The vertex is (-2, 11), then the vertex form of the quadratic is:
f(x) = 5*(x + 2)^2 - 11
How to write the quadratic equation in vertex form?A quadratic equation with a leading coefficient a and a vertex (h, k) can be written in vertex form as:
y = a*(x - h)^2 + k
And for a quadratic equation of the form:
y = a*x^2 + b*x + c
The vertex is at:
h = -b/2a
In this case, our equation is:
f(x) =5x^2 + 20x + 9
Then:
h = -20/2*5 = -2
Evaluating in x = -2 we get:
f(-2) = 5*(-2)^2 + 20*-2 + 9
f(-2) = 5*4 - 40 + 9
f(-2) = 20 - 40 + 9 = -20 + 9 = -11
The vertex is (-2, -11), and the leadin coefficient is a = 5, then the vertex form is:
f(x) = 5*(x + 2)^2 - 11
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NO LINKS!! Please help me with this probability question Part 3j
Answer:
b) 64 to 76 inches.
Step-by-step explanation:
In a normal distribution, 95% of the population is within 2 standard deviations of the mean.
Given values:
[tex]\textsf{Mean}\; \mu=70\; \sf inches[/tex][tex]\textsf{Standard deviation}\; \sigma=3\; \sf inches[/tex]Given that the mean height is 70 inches and the standard deviation is 3 inches:
[tex]\implies \mu -2 \sigma = 70-2(3)=64[/tex]
[tex]\implies \mu+2 \sigma = 70+2(3)=76[/tex]
Therefore, an appropriate height range for 95% of all people in the sample would be:
64 to 76 inches.Find the difference between the sums to ten terms of the AP and GP whose first two terms are-2 and 4.
The difference between the sum of first 10 terms of AP and GP where the first term and second term is 2 and 4 respectively is -932
What is Arithmetic Progression and Geometric Progression?
An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.
The general form of a GP is a, ar, ar2, ar3 and so on
Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
Given data ,
First term = -2
Second term = 4
A)
For Arithmetic Progression
First term a = -2
Second term = 4
Common difference d = Second term - First term
= 4 - ( -2 )
= 6
And Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
n = 10 terms
Sₙ = ( 10/2 ) [ (2x- 2) + ( 9 ) x 6]
Sₙ = 5 [ -4 + 54 ]
Sₙ = 5 x 50
Sₙ = 250
Therefore , Sum of first 10 terms of an AP is 250
B)
For Geometric Progression
First term a = -2
Second term = 4
Common ratio = Second term / First term
= 4 / -2
= -2
And Sum of first n terms of an GP : Sₙ = a( 1 - rⁿ ) / ( 1 - r )
n = 10
Sₙ = 2( 1 - ( -2 )¹⁰ ) / 1 - ( -2 )
Sₙ = 2 ( 1 - 1024 ) / 3
Sₙ = ( 2 x (-1023) ) / 3
Sₙ = 2 x ( - 341 )
Sₙ = - 682
Therefore , Sum of first 10 terms of an GP is -682
The difference between the sum of first 10 terms of AP and GP is GP - AP
= -682 - 250
= -932
Hence , The difference between the sum of first 10 terms of AP and GP where the first term and second term is 2 and 4 respectively is -932
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right answers only please
Given graph represent the graph of g(x) = [tex]-x^{2} (x -2)[/tex]
Given,
In the question;
The equation is:
g(x) = - [tex]x^{2} (x -2)[/tex] or h(x) = [tex]x^{2} (x -2)[/tex]
To find the is this the graph of g(x) or h(x).
Graph is given in the figure.
Now, According to the question;
g(x) = [tex]-x^{2} (x -2)[/tex] and h(x) = [tex]x^{2} (x -2)[/tex]
g(x) = 0 h(x) = 0
[tex]-x^{2} (x -2) = 0[/tex] [tex]x^{2} (x -2)[/tex] = 0
x = 0, 2 x = 0, 2
If we put x = 1 then,
g(1) = [tex]-(-1)^2(1-2)[/tex] and h(1) = [tex](1)^2(1-2)[/tex]
g(1) = -1 (-1) h(1) = 1(-1)
g(1) = 1 h(1) = -1
But as shown in graph, graph take positive value at x = 1
∴Given graph is the graph of g(x) = [tex]-x^{2} (x -2)[/tex]
Hence, Given graph represent the graph of g(x) = [tex]-x^{2} (x -2)[/tex]
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Approximate the following square root to the nearest integer.
