If A is 5, b is 5, and C is 6 the quadratic equation is in standard form using those numbers will be y = 5x² + 5x + 6 and the vertex of the parabola is (-0.2, 5.2)
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
It is given that,
a = 5, b = 5 and c = 6
The quadratic equation is in standard form as,
y = ax² + bx + c
Put the values as
y = 5x² + 5x + 6
Differentiate the above equation and equate to 0 to obtain the vertex point,
y' = 10x + 5
0=10x + 5
5x + 1 = 0
5x = -1
x = -0.2
Substitute the value of x as
y = 5x² + 5x + 6
y = 5(-0.2)² + 5(-0.2) + 6
y = 5.2
The vertex of the parabola is (-0.2, 5.2)
Thus, if A is 5, b is 5, and C is 6 the quadratic equation is in standard form using those numbers will be y = 5x² + 5x + 6 and the vertex of the parabola is (-0.2, 5.2)
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Find the 63rd term of the following arithmetic sequence.
17, 21, 25, 29, ...
Answer:
265
Step-by-step explanation:
the nth term of an arithmetic progression is given by
[a+(n-1)d]
where "a" is the first term, "d" is the common difference and "n" is the term you're looking for
from the question, a= 17
d=4
n=63
substituting, [17+(63-1)4]=[17+248]=265
Find the area of a circle
Answer: 452 cm squared
Step-by-step explanation:
Since the diameter is the radius times two, the radius of this circle is 24 divided by 2 which is 12. To find the area of a circle you multiply the radius by pi. Pi= 3.14, so 3.14(pi) times 12(radius)= 452.16 cm.
Answer:
452.16 ft²
Step-by-step explanation:
find radius
24 : 2 = 12 ft
find area (πr²)
π12² =
3.14 * 12² =
3.14 * 144 =
452.16 ft²
10. Which expression is equivalent to
(7.9x + 2)(0.5x)?
A. 3.95x² + 1
B. 3.95x2 + X
C. 7.9x² + 1
D. 7.9x² + 0.5x
Answer:
a.3.95x^2+1
9999999999999999999999999
let x1,x2,...,xn be a random sample of size n from the exponential dis- tribution with rate λ. find a 97% confidence interval (using explicitly computed critical values) for λ based on the x(1), the minimum of the sample. (hint: consider the distribution of nλx(1).
For given[tex]$\mathrm{n}$[/tex] and [tex]$\mathrm{X}_{(1)}$[/tex], we can obtain the confidence interval [tex]$(\mathrm{a}, \mathrm{b})$[/tex].
Let[tex]$\mathrm{X}_1, \mathrm{X}_2, \ldots, \mathrm{X}_{\mathrm{n}}$[/tex] be a sequence of size [tex]$\mathrm{n}$[/tex] from the exponential distribution with rate[tex]$\lambda$.[/tex] Then the probability density function of the random is a given [tex]$\mathrm{f}\left(\mathrm{x}_{\mathrm{i}}, \lambda\right)=\lambda \exp (-\lambda \mathrm{x}) ; \quad 0 \leq \mathrm{x} < \infty$[/tex]
Let us consider a ordered random sample of size [tex]$\mathrm{n}$[/tex] as [tex]$\mathrm{X}_{(1)}, \mathrm{X}_{(2)}, \ldots, \mathrm{X}_{(\mathrm{n})}$[/tex]. Then [tex]$\mathrm{X}_{(1)}$[/tex] is the smallest of the sample. The density function of the smallest sample [tex]$\mathrm{X}_{(1)}$[/tex] is give by
[tex]$$\mathrm{f}\left(\mathrm{X}_{(1)}, \lambda\right)=\mathrm{n}\left[1-\mathrm{F}_{\mathrm{x}}(\mathrm{x}, \lambda)\right]^{\mathrm{n}-1} \times \mathrm{f}(\mathrm{x}, \lambda)$$[/tex]
As the cumulative density is given by
[tex]=\int_0^{\mathrm{x}} \mathrm{f}(\mathrm{x}, \lambda) \mathrm{dx} \\&=\int_0^{\mathrm{x}} \lambda \times \exp (-\lambda \mathrm{x}) \mathrm{dx} \\&=1-\exp (-\lambda \mathrm{x})\end{aligned}$$[/tex]
The density of the minimum of the sample is given by
[tex]=\mathrm{n} \times[1-(1-\exp (-\lambda \mathrm{x}))]^{\mathrm{n}-1} \times \lambda \times \exp (-\lambda \mathrm{x})$[/tex]
[tex]$$\begin{aligned}&=\mathrm{n} \times[\exp (-\lambda \mathrm{x})]^{\mathrm{n}-1} \times \lambda \times \exp (-\lambda \mathrm{x}) . \\&=\mathrm{n} \lambda \times \exp (-\mathrm{n} \lambda \mathrm{x})\end{aligned}$$[/tex]
Thus, here [tex]$\mathrm{X}_{(1)}$[/tex] follows gamma distribution with parameter [tex]$\alpha=1 \quad$[/tex] and [tex]$\beta=\frac{1}{n \lambda}$[/tex].
