the parent function of a quadratic equation is vertically stretched by a factor of 2, then translated 5 units to the right and 1 unit down. write the equation of the new function in vertex form
Answers
A vertical stretch appears as a multiplier for the function value. Translation right appears as a value subtracted from the independent variable. Translation up appears as a value added to the function value.
For function f(x), stretching by a factor of 2, then translation 5 right and -1 up will give the function
... g(x) = 2f(x-5) -1
When f(x) = x², this becomes ...
... g(x) = 2(x -5)² -1
... g(x) = 2x² -20x +49
The equation of the new function in vertex form after the parent function of a quadratic equation is vertically stretched by 2, translated 5 units to the right and 1 unit down is y = 2(x - 5)^2 - 1.
Explanation:The parent function of a quadratic equation is given by f(x) = x^2. When it is vertically stretched by a factor of 2, it becomes 2f(x) = 2x^2. 5 units translation to the right will give f(x - 5) = 2(x - 5)^2 and a 1 unit downward shift gives f(x) = 2(x - 5)^2 - 1. Therefore, the equation of the new function in vertex form is y = 2(x - 5)^2 - 1.
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Related Questions
A rental car cost a one time fee of $30 and then an additional $15 for each day it is rented. If the Webb family’s total bill was $135, how many days did they rent the car?
Answers
Answer:
7 days because 15 times 7 =105 and if you add 30 to that you get 135.
Step-by-step explanation:
The Webb family rented the car for 7 days.
To find the number of days the Webb family rented the car, we can set up an equation using the given information. Let's say the number of days the car was rented is x. The total cost would then be $30 (one-time fee) plus $15 (daily fee) multiplied by x. This can be represented as the equation: 30 + 15x = 135. To solve for x, we need to isolate it by subtracting 30 from both sides: 15x = 105. Then, divide both sides by 15: x = 7. Therefore, the Webb family rented the car for 7 days.
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Vertex of y=2x^2-16x+8
Answers
First you use the formula (-b/2a) to find the axis of symmetry(or the x value) and then you plug that into the equation to find the y value.
a = 2
b= -16
16/2(2)=16/4=4
(4, x ) so we have the x-value and now we plug 4 into the original equation
y=2(4)^2-16(4)+8
y=2(16)-64+8
y=32-64+8
y=-24
So the vertex is at (4,-24)
Work out the size of angle y.
Answers
2x+16=3x-12
16+12=3x-2x
28=x
now,since this is a fig of 2 parallel line with a bisector then line EF =180 degrees.
therefore,3x+12+y=180
3(28)+12+y=180 [we already found the value of x]
96+y=180
y=180-96
y=84.
HELP....PLZ thanks!!!!!!!!!!!!
Answers
Answer:
64mph
56mph
higher
64mph
56mph
higher
It's too short. Write at least 20 characters to explain it well.
To make 6 glasses of lemonade Karla uses 5.5 cups of water how much water should she use for 10 cups
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What is 9,032,504.75 in word form?
Answers
Nine million thirty two thousand five hundred four and seventy five hundredths.
nine million thirty-two thousand five hundred four and seventy five tenths. :)
50 points
In this figure, the horizontal lines are parallel, and AB=BC=CD. Find KL and FF. I need an explanation and all work shown.
Answers
AB=BC=CD together with the fact the horizontal lines are parallel implies that HG=GF=FE (can be proved using triangle similarity). So knowing FE=5.1 implies FG=5.1
Since we now know that the horizontal lines are equidistant, it means that ML=LK=KJ (same argument as above). Therefore KL=7.6.
Let me know if you have questions!
Since the horizontal lines are parallel, and AB=BC=CD, the lengths of KL and FG are: D. KL = 7.6; FG = 5.1.
What are parallel lines?In Mathematics and Euclidean Geometry, parallel lines are two lines that are always the same distance apart and never meet.
This ultimately implies that, parallel lines are always coplanar lines and straight lines that have an equal distance between each other.
By critically observing the figure, we can logically deduce that the horizontal lines are all parallel to each other with two transversals;
AB = BC = CD (Given)
AB = LM = 7.6
BC = KL = 7.6
CD = JK = 7.6
AB = GH = 5.1
BC = FG = 5.1
CD = EF = 5.1
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mikaela travels 15 blocks on skateboard in 5 minute.at this speed,how many blocks can she travel on her skateboard in 12 minutes?
Answers
Answer:
She can travel 36 blocks in 12 minutes.
Step-by-step explanation:
First you must find out how many blocks he can skateboard in 1 minute.
15/5
He can skateboard 3 blocks in 1 minute.
The equation I will use is b * m
b = blocks
m = minutes
so in this situation you must multiply 3 * 12 to get your answer.
which is b = 36
Answer:
She can travel 36 blocks in 12 minutes.