√10~
Determine the point estimate of the population mean and margin of error for the confidence interval.
Lower bound is 19, upper bound is 25.
The point estimate of the population mean is 22 and margin of error for the confidence interval is 3.
How to find the point estimate?1. Point estimate
Point estimate = Upper bound+ Lower bound/2
Point estimate = (25+19) /2
Point estimate = 44/2
Point estimate = 22
2. Margin error
Margin error = Upper bound - Lower bound/2
Margin error = ( 25-19) /2
Margin error = 6 /2
Margin error = 3
Therefore the point estimate is 22.
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The sUm of the measures
of the interior angles of
polygon is 2,880°. How
many sides does the
polygon have?
A house on the market was valued at $365,000. After several years, the value increased by 8%. By how much did the house's value increase in dollars? What is
the current value of the house?
Answer:
394,200
Step-by-step explanation:
You have to multiply the house value by 1.08 or 108%
365,000*1.08=394,200
Suppose 57% of the doctors in a hospital are surgeons.
If a sample of 465 doctors is selected, what is the probability that the sample proportion of surgeons will differ from the population proportion by greater than 6%? Round your answer to four decimal places.
The probability that the proportion of surgeons will differ from the population proportion by greater than 6%-22.22%
How to solve for the probabilityP of 6%
= P (p > 0.06)
we would have to use the formula that is given below
[tex]P[z > \frac{p-P}{\sqrt{} \frac{PQ}{n} }[/tex]
where we have n = 465
p = 6%
P = 0.57
Q = 1 - 0.57 = 0.43
We would have to put the values into the equation that we have here as:
0.06 - 0.057 = -0.51
0.57 x 0.43 / 465 = 0.000527
√0.000527 = 0.022956
The probability = -0.51 / 0.022956
= -22.22%
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A number cube with faces labeled from 1 to 6 will be rolled once.
The number rolled will be recorded as the outcome.
Give the sample space describing all possible outcomes.
Then give all of the outcomes for the event of rolling a number greater than 3.
If there is more than one element in the set, separate them with commas
The Sample space for number greater than 3= {4, 5, 6}
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
A number cube with faces labeled from 1 to 6 will be rolled once.
so, Sample Space = { 1, 2, 3, 4, 5, 6}
sample space for number greater than 3= {4, 5, 6}
Thus, the probability is 3/6 or 1/2.
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2.1 & 2.2 Assessment: Vertex & Standard Form of Quadratic Functions
What is the equation, written in vertex form, of a parabola with a vertex of (1, -9) that
passes through the point (2, -7)?
Work to Support Your Answer (Required for Credit!)
The equation of the parabola, in vertex form is
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=1\\ k=-9 \end{cases}\implies y=a(x-1)^2 - 9\qquad \textit{we also know that} \begin{cases} x=2\\ y=-7 \end{cases} \\\\\\ -7=a(2-1)^2-9\implies 2=a(1)^2\implies 2=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} y=2(x-1)^2 -9 \end{array}} ~\hfill[/tex]
Determine which integer will make the inequality 4x + 6 < 2x + 12 false.
Answer:
x>=3 make the inequality false
Step-by-step explanation:
4x-2x<12-6
2x<6
x<3
Answer:
Any number higher than 3
Ex. 4, 5, 6, 7, 8, 9, 10, etc
Step-by-step explanation:
4x + 6 < 2x + 12
-2x -2x
---------------------
2x + 6 < 12
-6 -6
------------------
2x < 6
÷2 ÷2
-----------
x < 3
Since x is less than 3, any number higher than 3 will make the inequality false. For Ex. 4
4(4) + 6 < 2(4) + 12
16 + 6 < 8 + 12
22 < 20 (false)
I hope this helps!
August hosted two dinner parties for his friends. Twenty guests attended the first party, and twenty-seven guests attended the second party. What is the percentage increase of the number of guests from the first party to the second party?
