We will see that:
h(g(g(x)) = -78 + 24x
Which means that the statement is false.
Is the statement true?
Here we have that:
g(x) = 13 - 2x
h(x) = 6x
Now we want to find the composition of functions:
h(g(g(x))
First, let's find g(g(x)) = 13 - 2*g(x) = 13 - 2*(13 - 2x) = 13 - 26 + 4x
g(g(x)) = -13 + 4x
Now let's evaluate h(x) in that:
h(g(g(x)) = 6*g(g(x)) = 6*(-13 + 4x) = -78 + 24x
This is not equal to what we have in the question, so we conclude that the statement is false.
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Find (a) arc length and (b) Area of a sector.
Answer:
a) 38.40 yd (2 dp)
b) 211.18 yd² (2 dp)
Step-by-step explanation:
Formula
[tex]\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right)[/tex]
[tex]\textsf{Area of a sector}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2[/tex]
[tex]\quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in degrees)}[/tex]
Calculation
Given:
[tex]\theta[/tex] = 200°r = 11 yd[tex]\begin{aligned}\implies \textsf{Arc length} &=2 \pi (11)\left(\dfrac{200^{\circ}}{360^{\circ}}\right)\\ & = 22 \pi \left(\dfrac{5}{9}\right)\\ & = \dfrac{110}{9} \pi \\ & = 38.40\: \sf yd \:(2\:dp)\end{aligned}[/tex]
[tex]\begin{aligned} \implies \textsf{Area of a sector}& =\left(\dfrac{200^{\circ}}{360^{\circ}}\right) \pi (11)^2\\& = \left(\dfrac{5}{9}\right)\pi \cdot 121\\& = \dfrac{605}{9} \pi\\& = 211.18\: \sf yd^2 \:(2\:dp)\end{aligned}[/tex]
Please note: As you have not specified if π should be approximated, I have not used an approximation for π.
Eight crore thirty four lakh twenty two thousand fifty seven
simplify -3sqrt84x^3
answer asap please
Answer to your question
-6x sqrt21x
Graph the circle with center (−3, −3) that passes through (2, −3). Find the area in terms of π and to the nearest tenth. Use 3.14 for π.
[tex]\fcolorbox{red}{blue}{Answer}[/tex]
78.5 units²
Step-by-step explanation:
[tex] \textsf{\large{\underline{To find :-}}}[/tex]
The area of circle on graph
[tex] \textsf{\large{\underline{Given :-}}}[/tex]
[tex] \sf (x_1,y_1) = (-3,-3) \\ \sf (x_2,y_2) = (2,-3)[/tex]
[tex] \textsf{ \huge{\underline{\underline{Solution :-}}}}[/tex]
We can see in the above question that we have been provided the center of thee circle and line of the circle passes through a point.
So to find the radius we have to find the distance between center of circle and the point from which line passes.
[tex] \sf \blue{ Distance = \sqrt{ {(x_2 - x_1)}^{2} + {(y_2 - y_1)}^{2} } }[/tex]
Now substituting the required values
[tex] \sf \implies\sqrt{ { \{2 - ( - 3) \}}^{2} + { \{ - 3 - ( - 3) \}}^{2} } \\ \\ \sf \implies \sqrt{ {(2 + 3)}^{2} + {( - 3 + 3)}^{2} } \\ \\ \sf \implies \sqrt{ {5}^{2} + {0}^{2} } \\ \\ \sf \implies \sqrt{25} \\ \\ \sf \implies 5 \: units[/tex]
So the radius will be 5 units
Now we will simply formula for area of circle
[tex] \sf \green{ Area \: of \: circle = \pi {r}^{2} }[/tex]
Now substituting the required values
[tex] \sf \hookrightarrow Area = 3.14 \times {5}^{2} \\ \\ \sf \hookrightarrow Area = 3.14 \times 25 \\ \\ \red{\boxed {\hookrightarrow \frak{78.5 \: {units}^{2} } }}[/tex]
The graph of the circle is plotted with clarity and the area is obtained as 78.5 square units.
