If k(x) = x^2 and p(x) = k(x) + n, what is the value of n?
Pleaseee help ASAP!
I will give brainliest :)
Answers
Answer:
The value of n is -6
Step-by-step explanation:
If the function f(x) is translated k units up, then its image is g(x) = f(x) + kIf the function f(x) is translated k units down, then its image is g(x) = f(x) - kThe vertex form of the quadratic function is f(x) = a(x - h)² + k, where a is the coefficient of x² and (h, k) is the vertex∵ k(x) = x²
→ Its graph is a parabola with vertex (0, 0)
∴ The vertex of the prabola which represents it is (0, 0)
∵ The given graph is the graph of p(x)
∵ Its vertex is (0, -6)
∴ h = 0 and k = -6
∵ a = 1
→ Substitute them in the form above
∴ p(x) = 1(x - 0)² + -6
∴ p(x) = x² - 6
→ Substitute x² by k(x)
∴ p(x) = k(x) - 6
∵ p(x) = k(x) + n
→ By comparing the two right sides
∴ n = -6
∴ The value of n is -6
Look at the attached figure for more understanding
The red parabola represents k(x)
The blue parabola represents p(x)
The value of the n is -6.
Equation of a parabolay = a(x-h)2 + k
where,
(h, k) are the coordinates of the vertex of the parabola in form (x, y);
a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.
Given to usk(x) = x^2
p(x) = k(x) + n
Substitutionsubstituting the value of k(x) in p(x).p(x) = k(x)+n
p(x) = x² + n
ComparingComparing with the Equation of a parabola,
y = a(x-h)2 + k
p(x) = x² + n
Therefore, the value of n is k which is the y coordinate of the vertex of the parabola.
Coordinates of the vertex of the parabolaLooking at the coordinates of the vertex of the parabola,
(h, n) = (0, -6)
Hence, the value of the n is -6.
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Related Questions
simplify (3a²b²)²+(ab)²
Answers
Answer:
[tex]a^{2} b^{2}[/tex] (9[tex]a^{2} b^{2}[/tex] + 1)
Step-by-step explanation:
simplify (3a²b²)²+(ab)²; for the first term, square the 3 and multiply the exponents by 2, also multiply the exponents by 2 in the second term
[tex]9a^{4} b^{4} + a^{2} b^{2}[/tex] ; factor out [tex]a^{2} b^{2}[/tex]
[tex]a^{2} b^{2}[/tex] (9[tex]a^{2} b^{2}[/tex] + 1)
= 4a^2b^2
help please!!!!!!!!
Answers
That should be correct
In a 650g bag of mixed dried fruits, the ratio of mangos to apples to pears is 12:8:6 by mass. Determine the masses of the mangos, apples, and pears in the bag.
Answers
Answer:
mass of mangos = 300g
mass of apples = 200g
mass of pears = 150g
Step-by-step explanation:
lets first reduce the ratio
12:8:6
is the same as
6:4:3
this means the the denominator of our fractions will be 6 + 4 + 3 = 13
hence
mangos = 6/13 of 650g
6/13 * 650 = 300
apples = 4/13 of 650g
4/13 * 650 = 200
pears = 3/13 of 650g
3/13 * 650 = 150
What is the volume of the following rectangular prism?
Answers
Answer:
1/2 * 7/4 = 7/8
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Which expression is equivalent to (4n³p)²(2n²p⁴)³?
a. 128n³⁶p²⁴
b.48n¹²p¹⁴
c.128n¹²p¹⁴
d.48n³⁶p²⁴
Answers
Answer:
C: 128n¹²p¹⁴
Step-by-step explanation:
I plugged this into my TI-89 calculator and got this answer. Let me know if you need the step by step explanation and I'll be more than happy to hand-solve it for you!
Part B
Joe recevied a large jug of antifreeze coolant that is labeled as containing 120
fluid Ounces. He needs to transfer the coolant into pint-sized bottles using the
conversion chart shown below. How many pint-sized bottles will he
need? Explain how you got your answer.
1 gallon (gal) = 4 quarts (at)
1 quart = 2 pints (pt)
1 pint = 2 cups (c)
1 cup = 8 fluid Ounces (fl oz.)
In the box below, write the number of pint-sized bottles he will need and
explain how you got your answer.