A.
35%
B.
30%
C.
65%
D.
70%
Answer:
A 35%
Step-by-step explanation:
take the higher number (27) and subtract the smaller number (20) from it. there's your difference. afterwards, take the difference (7) and divide it by the smaller number (20). this gives you .35. convert it into percentage move the decimal point to the right two spots and slap a percentage sign onto it (shift+3). giving you 35%, or A.
Answer:
a) 35%
Step-by-step explanation:
Given information,
→ 20 guests attended the 1st party, and 27 guests attended the 2nd party.
Now we have to,
→ find the % increase of number of guests from first party to second party.
Let's solve the problem,
→ ((27 - 20)/20) × 100
→ (7/20) × 100
→ 0.35 × 100
→ 35%
Hence, the answer is 35%.
ms.folk at least 250 candies to reward her students she has 50 candies already and will buy more candy in bags with 20 candies in each write an inequality that can be used to find how many bags of candy Ms. Folk needs to buy to have at least 250 candies
50 + 20x ≥ 250 is the inequality that can be used to find how many bags of candy Ms. Folk needs to buy to have at least 250 candies.
How to solve equations in word problems?
Systems of linear equations must be used to solve some word problems. Here are some hints to help you determine when you need to create a system of linear equations in a word problem:i) There are two separate numbers at play, such as the total number of adults and children, the total number of large boxes and little boxes, etc.(ii) Each quantity has a value attached to it, such as the cost of an adult or kid ticket, the number of products in a large box as compared to a small box, etc.Let x be the number of bags she bought:
50 + 20x ≥ 250
3x ≥ 200
x ≥ 200/3
x ≥ 66.67
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A farmer owns a total of 8 4/5 acres of land. The land is separated into 4 equally sized sections. How many acres are in each section?
Write your answer as a mixed number or simplest form
Answer:
2 1/5
Step-by-step explanation:
8 4/5=44/5
(44/5)/(4)=(44/5)*(1/4)
(44/5)*(1/4)=44/20
44/20=2 1/5
A patient is using a bicycle as part of their physiotherapy routine. The diameter of the bicycle’s wheel is 590 mm. While in session, the wheel is rotating at a speed of 82 rpm (revolutions per minute). If the patient is riding the bicycle for 1 h and 10 minutes, determine the number of kilometres the patient has travelled. Round to the nearest tenth.
The total distance traveled by the patient in 1 hour and 10 minutes is 10.6 kilometers.
What is the distance?The distance is the length from one point to the end.
For our purpose, distance represents the product of speed and time.
Diameter of the bicycle's wheel = 590 mm
Speed (Revolutions) per minute = 82 rpm
Time riding the bicycle = 1 hr and 10 minutes = 70 minutes
1 Kilometer = 1,000,000 Millimeters
Distance per rotation = pi x diameter
= 3.14 x 590
= 1,852.6 mm/minute
Total distance traveled in kilometers = (1,852.6 x 82 x 70) ÷ 1,000,000
= 10,633,924 ÷ 1,000,000
= 10.6 kilometers
Thus, we can conclude that the patient traveled 10.6 kilometers by bicycling for one hour and 10 minutes.
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Which value of x makes the following statement true? 1.4 - x = a positive number
Answer:1.4<x
math math math
Answer:daddy
Step-by-step explanation:gay
A rectangular playground is enclosed by 440 feet of fencing. If the length of the playground is 20 feet less than 3 times the width, find the dimensions of the playground.
The dimensions of the playground are;
Width = 60 feet
Length = 160 feet
How to determine the dimensionsThe formula for calculating perimeter of a rectangle is expressed as;
Perimeter = 2( l + w)
Where;
l is the length of the rectanglew is the width of the rectangleWe have the values as;
Perimeter = 440 feet
Length = 3w - 20
Width = w
Now, substitute the values into the formula, we have;
440 = 2( 3w - 20 + w)
expand the bracket
440 = 2( 4w - 20)
440 = 8w - 40
collect like terms
8w = 480
Make 'w' the subject of formula
w = 60 feet
Length = 3(60) - 20
Length = 180 - 20
Length = 160 feet
Hence, the values are 60feet and 160 feet
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Simplify the expressions
a) (30+10 ÷ 2)-5-10
b) (30 + 10) = 2.5-10
c) 30 + 10 = 2(5-10)
(d) 30+ (10 ÷ 2·5)-10
The solution of the expressions are
(a) (30+10 ÷ 2)-5-10 = 20
(d) 30+ (10 ÷ 2·5)-10 = 24
What is meaning of expressions?