Step-by-step explanation:
First you must find out how many blocks he can skateboard in 1 minute.
15/5
He can skateboard 3 blocks in 1 minute.
The equation I will use is b * m
b = blocks
m = minutes
so in this situation you must multiply 3 * 12 to get your answer.
which is b = 36
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Step-by-step explanation:
:)
HELP ME -(6x+7)+8=19?
Answers
Hey there,
The answer your looking for is X = -3
- Ari -
The answer is x = -3 because:
-(6x+7)+8=19
-6x-7+8=19
-6x+1=19
-6x+18
x=-3
Eva sees a dolphin 3.2 meters below sea level and a bird 47/10 meters above sea level.
Which of the following expressions represents the vertical distance between the dolphin and the bird?
47/10-(3.2)
3.2-47/10
none of the above
Answers
Answer:
[tex]A[/tex], | [tex]\frac{47}{10} -(3.2)[/tex] |
To find the vertical distance between a dolphin below sea level and a bird above sea level, the absolute values of their distances from sea level must be added, resulting in a distance of 4.7 + 3.2 meters, which means the correct answer is 'none of the above'.
Explanation:The question is asking to calculate the vertical distance between a dolphin below sea level and a bird above sea level. To find this vertical distance, you would add the absolute values of their distances from sea level. Since sea level is our reference point, and the dolphin is at 3.2 meters below it while the bird is at 47/10 or 4.7 meters above, the expression to represent the vertical distance between the dolphin and the bird would be:
4.7 + 3.2
The correct answer is none of the above since neither of the provided expressions represents the sum of the two distances. Instead, each expression attempts to subtract one distance from the other, which is not the correct method for finding the vertical distance between two objects on opposite sides of the sea level reference point.
All angles in the diagram are measured to the nearest degree.
Work out the upper bound and lower bound of angle x.
Answers
Answer:
=59+108+81+x=360
=248+x=360
=112
Considering the nearest-degree measurements, angle x falls between 58.5 and 108.5 degrees, determined by adjusting the upper and lower bounds based on the provided angles in the diagram.
Given that the angles in the diagram are measured to the nearest degree, we can determine the upper and lower bounds of angle x using the provided angles: 59 degrees, 108 degrees, and 81 degrees.
To find the upper bound of angle x, we select the largest angle, which is 108 degrees. The upper bound is obtained by adding 0.5 degrees to this angle (since measurements are to the nearest degree). Therefore, the upper bound of angle x is 108 + 0.5 = 108.5 degrees.
For the lower bound, we choose the smallest angle, which is 59 degrees. The lower bound is found by subtracting 0.5 degrees from this angle. Thus, the lower bound of angle x is 59 - 0.5 = 58.5 degrees.
In conclusion, the measure of angle x lies between the lower bound of 58.5 degrees and the upper bound of 108.5 degrees.
For more such information on: angle
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What were the two whole numbers?
Answers
Answer:
Ah, this is an example of the distribution property, as you would need to distribute the 5 to the 8 and 3. Here's the step-by-step process:
[tex]5(8+3)[/tex]
Let's first multiply the 5 and 8
[tex]5(8)=40[/tex]
Now, the 5 and 3
[tex]5(3)=15[/tex]
We now have two whole numbers, and therefore our answer:
40 + 15
Margo borrows $400 agreeing to pay it back with 5% annual interest after 6 months. How much interest will she pay?
Answers
She will pay $20 in interest
20 dollars of interest would be payed
Hope this helps
the point-slope form of a equation of the line that passes through (-4, -3) and (12, 1) is y-1= 1/4 (x - 12) What is the standard form of the equation for this line?
Answers
x-4y=8
Hope this helps!
what is the simplified form of the following expression? Assume x is greater than or equal to 0 and y is greater than or equal to 0. 2(4sq root16x)-2(4sq root 2y)+34 sq root 81x)-4(4sq root32y)
Answers
The simplified expression is [tex]\(338\sqrt{x} - 40\sqrt{2y}\),[/tex] combining like terms of square roots of variables.
