A rectangular prism has a length that is 3 inches shorter than the height and a width that is 5 inches longer than the height. Fill in the blanks to create an equation for the volume of the prism as a function of the height.

Answer:

(1) Natural numbers are a part of the number system which includes all the positive integers from 1 till infinity. Example, 1, 2, 3, 4,... are natural numbers.

Step-by-step explanation:

(2) Number Trick 1:

Let the single digit be: 1

Multiply by 2: 1 x 2 = 2

Add 8 to your answer: 2 + 8 = 10

Divide your answer by 2: 10 ÷ 2 = 5

Subtract original number: 5 - 1 = 4

(3) Final result is 4.

The trick will always work for all NATURAL NUMBERS.

The inequality that describes this scenario would be; A. 200 + 256C ≥ 870.

Inequality is defined as the relation which makes a non-equal comparison between two given functions. If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.

Given that lisa checks and finds that she has 200 gigabytes available on her phone. It is going to use memory cards that each hold 256 gigabytes.

Let consider that C represent the number of memory cards that Lisa buys.

Then the inequality ;

200 + 256C ≥ 870

Hence, The inequality that describes this scenario would be; A. 200 + 256C ≥ 870.

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The biggest  area of a quadrilateral we can fit in a circle of a 20π units is 200 sq units.

GIVEN:

SOLVING:

Area of the quadrilateral is

hence,The biggest  area  of a quadrilateral we can fit in a circle of a 20π units is 200 sq units.

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Answer:

neither of them are right

The expression for f(x) is: [tex]f(x)=(x+4) , (x-2) , (x-9) ,(x+5),(x+5),(x+5)[/tex]

We know that for any polynomial equation with roots:

[tex]a_{1}, a_{2}, a_{3} ,...[/tex]

with multiplicity:

[tex]m_{1}, m_{2}...[/tex]

the equation for the polynomial is given by:

[tex]f(x)=(x-a_{1}) ^{m_{1} }, (x-a_{2}) ^{m_{2} }...[/tex]

If the leading coefficient is negative we may take '-' sign in the starting of the expression.

Here we are given that, f(x) has a leading coefficient of 1, roots -4, 2, and 9 with multiplicity  1, and root -5 with multiplicity 3

Hence, f(x) is given by:

= [tex]f(x)=(x-(-4)) ^{1 }, (x-2) ^{1}, (x-9) ^{1},(x-(-5)) ^{3}[/tex]

= [tex]f(x)=(x+4) , (x-2) , (x-9) ,(x+5),(x+5),(x+5)[/tex]

Hence, the expression for f(x) is: [tex]f(x)=(x+4) , (x-2) , (x-9) ,(x+5),(x+5),(x+5)[/tex]

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Answer:

11. -3/2

12. -1

Step-by-step explanation:

To find slope, subtract the y's and put that on top of a fraction. Then subtract the x's and put that on the bottom of the fraction. Simplify if you can.

Subtract y's 2 - -4 is

2+4 which is 6, put that on top.

0 - 4 is -4 put it on the bottom.

Slope is 6/-4. Simplified, this is -3/2

The other question, same thing:

y-y over x-x

-4 - -3 / -2 - - 3

= -4+3 / -2 + 3

= -1 / 1

= -1

Answer:

390

Step-by-step explanation:

Paul receive about 13 advertisement via email each day. about how many advertisement emails will he receive in 30 days?

13 × 30 = 390

Answer:

Step-by-step explanation:

rearrange this equation y – 7=3(x−4) into this Ax+By = C

its pretty simple if you think about it :)

firstly, lets multiply the 3 with x - 4

y - 7 = 3x -12

we are going to bring the 3x to the right side to make the arrangement possible

-3x - y = -5 (minus twelve plus seven)

therefore, A is -3, B is -1 and C is -5

Answer:

1/25 or 0.04

Step-by-step explanation:

evaluated in fraction and decimal form i hope this helped :)

Root 13 is a non-recurring, infinite decimal. Since 13 is not a perfect square, its square root cannot be determined precisely. 13 cannot be expressed as a fraction, which is the definition of a rational number, because it cannot be expressed as a ratio of integers.

An illustration of a rational number?

If p and q are integers and q is not equal to 0, then the number is in the form of p/q and is said to be rational. Rational number examples include 1/3, 2/4, 1/5, 9/3, and so on.

Irrational number examples include: Any real number that cannot be expressed as a fraction is considered to be illogical.

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The required point on the cartesian plane is (0,1).

Definition of a Cartesian Plane. The intersection of two perpendicular lines results in the formation of the cartesian plane, a two-dimensional coordinate plane. The X-axis is the horizontal line, and the Y-axis is the vertical line.

