Answers
Answer:
[tex]\large\boxed{B.\ 4x^2-41x+105}[/tex]
Step-by-step explanation:
[tex]f(x)=4x-\sqrt{x}\\\\g(x)=(x-5)^2\\\\f(g(x))\to\text{put}\ x=(x-5)^2\ \text{to}\ f(x):\\\\f(g(x))=f\bigg((x-5)^2\bigg)=4(x-5)^2-\sqrt{(x-5)^2}\\\\\text{use}\\(a-b)^2=a^2-2ab+b^2\\\sqrt{x^2}=|x|\\\\f(g(x)=4(x^2-2(x)(5)+5^2)-|x-5|\\\\x>5,\ \text{therefore}\ x-5>0\to|x-5|=x-5\\\\f(g(x))=4(x^2-10x+25)-(x-5)\\\\\text{use the distributive property:}\ a(b+c)=ab+ac\\\\f(g(x))=(4)(x^2)+(4)(-10x)+(4)(25)-x-(-5)\\\\f(g(x))=4x^2-40x+100-x+5\\\\\text{combine like terms}\\\\f(g(x))=4x^2+(-40x-x)+(100+5)\\\\f(g(x))=4x^2-41x+105[/tex]
Answer: Option B
[tex]f(g(x)) = 4x^2 -41x + 105[/tex]
Step-by-step explanation:
We have 2 functions
[tex]f(x) = 4x -\sqrt{x}[/tex]
[tex]g(x) = (x-5)^2[/tex]
We must find [tex]f(g(x))[/tex]
To find this composite function enter the function g(x) within the function f(x) as follows
[tex]f(g(x)) = 4(g(x)) -\sqrt{(g(x))}[/tex]
[tex]f(g(x)) = 4(x-5)^2 -\sqrt{(x-5)^2}[/tex]
By definition [tex]\sqrt{a^2} = |a|[/tex]
So
[tex]f(g(x)) = 4(x-5)^2 -|x-5|[/tex]
Since x is greater than 5 then the expression [tex](x-5)> 0[/tex].
Therefore we can eliminate the absolute value bars
[tex]f(g(x)) = 4(x-5)^2 -(x-5)[/tex]
[tex]f(g(x)) = 4(x^2 -10x + 25) -(x-5)[/tex]
[tex]f(g(x)) = 4x^2 -40x + 100 -x+5[/tex]
[tex]f(g(x)) = 4x^2 -41x + 105[/tex]
Related Questions
Select ALL the correct answers.
Ms. Simon uses six different colored pens to grade papers. She has one of each of the following colors: red, purple, green, blue, orange, and black. Determine which statements are true.
A.The probability of randomly not choosing a black pen is.
B.The probability of randomly choosing a black pen is.
C.The probability of randomly choosing either a red or blue pen is.
D. The probability of randomly choosing an orange pen is about 0.17.
E. The probability of randomly not choosing a purple or blue pen is about 0.67.
F. The probability of randomly choosing a green or red pen is about 0.5.
I WILL NAME THE BRAINLESS IF CORRECT!!
Answers
The correct probabilities are that not choosing a black pen is about 0.83, choosing a black pen is about 0.17, choosing a red or blue pen is about 0.33, choosing an orange pen is about 0.17, not choosing a purple or blue pen is about 0.67, and finally, choosing a green or red pen is about 0.33.
Explanation:In this mathematics problem, we discuss the probabilities related to Ms. Simon and her colored pens, specifically black and red.
A. The probability of randomly not choosing a black pen is 5/6 or about 0.83 (there are five other colors).
B. The probability of randomly choosing a black pen is 1/6 or about 0.17 (only one black pen out of six).
C. The probability of randomly choosing a red or blue pen is 2/6 or about 0.33 (two desired colors out of six).
D. This is correct because The probability of randomly choosing an orange pen is 1/6, which rounds to about 0.17.
E. The probability of randomly not choosing a purple or blue pen is 4/6 or about 0.67 (four other colors), so this is correct.
F. The probability of randomly choosing a green or red pen is 2/6 or about 0.33 (not 0.5 as stated).
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What is the smallest solution to this equation?
Answers
Answer:
x = - 6
Step-by-step explanation:
Given
[tex]\frac{2}{3}[/tex] x² = 24 ( multiply both sides by 3 )
2x² = 72 ( divide both sides by 2 )
x² = 36 ( take the square root of both sides )
x = ± [tex]\sqrt{36}[/tex] ← note plus or minus
x = ± 6
solutions are x = - 6, x = + 6
The smallest solution is x = - 6
What is the measure of ∠ D?
101°
112°
122°
111°
Answers
Answer:
101
Step-by-step explanation:
360 - (78+91+90)
360- 259 = 101
HOPE THIS HELPS!!
