The equation of the parabola is y = -x² - 2x + 5
What is a Parabola?
A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line
The equation of the parabola is given by
( x - h )² = 4p ( y - k )
where ( h , k ) is the vertex and ( h , k + p ) is the focus
y is the directrix and y = k - p
The equation of the parabola is also given by the equation
y = ax² + bx + c
where a , b , and c are the three coefficients and the parabola is uniquely identified
Given data ,
The equation of the parabola with the points
A ( -5 , -10 ) , B ( -3 , 2 ) and C ( 2 , -3 )
So , from the equation of parabola ,we get
y = ax² + bx + c
Substituting the values of x and y , in the equation of point A , we get
-10 = a ( -5 )² - 5b + c
-10 = 25a - 5b + c be equation (1)
Substituting the values of x and y , in the equation of point B , we get
2 = a ( -3 )² - 3b + c
2 = 9a - 3b + c be equation (2)
Substituting the values of x and y , in the equation of point C , we get
-3 = a ( 2 )² + 2b + c
-3 = 4a + 2b + c be equation (3)
By the method of brute force , we can solve the equations and derive the equation for the parabola
So , the equation for the parabola will be
y = -x² - 2x + 5
Now , substituting the values of x and y from the points , we get
For point A ( -5, -10 )
-10 = - 25 + 10 + 5
-10 = -10
Therefore , the equation is TRUE
Now , substituting the values of x and y from the points , we get
For point B ( -3, 2 )
2 = -9 + 6 + 5
2 = 2
Therefore , the equation is TRUE
Now , substituting the values of x and y from the points , we get
For point C ( 2 , -3 )
-3 = -4 - 4 + 5
-3 = -3
Therefore , the equation is TRUE
Hence , the equation of the parabola is y = -x² - 2x + 5
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The number of books in Hannah's home library can be described by n(x) = 4x + 2, where x is the number of months that have passed since she began expanding her library. Describe how n(x) is related to its parent function and interpret the function in the context of the situation.
n(x) is a vertical dilation of scale factor 4 followed by a translation of 2 units upwards of the parent linear function.
How is n(x) related to the parent function?
The parent linear function is:
f(x)= x
And the function n(x) is:
n(x) = 4x + 2
If first we apply a vertical dilation of scale factor 4 to the parent linear function, we will get:
n(x) = 4*f(x)
And if now we apply a translation of 2 units upwards, then we get:
n(x) =4*f(x) + 2
Replacing f(x) by x we get:
n(x) = 4*x + 2
And we returned to n(x), so these are the transformations that define our function in terms to the parent function.
And the slope 4 means that each month 4 books are added, the y-intercept 2 means that she starts with 2 books.
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Which angles are adjacent to each other? Select all that apply.
PLEASE HELP!!!
the second and last one
The answer is
AEB and IAE
DEA and CED
v=u+at
u=2 a=-7 t=0.5
work out value of v
given the equation y=x^2+8
Find the cordinates of the vertex it desribes
Find the x intersepts
Find the y intercept
Find the line of symetry
Answer:
Line of symmetry: -b/2a = 0 because b is 0 and a is 1
y-intercept is when x=0, therefore it is at 8.
x-intercept is when y=0, and you would get sqrt(-8), therefore there are no real zeros for this equation.
Vertex: (0,8)
Step-by-step explanation:
To find the vertex, plug in the x-value from the line of symmetry because the vertex happens at the line of symmetry. When you set x=0, then the y-value of the vertex is 8, therefore, the vertex is at (0,8).
Write an expression for the missing dimension of each shaded figure and a multiplication expression for its area. Then, expand and simplify the multiplication expression.
The dimensions and area of the parts of the composite figure are as follows;
The dimension of the missing figure is; 17 - xThe multiplication expression for the area of the shaded figure is 204 - 12·x unit²What is a composite figure?A composite figure is a figure that consists of two or more simpler figures.
The width of the whole figure of length 14 consists of the the missing dimension and the expression (x - 3)
Therefore;
14 = Missing dimension + (x - 3)
Missing dimension = 14 - (x - 3) = 17 - x
The expression for the missing dimension is = 17 - x
The area of the large rectangle = 14 × 12 = 168
Area of the smaller unshaded rectangle = (x - 3) × 12 = 12·x - 36
Area of the shaded figure = Area of the whole figure less the area of the unshaded figure
Therefore;
Area of the shaded figure = 168 - (12·x - 36) = 204 - 12·x
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A poorly-built machine has three components that can independently fail with a
probability of 1/3. The machine will fail if any component fails. What is the probability
that the machine fails?
===========================================================
Explanation:
Each component has 1/3 as the probability of failure.
1 - 1/3 = 2/3 is the probability a particular component works.
Each component is independent of one another, allowing us to multiply the probabilities: (2/3)*(2/3)*(2/3) = 8/27
8/27 is the probability that all three components work simultaneously, and it's the probability that the machine works.