In a graph (1,7) lies in the first quadrant

And if we go 1 unit left then that means that we will be on the y axis

Then if we go down 6 units we will reach at point 1 unit away from the origin on the y axis . This particular point can be represented as (0,1).

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Answer: I think it's 9 days.

Step-by-step explanation:

The answer to all the subparts of the congruency of triangles is shown:

In ΔABC and ΔPQR  

Thus from SSS congruence, we get ΔABC ≅ ΔPQR  

In ΔGHJ and ΔUVW

Thus from SSS congruence, we get ΔGHJ ≅ ΔUVW

However, ΔGHJ and ΔPQR are not congruent because there are no two sides that are equal.

Also, ΔPQR and ΔUVW are not congruent because of the same reason mentioned above.

Therefore, the answer to all the subparts of the congruency of triangles is shown:

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The diameter is decreasing at a rate of  - 0.101 cm/min

Given that,

Surface area is decreasing at a rate of [tex]7cm^{2}[/tex]/min,

We know that,

Surface Area of a sphere:

S = 4 π r2

dS/dt = - 7cm2/min

our aim is to find rate of decrease of Diameter:

dD/dt =?

Substitute r in the equation with radius = 1/2*Diameter:

r = 1/2D

Take the derivative of the surface area function with respect to time:

d/dt [S = 4 π (1/2D)2]

d/dt [S = 4 π 1/4*D2]

d/dt [S = π *D2]

dS/dt = 2πD*dD/dt

Solve for dD/dt:

dD/dt = dS/dt / 2πD

Substitute, dS/dt = - 7cm2/min and D = 11 cm

dD/dt = dS/dt / 2πD

dD/dt = - 7cm2/min / 2π*11cm

dD/dt = - 7cm2/min / 22π cm

dD/dt = - 7cm / 22π min

dD/dt = - 0.101 cm/min

Therefore, the diameter is decreasing at a rate of - 0.101 cm/min

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0.101331789 cm/min is the rate at which the diameter decreases when the diameter is 11 cm

if a snowball melts so that its surface area decreases at a rate of 7 cm2/min,

find the rate at which the diameter decreases when the diameter is 11 cm.

Surface area: S

radius: r

diameter: e

time: t

[dS/dt] = [dS/de]*[de/dt] => de/dt = [dS/dt] / [dS/de]

S = 4pi*r^2 = 4p*i(e/2)^2 = pi*e^2 => dS/de =2pi*e

dS/dt = 7cm^2 / min

de / dt = [2pi*e] / [7cm^2/min] =[7cm^2/min] /  [2pi*11cm]

= 0.101331789 cm/min

Hence , 0.101331789 cm/min is the rate at which the diameter decreases when the diameter is 11 cm

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The number of the students should be sampled to be within 0.25  alcoholic drinks of population mean with 95% probability is 62.

α is the result of subtracting one from confidence interval as well as dividing by two.

α =  (1 - 0.95) ÷ 2 = 0.25

Find z in the Z-table because z does have a p-value of 1 - α.

As a result, the p-value of z is  (1 - 0.025) = 0.975.

Thus, z  = 1.96

Now find M as;

M = z × (σ ÷ √n)

In which,

When M = 1,

The standard deviation, in accordance with the question, is approximately 1.

σ = 1

M = z × (σ ÷ √n)

0. 25 = 1.96 × (1 ÷ √n)

√n = 1.96 × (1 ÷ √n)

Squaring both sides,

(√n)² = ((1.96 × 1) ÷ 0.25)²

n = (7.84)²

n = 61.4656

n ≈ 62

Thus, the number of the students should be sampled to be within 0. 25 alcoholic drink of population mean with 95% probability is 62.

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The given figure is a Rhombus hence the last diagram is correct.

In planar Euclidean geometry, a rhombus—also known as a rhombi or rhombus—is a quadrilateral having four sides of equal length.

The given figure is a rhombus. All the sides are equal but the angles are not 90°. Hence its is not a square or a rectangle.

The correct diagram is attached below.

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Answer:

45 large dogs

Step-by-step explanation:

Step 1:

60 x 3 = 180

180 ÷ 4 = 45

Simple Interest is the amount repaid for using the borrowed funds over a predetermined amount of time. When the total principal amount and the rate of interest for a certain amount of time surpass the due date for payment, this is known as compound interest.

Total to Calculate Interest on - $150

Annual Interest Rate - 4%

Monthly interest -  $0.50

Yearly interest -  $6.00

Total to Calculate Interest on - $180

Annual Interest Rate - 3.5

Monthly interest -  $0.53

Yearly interest - $6.30

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The system of inequalities has no solution because the lines do not meet at any point

The system of inequalities is given as

y ≥ x² + 3

y < x + 1

From the above system of inequalities, we can see that the function types are

Next, we plot the graph of both inequalities in the system (see attachment for the graph)

From the graph, we can see that the lines and the curves of the functions do not intersect

This means that the system has no solution

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Answer

It will take 3 hours to get to your cousin's house.

