Answer:
[tex]f(x)=-x^2[/tex]
Step-by-step explanation:
Vertex form of a quadratic function:
[tex]f(x)=a(x-h)^2+k[/tex]
where:
(h, k) is the vertexa is some constantIf the vertex is at the origin, then (h, k) = (0, 0)
[tex]\implies f(x)=a(x-0)^2+0[/tex]
[tex]\implies f(x)=ax^2[/tex]
Comparing this with the answer options suggests that the function with a vertex at the origin is [tex]f(x)=-x^2[/tex]
A composite figure is shown.
Diagram shows a composite shape formed by placing a cube before a square prism and a square pyramid next to it that share a common square base. Cube has sides labeled 6 feet. Length of the square prism is 20 feet and height of the pyramid is 4 feet.
What is the surface area for each part of the figure? What is the total surface area of the figure?
The surface area of the pyramid is
square feet.
The surface area of the square prism is
square feet.
The surface area of the cube is
square feet.
The total surface area is
square feet.
The surface area of the pyramid is 60 square feet
The surface area of the square prism is 480 square feet
The surface area of the cube is 180 square feet
The total surface area is 720 square feet
Area of Composite figuresFrom the question, we are to calculate the surface area of each part of the composite figure
For the cubeSurface area of a cube is given by
[tex]S = 6l^{2}[/tex]
Where [tex]l[/tex] is the length of a side
But only have 5 surfaces of the cube are part of the composite figure
∴ Surface area of the cubic part of the figure = [tex]5l^{2}[/tex]
From the given information,
[tex]l = 6 \ feet[/tex]
∴ Surface area of the cubic part of the figure = 5 × 6²
Surface area of the cubic part of the figure= 180 square feet
For the square prismThe surface area of a square prism is given by the formula,
[tex]S = 2l^{2} + 4lh[/tex]
Where [tex]l[/tex] is the length of the sides and
[tex]h[/tex] is the height
But the square surfaces are not part of the surface of the figure
∴ Surface area of the square prism in the figure = [tex]2l^{2} + 4lh - 2l^{2}[/tex]
Surface area of the square prism in the figure = [tex]4lh[/tex]
From the given information,
[tex]l = 6 \ feet[/tex]
[tex]h = 20 \ feet[/tex]
Thus,
Surface area of the square prism part of the figure = 4×6×20
Surface area of the square prism part of the figure = 480 square feet
For the pyramid
The pyramid is a square pyramid
The surface area of a square pyramid is given by
[tex]S = l^{2} + 2l\sqrt{\frac{l^{2} }{4}+h ^{2} }[/tex]
Where [tex]l[/tex] is the base length
and [tex]h[/tex] is the height of the prism
But the square base is not part of the surface of the figure
∴ Surface area of the pyramid part of the figure = [tex]l^{2} + 2l\sqrt{\frac{l^{2} }{4}+h^{2} }\ - ( l^{2})[/tex]
Surface area of the pyramid part of the figure = [tex]2l\sqrt{\frac{l^{2} }{4}+h^{2} }[/tex]
From the given information,
[tex]l = 6 \ feet[/tex]
[tex]h = 4 \ feet[/tex]
∴ Surface area of the pyramid part of the figure = [tex]2(6)\sqrt{\frac{6^{2} }{4}+4^{2} }[/tex]
= [tex]12\sqrt{\frac{36 }{4}+16}[/tex]
= [tex]12\sqrt{9+16 }[/tex]
= [tex]12\sqrt{25}[/tex]
= 12 × 5
= 60 square feet
Hence, the surface area of the pyramid is 60 square feet
Thus,
The total surface area = 180 square feet + 480 square feet + 60 square feet
The total surface area = 720 square feet
Hence, the total surface area is 720 square feet
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Answer:
1: 60
2: 480
3: 180
4: 720
Step-by-step explanation:
plato answer :)
What is the probability of getting two heads if you flip two fair coins? answer as a simplified fraction
Answer: [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
use probability
the chances of you getting heads on a coin is 50% therefore, flipping two coins is just
[tex]\frac{1}{2} * \frac{1}{2}= \frac{1}{4}[/tex]
Answer:
the probability of getting two heads is 1/4
Step-by-step explanation:
H = (HH) => n(H) = 1
n(S) = 4
P(E) = number of favourable outcomes/total number of outcomes = n(E) / n (S)
PH = n(H)/n(S)
= 1/4
Find the missing side length of side c, a and b are both 25
Answer: x=25, y=2
Step-by-step explanation:
use Pythagorean theorem to get that 1250= c^2. then sqaure root both sides. c= sqrt(1250). jailbreak to get c=(5 x 5 x 5 x 5 x 2), and take the fives out from under the square root to get 25 x sqrt2.
Which expression is equivalent to the given expression
Answer:
i think the answer is A. 2x^3y^2
3x-2y=12
6x-4y-24
OIt has infinitely many solutions.
OIt has no solution.
O It has one solution (2, -3).