An expression is a combination of operations, variables, and numbers.
What is BODMAS rule?
According to the BODMAS rule, if an expression contains brackets ((), {}, []) we have first to solve or simplify the bracket followed by 'order' (that means powers and roots, etc.), then division, multiplication, addition and subtraction from left to right.
Given expression is
(30+10 ÷ 2)-5-10
Applying BODMAS rule:
= (30 + 5) - 5 - 10
= 35 - 5 - 10
= 30 - 10
=40
Second expression is:
30+ (10 ÷ 2·5)-10
= 30 + (10 ÷ 10) - 10
= 30 + 1 - 10
= 31 -10
= 21
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Tater and Pepper Corp. reported free cash flows for 2021 of $47.1 million and investment in operating capital of $30.1 million. Tater and Pepper incurred $14.4 million in depreciation expense and paid $30.5 million in taxes on EBIT in 2021.
If Tater and Pepper incurred $14.4 million in depreciation expense and paid $30.5 million in taxes on EBIT in 2021. The EBIT is $93.3 million.
How to find EBIT?First step is to find the operating cash flow
Operating cash flow =$47.1 million + $30.1 million
Operating cash flow = $77.1 million
Now let find the EBIT
EBIT = Operating cash flow + Depreciation expenses - taxes
EBIT = $77.1 million + ($30.5 million - $14.4 million)
EBIT = $93.3 million
Therefore the EBIT is $93.3 million.
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Mike has some t-shirts. 1/4 of the
t-shirts are pink, 1/2 of the
remaining tshirts are white and the rest are
purple. What fraction is purple?
Mike has some t-shirts. 1/4 of the t-shirts are pink, 1/2 of the remaining t-shirts are white and the rest are purple, then the fraction of purple is 3/8
Mike has some t-shirts
The fraction of pink t-shirts = 1/4
The remaining t-shirts = 1 - (1/4)
= 3/4
1/2 of the remaining t-shirts are white
Then the fraction of white t-shirt = 3/4 × 1/2
= 3/8
The fraction of purple t-shirt = 1 - (1/4 + 3/8)
= 3/8
Hence, Mike has some t-shirts. 1/4 of the t-shirts are pink, 1/2 of the remaining t-shirts are white and the rest are purple, then the fraction of purple is 3/8
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the set of the sets of odered pairs shown represents a function of f. {(-5,3), (4,9), (3,-2). give an orderd pair that could be added to the set so that it remains a function
The three ordered pairs that could be added to the set so that f remains a function is D) (-3, -2), (1, 6), and (2, 3)
How to get the ordered pairs?We are told that the displayed set of ordered pairs represents a function f.
{(-5,3),(4,9),(3,-2),(0,6)}
We must determine which three ordered pairs can be added to the set while the function remains unchanged. It is a mapping between elements of two sets A and B, with each element of set A uniquely mapped to each element of set B.
Alternatively, we can say that each element has only one image. For D,(-3,-2),(1,6) and (2,3) (2,3)
The image of f -3 is -2.
The image of one is six.
3 is the image of 2
It is correct because each element has a unique image while maintaining the same function.
As a result, option D is correct.
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Complete question
The set of ordered pairs shown represents a function f. {(-5, 3), (4, 9), (3, -2), (0, 6)} Which three ordered pairs could be added to the set so that f remains a function? a. (-3, -2), (4, 0), and (0, -1) B) (1, 6), (2, 3), and (-5, 9) C) (4, 0), (0, -1), and (-5, 9) D) (-3, -2), (1, 6), and (2, 3)
A 800 g of rock was analysed and
found to contain 58 g of gold. What
percentage of the rock is the gold?