Y
Answers
Answer:
7.5,
Step-by-step explanation:
8 x 15 = 120
So 15 cups
And then since 2 cups equal a pint
15 divided by 2
Which is 7.5 pints
a) Match the graph shown with one of the following equations.
b) Which one of the following points lies on the line 3y = 2x - 1?
Answers
The graph have a negative slope and a positive y intercept. The graph is given by y = -x + 2. The point (2, 1) lies on th line 3y = 2x - 1
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The graph have a negative slope and a positive y intercept. The graph is given by y = -x + 2
Given the equation:
3y = 2x - 1
When x = 2:
3y = 2(2) - 1
y = 1
The point (2, 1) lies on th line 3y = 2x - 1
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GEOMETRY QUESTION, HELP PLEASEEE.
Answers
Answer:
The pre-image C is (2, 5)
Step-by-step explanation:
If the point (x, y) rotated about the origin by angle 90° clockwise, then its image is (y, -x)If the point (x, y) rotated about the origin by angle 180° clockwise, then its image is (-x, -y)If the point (x, y) rotated about the origin by angle 270° clockwise, then its image is (-y, x)∵ Point C was rotated 270° clockwise around the origin
∵ C' = (-5, 2)
→ By using the 3rd rule above
∵ The image of the point (x, y) is (-y, x)
∴ (-y, x) = (-5, 2)
→ That means -y = -5 and x = 2
∴ x = 2
∴ -y = -5
→ Divide both sides by -1
∴ y = 5
∴ The pre-image C = (2, 5)
if you multiply 5 and then blank and it equals 565 what the missing number?
Answers
When
4a- a x 3a + 7a
is simplified it is equivalent to?
Answers
Answer:
-3a^2+11a
Step-by-step explanation:
Answer:
4a-a×3a+7a
or, 3a×3a+ 7a
or,9a+7a
or,16a
:. a =16
Geoffrey friend baked a cream pie yesterday. Geoffrey ate 6.3 slices yesterday and 1.3 slices today. How many slices has Geoffrey eaten so far?
Answers
Answer:
7.6
Step-by-step explanation:
1.3 + 6.3 = 7.6
Samantha buys $128 worth of goods at a 25% discount. If the sales tax rate is 6.4%, what is the total amount she will pay?
Answers
Answer:
To do this, you need to find the amount of discount of the original price. To find a percent of a number you first convert the percent to a decimal (i.e. 25% = 0.25). Then you multiply this decimal by the original price. Therefore, the sale price is $17.21. If example.
Step-by-step explanation:
Answer:
102.144
Step-by-step explanation:
128 times 0.25 = 32
128 - 32 = 96
96 times 1.064 = 102.144
She will need to pay 102.144
I'm stuck on this one. I'm sorry of you know everything but there are other people who can't comprehend some problems without being their to actually see and experience it with a teacher. Just help me with this one -
Answers
Answer:
Expand the brackets, and simplify.
(4t - 8/5)-(3-4/3t) = (4t +4/3t) + ( -8/5 - 3) = 5 1/3t - 23/5 = 16/3t - 23/5
5(2t + 1) + (-7t + 28) = 10t + 5 - 7t + 28 = 3t + 33
(-9/2t + 3) + (7/4t + 33) = (-9/2t + 7/4t) + (3 + 33) = -11/4t + 36
3(3t - 4) - (2t + 10) = 9t - 12 - 2t - 10 = 7t - 22
Help me answer number 15 please
Answers
Directions: Select the appropriate comparing symbol from the dropdown list below to evaluate each pair of numbers.
Problem .998 _____ .9899 *
Answers
Answer:
.998 is greater than .9899
Explanation: .998 is greater than .9899
Sebastian drove for 2.2 hours at an average rate of 43.5 miles per hour. He calculates that he drove 95.7 miles. He knows the answer should be near 80, because 40 times 2 is 80. Which best explains Sebastian’s actual solution?
The actual product is reasonable because it is near 80 but greater than 80. Both factors were rounded down, making the estimate lower than the actual product.
The actual product is unreasonable. It should be near 80 but less than 80 because both factors were rounded down.
The actual product is reasonable because the estimate and actual answers both have two places to the left of the decimal.
The actual product is unreasonable because the estimate has zero places to the right of the decimal and the actual product has one decimal place to the right of the decimal.
Answers
Answer:
The actual product is reasonable because it is near 80 but greater than 80. Both factors were rounded down, making the estimate lower than the actual product.