O It has one solution (4, 0).
A system of two equations is shown below. What will you need to multiply the
top equation by in order to solve this system using the elimination method?
x + y = 4
3x+4y=14
A. 3
OB. 4
C. -2
D. -3
The rule is "Multiply by 8." Which statement is true? Number of Packages 3 5 6 8 Number of Juice Boxes 24 40 48 ? A. The number of juice boxes will always be greater than 24. B. The number of packages will always be greater than the number of juice boxes. C. The number of juice boxes must be an even number. D. The number of juice boxes will always be 21 more than the number of packages.
I need the answer ASAP!
The statement (C) the number of juice boxes must be an even number is correct.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
We have a rule is “Multiply by 8"
Number of Packages: 3 5 6 8
Number of Juice Boxes: 24 40 48
The statements are:
A. The number of juice boxes will always be greater than 24. B. The number of packages will always be greater than the number of juice boxes. C. The number of juice boxes must be an even number. D. The number of juice boxes will always be 21 more than the number of packages.Number of package starts from 3
Applying the rule: "Multiply by 8.
Number of Juice Boxes = 3×8 = 24
The statement should be the number of juice boxes will always be greater than and equal to 24.
When we multiply even with odd we get an even number.
8 is an even number.
Thus, the statement (C) the number of juice boxes must be an even number is correct.
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A cube's edge lengths are each 5 inches. A rectangular prism's length and width are also 5 inches, but its height is 7
1
2
inches.
How many cubic inches larger is the rectangular prism than the cube?
The rectangular prism is 187.5 - 125 = 62.5 cu.inches greater than the volume of cube.
What is Volume?Volume is defined as the space occupied by a three dimensional figure.
It is given that
A cube's edge lengths are each 5 inches
A rectangular prism's length and width are also 5 inches, but its height is [tex]\rm 7\dfrac{1}{2}[/tex]
The volume of the cube is given by side * side * side
Volume of cube = 5 *5 * 5 = 125 cu. inches
The volume of cuboid = length * width * height
Volume of Cuboid = 5 * 5 * 15/2Volume of Cuboid = 187.5 cu.inches.
Therefore the rectangular prism is 187.5 - 125 = 62.5 cu.inches greater than the volume of cube.
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Karl wants to rent a bike for at most $55. He can rent a bike for $7 per hour plus a $9.50 flat fee. Any portion of an hour is charged as a full hour.
What is the maximum number of hours Karl can Rent the bike?
find the value of x in the following equation 8x- 6=50
Answer:
x = 7
Step-by-step explanation:
8*7 - 6 = 50
A solid cylinder has a radius of rm and a height of 12 m.
The volume of the cylinder is 507 m³.
Find the value of r.
Answer:
6.5m
Step-by-step explanation:
V=TTr²h
507TT=TTr²12
cancel TT on both sides
507=12r²
169\4=r²
r=13/2
Find the slope
Will mark brainlist
Answer:
2/3
Step-by-step explanation:
pls help! look at the photo ill give brainliest!
Step-by-step explanation:
Ashley is the utilities manager at a paper mill. She's watching over one of her holding tanks. It takes 4/5 of an hour to fill 1/2 the tank
First we convert 4/5 of an hour in to
minutes
4/5 6048 minutes
In 48 minutes ----> 1/2 tank filled
In 60 minutes ----> 60 * 1/2 divide by 48
30 divide by 48=\frac{30}{48}
48
30
All 15%
Simplify the fraction by dividing top and
bottom by 6
30/48 = 5/8
3p+6
Which phrase represents the algebraic expression 7p-9?
Answer:
The answer is the sum of three times a number and six, divided by the difference of seven times the number and nine
Step-by-step explanation:
3p = three x a number
7p = seven x a number
3p+6 = sum of three x a number plus six
7p-9 = difference of seven x the number minus nine
(3p+6)/(7p-9) = sum of three times x number plus six, divided by the difference of seven x the number - nine
Five identical machines cover a total of 32 1/2 ft.² of floor space how much floor space occupied by each machine
Using proportions, it is found that the floor space occupied by each machine is of 6.5 ft².
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, five identical machines cover a total of 32 1/2 ft² = 32.5 ft², hence the space occupied by each machine is given as follows, applying the proportion:
32.5 ft²/5 = 6.5 ft².
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30 POINTS FOR THE BRAINLIEST!!!!!
Find the exact value of x and y. (Do not round - no decimals)
Answer x = ____ units
Answer y = ____ units
Explain how you found side length measure below. Be sure to show all of your work.
Monitors manufactured by TSI Electronics have life spans that have a normal distribution with a variance of 4,000,000 and a mean life span of 19,000 hours. If a monitor is selected at random, find the probability that the life span of the monitor will be more than 20,179 hours. Round your answer to four decimal places.