How to graph a circle?The graph of a circle can be plotted by knowing its centre and radius.
If radius is not given, then it can be found by knowing the coordinate of any point lying on it.
The radius can be calculated by the distance formula.
The centre of the given circle is at (-3, -3) and it passes through (2, -3).
Now, radius is the distance between the centre and a point lying on circle.
The radius can be calculated by distance formula as below,
√((-3 - 2)² + (-3 - (-3))²) = 5
The graph of the given circle can be drawn as follows,
Now, the area of the circle is πr² = 3.14 × 5² = 78.5
Hence, the graph of the circle is drawn properly and the area is given as 78.5 square units.
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Handedness: 18 left-handed
22 right-handed
The incomplete table above summarizes the number of left-handed students and right-handed students by gender for the eighth grade students at Keisel Middle School. There are 5 times as many right-handed female students as there are left-handed female students, and there are 9 times as many right-handed male students as there are left-handed male students. if there is a total of 18 left-handed students and 122 right-handed students in the school, which of the following is closest to the probability that a right-handed student selected at random is female? (Note: Assume that none of the eighth-grade students are both right-handed and left-handed.)
A) 0.410
B) 0.357
C) 0.333
D) 0.250
If shoppers enter a store at an average rate of r shoppers per minute and each stays in the store for average time of T minutes, the average number of shoppers in the store, N, at any one time is given by the formula N=rT. This relationship is known as Little's law.
The owner of the Good Deals Store estimates that during business hours, an average of 3 shoppers per minute enter the store and that each of them stays an average of 15 minutes. The store owner uses Little's law to estimate that there are 45 shoppers in the store at any time.
Little's law can be applied to any part of the store, such as a particular department or the checkout lines. The store owner determines that, during business hours, approximately 84 shoppers per hour make a purchase and each of these shoppers spend an average of 5 minutes in the checkout line. At any time during business hours, about how many shoppers, on average, are waiting in the checkout line to make a purchase at the Good Deals Store?
Answer:
Let x be the number of left handed female students and let y be the number of left handed male students.
Then the number of right handed female students will be 5x and the number of right handed male students will be 9y. Since the total number of left handed students is 18 and the total number of right handed students is 122, the following system of equations must be satisfied.
x+y=18 and 5x+9y=122
Solving this system gives x=10 and y=8.
Thus, 50 of the 122 right handed students are female. Therefore, the probability that a right handed student selected at random is female is the fraction 50/122
which to the nearest thousandth is 0.410.
T is average time spend by shoppers in minutes
N average number of shoppers.
Here, shoppers/hour =84.
Hence r=
60
84
T=5
Hence N=rT=
60
84
×5=7
Average number of shoppers waiting at checkout =7
Answer:
EMMA ITS KAIDN. text back.
Step-by-step explanation:
I had already answered this.
The average speed of a car on the highway is 65 miles per hour? How many feet per
second is this?
Answer:
95.3333 ft/s
Step-by-step explanation:
A loaf of bread and 4 scones cost £3.30. If the loaf costs 90 pence how much would one scone cost ? .
Answer:
Step-by-step explanation:
Givens
4 scones
1 loaf of bread
Total cost = 3.30
Equation
Let the loaf of bread = b
Let the scones = s
Cost = b + 4s
Solution
Substitute the givens into the equation
b + 4s = Cost
90 + 4s = 3.30 Subtract 90 from both sides
90-90 + 4s = 3.30-90 Combine
4s = 2.40 Divide by 4
4s/4 = 2.40/4
s = 0.6 of a pound
Answer: 1 scone = 60 pence.
I don't know what to do! please help!
Answer:
128
Step-by-step explanation:
As they have added the same shape onto the top of the rectangle as they have taken away from the bottom, just do 16x8.
SOMEBODY HELP ME PLEASE
Answer:
68
Step-by-step explanation:
the interior angles of a triangle always adds up to 180. So if you add 59 and
53 together you would get 112. Then subtract that from 180 and you would get 68.
