation h(x) = -16x2 + 48x + 6 models the relationship between time x and the height of the t-shirt h(x). List the calculation you must complete to find the answer to each question.
1. How high off the ground is the t-shirt launcher?
2. How high is the t-shirt after 1 second?
3. When does the t-shirt reach its maximum height?
4. What is the maximum height of the t-shirt?
5. When will the t-shirt reach the ground again if nobody catches it?
Answer:
1) 6 feet
2) 38 feet
3) at 1.5 seconds
4) 42 feet
5) in 3.12 seconds
Step-by-step explanation:
A sheet of cardboard 12 inches square is used to make an open box by cutting out squares of equal size from the four corners and bending up the sides. What size should the squares be to obtain a box with the largest possible volume
Answer:
[tex]x=6+3\sqrt{2}[/tex] is the size of the square
Step-by-step explanation:
Let the side of the square cut from the cardboard be “x”
Size of the square base = [tex]12 -2x[/tex], height of the box = x
Volume of square box = Area * height = [tex](12-2x)^2 * x[/tex]
Differentiating the above equation and equating it to zero, we get –
d/dx [tex]((12-2x)^2 * x)[/tex]
d/dx[tex]{(144 + 4x^2 -48x)*x}[/tex]= d/dx [tex](144x + 4x^3 -48x^2)[/tex]
d/dx [tex](144x + 4x^3 -48x^2) = 0[/tex]
[tex]144+8x^2-96X= 0\\18 +X^2-12X = 0[/tex]
On solving above equation, we get –
[tex]x=6+3\sqrt{2} \\ x=6-3\sqrt{2}[/tex]
Matteo is following this recipe to make a cake.
He wants to make five of these cakes.
How much of each ingredient does he need?
Recipe: Makes 1 cake
3 ounces butter
4 ounces sugar
5 ounces of flour
2 eggs
1 teaspoon (tsp) baking powder
A water slides at a party of s 15 feet tall.The base of the water slide is 8 feet long.what is the length of the slide?
Answer:
It would be 17 feet.
Step-by-step explanation:
So to do this, there is a right triangle being made with the height of the water slide and its base (length). With this, the Pythagorean Theorem can be used to find the hypotenuse of these lengths by the equation:
a^2 + b^2 = c^2
So by plugging in the given legs of the triangle, the answer can be found.
15^2 + 8^2 = c^2
225 + 64 = c^2
289 = c^2
c = 17
A calculator costs $85 at staples if the calculator is 20% off how much do you pay?
Answer:
$ 17 off
Step-by-step explanation:
20% is one fifth of the price
So divide 85 by 5 you get 17
Since you only get one 1/5 of the price off you save $17
Just to check and make sure you can do 17 * 5 = 85
Item 19 Your pump empties the water from a swimming pool in 6 hours. When your friend's pump is used together with your pump, the pool is emptied in 1.5 hours. How long (in hours) does it take your friend's pump to empty the pool when working alone
Answer:
0.75 hours
Step-by-step explanation:
Time taken by my pump = 6 hours
Time taken by friend's pump = x
Combined time = 1.5 hours
Rate :
my pump = 1/6
Combined rate = 1/1.5
Combinwd rate = 1/6 + 1/x
Hence :
1/6 + 1/x = 1/1.5
(x + 6) / 6x = 1.5
x + 6 = 9x
x - 9x = - 6
-8x = - 6
x = - 6 / - 8
x = 0.75 hours
Awnser this please and thank you if u don’t not give me bad awnsers I will give u a brainliest
Answer:
slope = 20
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (10, 200) ← 2 points on the line
m = [tex]\frac{200-0}{10-0}[/tex] = [tex]\frac{200}{10}[/tex] = 20
Rahul has 5 BLUE BLOCKS, 3 PINK BLOCKS AND 4 GREEN BLOCKS. He wants to count the total number of blocks he is having. In how many ways he can find the answer? Form a mathematical expression to find the total number of blocks and identify the property used.
