#1 Write the quadratic function in vertex
form given a vertex of (-1,-2) and a
second point on the graph at (3,-10)
A. y = -3(x - 1)² + 2
B. y=-34 (x + 1)² + 2
C. y = -2(x - 1)²-2
D. y=-2 (x + 1)²-2
Answers
The quadratic function in vertex form is y = -1/2(x + 1)^2 - 2
How to determine the quadratic function in vertex form?The vertex is given as
(h, k) = (-1,-2)
The point is also given as
(x, y) = (3, -10)
Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
Substitute (h, k) = (-1,-2) in y = a(x - h)^2 + k
y = a(x + 1)^2 - 2
Substitute (x, y) = (3, -10)
-10 = a(3 + 1)^2 - 2
So, we have
-10 = a(4)^2 - 2
Add 2 to all sides
-8 = a(16)
Divide by 16
a = -1/2
Substitute a = -1/2 in y = a(x + 1)^2 - 2
y = -1/2(x + 1)^2 - 2
Hence, the equation is y = -1/2(x + 1)^2 - 2
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Related Questions
Solve for d. −8+6=−10+10
Answers
we need to find d=equation, so:
−8+6=−10+10
-8d=-10k+10-6
-8d=-10k+4
d=(-10k+4)/(-8)
\(\begin{gathered} d=\frac{-10}{-8}k+\frac{4}{-8} \\ d=\frac{5}{4}k-\frac{1}{2} \end{gathered}\)So the answer is:
d=(5/4)k-1/2
or
d=1.25k-0.5
Which inequality is true when the value of U is 17
Answers
TRIANGLE ABC IS DILATED BY A SCALE FACTOR OF 0.5 WITH THE ORIGIN AS THE CENTER OF DILATION, RESULTING IN THE IMAGE TRIANGLE A'B'C. IF A=(2,2). IF A (2,2), B= (4,3) AND C=(6,3), WHAT IS THE LENGTH OF LINE B'C'?
Answers
Answer: The length of the line B'C" is 1 unit.
Step-by-step explanation:
Given: Triangle ABC is dilated by a scale factor of 0.5 with the origin as the center of dilation , resulting in the image Triangle A'B'C'.
If A (2,2), B= (4,3) and C=(6,3).
Distance between (a,b) and (c,d): \(D=\sqrt{(d-b)^2+(c-b)^2}\)
Then, BC \(=\sqrt{(3-3)^2+(6-4)^2}\)
\(\\\\=\sqrt{0+2^2}\\\\=\sqrt{4}\\\\=2\text{ units}\)
Length of image = scale factor x length in original figure
B'C' = 0.5 × BC
= 0.5 × 2
= 1 unit
Hence, the length of the line B'C" is 1 unit.
Explaining the Multiplication and
Explain the rules for multiplication and division comet
units. How do you know when to multiply and when
divide to convert units of measurement
Write three to four sentences
Answers
sample response: To convert larger units to smaller units, multiply. When the units are smaller, you need more of them to express the same measure. To convert smaller units to larger units, divide. When the units are larger, you need fewer of them to express the same measure.
Find the least number which should be Subtracted from 56037 so that the difference is exactly divisible by 139.
Answers
Answer:
Answer will be 55898.
Step-by-step explanation:
In a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, Paul has scored 82 , 88 , and 87 on the first three. What range of scores on the fourth test will give Paul a C for the semester (an average between 70 and 79 , inclusive)? Assume that all test scores have a non-negative value.
Answers
Scores between 23 & 59 will give Paul a C for the semester (an average between 70 and 79).
The sum of the scores on the first three, hundred point tests
= 82 + 88 + 87 = 257.
The total score required in four 100-point tests to get an average score of 70 = 70X4= 280.
The total score required in four 100-point tests to get an average score of 79 = 79X4= 316.
Therefore, the score on the fourth test should be between (280-257) & (316-57) i.e, 23 & 59 to get an average score of 70 & 79.
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HALP HALP HALP PLS HALP
Answers
Answer:
a) 0.375 or 3/8
b) 0.5384615385 or 7/13
In a survey, the planning value for the population proportion is p*= 0.25. How large a sample should be taken to provide a 95% confidence interval with a margin of error of 0.06? Round your answer up to the next
whole number.
Answers
The sample should be taken to provide a 95% confidence interval is 200.
What is a confidence interval?A confidence interval is made up of the mean of your estimate plus and minus the estimate's range. This is the range of values you expect your estimate to fall within if you repeat the test, within a given level of confidence.
