Answer:
A. A translation right 2 units:
We know that given f(x), the function g(x) = f(x+m), is the same function f(x) but shifted m units to the left. In that sense, a translation right 2 units would be:
g(x) = f(x-2).
B. A translation left 2 units:
We know that given f(x), the function g(x) = f(x+m), is the same function f(x) but shifted m units to the left. In that sense, a translation left 2 units would be:
g(x) = f(x+2).
C. A translation up 2 units:
We know that given f(x), the function g(x) = f(x) + m, is the same function f(x) but shifted m units up. In that sense, a translation up 2 units would be:
g(x) = f(x) + 2
D. A translation down 2 units:
We know that given f(x), the function g(x) = f(x) + m, is the same function f(x) but shifted m units up. In that sense, a translation down 2 units would be:
g(x) = f(x) - 2
Final answer:
The function f(x) translated to g(x) via a translation right 2 units, which shifts the graph of the function 2 units to the right on the x-axis.
Explanation:
The transformation that transformed the parent function, f(x), to g(x) is a translation right 2 units. This is because when the argument of the function f(x) becomes f(x-2), the graph of f(x) is shifted to the right by 2 units along the x-axis. To understand this, let us consider the original function y = f(x).
The graph of the new function y = f(x-2) is the same as the original, but every point on the graph has been moved 2 units to the right. This can also be viewed as if the x-axis (and origin) has shifted 2 units to the left while the graph remains stationary.
For which intervals is the function positive?
Select each correct answer
(−1.5,−1)
(4,∞)
(−2, 0)
(2,2.5)
(−∞,−2)
(0,4)
Answer: -2,0 0,4
Step-by-step explanation:
let me know if you need help still UwU
Answer:
The function is positive from (-∞,-2) and (0,4).
Explanation:
To find the intervals where the function is positive, note where the line of the graph is above the x-axis.
As the functions goes toward negative infinity, the arrow of the graph is pointed up, so the function is positive starting from -∞ until x = -2, where it becomes negative.
The function once again goes above the x-axis at x = 0 and stays positive until x = 4. After this point, the function decreases forever, so (-∞,-2) and (0,4) are the only intervals where the function is positive.
Help needed! Due by 6/22/19
[tex]y=\dfrac{k}{x}[/tex]
1.
[tex]12=\dfrac{k}{13}\\\\k=156[/tex]
2.
[tex]y=\dfrac{156}{x}[/tex]
3.
[tex]y=\dfrac{156}{44}=\dfrac{39}{11}[/tex]
Area of a square with half diagonal 12
Answer:
288 square units
Step-by-step explanation:
The formula for the area of a square when you know its diagonal is: [tex]\frac{1}{2} d^2[/tex]
So, since we know the half diagonal is 12, we need to multiply that by 2 to get the diagonal, which is 24.
Put 24 into the formula. [tex]\frac{1}{2} * 24^2[/tex]
Simplify the exponent. [tex]\frac{1}{2} * 576[/tex]
Finally, multiply. [tex]288[/tex]
Maggie has a container in the shape of a right prism. The formula for its surface area is SA = Ph + 2B. Solve for h.
A.h = SA minus two times B over P
B.h = SA plus two times B over P
C.h = SA plus P over two times B
D.h = SA minus P over two times B
Answer:
A. [tex]h=\frac{SA-2B}{P}[/tex]
Step-by-step explanation:
We have been given a formula for the surface area of a container in shape of right prism. We are asked to solve for h for our given formula.
[tex]SA=Ph+2B[/tex]
First of all, we will switch sides for our given equation as:
[tex]Ph+2B=SA[/tex]
Now, we will subtract 2B from both sides of our equation.
[tex]Ph+2B-2B=SA-2B[/tex]
[tex]Ph=SA-2B[/tex]
Now, we will divide both sides of our equation by P.
[tex]\frac{Ph}{P}=\frac{SA-2B}{P}[/tex]
[tex]h=\frac{SA-2B}{P}[/tex]
Therefore, option A is the correct choice.