Answer:
a) He can find the answer in one way
b) We make use of Addition property of mathematics
c) Total number of blocks = 12 blocks
Step-by-step explanation:
a) He can find the answer in one way
b) We make used of addition property of mathematics
c) The total number of blocks he is having is calculated as:
Blue blocks + Pink blocks + Green blocks
Where
Blue blocks = 5
Pink blocks = 3
Green blocks = 4
Hence:
Total number of blocks = 5 + 3 + 4 = 12 block
Mr. Falk is going to replace the carpet in his basement. The basement is
rectangular with a length of 27 feet and a width of 18 feet. If the cost of the
carpet is $32 per square yard, what will be the total cost?*
==========================================================
Explanation:
1 yard = 3 feet
We'll divide by 3 to convert from feet to yards
27 feet = 27/3 = 9 yards18 feet = 18/3 = 6 yardsThe basement is 9*6 = 54 square yards in floor area.
At $32 per square yard, the total cost to carpet the floor is 32*54 = 1728 dollars.
(7.5)What is the value of x?
X
オー2
x + 5
x + ]
A
7.5
B.
10
C
2.5
D
5
Answer:
D 5
Step-by-step explanation:
the same scaling factor s applies to all sides when transforming from the small to the large triangle.
x×s = x + 5
(x-2)×s = x +1
=> s = (x+5)/x
=> (x-2)×(x+5)/x = x + 1
=> x² + 3x - 10 = x² + x
=> 3x - 10 = x
=> 2x = 10
=> x = 5
please help!!!!!! this is due soon
Which of the following rational numbers lies between 1/3 and 2/3?
24/48, 20/48, 18/48, 17/48
==========================================================
Explanation:
1/3 = 0.333 approximately
2/3 = 0.667 approximately
We're looking for values between 0.333 and 0.667
We can rule out choice A because 1 doesn't fit the description.
Choice C can be ruled out as well because 9/12 = 0.750 isn't between 0.333 and 0.667
--------------------------
Choice B works because all the decimals shown below are between 0.333 and 0.667
24/48 = 0.50020/48 = 0.417 (approximate)18/48 = 0.37517/48 = 0.354 (approximate)Someone please help me out!!
Answer:
D 3/4
Step-by-step explanation:
imagine a circle with its center in point A and going through point C.
the radius of that circle is 50 (AC).
remember, tan of an angle is sin/cos of that angle.
now rotate in our imagination that triangle to the right around point A, so that the side AB becomes the bottom base line.
now you see that 30 = sin(A)×radius = sin(A)×50
and 40 = cos(A)×radius = cos(A)×50
so, tan(A) = (sin(A)×50)/(cos(A)×50) = sin(A)/cos(A) = 30/40
= 3/4
Math screen shot photo
Answer:
30625
Step-by-step explanation:
Answer:
175²
Step-by-step explanation:
7 × 7 × 5 × 5 × 5 × 5
= (7 × 7) × (5 × 5 × 5 × 5)
= 7² × 5⁴
= 49 × 625
= 30.625
[tex] \sf = \sqrt{30.625} [/tex]
[tex] \sf = \sqrt{175 \times 175} [/tex]
[tex] \sf = 175[/tex]
[tex] \sf = {175}^{2} [/tex]
Conclusion:
Exponential Form of 7 × 7 × 5 × 5 × 5 × 5 adalah 175².
Austin’s monthly gross pay is $4,200. Federal withholding is 16.05% of his pay. His other deductions total $321.30. What is his net pay.
Answer:
$3,204.6
Step-by-step explanation:
$ 4,200 represents 100% of his salary
x amount of $ represents 16.05 % in federal withholding
after you line up $ with $ and % with % think cross multiplication
x = 4,200* 16.05/ 100 = $674.1 is the amount in federal withholding
Net pay = 4,200 -674.1 -321.30 = $3,204.6
A car dealership offers two types of discounts.
Discount 1: Take 5% off the original price of a car built last year, and then receive a $3,500 rebate.
Discount 2: Take 10% off the original price of a car built this year, and then rece ve a $1,250 rebate.
