The side length, s, of a cube is 4x2 + 3. If V = s3, what is the volume of the cube?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Expressions that add up to one another make form an equation. A formula is an equation containing two or more variables that shows how the variables relate to one another. A line with the equation y=mx+b, where m denotes the slope and b the y-intercept, is an example of a linear equation.

Given that we've done it

h(t)=-16t²+305

Here, h stands for the penny's height.

The time is expressed as t in seconds.

Now, t equals 4 seconds.

The distance the penny must travel before it touches the earth is explained by

h(4)=- 16(4)² + 305

h(4)=- 16 x 16+ 305

h(4)= 256 - + 305

h(4)= 49 feet

Hence, penny need to travel 49 feet before it hits the ground

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The expression of the given quadratic equation in factor form is (x - 3)(x - 6) = 0 with a solution of x = 3 or 6.

We are given the quadratic expression;

(x - 3)² = 3(x - 3)

By expansion of the brackets, we have;

x² - 6x + 9 = 3x - 9

x² - 6x + 9 - 3x + 9 = 0

x² - 6x - 3x + 18 = 0

By grouping into brackets we have;

(x² - 6x) - (3x - 18) = 0

By bringing out common factors, we have;

x(x - 6) - 3(x - 6) = 0

Thus, we can write it in factor form as;

(x - 3)(x - 6) = 0

x = 3 or 6

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Answer:

6(4u+3u)

Step-by-step explanation:

4u+3u= 7u

you add the 4u and the 3u because they're inside the parentheses

and then you get 6(7u)  

The potential input and output values of a function are its domain and range respectively as ( 3500 , ∞)

It is specified as follows

the region

This is a list of the function's potential S values

Due to the fact that S refers to a physical quantity, it cannot be less than 0. (i.e. tons of sugar)

Any number greater than zero may be used as S's value.

Thus, the following is the function's domain:

The variety

This represents the function's potential C values.

It is specified as follows:

When S = 0

C = 120 x 0 + 3500 = 3500

The preceding implies that:

C must be more than 3500.

Any number higher than 3500 can be used as the value of C.

Thus, the function's range is as follows: (3500 , ∞ )

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The probability that the dial stops on a yellow or blue slice is 50%.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the event's impossibility and 1 indicates certainty.

An event's likelihood of occurring increases with its probability. The flip of a fair (unbiased) coin serves as a straightforward illustration. Since there are no other possible outcomes and the coin is fair, the probability of both the outcomes, "heads" and "tails," is half.

The total no. of outcomes in the events = 10

Outcomes favourable to yellow and blue = 3 + 2  

                                                                     = 5

Probability = outcomes favourable/total no. of outcome

                  =  5/10

                  = 1/2

                  = 1/2 × 100%

                  = 50%

Thus, The probability that the dial stops on a yellow or blue slice is 50%.

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Answer: The total cost to order 12 tickets is $378.05

Step-by-step explanation:

Let y represent the cost for x number of tickets.

Since the cost for 5 tickets is $174.45, it can be represented by the point (5, 174.45).

The cost for 8 tickets is $271.95, it can be represented by the point (8, 271.95).

y = 32.5x - 11.95

The cost for 12 tickets is:

y=32.5(12) - 11.95 = 378.05

Hence the total cost to order 12 tickets is $378.05

Answer: 13.56 kg

Step-by-step explanation:

We can make two equations:

1) A = B + 2.5

2) C = B - 4.86

Replace C with 6.2.

(6.2) = B - 4.86 can be rewritten as 6.2 + 4.86 = B.

B = 11.06

Add 2.5 to 11.06 and you get 13.56 kg.

You can get the answer by reciprocating the multiplying factor of 10%

88*10/11

= 80 kg

Therefore, Hamid's original weight was 80 kgs

Answer:

can you translate this because I don't understand

We need to know to solve equations by elimination method to solve the problem. The solution for the given pair of equations is g=0 and h=7.

When we solve a given pair of equations by elimination method, we need to express one of the variables in terms of the other variable and then substitute this value in the other equation to find the value of one of the variables. We use the value of this variable to find the value of the other variable. In this question we have a pair of equations and we need to solve for the variables g and h.

5g+2h=14..(i)

3g-4h=-28..(ii)

From equation (i)

2h=14-5g⇒h=7-5g/2

Substitute this in equation (ii)

3g-4(7-5g/2)=-28

3g-28+10g=-28

13g=0

g=0

Using value of g to find out h

h=7-5g/2=7

Therefore the solution of the given pair of equations is g=0 and h=7.

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Answer:  See the graph I attached below.

Step-by-step explanation:  Remember to use the slope-intercept form of the equation:

y = mx+b

m = slope

b = y-intercept

Therefore, y=1/2x-3 has a slope of 1/2 and intercepts the y-axis at -3

The given side lengths of AC, BC, and EF, of the similar triangles, using the ratio of similarity between segments of similar figures, gives;

The measure of side DF as 15 centimeters

When two figures are similar, the corresponding side pairs have the same ratio of one to the other.

