Consider the following functions.S(x) = x2 - 4x + 4 and g(x) = x - 2Step 1 of 2: Find• ()a). simplify your answer.AnswerKeybo(*)(x) =Subn
Answers
Answer:
[tex]x-2[/tex]Explanation:
Here, we want to simplfy the given expression
From what we have:
[tex](\frac{f}{g})(x)\text{ = }\frac{f(x)}{g(x)}[/tex]Substituting the values, we have it that:
[tex]\frac{x^2-4x+4}{x-2}\text{ = }\frac{(x-2)(x-2)}{x-2}\text{ =x-2}[/tex]Related Questions
Write an equation in slope-intercept form for the line through (-1, 1) and (0,3).
Answers
The slope intercept form of a line can be written as:
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept.
We have two points of the line: (-1,1) and (0,3).
Knowing that for x=0, the value of y=3 tells us that the y-intercept b is b=3:
[tex]\begin{gathered} y=mx+b \\ 3=m\cdot0+b \\ 3=b \end{gathered}[/tex]Using the other point and replacing the values of x and y in the equation we can calculate the value of the slope m:
[tex]\begin{gathered} y=mx+3 \\ 1=m\cdot(-1)+3 \\ 1-3=-m \\ -2=-m \\ m=2 \end{gathered}[/tex]Then, with m=2 and b=3, the equation becomes:
[tex]y=2x+3[/tex]Answer: y=2x+3
mputing and Using a Least-Squares Regression LineVehiclesight (tons) Gas mileage (mpg)1.6291.6451.75261.952221821211822.32.5The table shows the weight and gas mileage of severalvehicles.What is the equation of the least-squares regressionline, where ŷ is the predicted gas mileage and x is theweight?ŷ=V+According to the regression equation, a car that weighs1.8 tons would have a gas mileage of aboutmiles per gallon.
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From the table, we have the following points:
(x, y) ==> (1.6, 29), (1.6, 45), (1.75, 26), (1.95, 22), (2, 18), (2, 21), (2.3, 21), (2.5, 18)
Let's find the regression line.
Apply the slope-intercept form:
y = mx + b
Where m is the slope and b is the y-intercept.
To find the slope, apply the formula:
[tex]m=\frac{n(\Sigma xy)-\Sigma x\Sigma y}{n(\Sigma x^2)-(\Sigma x)^2}[/tex]Where:
• ∑x = 1.6 + 1.6 + 1.75 + 1.95 + 2 + 2 + 2.3 + 2.5 = 15.7
• ∑y = 29 + 45 + 26 + 22 + 18 + 21 + 21 + 18 = 200
• ∑xy = 1.6⋅29 + 1.6⋅45 + 1.75⋅26 + 1.95⋅22 + 2⋅18 +2⋅21 +2.3⋅21 + 2.5⋅18 = 378.1
• ∑x² = 1.6² + 1.6² + 1.75² + 1.95² + 2² + 2² + 2.3² + 2.5² = 31.525
,• n is the number of data = 8
Now, plug in values into the equation and solve for m:
[tex]\begin{gathered} m=\frac{8(378.1)-15.7*200}{8(31.525)-(15.7)^2} \\ \\ m=-20.175\approx20.2 \end{gathered}[/tex]The slope, m = -20.2
To find the y-intercept, b, apply the formula:
[tex]\begin{gathered} b=\frac{(\Sigma y)(\Sigma x^2)-\Sigma x\Sigma xy}{n(\Sigma x^2)-(\Sigma x)^2} \\ \\ b=\frac{200(31.525)-15.7*200}{8(31.525)-15.7^2} \\ \\ b=64.594\approx64.6 \end{gathered}[/tex]Therefore, the regression equation is:
y = 64.6 + (-20.2)x
(b). Substitute 1.8 for x in the equation and solve for y:
y = -20.2(1.8) + 64.6
y = 28.24 = 28.
