The grid above shows the graph of the parent function f(x)= |x| and a translated functions graph. Write the equation for the translated graph.
Answers
Using translation concepts, the equation for the translated graph is given by:
g(x) = |x + 2| + 1.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x). Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis, or rotations of a degree measure around the origin.
From the graph, we have that the parent function was:
Shifted left 2 units, hence x -> x + 2.Shifted up 1 unit, hence y -> y + 1.Hence, considering the parent function f(x) = |x|, the equation for the translated graph is given by:
g(x) = |x + 2| + 1.
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Related Questions
What is the measure of 24 in the triangle shown?
32°
117°
22
148
Answers
The sum of three angles of a triangle is 180° . 32° is the angle at 24 when other two angles are 85° and 63°.
What is angle sum property?The sum of three angles of a triangle is 180° .
Given two angles of a triangle are 85° and 63°. We need to find the third angle at 24.
The angle at 24 be x.
By angle sum property,sum of three angles of a triangle is 180°.
The two angles are 85° and 63° and third angle is x.
85°+63°+x=180°
148°+x=180°
x=180°-148°
x=32°
Therefore the angle at 24 is 32° when other two angles are 85° and 63°.
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A diamond is purchased for $ 2500 . Suppose its value increases 5 % each year.
a. What is the value of diamond after 8 years?
Answers
Answer:
$3500
Step-by-step explanation:
x = value of diamond with an increase of 5% every year for 8 years
x= 2500(0.05)
x= 125(8)
x = 1000
2500 + 1000 = $3500
The value of the diamond after 8 years is the amount of $3693.63.
What is Compound interest?Compound interest is defined as interest paid on the original principal and the interest earned on the interest of the principal.
To find the value of the diamond after 8 years, we need to calculate the compound interest.
The formula for compound interest is:
A = P(1+r/100)ⁿ
here:
A = final amount
P = principal amount
r = annual interest rate (as a decimal)
t = time in years
Using this formula, we can calculate the value of the diamond after 8 years:
P = 2500
r = 5% = 0.05
t = 8
A = 2500 (1 + 0.05/1)¹ˣ⁸
A = 2500 (1.05)⁸
A = 2500 (1.4775)
A = $3693.63
Therefore, the value of the diamond after 8 years is $3693.63.
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The Americans with Disabilities Act requires that wheelchair ramps have at least a 12 -inch run for each rise of 1 inch.
b. The maximum length that the law allows for a ramp is 30 feet. How many inches tall is the highest point of this ramp?
Answers
The highest point of this ramp will be at 30 inches.
It is given that Wheelchair ramps have at least a 12 -inch run for each rise of 1 inch and Max length for a ramp is 30 feet.
We have to find the highest point of ramp in inches.
What will be the value of 10 feet in inches ?
As we know that 1 feet = 12 inches , the value of 10 feet in inches will be ; 10 × 12 inches or 120 inches.
As per the question ;
Wheelchair ramps have at least a 12 inch run for each rise of 1 inch.
Max length for a ramp = 30 feet
or
Max length for a ramp = 30 × 12 inches
or
Max length for a ramp = 360 inches
The highest point of this ramp will be at ;
= 360 ÷ 12
= 30 inches
Thus , the highest point of this ramp will be at 30 inches.
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Is the relation a function… yes or no?
Answers
Answer: Functions are relations with one output for any unique input.
Step-by-step explanation:
A cell phone tower covers a circular area with a radius of 15 miles.
(a) If the tower is located at the origin, write an equation for this circular area of coverage.
Answers
If the tower is located at the origin, the equation of its circular area of coverage is [tex]x^{2} +y^{2} = 225[/tex]
A circle is a closed curve that is drawn from a fixed point. This point is called the center. All points on the curve are equidistant from this center point.
The equation of a circle with center at (h, k) and radius r is given by:
[tex](x - h)^{2} + (y-k)^{2} = r^{2}[/tex]
According to the given condition,
center is origin i.e., (h, k) is (0,0)
and r = 15.
Substituting these values in the equation above,
[tex](x - 0)^{2} + (y-0)^{2} = 15^{2}[/tex]
[tex]x^{2} + y^{2} = 225[/tex]
Thus, the equation of the tower located at origin and having coverage area of radius 15 miles is [tex]x^{2} + y^{2} = 225[/tex].
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8) Sam's test score is between 100 and 107. His friend Tammy scored about 15 less points.