Explanation

Firstky, note that Speed is given as

For this question, we are told that the distance to your cousin's house is 150 miles.

The speed is an average rate of 50 miles per hour.

We are then asked to calculate how long it will take to get to your cousin's house.

Speed = 50 miles/hour

Distance = 150 miles

Time = ?

Hope this Helps!!!

Answer:

3rd Graph = 1st box

2nd Graph = 2nd Box

4th Graph = 3rd Box

The correct answer is option D

3(c) - 2 represents the total cost of three dance tickets at a cost of c each, less a one-time $2 discount.

         y = mx+b, where m is the slope and b is the y-intercept.

Based on the question. We have the parameters listed below.

The total cost of three dance tickets is 3c (at c for each)

One-time offer = $2

Because discounts are always subtracted from the total cost,

the equation represents,

the total cost of three dance tickets at a cost of c each, less a one-time discount $2

=  3(c) - 2

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[tex]\cfrac{1}{3}x^2~~ = ~~\cfrac{4}{27}\implies \cfrac{x^2}{3}~~ = ~~\cfrac{4}{27}\implies x^2=\cfrac{(3)4}{27}\implies x^2=\cfrac{12}{27} \implies x=\pm\sqrt{\cfrac{12}{27}} \\\\\\ x=\pm\cfrac{\sqrt{12}}{\sqrt{27}} \implies x=\pm\cfrac{\sqrt{2^2\cdot 3}}{\sqrt{3^2\cdot 3}}\implies x=\pm\cfrac{2\sqrt{3}}{3\sqrt{3}}\implies x=\pm\cfrac{2}{3}[/tex]

The x- and y-intercepts of the graph of x+y=18 are; (18, 0) and (0, 18) respectively.

The x-intercept of a function of variable x ( y = f(x) ) form is an intersection fo the x-axis and the curve of the function. The x-intercept for a function y = f(x) is a solution to the equation f(x) = 0 because at that value of x, the function f(x) lies on x-axis, where y is 0. Values of x-intercept for a function f(x) are also called roots or solution of f(x) = 0 equation.

For x intercept, y = 0

x + y = 18

x + 0 = 18

x = 18

Hence, the x-intercept is (18, 0)

For y intercept, x = 0

x + y = 18

0 + y = 18

y = 18

Hence, the y-intercept is (0, 18)

The x- and y-intercepts of the graph of x+y=18 are; (18, 0) and (0, 18) respectively.

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(d) f(1) = 4 f(n) = 4 + d(n-1) , n>0 is the arithmetic formula to find the number of layers in the project

In the above question it is given that

A project is being created by a group of students by arranging layers.

The first layer is having 4 layers and as we move to the next layers, it is getting 2 times of the number of layers in the first layer.

i,.e f(1) = 4

Number of layers in the second layer = 8 layers

f(2) = 4.2 = 8

Now, we need to find the general arithmetic formula to determine the subsequent n number of layers in the project

As the subsequent layers are getting n times of the first layer, so we'll also find the similar arithmetic formula where addition to the first layer with n times of it is happening

So, after checking all the given options we find, (d) as the appropriate option

f(1) = 4

f(n) = 4 + d(n-1) , n>0

We'll find the number of layers in the 3 layers

Here, n = 3

Putting in the formula, we'll find.

f(3) = 4 + d(3-1)

f(3) = 4 + d(2)

where d(2) = 8 (given)

so, f(3) = 4 + 8 = 12

Hence, f(1) = 4 f(n) = 4 + d(n-1) , n>0 is the arithmetic formula to find the number of layers in the project

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Answer

Option C is correct.

8.0 × 10³ miles = 8 thousand miles.

Explanation

The number given in scientific notation is

8.0 × 10³ miles

= 8.0 × 1000 miles

= 8000 miles

= 8 thousand miles.

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Answer:

where is the question? plssss so im sorrry but where is the question i don't see a question?

Answer:

x = 9.629 meters

Step-by-step explanation:

x / 10.25 = 1.55 / 1.65

x = 1.55 / 1.65 * 10.25

x = 9.629 meters

Answer:

32 units

Step-by-step explanation:

calculate the distance using the absolute value of the difference.

| - 9 - 23 | = | - 32 | = 32

or

| 23 - (- 9) | = | 23 + 9 | = | 32 | = 32

Answer:

a = 84

Step-by-step explanation:

[tex]\frac{a}{6} - 5 = 9\\\frac{a}{6}} - \frac{5*6}{6} = \frac{9*6}{6}\\ a - 30 = 54\\ a = 54 + 30\\ a = 84[/tex]