ANSWER:
(A). y = 64.6 + (-20.2)x
(B). 28
Answer:
here's your answer :)
Step-by-step explanation:
Find the missing quantity with the information given. Round rates to the nearest whole percent and dollar amounts to the nearest cent
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Given:
Original Price $4.50
Markdown=$1.30
[tex]\begin{gathered} \text{ \% Markdown=}\frac{1.30}{4.50}\times100 \\ \text{ \% Markdown=}28.89\text{ \%} \end{gathered}[/tex]I will send a picture of the problem and or question
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The equivalency for grams to centigrams is:
1 gram = 100centigrams
To convert the units you can apply cross multiplication:
1gr_____100cgr
443gr____xcgr
[tex]\begin{gathered} \frac{100}{1}=\frac{x}{443} \\ x=443\cdot100=44300 \end{gathered}[/tex]This means that 443 grams equals to 44300 centigrams
*-*-*-*
The scale is done in a base of 10 and the grams are in its center with value 1.
To convert from smaller units to grater units you have to divide the given measurement by 10
And to convert from greater units to smaller units you have to multiply by 10.
For example if you have 1mg and want to convert it to grams you have to divide the value 3 times by 10, i.e. divide the value by 1000
[tex]\frac{1mg}{1000}=0.001g[/tex]If you want to convert 1 Kg into 1 decagram, multiply the value two times by 10, i.e. multiply it by 100
[tex]1\operatorname{kg}\cdot100=100\text{dag}[/tex]Identify the property of real numbers illustrated in the following equation.(+6) + [y? • (-4)] = [y2 • (-4)] + (-6)
Answers
Given
[tex]\mleft(+6\mright)+\mleft[y^2•(-4)\mright]=\mleft[y^2•(-4)\mright]+(-6)[/tex]Answer
Commutative property of addition
Which statements about the opposite of −12 are true? Select each correct answer. Responses −12 and its opposite are on located on the same side of zero on a number line. negative 12, and its opposite are on located on the same side of zero on a number line. The opposite of −12 is −1/12. The opposite of , negative 12, is , negative fraction 1 over 12, . −12 and its opposite are located the same distance from zero on a number line. negative 12, and its opposite are located the same distance from zero on a number line. The opposite of the opposite of −12 is −12.
Answers
Answer:
The opposite would be +12.
Step-by-step explanation:
In math, an opposite number is the number on the other side of zero on the number line that is the same distance from zero. For example, the number 5 is five spaces from zero on the right-hand side of the number line while the opposite. So the opposite would be -5 because it is five spaces from zero on the left side of a number line.
Please help ASAP!! 31 points and brainliest!
I really need help! Please show your work so I can understand how to get the answers too!
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A relation is a function if it has only One y-value for each x-value. Functions f(2/3)=2/9 for f(x)=2x²-4x+2 and f(1/4)==-21/4 for f(x)=4x²+2x-6
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function is
f(x)=2x²-4x+2
Put x=2/3
f(2/3)=2(2/3)²-4(2/3)+2
=2(4/9)-8/3+2
=8/9-8/3+2
=(8-24+18)/9
f(2/3)=2/9
Now f(x)=4x²+2x-6
Put x=1/4
f(1/4)=4(1/4)²+2(1/4)-6
=4/16+2/4-6
=1/4+1/2-6
= 1+2-24/4
f(1/4)==-21/4
Hence functions f(2/3)=2/9 for f(x)=2x²-4x+2 and f(1/4)==-21/4 for f(x)=4x²+2x-6
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Two question I want to verify my answerSolve for y in terms of x 2x =1-5yAnd Simplify the given expression Write answer with a positive exponent (X^-3/y^4)^-4
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Part 1
we have
2x =1-5y
solve for y
step 1
Adds 5y both sides
2x+5y=1
step 2
subtract 2x both sides
5y=-2x+1
step 3
Divide by 5 on both sides
y=-(2/5)x+1/5
Part 2
we have the expression
[tex](\frac{x^{-3}}{y^4})^{-6}=(\frac{y^4}{x^{-3}})^6=(y^4x^3)^6=y^{(24)}x^{(18)}[/tex]Please provide deep explanation, so i can understand and learn. Thank you
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Assume the height of the box is x.
5 reams of paper have 5 x 500 = 2500 sheets of paper.
This means that each sheet of paper has a thickness of x/2500.
