The equation of the parabola is y = (-3/2)x + 1.
The general vertex form of the equation of a parabola is y = a(x - h)2 + k
where (h, k) are the coordinates of the vertex
Here, we are given that vertex = (0, 1)
Thus, the equation of the parabola is-
y = a(x - 0)2 + 1
y = 2ax + 1
Also, we are given that the parabola passes through (12, -17).
Thus, (12, -17) must satisfy the equation of the parabola
⇒ -17 = 2a(12) + 1
-17 = 24a + 1
24a = -17 -1
24a = -18
a = -18/24
a = -3/4
Thus, the equation of the parabola becomes-
y = 2(-3/4)x + 1
y = (-3/2)x + 1
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marvin was completing the square, and his work is shown below. identify the line where he made his mistake. (2 points) f(x)
He made the mistake on line 1.
2x^2 - 8x + 5....move the 5 to the other side
2x^2 - 8x = -5....now divide by 2
x^2 - 4x = -5/2
x^2 - 4x + 4 = -5/2 + 4
(x - 2)^2 = -5/2 + 8/2
(x - 2)^2 = 3/2
x - 2 = (+-)sqrt 3/2
x = 2 + sqrt 3/2 or x = 2 - sqrt 3/2
He made mistake on line 1.
Complete question -Marvin was completing the square, and his work is shown below. Identify the line where he made his mistake. f(x) = 2x2 − 8x + 5. Line 1: f(x) = 2(x^2 − 8x) + 5 Line 2: f(x) = 2(x^2 − 8x + 16) + 5 − 32 Line 3: f(x) = 2(x − 4)^2 − 27
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Question Write an absolute value equation that has the solutions x=2 and x=9
Absolute value equation that has the solutions x=2 and x=9 is |x - 5.5| = 3.5
5.5 is the mid-point between 2 and 9: (2+9)/2=5.5and the equation says that the points x= 2 and x= 9 are equally remoted at the distance of 3.5 from their mid-point.3.5 is the half of the distance 9-2 = 7 between the given points (the given values) x= 2 and x= 9.absolute value equation is |x - 5.5| = 3.5
Generalizations of the absolute cost for actual numbers arise in a huge form of mathematical settings. as an example, an absolute value is likewise defined for the complicated numbers, the quaternions, ordered jewelry, fields and vector spaces. absolutely the price is closely associated with the notions of value, distance, and norm in numerous mathematical and bodily contexts.
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rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents. (1 point) three to the one third power all over three to the one sixth power
The expression with rational exponents as a radical expression by extending the properties of integer exponents is, [tex]\sqrt[6]{3}[/tex]
Define exponents for integers?The exponents that should be integers are those that are. It may be an integer that is either positive or negative. It specifies how many times the base number should be multiplied by itself using positive integer exponents.
Given:
The given expression is,
[tex]\frac{3^{\frac{1}{3}}}{3^{\frac{1}{6} } }[/tex]
We know that,
[tex]\frac{x^{a} }{x^{b}}= x^{a-b}[/tex]
[tex]\frac{3^{\frac{1}{3}}}{3^{\frac{1}{6}}} = 3^{\frac{1}{3}-\frac{1}{6}}[/tex]
[tex]\frac{3^{\frac{1}{3}}}{3^{\frac{1}{6}}}=3^{\frac{1}{6} }[/tex]
Therefore,
[tex]\frac{3^{\frac{1}{3}}}{3^{\frac{1}{6}}}=\sqrt[6]{3}[/tex]
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Consider the quadratic polynomial ax 2 bx c. suppose the coefficients are given by rolling a fair die three times. what is the probability that the roots of the polynomial are equal?
Complete the square to write
ax² + bx + c = a (x + b/(2a))² - (b² - 4ac)/(4a)
The quadratic has a double root at x = -b/(2a) if the constant term (b² - 4ac)/(4a) vanishes, which happens if b² - 4ac = 0.