We make use of the condition that if Y follows Gamma distribution with parameter with parameter [tex]$\alpha$[/tex]and [tex]$\beta$[/tex]. Then, we have
[tex]$\frac{2 \mathrm{Y}}{\beta} \sim \chi^2(2 \alpha, \mathrm{n}-1)$[/tex]
Thus we have that
[tex]\mathrm{T}=\frac{2 \mathrm{X}_{(1)}}{\frac{1}{\mathrm{n} \lambda}} \sim \chi^2(2, \mathrm{n}-1)$$[/tex]
[tex]$$\begin{aligned}\mathrm{b} &=\frac{\chi^2\left(1-\frac{\alpha}{2}, \mathrm{n}-1\right)}{2 \mathrm{X}_{(1)} \times \mathrm{n}} \\&=\frac{\chi^2\left(1-\frac{0.03}{2}, \mathrm{n}-1\right)}{2 \mathrm{X}_{(1)} \times \mathrm{n}} \\&=\frac{\chi^2(0.985, \mathrm{n}-1)}{2 \mathrm{X}_{(1)} \times \mathrm{n}} \\\mathrm{a} &=\frac{\chi^2\left(\frac{0.03}{2}, \mathrm{n}-1\right)}{2 \mathrm{X}_{(1)} \times \mathrm{n}} \\&=\frac{\chi^2(0.015, \mathrm{n}-1)}{2 \mathrm{X}_{(1)} \times \mathrm{n}}\end{aligned}$$[/tex]
Therefore for given[tex]$\mathrm{n}$[/tex] and [tex]$\mathrm{X}_{(1)}$[/tex], we can obtain the confidence interval [tex]$(\mathrm{a}, \mathrm{b})$[/tex].
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Which expression is equivalent to 8(x+3)−14(20x−56)
8(101 -34x) is the equivalent expression of 8(x+3)−14(20x−56)
What is the equivalent expression?
Equivalent expressions can be defined as expressions that are the same, even though they may look a little different. If you plug in the same variable value into equivalent expressions, they will each give you the same value when you simplify
Given 8(x+3)−14(20x−56)
By eliminating the parenthesis:
8(x+3)−14(20x−56) = ( 8(x) + 8(3) ) - ( 14(20x) - 14(56) )
= 8x + 24 - 280x + 784 Add/Subract like terms
= -272x + 808
= 8(-34x + 101)
= 8 (101 -34x)
Therefore the equivalent expression for 8(x+3)−14(20x−56) is 8(101 -34x)
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what is the value of 7 p + q/3 when p=6 and q=12
Answer:
46
Step-by-step explanation:
"Here are some values of sequence D"
n | D(n)
1 | 13
5 | 7
7 | 4
A) "Write a recursive definition for the sequence"
B) "Write a definition for this sequence for the nth term"
Answer:
See below
Step-by-step explanation:
A) Recursive Definition
The value of each term in a sequence that starts at 13 is reduced by 1.5 for each step in the sequence.