Two sheets of paper have a thickness of 2 times x/2500.
Simplifying the fraction:
[tex]2\cdot\frac{x}{2500}=\frac{x}{1250}[/tex]Two sheets of paper have a thickness of 1/1250th of the height of the box.
Assume the height is x = 20 cm, then two sheets are 20/1250 = 0.016 cm thick.
Fill in the table using this function rule. y = -10x +3 y X 6 ? 1 0 a 1
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the function is
[tex]y=-10x+3[/tex]we must replace the value of x and obtain y
x=-5
[tex]\begin{gathered} y=-10(-5)+3 \\ y=50+3 \\ y=53 \end{gathered}[/tex]x=-1
[tex]\begin{gathered} y=-10(-1)+3 \\ y=13 \end{gathered}[/tex]x=0
[tex]\begin{gathered} y=-10(0)+3 \\ y=3 \end{gathered}[/tex]x=1
[tex]\begin{gathered} y=-10(1)+3 \\ y=-7 \end{gathered}[/tex]I need help with this problem Math relatedsimplify in radical form:^3{120a^4b^5c
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Sara, this is the solution:
∛ 120a^4b^5c
Lets solve factor by factor:
∛ 120 = ∛ 8 * 15 = 2∛ 15
∛a^4 = a^4/3
∛b^5 = b^5/3
∛c (We can't simplify this factor)
In consequence, we have:
2a^(4/3) b^(5/3)∛ 15c
In an all boys school, the heights of the student body are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. What is the probability that a randomly selected student will be taller than 71 inches tall, to the nearest thousandth?
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Answer:
0.010
Step-by-step explanation:
We solve the above question using z score formula
z = (x-μ)/σ, where
x is the raw score = 63 inches
μ is the population mean = 70 inches
σ is the population standard deviation = 3 inches
For x shorter than 63 inches = x < 63
Z score = x - μ/σ
= 63 - 70/3
= -2.33333
Probability value from Z-Table:
P(x<63) = 0.0098153
Approximately to the nearest thousandth = 0.010
Therefore, the probability that a randomly selected student will be shorter than 63 inches tall, to the nearest thousandth is 0.010.
Help first one to get this correct will be marked
Answers
Answer:
1st one
Step-by-step explanation:
1st one
You have one input (x) with more than one output (y)
(-9, -9) and (-9, 6)
the scale of a map is 1cm: 7milesthe distance between two cities is 102.2 miles.find the distance between the two cities on the map
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Ok, so:
We know that the scale given is the next one:
1cm = 7miles.
Now, let me draw something here below:
So, the cities are separated by a distance of 102.2 miles.
If 1 cm = 7 miles,
Then, we're going to convert 102.2 miles to our map scale.
102.2 miles * ( 1cm / 7 miles).
And we obtain:
14.6cm
Given a function described as the equation y= 4x - 4, what is y when x is 1, 2, and 3?A 2, 8, 16B 4,8, 12C 0,4,8D 0, 6, 12
Answers
Answer
C. 0, 4, 8
Explanation
Given function:
y = 4x - 4
What to find:
To find y when x = 1, 2, and 3
Step-by-step solution:
When x = 1
y = 4(1) - 4
y = 4 - 4
y = 0
When x = 2
y = 4(2) - 4
y = 8 - 4
y = 4
When x = 3
y = 4(3) - 4
y = 12 - 4
y = 8
ty received test Graves of 71%, 82%, 71%, 78% and 78%.A) what grade would he need to make on the 6th test to get a C if a C is at least 75% but less than 80%?B) is it possible for tie to get a b or better for his test average at least 80%?
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As given that first 5grades are: 71%, 82%, 71%, 78% and 78%.
