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When we have a function f(x) we can evaluate it for different arguments (the value of x) by replacing the argument in the definition of the function.
In this case, we know h(x) and we have to express h(3x). To do this, we replace x in the original function with 3x:
[tex]\begin{gathered} h(x)=3x^2-4 \\ h(3x)=3(3x)^2-4=3\cdot(3^2x^2)-4=3\cdot9x^2-4=27x^2-4 \end{gathered}[/tex]Answer: h(3x) = 27x²-4
Related Questions
Jeff decides to lease a $35,000 vehicle for 4 years. It is estimated that the car will be resold in two years at a price of$17,955. If the annual interest is 3%, what is the financing fee?$44.89O $87.50$66.19$151.30
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I don’t know if I’m right I need to know
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ANSWER
[tex]x=3[/tex]EXPLANATION
We want to identify the positive solution to the graph.
The solutions to a quadratic graph are the points where the graph touches the x-axis on the coordinate plane. The positive solution to the graph is the point where the graph touches the positive x-axis.
Hence, the positive solution to the given graph is x = 3.
Solve the system by graphing. (If there is no solution, enter NO SOLUTION.)x + 2y < 6y < x − 5
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From the problem, we have the inequalities :
[tex]\begin{gathered} x+2y<6 \\ yNote that the boundary line is dashed if the symbols are < or >.Let's graph first the first inequality :
[tex]\begin{gathered} x+2y<6 \\ \text{Change the symbol into ''=''} \\ x+2y=6 \\ \text{Solve for the intercepts} \\ \text{when x = 0} \\ 0+2y=6 \\ y=\frac{6}{2}=3 \\ \\ \text{when y = 0} \\ x+2(0)=6 \\ x=6 \end{gathered}[/tex]Plot the points (0, 3) and (6, 0)
The region will pass through the origin if (0, 0) satisfies the inequality.
Test for (0, 0)
[tex]\begin{gathered} x+2y<6\text{ } \\ 0+0<6 \\ 0<6 \\ \text{TRUE!} \end{gathered}[/tex]Since it is true, the region will pass through the origin.
The graph will be :
Next is to graph the second inequality :
[tex]\begin{gathered} yPlot the points (0, -5) and (5, 0)Check again origin (0, 0) to the inequality :
[tex]\begin{gathered} ySince it is false, the region will not pass through the origin.Tha graph will be :
The solution to the system is the overlapping region between the two inequalities.
Find the length of the third side. If necessary, write in simplest radical form.DV895
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In order to solve the missing side for a right triangle, we can use the Pythagorean theorem
[tex]a^2+b^2=c^2[/tex]then, we rewrite the expression for on of the sides different from the hypotenuse
[tex]\begin{gathered} a^2=c^2-b^2 \\ a=\sqrt[]{c^2-b^2} \end{gathered}[/tex]replace with the values
[tex]\begin{gathered} a=\sqrt[]{(\sqrt[]{89})^2-5^2} \\ a=\sqrt[]{89-25} \\ a=\sqrt[]{64} \\ a=8 \end{gathered}[/tex]Enter in the coordinates for each point in the graph below.Quezon 2Not yetansweredPoints out of16.00H.c.5FlagquestionE.5-1990GD
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ANSWER:
A. (-7,2)
B (-5, -2)
C (-3, 5)
D (-2, -7)
E (2, 3)
F (3,3)
G (5,-6)
H (6, 6)
Jan is trying to fix her circular window and needs to know how much space it takes up. It has a diameter of 10 inches.
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ANSWER
The area is 78.54 in²
EXPLANATION
We need to find the area of this circle. The area of a circle with radius r is:
[tex]A=\pi r^2[/tex]The diameter of a circle is twice the radius, so if the diameter is 10 inches, then the radius is 5 inches:
[tex]A=\pi\cdot5^2=25\pi=78.54in^2[/tex]This answer is rounded to the nearest hundredth.
Needed help to catch up before summer come any help will be good thank you
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We have the following set of inequations
[tex]\begin{cases}y-2<-5{} \\ y-2>{5}\end{cases}[/tex]Let's solve both for y, it will give us
[tex]\begin{cases}y<-5{+2} \\ y>{5}+2\end{cases}\Rightarrow\begin{cases}y<-3 \\ y>7\end{cases}[/tex]Therefore y must be smaller than -3 and bigger than 7, then, the set between -3 and 7 is not part of the solution. the solution in fact is
[tex]S=(-\infty,-3)\cup(7,+\infty)[/tex]Let's do it in the graph!