PLEASE HELP <3 Figure out which ones best fit the graph
The scenario that match this graph is 12 gallons are presently in the bath tube draining at 3 gallons per minute.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
From the graph using points (0, 12) and (4, 0):
y intercept = 12; slope = (0 - 12)/(4 - 0) = -3
The scenario that match this graph is 12 gallons are presently in the bath tube draining at 3 gallons per minute.
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A circle has a radius of 16 m. What is its circumference?
Use 3.14 for it, and do not round your answer. Be sure to include the correct unit in your answer.
16 m
Answer:
C=100.53 CM²
Step-by-step explanation:
Formula to the circumference of a circle is 2π·r
2π=6.28
6.28·16=100.53 CM²
Jacqueline is cleaning the barn and needs to give her horse freshwater.the water trough holds 70 gallons of water the hose she has to use as a flow rate of 6 gallons per minute. how long will it take to fill the water trough?
please awnser the equation below
Answer:
the answer for all of this question should be
C=( -10, -2)
D=(0, -2)
E=(0,8)
F=(-10,8)
so remember the quadruants and remember if the x is negative or positive and if the y is either negative or positive so hopefully those are the correct one and if not tell me whats wrong so i can edit it to make it better.
Step-by-step explanation:
PLEASE HELP! URGENT! ASAP! WILL GIVE BRAINLEST!
Answer:
The correct answer is the last one, [tex]\frac{\pi }{6}[/tex].
Step-by-step explanation:
Assuming you need this urgently so I won't explain.
Hope this helps:) Goodluck!
Answer:
5π/6, 7π/6
Step-by-step explanation:
Solving :
cos⁻¹ (-[tex]\frac{\sqrt{3} }{2}[/tex])
cos⁻¹ (-cos30°)
cos 30° is negative in Quadrant II and Quadrant III
Value in QII :
cos (180° - 30°)cos (150°)5π/6Value in QIII :
cos (180° + 30°)cos (210°)7π/6The answer is 5π/6, 7π/6
What is the answer please?
Answer:
If yo translate ABC down 5 units and to the right 2 units, it coincides with GHI.
Step-by-step explanation:
You just have to follow the directions
Simplify the expression. Write your answer as a power.
6¹⁰/6⁴
The simplified expression is
Answer:
The answer is 6^6
Step-by-step explanation:
When you divide exponents, you actually substract the exponent from the equation
Answer:
[tex]6^4[/tex]
Step-by-step explanation:
Recall the exponent quotient rule [tex]\displaystyle \frac{x^a}{x^b}=x^{a-b}[/tex]
This means that [tex]\displaystyle \frac{6^{10}}{6^4}=6^{10-6}=6^4[/tex]
There are four people in an elevator that is about to make four stops on four different floors of the building. What is the probability that each person gets off on a different floor
The probability that each person gets off on a different floor is; 3/32
How to find the Probability?
We are told that there are 4 people on the elevator. We are also told that there are four stops on four different floors. Thus;
Total number of ways to get off on the floors = 4 * 4 * 4 * 4 = 256 ways
Now, the number of ways that each person can get off on a different floor is 4! = 24. Thus, the probability that each person gets off on a different floor is;
P(each person gets off on a different floor) = 24/256 = 3/32
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In a group of 30 high school students, 15 play football, 19 play basketball and 6
do not play either sport. DRAW a Venn Diagram in the space below to DETERMINE
how many students play basketball but not football.
Answer:
Hope the picture will help you........
Please help!
A card is selected at random from the set of cards below.
A sample space for the experiment is {F, G, H, J, K, L, M}. Let W represent the event “the card is white”, let S represent “the card is shaded”, and let E represent “the number is even”. Select all that apply.