Let the 6th grade be C
a). Then:
[tex]75\leq\frac{71+82+71+78+78+C}{6}\leq80[/tex]Simplifying it:
[tex]\begin{gathered} 75\leq\frac{71+82+71+78+78+C}{6} \\ 75\times6\leq380+C \\ 450\leq380+C \\ 450-380\leq C \\ 70\leq C \end{gathered}[/tex]And:
[tex]\begin{gathered} \frac{380+C}{6}\leq80 \\ 380+C\leq480 \\ C\leq100 \end{gathered}[/tex]So C should be in between 70 to 100.
b). For at least 80%:
[tex]\begin{gathered} \frac{71+82+71+78+78+C}{6}\ge80 \\ 380+C\ge80\times6 \\ 380+C\ge480 \\ C\ge100 \end{gathered}[/tex]It is not possible for getting b grade as one cannot achieve more than maximum marks if the maximum marks are 100.
Suppose angles a and B are the two acute angles in a right triangle and that b < a. Apply the relationship between sine and cosine todetermine which statements are correct.sin(6x - 10) = cos(4x + 10)A)x = 9B)a = 46°a = 48°D)B = 42°E)B = 44
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The right statements are: A, B and E
Sin(A)=cos(B)
then we check if using x=9 this holds true:
sin(6x-10)=cos(4x+10)
sin((6*9)-10) = sin(44º)
cos(4x+10)=cos(46)
Sin(44)=0.694=cos(46)
then a is true
Now, we know that b
Answer two questions about Equations A and B
A. 2r-1= 5x
B. -1 = 3x
1) How can we get Equation B from Equation A?
Choose 1 answer:
Add/subtract the same quantity to/from both sides
Add/subtract a quantity to/from only one side
Rewrite one side (or both) by combining like terms
Rewrite one side (or both) using the distributive property
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In the given equation A, we can (A) subtract the same quantity from both sides.
What are equations?In a mathematical equation, the equals sign is used to express that two expressions are equal. An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. Like 3x + 5 = 15, for example. There are many different types of equations, including linear, quadratic, cubic, and others. The three primary forms of linear equations are point-slope, standard, and slope-intercept.So, obtain equation B from equation A:
Equation A: 2x - 1 = 5xEquation B: -1 = 3xWe can subtract (2x) from both sides to get equation B as follows:
2x - 1 = 5x2x - 2x - 1 = 5x - 2x-1 = 3xTherefore, in the given equation A, we can (A) subtract the same quantity from both sides.
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The path of the baseball follows the equation h= -4.9t^2 + 60t + 1.5 where h represents the height of the baseball, t seconds after the baseball was hit. How long will it take the baseball to return to the ground?
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SOLUTION
Given the question in the question tab, the following are the steps to solve the problem:
Step 1: Write out the equation for the path of the baseball where h is height and t is time in seconds
[tex]h=-4.9t^2+60t+1.5[/tex]Step 2: Rewrite the new equation
The height of the baseball when it returns to the ground is zero(0). Therefore, at that point where the baseball returns to the ground, the function becomes:
[tex]0=-4.9t^2+60t+1.5[/tex]Step 3: We solve the quadratic equation to get the value of t:
[tex]\begin{gathered} 0=-4.9t^2+60t+1.5 \\ u\sin g\text{ quadratic formula which states that:} \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ a=-4.9,b=60,c=1.5 \\ \text{Substituting the values, we have:} \\ \frac{-60\pm\sqrt[]{60^2-4(-4.9)(1.5)}}{2(-4.9)} \\ =\frac{-60\pm\sqrt[]{3600+29.4}}{-9.8} \\ =\frac{-60\pm60.2445}{-9.8} \\ =\frac{-60+60.2445}{-9.8}\text{ or }\frac{-60-_{}60.2445}{-9.8} \\ =\frac{0.2445}{-9.8}or\frac{-120.2445}{-9.8} \\ t=-0.024948979\text{ or }12.26984184 \\ t\approx-0.0249\text{ or 12.270} \end{gathered}[/tex]Since the value for time cannot be negative, hence the time it will it take the baseball to return to the ground is approximately 12.270 seconds
which is the BEST first step in order to solve this equation15 + 2/3 a = -5a.subtract 15 from both sides b.subtract 2/3 feom both sides c.add 5 to both sides d.multiply by 3 on both sides
Answers
In order to solve this equation, we need to isolate the variable a in one side of the equation.
Since we have the number 15 in the same side of the variable, the best first step would be removing this number 15 from this side, and we do this by subtracting 15 from both sides.