A customer is deciding between two cars. Car R was bure ast year and has an original price of $25,340. Car 5 was built this vear and has an original price of 522.960. .
Based on this information, which statement is true?
F The customer would pay $19,524 for cars S.
G The customer would pay $24.078 For Cars R.
H The customer would pay $21,824 For Cars S.
J The customer wou d pay $23.10 O Car R.
Question:
Based on the same question options as found an online resource, we have;
Statement
G. The customer would pay $24,073 for car R
Answer:
The true statement
G. The customer would pay $24,073 for car R
Step-by-step explanation:
Discounts are deductions from the original price of a commodity or service
A rebate is a partial refund after payment is made
The discount offered by the car dealership are;
Discount 1;
5% reduction off a car built last year's original price, + $3,500 rebate
Discount 2;
10% reduction off a car built this year's original price + $1,250 rebate
The year car R was built = Last year
The original price for car R = $25,340
Let 'A' represent the amount the customer would pay, let, 'p' represent the price of the car, let 'd' represent the discount offered, and let 'r' represent the rebate
Given that the payment is made before the rebate, we have;
The amount the customer will pay, A = p - (p×d)
Therefore;
The amount the customer would pay for car R = $25,340 - (0.05 × $25,340) = $24,073
The amount the customer would pay for car S = $22,960 - (0.1 × $22,960) = $20,644
Therefore, the true statement, is the customer would pay $24,073
Answer:
$24,073
Step-by-step explanation:
A 41 gram sample of a substance that's used to detect explosives has a k-value of 0.1392. Find the substance's half life, in days.
Answer:
The substance half-life is of 4.98 days.
Step-by-step explanation:
Equation for an amount of a decaying substance:
The equation for the amount of a substance that decay exponentially has the following format:
[tex]A(t) = A(0)e^{-kt}[/tex]
In which k is the decay rate, as a decimal.
k-value of 0.1392.
This means that:
[tex]A(t) = A(0)e^{-0.1392t}[/tex]
Find the substance's half life, in days.
This is t for which [tex]A(t) = 0.5A(0)[/tex]. So
[tex]A(t) = A(0)e^{-0.1392t}[/tex]
[tex]0.5A(0) = A(0)e^{-0.1392t}[/tex]
[tex]e^{-0.1392t} = 0.5[/tex]
[tex]\ln{e^{-0.1392t}} = \ln{0.5}[/tex]
[tex]-0.1392t = \ln{0.5}[/tex]
[tex]t = -\frac{\ln{0.5}}{0.1392}[/tex]
[tex]t = 4.98[/tex]
The substance half-life is of 4.98 days.
NEED ASAP URGENT
Which similarity statement expresses the relationship between the two triangles?
triagleZYX- triangleCAB
triangleZYX-triangleACB
triangleZYX-triangleCBA
triangleZYX - triangleABC
Given:
The figure of two triangles.
To find:
The similarity statement for the given triangles.
Solution:
The corresponding sides of similar triangles are proportional.
In the given triangles,
[tex]\dfrac{XY}{AB}=\dfrac{6}{12}[/tex]
[tex]\dfrac{XY}{AB}=0.5[/tex]
Similarly,
[tex]\dfrac{YZ}{BC}=\dfrac{3}{6}[/tex]
[tex]\dfrac{YZ}{BC}=0.5[/tex]
And,
[tex]\dfrac{XZ}{AC}=\dfrac{7}{14}[/tex]
[tex]\dfrac{XZ}{AC}=0.5[/tex]
Since [tex]\dfrac{XY}{AB}=\dfrac{YZ}{BC}=\dfrac{XZ}{AC}[/tex], therefore
[tex]\Delta XYZ\sim \Delta ABC[/tex]
It can be written as:
[tex]\Delta ZYX\sim \Delta CBA[/tex]
Therefore, the correct option is A.