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
NEED HELP NOW. WILL GIVE BRAINLIEST
Answers
Answer: y = -2x² + 920x - 84168
suppose: the equation of the parabola is y = ax² + bx + c
because the parabola passes through (126,0); (134,3200); (334,0)
=> we have the equations:
126².a + 126b + c = 0
134².a + 134b + c = 3200
334². a + 334b + c = 0
⇒ a = -2
b = 920
c = -84168
=> the equation of the parabola is y = -2x² + 920x - 84168
Step-by-step explanation:
Answer:
yea listen to the other person
Step-by-step explanation:
A news service conducted a survey of 1026 adults ages 18 years or older in a certain country, August 31minus−September 2, 2015. The respondents were asked, "Of every tax dollar that goes to the federal government, how many cents of each dollar would you say are wasted?" Of the 1026 individuals surveyed, 36% indicated that 51 cents or more is wasted. The news service reported that 3636% of all adults in the country 18 years or older believe the federal government wastes at least 51 cents of each dollar spent, with a margin of error of 55% and a 99% level of confidence. Complete parts (a) through (e) below. What is the researchobjective?
A. To determine the number of adults in the country paying their taxes to the federal government
B. To determine the percent of adults in the country who believe the federal government wastes 51 cents or more of every dollar
C. To determine the number of adults in the country
D. To determine the number of adults in the country who believe the federal government wastes 51 cents or more of every dollar
Answers
Answer:
B. To determine the percent of adults in the country who believe the federal government wastes 51 cents or more of every dollar.
Step-by-step explanation:
Given that:
sample size = 1026
sample proportion = 0.36
Margin of error = 55% = 0.55
Confidence interval level = 99%
The purpose of this question is to determine the research objective:
The research objectives indicate the intention of the study, the objectives,\ or the main idea. This main idea arises from a need (the research problem) and refined into specific questions (i.e. the research questions). From, the given information, the research objective is to determine the percent of adults in the country who believe the federal government wastes 51 cents or more of every dollar.
jack needs 22 pirates for every 2 ships he manages
Answers
Proving the Parallelogram Side Theorem
Given: ABCD is a parallelogram.
Prove: AB=CD and BC=DA
Angles Segments Triangles Statements Reasons ZBAC ZBCA DAC ZDCA B с Statements Reasons A Assemble the proof by dragging tiles to the Statements and Reasons columns.
Answers
Answer:
A parallelogram is a quadrilateral that has two parallel and equal pairs of opposite sides.
From the given diagram,
Given: AD = BC and AD || BC, then:
i. AB = DC (both pairs of opposite sides of a parallelogram are congruent)
ii. <ADC = < BCD and < DAB = < CBA
thus, AD || BC and AB || DC (both pairs of opposite sides of a parallelogram are parallel)
iii. < BAC = < DCA (alternate angle property)
iv. Join BD, line AC and BC are the diagonals of the quadrilateral which bisect each other. The two diagonals are at a right angle to each other.
v. <ADC + < BCD + < DAB + < CBA = (sum of angles in a quadrilateral equals 4 right angles)
Therefore, ABCD is a parallelogram.
Step-by-step explanation:
The solution is, ABCD is a parallelogram.
What is parallelogram?A parallelogram is a quadrilateral that has two parallel and equal pairs of opposite sides.
here, we have,
From the given diagram,
Given: AD = BC and AD || BC, then:
i. AB = DC (both pairs of opposite sides of a parallelogram are congruent)
ii. <ADC = < BCD and < DAB = < CBA
thus, AD || BC and AB || DC (both pairs of opposite sides of a parallelogram are parallel)
iii. < BAC = < DCA (alternate angle property)
iv. Join BD, line AC and BC are the diagonals of the quadrilateral which bisect each other.
The two diagonals are at a right angle to each other.
v. <ADC + < BCD + < DAB + < CBA = (sum of angles in a quadrilateral equals 4 right angles)
Therefore, ABCD is a parallelogram.
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Match the graph shown with the following equation
Answer a and b please
Answers
Answer:
a) D b)B
Step-by-step explanation:
a) the graph is of negative slope as it slants downwards hence slop/gradient is negative. y intercept is positive so only option d is right
b) sub each option point into 3y = 2x - 1 if they equate to be the same, it is correct.
3(2) = 2(6) - 1
6 = 11 (not equal)
3(1) = 2(2) - 1
3 = 3 (equal) this is the answer
of course you can sub in the rest to confirm but I'm lazy so yeah I'll stop here
Topic: Linear Graphs and its equations
If you would like to venture further, you can check out my Instagram page (learntionary) where I post notes and mathematics tips. Thanks!
