Write in vertex form and state the vertex of the graph:

f(x)=20x+9+5[tex]x^{2}[/tex]

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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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

Answer:1.4<x

math math math

Answer:daddy

Step-by-step explanation:gay

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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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:

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:

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

The 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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The probability that the proportion of surgeons will differ from the population proportion by greater than 6%-22.22%

P 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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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

The dimensions of the playground are;

Width = 60 feet

Length = 160 feet

The formula for calculating perimeter of a rectangle is expressed as;

Perimeter = 2( l + w)

Where;

We 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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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!

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)

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)

Answer:

7.25 %

Step-by-step explanation:

58 out of 800g  is    58 / 800 = .0725    which is  7.25 %

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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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?

Let x be the number of bags she bought:

50 + 20x ≥ 250

3x ≥ 200

x ≥ 200/3

x ≥ 66.67

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Answer:

the length of WZ is 10

Step-by-step explanation:

The point estimate of the population mean  is 22 and margin of error for the confidence interval is 3.

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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[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]

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 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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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

The total distance traveled by the patient in 1 hour and 10 minutes is 10.6 kilometers.

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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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.

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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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

Answer:

The new value is $292,110

Step-by-step explanation:

321,000 - (1 - 0.09) = 292,110

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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The Sample space for number greater than 3= {4, 5, 6}

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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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%.