To simplify the given expression, let's simplify each term separately:
1. [tex]\(2 \cdot 4\sqrt{16x}\)[/tex]
- Simplify \(4\sqrt{16x}\): Since [tex]\(16x = (4 \cdot 4) \cdot x = 4^2 \cdot x\), the square root of \(16x\) is \(4\sqrt{x}\).[/tex]
- Substitute this result into the expression:[tex]\(2 \cdot 4 \cdot 4\sqrt{x} = 32\sqrt{x}\).[/tex]
2. [tex]\(2 \cdot 4\sqrt{2y}\) - Simplify \(4\sqrt{2y}\): Since \(2y\) doesn't have a perfect square factor, we leave it as is. - Substitute this result into the expression: \(2 \cdot 4\sqrt{2y} = 8\sqrt{2y}\).[/tex]
3. [tex]\(34\sqrt{81x}\) - Simplify \(\sqrt{81x}\): Since \(81x = (9 \cdot 9) \cdot x = 9^2 \cdot x\), the square root of \(81x\) is \(9\sqrt{x}\).[/tex]
- Substitute this result into the expression: [tex]\(34 \cdot 9\sqrt{x} = 306\sqrt{x}\).[/tex]
4. [tex]\(4 \cdot 4\sqrt{32y}\) - Simplify \(4\sqrt{32y}\): Since \(32y = (4 \cdot 8) \cdot y = 4^2 \cdot 8y\), the square root of \(32y\) is \(4\sqrt{8y}\). - Rewrite \(\sqrt{8y}\) as \(2\sqrt{2y}\) since \(8 = 4 \cdot 2\). - Substitute this result into the expression: \(4 \cdot 4 \cdot 2\sqrt{2y} = 32\sqrt{2y}\).[/tex]
Now, combine all the simplified terms:
[tex]\[ 32\sqrt{x} - 8\sqrt{2y} + 306\sqrt{x} - 32\sqrt{2y} \][/tex]
Combine like terms:
[tex]\[ (32\sqrt{x} + 306\sqrt{x}) - (8\sqrt{2y} + 32\sqrt{2y}) \][/tex]
[tex]\[ 338\sqrt{x} - 40\sqrt{2y} \][/tex]
Therefore, the simplified form of the expression is [tex]\(338\sqrt{x} - 40\sqrt{2y}\).[/tex]
The simplified form of the expression is 338√x - 72√2y, after applying the square roots to known perfect squares and combining like terms.
To simplify the expression, first apply the square root to known perfect squares and distribute the multiplication:
2(4√16x) becomes 2(4×4√x) because √16 = 4, so this part simplifies to 32√x.
2(4√2y) stays as is because √2y cannot be simplified further without more information about y, so this part is 8√2y.
34√81x can be simplified because √81 = 9, resulting in 34×9√x, which is 306√x.
4(4√32y) becomes 4(4×√16×√2y) because √32 = √16×√2, so this part simplifies to 64√2y.
Combining all the parts, we subtract the like terms:
32√x - 8√2y + 306√x - 64√2y
This simplifies further to 338√x - 72√2y
That is the final simplified expression.
what is the simplified form of the expression 1/2 (2x + 6).
Answers
Substitute the one half to both of the numbers inside the parentheses.
1/2*2 is one which would just be x
1/2*6 is three
X+3
The answer would be x+3
(3a^3b^-2c^0d)^3/6a^3b^-8c*b^2d
Answers
Answer:
[tex]4.5a^6d^2[/tex]
Step-by-step explanation:
Use:
[tex](ab)^n=a^nb^n\\\\(a^n)^m=a^{nm}\\\\a^n\cdot a^m=a^{n+m}\\\\\dfrac{a^n}{a^m}=a^{n-m}\\\\a^0=1\ for\ a\neq0[/tex]
----------------------------------------------------------------------------------
[tex]\dfrac{(3a^3b^{-2}c^0d)^3}{6a^3b^{-8}c\cdot b^2d}=\dfrac{3^3(a^3)^3(b^{-2})^3(1^3)d^3}{6a^3b^{-8+2}d}=\dfrac{27a^9b^{-6}d^3}{6a^3b^{-6}d}\\\\=\dfrac{27}{6}a^{9-3}b^{-6-(-6)}d^{3-1}=4.5a^6b^0d^2=4.5a^6d^2[/tex]
leons older brother is 4and 3/4 feet tall. Leon is 1/3 foot shorter than his brother. How tall is leon
Answers
Answer: [tex]4\frac{5}{12}\ feet[/tex]
Step-by-step explanation:
The height of Leon's older brother = [tex]4\frac{3}{4}[/tex] feet
[tex]=\frac{16+3}{4}=\frac{19}{4}[/tex] feet
Since, Leon is 1/3 foot shorter than his brother.
Then, the height of Leon = [tex]\frac{19}{4}-\frac{1}{3}[/tex]
First we need to make them like fractions by multiplying 3 on the numerator and denominator of the first fraction and 4 on the numerator and denominator of the second fraction.
Then, the height of Leon = [tex]\frac{57}{12}-\frac{4}{12}[/tex]
[tex]=\frac{57-4}{12}\\=\frac{53}{12}=4\frac{5}{12}[/tex] feet
Hence, The height of Leon =[tex]4\frac{5}{12}\ feet[/tex]
Use the interactive ruler to measure the distance from the center of dilation, C, to the image and pre-image. The distance from point C to point A is units. The distance from point C to point A' is units. The distance from point C to point A' is the distance from point C to point A.