1 - 8/27 = 19/27 represents the probability that at least one component fails, and hence causes the entire machine to fail also.
19/27 = 0.7037 = 70.37% approximately. It appears this machine fails pretty often.
Help! Im being timed
What statment about the graph is true?
The graph is a function with the domain {-6 < x < 0} and the range {0 ≤ y ≤ 5}.as stated
Describe range.The term "range" refers to every potential value in a graph's output.
The result of range is seen in the y coordinate, and the range of potential values is given here.
0 ≤ y ≤ 5
Describe domain.The term "domain" refers to every conceivable value in a graph's input.
The x coordinate is the input, and the extent of potential values is
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Please help me please
On a certain hot summer's day, 524 people used the public swimming pool. The daily prices are $1.25 for children and $2.25 for adults. The receipts for admission totaled $891.00 How many children and how many adults swam at the public pool that day?
Answer:
236 for children and 288 for adults
Step-by-step explanation:
→ Set up 2 simultaneous equations
a + c = 524
2.25a + 1.25c = 891
→ Multiply 1st equation by 1.25
1.25a + 1.25c = 655
2.25a + 1.25c = 891
→ Minus from each other
-a = -236 ⇔ a = 236
→ Substitute into first equation
236 + c = 524 ⇔ c = 288
Find the solution for this system of equations. 12x 15y = 34 -6x 5y = 3 x = y =
The solution for this system of equations. 12x+ 15y = 34 -6x+ 5y = 3
is (x,y) =(2/3, 8/5)
Given a system of equations,
12x + 15y = 34 ------(1)
-6x + 5y = 3 ------(2),
To solve this we use the elimination method
In the elimination method, you either add or subtract the equations to get an equation in one variable.
Equation (1) + 2 × Equation (2),
We get,
(12x+15y=34)+(-12x+10y=6)
⇒ 15y+10y=34+6
⇒ 25y=40
⇒ y=40/25
⇒ y=8/5
From equation (2),
⇒ -6x+5(y)=6
⇒ -6x+5(8/5)=6
⇒ -6x+8=6
⇒ -6x=-2
⇒ x=2/3
Hence the solution for this system of equations. 12x 15y = 34 -6x 5y = 3
is (x,y =(2/3, 8/5)
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the bayley scales of infant development yield scores on two indices-the psychomotor development index (pdi) and the mental development index (mdi)- which can be used to assess a child's level of functioning in each of these areas at approximately one year of age. among normal healthy infants, both indices have a mean value of 100. as part of a study assessing the development and neurologic status of children who have undergone reparative heart surgery during the first three months of life, the bayley scales were administered to a sample of one-year-old infants born with congenital heart disease
As the test's p-value above the 0.05 level of significance, we cannot reject the hypothesis.
X=97.77 is the mean on the PDI.
a )
The population standard deviation of the PDI:S = 14-69
The PDI sample size is n=70.
The test statistic value is
=X -μ/б-√n
97.77 - 100/14.69√70
Z = - 1.27
The test's p-value is 1.
Value of p = 2p (z - 1.27).
=2 ( = NORMSDIST (-1.27) )
= - 2 (0.1020 )
p-value = 0.2041
Since , the p -value of the test is greater the the 0.05 level of significance, so we fail to reject hypothesis
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Write an equation of the line that passes through (-4,-1) and is perpendicular to the line y =4/3x-1
Answer:
y = -3/4 -1
Step-by-step explanation:
The slope will be a negative recipricol of the original line
Edit : Grammar
If you cross 2 parrots that are heterozygous for color and barring, what is the possibility, in the form of a ratio, of a blue and unbarred parrot as offspring? green parakeets dominant (g) blue are recessive (g) barred wing pattern dominant (b) unbarred recessive (b).
1/16 is the ratio of a blue and unbarred parrot as offspring
Dihybrid cross:
Dihybrid cross is a cross between two individuals with two observed traits that are controlled by two distinct genes. The idea of a dihybrid cross came from Gregor Mendel when he observed pea plants that were either yellow or green and either round or wrinkled. Crossing of two heterozygous individuals will result in predictable ratios for both genotype and phenotype in the offspring. The expected phenotypic ratio of crossing heterozygous parents would be Deviations from these expected ratios may indicate that the two traits are linked or that one or both traits has a non-Mendelian mode of inheritance.
When two heterozygous parents for color (Gg) and barring (Bb) are crossed, each parent's genotype is GgBb. Each parent produces four gametes, such as GB, Gb, gB, and gb. As a result, the total number of offspring will be 16, as each parent produces four gametes. Nine will be G B_, three will be G bb, three will be ggB_, and one will be ggbb.