The solution to the inequations is in blue on the graph.
If 12(5r + 6t) = x, then in terms of w, what is 48(30r + 361)?
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w=12(5r+6t)
Using distributive property:
w=60r+72t
and
48(30r+36t)=1440r+1728t
Now, let's multiply both sides of w=60r+72t by 24:
24*w=24*(60r+72t)
Using distributive property again:
24w=1440r+1728t
Therefore, 48(30r + 361) is equal to 24w.
Answer question number 18. The question is in the image.
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18.
Given:
[tex]g(x)=3sin2x[/tex]Required:
We need to graph the function and find the transformation from the parent function.
Explanation:
The given equation is of the form.
[tex]g(x)=Asin(Bx+C)[/tex]where A =3, B=2, and C=0.
We know that A is amplitude.
[tex]Amplitude=3[/tex][tex]Period=\frac{2\pi}{|B|}[/tex]Substitute B=2 in the equation,
[tex]Period=\frac{2\pi}{|2|}[/tex][tex]Period=\pi[/tex]Recall that the amplitude of a function is the amount by which the graph of the function travels above and below its midline.
The distance between the maximum point and midline is 3.
The time interval between two waves is known as a Period
The time interval between two waves is pi.
The graph of the function.
[tex]The\text{ parent function is f\lparen x\rparen=sinx.}[/tex]Recall that the amplitude stretches or compresses the graph vertically.
Here we have amplitude =3. it is a positive value.
The parent function stretches vertically by 3 units.
Recall that the period stretches or compresses the graph horizontally.
Here we have the period is pi.
The parent function compresses horizontally by pi.
Final answer:
[tex]Amplitude=3[/tex][tex]Period=\pi[/tex]The transformation is stretched vertically by 3 units and compressed horizontally by pi.
Write an Equation: Gary worked for 20 hours tutoring students at the library. He uses $35 to pay for gas on his way home. If he has $60 left after paying for gas, how much money, x, in dollars, was Gary paid per hour?
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Answer:4.75 in us dollars it will be 5.31
Step-by-step explanation:
first you divide 95 by 20 witch will give you 4.75 and if you want to check that answer you do 4.75 times 20 and it will give 95
What is the minimum? Where is the function increasing? Where is the function decreasing?
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As given by the question
There are given that the graph.
Now,
The minimum value of the given graph is shown below:
[tex](2,\text{ -1)}[/tex]2. Perform cach of the following calculations using a single multiplication. Do not round your final answers.(a) Decrease 160 by 10% (b) Decrease 450 by 6%(c) Decrease 122,000 by 12%(d) Decrease $1,820 by 3%(c) Decrease $12,500 by 15%(f) Decrease $4.50 by 8%
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We have the following:
(a) Decrease 160 by 10%
[tex]160\cdot(\frac{100-10}{100})=144[/tex](b) Decrease 450 by 6%
[tex]450\cdot(\frac{100-6}{100})=423[/tex](c) Decrease 122,000 by 12%
[tex]122000\cdot(\frac{100-12}{100})=107360[/tex](d) Decrease $1,820 by 3%
[tex]\begin{gathered} 1820\cdot(\frac{100-3}{100})=1765.4 \\ \end{gathered}[/tex](e) Decrease $12,500 by 15%
[tex]12500\cdot(\frac{100-15}{100})=10625[/tex](f) Decrease $4.50 by 8%
[tex]4.5\cdot(\frac{100-8}{100})=4.14[/tex]from this part ,find the estimated y-intercept .Round your answer to the three decimal places.
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y - incercept = 371.4
The table shows conversions of common units of capacity.Units of CapacityCustomary System UnitsMetric System Units1 gallon3.79 liters1 quart0.95 liters1 pint0.473 liters1 cup0.237 litersApproximately how many centiliters are in 3 quarts? Round answer to the nearest unit.
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Given data:
The value o 1 quart is 1 quart=0.95 liters.
Multiply the above expression with 3 on both sides.
3(1 quart)=3(0.95 liters)
3 quarts =2.
Nina deposited $20.59 in her checking account. Later that week, she wrote a checkfor one-third the amount in the account, and then another check for $9.74. If shehad $108.60 left in her account, how much did she have to begin with.
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1) Reading carefully, we can do it step by step.
2) She had deposited $20.59 and wrote a check, since she wrote a check we can understand that as a debit so we can write out the following:
[tex]\begin{gathered} 20.59-\frac{20.59}{3}= \\ 20.59-6.86 \\ 13.7 \end{gathered}[/tex]Note that we rounded off to the nearest hundredth.
2.2) So now, she wrote another check, i.e. -$9.74
[tex]\begin{gathered} \$13.7-\$9.74 \\ \$4 \\ 108.60 \\ 108.60+\mleft(20.59-6.86-9.74\mright)=112.59 \end{gathered}[/tex]Lisa's rectangular living room is 20 feet wide. If the length is 5 feet less than twice the width, what is the area of her living room?
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1) Let's gather all the data
Width: 20'
Length: 2w-5
2) Now we can plug that into the formula for the are of a rectangle, like this
[tex]\begin{gathered} A=wl \\ A=20\cdot(2(20)-5) \\ A=20\cdot(40-5) \\ A=20\cdot35 \\ A=700ft^2 \end{gathered}[/tex]Notice that we have plugged into that the width w=20. Therefore the area of the living room is 700ft²
are the triangles similar? if so what is the scale factor?
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a) Yes, The scale factor is 3/2
Explanation
Step 1
to check if the triangles are similar, we need to prove that the ratios of the longest side and one sideof the triangle are similar
so
let
[tex]ratio=\frac{longest\text{ side}}{side}[/tex]hence
[tex]\begin{gathered} ratio_1=\frac{8}{5}=1.6 \\ ratio_2=\frac{12}{7.5}=1.6 \end{gathered}[/tex]therefore, the triangles are similar
Step 2
now, to find the scale factor we use the formula
[tex]scale\text{ factor =}\frac{final\text{ length }}{original\text{ length}}[/tex]so, let's take the longest side on each triangle
[tex]\begin{gathered} final\text{ length=12} \\ original\text{ length=8} \end{gathered}[/tex]replace and calculate
[tex]\begin{gathered} scale\text{ factor =}\frac{final\text{ length }}{original\text{ length}} \\ scale\text{ factor =}\frac{12}{8}=\frac{3}{2} \end{gathered}[/tex]therefore, the answer is
a) Yes, The scale factor is 3/2
I hope this helps you
For the function N(t) = 4t + 5] + 3. evaluate N(2).
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Answer:
Explanation:
Putting in x = 2 in the function gives
[tex]N(2)=4|2+5|+3[/tex][tex]N(2)=31[/tex]which is our answer!
What point is a solution to the linear inequality y > 4x -3?
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Answer:
(0,-3 )and (0.75,0)
Step-by-step explanation:
y=4x_3
Find the value of 2[3(x2 – 5) + 5y] when x = 9 and y = 3.
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Answer
The value of the expression is 486
Step-by-step explanation
Given the expression
2[3(x^2 - 5) + 5y]
To solve this, we will be applying the PEMDAS rule
Where x = 9 and y = 3
Step 1: solve the smaller parenthesis first
2[3(9^2 - 5) + 5*3]
2 [ 3(81 - 5) + 15]
2 [ 3(76) + 15]
2 [ 228 + 15]
Solve the larger parenthesis
2 [ 243] = 486
Hence, the value of the expression is 486
Millie Gaines 4% by selling her cycle for 6644.80 rupees find a cp for cycle
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
bike price = 644.80 rupees
gain = 4% = 0.04
cp = cost price = ?
Step 02:
cost price = bike price - bike price*gain
= 644.80 rupees - 644.80 rupees * 0.04
= 644.80 rupees - 25.729 rupees
= 619 rupees
The answer is:
The cost price is 619 rupees.
i just need a tutor to tell me if my answers are correct or wrong
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Given the expression below,
Hi I need help with a couple of questions. It's math algebra
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The equation above is the formula of the speed (s) in terms of the distance (d) and the time (t).
For the distance 132 mi
With a speed of 8 miles per hour it takes the next hours:
[tex]\begin{gathered} \\ \text{Solve t:} \\ s\cdot t=d \\ t=\frac{d}{s} \\ \\ t=\frac{132mi}{8\frac{mi}{h}}=16.5h \end{gathered}[/tex]With a speed of 12 miles per hour it takes the next hours:
[tex]t=\frac{132mi}{12\frac{mi}{h}}=11h[/tex]Then, the possible number of hours that take to the kayaker to travel 132 miles is between 11 and 16.5
evaluate 2x + y when x = 15 and y = 4
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Given the following expressions:
[tex]\text{ 2x + y}[/tex]With x = 15 and y = 4, let's evaluate by substituting the values to the respective variables.
We get,
[tex]\text{ 2x + y}[/tex][tex]\text{ 2(15) + (4)}[/tex][tex]\text{ 30 + 4}[/tex][tex]\text{ = 34}[/tex]Therefore, 2x + y when x = 15 and y = 4 is 34.
what is x? how would i find the value of
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Given the Right Triangle ABC, you know that:
[tex]\begin{gathered} AB=29 \\ BC=9 \end{gathered}[/tex]In order to find the measure of the angle "x", you need to use the following Inverse Trigonometry Function:
[tex]\theta=sin^{-1}(\frac{opposite}{hypotenuse})[/tex]In this case, you can identify that:
[tex]\begin{gathered} \theta=x \\ opposite=BC=9 \\ hypotenuse=AB=29 \end{gathered}[/tex]Therefore, when you substitute values and evaluate, you get:
[tex]x=sin^{-1}(\frac{9}{29})[/tex][tex]x\approx18\text{\degree}[/tex]Hence, the answer is:
[tex]x\approx18\text{\degree}[/tex]Write the equation 4x + 8y = -24 in slope-intercept form. Then graph the equation. O None of the other answers are correct
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4x + 8y = - 24
8y = -4x - 24
divide both sides by 8
y = -1/2x - 3
[tex]y\text{ = }\frac{-1}{2}x\text{ - 3}[/tex]Using y = mx + c
To obtain y intercept, make x = 0
so y = -1/2(0) -3
y = -3
(0,-3)
To obtain x intercept, make y = 0
so that 0 = -1/2x -3
1/2x = -3
x = -6
(-6,0)
Taking the points (0,-3) and (-6,0) to plot the graph
Fred's car van travel 368 miles on one tank of gas. His has tank holds 16 gallons what is the unit rate for mules per gallon
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16 gallons is needed for 368miles
Therefore
1 gallon is needed for 368/16 = 23miles
Hence the rate for miles per gallon is
Find the coordinates of point Q that lies along the directed line segment from R(-2, 4) to S(18, -6) and partitions the segment in the ratio of 3:7.A. (4, 1)B. (16, -2)C. (6, -3)D. (8, -1)
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The coordinates of the point which partitions a directed line segment AB at the ratio a:b from A(x1, y1) to B(x2, y2) is computed as follows:
[tex](x,y)=(x_1+\frac{a}{a+b}(x_2-x_1),y_1+\frac{a}{a+b}(y_2-y_1_{}))[/tex]In this case, the segment goes from R(-2, 4) to S(18, -6), and the partition ratio is 3:7. Substituting into the above formula, we get:
[tex]\begin{gathered} (x,y)=(-2+\frac{3}{3+7}(18-(-2)),4+\frac{3}{3+7}(-6-4)) \\ (x,y)=(-2+\frac{3}{10}\cdot20,4+\frac{3}{10}(-10)) \\ (x,y)=(4,1) \end{gathered}[/tex]Question 3 of 5 Shayla spent $260 on 4 chairs. To find out how much she spent on each chair, she did the following work in long division. 15 4) 260 60 0 Did she do the problem correctly? Why or why not?
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we know that
To find out how much she spent on each chair
Divide the total cost by the number of chairs
so
[tex]\frac{260}{4}=65[/tex]therefore
She spent on each chair $65
in a recent survey, 60% of the community favored building a health center in their neighborhood. If 14 citizens are chosen, find the probability that exactly 11 of them favor the building of the health center. Round to the nearest thousandth.
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Answer:
0.085
Explanation:
To find the probability, we will use the binomial distribution because there are n identical events ( 14 citizens), with a probability of success (p = 60%). Then, the probability can be calculated as:
[tex]P(x)=\text{nCx}\cdot p^x\cdot(1-p)^{n-x}[/tex]Where nCx is equal to
[tex]\text{nCx}=\frac{n!}{x!(n-x)!}[/tex]So, to find the probability that exactly 11 of them favor the building of the health center, we need to replace x = 11, n = 14, and p = 0.6
[tex]14C11=\frac{14!}{11!(14-11)!}=\frac{14!}{11!(3!)}=364[/tex][tex]\begin{gathered} P(11)=364(0.6)^{11}(1-0.6)^{14-11} \\ P(11)=0.085 \end{gathered}[/tex]Therefore, the probability that exactly 11 of them favor the building of the health center is 0.085