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
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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
Let f(x) = 2x² + 14x – 16 and g(x) = x+8. Perform the function operation and then find the domain of the result.(x) = (simplify your answer.)
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We need to find the following division of the functions f(x) and g(x):
[tex]\frac{f}{g}(x)=\frac{f(x)}{g(x)}=\frac{2x^2+14x-16}{x+8}[/tex]We can note that the numerator can be rewritten as
[tex]2x^2+14x-16=2(x^2+7x-8)=2(x+8)(x-1)[/tex]Then the division can be written as:
[tex]\frac{f}{g}(x)=\frac{f(x)}{g(x)}=\frac{2(x+8)(x-1)}{x+8}[/tex]From this result, we can cancel out the term (x+8) from both sides and get,
[tex]\frac{f}{g}(x)=\frac{f(x)}{g(x)}=2(x-1)[/tex]Therefore, the result of the division is:
[tex]\frac{f}{g}(x)=2(x-1)[/tex]which domain is all real numbers:
[tex]x\in(-\infty,\infty)[/tex]A. Determine the slope intercept equation of each line given two points on the line 1. (1, -3) and (-2, 6)
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ANSWER
y = -3x
EXPLANATION
We have to determine the slope-intercept form of the equation of the line.
The slope-intercept form of a linear equation is given as:
y = mx + c
where m = slope
c = y intercept
First, we have to find the slope:
[tex]m\text{ = }\frac{y2\text{ - y1}}{x2\text{ - x1}}[/tex]where (x1, y1) and (x2, y2) are two points the line passes through.
Therefore:
[tex]\begin{gathered} m\text{ = }\frac{6-(-3)}{-2-1}=\frac{6+3}{-3}=\frac{9}{-3} \\ m=-3 \end{gathered}[/tex]Now, we have to use the point-slope method to find the equation:
y - y1 = m(x - x1)
=> y - (-3) = -3(x - 1)
y + 3 = -3x + 3
y = -3x + 3 - 3
y = -3x
That is the slope intercept form of the equation.
The relation between the number of batteries (n) and the maximum height reached by the drone (h) in feet (ft) is given. Complete the table and check the correct box(es) given below.
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We use the equation: h = 100(n + 2), so:
For n = 1:
[tex]h=100(1+2)=100(3)=300[/tex]For n = 3:
[tex]h=100(3+2)=100(5)=500[/tex]We can see that this is the correct equation. Therefore, given h we find n:
For h = 700
[tex]\begin{gathered} 700=100(n+2) \\ \frac{700}{100}=\frac{100}{100}(n+2) \\ 7=n+2 \\ 7-2=n+2-2 \\ n=5 \end{gathered}[/tex]For h = 900
[tex]\begin{gathered} 900=100(n+2) \\ \frac{900}{100}=\frac{100}{100}(n+2) \\ 9=n+2 \\ 9-2=n+2-2 \\ n=7 \end{gathered}[/tex]Answer:
(n): 1 3 5 7
(h): 300 500 700 900
Correct equation: h = 100(n + 2)
4. Betty Kusack and Theresa Peña together can do a job in 20 hours. Working alone,Betty can do the job in 60 hours. How long would it take Theresa, working alone, todo the job?AnswerH
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Given:
Betty and Theresa together complete a job in 20 hours.
Betty alone does a work in 60 hours.
The aim is to find the time Theresa will take to complete the job alone.
Therefore,
Betty and Theresa's 1 day work:
[tex]=\frac{1}{20}[/tex]Betty's 1 day work when he works alone:
[tex]=\frac{1}{60}[/tex]Now, Theresa's 1 day work when he works alone is given by:
[tex]\begin{gathered} =\frac{1}{20}-\frac{1}{60} \\ =\frac{3-1}{60} \\ =\frac{2}{60} \\ =\frac{1}{30} \end{gathered}[/tex]Hence, Theresa can do the job in 30 hours working alone.
3.2 Similar FiguresIf ASRT - ACBD, find the value of x.Show all work.Hint: Don't let your eyes deceive you pay attention tothe similarity statement.
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Find the ratio of corresponding sides:
SRT to CBD =
70/50 = 1.4
SR / 60 = 1.4
SR = 60 x 1.4
SR = 84
84= 11x-4
Solve for x:
84+4 = 11x
88= 11x
88/11 = x
8=x
Solve triangle EFG with the given parts.f = 17.78, F = 27.3°, G = 102.1°
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STEP - BY - STEP EXPLANATION
What to find?
g, E and e
Given:
Step 1
Find the measure of side g using the sine ratio.
[tex]\begin{gathered} \frac{sinF}{f}=\frac{sinG}{g} \\ \\ \frac{sin27.3}{17.78}=\frac{sin102.1}{g} \\ \\ gsin27.3=17.78sin102.1 \\ \\ g=\frac{17.78sin102.1}{sin27.3} \\ \\ g\approx37.9 \end{gathered}[/tex]Step 2
Find angle E.
[tex]E+F+G=180(sum\text{ of interior angle in a triangle\rparen}[/tex][tex]\begin{gathered} E+27.3+102.1=180 \\ \\ E=180-102.1-27.3 \\ \\ E=50.6° \end{gathered}[/tex]Step 3
Find side e using the sine ratio.
[tex]\begin{gathered} \frac{sinE}{e}=\frac{sinF}{f} \\ \\ \frac{sin50.6}{e}=\frac{sin27.3}{17.78} \\ \\ esin27.3=17.78sin50.6 \\ \\ e=\frac{17.78sin50.6}{sin27.3} \\ \\ e\approx29.96 \end{gathered}[/tex]ANSWER
g=37.9
E=50.6°
e = 29.96
Given the matrices A and B shown below, find – į A+ B.89A=12 4.-4 -10-6 12B.=-3-19-10
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Given:
[tex]\begin{gathered} A=\begin{bmatrix}{12} & {4} & {} \\ {-4} & {-10} & {} \\ {-6} & {12} & {}\end{bmatrix} \\ B=\begin{bmatrix}{8} & {9} & {} \\ {-3} & {-1} & {} \\ {-9} & {-10} & {}\end{bmatrix} \end{gathered}[/tex]Now, let's find (-1/2)A.
Each term of the matrix A is multiplied by -1/2.
[tex]\begin{gathered} \frac{-1}{2}A=\frac{-1}{2}\begin{bmatrix}{12} & {4} & {} \\ {-4} & {-10} & {} \\ {-6} & {12} & {}\end{bmatrix} \\ =\begin{bmatrix}{\frac{-12}{2}} & {\frac{-4}{2}} & {} \\ {\frac{4}{2}} & {\frac{10}{2}} & {} \\ {\frac{6}{2}} & {-\frac{12}{2}} & {}\end{bmatrix} \\ =\begin{bmatrix}{-6} & {-2} & {} \\ {2} & {5} & {} \\ {3} & {-6} & {}\end{bmatrix} \end{gathered}[/tex]Now let's find (-1/2)A+B.
To find (-1/2)A+B, the corresponding terms of the matrices are added together.
[tex]\begin{gathered} \frac{-1}{2}A+B=\begin{bmatrix}{-6} & {-2} & {} \\ {2} & {5} & {} \\ {3} & {-6} & {}\end{bmatrix}+\begin{bmatrix}{8} & {9} & {} \\ {-3} & {-1} & {} \\ {-9} & {-10} & {}\end{bmatrix} \\ =\begin{bmatrix}{-6+8} & {-2+9} & {} \\ {2-3} & {5-1} & {} \\ {3-9} & {-6-10} & {}\end{bmatrix} \\ =\begin{bmatrix}{2} & {7} & {} \\ {-1} & {4} & {} \\ {-6} & {-16} & {}\end{bmatrix} \end{gathered}[/tex]Therefore,
[tex]undefined[/tex]help me please.......
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Let
x -----> the larger room
y -----> the smaller room
we have that
x=2y
we have
y=25 3/4 ft
Convert to an improper fraction
25 3/4=25+3/4=103/4 ft
Find the value of x
x=2y
x=2(103/4)
x=103/2 ft
Convert to mixed number
103/2=51.5=51+0.5=51 1/2 ft
the answer is51 1/2 fthe larger roomhe larger room
the four faced of a rectangular pyrimid below are painted yellow. how many square feet will be painted
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The number of square feet to be painted is equal to the surface area of the four face painted yellow.
Total Surface Area (TSA) =
[tex]4(\frac{1}{2}bh)[/tex]By Pythagoras Theorem,
[tex]\begin{gathered} h^2+1.5^2=5^2 \\ h^2=5^2-1.5^2 \\ h=\sqrt[]{25-2.25}\text{ =}\sqrt[]{22.75}=4.7697\text{ fe}et \end{gathered}[/tex]Charlene and Gary want to make perfume. In order to get the right balance of ingredients for their tastes they bought 2ounces of rose oil at $4.36 per ounce, 5 ounces of ginger essence for $2.15 per ounce, and 4 ounces of black currant essence for $2.27 per ounce. Determine the cost per ounce of the perfume.
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First, lets calculate how much the expended in the perfume:
[tex]2\times(4.36)+5\times(2.15)_{}+4\times(2.27)=28.55[/tex]So, for 11 ounces of perfume, they need $28.55, so the minimum that the perfume need to cost per ounce is:
[tex]\frac{28.55}{11}=2.5954\cong2.6[/tex]So, about $2.6 per ounce of perfume.
Select all the equations that share a solution with this system of equations. (Hint: try adding and subtracting the equations.) 5x + 4y = 24 2x – 7y = 26 7x – 3y = 50 7x + 3y = 50 3x - 3y = -2 36 x+ 11y = -2
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Select all the equations that share a solution with this system of equations. (Hint: try adding and subtracting the equations.)
5x + 4y = 24
2x – 7y = 26
____
a) 7x – 3y = 50
b) 7x + 3y = 50
c) 3x - 3y = -2
d) 3 x+ 11y = -2
_____________________________
Try adding and subtracting the equations
5x + 4y = 24
+(2x – 7y = 26)
_______________
7x -3y= 50
5x + 4y = 24
-2x + 7y = -26
______________
3x + 11y = -2
Do you have any questions regarding the solution?
Write the slope-intercept form of the equation of each line.4) -3+y=2/5x
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where
[tex]\begin{gathered} \text{slope}=\frac{2}{5} \\ y-\text{intercept}=3 \end{gathered}[/tex]Explanation
the equation of a line in slope-intercept form is given by:
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \end{gathered}[/tex]Step 1
then, isolate y
[tex]-3+y=\frac{2}{5}x[/tex]i) add 3 in both sides
[tex]\begin{gathered} -3+y=\frac{2}{5}x \\ -3+y+3=\frac{2}{5}x+3 \\ y=\frac{2}{5}x+3 \end{gathered}[/tex]Hence, the answer is
[tex]y=\frac{2}{5}x+3[/tex]where
slope=2/5
y-intercept=3
I hope this helps you
A health club charges a one time initiation fee of $120.00 plus a membership fee of $30.00 per month. a. Write an expression for the cost function C(x) that gives the total for membership at the health club for x months. b. Draw a graph of the function in (a).c. The health club decided to give it's member an option of a higher initiation fee but a lower monthly membership charge. If the initiation fee is $420 and the monthly membership fee is $10, use a different color and draw on the same set of axes the cost graph under the plan. d. Determine after how many months the second plan is less expensive for the member. a. C(x) = _______ (Do not factor)
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a.
Given that a health club charges a one-time initiation fee of $120.00 plus a membership fee of $30.00 per month.
The total cost will be equal to the fixed one-time charge plus the charge per month times the number of months.
It can be represented by the expression C(x);
[tex]C(x)=120+30x[/tex]b.
Graphing of the function, we would have;
c.
If the health club decided to give its members an option of a higher initiation fee but a lower monthly membership charge. If the initiation fee is $420 and the monthly membership fee is $10, we will have the function as;
[tex]F(x)=420+10x[/tex]graphing the above function, we have;
the first plan is represented by the blue line while the second plan is represented by the red line.
d.
The number of months after which the second plan is less expensive is the value of x when the two lines meet.
the two lines meet at point;
[tex](15,570)[/tex]The value of the x coordinate is 15.
So, The number of months after which the second plan is less expensive is
[tex]15\text{ months}[/tex]. . Read the problem and write your answer for each part. Make sure to label each part: , , .jasmine is tracking the growth of a specific bacteria bacteria for a science experiment. She assumes that there are bacteria () in a Perti dish at 12:00 midnight. Jamie observes that the number of bacteria increases by 25 every hour . write an equation that describes the relationship between total number of bacteria () and time () in hours, assuming there are () bacteria in the perti dish at = 0. . if Jamie starts with bacteria in the perti dish, how many bacteria will be present after 6 hours? . if Jamie starts with bacteria in the perti dish, draw a graph that displays the total number of bacteria with respect to time from 12:00 midnight ( = ) to 8:00 am. ( = ). Label each axis and label points on your graph at times = , , , .use the coordinate plane below to draw your graph.