Confidence is another name for probability in statistics.
Given the planning value for the population proportion,
probability, p = 0.25
q = 1 - p = 1 - 0.25
q = 0.75
margin of error = E = 0.06
value of z at 95% confidence interval is 1.96,
the formula for a sample is,
n = (z/E)²pq
n = (1.96/0.06)²*0.25*0.75
n = 200.08
n = 200 approx
Hence sample size is 200.
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Jalen lost 12 pounds in the first 3 weeks of his diet. After this point, his weight loss rate slowed by half. If he lost a total of 84 pounds, how many weeks did it take him? lbs 100
Answers
Answer:
Step-by-step explanation:
Jalen lost 12 pounds in the first 3 weeks
12/3=4 per week
than the weight loss slowed by half, meaning he lost 6 pounds in 3 weeks
6/3=2 per week
84-12=72 to loose after 3 weeks
72/2=36 weeks
to loose 84 pounds you need 3+36=39 weeks
for 100 lbs
100-12=88
88/2=44
44+12=56 weeks
Which choice is equivalent to √3 *√8*√5
A. 2√30
B. 4√30
C. 10√12
D. 24√5
Answers
\(\implies {\blue {\boxed {\boxed {\purple {\sf { A. \:2 \sqrt{30} }}}}}}\)
\(\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}\)
\( = \sqrt{3} \times \sqrt{8} \times \sqrt{5} \)
\( = \sqrt{3 \times 2 \times 2 \times 2 \times 5} \)
\( = \sqrt{ ({2})^{2} \times 2 \times 3 \times 5} \)
\( = 2 \sqrt{2 \times 3\times 5} \)
\( = 2 \sqrt{30} \)
Note:\( \sqrt{ ({a})^{2} } = a\)
\(\bold{ \green{ \star{ \orange{Mystique35}}}}⋆\)
Answer:
A. 2√30
Step-by-step explanation:
\( \small \sf \: \sqrt{3} \times \sqrt{8} \times \sqrt{5} \\ \)
split √8
\( \small \sf \leadsto \sqrt{3 × 2 × 2 × 2 × 5} \)
\( \small \sf \leadsto \: 2 \sqrt{2 \times 3 \times 5} \)
\( \small \sf \leadsto \: 2 \sqrt{30} \)
For one year of internet service, the total cost is $400 which includes a one time set-up fee of $40. What is the monthly fee?
Answers
Answer:
The monthly fee is $30. (400-40 = 360 ; 360/12= 30)
Answer:
30$
Step-by-step explanation:
Simplify (w3)4•(w5)2
Answers
Answer:
\(w^{22}\)
Step-by-step explanation:
\((w^3)^4\cdot(w^5)^2=w^{3*4}\cdot w^{5*2}=w^{12}\cdot w^{10}=w^{12+10}=w^{22}\)
In a city of 32,000 people, there 10,000 under 25 years of age. What percent of the populations under 25?
Answers
Answer:
31.25%
Step-by-step explanation:
10 out of 32 is 31.25% all i did was that since its the same but just times 1000
To solve 12x = 192,_______ both sides of the equation by 12.
Answers
Answer:
To solve this equation, divide both sides by 12.
Step-by-step explanation:
You have to get x alone, and in order to do this, divide by 12
solve the PDE using separation of variables method Uxx = 1/2 Ut 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)
Answers
The general solution of the partial differential equation is:
U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)
How to solve Partial Differential Equations?The partial differential equation (PDE) is given as:
Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)
Assume that the solution can be written as a product of two functions:
U(x, t) = X(x)T(t)
Substituting this into the PDE, we have:
X''(x)T(t) = (1/2)X(x)T'(t)
Dividing both sides by X(x)T(t), we get:
(X''(x))/X(x) = (1/2)(T'(t))/T(t)
Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:
(X''(x))/X(x) = -λ²
(1/2)(T'(t))/T(t) = -λ²
Simplifying the second equation, we have:
T'(t)/T(t) = -2λ²
Solving the second equation, we find:
T(t) = Ce^(-2λ²t)
Applying the boundary condition U(0, t) = 0, we have:
U(0, t) = X(0)T(t) = 0
Since T(t) ≠ 0, we must have X(0) = 0.
Applying the boundary condition U(3, t) = 0, we have:
U(3, t) = X(3)T(t) = 0
Again, since T(t) ≠ 0, we must have X(3) = 0.