Let A, B, and C be random variables representing the value of the first, second, and third roll of the die. They are independent and identically distributed with PMF
Pr [X = x] = 1/6
if x ∈ {1, 2, 3, 4, 5, 6}, and 0 otherwise.
We want to find
Pr [B² - 4AC = 0]
Note that
B² - 4AC = 0 ⇒ B² = 4AC ⇒ (B/2)² = AC
which tells us that B must be even, and also that AC is a perfect square. Then there are 5 possible outcomes that satisfy the conditions:
• If B = 2, then AC = 1 ⇒ A = C = 1
• If B = 4, then AC = 4 ⇒ A = 1, C = 4 or A = C = 2 or A = 4, C = 1
• If B = 6, then AC = 9 ⇒ A = C = 3
and there are 6³ = 216 total possible outcomes in the sample space. So,
Pr [B² - 4AC = 0] = 5/216
Transformation that result in a change in the size of a figure are called ____.
Answer:
Transformation that result in a change in the size of a figure are called dilations.
Select the correct answer. wanda is a cake designer with a specialty in rectangular silk screen photo cakes. for every cake that she makes, the width of the cake is 4 inches more than the width of the photo in the center of the cake, and the length of every cake is two times its width. the area of the cake wanda is currently working on is at least 254 square inches. if x represents the width of the photo, which inequality represents this situation? a. b. c. d.
The equation representing the inequality is 2·x² + 16·x + 32 ≥ 254
The width of the photo on the cake is x.
The dimensional relationship mentioned between the dimensions of the cake & the photo on the cake mentioned in the question are:
Width of cake = Width of photo + 4 inches
i.e., W = x + 4
And, Length of the Cake is twice the Width of the cake
i.e., L = 2*W
Also, It is mentioned that the Area of the Cake is 254 sq inches.
We know Formula to calculate the Area of a rectangle is :
=> Area = Length * Width
=> 254 ≤ 2*W * (x+4) => 254 ≤ 2(x+4)*(x +4)
=> 2·x² + 16·x + 32 ≥ 254
Hence, The inequality representing this case is 2·x² + 16·x + 32 ≥ 254
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Write an equation of a line that is perpendicular to y = 4x + 8 and passes through (−8, 4).
The equation of line is y= -1/4x + 2
What is Equation of line?The slope of the line and a point on the line can be used to create the equation of a line. To better comprehend how the equation for a line is formed. The slope of the line, which can be stated as a numeric integer, fraction, or the tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis.
The general form is [tex](y- y_1)= m(x - x_1)[/tex]
given:
line that is perpendicular to y = 4x + 8 and passes through (−8, 4).
Here the slope of given line is 4.
So, the slope of perpendicular lines is
m = -1/4
Now, as the line passes through (-8, 4)
Then using
(y - y1) = m (x- x1)
y- 4= -1/4(x- (-8))
y-4 = -1/4 ( x+8)
y-4 = -1/4 x - 2
y= -1/4x + 2
Hence, the equation of line is y= -1/4x + 2.
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Answer: y= -1/4x + 2
Step-by-step explanation: chose the answer and got it right on my test
Solve the following proportion.
x/-8 = 12/6
A -12 B -14
C -16 D -18
Step-by-step explanation:
Multiply both sides of the equation by 24, the least common multiple of −8,6
−3x=4×12
Multiply 4 and 12 to get 48.
−3x=48
Divide both sides by −3.
x= −3/48
Divide 48 by −3 to get −16.
The answer is x=−16
What is the value of x?
Answer:
x = 7
y = 3
Step-by-step explanation:
Because the opposite side, Line segment QR, is 11. So, you need to find a number that when multiplied by 2 and then subtracted by 3 is equal to 11.
First, I just guessed, that 7 times 2 is 14, and then minus 3 is equal to 11
Here is how I worked it out:
2x-3=11
2x=14
x=7
8y+5=6y+11
2y=6
y=3
The value of the variable x and y will be 7 and 3, respectively.
What is a rectangle?It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.
The rectangle PQRS is shown.