Answer:
A
Step-by-step explanation:We have been given a formula for the surface area of a container in shape of right prism. We are asked to solve for h for our given formula
First of all, we will switch sides for our given equation as:
Now, we will subtract 2B from both sides of our equation.
Now, we will divide both sides of our equation by P.
therefore its option A
What is the length of the unknown leg in the right triangle ?
Answer: [tex]\sqrt{32}\text{ mi}[/tex]
Step-by-step explanation:
The Pythagoras theorem of right triangle says that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
From the given figure , the hypotenuse of the right triangle = [tex]\sqrt{113}\text{ mi}[/tex]
Then According to Pythagoras theorem , we have
[tex](\sqrt{113})^2=x^2+(9)^2\\\\\Rightarrow\ x^2=113-81\\\\\Rightarrow\ x^2=32\\\\\Rightarrow\ x=\sqrt{32}\text{ mi}[/tex]
write the equation of the line that passes through the points (7,-4) and (-1,3), first in point slope form
The given line that passes through the points (7,-4) and (-1,3).
The slope is
[tex]m = \frac{3 - - 4}{ - 1 - 7} = - \frac{7}{8} [/tex]
The point-slope form is obtained using:
[tex]y-y_1= m (x-x_1) [/tex]
When (7,-4) is used the point-slope form is
[tex]y + 4= - \frac{7}{8} (x - 7) [/tex]
We expand now to get;
[tex]y = - \frac{7}{8}x + \frac{49}{8} - 4[/tex]
This implies that,
[tex]y = - \frac{7}{8}x + \frac{17}{8}[/tex]
Let f(x)=x2+4x+12 . What is the vertex form of f(x)? What is the minimum value of f(x)?
[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+4}x\stackrel{\stackrel{c}{\downarrow }}{+12} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{4}{2(1)}~~,~~12-\cfrac{4^2}{4(1)} \right)\implies (-2~~,~~12-4)\implies (-2~,~8)[/tex]
well, the quadratic has a leading term with a positive coefficient, meaning is a parabola opening upwards, like a "bowl", comes from above down down down, reaches a U-turn, namely the vertex, and goes back up up up.
so the minimum value is at the vertex of course, and the minumum is well, just the y-coordinate of the vertex, 8.
If 4x = 12, then 12x= what
For f(x) = 2x+1 and g(x)=x^2-7, find (f*g)(x).
Answer:
[tex](f*g) (x) =2x^3-13x^2-7 [/tex]
Step-by-step explanation:
We have the following functions
[tex]f (x) = 2x+1[/tex]
[tex]g (x) = x^2-7[/tex]
To find [tex](f*g)(x)[/tex] we must multiply the function f (x) with the function g (x)
Then we perform the following operation
[tex](f*g) (x) =(2x+1)(x^2-7)[/tex]
Apply the distributive property
[tex](f*g) (x) =2x^3-14x^2+x^2-7 [/tex]
[tex](f*g) (x) =2x^3-13x^2-7 [/tex]
Finally we have that:
[tex](f*g) (x) =2x^3-13x^2-7 [/tex]
To the nearest hundredth of a centimeter, what is the length of the hypotenuse?
[1] cm
92.58 cm
Answer:
106.90 cm
Step-by-step explanation:
Given
Angle=30 degrees
Base=92.58 cm
So,
We will have to use the triangular ratios to find the hypotenuse.
The triangular ratio that will be used for this will be cosine because we know the value of angle and base since it involves both cosine will be used.
cosθ=Base/Hypotense
cos30=92.58/Hypotenuse
0.8660=92.58/Hypotenuse
Hypotenuse=92.58/0.8660
=106.90 cm ..
Answer:
Hypotenuse = 107.02
Step-by-step explanation:
Points to remember
If angles of a triangle are 30°, 60° and 90° then the sides are in the ratio
1 : √3 : 2
It is given a right angled triangle with angles 30°, 60°, 90°
and height = 95.58 cm
To find the hypotenuse
From the figure we can write,
Base : Height : Hypotenuse = 1 : √3 : 2 = Base : 92.58 : Hypotenuse
Therefore Hypotenuse = (92.58 * 2)/√3
= 107.02 cm
Which function passes through the points (2, 15) and (3, 26)?