Therefore, 1/16 is the ratio of a blue and unbarred parrot as offspring
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rewrite the equation so that it does not have fractions (please answer quickly)
Answer: 4 - 0.75x = 0.83333333333
Step-by-step explanation:
3/4 = 0.75
5/6 = 0.83333333
So 4 - 0.75x = 0.83333333
The original price of the shoes was $120, the discount made them $72. What is the percent of the shoes he did NOT pay?
For 50 points and brainliest!
pls answer ASAP and check the directions
ty :))
Answer:
Step-by-step explanation:
so by putting (0,0) into the first equation it's false, y of 0 does not become greater than 4
for the second equation, putting in (0,0) it is true. 6 is greater than 0
i'm attaching a graph also :) of both equations graphed together
[tex]\sf y > -2x+4\\\\Broken\ line\\\\Substitute\ (0,0)\\\\0 > -2(0)+4\\0 > 4\\\\False[/tex]
[tex]\sf 3x+2y \leq 6\\\\Solid\ line\\\\Substitute\ (0,0)\\\\3(0)+2(0) \leq 6\\0\leq 6\\\\True[/tex]
Given the roots 2, -3, 4 that has to pass through the point (1, 10). What type of polynomial is this?
The polynomial passes through the point (1, 10), and having the roots 2, -3, and 4 is a cubic polynomial.
What is a polynomial?A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.
The polynomial having the highest power of 3 is called the cubic polynomial.
Given that the roots 2, -3, and 4 that has to pass through the point (1, 10).
The polynomial will be written as,
Y = (x-2)(x+3)(x-4)
Y = x³+x²-6x-4x²-4x=24
Y = x³-3x²-10x+24
Therefore, the polynomial passes through the point (1, 10), and having the roots 2, -3, and 4 is a cubic polynomial.
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Rhombus $abcd$ has perimeter $148$, and one of its diagonals has length $24$. How long is the other diagonal?.
The other diagonal is $70 long.
Given:
Rhombus $abcd$ has perimeter $148$, and one of its diagonals has length $24$.
P = 148 and d = 24
Area [tex]= 1/4 d \sqrt{P^2-4d^2}[/tex]
= 1/4(24)[tex]\sqrt{148^2 - 4*24^2}[/tex]
= 6 [tex]\sqrt{21904-4*576}[/tex]
= 6*[tex]\sqrt{21904-2304}[/tex]
= 6*[tex]\sqrt{19600}[/tex]
= 6*140
= 840
Area = d*d1 / 2
840 = 24 * d1 / 2
840 * 2 = 24 * d1
1680/24 = d1
d1 = $70
Therefore The other diagonal is $70 long.
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Answer:
70
Step-by-step explanation:
The four sides of a rhombus all have equal length, so if the perimeter is 148, then each side has length 148/4 = 37. Also, the diagonals of a rhombus bisect each other at right angles, so the diagonal of length 24 is cut into two pieces of length 12. We can show this information in a diagram (shown below.)
Applying the Pythagorean Theorem to any of the four right triangles in our diagram, we have
12² + x² = 37².
Solving this equation for positive x, we get x = √37² - 12² = √1369 - 144 = √1225 = 35. The length of the long diagonal is x + x = 70.
Graph this inequality:
y≤-2
Form a polynomial with real coefficients having the given degree and zeros. Degree 4; zeros: multiplicity 2 Question content area bottom Part 1 Let a represent the leading coefficient. The polynomial is . (Type an expression using x as the variable. Use integers or fractions for any numbers in the expression. Simplify your answer.)
The equation of the polynomial equation P(x) = (x + 3)²(x - 5)²
How to determine the polynomial equation?The given parameters are
Degree of polynomial = 4-3 is a zero of multiplicity 25 is the only other zeroThe sum of multiplicities of the polynomial equation must be equal to the degree.
This means that the multiplicity of the zero 5 is 2
The equation of the polynomial is then calculated as
P(x) = (x - zero)^multiplicity
So, we have
P(x) = (x - (-3))² * (x - 5)²
This gives
P(x) = (x + 3)²(x - 5)²
Hence, the equation is P(x) = (x + 3)²(x - 5)²
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Possible question
Form a polynomial with real coefficients having the given degree and zeros.
Degree 4;
Zeros: -3 and 5 with multiplicity 2
find the annual salary of a person who is paid $3,800.00 per month
solve by the chain rule
4^5x-9
By chain rule, the first derivative of the composite function f(x) = [tex]4^{5\cdot x - 9}[/tex] is equal to [tex]4^{u}[/tex] · 5 · ㏑ 4.
