Which of the following polynomial functions is graphed below?
-70
60
50
20
-10
O A. f(x) = (x + 5)(x − 1)2(x+1)
B. f(x) = (x - 5)(x-1)²(x - 1)
OC. f(x) = (x+2)(x-3)²(x+4)
D. f(x)=(x-2)²(x-3)(x-4)
-10-
-20
-30-
-40
10

The dimension of the original photo is 11 inches by 11 inches.

Given that, the area of the reduced photo is 64 square inches.

In the equation [tex](x -3)^{2} = 64[/tex], x represents the side measure of the original photo.

We have to determine the dimensions of the original photo.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Now, solve the equation for the value of x.

By square rooting on both the side, we get

[tex]\sqrt{(x-3)^{2} } =\sqrt{64}[/tex]

⇒[tex](x-3)=[/tex]±[tex]8[/tex]

⇒[tex]x=8+3=11[/tex] and [tex]x=-8+3=-5[/tex]

The length and width can not be negative.

Therefore, the dimension of the original photo is 11 inches by 11 inches.

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Answer: A) 11 inches by 11 inches

Step-by-step explanation:

Edg 2022

Since, Maxwell wants to know how much space his globes occupies he has to find its volume.

Volume is the amount of space an object or substance occupies.

Every three dimensional object occupies a space.

Volume is measured in cubic units.

Therefore, the three dimensional object that has a width, length and height will have its volume as follows;

volume = lwh

where

Therefore, the space occupied by the globe is the volume of the globe.

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Answer:

D) [tex]22\:\text{m/s}^2[/tex]

Step-by-step explanation:

Acceleration is the derivative of velocity, which is the derivative of position, so we must differentiate the function twice:

Position of Particle: [tex]s(t)=t^3-4t^2+2t+8[/tex]

Velocity of Particle: [tex]v(t)=3t^2-8t+2[/tex]

Acceleration of Particle: [tex]a(t)=6t-8[/tex]

After [tex]t=5[/tex] seconds, the acceleration of the particle is [tex]a(5)=6(5)-8=30-8=22\:\text{m/s}^2[/tex]

The acceleration of the particle after 5 seconds is 38 m/s².

Acceleration is the rate of change of velocity or the slope of velocity.

We know that the first derivative of motion or speed is velocity and the second derivative of motion or speed is acceleration.

∴ We have to take the derivative of s = t³ + 4t² + 2t + 8 twice to obtain the equation of acceleration and replace t with 5 to get the acceleration value after 5 seconds.

Now, s = t³ + 4t² + 2t + 8 meters.

ds/dt = 3t² + 8t + 2 m/s.

d²s/dt² = 6t + 8m/s²

Now, at t = 5 seconds d²s/dt² = 6t + 8 is,

d²s/dt² = 6(5) + 8 m/s².

d²s/dt² = 38 m/s².

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Answer:

[tex]\frac{1}{13}[/tex]

Step-by-step explanation:

The total number of cards in a standard deck of cards is 52, in which there:

King: 4 cards <----------

Queens: 4 cards

Jack: 4 cards

Ace: 4 cards

Club/Diamond/Heart/Spade: 13 cards

Moreover, 26 of the 52 cards are red, and the remainder 26 are of black.

So the probability that a "king" card will be picked is [tex]\frac{4}{52}[/tex], which can be further simplified [tex]\frac{1}{13}[/tex]

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{0}}} \implies \cfrac{-2 -1}{1 +0} \implies \cfrac{ -3 }{ 1 }\implies -3[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{-3}(x-\stackrel{x_1}{0}) \\\\\\ y-1=-3x\implies y=-3x+1[/tex]

Answer:

d

Step-by-step explanation:

The region [tex]D[/tex] is essentially parameterized in three dimensions by

[tex]\Phi(u,v) = (u^2, u+v, 0)[/tex]

with [tex]1\le u\le8[/tex] and [tex]0\le v\le6[/tex].

The normal vector to [tex]D[/tex] is

[tex]\vec n = \dfrac{\partial\Phi}{\partial u} \times \dfrac{\partial\Phi}{\partial v} = (0,0,2u)[/tex]

with norm [tex]\|\vec n\| = 2u[/tex].

Then the surface integral is

[tex]\displaystyle \iint_D y \, dA = 2 \int_0^6 \int_1^8 (u+v)u \, du \, dv \\\\ = 2 \int_0^6 \left(\frac{1022}3 + 63 v\right) \, dv = \boxed{3178}[/tex]

Answer:

0.1235

Step-by-step explanation:

I'm not exactly sure what you mean, but I'm guessing that it's how much is needed to get 10 as the whole number. In that case, you just do 10-9.8765 to get 0.1235. So, 9.8765+0.1235=10. Hope this helped!

The inequalities are; 5¹/₄ tons = 10500 pounds; 1/2 ton + 3/4 ton > 2800 pounds; 2 tons > 60000 pounces; 1¹/₄tons > 20000 ounces

1) 5¹/₄ tons when converted to pounds is 10500 pounds.

Thus; 5¹/₄ tons = 10500 pounds.

2) 1/2 ton + 3/4 ton = 5/4 tons

Converting 1.25 to tons gives 2500 tons. Thus;

1/2 ton + 3/4 ton > 2800 pounds

3) Converting 2 tons to Ounces gives 64000 ounces. Thus;

2 tons > 60000 pounces.

4) 1¹/₄tons - ¹/₂ton = ³/₄ tons

Converting to ounces gives 24000 ounces

Thus; 1¹/₄tons > 20000 ounces

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Answer:

b

Step-by-step explanation:

answer is b

Answer: The save $1134.48

Step-by-step explanation:

3912 x 0.29 = 1134.48

The amount of money that the family saves in a month will be $1,017.12.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

A family has a month-to-month payment of $3912. Their month-to-month uses are displayed in the diagram underneath.

Rent 21%

Food 24%

Transportation 11%

Other Expenses 18%

Savings 26%

Then the amount of money that the family saves in a month is calculated as,

⇒ $3,912 x 0.26

⇒ $1,017.12

The amount of money that the family saves in a month will be $1,017.12.

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Answer:

0.75gal.

Step-by-step explanation:

(4gal.) (2qt) - (3gal.) (3qt) =

the easiest way to solve this would be get everything in the same units,

lets make the qt to gallons

2qt = 0.5gal                          divide the volume value by 4

3qt = 0.75gal

 (4gal.) + (0.5gal.) - (3gal.) + (0.75gal.)

= (4.5gal.) - (3.75gal.)

= 0.75gal.

Considering it's volume of 113 cm³, the approximate radius of the sphere is given by:

A. 3 cm

The volume of an sphere of radius r is given by:

[tex]V = \frac{4\pi r^3}{3}[/tex]

In this problem, we have that V = 113 cm³, hence the radius in cm is given as follows:

[tex]V = \frac{4\pi r^3}{3}[/tex]

[tex]113 = \frac{4\pi r^3}{3}[/tex]

[tex]r^3 = \frac{113 \times 3}{4\pi}[/tex]

[tex]r = \sqrt[3]{\frac{113 \times 3}{4\pi}}[/tex]

r = 3 cm.

Hence option A is correct.

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Answer:

is 3 cm

Step-by-step explanation:

The length and width of the piece of​ metal are 20 and 30 inches respectively.

The term “volume” refers to the amount of three-dimensional space taken up by an item or a closed surface. It is denoted by V and its SI unit is in cubic cm.

Dimension of the rectangle;

Width(w)

Length,L= 10 + w

volume of the box = length  * width * height

Dimension of the box;

length of box, (x + 10) - 4  = x + 6

width of box,(x - 4)

height of box =  2

The volume of the box is 1102 in³;

⇒V=lwh

⇒V=2 (x -4)( x + 6) =

⇒1102 in³ = 2x² + 4x - 48

⇒2x² + 4x - 880 = 0

⇒x  + 2x - 440 = 0

⇒(x + 22)(x - 20) = 0

⇒x = 20

⇒x=-22 (value of the dimesion will not be negative.

The width of an original piece of metal is;

Width,w=20 inches

length,l= 30 inches

Hence. the length and width of the piece of​ metal are 20 and 30 inches respectively.

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Answer:

A=l*w

Step-by-step explanation:

so We Derive Their Formula

L=A/w

Answer:

  68 texts per day

Step-by-step explanation:

The description of the variables in the equation tells you that you want to find t (texts sent per day) for the given value of 'a' (age in years).

__

Substitute the number (15) for the variable (a) and do the arithmetic:

  t = -1.63a +92.14

  t = -1.63(15) +92.14 = -24.45 +92.14

  t = 67.69

Keiko's trend line estimates a 15-year-old would send about 68 texts per day.

Answer:

[tex]log_2(10)[/tex]

Simplify the equation using logarithms.

[tex]2^3x=10[/tex]

[tex]log_1_0(2^3x)=log_1_0(10)[/tex]

log rule ⇩

[tex]log_a(x^y)=y*log_a(x)[/tex]

move exponent out of log.

[tex]x*log_1_0(2)=log_1_0(10)[/tex]

isolate variable further

[tex]x*log_1_0(2)=log_1_0(10)[/tex]

[tex]x=\frac{log_{10}(10)}{log_{10}(2)}[/tex]

formula for combining logs. ⇩

[tex]\frac {log_b(x)}{log_b(a)}=log_a(x)[/tex]

the result ⇩

[tex]x=log_2(10)[/tex]

Answer:

B

Step-by-step explanation:

I got it right on the test

Answer:

B

Step-by-step explanation:

Answer:

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Answer:

Calculator soup can help just search for whatever your learning and add a calculator at the end

Answer:

you're right

Step-by-step explanation:

the answer is false because side AD and sides AE are not the same length, so AB/BD does not equal AC/CE

Since diagonals bisect each other, both halves of a diagonal have the  same length.

[tex]5y-5=y+23\\4y=28\\y=7\\\\2x-0=x+2\\x=2[/tex]

Therefore b)

Answer: g(x)

Step-by-step explanation:

Answer:

Decimal = 0.05

Percentage = 5%

Explanation:

Total count : 20

Sarah count : 1

probability = favorable outcomes/total outcomes

                   =     1/20

                   =     0.05

Answer:

There were 67 coins in the bag, 36 of which were 50-cent coins and 31 of which were 20-cent coins.

Let x be the number of 50-cent coins in the bag,

And y be the number of 20-cent coins.

From the problem,

we know that y = x - 5,

Since there were 5 fewer 20-cent coins than 50-cent coins.

We can also set up an equation for the total value of the coins in the bag,

⇒ 0.5x + 0.2y = 24.20

Now we can substitute y = x - 5 into the equation,

⇒ 0.5x + 0.2(x - 5) = 24.20

Simplifying, we get,

⇒ 0.7x - 1 = 24.20

⇒ 0.7x = 25.20

⇒ x = 36

So there were 36 50-cent coins in the bag.

Using y = x - 5,

We can find that there were 31 20-cent coins.

Therefore, there were a total of 67 coins in the bag (36 + 31 = 67).

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7-digit:9999999

9-digit: 1000000

Answer:

Step-by-step explanation:

Formula:

Let b be the base (circle) of the cone

and h be the height of the cone

[tex]\text{volume of the cone} =\frac{1}{3} \times b\times h[/tex]

……………………………………………

→ b = π × r²

  = π × 6²

  = (22÷7) × 36

  = 113.142857142857 cm²

→ h = 7

[tex]\text{volume of the cone} =\frac{1}{3} \times b\times h[/tex]

The volume = (1÷3)×(113,142857142857)×(7)

                    = 264 cm³

===================

 METHOD 2 :

Volume = (1÷3)×(22÷7)×36×7

             = (1÷3)×22×36

             = 22×12

             = 264