Darren is painting a wooden block as part of his art project. The block is a rectangular prism that is 12 cm long by 9 cm wide by 5 cm high. Describe the rectangles that make up the net for a prism
Answers
Answer:
The answer in the procedure
Step-by-step explanation:
we know that
The rectangles that make up the net for a prism are six rectangles
two rectangles are L by W ----> 12 cm by 9 cm
two rectangles are L by H ----> 12 cm by 5 cm
two rectangles are W by H ---> 9 cm by 5 cm
Final answer:
The rectangular prism net Darren is painting consists of two 12x5 cm rectangles for the top and bottom, two 9x5 cm rectangles for the front and back, and two 12x9 cm rectangles for the sides.
Explanation:
Darren is working on an art project involving painting a wooden block that is in the shape of a rectangular prism. To understand the net for this prism, we need to describe the rectangles that would make it up when the prism is unfolded into a flat shape.
The net of a rectangular prism is made up of six rectangles, each corresponding to a face of the prism. For Darren's block, which has dimensions of 12 cm in length, 9 cm in width, and 5 cm in height, we can determine the rectangles as follows:
When painting, Darren would treat each of these rectangles as separate sections to ensure complete coverage.
When constructing an inscribed polygon with a compass and straightedge ,how should you start the construction?
Answers
Place a point on your paper and then use a compass to construct a circle.
Answer with explanation:
To construct an inscribed polygon with a compass and straightedge:
The first step is:
1.⇒Draw the polygon either it is Regular or Irregular
→A polygon is said to be regular, if it's all sides and all Interior Angles are equal.
→Draw the perpendicular bisector of all the sides of Polygon.
→The point where these two perpendicular bisector meet is center of the circle.
→Draw the circle which will pass through all the vertices of the Polygon you have drawn.
PLZ HURRY IT'S URGENT!!
A square tray has an area of 196 square inches. What is the length of one side of the tray? A. 12 inches B. 13 inches C. 14 inches D. 16 inches
Answers
Answer:
C. 14 inches
Step-by-step explanation:
The area of a square is given by
A = s^2
We know the area is 196 in ^2
196 in^2 = s^2
Take the square root of each side
sqrt(196) = sqt (s^2)
14 =s
Each side is 14 inc
Answer:
C.14
Step-by-step explanation:
a=length time width so 14*14=196
Distributive Property
Drag the item from the item bank to its corresponding match.
Use these choices for the A, B, C, D, E
3(4 + 7)
5(9 - 6)
66 × 7
8 (4 + 2)
97 × 4
A. (3 × 4) + (3 × 7)
B. (5 × 9) - (5 × 6)
C. 32 +16 = 48
D. 4(100 - 3)
E. 7(60 + 6)
Answers
Answer:
A. (3 × 4) + (3 × 7)
3(4 + 7)
B. (5 × 9) - (5 × 6)
5(9 - 6)
C. 32 +16 = 48
8 (4 + 2)
D. 4(100 - 3)
97 × 4
E. 7(60 + 6)
66 × 7
Step-by-step explanation:
A man bought a refrigerator at a discount of 12 percent. It's usual price was $900.How much did he pay for the refrigerator
Answers
Multiply by .88, he paid $792
Answer:
$792
Step-by-step explanation:
Please help anyone and explain please
Answers
So if you distribute 4 in the first parentheses, you get 12x+20y+8z.
Then you distribute 3 in the second parentheses. You'll get 3x-3z. That all equals 12x+20y+8z+3x-3z.
Now you have to start combining numbers with the same variable. Start with x. 12x+3x is 15x.
y has no other common variable, it's left alone.
8z-3z is 5z
All together now with the numbers in simpler form, the equation is 15x+20y+5z
Jenna's would be the right answer because when you distribute 5 in her answer you get 15x+20y+5z
Answer:is jennas right i think i got it ty
Find the area of the polygon XYZ that has its vertices at X(–3, 6), Y(–3, 1), and Z(5, 1).
Answers
Hope you can understand
Six out of the 114 elements are noble gases. You write the names of all the elements on cards and select a card at random. What is the probability of not picking a noble gas?
Answers
Answer:
18/19 = About 95%
Step-by-step:
If only six are noble gases, 108 are not noble gases.
114-6= 108
So, the probability of not picking a noble gas is 108 out of 114. This simplifies to 18/19 which is about 95%.
help me asap.........
Answers
Answer:
F. 4h ≥ 18
Step-by-step explanation:
Liang wants ...
distance ≥ goal
We know that ...
distance = speed · time . . . . . . where speed = 4 mph, and time = h hours
Then the appropriate inequality for Liang's goal of 18 miles or more is ...