Answer:
7.25 %
Step-by-step explanation:
58 out of 800g is 58 / 800 = .0725 which is 7.25 %
HELP PLEASE!! Dominique is selling merchandise for a school fundraiser. She is selling calendars for $8 each and coffee mugs for $12 each. She must sell at least $800 of merchandise, including at least 60 calendars, to meet her goals.
If x represents the number of calendars and y represents the number of mugs, which system of inequalities represents this scenario?
8x + 12y ≥ 800 and x ≥ 60
8x + 12y ≥ 800 and y ≥ 60
8x + 12y > 800 and y > 60
8x + 12y > 800 and x > 60
The inequality that represents the given situation is option A 8x + 12y ≥ 800 and x ≥ 60.
Given,
The cost for one calendar = $8
The cost for one coffee mug = $12
Dominique must sell at least $800 of merchandise and it should include at least 60 coffee mugs.
Here,
x be the number of calendars and y be the number of coffee mugs;
We have to find an inequality which represents the given situation;
So,
The inequality be;
8x + 12y ≥ 800 and x ≥ 60
That is,
The inequality that represents the given situation is option A 8x + 12y ≥ 800 and x ≥ 60.
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A house was valued at $321,000. Over several years, the value decreased by 9%, giving the house a new value.
Answer:
The new value is $292,110
Step-by-step explanation:
321,000 - (1 - 0.09) = 292,110
What is the equation of this graphed line
Answer: y = -9/8 + 7
Step-by-step explanation:
point a = (0,7), point b = (8,-2)
y = mx + b
b = 7
y = mx + 7
-2 = 8m + 7
-9 = 8m
m = -9/8
y = -9/8 + 7
Answer:
y= -9/8x+7
Step-by-step explanation:
find the slope
y2-y1/x2-x1
-2-7/8-0
-9/8
y=mx+b
m=slope
b=y intercept
y= - 9/8x + b
y= -9/8x+7
If WX equals to XY , what is the length of WZ?
Answer:
the length of WZ is 10
Step-by-step explanation:
There are 207 public libaries in New York City. The population in New York City is 8.805 million. What was the rate of libraries per 100,000? Give your answer to the nearest hundredth.
The rate of libraries per 100000 is 88.05 .
In the question ,
it is given that ,
the number of public libraries in New York City = 207 libraries
the population of the New York City = 8.805 million
we have to find the rate of libraries per 100000 .
for this we first have to express the population in numbers .
the population 8.805 million expressed in numbers is 8805000 ,
the rate of libraries per 100000 is
= 8805000/100000
On further simplification ,
we get ,
= 88.05
Therefore , The rate of libraries per 100000 is 88.05 .
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Pedro and Rebecca were trying to solve the equation:
0.1x^2 - 0.7x + 1.2 = 0
Pedro said, “I can multiply the entire equation by 10 and then factor. Then I can solve using the zero product property.”
Rebecca said, “I'll solve using the quadratic formula with a = 0.1 1, b = -0.7 and c = 1.2"
WHOs Strategy works?
A - Only Pedro's
B - Only Rebecca's
C - Both
D - Neither
The correct strategy between Pedro and Rebecca trying to solve the quadratic equation: 0.1x^2 - 0.7x + 1.2 = 0 is A - Only Pedro's
How to determine the correct strategyThe given function is a quadratic function which is solved by several method including the method both Pedro and Rebecca are trying to use
Pedro's method is the factorization method and the steps mentioned are correct
However Rebecca's method has some error
The equation is: 0.1x^2 - 0.7x + 1.2 = 0
factor of the leading coefficient a is 0.1, Rebecca is using 0.11
The error of using 0.11 instead of 0.1 will make the method ineffective
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I don’t know it and I need help. question is in picture
(2x²-3x+1)-(-x² + 2x − 2) - (2x - 3)² =
Answer:
6x^2-17x+12
Step-by-step explanation:
Distribute
2x^2-3x+1+x^2-2x+2(-2x+3)^2
Square (2x+3)
(-2x+3)(-2x+3)
FOIL
4x^2-6x-6x+9
Combine like terms
4x^2-12x+9
re-write equation
2x^2-3x+1+x^2-2x+2+4x^2-12x+9
Combine like terms
6x^2-17x+12