Part A
Write a compound inequality that describes Tammy's test score x.
Part B
How much did Tammy score?
Answers
The compound inequality that describes Tammy's test score x 85 < x < 92 and Tammy's test score is between 85 and 92
Part A: Write a compound inequality that describes Tammy's test score x.The given parameters are
Sam's test score is between 100 and 107
This means that
100 < Sam's score < 107
From the question, we have:
Tammy scored about 15 fewer points.
This means that
Tammy = Sam - 15
So, we have
Sam = Tammy + 15
Where
Tammy = x
This gives
Sam = x + 15
So, we have
100 < x + 15 < 107
Subtract 15 from the sides of the inequality
So, we have
85 < x < 92
This means that the compound inequality that describes Tammy's test score x 85 < x < 92
Part B: How much did Tammy score?In part (a) of this solution, we have the following compound inequality
85 < x < 92
The above compound inequality means that Tammy's test score is between 85 and 92
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1/5 (15b - 7) = 3b – 9
Answers
Answer: -7/5=-9
Step-by-step explanation:
I hope it helps
Answer: - 7/5 = -9
Step-by-step explanation: Combine like terms into single fraction, multiple by 1, subtract 3, simply.
Read the question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.
Suppose one base angle of an isosceles triangle has a measure of 44°. What is the measure of the vertex angle?
a. 108°
b. 92°
c. 56°
d. 44°
Answers
The measure of the vertex angle is 92°
Here,
The triangle is isosceles and one base angle of an isosceles triangle has a measure of 44°
We have to find the measure of the vertex angle.
What is Isosceles triangle?
A triangle is said to be isosceles if there is any two corresponding sides are equal and there angle are equal.
Now,
The triangle is isosceles triangle.
Hence, there corresponding sides and there angles are equal.
So, Both base angles of a triangle are equal.
And, Sum of angles of a triangle are 180°
Let the measure of the vertex angle is x°
Hence,
⇒ 44° + 44° + x° = 180°
⇒ x° = 180° - 88°
⇒ x° = 92°
Therefore, The measure of the vertex angle is 92°
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What is the slope of the line that passes through the given points?
d. Use the slope formula to show in part (a) that it does not matter which point you choose for (x₁, y₁) .
Answers
Lets consider an example to to show that it does not matter which point you choose for (x₁, y₁) .
Let the points be -
(2,1) and (4,7)
where x1 and x2 are 2, 4
y1 and y2 are 1,7.
So the formula for slope will be -
m = y2 - y1 / x2 - x1
⇒ 7 - 1 / 4 - 2
⇒ 6 / 2
⇒ 3 .......(1)
So, the slope of the equation is 3 for x1, x2 = 2, 4 and y1, y2 = 1,7
Now, let us consider,
x2 = 2 and x1 = 4 , y1 = 7 and y2 = 1
m = 1 - 7 / 2 - 4
m = -6 / -2
m = 3 ...........(2)
From (1) and (2), we can infer that it does not matter which point you choose for (x₁, y₁).
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Write an equation of the line through each pair of points in slope-intercept form.
(-12,-6) and (8,9)
Answers
The equation of line is:
y = (5/2) x - 11
Given,
Points (x₁, y₁) = (-12, -6) and (x₂, y₂) = (8, 9)
We can find the slope using the equation for slope
m = (y₂ - y₁) / (x₂ - x₁)
= (9 -(-6)) / (8-(-12))
= (9+6) / (8 + 12)
= 15/20 = 3/4
We know the slope and a point, so we can use point slope form to make an equation
y-y₁ = m(x-x₁)
y - (-6) = 3/4 (x-(-12))
Distribute
y+6 = 3/4x – 3/4 × 2
y+6 = 3/4x - 3/2
Add -6 to each side
y + 6 -6 = 3/4x - (3/2)-6
y = 3/4x - (-9/2)
y = 3/4x + 9/2
This is in slope intercept form (y= mx+b)
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Find the sum of each series. Σ¹° n=4 (0.8 n-0.4)
Answers
The given series is an arithmetic series and its sum is 36.4
The summation or sigma notation is used to express long summation into a single formula.
The series, given in a summation notation, is:
[tex]\sum\limits^{10}_{n=4} {(0.8n-0.4)}[/tex]
The formula inside the sum notation represent the nth term, a(n).
Let evaluate the terms for some n, starts from n = 4 as indicated by the lower limit of the summation notation:
a(4) = 0.8 (4) - 0.4 = 2.8
a(5) = 0.8 (5) - 0.4 = 3.6
a(6) = 0.8 (6) - 0.4 = 4.4
This form a new arithmetic series, with the first term, let say f(1) =2.8 and common difference, d = 0.8.
The number of terms in this new geometric series is given by the upper and lower limit of the summation notation:
number of terms = 10 - 4 + 1 = 7
Use the sum formula for an arithmetic series,
S(n) = n/2 [2.f(1) + (n - 1) . d]
Substitute n = 7, f(1) = 2.8, and d = 0.8 into the formula:
S(7) = 7/2 [2. (2.8) + (7 - 1) . (0.8)]
S(7) = 36.4
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If x varies partly as y and partly as the square of y when y =2,x=5 bad when y=5,x=57.5 find x when y =4
Answers
The value of x when y = 4 is 0. 25
How to determine the valueFrom the information given, we have that;
x varies directly as yx also varies partly as y²This is expressed as;
x ∝ 1/ y²
x = y/y²
Let's substitute the value of y as 4 into the equation;
x = 4 / 4²
Find the square
x = 4 / 16
Find the ratio
x = 1/ 4
x = 0. 25
Thus, the value of x when y = 4 is 0. 25
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I need help with this question please, my exam is tomorrow.
Answers
Answer:
Center: (2,2)
Radius: 2
Answers:
Center = (2,2)
Radius = 2
=================================================
Explanation:
Consider (A+B)^2 = A^2+2AB+B^2 after using the FOIL rule.
If A = x, then we have (x+B)^2 = x^2+2Bx+B^2
The coefficient of the x term is 2B. It divides in half to get B, and it squares to B^2 as the final term.
In short, if we want to complete the square on something like x^2-4x, then we do two things:
Divide the x coefficient in halfSquare the resultSo we go from -4 to -2 after dividing in half, and then from -2 to 4 after squaring. We'll add 4 to both sides to complete the square for the x terms.
[tex]x^2+y^2-4x-4y+4 = 0\\\\(x^2-4x)+(y^2-4y)+4 = 0\\\\(x^2-4x+4)+(y^2-4y)+4 = 4\\\\(x-2)^2+(y^2-4y)+4 = 4\\\\[/tex]
We'll do the same thing for the y terms. Though notice we already have a +4 on the left side. So we can have it absorb into the y terms parenthesis grouping like so
[tex](x-2)^2+(y^2-4y)+4 = 4\\\\(x-2)^2+(y^2-4y+4) = 4\\\\(x-2)^2+(y-2)^2 = 4\\\\[/tex]
Now compare that to the circle template
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
We see that
h = 2k = 2r = 2This circle has its center at (h,k) = (2,2)
The radius is r = 2
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i don't understand this please help :)
Two angles are supplementary is the measure of one angle is 54.3 degrees what is the measure of the other angle? Answer to the first decimal place, ie 79.5.
Answers
Answer =125.7
Answer: 125.7 degrees
Step-by-step explanation:
supplementary angles add up to 180 degrees.
angle 1 + angle 2 = 180
54.3+angle 2=180.0
54.3-54.3+angle 2=180.0-54.3
angle 2=180.0-54.3
angle 2=125.7 degrees
Express 48 as sum of two odd prime
Answers
Answer:
19 , 29
Step-by-step explanation:
19 + 29 = 48
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Find the coordinates of the midpoint of a segment with the given endpoints. A(13,14), C(3,5)
Answers
The coordinates of the midpoint of a segment with the given endpoints will be (8, 9.5).
What is the mid-point of the line segment?Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).
Then the coordinate of the mid-point of the line segment is given as,
(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]
The endpoints are A(13, 14) and C(3, 5).
Then the coordinates of the midpoint of a segment with the given endpoints will be
(x, y) = [(13 + 3) / 2, (14 + 5) / 2]
(x, y) = (16/2, 19/2)
(x, y) = (8, 9.5)
The coordinates of the midpoint of a segment with the given endpoints will be (8, 9.5).
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A triangle has side lengths of (8w + 8x) (8w+8x) centimeters, (3w + 10y) (3w+10y) centimeters, and (4y + 8x) (4y+8x) centimeters. which expression represents the perimeter, in centimeters, of the triangle?
Answers
The expression that represents the perimeter of the triangle in centimeters is; 73[tex]w^{2}[/tex] + 128wx + 128[tex]x^{2}[/tex] + 60wy + 116[tex]y^{2}[/tex] + 64xy
We are given the measurement of each side length of the triangle, i.e.
(8w +8x) (8w+8x)
(3w + 10y) (3w+10y)
(4y + 8x) (4y+8x)
After simplifying the measurement on each side, we get;
(8w +8x) (8w+8x)= 64[tex]w^{2}[/tex] + 128wx + 64[tex]x^{2}[/tex]
(3w + 10y) (3w+10y)= 9[tex]w^{2}[/tex] +60wy +100[tex]y^{2}[/tex]
(4y + 8x) (4y+8x)= 16[tex]y^{2}[/tex] + 64xy + 64[tex]x^{2}[/tex]
To find the perimeter of the triangle, we get the addition of all side lengths
Thus, Perimeter (P) = 64[tex]w^{2}[/tex] + 128wx + 64[tex]x^{2}[/tex] + 9[tex]w^{2}[/tex] +60wy +100[tex]y^{2}[/tex] + 16[tex]y^{2}[/tex] + 64xy + 64[tex]x^{2}[/tex]
P= 73[tex]w^{2}[/tex] + 128wx + 128[tex]x^{2}[/tex] + 60wy + 116[tex]y^{2}[/tex] + 64xy
Therefore, the perimeter of the triangle is given by; 73[tex]w^{2}[/tex] + 128wx + 128[tex]x^{2}[/tex] + 60wy + 116[tex]y^{2}[/tex] + 64xy
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Evaluate -8 × |2|.
-16
-10
16
10
Answers
Answer:
[tex] - 8 \times |2 = - 16| [/tex]
What is the positive solution to this equation?
3x²+2x = 16
Enter your answer in the box.
X =
Answers
Answer: 2
Step-by-step explanation: There are two solutions: 2, and -8/3. 2 is the positive solution.
-12x - 17 = -89
i neeeed help
Answers
Answer:
x = 6
Step-by-step explanation:
- 12x - 17 = - 89 ( add 17 to both sides )
- 12x = - 72 ( divide both sides by - 12 )
x = [tex]\frac{-72}{-12}[/tex] = 6
Find the geometric mean between pair of numbers.
7 and 11
Answers
The geometric mean between pair of numbers 7 and 11 is 8.77
We know that for a sequence of numbers x1, x2,.., xn
The formula of geometric mean is,
[tex]\Pi=\sqrt[n]{x_1.x_2.x_3...x_n}[/tex]
In this question, we have been given two numbers 7 and 11
We need to find the geometric mean between pair of numbers, 7 and 11.
Using the formula for the geometric mean,
[tex]\Pi=\sqrt[n]{x_1.x_2.x_3...x_n}[/tex]
In this question, we have two numbers.
So, the value of n is 2.
[tex]\Pi=\sqrt{7\times 11}\\\\ \Pi=\sqrt{77}\\\\ \Pi=8.77[/tex]
Therefore, the geometric mean between pair of numbers 7 and 11 is 8.77
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Sammie was looking for a dress to wear to the wedding. She found one that she liked for 20% off. To go along with it, she also purchased a necklace for $7.50. Which expression represents the amount Sammie spent?
Answers
The expression that represents the amount spent is 0.8x + 7.50
Which expression represents the amount Sammie spent?The given parameters are
Discount = 20%
Necklace = 7.50
Let the cost of the dress be x
So, the expression that represents the amount Sammie spent is
Expression = (1 - Discount) * x + Necklace
This gives
(1 - 20%) * x + 7.50
Evaluate
0.8x + 7.50
Hence, the expression that represents the amount spent is 0.8x + 7.50
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Which equation has the variable, or missing number, in the correct place to match the given situation?
The Lerch family drove a total of 482 miles, starting on Friday and ending on Sunday. They drove 138 miles on Friday and 225 miles on Saturday. How many miles did they drive on Sunday?
Answers
From the total amount of miles driven, it is found the equation that matches the given situation is:
138 + 225 + x = 482.
Solving the equation, it is found that they drove 119 miles on Sunday.
How to find the total amount of miles driven?The total amount of miles driven is given by the addition of the number of miles driven on Friday, Saturday and Sunday.
The separate amounts are given as follows:
Friday: 138 miles.Saturday: 225 miles.Sunday: x miles.Total: 482 miles.Hence the equation that matches the given situation is:
138 + 225 + x = 482.
Solving the equation, we have that:
x = 482 - (138 + 225)
119.
They drove 119 miles on Sunday.
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Write the equation of the line that passes through (5, −2) and is perpendicular to y equals 5 thirds times x minus 3 period
Answers
Answer:
5y =x-15
Step-by-step explanation:
yes
The equation of the line is y = -3x/5 + 1 that passes through (5, −2), and is perpendicular to y = (5/3)x - 3.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given that:
The line passes through (5, −2) and is perpendicular to y = (5/3)x - 3
The slope of the line y = (5/3)x - 3
m = 5/3
The slope of the line perpendicular to the above line:
M = -3/5
The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
The equation of the line
y + 2 = (-3/5)[x - 5]
y = -3x/5 + 1
Thus, the equation of the line is y = -3x/5 + 1 that passes through (5, −2), and is perpendicular to y = (5/3)x - 3.
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Solve the inequality.
x+13<41
Answers
For the given inequality x+13<41, x is less than 28
Inequality involves two algebraic expressions linked by the signs of inequality. These signs include less than (<), greater than (>) or less than equal to (<=) and greater than equal to (>=).
Let's solve the inequality
x+13<41
Move the like terms on the same side
x< 41-13
x< 28
Therefore, x is less than 28
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URGENT HELP PLEASE!!! In the figure below, FG=6 and GH=8. Find FH.
Answers
Answer:
14
Step-by-step explanation:
Adding FG and GH is the answer to the wholr line. Im 90% sure thats the right answer thats whst i learnt 7 days ago.
Ten students sit a test consisting of 20 questions. Two students get 8 questions correct and one student gets 9 questions correct. The remaining seven students all get at least 10 questions correct and the average number of questions answered correctly by these seven students is an integer. If the average number of questions answered correctly by all ten students is also an integer, then that integer is
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Answers
Answer:
14
Step-by-step explanation:
That equation, with the given constraints, is easily solved using logical reasoning.10y is a multiple of 5, and 25 is a multiple of 5; that means 7x is a multiple of 5.And we know x is a number between 10 and 20. So x has to be 14
Find the simple interest paid on a 8 year loan
of $2764 at 12.25% interest
Answers
Answer: 1,585.12 is your interest. full is 4349.12
Step-by-step explanation: brainlist pls
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Answers
y = -1/2x - 8
To identify the equation of the line, we can start with the B, or the y-intercept. The y-intercept is the value that begins the line on the y-axis. For this case, that’s -8. The slope is the format of rise/run in which a point goes from one place to another. If for any reason one has to go down or to the left to find the slope, the slope is negative. It helps to count from one point to another starting at the y-intercept, so let’s do so:
The y-intercept is (0,-8). Upon beginning there, we can count down 1 point and to the right 2 to get to the point of (2,-9).
The equation of the line is:
y = -1/2x - 8
Answer: y=-0.5x-8
Step-by-step explanation:
Choose two points on the line: (0,-8) and (-6,-5)
Hence,
x₁=0 x₂=-6 y₁=-8 y₂=-5
[tex]\displaystyle\\The\ slope=\frac{y_2-y_1}{x_2-x_1}\\\\The\ slope=\frac{-5-(-8)}{-6-0} \\\\The\ slope=\frac{-5+8}{-6} \\\\The\ slope=\frac{3}{(3)(-2)}\\\\The\ slope=\frac{1}{-2} \\\\The\ slope=-\frac{1}{2}\\\\The\ slope=-0.5[/tex]
[tex]y=kx+b\\k=the\ slope=-0.5\\(0,-8) \ hence,\\-8=-0,5*0+b\\-8=0+b\\-8=b\\Thus,\\y=-0.5x-8[/tex]
what is cube root of 16 as a power of 2?
Answers
Answer: The prime factorization of 16 is 2 × 2 × 2 × 2, hence, the cube root of 16 in its lowest radical form is expressed as 2 ∛2.
Cube Root of 16.
Step-by-step explanation:
The solution for the cube root of 16 as a power of 2 is,
⇒ ∛16 = 2 ∛2
We have to given that,
To find the cube root of 16 as a power of 2.
The prime factorization of 16 are,
16 = 2 x 2 x 2 x 2
Take cube root,
⇒ ∛16 = ∛2 x 2 x 2 x 2
⇒ ∛16 = 2 ∛2
Therefore, The solution for the cube root of 16 as a power of 2 is,
⇒ ∛16 = 2 ∛2
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