A.
y = 11x + 7
B.
y = 11x − 7
C.
y = 7x + 11
D.
y = -11x − 7
E.
y = 7x − 11
Answer:
B
Step-by-step explanation:
We can solve this by finding the slope of the function that passes through the points (2,15) and (3,26). We can use the "formula" rise over run.
So we have:
(26-15)/(3-2) which gives us 11 as our slope. Now we must find the y intercept!
It is -7.
So the answer is B
Answer:
the equation is y = 11x - 7
B is correct option.
Step-by-step explanation:
The function passes through the points (2, 15) and (3, 26)
Slope can be calculated by the formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
using this formula, the slope is given by
[tex]m=\frac{26-15}{3-2}\\\\m=\frac{11}{1}\\\\m=11[/tex]
The slope intercept form of line is y = mx+b
here, m = 11
hence, the equation is y = 11x +b
Now, using the point (2,15) to find b
15=11(2)+b
15 = 22 +b
b = -7
Hence, the equation is y = 11x - 7
B is correct option.
What is the other solution?
Answer:
-6
Step-by-step explanation:
m^2 - 36 = 0
Add 36 to each side
m^2 -36+36 = 0+36
m^2 = 36
Take the square root of each side
sqrt( m^2) = ± sqrt(36)
m = ±6
We know one root is 6
The other root is -6
Can someone help me please
Answer:
A and B are the solutions....
Step-by-step explanation:
7 and 12 are smaller than 17.
Answer:
A. [tex]x=7[/tex]
B. [tex]x=12[/tex]
Step-by-step explanation:
Check each option individually.
A. [tex]17>7[/tex] is true, so it is a correct choice.
B. [tex]17>12[/tex] is true, so it is a correct choice.
C. [tex]17>17[/tex] is false, so it is an incorrect choice.
Mrs. Culland is finding the center of a circle whose equation
is x2 + y2 + 6x + 4y - 3 = 0 by completing the square. Her
work is shown.
x2 + y2 + 6x + 4y – 3 = 0
x2 + 6x + y2 + 4y - 3 = 0
(x2 + 6x) + (y2 + 4y) = 3
(x2 + 6x + 9) + (x2 + 4y + 4) = 3 + 9 + 4
Answer:
The center of the circle is (-3,-2)
Step-by-step explanation:
we know that
The equation of a circle in standard form is equal to
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
where
(h,k) is the center
r is the radius
In this problem we have
[tex]x^{2} +y^{2}+6x+4y-3=0[/tex]
Completing the square
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex](x^{2}+6x) +(y^{2}+4y)=3[/tex]
Complete the square twice. Remember to balance the equation by adding the same constants to each side.
[tex](x^{2}+6x+9) +(y^{2}+4y+4)=3+9+4[/tex]
[tex](x^{2}+6x+9) +(y^{2}+4y+4)=16[/tex]
Rewrite as perfect squares
[tex](x+3)^{2} +(y+2)^{2}=16[/tex]
therefore
The center of the circle is (-3,-2)
Answer: ITS D !! ON EDGE
Step-by-step explanation:
How can △WXY be mapped to △MNQ?
First, translate vertex w to vertex M. Next, reflect △WXY across the line containing
1) line segment WX
2) line segment WY
3) line segment XY
4) line segment MQ
Answer:
A: Line Segment WX
Step-by-step explanation:
100% on edge 2020
Answer:
WX is correct
Step-by-step explanation:
Got a 100 in edge quiz.
Solve: 12x^2+5x-4=12^2x+6
okay so we need to solve for x.
--
FIRST STEP: 12x^2+5x-4=12^2x+6 would turn into x2 + 5x - 4 = 2x + 6 so it'd have equal bases.