Using the normal distribution, it is found that there is a 0.2776 = 27.76% probability that the life span of the monitor will be more than 20,179 hours.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 19000, \sigma = \sqrt{4000000} = 2000[/tex]
The probability that the life span of the monitor will be more than 20,179 hours is one subtracted by the p-value of Z when X = 20179, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{20179 - 19000}{2000}[/tex]
Z = 0.59.
Z = 0.59 has a p-value of 0.7224.
1 - 0.7224 = 0.2776.
0.2776 = 27.76% probability that the life span of the monitor will be more than 20,179 hours.
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What is the surface area of the rectangular prism
represented by the net shown?
6 in.
1.5 in.
1.5.in.
Answer:
40.5 inch²
Step-by-step explanation:
(((6×1.5)×4)+((1.5×1.5)×2) = 40.5
7 of 10
Work out
(1.5 × 10¹⁰) ÷ (3 × 10-4)
Give your answer in standard form.
Answer:
5 × 10¹³
Step-by-step explanation:
(1.5 × 10¹⁰) ÷ (3 × 10⁻⁴) = 50,000,000,000,000
What number would you add to both sides of x² + 7x = 4 to complete the square?
Answers:
A. 2²
B. 7²
C. 7²/2
D. [⁷/2]²
The number would you add to both sides of x² + 7x = 4 to complete the square option C 7²/2.
What is completing the squares method for solving the quadratic method?Suppose the considered quadratic equation is of the form
ax^2 + bx + c = 0
Then, completing the squares method tries to make a squared term in terms of x in the left side, so that x comes in linear form, instead of quadratic.
The given quadratic equation is
x² + 7x = 4
add 7²/2 to both sides of x² + 7x = 4 to complete the square
7²/2 = 49/4
x² + 7x + 49/4 = 4+ 49/4
(x + 7/2)² = 4+ 49/4
Thus, option C 7²/2 is correct.
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Solve for x. Round to the nearest tenth, if necessary.
56
Z
43°
x
M
60.2 is the value of x in Trigonometric ratios
What are the trigonometric ratios?
Trigonometric ratios are used to describe the side ratios of a right triangle. The sine (sin), the cosine (cos), and the tangent are three popular trigonometric ratios (tan).
Greek is the language of measuring, "metric," and "trigon" is the language of triangles. It is possible to measure a right triangle specifically using its trigonometric ratios.
43 degree as reference angle
using tan rule
tan 43 = opposite / adjacent
0.93 = x / 56
x = 56/0.93
x = 60.21
x = 60.2
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The mapping diagram shows a function R(x)
Answer:
Answer is C
Step-by-step explanation:
It's the same as the mapping diagram but the values are flipped. It's going backward instead of forwards.
What’s the result of adding these two equations? Please help
Answer:
u should subract those not add
A city has 5 new houses for every 9 old houses. If there are 35 new houses in the city, how many old houses are there?
Answer:
20 I guess
Step-by-step explanation:
because maybe 1 is 9
Must show work-Solve the conjunction and describe the solution set. −5 < 2x + 3 < 9
The solution set of the inequality −5 < 2x + 3 < 9 is (-4,3)
How to solve the inequality?The compound inequality is given as:
−5 < 2x + 3 < 9
Expand the inequality
−5 < 2x + 3 or 2x + 3 < 9
Rewrite as:
2x + 3 > -5 or 2x + 3 < 9
Subtract 3 from both sides
2x > -8 or 2x < 6
Divide both sides by 2
x > -4 or x < 3
Rewrite as:
(-4,3)
Hence, the solution set of the inequality is (-4,3)
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Find each square root after supplying:
Answer:
1) 5
2) 0.8
3) -1.3
4) -[tex]\frac{4}{9}[/tex]
5) ±10
6) ±[tex]\frac{7}{12}[/tex]
Step-by-step explanation:
Which of the
following ordered
pairs make this
equation true?
Answer:
D. (2, 3)
Step-by-step explanation:
The equation will be true when the values of x and y are substituted and the result matches what you know about sums.
__
The values in each ordered pair are (x, y).
A.x = -2, y = -3
Substituted into the equation, we get ...
-3 = -2 +1 . . . . . . false
__
B.x = 5, y = 4
Substituted into the equation, we get ...
4 = 5 +1 . . . . . . false
__
C.x = 0, y = -1
Substituted into the equation, we get ...
-1 = 0 +1 . . . . . . false
__
D.x = 2, y = 3
Substituted into the equation, we get ...
3 = 2 +1 . . . . . . true
Is 35 cm greater than 3.5 m
Answer:
no
Step-by-step explanation:
3.5m=350cm
35cm<350cm
How many 5-digit numbers are there, that are "even"? Show all work/ calculations.
Answer: The correct answer is 13776.
Explanation: There are 3024 five-digit numbers that begin with the digit 4 with no repetition.
Based on the work below, is (4, 7) a solution to the equation given?
Answer:
No
Step-by-step explanation:
If a ordered pair is a solution for an equation, then it will satisfy the equation. That is, after substituting the x and y values in the equation, both sides of the equation will be same.
Here 29 ≠ 45.
So, (4,7) is not a solution