4h ≥ 18
Simplify the following radicals (in exponential notation) (x^9y^6z^15)^1/3
Answers
[tex]\bf (x^9y^6z^{15})^{\frac{1}{3}}\implies \stackrel{\textit{distributing the exponent}}{\left(x^{9\cdot \frac{1}{3}}y^{6\cdot \frac{1}{3}} z^{15\cdot \frac{1}{3}} \right)}\implies x^3y^2z^5[/tex]
Martin has a business washing cars. Last year he washed 20 cars a week. This year, he wants to increase his business to 1,200 cars a year. How many cars will he have wash each month on average?
Answers
Great Question!
The last year part is extra information. 1200÷12 (months in a year)= 100
He will have to wash 100 cars each month.
In the total number of People attending the Game was 64,000, how many people were supporters of the home team
Answers
Answer:
51200 people
Step-by-step explanation:
Multiply the total number by the corresponding decimal to the percentage desired.
64000*.8=51200
I need to find tan c please
Answers
Answer: It is 15/17
Step-by-step explanation:
Tan is adjacent over hypotenuse
Rectangular is 3/4 yard long and 1/2 yard wide, what is the area?
Answers
so, 3•1.
that would equal 3. so, your answer is 3/4yards squared.
use the elimination method to solve the system of equations.choose the correct ordered pair. -3y=x-5 x+5y=7.
Answers
Answer:
B. (2, 1)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}-3y=x-5&\text{subtract x from both sides}\\x+5y=7\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-x-3y=-5\\x+5y=7\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad2y=2\qquad\text{divide both sides by 2}\\.\qquad\qquad y=1\\\\\text{Put the value of y to the second equation:}\\x+5(1)=7\\x+5=7\qquad\text{subtract 5 from both sides}\\x=2[/tex]
The solution of the system of equations is (2, 1).
What is the elimination method?The elimination method is a process that uses elimination to reduce the simultaneous equations into one equation with a single variable.
The given system of equations are;
[tex]\rm -3y=x-5\\\\x+5y=7[/tex]
From equation 1
[tex]\rm -3y=x-5\\\\x = -3y+5[/tex]
Substitute the value of x in the equation 2
[tex]\rm x+5y=7\\\\-3y+5+5y=7\\\\2y =7-5\\\\2y=2\\\\y=\dfrac{2}{2}\\\\y=1[/tex]
Substitute the value of y in the equation 1
[tex]\rm -3y=x-5\\\\-3(1)=x-5\\\\-3=x-5\\\\x=5-3\\\\x=2[/tex]
Hence, the solution of the system of equations is (2, 1).
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Which statement about the dilation of these triangles is true?
Answers
Answer:
answer is b
Step-by-step explanation:
The Scale factor is 2.
What is dilation?A dilation in mathematics is a function f from a metric space M into itself that, for any locations x, y in M, fulfills the identity d=rd, where d is the distance between x and y and r is some positive real number. Such a dilatation is a resemblance to the space in Euclidean space.
Given
in pre -- image sides are 4, 5, 3
in the image, the sides are 4(2), 5(2), 3(2)
The scale factor is 2.
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Given: p: 3x + 7 = –5 q: 4x + 12 = –4 Which is the contrapositive of p → q?
Answers
Answer:
D :If 4x + 12 ≠ –4, then 3x + 7 ≠ −5.
If 4x + 12 ≠ –4, then 3x + 7 ≠ −5. Then the correct option is D.
What is a contrapositive?If the statement is: p ⇒ q
Then the Contrapositive statement will be: ~q ⇒ ~p
p: 3x + 7 = –5 q: 4x + 12 = –4
The value of x in both cases is the same. Then the p and q are converses with each other.
If 4x + 12 ≠ –4, then 3x + 7 ≠ −5.
Then the correct option is D.
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which is the equation of the line that is parallel to y=-4x+3 and has a y intercept of -1/3
Answers
Answer:
y= -4x-1/3
Step-by-step explanation:
i think. but dont quote me on that. and Stan BTS!!!!!!
7.5 cm=__ m
A.0.0075
B.0.075
C.0.75
D.750
Answers
Your answer is B. 0.075 m
The answer is B I think
On a scale drawing, the height of a tree is 3.75 inches.if the scale of the drawing is 1 in: 50ft,how tall is the tree?
Answers
Answer:
187.5
Step-by-step explanation:
50 × 3 =150
50 ÷ 4 = 12.5
12.5 ×3= 37.5
150 + 37.5 =187.5
Answer:
187.5
Step-by-step explanation
50 × 3 =150
50 ÷ 4 = 12.5
12.5 ×3= 37.5
150 + 37.5 =187.5
Alan earned 23$ 26$ 25$ 24$ 23$ 24$ 6$ 24$ and 23$ gardening. What is the amount he earned?
Answers
Answer:
151
Step-by-step explanation:
23+26=$49
49+25=74
74+24=98
98+6=104
104+24=128
128+23=151
Alan earned a total of $198 from gardening by adding all individual earnings together.