From the rectangle PQRS, the side PQ and RS are congruent. And the side PS and QR are also congruent.
PQ = SR
6y + 11 = 8y + 5
2y = 6
y = 3
PS = QR
2x - 3 = 11
2x = 14
x = 7
The value of the variable x and y will be 7 and 3, respectively.
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Given △XYZ with vertices X(2, 4), Y(6, 0), and Z(7, 2) what is its image after the composition
Translation: (x, y) → (x + 12, y + 4)
Translation: (x, y) → (x − 5, y − 9)
The image after the composition is X''(9, -1), Y'(13, -5), and Z''(14, -3)
How to determine the image after the composition?The vertices of the triangle are given as:
X(2, 4), Y(6, 0), and Z(7, 2)
The compositions of translations are given as:
Translation: (x, y) → (x + 12, y + 4)
Translation: (x, y) → (x − 5, y − 9)
So, we have:
Translation: (x, y) → (x + 12, y + 4)
X'(2 + 12, 4 +4), Y'(6 + 12, 0 + 4), and Z'(7 + 12, 2 + 4)
Evaluate
X'(14, 8), Y'(18, 4), and Z'(19, 6)
Translation: (x, y) → (x − 5, y − 9)
X''(14 - 5, 8 - 9), Y'(18 - 5, 4 - 9), and Z'(19 - 5, 6 - 9)
Evaluate
X''(9, -1), Y'(13, -5), and Z''(14, -3)
Hence, the image after the composition is X''(9, -1), Y'(13, -5), and Z''(14, -3)
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jon and alex play a game where they each need to kick a ball into a net. they will each kick 11 balls, but alex has a slight edge, with a 60% chance of scoring to jon's 40%. what is the probability that jon will score exactly 8 times?
The probability of scoring a goal exactly 8 times by Jon is given by 0.0234. It is obtained using the prerequisite knowledge of binomial distribution and probability.
What is Binomial Distribution in Probability?
When each trial has a probability of occurring equally likely, then the number of trials or observations is outlined using the binomial distribution. The chance of observing a specific number of successful outcomes in a specific number of trials is determined by using the binomial distribution.
Calculation of the probability of the given event
Total no. of possible outcomes, n = 11
The probability that Jon will kick the ball in the net, p(x) = 0.4
The probability that Alex will kick the ball in the net, q(x) = 0.6
Using Binomial Distribution, we get,
P(x = r) = C(n,r) × (p)r × q(n - r)
where x is the score made by Joe
P(x = 8) = C(11,8) × (0.4)8 × (0.6)3
= 0.0234
Hence, the probability that Jon will score exactly 8 times is 0.0234.
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what is the greatest commen factor of 392
Answer: it's 3 love
Answer: 392
Step-by-step explanation: all the common factors are
1,2,4,7,8,14,28,49,56,98,196,392 so the greatest would be 392
hope this was helpful- hailey <3 :)
Please Please help asap!!! Thank you
Step-by-step explanation:
well, the starting equation and the target format have been given.
let's do the multiplications and compare the target with the starting information.
from there we see what is different or missing.
x² + 14x + 13 = 0
and
(x - p)² = q
x² - 2px + p² = q
x² - 2px + (p² - q) = 0
now let's compare the different parts :
x² = x²
-2px = 14x
-2p = 14
p = -7
p² - q = 13
-7² - q = 13
49 - q = 13
36 - q = 0
q = 36
so, the square (x - p)² = (x + 7)² is completed when
x² + 14x + 49 = 0
but we have only "+ 13". so we need to add 36 to get 49. but we need to do it on both sides, to keep the equation true :
x² + 14x + 13 + 36 = 36
x² + 14x + 49 = 36
(x + 7)² = 36
just as we calculated already above.
and now this can be solved by pulling the square root on both sides (a quadratic equation has always 2 solutions)
x + 7 = ±6
x1 = 6 - 7 = -1
x2 = -6 - 7 = -13
point m is the midpoint of segment kl. point n is the midpoint of segment ml. a line with the points of k, l, m, and n, in which point m is the midpoi
The second point on the line k,m,n,l is where the midpoint, m, is found by adding kl to the equation.
What do you mean by the segment's midpoint?A segment's midway is the point on a reference line where two congruent segments meet. The segment's midpoint seems to be the point located halfway between the ends of two segments.
According to the given information:The midpoint is the point on the section that lies halfway between the endpoints.
A line segment's midpoint can be calculated by using two endpoints (x1, y1) and (b, c) (x2, y2).
Add all of the x coordinates together and divide by two to determine the x coordinate of the midpoint.
Add all of the y-coordinates together and divide by two to get the y value of the midway.
It is critical to understand that a midpoint is indeed the midpoint of a line segment.
m = ((x + X)/2,(y + Y)/2) then determines the midpoint m.
We must demonstrate that the distance between m and l is equal to the distance between m and k and that this value is half the distance from k to l to show that m is, in fact, the midpoint of the horizontal line kl.
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point m is the midpoint of segment kl. point n is the midpoint of segment ml. a line with the points of k, l, m, and n, in which point m is the midpoint?
ayuda por favor no le entiendo
la 2. es multiplicand 20 por 18 da 360 y ese número se multiplicand por 500 da 180000 . 3se suma y da 1025 la.4 se reparte en 9625 a cada amigo
Mathematicians use multiplicand to calculate the merchandise of two or more numbers. it's a fundamental operation in mathematics that is frequently utilized in everyday life. once we need to combine groups of similar sizes, we utilize multiplicand. On this page, let's study more about multiplicand.
The fundamental concept of repeatedly adding the same number is represented by the process of the multiplicand. The results of multiplying two or more numbers are referred to as the product of those numbers, and therefore the factors that are multiplicand are referred to as the factors. Repeated addition of the identification number is made easier by multiplying the numbers.
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what are the two next numbers in this sequence.
12,14,18,26,42, ,
Answer:
74 , 138
Step-by-step explanation:
12 + 2 = 14
14 + 4 = 18
18 + 8 = 26
26+16 = 42
42+32= 74
74+64 =138
please make my answer as brainelist
Diven that 4x^3+x^(5/2) all over √x can be written in the form 4x^a+x^b, write down the value of a and the value of b
The value of a and the value of b is 6 and 5.
We can solve this problem by few steps, If we change the representation of power by replacing all powers according to √x or [tex] {x}^{1/2} [/tex]. We know that, [tex] {x}^{m/n × n/b } = {x}^{m/b} [/tex]
So, using this we can write, [tex] {4x}^{1/2 \times 6} + {x}^{1/2 \times 10/2} = {4 \sqrt{x} }^{6} + { \sqrt{x} }^{5} [/tex]..............(1)
Now if we compare the value of ( 1 ) with
[tex] {4 \sqrt{x} }^{a} + { \sqrt{x} }^{b} [/tex], we can easily find out the value of a and b and it is, a = 6 and b = 5
Thus, the value of a and b is 6 and 5.
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The complete question is -
Driven that 4x^ 3+x^ (5/2) all over √x can be written in the form 4√x^a+√x^ b, write down the value of a and the value of b.
-12 < 7x + 9 < 16
What is the solution?
Answer:
-3<x<1
(-3,1)
Step-by-step explanation:
subtract 9 to all 3 sides to get -21<7x<7divide by 7 on all 3 sides to get -3<x<1it is shown as (-3,1) because x is anything inbetween -3 and 1 and those numbers are not included so you use ( ) as opposed to [ ]
Kurt organized a bike race that was 84 miles long. All 469 riders completed the race. How many miles were biked in all?
Kurt organized a bike race that was 84 miles long. All 469 riders completed the race. 39,396 miles were biked in all
Kurt organized a bike race = 84 miles long
All 469 riders completed the race
miles were biked in all :
Total miles =84 Multiply By 469
=39,396 miles
39,396 miles were biked in all
Miles :
A mile is a unit of distance equal to 1760 yards or approximately 1.6 kilometers
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A 84-mile cycling race that Kurt planned took place. The race was completed by all 469 cyclists. All told, 39,396 miles were pedaled
Kurt planned an 84-mile cycling race.