SECOND STEP: move any number with "x" in it to the left side. it ends up as x2 + 3x - 4 = 6
THEN, we use the AC method to eliminate any unnecessary numbers.
you should end up with ( x - 2) (x + 5) = 0
SO, the answer is your third option. ( x = 2, x = -5)
Answer:
x=-5&x=2
Step-by-step explanation:
Since the bases on both sides of the equation are the same, they will cancel each other leaving the exponents
x²+5x-4 = 2x + 6
Collect like terms
x²+5x-2x-4-6=0
x²+3x-10=0
The highest power is 2 , so factorize
x²+5x-2x-10=0
x(x+5)-2(x+5)=0
(x+5)(x-2)=0
x = -5 or x = 2
Check
When x = -5
-5²+3*-5-10=0
25-15-10 =0
0=0
:.x=-5
When x=2
2²+3*2-10=0
4+6-10=0
0=0
A company uses two vans to transport
workers from a free parking lot to the
workplace between 7:00 and 9:00 a.m.
One van has 14 more seats than the
other. The smaller van makes two trips
every morning while the larger one
makes only one trip. The two vans can
transport 65 people, maximum.How many seats does the larger van have
Answer:
31 seats
Step-by-step explanation:
Let x be the smaller van, and y be the larger one.
We know that y = x + 14
We also know that 2x + y = 65
If we replace y by its value in the second equation we have:
2x + (x + 14) = 65, then we solve
2x + x + 14 = 65
3x + 14 = 65
3x = 51
x = 17
We now know the smaller van has 17 seats.
To find how many seats are in the big one, we take the first equation:
y = x + 14
y = 17 + 14
y = 31
Question 101 points)
Which equation in slope-intercept form represents the line that passes through (5, 1) and
(-4,7)
Answer:
[tex]\large\boxed{y=-\dfrac{2}{3}x+\dfrac{13}{3}}[/tex]
Step-by-step explanation:
[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\===============================[/tex]
[tex]\text{We have the point:}\\\\(5,\ 1)\ \text{and}\ (-4,\ 7).\ \text{Substitute:}\\\\m=\dfrac{7-1}{-4-5}=\dfrac{6}{-9}=-\dfrac{6:3}{9:3}=-\dfrac{2}{3}\\\\\text{We have the equation in form:}\\\\y=-\dfrac{2}{3}x+b\\\\\text{Put the coordinates of the point (5, 1) to the equation:}\\\\1=-\dfrac{2}{3}(5)+b\\\\1=-\dfrac{10}{3}+b\qquad\text{add}\ \dfrac{10}{3}\ \text{to the both sides}\\\\\dfrac{3}{3}+\dfrac{10}{3}=b\to b=\dfrac{13}{3}\\\\\text{Finally:}\\\\y=-\dfrac{2}{3}x+\dfrac{13}{3}[/tex]
You and your friends decide to camp for one night. Look at the diagram of your tent below. It is drawn on 1 cm squared paper. The scale is 1 cm : 0.25 m
What are the dimensions of the tent’s porch area in metres?
m multiplied by
m
The dimension of a sleeping bag and ground mat is 2 m x 1 m. Each sleeping bag and ground mat must be 0.25 metres away from the edge of the tent.
How many people can sleep in the tent?
people
Answer:
1.Area of Porch =2.5m²
2.Number of people =3 people
Step-by-step explanation:
The porch area from the diagram has a dimension of 4 units by 10 units
One units =1cm
Thus the porch is drawn with dimensions of 4cm by 10 cm
Taking length is 10 cm and width as 4 cm, convert these dimensions according to the scale.
The scale is 1cm=0.25m
The width will be= 0.25×4=1 m
The length will be=0.25×10= 2.5m
Area of the porch is given by the formula;
length×width because its has a shape of a rectangle
Area of porch will be
=1m ×2.5m =2.5m²
2.
Find the dimensions of the tent
14 units by 10 units
Applying the scale on the dimensions by multiplying by 0.25
14×0.25=3.5m
10×0.25=2.5m
Width=2.5m
length=3.5m
Subtract the edge distance on both the length and width
Length will be=3.5-(0.25×2)=3.0m
Width will be=2.5-(0.25×2)=2.0m
Find the area remaining to be covered by the people while sleeping
=3.0×2.0=6m²
Area covered by sleeping bag and a ground mat
2m×1m=2m²
Number of people that can sleep in the tent
6m²÷2m²=3 people
Answer: Area of porch in metres [tex]= 2.5 m^{2}[/tex]
No. of people that can sleep in the tent = 0 (according to the given conditions)
Step-by-step explanation:
In the given figure we have the scale of 1 cm : 0.25 m which denotes that we have 0.25 m length in actual for every 1 cm on the figure. Also, each square in the figure measures 1 cm on each side.
From the fig. the dimensions of tent porch area are:
Length = 10 cm = [tex]10 \times 0.25[/tex]
[tex]= 2.5 m[/tex] on ground
Breadth= 4 cm = [tex]4 \times 0.25[/tex]
[tex]= 1 m[/tex] on ground
∴ Area of porch in metres = [tex]1\times 2.5[/tex]
Area of porch in metres [tex]= 2.5 m^{2}[/tex]
From the attached image it is visible that we cannot place any mat and sleeping bag of the given dimensions inside the tent satisfying the given condition of keeping the ground mat 0.25 metres away from the edge of the tent.
Based on the graph below, how would you describe the curve?
A. The curve is a 'one-to-one' function
B. The curve is a linear function
c. The curve is not a function
D. The curve is a 'many-to-one" function
D. is the correct answer
Hopes this helps
reduce the fraction: x-y/x^2-1 times x-1/x^2-y^2
Answer:
l
Step-by-step explanation:
Answer: [tex]\frac{1}{(x+1)(x+y)}[/tex]
Step-by-step explanation:
Given the expression:
[tex](\frac{x-y}{x^2-1})(\frac{x-1}{x^2-y^2})[/tex]
The first step is to multiply the numerator of the first fraction by the numerator of the second fraction and the denominator of the first fraction by the denominator of the second fraction. Then:
[tex]=\frac{(x-y)(x-1)}{(x^2-1)(x^2-y^2)}[/tex]
Since [tex](x^2-1)[/tex] and [tex](x^2-y^2)[/tex] are perfect squares, you can factorize them in the form:
[tex]a^2-b^2=(a+b)(a-b)[/tex]
Then:
[tex]=\frac{(x-y)(x-1)}{(x+1)(x-1)(x+y)(x-y)}[/tex]
Simplifying, you get:
[tex]=\frac{1}{(x+1)(x+y)}[/tex]
again can someone help me please
Answer:
4,-2 and 1
Step-by-step explanation:
These are all quantities greater than -5
-5 < 4
-5 < -2
-5 < 1
So C, D and E
What is the answer to this question
Yesterday, a factory used 2/3 of a tub of peanut butter. They use 1/6 of a tub of peanut butter for each batch of peanut butter cookies. How many batches of peanut butter cookies did the factory make yesterday?
The number of batches is 4.
What is the unitary method?When a problem arises if 4 is required for 2 of these things then how many things does 20 require?
We use the unitary method to solve the problem where we find how much is required for one thing and then multiply it by the required.
Solving the given problem.1/6 tub of peanut butter is used for one batch of cookies.
2/3 of it was used for the whole day.
So to find the total number of batches we divide the total tub used by the amount of tub used for one batch of cookies hence = 2/3/(1/6) = 4
Hence the answer to the given problem is 4.
Learn more about the Unitary method here
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-2x-2=14 ....how to you solve this equation... plz include the process
Answer:
x = -8
Step-by-step explanation:
-2x-2=14
We want to solve for x
Add 2 to each side
-2x-2+2 = 14+2
-2x=16
Divide each side by -2
-2x/-2 =16/-2
x = -8
The vertex of the parabola below is at the point (3,2) and the point (4,6) is on the parabola. What is the equation of the parabola?
Answer:
[tex]\large\boxed{y=4(x-3)^2+2\ \bold{vertex\ form}}\\\boxed{y=4x^2-24x+38\ \bold{standard\ form}}[/tex]
Step-by-step explanation:
The vertex form of a parabola:
[tex]y=a(x-h)^2+k[/tex]
(h, k) - vertex
We have the vertex at (3, 2) → h = 3 and k = 2.