The student is asking about the total amount earned by Alan from gardening. To find the total, we simply add all the amounts mentioned: 23 + 26 + 25 + 24 + 23 + 24 + 6 + 24 + 23. Adding these up, Alan earned a total of $198 from gardening.
Find the probability that a randomly selected dog is Male given it is a boxer. Enter your answer in decimal form rounded to two decimal places.
Answers
Answer:
0.63
Step-by-step explanation:
M: The selected dog is a male. P(M) = 24/40 = 0.6
B: The selected dog is a boxer. P(B) = 22/40 = 0.55
M and B: 14/40 = 0.35
P(M/B) = 0.35 / 0.55 = 0.63
Identify which of the following represents a function. Select all that apply
Answers
Answer:
A and E
Step-by-step explanation:
Sarah randomly selected 80 shoppers at a grocery store to taste two different type of greek yogurt. Yogurt brand B was chosen as the favorite by 35 of them. To the nearest percent what is the 95% confidence interval (z*-score 1.96) for the proposition of shoppers who tasted the two types of yogurt and preferred brand B? PLEASE HELP!!!!!
Answers
Answer:
D: 56 and 77
Step-by-step explanation:
Need help ASAP
1) A new truck that sells for $42,000 depreciates 11% each year. write a function that models the value of the truck. Find the value of the truck after 8 years. Round to the nearest dollar.
2) Earl mows lawns one weekend. He earns $15 for each lawn that he mows. He spends $50 on gas and other supplies. What function equation represents Earl's profit from mowing x lawns?
A)f(x)=50x-15
B)f(x)=50x+15
C)f(x)=15x-50
D)f(x)=15+50
3) find the common geometric series.
-2,-4,-8,-16.....
Answers
Answer:
[tex]\boxed{1) V = 40 000(0.89)^{n}, \text{\$15 746; }\text{2) C) f(x) = 15x - 50 ; 3) }a_{n} = -2^{n}}[/tex]
Step-by-step explanation:
1) Depreciation
The formula for the value V of an asset after depreciation by an annual percentage rate is
V = P(1 - r)ⁿ
where
P = present value
r = annual percentage rate
n = number of years
Data:
V = 40 000
r = 11 % = 0.11
n = 8 yr
Calculations:
(a) Function model
V= 40 000(1 - 0.11)ⁿ = 40 000(0.89)ⁿ
The function model is [tex]\boxed{ V= 40 000(0.89)^{n} }[/tex]
(b) Future value
V = 40 000(0.89)ⁿ = 40 000 × 0.393 659 = $15 746
In eight years, the truck will be worth [tex]\boxed{ \text{\$15 476}}.[/tex]
2) Profit function
Income from 1 lawn = $15
Income from x lawns = 15x
Less gas and supplies = -50
Net income = 15x – 50
The function is [tex]\boxed{f(x) = 15x - 50}[/tex].
3) Geometric series
(a) Calculate the common ratio
a₁ = -2
a₂ = -4
a₃ = -8
a₄ = =16
The ratios of consecutive pairs are
a₄/a₃ = -16/(-8) = 2
a₃/a₂ = -8/(-4) = 2
a₂/a₁ = -4/(-2) = 2
All adjacent pairs have the same common ratio r = 2.
(b) Write the formula for the series
The formula for the nth term of a geometric series is
aₙ = a₁rⁿ⁻¹
If a₁ = -2, the formula for the series is
aₙ = -2(2)ⁿ⁻¹ = -2ⁿ
The formula for the series is [tex]\boxed{a_{n} = -2^{n}}[/tex].
A 3cm x 2cm rectangle sits inside a circle with radius of 4 cm. What is the area of the shaded region? Round your final answer to the nearest hundredth.
Answers
Answer:
The area of the shaded region is [tex]44.24\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The area of the shaded region is equal to the area of the circle minus the area of rectangle
step 1
Find the area of circle
The area of the circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=4\ cm[/tex]
substitute
[tex]A=\pi (4)^{2}[/tex]
[tex]A=16\pi\ cm^{2}[/tex]
step 2
Find the area of rectangle
The area of rectangle is equal to
[tex]A=(3)(2)=6\ cm^{2}[/tex]
step 3
Find the difference
[tex]16\pi\ cm^{2}-6\ cm^{2}[/tex]
assume
[tex]\pi=3.14[/tex]
[tex]16(3.14)\ cm^{2}-6\ cm^{2}=44.24\ cm^{2}[/tex]
In Hillcrest School, 36% of middle school students are in Grade 6, 31% are in grade 7, and 33% are in grade 8.
If a middle school student is selected randomly, what is the probability that the student is either in grade 6 or in grade 7?
Answers
Answer:
0.67
Step-by-step explanation: