The equation y = 2x² - 12x + 23 describes the function graph that includes a vertex at (3, 5) and passes through the point (5, 13).
What does a parabolic equation look like in vertex form?The vertex of a parabolic equation is at the point and the vertex form is y = a(x - h)2 + k, where a, h, and k are constants (h, k).
How do you answer this dilemma?Find the function whose graph has the vertex at (3, 5) and passes through the point in the question (5, 13).
Assuming it to be a parabolic function, we know that a parabolic equation's vertex form is y = a(x - h)2 + k, where a, h, and k are constants, and the vertex is located at the position (h, k).
As the vertex of the necessary function is at the position (3, 5), we may substitute h = 3 and k = 5 to obtain the following equation in the above equation:
y = a(x - 3)² + 5
Now that we know that the graph passes through the point (5, 13), we can change the original equation to read:
13 = a(5 - 3)² + 5,
or, 13 = 4a + 5,
or, 4a = 13 - 5 = 8,
or, a = 2.
We obtain the following from the equation y = a(x - h)2 + k by inserting a = 2, h = 3, and k = 5:
y = 2(x - 3)² + 5,
alternatively, y = 2(x² - 6x + 9) + 5,
alternatively, y = 2x² - 12x + 18 + 5,
Alternatively, y = 2x² - 12x + 23.
As a result, the function graph with the vertex at (3, 5) and the point of intersection (5, 13) yields the equation y = 2x² - 12x + 23.
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What is the value of r in the equation 6(1 + 2r) - 3(1 - 8r) = 75?
Answer:
2
Step-by-step explanation:
[tex]6(1+2r)-3(1-8r)=75 \\ \\ 6+12r-3+24r=75 \\ \\ 3+36r=75 \\ \\ 36r=72 \\ \\ r=2[/tex]
f(x) = 3 x + 1 and g (x) = 2x - 3. find f (g(x)) and g (f(x))
Step-by-step explanation:
f(x} = 3x + 1
g(x} = 2x -- 3
f(g(x)) = 3x + 1. (Calm down right?)
Let the x in the expression be (2x -- 3)
N.B x = g{x}
f(g(x)) = 3(2x --3} + 1
Open bracket
f(g(x)) = 6x -- 9 + 1
f(g(x)) = 6x -- 8...
2... Solve for g(f(x)), using the same strategy
g(f(x)) = 2x -- 3
x = f(x)
g(f(x)) = 2(3x + 1) -- 3
g(f(x)) = 6x + 2 -- 3
g(f(x)) = 6x -- 1
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Answer:
Step-by-step explanation:
f(g(x)) means substituting g(x) in f(x)
ie, 3(2x-3)+1 = 6x-9+1 = 6x - 8
g(f(x)) means substituting f(x) in g(x)
ie, 2(3x+1)-3 = 6x2-3 = 6x - 1
Select the correct answer from each drop down-menu.
Which are the best definitions for theorem, conjecture, and axiom?
A statement that is assumed to be true without proof is a(n)
. A statement that has been shown to be true by vigorous application of logic is a(n)
. A(n)
is a statement that is believed to be true but hasn't been proven.
A statement that is assumed to be true without proof is a(n) Theorem
A statement that has been shown to be true by vigorous application of logic is a(n) ---> Conjecture
A(n) Axiom is a statement that is believed to be true but hasn't been proven.
What's the big difference between a definition and a theorem?A definition is both a precise and a general statement of the significance of a mathematical term.
It does this by laying down all of the characteristics of the word together with the structures that need to be true.
This is how the meaning of the word is defined. A mathematical assertion that can be demonstrated using logically sound mathematical reasoning is called a theorem.
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Evaluate the expression when a = 2 and x = -4.
2a-x
The expression when a = 2 and x = -4, given 2a-x. The value will be 8.
What are mathematical operations?In mathematics, an operation is a function that transforms zero or more arguments or operands into a clearly defined output value. The number of operands in the operation determines how difficult it is.
Unary operations (i.e., operations of arity 1), which include additive inverse and multiplicative inverse, as well as binary operations (i.e., operations of arity 2), which include addition and multiplication, are the operations that are most frequently studied. The nullary operation, also referred to as a zero-arity operation, is a constant. The mixed product is an example of a ternary operation, also referred to as an operation of arity 3.
The arity is typically assumed to be limited. Even yet, infinitary operations are occasionally taken into account, in which case the "typical" operations of finite dimensionality are referred to as finiteary operations.
Similar to an operation, but with partial function in place of a function, is the definition of a partial operation.
Since, a= 2 and x= -4, then,
2(2)-(-4)= 8
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Flora is buying dog food for her dog. She wants to buy enough to last five weeks (35 days). If her dog eats 2 cups in a day, and there are 24 cups in each bag, how many bags of dog food does Flora need to buy to last 5 weeks? ⛔️ SOLVE USING A PROPORTIONAL RELATIONSHIP GRAPH! ⛔️
When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b.
Flora needs 3 bags of dog food.
How to find the food bags needed?When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b.
An equation in which two ratios are made equal is known as a percentage.
As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls.
Given,
Dog eats 2 cups in a day
There are 24 cups in each bag
Solution:
Dog eats one bag of food in 24 cups/2 cups = 12 days
One food bag is sufficient to feed the dog for 12 days
For 35 days, the number of food bags needed is
1/x = 12/35 where x be the number of food bags needed for the dog.
x = 2.92
That is 3 bags of dog food are needed for 35 days to feed the dog.
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A saleswoman earns 9% commission on all the merchandise that she sells. Last month she sold $6000 worth of merchandise. How much commission (in dollars) did she earn last month?
Answer: she gets 540
Step-by-step explanation:
She earns 540 dollars since the saleswoman only gets 9% of it and she sold $6000 dollars worth of merchandise you divide by percentage
Example: 1. Find the percentage of the original or real number. In this case, it's 500.
2. Multiply the final number by 100. 500 x 100 = 50,000.
3. Divide the result of the multiplication by the percentage. 50,000 divided by 40% = 1,250. Thus, 500 is 40% of 1,250.
Can somebody help me with this please?
From the given figure < BAC = 180 - ( < ABC + < BCA ) because they are sum of angles in a triangle
How to find < BACgiven data
< ABC = 52 degrees
< BCA = 88 degrees
calculation for angle BAC
< ABC + < BCA + < BAC = 180 degrees ( sum of angles in a triangle )
< BAC = 180 - ( < ABC + < BCA )
< BAC = 180 - < ABC - < BCA
plugging in the values gives
< BAC = 180 - 52 - 88
< BAC = 180 - 140
< BAC = 40 degrees
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6. Joshua took a bus from Orlando to Atlanta. The bus traveled 420 miles in 6 hours. What was the
average speed of the bus?
a) 60 miles per hour
b) 65 miles per hour
c) 70 miles per hour
d) 75 miles per hour
Determine the angle of rotation
Answer: b
Step-by-step explanation:
:)
let’s review some basics of probability. a bag of skittles has 9 reds, 10 oranges, 7 yellows, 8 purples, and 6 greens. what is the probability of a red skittle if one is selected at random?
Answer:
7/20
Step-by-step explanation:
is always right use without the s
The subtraction of 8 from a number is 2. What is the number?
Answer:6
Step-by-step explanation:
8-6 = 2
Answer:
10
Step-by-step explanation:
Let the number be equal to y
y-8=2y=8+2y=10Information is given about a polynomial f(x) whose coefficients are real
numbers. Find the remaining zeros of f.
Degree 3; zeros: -4, -2- i
The remaining zero(s) of f is
(Use a comma to separate answers as needed.)
Answer: -2+i
Step-by-step explanation:
By the conjugate root theorem, since the coefficients are real, the complex conjugate of a root must also be a root.
If Aaron buys 5 watermelons for 9 how much would 4 cost at the same rate?
Answer: $ 7.20
Step-by-step explanation:
(9x4)/5
36/5
= 7.2
= $7.20
a 13-foot ladder is leaning against a wall. if we pull the ladder away from the wall at a rate of 1ft/s, how fast is the top of the ladder moving down the wall when the bottom of the ladder is 12ft from the wall?
After solving the question using Pythagoras' theorem we get, The ladder moving down the wall at 8 feet per second.
According to the question,
The bottom(base) of the ladder is 12 feet,
the height of the ladder is 13 feet.
Now, We have to find the top of the ladder moving down the wall
by using Pythagoras' theorem,
hypotenuse ^2 = base^2 + perpendicular ^2
13^2 = x^2 + y^2
169 = x^2 + y^2
After using Pythagoras' theorem
we have this equation and now we will differentiate both sides:
0 =2x*dx/dt + 2y*dy/dt
0 =24*1 + 3* dy/dt
dy/dt = - 8 feet per second
Positive whole number we have to take.
So, dy/dt = 8 feet per second
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The graph of a function f(x) passes through the following points:
(0,-2), (1,0), (-1,0)
Which of the following could be f(x)?
> f(x) = -2x - 2
> f(x) = 2x - 2
> f(x) = (2\sqrt[x])-2
> f(x) = 2x^2 - 2
*109
eight feral 103721
Dante buys candy that costs $7 per pound. He will spend at least $42 on candy. What are the possible numbers of pounds he will buy? Use p for the number of pounds Dante will buy. Write your answer as an inequality solved for p
Answer:
p [tex]\geq[/tex] 6
Step-by-step explanation:
If one pound costs $7 and he's going to spend at least $42, then he will buy at least as many pounds as what costs $42.
42 divided by 7 equals 6, so he will buy at least 6 pounds of candy.
if a circle has a radius of 7 m then what is the circumference exactly
Darcie wants to simplify 20 over 24 fully.
What number should she divide both the
numerator and the denominator by in order
to simplify the fraction fully in one step?
Answer: 4
Step-by-step explanation:
This simplifies to 5/6.
So 20 / 5 = 4
and 24 / 6 = 4
If the measure of angle 2 is 70 degrees, what is the measure of angle 7?
A. 70; Ls 2 and 7 corresponding angles
B. 70; Ls 2 and 7 are alternate exterior angles
C. 120; 2s 2 and 7 are supplementary angles
D. Unable to determine
Answer:
B
Step-by-step explanation:
∠ 2 and ∠ 7 are alternate exterior angles and are congruent, then
∠ 7 = ∠ 2 = 70°
help fast i need to get this answer
Answer:
x = 3
Step-by-step explanation:
Plug in 1 for x:
- | 1 + 1 | + 5 = - |2| + 5 = -2 + 5 = 3
Find the volume of a solid bounded by the paraboloids [tex]\displaystyle{z=4x^2+4y^2}[/tex] and [tex]\displaystyle{z=5-6x^2-y^2}[/tex]
The two surfaces meet in an ellipse in some plane with [tex]0\le z\le5[/tex], since
[tex]4x^2 + 4y^2 = 5 - 6x^2 - y^2 \implies 10x^2 + 5y^2 = 5 \implies 2x^2 + y^2 = 1[/tex]
so the solid is bounded by the elliptical cylinder with this equation. In cylindrical coordinates, with
[tex]\begin{cases}x = \frac1{\sqrt2} r \cos(\theta) \\ y = r \sin(\theta) \\ z = \zeta \\ dV = dx\,dy\,dz = \frac1{\sqrt2} r \, dr \, d\theta \, d\zeta\end{cases}[/tex]
the solid is the set
[tex]\begin{array}{c} R = \left\{(r,\theta,\zeta) ~:~ 0\le r\le1 \text{ and } 0 \le\theta\le2\pi \text{ and } \right. \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \left.3r^2 - r^2 \cos(2\theta) \le \zeta \le 5 - 2r^2 - r^2 \cos(2t)\right\} \end{array}[/tex]
and the volume is given by the integral
[tex]\displaystyle \iiint_R dV = \frac1{\sqrt2} \int_0^{2\pi} \int_0^1 \int_{3r^2 - r^2 \cos(2\theta)}^{5 - 2r^2 - r^2 \cos(2\theta)} r \, d\zeta \, dr \, d\theta \\\\ ~~~~ = \frac1{\sqrt2} \int_0^{2\pi} \int_0^1 r(5 - 5r^2) \, dr \, d\theta \\\\ ~~~~ = \frac{10\pi}{\sqrt2} \int_0^1 (r - r^3) \, dr \\\\ ~~~~ = 5\sqrt2\,\pi \left(\frac12 - \frac14\right) = \boxed{\frac{5\pi}{2\sqrt2}}[/tex]
A match-seller arranges his matchboxes in a
triangular pattern as shown in Fig. 18.4. He
continues until there are 11 matchboxes in
the bottom row of the triangle. How many
matchboxes are in the complete pattern?
MATO
MATCHES
MATCHES
Fig. 18.4
MATCHES
MATCHES
MATCHES
MATCHES
MATCHES
MATCHES
MATCHES
MATCHES
Using the properties of an arithmetic sequence we can conclude that the total number of match boxes is 66.
There is a consistent distinction between the words in a sequence of numbers known as a "arithmetic progression" or "arithmetic sequence" (AP).
In an arithmetic series, the space between subsequent terms is constant. The numbers 3, 5, 7, and 9 come to mind. because there is always a two-term difference between two succeeding terms, it is arithmetic.We know that the bottom row of the pyramid has 11 matchboxes .
As we can see in the figure that the each succeeding step has one matchbox less.
Therefore the number of matchboxes in each row is in an AP.
Therefore the AP has a common difference of -1 and the first term is 11
The last term of the AP is 1.
Therefore
aₙ = a + (n-1)d
or, 1 = 11 + (n-1)(-1)
or, n = 11
We know that the sum of all terms of an AP is given by
S=n/2{2a+(n-1)d}
or, S = 11/2 {2×11 + (10)(-1)}
or, S = 66
Therefore from the arithmetic progression we calculate that the total number of match boxes is 66.
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Disclaimer: The missing diagram is attached below.
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answer these 2 questions for a cookie
Answer:
1. C
2. D
5. C
Step-by-step explanation:
Answer:
C as j is a variable
D
C as 13+9+1.9= 23.9
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what is the maximum number of balls of clay of radius 2 that can completely fit inside a cube of side length 7 assuming the balls can be reshaped but not compressed before they are packed in the cube?
Answer:
Number of balls of clay: 10
Step-by-step explanation:
The volume of the cube is [tex]$V_{\text{cube}}=7^3=343,$[/tex]
and the volume of a clay ball is: [tex]$V_{\text{ball}}=\frac43\cdot\pi\cdot2^3=\frac{32}{3}\pi.$[/tex]
Since the balls can be reshaped but not compressed, the maximum number of balls that can completely fit inside a cube is
[tex]\[\left\lfloor\frac{V_{\text{cube}}}{V_{\text{ball}}}\right\rfloor=\left\lfloor\frac{343}{\frac{32\pi}{3} }\right\rfloor.\][/tex]
Approximating with [tex]$\pi\approx3.14[/tex]
We have:
[tex]\[\left\lfloor\frac{V_{\text{cube}}}{V_{\text{ball}}}\right\rfloor=10.23565228[/tex]
We simplify to get:
[tex]\[\left\lfloor\frac{V_{\text{cube}}}{V_{\text{ball}}}\right\rfloor\approx10[/tex]
So:
[tex]\boxed{number\ of\ balls = 10}.$[/tex]
4. Mrs. Sparks is a 9th grade Algebra 1 teacher. She teaches three
Algebra 1 courses and all the classes recently took a chapter exam.
Below are the scores.
Class 1
45
68
77
90
90
95
100
100
86
90
50
55
Class 2
64
65
70
40
100
87
84
88
90
90
95
80
Class 3
70
75
75
90
100
80
55
65
76
80
88
99
a. Find the mean, median, mode and range of Class 1.
b. Find the mean, median, mode and range of Class 2.
c. Find the mean, median, mode and range of Class 3.
d. Find the standard deviation of Class 1.
e. Find the standard deviation of Class 2.
f. Find the standard deviation of Class 3.
g. Which class had a higher standard deviation and what does that mean?
h. In your opinion, which class did better on the exam? Explain your answer.
The mean of Class 1 is 78.83.
The median of Class 1 is 88
The mode of Class 1 is 90
The mean of Class 2 is 79.42
The median of Class 2 is 85.50
The mode of Class 2 is 90
The mean of Class 3 is 79.42
The median of Class 3 is 78
The mode of Class 3 are 75 and 80
The standard deviation of Class 1 is 18.81
The standard deviation of Class 2 is 16.15
The standard deviation of Class 3 is 12.70.
The class that had the higher standard deviation is class 1.
The class that did better on the exam is class 3 because it has the higher mean and the lowest standard deviation.
What is the mean, median and mode?Mean is the average of a set of numbers.
Mean = sum of numbers / total number
Mean of Class 1 = (45 + 50 + 55 + 68 + 77 + 86 + 90 + 90 + 90 + 95 + 100 + 100) / 12 = 78.83
Mean of Class 2 = (40 + 64 + 65 + 70 + 80 + 84 + 87 + 88 + 90 + 90 + 95 + 100) / 12 = 79.42
Mean of Class 3 = (55 + 65 + 70 + 75 + 75 + 76 + 80 + 80 + 88 + 90 + 99 + 100) / 12 = 79.42
Median is the number that is at the center of the dataset that is arranged in either ascending or descending order.
Median of Class 1 = (86 + 90) / 2 = 88
Median of Class 2 = (84 + 87) / 2 = 85.50
Median of Class 3 = (76 + 80) / 2 = 78
Mode is the number that occurs most frequently in a dataset.
Standard deviation is used to calculate the average variation of a dataset.
Standard deviation = [tex]\sqrt{\frac{(x - u)^{2} }{n} }[/tex]
Where:
x = number in the dataset u = mean n = total numbers in the dataset.Standard deviation of Class 1 = 18.81
Standard deviation of Class 2 = 16.15
Standard deviation of Class 3 = 12.70
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Answer:
Down below!
Step-by-step explanation:
A.
The mean 78.83.
The median 88
The mode 90
The range 55
B.
The mean 79.42
The median 85.50
The mode 90
The range 60
C.
The mean 79.42
The median 78
The mode 75 and 80
The range 45
D. 18.81
E. 16.15
F. 12.70
G. The class that had the higher standard deviation is class 1.
H. The class that did better on the exam is class 3 because it has the higher mean and the lowest standard deviation.
g(x)=1/4x+1
what is g(-16)?
When we're solving with functions, it's no different than solving from a regular equation.
In most cases, we only need to substitute x with a given value.
Solving the Question
[tex]g(x)=\dfrac{1}{4}x+1[/tex]
⇒ To find g(-16), plug in -16 as x:
[tex]g(-16)=\dfrac{1}{4}(-16)+1\\\\g(-16)=-4+1\\\\g(-16)=-3[/tex]
Answer-3
True or false? A corollary is a statement that can be easily proved using a
theorem.
O A. True
OB. False
SUBMIT
answer to this question for anyone who needs it
The theorem can be used to readily show the corollary because, according to its statement, it considerably depends on it. Consequently, the assertion is accurate.
The given statement is True.
Is the meaning of corollary?The term "corollary" refers to an outcome that follows logically from another action. You could claim that your rediscovered passion of reading is a corollary to the recent opening of a bookstore in your area. The term corollary describes the result of an action, such as the need to study more as a corollary to receiving a poor grade.
Briefing:A theorem states that two angles that add up to 180° and form a straight line are regarded as "supplementary."
A corollary of this is known as the "Vertical Angle Theorem," which asserts that where two lines intersect, their angles across from each other are equal (in the diagram, a=c and b=d).
The theorem can be used to readily show the corollary because, according to its statement, it considerably depends on it. Consequently, the assertion is accurate.
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Given the equation 13.25y = 79.5, determine the value of y.
6.00
66.25
92.75
1053.38
Given the equation 13.25y = 79.5, the value of y is A. 6.00.
What is an equation?An equation is a mathematical statement that states that two mathematical expressions are equal in value.
Equivalent values are also expressed as algebraic equations sharing the same root.
We depict equations by using the equation symbol (=).
13.25y = 79.5
y = 6 (79.5/13.25)
Check:
13.25y = 79.5
13.25(6) = 79.5
79.5 = 79.5
Thus, given the equation 13.25y = 79.5, the value of y cannot be 66.25, 92.75, or 1,053.38 but Option A.
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3 5/11 as a decimal exspansion
Answer: 3 5/11 should be 3.4545454545 as a decimal
Hope this helps!
Answer:
3 + 0.4545454545454545 = 3.454545454545455
Step-by-step explanation:
3 5/11 as a decimal exspansion
3 + (5 : 11) =
3 + 0.4545454545454545 =
3.454545454545455
Evaluate m + (n-1)^2 if m = 3 and n = -4
Answer:
Step-by-step explanation:Answer: using identity[(a+b)(a-b) = a^2 - b^2]. (m+n)(m-n) = m^2 - n^2. m^2 - n^2 = (3)^2 - (4)^2 = -7.