Paul drives 728 miles in 14 days.

He drives the same number of miles each day.

How many miles does he drive in 1 day?

Answer:

A. Domain : (-∞, ∞)

B. Function is increasing in the interval (-2, 0) and (2, ∞)

   Decreasing in the interval of (-∞, -2) and (0, 2).

Step-by-step explanation:

A. Given function is, y = |2x - 1|

This function is the transformed form of the parent function, y = |x|

Domain of the parent function is { x | x is a set of real numbers}

Therefore, domain of the transformed function will be the same as the domain of the parent function.

Domain of the function = {x | x is a real number}

B. Given function is f(x) = [tex](x^2-4) ^{\frac{2}{3} }[/tex]

Domain of the function : (-∞, ∞)

Critical points of the function are,

⇒ x = 0, ±2

Now we find the three intervals where we have to check the function to be increasing or decreasing.

(-∞ -2), (-2, 0), (0, 2), (2, ∞)

Derivative of the function f(x),

f'(x) = [tex]\frac{4x}{3(x^2-4)^{\frac{1}{3} } }[/tex]

Here, f'(x) < 0 for (-∞, -2)

f'(x) > 0 for (-2, 0)

f'(x) < 0 for (0, 2)

f'(x) > 0 for (2, ∞)

Therefore, given function is increasing in the interval (-2, 0) and (2, ∞)

And it's decreasing in the interval of (-∞, -2), and (0, 2).

Answer:

m<OMN = 25

m<LMN = 41

Step-by-step explanation:

m<OMN = 2x + 9

m<LMN = 6x - 7

m<OML = 66

m<OMN + m<LMN = m<OML

2x + 9 + 6x - 7 = 66

8x + 2 = 66

8x = 64

x = 8

m<OMN = 2x + 9 = 2(8) + 9 = 16 + 9 = 25

m<LMN = 6x - 7 = 6(8) - 7 = 48 - 7 = 41

Answer:

m<OMN = 25

m<LMN = 41

Answer:

one dollar 75 cents

Step-by-step explanation:

lets write the original equation again

5v+7f=28.70

now, lets put in the cost of the fruit to find cost of veggies

5v+7(2.85)=28.70

5v+19.95=28.70

5v=8.75

5=1.75

Answer:

Answer: $1.75

Step-by-step explanation:

Each pint of fruit = $2.85

7 pints of fruit = 2.85 x 7 = 19.95

5 pints of veggies will cost

28.70 - 19.95 = 8.75

Each pint of veggies = 8.75 / 5 = 1.75

Answer:

88.33.. ft²

Step-by-step explanation:

The area (A) of a rhombus is calculated as

A = [tex]\frac{1}{2}[/tex] product of diagonals , thus

A = 0.5 × 14.6 × 12.1 ≈ 88.33 ft²

Answer:

We could try another method to check, where we highlight each right angle as each is congruent from centre point.

1/2 7.3 base = 3.65 x 6.05 = 22.0825 x 4 = 88.33unit^2

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

C is the only viable answer, because it it the only one that decreases as x approaches infinity. Exponential decay decreases, hence the decay part.

The graph of the unknown function C represents exponential decay.

The correct option is C.

An exponential function's curve is created by a pattern of data called exponential decay, which exhibits higher decreases over time.

The exponential decay function:

Aₙ = A₀(1-r)ˣ, where y = Final amount, A₀ = Initial amount, r = Rate of decay in decimal form, x = Time.

Given:

Two graphs of the unknown functions are given.

And when the value of x approaches to positive infinity,

the value of y decrease exponentially.

And from the above definition,

the graph is C.

Therefore, the graph is C.

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Answer:

Step-by-step explanation:

The  system is common use is the decimal system which is based on 10;

So for example the number 45 :

45 = 4 * 10^1 + 5 * 10^0  and

132 = 1*10^2 + 3*10^1 + 2*10^0.

The single  digits in the decimal system are 0,1,2,3,4,5,6,7,8 and 9 .

Then we have 10, 11 and so on

Then there is the binary system which is based on 2 digits

In this system there are only 2 digits 0 and 1, so

10 binary = 1*2^1 + 0*2*0  which is equivalent to 2 in the decimal system.

111 binary = 1*2^2 + 1*2^1+ 1*2*0  = 4 + 2 + 1 = 7 decimal

Another system is the octal system, based on 8.

The digits are 0,1,2,3,4,5,6,7

So 10 octal = 8 + 0 = 8 decimal

and  17 octal = 1*8^1 + 7* 8^0  =   8 + 7 = 15 decimal.

Answer:

The Answer is D. (x - 1) (3x - 8)

Step-by-step explanation:

So, we start with [tex]3x^2 - 11x +8[/tex].

First step is to break the expression into groups, by doing this, you get:

[tex]\left(3x^2-3x\right)+\left(-8x+8\right)[/tex]

Next, factor out the 3x from  [tex]\left(3x^2-3x\right)[/tex]. By doing this, you should get:

3x(x - 1)

Then, factor out the 8x from  [tex]\left(-8x+8\right)[/tex]. By doing this, you will get:

-8(x - 1)

Last, factor out the common term, x - 1, When you do this, you get:

(x - 1) (3x - 8)

Hope this helps!

Answer:

D.(x − 1)(3x − 8)

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

[tex]x^2-8x+16= \\\\(x-4)(x-4)=\\\\(x-4)^2[/tex]

You can confirm this by working in reverse:

[tex](x-4)^2= \\\\(x-4)(x-4)=\\\\x^2-4x-4x+16=\\\\x^2-8x+16[/tex]

Hope this helps!

Answer:

(x−4)^2

Step-by-step explanation:

I did the test

Answer:

[tex](-3,6) \implies (0,5)\\(9,-8) \implies (6,-9)[/tex]

Step-by-step explanation:

The translation [tex]T_{(3,-1)}[/tex] shows that we need to add three units to the x-cordinates and -1 units to y-coordinates, as follows

[tex](-3,6) \implies (0,5)\\(9,-8) \implies (6,-9)[/tex]

Therefore, the image of the coordinates are

[tex](-3,6) \implies (0,5)\\(9,-8) \implies (6,-9)[/tex]

Answer:

33units^2 is the answer

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

sqrt(254) is in between 15 and 16, closer to sqrt(256), which is 16

sqrt(62) is in between 7 and 8, closer to sqrt(64), which is 8

thus 16/8 is 2

Answer:

1= 105, 2= 75

Step-by-step explanation:

Based on the 75 degree angle, since alternate interior angles have the same measurements, angle 2 will also measure 75 degrees. Furthermore, since angle 1 and angle 2 are supplementary angles, angle 1 will be 105 degrees because 105 + 75 is 180.

Answer:

Step-by-step explanation:

Malcolm's transformation:

First, the blue image is reflected about the line y=-5

Then it is rotated 180 degrees around the point (0,-5)

(you can have other options this is just one example)

Ursa's transformation:

The blue image is reflected about the y axis

(you can have other options this is just one example)

First the blue image with coordinates (x, -y) is translated to get (-x, -y) then it is rotated 180° to get the point (-x, -y) which is the coordinate of the pink image.

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.

First the blue image is translated

Then it is rotated 180° to get the red figure with coordinates (-x, -y)

Two transformation that is equivalent to a reflection

Hence, the two transformations are;

First the blue image with coordinates (x, -y) is translated to get (-x, -y)

Then it is rotated 180° to get the point (-x, -y) which is the coordinate of the pink image.

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Answer:

2 half cubes

Step-by-step explanation:

this has only half the width, you just need 1 more to make a whole, therefore 2

Answer:

[tex]3[/tex]

Step-by-step explanation:

[tex]2x-18=-2y+12[/tex]

[tex]y=12[/tex]

[tex]2x-18=-2(12)+12[/tex]

[tex]2x-18=-24+12[/tex]

[tex]2x-18=-12[/tex]

[tex]2x-18+18=-12+18[/tex]

[tex]2x=6[/tex]

[tex]\frac{2x}{2} =\frac{6}{2}[/tex]

[tex]x=3[/tex]

Answer:

x = 3

Step-by-step explanation:

=> 2x-18 = -2y+12

Given that y = 12

Putting in the above equation to get the value of x

=> 2x-18 = -2(12)+12

=> 2x-18 = -24+12

=> 2x-18 = -12

Adding 18 to both sides

=> 2x = -12+18

=> 2x = 6

Dividing both sides by 2

=> x = 3

Answer:

D = 32

Step-by-step explanation:

A+ B + E = 180 since they form a triangle

14+ 45 + E = 180

E = 180 -14-45

E =121

E on either triangle is the same since they are vertical angles

C+D+E = 180 since they form a triangle

27+ D + 121 = 180

D = 180-121-27

D =32

Answer: 130ᴼ

Step-by-step explanation:

BD is a straight line so AEB and AED add to equal 180ᴼ

180 - 50 = 130

Answer:

AED = 130

Step-by-step explanation:

AEB and AED form a straight line so they add to 180 degrees

AEB + AED = 180

50 + AED = 180

Subtract 50 from each side

AED = 180-50

AED = 130

Answer:

Step-by-step explanation:

15/3= 5

Orrrr

15/-3=-5

Answer:

6

Step-by-step explanation:

Given the system of equations:

y = 6x-b  (eq. 1)

-3x+1/2y = -3 (eq. 2)

We can rewrite eq. 1 as follows:

-6x + y = -b

Dividing by 2:

(-6x + y)/2 = -b/2

-6x/2 + y/2 = -b/2

-3x + 1/2y = -b/2

The system of equations will have infinite number of solutions if both equations are equal. Therefore:

-b/2 = -3

b= -3*(-2)

b = 6

Answer:

B

Step-by-step explanation:

Under a reflection in the line y = x

a point (x, y ) → (y, x ), thus

J(0, - 3 ) → J'(- 3, 0 )

K(- 1, 0 ) → K'(0, - 1 )

L(- 2, - 1 ) → L'(- 1, - 2 )

Answer:

yee its B

Step-by-step explanation:

Answer:

X=55°

Y=30°

Step-by-step explanation:

2y=x+5

Y=1/2x+2.5

3y+30=4x-100

3(0.5x+2.5)+30=4x-100

1.5x+7.5+30=4x-100

4x-1.5x=137.5

2.5x=137.5

X=55°

Y=30°

Answer:

[tex]x = 55\\y = 30\\[/tex]

Step-by-step explanation:

Finding x:

4x - 100 + x + 5 = 180 (Angles on a straight line)

5x - 95 = 180

5x = 180 + 95

5x = 275

Dividing both sides by 5

x = 55

Finding y:

2y + 3y +30 = 180 (Angles on a straight line)

5y = 180-30

5y = 150

Dividing both sides by 5

y = 30

Answer:

$2.50

Step-by-step explanation:

67.50/27 = 2.50

Answer:

$2.50

67.50/27 = 2.50

Step-by-step explanation:

Answer: It should be x^2 + (x-2)^2 = 100

Step-by-step explanation: the ^ is used to indicate an exponent when superscript is not available.

The solution to the correct equation will be x = 8. x -2 would be 6

8^2 = 64. 6^2 = 36. 64+36 = 100.

The equation that represents x, the side length of the greater square should be considered as the [tex]x^2 + (x-2)^2 = 100[/tex]

Since

A group of students is given a 10 by 10 grid to cut into individual unit squares.

So here the equation be like [tex]x^2 + (x-2)^2 = 100[/tex]

Hence, The equation that represents x, the side length of the greater square should be considered as the [tex]x^2 + (x-2)^2 = 100[/tex]

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Answer:

A. Area in square inches =  1760 square inches

B. Area in square feet = 12.2 square feet

C. 1 square inch = [tex]\frac{1}{144}[/tex] feet

Step-by-step explanation:

Given,

Length of the rectangle (l) = 55 inches

Breath of the rectangle (b) = 32 inches

A. Area of the rectangle = length × breath

⇒ 55 × 32

⇒ 1760 square inches

Area in square inches =  1760 square inches

B. 1 foot = 12 inches

1 inch = [tex]\frac{1}{12}[/tex] feet

1 square inch = [tex]\frac{1}{144}[/tex] feet

∴ 1760 square inches = [tex]\frac{1760}{144}[/tex] feet

⇒ 12.2222 square feet

Area in square feet = 12.2 square feet

C. 1 square inch = [tex]\frac{1}{144}[/tex] feet

Answer:

150

Step-by-step explanation:

The arc would be the same as the angle that is in it's center because this is a circle.

The measure of arc AB is equal to the 150 degree, as central angle is equal to the intercepted arc. Option D is the correct option.

The central angle is the angle which is subtended by the arc of the circle at the center point of that circle. The formula which is used to calculate the central angle of the arc is given below.

[tex]\theta=\dfrac{s}{r}[/tex]

Here, (r) is the radius of the circle, (θ) is the central angle and (s) is the arc length.

In the given circle, suppose the center of it is O. The central angle AOB given as,

[tex]\angle AOB=150^o[/tex]

The central angle is equal to the intercepted arc of the angle. Thus,

[tex]\text {arc } AB=\angle AOB\\\text {arc } AB=150^o[/tex]

Thus, the measure of arc AB is equal to the 150 degree as central angle is equal to the intercepted arc. Option D is the correct option.

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Answer:

5

Step-by-step explanation:

You can draw a point at (5,3) and call it point A.

Connect point A with V and U to get VA = 4 and UA = 3.

You get a right triangle and use pythagoream theroem. The answer is the root of 4^2 + 3^2 which equals to 5.

The answer is 5

Answer:

B and D

Step-by-step explanation

Answer:

B and D

Step-by-step explanation:

Answer:

18% , 27 Hours

Step-by-step explanation:

On edge 2020

The percentage of the initial amount of medicine that will remain in the patient’s bloodstream after 10 hours is, 17.7%.

A function assigns the value of each element of one set to the other specific element of another set.

Since, The function that models the percentage, y, of an initial dose of medicine remaining in a patient's bloodstream after x hours is given as,

⇒ [tex]y = 100 (0.5)^{x/4}[/tex]

Now, if we substitute the value of x as 10 because we need to find the percentage of medicine in the body after 10 hours.

Therefore, the value can be written as,

⇒ [tex]y = 100 (0.5)^{x/4}[/tex]

Put x = 10;

⇒ [tex]y = 100 (0.5)^{2.5}\\[/tex]

⇒ y = 17.677

⇒ y = 17.7

Thus, the percentage of the initial amount of medicine that will remain in the patient’s bloodstream after 10 hours is 17.7%.

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Answer:

12

Step-by-step explanation:

Answer:

y=3/2x+11/2

Step-by-step explanation:

divide the whole thing by 2

2y=3x+11 divided by 2 equals

y-3/2x+11/2

then just plug in the 3 points