The race was completed by all 469 cyclists.
total number of miles cycled:
Miles total = 84; multiply by 469.
=39,396 miles
All told, 39,396 miles were pedaled
Miles:
Approximately 1.6 kilometers or 1760 yards make up a mile as a unit of measurement.
HELP QUICK PLS!!
A zoo feeds it’s monkeys a mixture of fruits and biscuits. The diagram shows the ratio of fruit mass to biscuit mass.
The table below shows the mass, in grams, of fruit and biscuits that the zoo fed two of the monkeys.
Based on the ratio, complete the missing value in the tables.
The mass of the biscuit and fruit are 20 and 64 grams respectively.
How to use ratio to find the missing values in the tables?A ratio indicates how many times one number contains another.
Therefore, the ratio of fruits and biscuit the zoo fed the monkeys is 7:5.
let's find the total number of the items.
Hence, using the table and ratio,
number of fruits = 7 / 12 × x
number of fruits = 28
Therefore,
28 = 7x / 12
cross multiply
12 × 28 = 7x
336 = 7x
divide both sides by 7
336 / 7 = 7x / 7
x = 48
Hence,
mass of biscuit = 5 / 12 × 48
mass of biscuit = 20
The second missing value of the table,
mass of biscuit = 5 / 12 × x
45 = 5x / 12
5x = 504
x = 504 / 5
x = 108
Hence,
mass of fruit = 7 / 12 × 108
mass of fruit = 756 / 12
mass of fruit = 63
Therefore, the mass of the biscuit and fruit are 20 and 64 grams respectively.
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Answer:yes
Step-by-step explanation:fact
Please help me! Find an equation for the perpendicular bisector of the line segment whose endpoints are (-8,-1) and (-4,5).
The equation of the perpendicular bisector of the line segment whose endpoints are (-8,-1) and (-4,5) is y = 3/2x + 7
How to find the perpendicular bisectorFirst we have to find the midpoint of the line
endpoints are (-8,-1) and (-4,5).
midpoint = -8 + -4/2 , -1 +5/2
= -6, 2
slope = -1 - 5 / -8 - -4
= -6 /-4
= 3 / 2
Equation for the line
y - 2 = 3/2(x + 6)
y = 3/2(x + 6)-2
y = 3/2x + 7
Hence the equation of the perpendicular bisector of the line segment whose endpoints are (-8,-1) and (-4,5) is y = 3/2x + 7
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Pls solve this question
also solve -2 1/4 - 4 5/8
Answer: -6 7/8
Step-by-step explanation:
-2 1/4 - 4 5/8=
(-2 1/4 - 4 5/8)*8/8= ==> Multiply by 8 since it is the LCM of 4 and 8 and will get rid of denominators
(-16 8/4 - 32 40/8)/8=
(-(16+2)-(32+5))/8=
(-18-37)/8=
-55/8=
-(48+7)/8=-6 7/8
Kinsley bought 8.01 ounces of chocolate. 3.89 ounces of it was milk chocolate and the
rest was dark chocolate. How much dark chocolate did Kinsley buy?
Answer:
4.12
Step-by-step explanation:
julian needs to spend at least 7 hours each week practicing the drums. he has already practiced hours this week. he wants to split the remaining practice time evenly between the last 2 days of the week. write an inequality to determine the minimum number of hours he needs to practice on each of the 2 days.
An inequality to determine the minimum number of hours he needs to practice on each of the 2 days 0.835.
What is inequality?Definition and importance Imbalance or monetary disparity alludes to the contrast between the rich and poor, the endlessly the less wealthy - it is shown by individuals' various situations inside the financial conveyance - abundance, pay and pay. Imbalance is huge in a general public where hardly any individuals own a lopsided measure of the financial pie. In order to solve the inequality, the variable should be on one side, without coefficients or constants. Divide to cancel out coefficients and add or subtract to remove constants. Once you have isolated the variable, you have solved the inequality. Approach the inequality as you would an equation. Social imbalance alludes to the lopsided economic wellbeing in any general public, coming about because of inconsistent open doors, and lower awards for exertion. This sort of divergence is brought about by a sensation of being unjustifiably treated, or of segregation in host of regions, like restricted admittance to quality training and occupations. Notwithstanding pay imbalance, individuals who have specific individual attributes, either from birth, or which have been constrained on them by others, are in many cases the subject of inconsistent social treatment. These attributes incorporate such things as race, skin tone, and eye shape, as well as parentage, the guardians' societal position, inability, orientation and orientation character.
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1/4 divided by 2/6 in simplest form
Answer:
1/4*6/2=6/8
3/4
Step-by-step explanation:
What's the algebraic expression of 3/4 a number b divided by 5
Please help T.T
3/4 a number b divided by 5 is 15b/4
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction).
3/4 a number b:
=3b/4
Divided by 5:
=3b/4/5
We have to multiply numerator with the dominator by 5 to remove the double fraction:
=3b*5/4
=15b/4
3/4 a number b divided by 5 is 15b/4
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the following data show the midterm and final exam scores in an english writing class.find the sample correlation coefficient of the midterm and final exam scores (round off to first decimal place).
Sample correlation B = R in output = 0.7 The above data is calculated from parameter estimation.
What is the sample correlation coefficient?The Pearson correlation coefficient (PCC) is a statistical measure of linear correlation between two data sets. It is also referred to as Pearson's r, the Pearson product-moment correlation coefficient (PPMCC), the bivariate correlation, or simply the correlation coefficient. It is a normalised covariance measurement, with the result always falling between 1 and 1. It is the ratio between the covariance of two variables and the product of their standard deviations. The measure, like covariance itself, can only account for linear correlations between variables and ignores numerous other kinds of connections or correlations.
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4th Time asking. Aaaaaaaaaaah. Can nobody anwser this......?
PLEASE I DONT HAVE MUCH TIME LEFT.
Answer:
x=4
Step-by-step explanation:
We can see that points A,E, and D form a triangle.
Points A, C, and C also form a triangle.
These two triangles are similar, while [tex]\triangle ACB[/tex] has side lengths twice as long as [tex]\triangle ADE[/tex]. this means that
[tex]2x+2=4x-6\\2x=8\\x=4[/tex]
boy can mow a lawn in 90 minutes and his sister can mow the same lawn in 60 minutes. how long will it take for both mowing at the same time to mow the lawn?
If boy can mow a lawn in 90 minutes and his sister can mow the same lawn in 60 minutes, then it will take 36 minutes to mow the lawn if both mowing at the same time
Given,
The time taken for the boy to mow a lawn= 90 minutes
The time taken for the sister to mow a lawn= 60 minutes
Work done by the boy in one minute= [tex]\frac{1}{90}[/tex]
Work done by the sister in one minute= [tex]\frac{1}{60}[/tex]
When both mowing at the same time
[tex]\frac{1}{90}+\frac{1}{60}=\frac{1}{36}[/tex]
Then, the time taken when both mowing at the same time = 36 minutes
Hence, if boy can mow a lawn in 90 minutes and his sister can mow the same lawn in 60 minutes, then it will take 36 minutes to mow the lawn if both mowing at the same time
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Which of the following graphs are functions? Select all that apply.
A
C
E
B
D
F
The graphs that could be functions from the graphs shown in the question are A and E.
What is a function?
A function is a mathematical rule. We know that a graph is a plot of data on the cartesian coordinates. The cartesian coordinates are x and y. The x axis is the vertical axis while the y axis is the horizontal axis.
Now we can see that there are bout six plots and we need to determine which of the plots does correspond to a function. We shall now look over the graphs to see how they correlate with functions.
It is clear that the graphs that could be functions from the graphs shown in the question are A and E.
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