The image of the point (4. 9) under a translation is (9. 13). Find the coordinates
of the image of the point ( 5. 2) ander the same translation,
Answers
Answer:
The coordinates of the image are (10,6)
Step-by-step explanation:
Translation
A point located at (x,y), translated by (a,b) maps to the point (x+a,y+b).
If we know the location of the point (x,y) and the location of its image (x',y'), we can know the values of (a,b) by subtracting:
(a,b) = (x',y') - (x,y)
We know the coordinates of the point (4,9) and the coordinates of its image (9,13). Calculate the translation:
(a,b) = (9,13) - (4,9) = (5,4)
If the point (5,2) is translated under the same conditions, then it will map to the point (5,2) + (5,4) = (10,6).
The coordinates of the image are (10,6)
does 2, 2, √4 make a right triangle
Answers
Answer:
No it can'tright angle triangle
Step-by-step explanation:
2, 2, √4 can't make a right triangle
By Pythagoras theorem the square of two sides equal to the third side of the triangle.
2^2+2^2=(√4)^2
4+4=4
8 is not equal to 4 so it not make right angle triangle.
the 6 term of a G.P is -2\27 and it's first term is 18.what is the common ratio
Answers
Answer:
r = - [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
The n th term of a GP is
[tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = 18 and a₆ = - [tex]\frac{2}{27}[/tex] , then
18 [tex]r^{5}[/tex] = - [tex]\frac{2}{27}[/tex] ( divide both sides by 18 )
[tex]r^{5}[/tex] = - [tex]\frac{1}{243}[/tex] ( take the fifth root of both sides )
r = [tex]\sqrt[5]{-\frac{1}{243} }[/tex] = - [tex]\frac{1}{3}[/tex]
What is the absolute value of −3.582?
Answers
Answer:
Its 3.582
Step-by-step explanation:
The absolute value is the numbers distance from zero, in other words just the positive version of it :)
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Find the total surface area of this cuboid.
5 cm
2.3 cm
7.5 cm
If anyone gets it right pls double check how you did it
Answers
86.25
Step-by-step explanation:
5×2.3×7.5= your answer
Find the y-intercept of the graph of the linear equation. 3/4 x + y = 10
Answers
Answer:
10
Step-by-step explanation:
slope intercept form is y=mx+b
in this case b is 10
y=-3/4x+10
What is the correct set.
470
с
b
O a=47, b=60, c=60
O a=180,b=47. c=180
O a=47, b=133, c=47
O a=133, b=47. c=133
Answers
An airplane flies across the country. Its distance from Portland, as a function of time, is modeled by y. 500x.
Which statement best describes the function?
A. The function is nonlinear
B. The function is linear at some points and nonlinear at other points.
c. The function is linear
D. Not enough information is given to decide
Answers
Answer:
I would say b
Step-by-step explanation:
I choose b because the question is linear and also non linear it only told us the distance which is 500x and no time but is saying as a function of time
C. The function is linear.
The given function is y = 500x, where x represents the time and y represents the distance from Portland. In this function, y is directly proportional to x, meaning that for every unit increase in x, y increases by a constant amount of 500.
Since the function is of the form y = mx, where m (in this case, 500) is the constant of proportionality, the function is linear.
Therefore, the correct answer is:
C. The function is linear.
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SUBSTITUTING INGREDIENTS
1. Your soup recipe calls for tdry mustard What can you substitute?
2. Your chocolate cake recipe calls for 2 ozunsweetened baking chocolate substitute ?What can you
3. Your muffin recipe calls for 2 c. self-rising flour. What can you substitute 3. Your meat sauce recipe calls for 2 T. fresh, chopped basil. What can you substitute?
4. Your cake recipe calls for 2 c. cake flour . What can you substitute ?
Answers
Answer:
1. 1 tablespoon Dijon mustard
2. Combine six Tablespoons of cocoa powder and two Tablespoon of vegetable oil, butter or shortening
3. 2 cups of all-purpose flour, 3 teaspoons baking powder, and ½ teaspoon salt
3. One teaspoon of dried basil leaves
4. Combine 1 3/4 cups all-purpose flour with 1/4 cup cornstarch
Step-by-step explanation:
CAn I have brainliest? TYSMMMMMMMMMM