A. The event S is {F, H, K, L, M}.
B. The event not E is {F, G, H, M}.
C. The event S or E is {F, H, J, K, L, M}.
D. The event S and E is {K, L, M}.
E. P(W or S) = 1
F. P(W and S) = 1
Answer:
See below ~
Step-by-step explanation:
True Statements
A. The event S is {F, H, K, L, M}.C. The event S or E is {F, H, J, K, L, M}.D. The event S and E is {K, L, M}.E. P(W or S) = 1what is the probability of drawing a king and a diamond from a standard deck of cards
Answer:
P(king or diamond) = P(king) + P(diamond) - P(king and diamond) P(king or diamond) = (4/52) + (13/52) - (1/52) P(king or diamond) = 16/52 Page 5 P(king or diamond) = 4/13.
Sharon brought $19.50 to the state fair. She bought a burger, a souvenir, and a pass. The burger was 1/3 as much as the souvenir, and the souvenir cost 1/2 the cost of the pass. Sharon had $2.00 left over after buying these items.
What was the cost of each item?
The cost of pass is $10.5, the cost of burger is $1.75, and the cost of souvenir is $5.25 if the Sharon brought $19.50 to the state fair.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let's suppose the cost of the pass is $x
The souvenir cost 1/2 the cost of the pass, which is x/2
The burger was 1/3 as much as the souvenir, which is (1/3)(x/2) = x/6
x + x/2 + x/6 + 2 = 19.50
x = 21/2
x = $10.5
The cost of pass = $10.5
The cost of burger = $1.75
The cost of souvenir = $5.25
Thus, the cost of pass is $10.5, the cost of burger is $1.75, and the cost of souvenir is $5.25 if the Sharon brought $19.50 to the state fair.
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77. the volume of a cube is increasing at a rate of [tex]10 \mathrm{~cm}^{3} / \mathrm{min}[/tex] . how fast is the surface area increasing when the length of an edge is [tex]30 \mathrm{~cm} ?[/tex]
Answer:
[tex]\displaystyle \frac{4}{3}\text{cm}^2/\text{min}[/tex]
Step-by-step explanation:
Given
[tex]\displaystyle \frac{dV}{dt}=10\:\text{cm}^3/\text{min}\\ \\V=s^3\\\\SA=6s^2\\\\\frac{d(SA)}{dt}=?}\:;s=30\text{cm}[/tex]
Solution
(1) Find the rate of the cube's edge length with respect to time at s=30:
[tex]\displaystyle V=s^3\\\\\frac{dV}{dt}=3s^2\frac{ds}{dt}\\ \\10=3(30)^2\frac{ds}{dt}\\ \\10=3(900)\frac{ds}{dt}\\\\10=2700\frac{ds}{dt}\\\\\frac{10}{2700}=\frac{ds}{dt}\\\\\frac{ds}{dt}=\frac{1}{270}\text{cm}/\text{min}[/tex]
(2) Find the rate of the cube's surface area with respect to time at s=30:
[tex]\displaystyle SA=6s^2\\\\\frac{d(SA)}{dt}=12s\frac{ds}{dt}\\ \\\frac{d(SA)}{dt}=12(30)\biggr(\frac{1}{270}\biggr)\\\\\frac{d(SA)}{dt}=\frac{360}{270}\biggr\\\\\frac{d(SA)}{dt}=\frac{4}{3}\text{cm}^2/\text{min}[/tex]
Therefore, the surface area increases when the length of an edge is 30 cm at a rate of [tex]\displaystyle \frac{4}{3}\text{cm}^2/\text{min}[/tex].
Can someone please help me with my math
Answer:
She has enough to make 4 batches of peanut butter and 6 batches of chocolate chip.
Step-by-step explanation:
26/2 = 13. There's enough flour to make the recipe 13 times over, however,
she only has the amount of butter to make a dozen of the first recipe. 9 divided by (3/4) = 12.
26/3 = 8.6, or 8 and 3/4ths of a batch with the flour. She has enough butter to make 9, but not enough flour, so she could make 8 batches of chocolate chip cookies.
She can make 12 batches of peanut butter cookies alone. Or she could make 8 batches of chocolate chip cookies alone. This means: It can't be C because she doesn't even have enough ingredients to make 22 batches of chocolate chip. It also can't be D because there's not enough ingredients for 28 batches of peanut butter or 12 chocolate chip.
to make 4 batches of PB:
[tex](4)\frac{3}{4}=3[/tex] cups of butter needed, and 4(2) = 8 cups flour needed.
so now she'd have 6 cups butter and 18 cups flour leftover.