B) Definition for nth Term
D(n) = D(1)+(n-1)(-1.5)
D(1) = 13
D(n) = 13+(n-1)(-1.5)
Examples:
D(5) = 13 + (5-1)*(-1.5)
D(5) = 13 + (4)*(-1.5)
D(5) = 13 - 6, or 7
------------------
D(7) = 13 + (7-1)*(-1.5)
D(7) = 13 + (6)*(-1.5)
D(7) = 4
Selecting the number of bins is an important decision when working with histograms. Are there any rules or recommendations for choosing the number or width of bins? what happens if we use too many or too few bins?.
When working with Histograms, choose from 5 to 20 bins. The greater the data collection, the more probable it is that you will require a high number of bins. For example, a collection of 12 data points may deserve 5 bins, whereas a set of 1000 numbers will most likely benefit from 20 bins. The exact number of bins is typically a matter of personal preference.
What is a Histogram?
A histogram displays numerical data by arranging it into equal-width "bins." Each bin is represented by a bar, the height of which corresponds to the number of data points in that bin. Bins are sometimes known as "intervals," "classes," or "buckets."
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5. Roger put down carpet in half of his bedroom, which is shown below. Which answer shows the area of his bedroom that has carpet?
Option(A) i.e, 60 sq. feet is an answer.
Define Area of rectangleThe area of a rectangle is the number of unit squares that its perimeter includes. A rectangle's area is the area it takes up within the confines of its four sides. The area of a rectangle is determined by its dimensions. A rectangle's area is essentially equal to the product of its length and breadth. A shape's area is defined as the "space enclosed within the perimeter or the boundary" of the given shape.
The area of a rectangle can be calculated using the formula Area of rectangle = length × width.
Given, length = 15 feet, width = 4 feet
put these values in given formula,
Area of rectangle = 15 * 4
= 60 square feet
Hence, the answer is option(A) i.e, 60 sq. feet.
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need help with this asap!!!!!
Answer:
that looks hard
Step-by-step explanation:
whats the co-ordinates of the midpoint of (3,11) and (7,21)
The coordinates of the mid- point are (5, 16)
Given,
The midpoint of the line, given any points A (x₁, y₁) and B(x₂, y₂) .
In the question, we are given that the midpoint is (3, 11) and (7, 21).
and, to find the co- ordinates of the line.
Now, We know that the Formula of mid point
M = ({(x₁ + x₂)/2},{(y₁ + y₂)/2}).
Here, the points are (3, 11) and (7, 21)
Therefore,
(x, y) = ({(x₁ + x₂)/2},{(y₁ + y₂)/2}).
=> (x, y) = [( [tex]\frac{3+7}{2}[/tex]) , ([tex]\frac{11 + 21}{2}[/tex]) ]
=> (x , y) = (10/2 , 32/ 2)
=> (x ,y) = (5 , 16)
Hence, The coordinates of the mid- point are (5, 16)
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I need help solving this math problem
Answer: y=15, AQ=31, QX=14
Step-by-step explanation:
2y+1+y+1=45
3y=45
•1/3 to both sides
y=15
then substitute 15 for y in the other equations to get the result
8. Kim made a pitcher of
lemonade. The pitcher already
contained 1 5/6 cups of
lemonade, and she added 2 2/3
more cups. How many cups
were in the pitcher when Kim
was finished?
Answer:
4 1/2
Step-by-step explanation:
Add the fractions:
11/6+8/3
11/6+16/6
27/6
27/6=4.5
Write the equation of a line with slope=2/3 and passes through the point (15/6, -4/11)
Answer: y=2/3x-2.03
Step-by-step explanation: This may not be exactly correct, and I don't know if you're using standard form, but I used demos the graphing calculator to make a graph, and that matches down to the 0.03 of the line.
I hope this helps, brainliest would be appreciated <3
What is the product of the complex numbers below? (4 - 21)(1 + 7) O A. 18 - 307 - OB B. -10 - 301 O C. -10 + 261 + O + D. 18 + 261
Given:
[tex](4-2i)(1+7i)[/tex]To find: The product of two complex numbers:
Explanation:
On expansion we get,
[tex](4-2i)(1+7i)=4+28i-2i-14(i^2)[/tex]As we know,
[tex]i^2=-1[/tex]So, we w
Bryce wrote the linear regression equation y = 1.123 x minus 6.443 to predict the armspan, y, of a person who is x inches tall. riley has an armspan of 67.5 inches. which is the best prediction of riley’s height? 54.36 inches 65.84 inches 66.55 inches 69.36 inches
Finding the numeric value of the regression equation, the best prediction of Riley's height is given by:
65.84 inches.
Finding the numeric value of a function or of an expressionTo find the numeric value of a function, we replace each instance of the variable in the function or in the expression by the desired value.
The regression equation in this problem gives the armspan of a person, represented by y, as a function of the height x as follows:
y = 1.123x - 6.443.
Riley has an armspan of 67.5 inches, hence y = 67.5, and we can find the best prediction for his height replacing the lone instance of y in the equation by 67.5 and solving for x, as follows:
67.5 = 1.123x - 6.443.
1.123x = 67.5 + 6.443
x = (67.5 + 6.443)/1.123
x = 65.84 inches, which is the best prediction.
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Answer:
It’s B
Step-by-step explanation:I did it on edge 2022 got it right!
Which mixed number is the GREATEST?
Brain pop btw
A 3 5/8
B 8 1/2
C 7 1/5
D 1 7/5
Answer: 8 1/2
I can't give an explanation though
An exponent is always smaller in value than the base. true/false
False. Exponent can be as big as it wants
Solving Inequalities with One Variable
Show work
21+21<63
Answer: infinitely many solutions
Step-by-step explanation:
21 + 21 < 63
Calculate
42 < 63
infinitely many solutions
Question 12 of 25
Which of these terms does not describe polygon A'B'C'D?
Polygons A'B'C'D' are not described by the rem preimage. The initial form before a change is known as the preimage. The transformation in the example below involves both a rotation and a dilation.
What are polygons?When three or more line segments are connected to one another, a polygon is created, which is a closed, two-dimensional, plane shape. Most frequently, when learning about geometry, we run into polygons.
A closed two-dimensional figure with three or more straight lines is what a polygon is defined as in geometry. Poly means "many" and gon means "angle" in Greek, making up the word "Polygon." We are surrounded by a wide variety of polygons.
An illustration of this is the hexagonal shape of a honeycomb. Every polygon has a unique structure, and they are all divided into different groups according to how many sides they have and other factors. This means that all polygons are closed plane shapes.
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HELP URGENT!!!!! WILL MARK BRAINLIEST!!!!
Which equation best fits the graph given?
a. f(x)=(x-1)^3 (x+2)^2
b. f(x)=(x+1)^2(x-2)^3
c. f(x)=(x-1)^2 (x+2)^3
d. f(x)=(x+1)^3(x-2)^2
e. None of the above
Briefly explain how you decided on the equation.
Answer:
D
Step-by-step explanation:
first find the zeros on the graph and their multiplicity.
zeros: -1, 2
mult: 3, 2
the equation that fits is f(x)=(x+1)^3(x-2)^2
Maggie used the commutative property to write 5 + .9y - & as the equivalent expression 6.9y+ 8-
5. Did Maggie apply
the commutative property correctly? Why or why not?
The commutative property is not applied properly
What is the commutative property?The commutative property is an algebraic property that states that
a + b = b + a and ab = ba
How to determine the true statement?The expression is given as
5 + .9y - 8
The second expression is given as
6.9y + 8 - 5
First, both expressions are not equivalent
This is because
5 + .9y - 8 = .9y - 3
6.9y + 8 - 5 = 6.9y + 3
Hence, Maggie did not apply the property properly
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While in Canada, Renita bought a
souvenir that is 14.5 centimeters
long. She knows that 1 inch equals
2.54 centimeters.What is the length of the souvenir in inches
pls help have to turn this in by midnight
Answer:
Point-slope form: y - 6 = -1/3(x + 6)
Slope-intercept form: y = -1/3x + 4
Please please answer the questions in the photo! ( will mark brainliest )
The reason for the required step using the property of equality are as follow:
7. Addition property of equality.
8. Symmetric property of equality.
9. Reflexive property of equality.
10.Symmetric property of equality.
As given,
The reason for the required step using the property of equality are as follow:
7. 4x - 10 = 7 - 2x
4x+2x - 10 = 7
6x -10 = 7
Here
Addition Property of Equality is applied.
If x, y, and z are real numbers, and x=y
then
x+ z=y+ z
8. 6 = x
x = 6
Here Symmetric Property of Equality is applied.
If x and y are real numbers, then
x = y
y = x
9. 4 = 4
Here Reflexive Property of Equality is applied.
If x is a real number, then
x = x
10. -3 = x
x = -3
Here Symmetric Property of Equality is applied.
If a is a and b are real numbers then,
a = b
b = a
Therefore, The reason for the required step using the property of equality are as follow:
7. Addition property of equality.
8. Symmetric property of equality.
9. Reflexive property of equality.
10.Symmetric property of equality.
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What x-value makes the set of ratios equivalent? Tiles 2 : 3 = 6 : x ,4 : 7 = x : 42 , 2x : 48 = 3 : 12, 12 : 15 = x : 20Pairs691624
What x-value makes the set of ratios equivalent? Tiles 2 : 3 = 6 : x ,4 : 7 = x : 42 , 2x : 48 = 3 : 12, 12 : 15 = x : 20
Part 1
we have
2 : 3 = 6 : x
value of x=9
Part 2
4 : 7 = x : 42
x=24
Part 3
2x : 48 = 3 : 12
2x=12
x=6
Part 4
12 : 15 = x : 20
x=16
8.
Mixed Practice: Simplify the expressions and express as a polynomial in standard form:
4. -3x(9x-4)
5.x(2x^2+x) 6. -5x^2-4x+1) 7. (3x-5y+z)-(2x-4y-z)
Answer:
4 = -27x^2+12x
5 = 2x^3+x^2
6 = -5x^2+4x-1
7 = x-y+2z
Step-by-step explanation:
Simple collecting like terms and distributive properties.
You are ordering shirts for a club at your school. The function f(x)=12x+25 represents the cost of ordered x shirts. How much would it cost to buy 68 shirts?
The Cost of 68 shirts is 841. The total cost formula is used to calculate a total by combining the variable and fixed costs of providing goods.
What is meant by total cost?Total cost = (average fixed cost x average variable cost) x number of units produced is the formula. To use this formula, you must first determine your fixed and variable costs. Total cost refers to the total cost of making an investment, which includes the investment cost as well as any broker commissions, taxes, licenses, and fees associated with the transaction. When calculating the return on investment, all of these costs should be considered. Total fixed costs are the sum of all a company's consistent, non-variable expenses.How to find Cost :
f(x) = 12x+25where f(x) is the cost of the shirt.X represents the number of shirts.Substitute x=68 in the above equation
so , f(x) = 12 (68)+25
f(x) = 841
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What is distance between (3, 8) and (5, 14)? Round to the nearest tenth if necessary (example 5.6).
Answer:
Step-by-step explanation:
1.\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}
2.\sqrt{\left(5-3\right)^2+\left(14-8\right)^2}
3.2\sqrt{10}
Question 1 of 21
If r= 1 and 0 = 5, what is the approximate arc length?
A. 2.618 units
B. 0.883 units
C. 15.708 units
D. 3.927 units
The distance between two places along a segment of a curve is known as the arc length.
What is arc length of a circle?
The distance between two places along a segment of a curve is known as the arc length. Curve rectification is the process of measuring the length of an irregular arc section by simulating it with connected line segments.
There are a finite number of segments in the rectification of a rectifiable curve. Using the arc length formula, one may determine a circle's arc length given its radius and center angle. Arc length is equal to r, where r is the radian unit. Arc length is equal to (r/180), where r is the radius in degrees.,
Given :[tex]$r=1, \theta=5 \pi / 6$[/tex]
Now, arc length
[tex]&=\theta / 2 \pi * 2 \pi r \\[/tex]
[tex]&=(5 \pi / 6) / 2 \pi \times 2 \times 3.14 \times 1 \\[/tex]
[tex]&=5 / 12 \times 6.28 \\[/tex]
[tex]&=31.4 / 12[/tex]
=2.618 units
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