How to determine the derivative of a composite function
Herein we have the case of a composite function, that is, a function of the form f[u(x)]. Chain rule is a derivative rule used to find the derivative of composite functions, which is now defined:
df / dx = (df / du) · (du / dx)
If we know that u(x) = 5 · x - 9 and f(u) = [tex]4^{u}[/tex], then the derivative of the compond function is:
df / du = [tex]4^{u}[/tex] · ㏑ 4
du / dx = 5
Then, by chain rule:
df / dx = [tex]4^{u}[/tex] · 5 · ㏑ 4
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how would you solve for v :
1/u + 1/v = 1/f
Step-by-step explanation:
[tex] \frac{1}{u} + \frac{1}{v} = \frac{1}{f} [/tex]
[tex] \frac{1}{v} = \frac{1}{f} - \frac{1}{u} [/tex]
[tex] \frac{1}{v} = \frac{u - f}{uf} [/tex]
[tex]v = \frac{uf}{u - f} [/tex]
Write an exponential decay function in the form f(x)=ab^x for each of Car A and Car B. Explain how you determined the value of b for each function.
Answer:
A: 8750(0.88^x)
B: 9995(0.82^x)
Step-by-step explanation:
You want an exponential decay function for cars A and B given their cost and their "decay factor."
Exponential functionIn general, an exponential function has the form ...
value = (initial value)·(growth factor)^x
The growth factor is usually defined as ...
growth factor = 1 + growth rate
where the "growth rate" is often expressed as a percentage or a fraction.
Your form for f(x) has a=(initial value) and b=(growth factor).
The value of x will be zero at the point where the initial value applies. It will increase by 1 unit for each interval in which the growth factor applies.
ApplicationCar A
The initial value is presumed to be the Cost. What is called the "growth rate" above is the opposite of what is called the "Decay Factor" in this problem. That is ...
(initial value) = Cost = 8750(growth factor) = 1 - Decay Factor = 1 -0.12 = 0.88x = years after 2015The exponential function is then ...
f(x) = 8750·(0.88^x)
Car B
For this car, we have ...
(initial value) = Cost = 9995(growth factor) = 1 - Decay Factor = 1 -0.18 = 0.82x = years after 2017The exponential function is then ...
f(x) = 9995·(0.82^x)
Given: തതതത is a midsegment of ∆. Show all work.
a. Find the value of x and y.
b. What is the length of തതതത?
Step-by-step explanation:
since it is a mid-segment, DGH and DEF are similar triangles with the constant scaling factor of 2 for the lengths of all sides and other lines in the triangle.
e.g.
DE = 2 × DG
DF = 2 × DH
and therefore,
28 = 2 × GH = 2× (x - 3)
14 = x - 3
x = 17
HF = x - 7 = 17 - 7 = 10
DH = HF = 10
so,
y + 8 = 10
y = 2
and DF = 10 + 10 = 20
Which point is located in Quadrant III?
[tex](- \frac{3}{2} , -\frac{1}{4} )[/tex] will be located in Quadrant III
What are Quadrants?
A two-dimensional Cartesian plane system's x- and y-axes divide the plane into four infinite regions known as quadrants. The x-axis, sometimes known as the horizontal line, and the y-axis, often known as the vertical line, meet at a right angle. The reference point is often where two lines connect. This point serves as the reference (or initial point) for all measurements made using the coordinate system.
Simply said, a quadrant is the area of a cartesian plane where the x- and y-axes cross each other.
Coordinate plane with four quadrants
According to those values, the graph is then divided into four quadrants or portions.
The first quadrant is located in the top right-hand corner of the graph. The values of x and y in this quadrant are both positive.Second Quadrant: The second quadrant is located in the upper left-hand corner of the graph. The value of x is negative while the value of y is positive in this quadrant.Third Quadrant: The third quadrant is located in the lower left-hand corner of the graph. It includes the negative x and y values.Fourth Quadrant: The fourth quadrant is located in the lower right corner and has a positive x value and a negative y value.Learn more about Quadrants from the link below
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PLEASE HURRY WILL GIVE BRAINILY Find the area of this triangle.
155
175
260
Area = [?] units²
Answer:
Area = 1/2 * base * height
Area = 1/2 * 155 * 175
Area = 13,563.75
The water level in a tream roe 2 1/4 inche every hour for 4 1/2 hour. How many inche did the water level rie during that time?
the water level in the stream rises by 10.125 inches.
What is water level?
The elevation of a sea, stream, lake, or reservoir's free surface in relation to a given vertical datum is referred to as the water level, also known as gauge height or stage.
Main body:
According to question water level in stream rises by 2.25 inches every hour.
Total rise can be calculated by using simple multiplication.
Total time for ride = 4.5 hours
Total rise in stream level = total time * total rise in 1 hour
= 2.25*4.5
= 10.125 inches
Therefore total rise in stream is 10.125 inches.
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How do you find the x for this ?
Effie and Kristen live 23.6 km apart. They decided to cycle to the pool at the park, which is located between their homes. If Jennifer lives 5.2 km closer to the park, how far did they each cycle?
Answer:
I think 28.6
Step-by-step explanation: