Identify the coordinates of the vertex of f(x) = -(x + 5)2 + 8, and identify whether it is an absolute minimum or absolute maximum.​

Answer: 3

Step-by-step explanation: This equation can be written as 4x+3x-4=17

We can now solve.

Moving the 4 to the other side (adding) and we get 21.

Now we have 4x+3x. Adding like terms, we get 7x = 21. Now we divide by 7.

X = 3.

Answer:

D) (f o g)(x) = 10x² - 60x + 93

Step-by-step explanation:

f(x) = 10x² + 3

g(x) = x - 3

⇒ (f o g)(x)

⇒ f(x - 3)

⇒ f(x - 3) = 10(x - 3)² + 3

⇒ f(x - 3) = 10(x² - 6x + 9) + 3

⇒ f(x - 3) = 10x² - 60x + 90 + 3

⇒ (f o g)(x) = 10x² - 60x + 93

Answer:

[tex]\textsf{D)} \quad (f \circ g)(x)=10x^2-60x+93[/tex]

Step-by-step explanation:

[tex]\textsf{If }\:f(x)=10x^2+3\:\textsf{ and }\:g(x)=x-3\:\textsf{ then}:[/tex]

[tex]\begin{aligned}(f \circ g)(x) & = f[g(x)]\\ & = f(x-3)\\& = 10(x-3)^2+3\\& = 10(x^2-6x+9)+3\\& = 10x^2-60x+90+3\\& = 10x^2-60x+93\\\end{aligned}[/tex]

Answer:

C) 26

Simplify using the FOIL method--used to multiply binomials--and then combine real and imaginary parts of the problem.

5 × 5 = 25 + positive 1(i) = 26

Answer:

option c, 26

Step-by-step explanation:

(5 + i)(5 - i)

Apply complex arithmetic rule: (a + bi)(a - bi) = a^2 + b^2

a = 5, b =1

(5)^2 + (1)^2

(5)^2 = 25

(1)^2 = 1

25 + 1

Answer:

B. None of these

Step-by-step explanation:

There are a total of 12 coins in your pocket.

The probability of drawing a nickel first is 5/12

Since you return the coin, the total number of coins in your pocket doesn't change.

The probability of drawing a dime second is 7/12

Since this is a compound probability problem, multiply the two probabilities together.

5/12 x 7/12 = 35/144

35/144  = 0.243

Answer:

Graph D

Step-by-step explanation:

Graph D is the graph of -2x + y < 5

Answer:

lol

Step-by-step explanation:

Answer:

[tex]0 \leqslant x \leqslant 20[/tex]

Answer:

I would edit this answer and tell you what I hope would be the correct answer if you give me the problem you are confused with

Step-by-step explanation:

I can't help you otherwise

Sorry

Answer:

4 days

Step-by-step explanation:

Answer:

D)

Step-by-step explanation:

Kevin starts with 0 poems but increases 3 each day

Let kevin = x

y = 3x

Anita has 4 poems to start with but increases 2 each day

Let anita = y

y = 2x + 4

As seen on this graph:

The point of intersection is (4,12)

The x axis being the number of days.

Thus the answer is D)

The expression that can be use to find the difference between the fraction of money Amar put in the bank and the fraction he spent on the book is 4 / 7 x - 1 / 3 x

Amar put 4/7 of the money he earned raking leaves in the bank. Therefore,

let the money she earned = x

Hence,

amount put in bank = 4 / 7 x

She spent 1 / 3 of the money on books. Therefore,

money spent on books = 1 / 3 x

Therefore, the expression that can be use to find the difference between the fraction of money Amar put in the bank and the fraction he spent on the book is as follow:

4 / 7 x - 1 / 3 x

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Answer:

y = 5x-17

Step-by-step explanation:

point slope form would be

y- -2   =  5(x-3)        or  re-arrange to:    y = 5x -17

Answer:

see attached image

Step-by-step explanation:

Answer:

if each was used only once, the answer would be 52080

Step-by-step explanation:

The radius of the yaw mark to the nearest tenth of a foot is 11.2 ft

The minimum speed  11.1634 miles per hour.

Yaw marks are always curved. They are, initiated by a steering input. They're what's left from a tire that is still rolling but is simultaneously sliding laterally.

The formula for determining radius from a chord and middle ordinate is

[tex]r^{2}= \frac{c^{2}}{8m}+\frac{m}{2}[/tex]

To find the radius of the yaw mark, we have to use the formula

[tex]r^{2}= \frac{c^{2}}{8m}+\frac{m}{2}[/tex]

where c is the length of the chord and m is the middle ordinate

As the tires leave a yaw mark with a 31 foot chord and a middle ordinate of 3 feet.

So,

[tex]r^{2}= \frac{31^{2}}{8*3}+\frac{3}{2}[/tex]

[tex]r^{2}= 40.041 +1.5\\r^{2}=41.541[/tex]

Now to find the minimum speed, we are going to use the formula: [tex]s=\sqrt{15fr}[/tex]

where 'f' is drag factor and 'r' is the radius

drag factor is 0.2, f=0.2

and r= 41.541 ft

So, [tex]s=\sqrt{15* 0.2*41.541}\\s=\sqrt{124.623}\\s= 11.1634 mph[/tex]

The minimum speed before the brakes are applied was 11.1634 miles per hour.

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a) Line AE, and Line BC are parallel

b) Line ED, and Line CD

c) 3

Step-by-step explanation:

Answer:

22.5¢ per oz

Step-by-step explanation:

24 oz cost = $5.30

1 oz cost = $5.40/24 = 22.5¢ per oz

Answer:

0.22.5

Step-by-step explanation:

Answer:

15%

Step-by-step explanation:

Percent increase in the original price of jacket = 15%

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given,

Original price of jacket = $110

Increased price of jacket = $126.5

Increased amount = $126.5 - $110

                               = $16.5

Increased amount in percentage = ($16.5/$110) × 100

                                                       = 0.15 × 100

                                                       = 15%

Hence, 15% is increase in the original price of jacket.

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Answer:

Step-by-step explanation:

Area of a triangle is a*b divided by 2

Lets assume a = 8 and b= 9

8 *

9=72

72/2=36

Answer:

The answer should be $1127.74

To write 28 + 24 as a product of two factors, we need to determine the HCF of the addends (28 and 24). This can be done by listing the factors of the addends. The greatest factor that is common in 28 and 24 is the HCF.

If the number is in bolded text, the number is a common factor.

Since 4 > 2 > 1, the HCF is 4.

Now, let us put the provided expression between parentheses.

Finally, factor four out of the expression, as it is the GCF of 28 and 24.

Therefore, 28 + 24 as a product of two factors is 4(7 + 6).

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Answer:

Step-by-step explanation:

1[tex]\frac{1}{2}[/tex]=1×[tex]\frac{2}{2}[/tex], +[tex]\frac{1}{2}[/tex]

(-[tex]\frac{3}{2}[/tex])÷[tex]\frac{3}{4}[/tex]×(-[tex]\frac{2}{3}[/tex])

[tex]\frac{3}{2}[/tex]×[tex]\frac{4}{3}[/tex]×[tex]\frac{2}{3}[/tex]

[tex]\frac{1}{2}[/tex]×4×[tex]\frac{1}{3}[/tex]

4×[tex]\frac{1}{3}[/tex]=[tex]\frac{1}{3}[/tex]+[tex]\frac{1}{3}[/tex]+[tex]\frac{1}{3}[/tex]+[tex]\frac{1}{3}[/tex]

=[tex]\frac{4}{3}[/tex]

The names of this polygon include:

The polygon given has three sides which means that it is a triangle. It is an acute triangle because the angles are all less than 90°.

It is also a scalene triangle because all the sides have different lengths from each other.

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Answer:

Step-by-step explanation:

I: acute triangle

L: Isosceles triange

(sorry if im wrong i have not done this in a good few years lol)

Answer:

the distance between the CD points is 5

Step-by-step explanation:

(-4,-6) (1,6)

it takes 4 to get from -4 to 0 plus 1 to get to 1

so 4+1=5

Answer:

P = 0.5Q - 20

Step-by-step explanation:

P = kQ + c

substitute Q = 60 , P = 10 into the equation

10 = 60k + c → (1)

substitute Q = 240, P = 100 into the equation

100 = 240k + c → (2)

subtract (1) from (2) term by term to eliminate c

90 = 180k ( divide both sides by 180 )

[tex]\frac{90}{180}[/tex] = [tex]\frac{1}{2}[/tex] = 0.5 = k

substitute k = 0.5 into (1) and solve for c

10 = 60(0.5) + c

10 = 30 + c ( subtract 30 from both sides )

- 20 = c

then

P = 0.5Q - 20

A rectangular fence is to a total perimeter of 200 feet. If the length is twice the width, find the measurements of the length and width of the rectangular fence.

In this question we are provided with the perimeter of a rectangle fence that is 200 feet. It is also given that the length of the fence is twice its breadth. We are asked to calculate it's dimensions.

First we will form an equation.

Let us assume the breadth as x

Then, length = 2x

It is given that the perimeter is 200 feet.

We know,

[tex] \bull \: \small\boxed{ \rm{ Perimeter_{(rectangle)} = 2(length + breadth)}}[/tex]

Substituting the values we get

[tex] \small\sf{ 200 = 2(2x + x)}[/tex]

Now we will solve this equation and find out the value of x.

[tex] \small\sf{ 200 = 2(2x + x)}[/tex]

[tex] \longmapsto \small\rm{ 200 = 2(3x )}[/tex]

[tex] \longmapsto \small\rm{200 = 6x} [/tex]

[tex] \longmapsto \small\rm{ \dfrac{ \cancel{200} \: \: 33.33}{ \cancel{6}} = x } [/tex]

[tex] \small\sf{x = 33.33} [/tex]

We will substitute the value of x = 33.33.

Length = 2x = 2 × 33.33 = 66.66 feet

Breadth = x = 33.33 feet

Answer: C ≈ 25.1

Step-by-step explanation:

      The circumference of a circle can be found with the following formula. We will plug in the diameter given, and solve.

C = dπ

C = (8)π

C ≈ 25.1

[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]

[tex] log_{4}x = k \\ \\ \longrightarrow \: log_{4}x = log_{2 {}^{2} }x \\ \\ \longrightarrow \: 2 log_{2}x \\ \\ now , \\ \\ log_{2}x = k \\ \\ \therefore \: 2( log_{2}x) = 2(k) \\ \\ \longrightarrow \: 2k[/tex]

hope helpful ~

Answer:

8 and 48

Step-by-step explanation:

Here is how to find it mathematically

x = one number     6x = other number    ( because 3x is 1/2 of x)

(x + 6x) /2 = 28

7x = 56

x = 8     then 6x = 48