Therefore the answer is a.
Find the slope of the lines (-3,-1) and (-6,-10)
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m = rise/run = (-10 - (-1))/(-6 - (-3)) = -9/-3 = 3
the slope of the line is equal to 3.
The table displays the mean name length for seven samples of students.Sample1Mean Name Length5.47.1236.345.2566.04.976.2What can be said about the variation between the sample means?The variation between the sample means is small.The variation between the sample means is large.The variation shows that the values are far apart.The variation cannot be used to make predictions.
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First option is correct.
For all the sample sizes, the sample mean is close to 6, give or take (
Is 1/4 n - 16 equivalent to 4(n - 4)?
Answers
Answer:
[tex]\frac{1}{4}n-16[/tex]is not equivalent to:
[tex]4(n-4)[/tex]Explanation:
The expression
[tex]\frac{1}{4}n-16[/tex]can be written as:
[tex]\frac{1}{4}(n-64)[/tex]It is not equivalent to:
[tex]4(n-4\text{)}=4n-16[/tex]8. Here is a graph of the equation 3x - 2y = 12.
Select all coordinate pairs that represent a solution to
the equation.
A. (2,-3)
B. (4,0)
C. (5,-1)
D. (0, -6)
E. (2,3)
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Answer:
A,B,D
Step-by-step explanation:
By replacing the points in the current equation you can get true statements which are correspondent to answer A,B,D
Can you write on the paper/photo? So can write on my paper too and write it down
Answers
Answer:
1) 4x + 12
2) new area = 16x + 48
3) Yes, the ratio is the same for positive values of x
Explanation:
The distributive property of multiplication is shown below
a(b + c) = ab + ac
The area of the given rectangle is expressed as
Area = 4(x + 3)
By applying the distributive property, it becomes
4 * x + 4 * 3
= 4x + 12
The equivalent expression is
4x + 12
If the dimensions of the rectangle are doubled, then
new length = 2(x + 3) = 2x + 6
new width = 4 * 2 = 8
Thus,
new area = 8(2x + 6) = 8 * 2x + 8 * 6
new area = 16x + 48
We would input values of x into both areas and find their ratios
For x = 1,
area = 4(1) + 12 = 16
new area = 16(1) + 48 = 64
ratio = 16/64 = 1/4
For x = 2,
area = 4(2) + 12 = 20
new area = 16(2) + 48 = 80
ratio = 20/80 = 1/4
For x = 3,
area = 4(3) + 12 = 24
new area = 16(3) + 48 = 96
ratio = 24/96 = 1/4
Thus, the ratio is the same for positive values of x
For each equation in the table, give the slope of the graph.
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y=-6 is 0 or m = 0
y=-6x is -6 or m = -6
Answer:
1. undefined
2. 0
3. -6
Step-by-step explanation:
Slope-intercept form: y = mx + b
m = slope
b = y-intercept.
Since the equation x = -6 is a vertical line, the slope is undefined.
Since y = -6 is a horizontal line, the slope is 0.
The slope of y = -6x is -6. This is because it is the coefficient of the variable x.