Therefore, we can conclude that X(x) must satisfy the following boundary value problem:
X''(x)/X(x) = -λ²
X(0) = 0
X(3) = 0
The general solution to this ordinary differential equation is given by:
X(x) = Asin(λx) + Bcos(λx)
Applying the initial condition U(x, 0) = 5*sin(4πx), we have:
U(x, 0) = X(x)T(0) = X(x)C
Comparing this with the given initial condition, we can conclude that T(0) = C = 5.
Therefore, the complete solution for U(x, t) is given by:
U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)
where:
Σ represents the summation over all values of n
λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).
To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):
X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0
X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0
From the first equation, we have Bₙ = 0.
From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.
This implies that 3λₙ = nπ, where n is an integer.
Therefore, λₙ = (nπ)/3.
Substituting the eigenvalues into the general solution, we have:
U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)
where Aₙ are the coefficients that can be determined from the initial condition.
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Which statement is false?
ОА.
The inequality sign always opens up to the larger number.
OB
The greater number in an inequality is always above the other number on the vertical number line.
P.S: Plato user and no links please people send them for no reason
Ос.
The smaller number in an inequality is always located to the left of the other number on the horizontal number line.
OD. The inequality Chign always opens up to the smaller number.
Answers
Answer:
D. The inequality sign always opens up to the smaller number.
Step-by-step explanation:
Well if A says sign always opens up to larger number and D says sign always opens up to smaller number so 1 of them must be false. Inequality signs always open up to greater number so the answer is D.
Find the value of each variable
X=
Y=
Please help:(
Answers
The missing sides of the right triangles are listed below:
Case 1
x = 13, y = 13√2
Case 2
x = 15√2, y = 15√2
Case 3
x = 6, y = √3
Case 4
x = 17√3, y = 17
Case 5
x = 10, y = 10
Case 6
x = 50, y = 25
Case 7
x = 2√7, y = 2√7
Case 8
x = 16√3, y = 48
Case 9
x = 11√3, y = 33
Case 10
x = 3√2, y = 2√6
Case 11
x = √10, y = 2√5
Case 12
x = 4√7, y = 8√7
How to determine sides of right triangles by trigonometric functions
Herein we find twelve cases of right triangles with two sides that must be determined by means of trigonometric functions. The fundamental trigonometric functions are defined below:
sin θ = y / r
cos θ = x / r
tan θ = y / x
Where:
y - Leg opposite to the angle.x - Leg adjacent to the angle. r - HypotenuseNow we proceed to determine the missing sides for each case:
Case 1
y = 13 / sin 45°
y = 13√2
x = 13 · tan 45°
x = 13
Case 2
x = 30 · sin 45°
x = 15√2
y = 30 · cos 45°
y = 15√2
Case 3
x = 3 / cos 60°
x = 6
y = 3 / tan 60°
y = √3
Case 4
x = 34 · cos 30°
x = 17√3
y = 34 · sin 30°
y = 17
Case 5
x = 10√2 · cos 45°
x = 10
y = 10√2 · sin 45°
y = 10
Case 6
x = 25√3 / sin 60°
x = 50
y = 25√3 / tan 60°
y = 25
Case 7
x = 2√14 · cos 45°
x = 2√7
y = 2√14 · sin 45°
y = 2√7
Case 8
x = 24 / cos 30°
x = 16√3
y = 24 / sin 30°
y = 48
Case 9
x = 22√3 · cos 60°
x = 11√3
y = 22√3 · sin 60°
y = 33
Case 10
x = √6 / tan 30°
x = 3√2
y = √6 / sin 30°
y = 2√6
Case 11
y = √10 / cos 45°
y = 2√5
x = √10 · tan 45°
x = √10
Case 12
x = 4√21 / tan 60°
x = 4√7
y = 4√21 / sin 60°
y = 8√7
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Find the number line with the correct letter placement for each value.
A=73,B=−67,C=127,D=−1.35
Choose one correct answer.''
Answers
Answer:
Step-by-step explanation:
a
true or false
A political party is a group of people who seek to control government by winning elections and holding office
Answers
Answer:
True
Step-by-step explanation:
Eg. Republican party nominates a candidate to be considered by the people [hopefully voted] into office. If they win the election, they control a part of government in office.