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Part A:
Let:
T(h)= Total Number of bacterias as a function of time
h = Number of hours
B = Initial number of bacterias
Since the number of bacteria increases by 25 every hour, we can defined the equation as:
[tex]T(h)=25h+B[/tex]Part B:
B = 5
h = 6
Evaluate the previous equation for those values:
[tex]\begin{gathered} T(6)=25(6)+5 \\ T(6)=150+5 \\ T(6)=155 \end{gathered}[/tex]there will be 155 baterias after 6 hours
Part C
Let's graph the equation:
[tex]T(h)=25h+5[/tex]How many values does the expression 6+ (7 + 3)² have? Write down the values.
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Answer:
3
Step-by-step explanation:
6
7
3
The values are the number that compose the expression
The confidence interval on estimating the heights of the students is given as (5.5, 6.5). Find the sample proportion of the confidence interval.
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Answer:
Step-by-step explanation:
the vertex of the parabola below is at the point (3,2) and point (4,6) is on the parabola
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By using the vertex and the given point, we conclude that the quadratic equation is:
y = 4*(x - 3)^2 + 2
How to find the equation of the parabola?A quadratic equation with a vertex (h, k) and a leading coefficient A can be written as:
y = A*(x - h)^2 + k
In this case, we know that the vertex is (3, 2), replacing that in the general equation we get:
y = A*(x - 3)^2 + 2
We also know that the curve passes through (4, 6), so when x = 4, the value of y must be 6, replacing that in the quadratic equation we can find the value of A.
6 = A*(4 - 3)^2 + 2
6 = A*(1)^2 + 2
6 - 2 = A*1
4 = A
So we conclude that the quadratic equation is:
y = 4*(x - 3)^2 + 2
Learn more about quadratic equations:
https://brainly.com/question/1214333
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Subtract the following polynomials 1) (2x + 43) - (-3x-9)2) (f+9) - (12f 79)3) (75 X²)+ 23 + 13) - (15 X² - X + 40)
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for 1.
2x+43+3x+9=5x+52
2.
f+9-12f+9=f-12f+9-9=-11f
3.
75x^2 +23x+13-15x^2+x-40=
=60x^2+24x-27
for 2)
23d^3+(7g^9)^13
remember that power to the power means that you need to multipy the exponents
=23d^3+7^13g^117
34x(2x-11)=68x^2-374x
2m(m+3n)=2 m^2+6mn
we have lenght
l=2x+5
w=x+7
area, A= lxw
A= (2x+5)(x+7)
this is the polynomial for the area
if we have x=12
l= (2*12)+5=24+5=29
w=12+7=19
A=29*19=551 ft^2
So I joined a ged class and this is apparently a “high school level” math problem, maybe for people in advanced classes but not regular. Anyway, I need help with solving this. Also the greater than sign with the problem that I’m doing has like an underline under it, which I think means greater than or equal to 3x + 9 > - x + 19
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Given the inequality:
[tex]3x+9\ge-x+19[/tex]Solve for x:
[tex]\begin{gathered} 3x+x\ge19-9 \\ 4x\ge10 \\ x\ge\frac{10}{4} \\ \\ x\ge\frac{5}{2} \end{gathered}[/tex]so, the answer will be:
[tex]\begin{gathered} x\ge\frac{5}{2} \\ x\in\lbrack\frac{2}{5},\infty) \end{gathered}[/tex]The first quartile of a data set is 32, and the third quartile is 52. Which of
these values in the data set is an outlier?
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Answer: As we know that the formula of outlier is
IQR = Q3 - Q1
= 52 - 32
= 20
52 + 1.5(20) = 82...
so anything above 82 is an outlier
now
32 - 1.5(20) = 2.
..anything below 2 is an outlier
so...the 83 is outlier
so correct option is D
hope it helps
Step-by-step explanation:
Which quadrant has ordered pairs (-x,-y)?