This means, to make 6 batches CC:
3(6) = 18 cups flour, and 1(6) = 6 cups butter needed. She has enough to make 4 batches of peanut butter and 6 batches of chocolate chip.
Eliminate the parameter in the equations x = 5cos(t) – 7 and y = 5sin(t) 9. how can the rectangular equation be described? circle ellipse parabola hyperbola
The equation here can be described to be a circle.
How to solve for the parameterWe have the following equations
x = 5cos(t) - 7, and
y = 5sin(t) + 9
When rearranged we have
x + 7 = 5cos(t),
y - 9 = 5sin(t)
Square both equations
(x + 7)² = 25cos²(t), and
(y - 9)² = 25sin²(t)
Sum the equations
(x + 7)² + (y - 9)² = 25cos²(t) + 25sin²(t)
(x + 7)² + (y - 9)² = 25
(x + 7)² + (y - 9)² = 5²
The equation above is that of a circle. The radius is 5 units. The center is (-7,9)
The formula for the equation of a circle is
(x -a)² + (y - b)² = R², this is similar to (x + 7)² + (y - 9)² = 5²
The equation can be described as a circle.
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Answer: cirlce
Step-by-step explanation:
did it
the perimeter of a rhombus whose sides are 12 units in length is:
48
144
192
Answer:
48
Step-by-step explanation:
12*4=48
Ali divided one fruit cake equally among six persons. What part of the cake he gave to each person?
Step-by-step explanation:
when we divide something equally among n people, it means we divide it equally into n parts, and every part is 1/n or 1 nth.
so, for six people or parts, everybody got 1/6 or 1 sixth of the cake.
The point S is on the line AB so that lengths AS:SB are in the ration 3:2. If A = (21,3) and B = (6, 33) then find the co ordinate of S
From the section formula, it was found that the coordinate for the point S is (12,21).
Section Formula
The coordinates of the point S which divides the line AB into two sections can be found from the application of the Section Formula that is presented below:
[tex]S=(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n})[/tex], where
[tex]ratio=\frac{m}{n}[/tex]
[tex]x_1[/tex] and [tex]y_1[/tex] are coordinates of A
[tex]x_2[/tex] and [tex]y_2[/tex] are coordinates of B
Find the point SThe question gives r=[tex]\frac{3}{2}[/tex], A=(21,3) and B=(6,33). From the ratio, you can find m=3 and n=2.
Next step, applying the internal section formula. Then, you have:
[tex]S=(\frac{3*6+2*21}{3+2}, \frac{3*33+2*3}{3+2})\\ \\ S=(\frac{18+42}{5}, \frac{99+6}{5})\\ \\ S=(\frac{60}{5}, \frac{105}{5})\\ \\ S=(12, 21)[/tex]
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please solve this problem using the pythagorean theorem, and give me the right answer and I will give you brainliest. :)
Answer:
its 1.6
Step-by-step explanation:
2 squared minus 1.2 squared is 2.56
the square root of that is 1.6
Plsssss helpppppoooooooooopppppppppppppppppppppp
Answer:
4
Step-by-step explanation:
emergency!!
Write the function f(x)=x² – 25x in the form f(x) = a(x - h)? +k. Identify the vertex.
Answer:
See below
Step-by-step explanation:
Complete the square
[tex]f(x)=x^2-25x\\\\f(x)+(\frac{-25}{2})^2=x^2-25x+(\frac{-25}{2})^2\\\\f(x)+156.25=x^2-25x+156.25\\\\f(x)+156.25=(x-12.5)^2\\\\f(x)=(x-12.5)^2-156.25\\\\f(x)=(x-\frac{25}{2})^2-\frac{625}{156}[/tex]
Identify vertex
[tex](h,k)\rightarrow(-\frac{25}{2},-\frac{625}{156})[/tex]