Substitute:
[tex]y=a(x-3)^2+2[/tex]
The point (4, 6) is on athe parabola. Put the coordinates of this point to the equation:
[tex]6=a(4-3)^2+2[/tex] subtract 2 from both sides
[tex]6-2=a(1)^2+2-2[/tex]
[tex]4=a\to a=4[/tex]
Finally:
[tex]y=4(x-3)^2+2[/tex] vertex form
use (a - b)² = a² - 2ab + b²
[tex]y=4(x^2-6x+9)+2[/tex] use the distributive property
[tex]y=4x^2-24x+36+2[/tex]
[tex]y=4x^2-24x+38[/tex] standard form
Answer:
y=4(x-3)^2+2
Step-by-step explanation:
Hopefully this helps :)
Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.
A(n) = -6 + (1 - 1)(1)
Answer:
-6
Step-by-step explanation:
A(n)=-6+(1-1)(1)
simplified, this equals:
A(n) = -6+(0)(1)
A(n)=-6+0
A(n) = -6, for any given n term.
Find the arc length of the partial circle
Answer:
7pi/2
Step-by-step explanation:
If was a full, the circumference or the arc length would be 2pi*r where r in this case is 7 so it would be 14pi.
Now this only a quarter of that, so this arc length is actually 14pi/4.
This can be reduced 14pi/4 =7pi/2
Answer:
3.5pi
Step-by-step explanation:
KA
Please explain how this function behaves when it approaches the given x values!
This is a piecewise function because it is defined by more than two functions. Basically, we want to take the limit here. Recall that if a function [tex]f(x)[/tex] approaches some value [tex]L[/tex] as [tex]x[/tex] approaches [tex]a[/tex] from both the right and the left, then the limit of [tex]f(x)[/tex] exists and equals [tex]L[/tex]. Here we won't calculate the limit, but apply some concepts of it. So:
a. [tex]as \ x \rightarrow +\infty, \ k(x) \rightarrow +\infty[/tex]
Move on the x-axis from the left to the right and you realize that as x increases y also increases without bound.
b. [tex]as \ x \rightarrow -\infty, \ k(x) \rightarrow 0[/tex]
Move on the x-axis from the right to the left and you realize that as x decreases to negative values y approaches zero.
c. [tex]as \ x \rightarrow 2, \ k(x) \rightarrow 0[/tex]
Since the function is continuous here, we can say that [tex]k(2)=0[/tex]
d. [tex]as \ x \rightarrow -2, \ k(x) \rightarrow 0[/tex]
The function is discontinuous here, but [tex]k(-2)[/tex] exists and equals 0 as the black hole indicates at [tex]x=-2[/tex].
e. [tex]as \ x \rightarrow -4, \ k(x) \rightarrow 2[/tex]
The function is also discontinuous here, but the black hole indicates that this exists at [tex]x=-4[/tex], so [tex]k(-4)=2[/tex]
f. [tex]as \ x \rightarrow 0, \ k(x) \rightarrow 4[/tex]
Since the function is continuous here, we can say that [tex]k(0)=4[/tex]
find the quotient 16 2/3 ÷ 5 5/7
Answer:
2 11/12
Step-by-step explanation:
(50/3)/(40/7)
=50/3*7/40
=5/3*7/4
=35/12
=2 11/12
let's convert firstly, the mixed fractions to improper fractions and then divide.
[tex]\bf \stackrel{mixed}{16\frac{2}{3}}\implies \cfrac{16\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{50}{3}}~\hfill \stackrel{mixed}{5\frac{5}{7}}\implies \cfrac{5\cdot 7+5}{7}\implies \stackrel{improper}{\cfrac{40}{7}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{50}{3}\div\cfrac{40}{7}\implies \cfrac{\stackrel{5}{\begin{matrix} 50 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}}{3}\cdot \cfrac{7}{\underset{4}{\begin{matrix} 40 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}}\implies \cfrac{35}{12}\implies 2\frac{11}{12}[/tex]