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ANSWER
Quadrant III
STEP-BY-STEP EXPLANATION:
Firstly, we need to draw the cardinal points and label each quadrant on it
Looking at the ordered pair (-x, -y), you will see that the x and y-values both fall on the negative side of the x-ais and y-axis
Hence, it falls on the quadrant III
(x - 5) (4x - 5) = 0 there are two answers
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The solutions are the values of x that makes the expression equal to zero:
x-5 =0
Add 5 to both sides
x=5
4x-5=0
Add five to both sides
4x=5
Divide both sides by 4
x= 5/4
x=1.25
Find the prime factorization of the following number write any repeated factors using exponents
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Notice that 100=10*10, and 10=2*5. 2 and 5 are prime numbers; therefore,
[tex]\begin{gathered} 100=10\cdot10=(2\cdot5)(2\cdot5)=2\cdot2\cdot5\cdot5=2^2\cdot5^2 \\ \Rightarrow100=2^2\cdot5^2 \end{gathered}[/tex]The answer is 100=2^2*5^2
Please it’s due todayAre there any limitations on the inputs of the equation?Does the graph have any symmetry?If so, where? When will the graph point upward? When will it point downward?
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We have the following:
1.
There is no limitation on the input values, the domain is all real numbers.
2.
Yes, it has an axis of symmetry at the point (0,0)
3.
The graph point upward in the interval:
[tex](0,\infty)[/tex]The graph point downward in the interval:
[tex](-\infty,0)[/tex]2×+22=2(x+11)whats the property
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Distributive property
In this property, multiplying the sum of two or more terms in that add up in a bracket by a number outside the bracket will be equal to multiplying each term in the bracket individually and then followed by sum of the product. In this question:
2x + 22 = 2(x + 11 ) in that when you perform product on the right side of the equation, the result is the same i.e 2x + 2*11 = 2x + 22
write an expression such that if you apply the distributive property to your expression it would give the same result presented. 8x + 12
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Solution:
Let's find a expression such that if you apply the distributive property to your expression it would give the same result presented:
• 8x + 12 = 2 (4x + 6)
,• 8x + 12 = 4 (2x + 3)
,• 8x + 12 = 8 (x + 1.5)
Any of these expressions could be the solution to the question.
when graphed on a coordinate plane,Bumby Avenue can be represented by the equation y=-4x-7. primrose can be represented by the equation 8x+2y=17. Are these streets parallel ?
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Answer:
The lines are not parallel because their slopes are opposite reciprocals.
Explanation:
The lines:
[tex]\begin{gathered} y=-4x-7 \\ \text{and} \\ 8x+2y=17 \end{gathered}[/tex]are not parallel because their slopes are not the same
Note:
Two straight lines are said to be parallel when their slopes are the same, and have different y-intercepts.
in a hurry! have to finish the practice test in 30mins, so I can take the real one!(CHECKING AWNSERS, SO ONLY NEED AWNSERS TO I CAN COMPARE)
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The expression can be simplified as,
[tex]\begin{gathered} \frac{3}{x+2}+\frac{2}{x-3}=\frac{3(x-3)+2(x+2)}{(x-3)(x+2)} \\ =\frac{3x-9+2x+4}{(x-3)(x+2)} \\ =\frac{5x-5}{(x-3)(x+2)} \end{gathered}[/tex]Thus, option (D) is the correct option.
3. What is the vertical shift for the absolute value function below?F(x) 9|x + 1|+ 2
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Answer:
The vertical shift is of 2 units up
Step-by-step explanation:
We have a function in the following format:
F(x) = a(x+b) + c
The vertical shift is given by c.
If c > 0, the shift is up.
If c < 0, the shift is down.
In this question:
F(x) = 9|x+1| + 2
So c = 2
The vertical shift is of 2 units up
You have a pizza with a diameter of 6 1/3 in., and a square box that is 6.38 in. Is the box big enough to fit the pizza inside?
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Pizza diameter D is given in mixed form:
[tex]\begin{gathered} D=6\frac{1}{3}\text{ in} \\ in\text{ fraction form:} \\ D=\frac{19}{3}\text{ in} \\ In\text{ decimals, } \\ D=6.33\text{ in} \end{gathered}[/tex]Now, me must compare D with the lenght of the square box.
Since the lenght of the box is L=6.38 in. Hence, the box is big enough to
fit the pizza.
[tex]\begin{gathered} \\ \\ \\ \end{gathered}[/tex]