triangle XZW ~ triangle XYV, find the perimeter of triangle XZW
Answers
176.4
Explanation
as the triangle are similar we can set a proportion
Step 1
find the YZ value
a) let
[tex]ratio1=\frac{hypotenuse}{rigth\text{ side}}[/tex]so,for triangle XZW
[tex]ratio=\frac{40+32}{28+YZ}[/tex]and for triangle XYV
[tex]ratio=\frac{40}{28}[/tex]as the ratios are equal, we can set a proportion
[tex]\frac{40+32}{28+YZ}=\frac{40}{28}[/tex]b) now,solve for YZ
[tex]\begin{gathered} \frac{40+32}{28+YZ}=\frac{40}{28} \\ \frac{72}{28+YZ}=\frac{40}{28} \\ cross\text{ multiply} \\ 72*28=40(28+YZ) \\ 2016=1120+40YZ \\ subtract\text{ 1120 in both sides} \\ 2016-1120=1120+40YZ-1120 \\ 896=40YZ \\ divide\text{ bothsides by 40} \\ \frac{896}{40}=\frac{40YZ}{40} \\ 22.4=YZ \end{gathered}[/tex]so
YZ=22.4
Step 2
find the length of the side WZ
a) let
[tex]ratio=\frac{hypotenuse\text{ }}{base}[/tex]hence
[tex]\begin{gathered} ratio_1=\frac{40+32}{WZ}=\frac{72}{WZ} \\ ratio_2=\frac{40}{30} \end{gathered}[/tex]set the proportion and solve for YZ
[tex]\begin{gathered} ratio_1=\text{ ratio}_2 \\ \frac{72}{WZ}=\frac{40}{30} \\ cross\text{ multiply} \\ 72*30=40WZ \\ 2160=40WZ \\ divide\text{ both sides by 40} \\ \frac{2160}{40}=\frac{40WZ}{40} \\ 54=WZ \end{gathered}[/tex]Step 3
finally, find the perimeter of triangle XZW
Perimeter is the distance around the edge of a shape,so
[tex]Perimeter_{\Delta XZW}=XY+YZ+ZW+WV+VX[/tex]replace and calculate
[tex]\begin{gathered} Per\imaginaryI meter_{\Delta XZW}=XY+YZ+ZW+WV+VX \\ Perimeter_{\Delta XZW}=28+22.4+54+32+40 \\ Perimeter_{\Delta XZW}=176.4 \end{gathered}[/tex]therefore, the answer is
176.4
I hope this helps you
Mary used the quadratic formula to find the zeros of the equation below. Select the correct zeros of the equation:3x^2 - 9x + 2 = 0Answer choices include:x = fraction numerator 9 plus-or-minus square root of 57 over denominator 6 end fractionx equals fraction numerator negative 9 plus-or-minus square root of 57 over denominator 2 end fractionx equals fraction numerator 9 plus-or-minus square root of 105 over denominator 2 end fractionx equals fraction numerator negative 9 plus-or-minus square root of 105 over denominator 6 end fraction
Answers
We have the next quadratic function given:
[tex]3x^2-9x+2=0[/tex]Mary used the next quadratic formula:
[tex]x=\frac{-b^\pm\sqrt{b^2-4ac}}{2a}[/tex]Replace using the form ax²+bx+c
Where a= 3
b=-9
c=2
Then:
[tex]\begin{gathered} x=\frac{-\lparen-9)\pm\sqrt{\left(-9\right)^2-4\left(3\right)\left(2\right)}}{2\left(3\right)} \\ x=\frac{9\pm\sqrt[]{57}}{6}\frac{}{} \end{gathered}[/tex]Therefore, the correct answer is "x = fraction numerator 9 plus-or-minus square root of 57 over denominator 6 end fraction"
Find the indicated quantity, given u = (4, -9), v = (-4, -7).Step 4 of 4: Find (u • v)4v.
Answers
Answer:
[tex]\begin{equation*} \langle-1316,-2303\operatorname{\rangle} \end{equation*}[/tex]Explanation:
Given the vectors:
[tex]\begin{gathered} u=\langle4,-9\rangle \\ v=\langle-4,-7\rangle \end{gathered}[/tex]The dot product of u and v is calculated below:
[tex]\begin{gathered} u\cdot v=4\times-4+-9\times-7 \\ =-16+63 \\ =47 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} (u\cdot v)4v=47\times4\langle-4,-7\rangle \\ =329\langle-4,-7\rangle \\ =\langle-4\times329,-7\times329\rangle \\ =\langle-1316,-2303\operatorname{\rangle} \end{gathered}[/tex]The indicated quantity is:
[tex]\begin{equation*} \langle-1316,-2303\operatorname{\rangle} \end{equation*}[/tex]
Margo borrows $1200, agreeing to pay it back with 4% annual interest after 17 months. How much interest will she pay?
Answers
Answer:
$68
Step-by-step explanation:
P = $1200
R = 4%
T = 17months (Convert to years; 17 months ÷ 12 months)
Formular for Interest; I = PRT
100
I = $1200 × 4 × 17
100 × 12
I = $68