Which of the following diagrams shows the numbers in the correct sets?
expand 5(8x - 3y) to its simplest form
Answer:
40x - 15y
Step-by-step explanation:
Multiply the brackets together
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Have a good day :)
Answer:
40x - 15y
Step-by-step explanation:
Use the distributive property:
5(8x) - 5(3y) =
40x - 15y
Tyler's mom purchased a savings bond for Tyler. The value of the savings bond increases by 4% each year. One year after it was purchased , the value of the savings bond was $156. Find the value of the bond when Tyler's mom purchased it. Explain your reasoning.
Answer:
Tyler's mom purchased a savings bond for Tyler. The value of the savings bond increases by 4% each year. One year after it was purchased, the value of the savings bond was $156.
Find the value of the bond when Tyler's mom purchased it. Explain your reasoning.
Step-by-step explanation:
LOOK AT PROVIDED IMAGES PLZ! Problem worth a lot of points if right!!
Answer:
add and subtract
32 + (-32) is an example of:
proportion
additive Inverse
absolute value
ratio
Answer:
Addituve Inverse
Step-by-step explanation:
Additive inverse simply means changing the sign of the number and adding it to the original number to get an answer equal to 0.
Answer:
additive Inverse or absolute value
Step-by-step explanation:
Isabel received a $90 gift card for a coffee store she used it in buying some coffee that cost $7.46 per pound after buying the coffee she had $67.62 left on her card how many pounds of coffee did she buy
Answer:
3 pounds
Step-by-step explanation:
Amount spent
90 - 67.62 = 22.38
coffee bought
22.38/7.46 = 3 pounds
Which explains how the table can be used to predict the cost of any number of students attending the game?
A.The table is a partial representation of a larger data set. It can be used to generate a graph that is a complete representation of the data set.
B. The table is a partial representation of a larger data set. It can be used to generate an equation that is a complete representation of the data set.
C. The table is a complete representation of the data set. To determine the cost of any number of students, find the number of students in the x-column.
D.The table is a complete representation of the data set. To determine the cost of any number of students, find the number of students in the y-column.
Answer:
The answer is B
Step-by-step explanation:
The table is a partial representation of a larger data set. It can be used to generate an equation that is a complete representation of the data set.
Find all possible values for each expression.
tan-1 1
Answer:
45 and 225degrees
Step-by-step explanation:
Given the expression
tan⁻¹1
Using the calculator
tan⁻¹1
tan⁻¹1 = 45degrees
Since tan is positive in the third quadrant
theta= 180 + theta
theta = 180 + 45
theta = 225degrees
Hence the values of theta are 45 and 225degrees
Please help
No links as they don’t work
Will mark brainliest
A boat spots a helicopter at an angle of elevation of 40 degree that is reporting a height of 900 feet above the water. How far is the horizontal distance from the boat to the helicopter?
Answer:
1072.58feet
Step-by-step explanation:
Given the following
Angle of elevation = 40degrees
Height of helicopter above the water = 900feet
Required
Horizontal distance H
Using the SOH CAH TOA identity
tan theta = opposite/adjacent
tan 40 = 900/H
H = 900/tan40
H = 900/0.8391
H = 1,072.58feet
Hence the horizontal distance from the boat to the helicopter is 1072.58feet
A tiene la mitad de lo que tiene B. Si A gana 66 y B pierde 90. A tendrá del doble de lo que le quede a B ¿cuanto tiene cada uno?
Respuesta:
a = 82; b 164
Explicación paso a paso:
a = 1 / 2b - - - (1)
a gana 66 = a + 66
b = b - 90
a = 2b
a + 66 = 2 (segundo - 90) - - - (2)
Ponga a = 1 / 2b en (2)
1 / 2b + 66 = 2 (b-90)
0.5b + 66 = 2b - 180
0.5b - 2b = - 180 - 66
-1,5b = - 246
b = 164
a = 1 / 2b
a = 1/2 * 164
a = 82
Please help!!! Giving brainliest and extra points!!!! (Click on the photo)
Answer:
2400 inches cubed
Step-by-step explanation:
The formula for the volume of a rectangular prism is:
V=whl
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So the formula is telling us to multiply the width, height, and length together. So in that case:
10 × 12 × 20 = 2400
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Have a good day :)