The ratio of dogs to cat at the animal shelter is 6.7. if there are 42 cats how many dogs are there
Answers
Answer:
36 dogs
Step-by-step explanation:
If our original rate is 6/7 (6 dogs per 7 cats) Then we can divide the number of cats by 7 to get 6. We are then going to do 6 x 6. We get 36 dogs.
which function will have the greatest value at
\(x = 16 \)
\( y = {10}^{16} \)
\(y = {x}^{2} - 17x + 182\)
\(y = {1.17}^{x} \)
Answers
The function that would have the greatest value at x = 16 include the following: B. y = x² - 17x + 182.
How to determine the corresponding output value for the given function?In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.
In this exercise, we would determine the corresponding output value for this function of y based on the x-value (x = 16) in simplified form as follows;
\(y = 10^{16}\)
y = 10,000,000,000,000,000.
y = x² - 17x + 182
y = 16² - 17(16) + 182
y = 256 - 272 + 182
y = 166.
\(y = 1.17^x\\\\y = 1.17^{16}\)
y = 12.330304108137675851908392069373.
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12 men and 10 women are asked about how long it takes them to get ready in the morning. The men had an average of 20 minutes with a standard deviation of 5 minutes while the women had an average of 28 minutes with a standard deviation of 10 minutes. Suppose you want to test the stereotype that women take longer getting ready than mean with alpha = 0.05.
Q1 What is the alternative hypothesis in this scenario? (Men are sample 1 and women are sample 2)
Mu1 < Mu2
Mu2 ? Mu2
Mu1 > Mu2
Q2 What is the test statistic?
a. -1.093
b. 0.532
c. -2.438
Q3 What is the critical value(s)?
a. 1.96
b. -1.645
c. -1.725
Answers
Answer:
Step-by-step explanation:
as much as I think I know this I don't I just need the points
cos s=-2/5 and sin t=4/5, s and t are in quadrant II
find cos(s+t) and cos(s-t)
No spam!
Answers
Your answer is attached.
Hope it helps you!
What is the solution to the system of linear equations?
(–4.5, 4.25)
(–1.7, –2.8)
(0, –7)
(3, 0.5)
Answers
Answer:
−903.65625
Step-by-step explanation:
((((−4.5)(4.25))(−1.7−2.8))(0−7))((3)(0.5))
=((−19.125(−1.7−2.8))(0−7))((3)(0.5))
=(((−19.125)(−4.5))(0−7))((3)(0.5))
=86.0625(0−7)(3)(0.5)
=(86.0625)(−7)(3)(0.5)
=−602.4375(3)(0.5)
=(−602.4375)(1.5)
=−903.65625
Determine whether the following equation defines y as a function of x. x² + y² = 7 Does the equation x² + y2 = 7 define y as a function of x? O yes no
Answers
Answer:
No
Step-by-step explanation:
No, the equation x² + y² = 7 does not define y as a function of x. This equation represents a circle centered at the origin with a radius of √7. For each value of x, there are two possible values of y (one positive and one negative) that satisfy the equation.
Answer:
No. The equation x² + y² = 7 does not define y as a function of x.
Step-by-step explanation:
The equation of a circle is:
\((x - h)^2 + (y - k)^2 = r^2\)
where:
(x, y) is a point on the circle.(h, k) is the center.r is the radius.From observation of the given equation, x² + y² = 7, we can see it represents a circle centered at the origin (0, 0) with a radius of √7.
In a function, for each x-value, there should be a unique y-value.
In the case of a circle, there are two possible y-values for each x-value due to the positive and negative square root.
Therefore, the given equation x² + y² = 7 does not define y as a function of x because it is a circle, and for each x-value there are two possible y-values.
Write each vector as a linear combination of the vectors in S. (Use
s1 and s2,
respectively, for the vectors in the set. If not possible, enter IMPOSSIBLE.)
S = {(1, 2, −2), (2, −1, 1)}
(a) z = (−3, −1, 1)
z =
(b) v = (−2, −5, 5)
v =
(c) w = (1, −23, 23)
w =
(d) u = (3, −6, −6)
u =
Answers
The equation can be written as a linear combination of the vectors in S:
z = 5*(1, 2, −2) -1*(2, −1, 1)
v = -2*(1, 2, −2) + 7*(2, −1, 1)
w = -12*(1, 2, −2) + 11*(2, −1, 1)
What is the linear combination?
Linear combination is the process of adding two algebraic equations so that one of the variables is eliminated. Addition or subtraction can be used to perform a linear combination.
(a) z = (−3, −1, 1)
We can write z as a linear combination of the vectors in S by using the following equation:
z = as1 + bs2
Here, we can find the values of a and b by solving the following system of equations:
-3 = a1 + b2
-1 = a2 + b(-1)
1 = a*(-2) + b*1
Solving this system of equations, we get:
a = 5
b = -1
Therefore, z can be written as a linear combination of the vectors in S as:
z = 5*(1, 2, −2) -1*(2, −1, 1)
(b) v = (−2, −5, 5)
we can write v as a linear combination of the vectors in S by using the following equation:
v = as1 + bs2
Here, we can find the values of a and b by solving the following system of equations:
-2 = a1 + b2
-5 = a2 + b(-1)
5 = a*(-2) + b*1
Solving this system of equations, we get:
a = -2
b = 7
Therefore, v can be written as a linear combination of the vectors in S as:
v = -2*(1, 2, −2) + 7*(2, −1, 1)
(c) w = (1, −23, 23)
we can write w as a linear combination of the vectors in S by using the following equation:
w = as1 + bs2
Here, we can find the values of a and b by solving the following system of equations:
1 = a1 + b2
-23 = a2 + b(-1)
23 = a*(-2) + b*1
Solving this system of equations, we get:
a = -12
b = 11
Therefore, w can be written as a linear combination of the vectors in S as:
w = -12*(1, 2, −2) + 11*(2, −1, 1)
Therefore, The equation can be written as a linear combination of the vectors in S:
z = 5*(1, 2, −2) -1*(2, −1, 1)
v = -2*(1, 2, −2) + 7*(2, −1, 1)
w = -12*(1, 2, −2) + 11*(2, −1, 1)
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HELP QUICK PLS HELP QUICK PLS
Answers
Answer:
I THINK ITS • (4X2+32X+64-π(x2+2x+1))Step-by-step explanation:
i hope it helps :)
12.
What is the area of a square if the sides are 2 1/2 meters long?
Answers
Answer:
6.25
Step-by-step explanation:
Find the value of x. Pythagorean theorem and its converse
Answers
find the reduced racial form of each expression:
1: 3^√4/9m^2 ?
2:√63-√700–√112 ?
3: (a^2b^8/a^1/3)^3/4 ?
4: ^4√1024x^9y^12 ?
5:4^3√81 - 2^3√72 - ^3√24 ?
6: ^5√2pq^6 • 2 √2p^3q ?
HELP PLEASE ILL DO ANYTHING. (show explanation pls)
Answers
The reduced radical forms of the expressions provided are as follows:
1. 3^(4/9m)
2. -11√7
3. a^(1/2) * b^6
4. 2x^(9/4) * y^3
5. 16 - ^3√24
6. 4p^(9/10)q^(7/10)
What is a reduced radical form?A reduced radical form is a way of simplifying expressions that contain radicals such as square roots and cube roots, as much as possible. In a reduced radical form, the radical is simplified to its lowest possible terms.
To obtain the reduced radical forms of the expresions, we can proceed with the workings:
1. 3^(√4/9m^2) = 3^(2/3 * 1/3√4m^2) (since √4 = 2)
= (3^(2/3))^(1/3√4m^2)
= (3^(2/3))^(2/3m)
= 3^(4/9m)
2. √63 = √(9 * 7) = 3√7
√700 = √(100 * 7) = 10√7
√112 = √(16 * 7) = 4√7
√63 - √700 - √112 = 3√7 - 10√7 - 4√7
= -11√7
3. (a^2b^8/a^1/3)^3/4 = (a^2/1/3√a)^3/4 * b^8^3/4
= (a^(2/3))^3/4 * b^6
= a^(1/2) * b^6
4. ^4√1024x^9y^12 = (^4√1024) * (^4√x^9) * (^4√y^12)
= 2 * x^(9/4) * y^(12/4)
= 2x^(9/4) * y^3
5. 4^3√81 = 4^3 * 3 = 64
2^3√72 = 2^3 * 2√9 = 16√9 = 48
^3√24 can't be simplified any further
4^3√81 - 2^3√72 - ^3√24
= 64 - 48 - ^3√24 or 16 - ^3√24.
6. ^5√2pq^6 • 2 √2p^3q
= 2p^(3/5)q^(6/5) * 2p^(3/2)q^(1/2)
= 4p^(9/10)q^(7/10)
So, the results are the simplified or reduced forms of the expressions.
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