Answers
Answer:
4,2, and one-half in the answer!!!! :)
Step-by-step explanation:
Having used the interactive ruler, the distance from the center of the dilation to the image and pre-image is 4 Units.
What is an Interactive ruler?
Also known as an Interactive Teaching Program (ITP) ruler, this virtual tool (which displays on the computer screen) is used to measure the lines and sides of a shape.
What is the distance from point C to point A is units?Having used the interactive ruler, the distance from point C to point A is units is 2 units.
Also, The distance from point C to point A' is 1.5 Units.
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Find the area. Use π = 3.14.
Answers
d.
5.3066 m2
that is your answer
Kyle is using the general form of a quadratic equation to derive the quadratic formula. He reaches the step in his proof that states x2 + b a x = - c a . Which term must he add to complete the square?
Answers
Answer:
[tex] \dfrac{b^2}{4a^2} [/tex]
Step-by-step explanation:
There are some fractions there that are not visible.
Here it is with the fractions in place.
[tex] x^2 + \dfrac{b}{a}x = -\dfrac{c}{a} [/tex]
To complete the square, take half of the x-term coefficient, and square it.
The x-term coefficient is [tex] \dfrac{b}{a} [/tex].
Take half of it, or [tex] \dfrac{b}{2a} [/tex].
Now square it: [tex] \dfrac{b^2}{4a^2} [/tex].
That is what you must add to complete the square.
Answer:
(b/2a)^2
Step-by-step explanation:
usatestprep
Hector is 5 years less than double Mary's age Mary is 12 years old how many years old is Hector
Answers
19 years old double her age is 24 then you subtract 5. 19
Hector is 19 years old.
12 x 2 = 24 - 5 = 19
(5,-7) (5,3) finding slope using formula.
Answers
m = (y2 -y1)/ (x2-x1)
m = (3-(-7))
--------
5-5
The slope is undefined since the denominator is zero
is 17/31 greater than 19/14
Answers
Answer:
No
Step-by-step explanation:
Put both in your calculator. Do it in this order.
17
÷
31
=
0.5484
=========
Now do the next one
18
÷
14
=
1.357
19/14 > 17/31
Answers . Jzhidkdjdisnsjkdjdkshxkdbdksnxn
Answers
what is the resulting polynomial when 3x+7 is multiplied by 2x-6
Answers
(3x+7)(2x-6)= 6x squared -4x-42
6x^2-4x-42
The product of the expressions (3x + 7) and (2x - 6) will be 6x² - 4x - 42.
What is polynomial?A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed.
The expressions are given below.
(3x + 7) and (2x - 6)
Then the product of the expressions (3x + 7) and (2x - 6) will be
(3x + 7) (2x - 6) = 6x² + 14x - 18x - 42
(3x + 7) (2x - 6) = 6x² - 4x - 42
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Find the values of y2.
y2=169
please i need help stuck on it :)
Answers
assuming you mean y² = 169
then taking the square root of both sides gives
y = [tex]\sqrt{169}[/tex] = ± 13
since 13² = 169 and (- 13)² = 169
The values of y are -13 and 13 in the equation y^2 = 169.
It is given that the expression [tex]\rm y^2 = 169[/tex]
It is required to find the values of y.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
We have a quadratic equation:
[tex]\rm y^2 = 169[/tex]
[tex]\rm y^2-169=0[/tex] (subtract 169 on both sides)
[tex]\rm y^2- 13^2=0[/tex] (169 = 13²)
(y+13)(y-13) = 0 (a²-b² = (a+b)(a-b))
Taking (y+13) = 0 ⇒ y = -13
Taking (y-13) = 0 ⇒ y = 13
Thus, the values of y are -13 and 13 in the equation y^2 = 169.
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Find the measure of z.
A. 80°
B. 83 °
C. 70 °
D. 87 °
Answers
The city of Minerva pays 916$ per year for health insurance for each of it's 72 municipal employees. What is the total cost that the city pays per year ?
Answers
So, this is a rate per person * number of people.
So,
$916 per person * 72 people = 65,952
The city pays $916 per year for health insurance for;
each of 72 municipal employees
So;
1 municipal employee gets ⇒ $916
72 employees get ⇒ How much?
Cross multiplying gives:
72/1 × $916 = $65,952
The total cost the city pays per year is $65,952.
Marcus needs 3 1/10 m of blue fabric and 1 1/5 m of yellow fabric to make his costume
How much more blue fabric than yellow fabric does Marcus need?
Express your answer as a mixed number in simplest form
Answers
Turn both into decimals or fractions with a common denominator: 3.1 OR 3 1/10 and 1.2 OR 1 2/10
Now you need to subtract : 3 1/10 - 1 2/10 = 1 9/10 OR 1.9
In mixed number form : 1 9/10