The given information on the two triangles are;

Triangle ∆ABC is similar to triangle ∆DEF

Triangle ∆ABC and triangle ∆DEF are right triangles

The length of segment AC = 9 centimeter

Length of segment BC = 15 centimeters

In triangle ∆DEF, we have;

Length of segment EF = 25 centimeters

Required;

The length of segment DF

Solution;

By comparison, the corresponding sides of the two triangles are;

AC corresponds to DF

BC corresponds to EF

In similar triangles, the ratio of the corresponding sides are the same, which gives;

[tex] \displaystyle{ \frac{AC}{DF} = \frac{BC}{EF} }[/tex]

[tex] \displaystyle{ \frac{9}{DF} = \frac{15}{25} }[/tex]

[tex] \displaystyle{ DF = \frac{9 \times 25}{15} = 15 }[/tex]

The measure of side DF is 15 centimeters

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Answer: -a-7

Step-by-step explanation:

Answer:

−a −7

Step-by-step explanation:

group the 'a's. 2a-8a+5a. It is -a. Next, group the numbers and simplify them. 7-14. It is equal to -7. If you put -a and -7 together, you get "-a-7" as an answer.

Answer:

      The graph of a line with 1/2 is only half of 1/4 the line with 4 is greater and way bigger than just half of 1/4.

Step 1:

Write the regression line equation.

Step 2:

y represents the cost and x represent the number of years.

From 2005 till 2022

x = 17 years

Step 3:

Let find the cost to go on a safari in 2022.

Final answer

The cost to go on a safari in 2022 = $74

The radius of the cylindrical container with a volume and height of 125.7cm³ and 10cm is 2cm.

The volume of a cylinder is expressed as;

V = π × r² × h

Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )

Given the data in the question;

To determine the radius of the cylindrical container, plug the given values into the formula above and solve for r.

V = π × r² × h

r² = V / ( π × h )

r² = 125.7cm³ / ( 3.14 × 10cm )

r² = 125.7cm³ / ( 31.4cm )

r = √( 125.7/31.4 cm² )

r = 2cm

Therefore, the radius of the container is 2 centimeters.

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Answer:

Length of segment PQ = 5

Step-by-step explanation:

Coordinates of P (-2, 4) and coordinates of Q are (3,4)

y coordinates are the same so the segment PQ is a horizontal line

The length is simply the difference between the x coordinates = 3 -(-2) = 3 + 2 = 5

Answer:

Acute

Step-by-step explanation:

Answer:

It is Acute.

Step-by-step explanation:

To be right triangle it has to be all perfect sides same length, to be obtuse has to be wider to the sides but this one is acute because it goes inside.  

Answer:

[tex]y - 3 = -\dfrac{1}{4}(x - 4)[/tex]

Step-by-step explanation:

This can be solved without too much calculation

First note that the lope of the graph is negative. If you look at the graph, as x increases, y decreases so that indicates a negative slope

We can safely eliminate the last two options because the coefficient of x in both is +1/4 indicating a positive slope

That leaves the first two for consideration

We can plug in the x, y  values for the given point (4, 3) which lies on the  line and see which of the equations is consistent, i.e whether the LHS and RHS of the equation match

Putting y = 3 and x = 4 in the first equation y - 4 = -1/4(x - 3) gives us
3 - 4 = -1/4(4-3) ??

-1 = -1/4(1) ?

-1 = -1/4? NO

So the correct choice is the second option and we can verify that by plugging in (4, 3) into y - 3 = -1/4(x - 4)

y - 3 = 3 - 3 = 0

x - 4 = 4 - 4 = 0

So 0 = -1/4(0) = 0

which is consistent

Solving a linear equation that comes from the relation:

TV = TU + UV

We will see that the value of x is 1.

I'm answering the question you wrote.

We know that point U is on the line segment TV, then we can write:

TV = TU + UV

This says that the total length of TV is equal to the sum of the two segments in it.

It says:

"the length of segment TV is equal to the sum between the lengths of segments TU and UV"

Here we know that:

TU = 4

UV = 5x

TV = 3x + 6

Then we can write the linear equation:

3x + 6 = 4 + 5x

And solve this for x.

3x + 6 = 4 + 5x

6 - 4 = 5x - 3x

2 = 2x

2/2 = x

1 = x

The value of x is 1.

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Answer: A≈1922.46

Step-by-step explanation: A=6a^2=6·17.92≈1922.46

Answer:

17.75

Step-by-step explanation:

The area of rectangle A is (A) 256 cm².

So, the area of rectangle A:

Therefore, the area of rectangle A is (A) 256 cm².

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Answer:

128 cm^2

Step-by-step explanation:

The area of rectangle B is 512 cm2. Since the dimensions of rectangle B are two times larger than the dimensions of rectangle A, the scale factor is 2.

To find the area of rectangle A, first square the scale factor, 2.

2^2 = 4

Next, divide the area of rectangle B by 4.

512 cm^2 ÷ 4 = 128 cm^2

"A number divided by 3 decreased by 2 is at most"  in equation form is 2y/3 -2 ≤ 2

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation

Given that: a number divided by 3 decreased by 2 is at most 2

We need to translate the word into an equation:

First, we will assign a letter to the said number. So let the number be y

The number divided by 3: y/3

Then decreased by 2: y/3 -2

And everything is at most 2 (it is less than or equal to 2): y/3 -2 ≤ 2

Therefore, the given word problem can be written as y/3 -2 ≤ 2

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The percentage of tip that Kylie left is 20%  

Finding percentage:

To find the percentage of the number in a given whole number divide the number by the whole number and multiply by 100. To find the percentage of the tip we will calculate the percentage of tips in the total cost.

Here we have,

To find the total plus tip, Kylie multiplied the cost of the meal by 1.2  

Let $ x be the cost of the meal

Then total cost plus including tip = x × 1.2 = 1.2x

From the above calculations,

The amount of tip paid by Kylie = 1.2x - x = 0.2x

There percentage of tip = (0.2x)/x × (100) = 20%      

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Answer:

The correct equation is b, x = 4.

Answer: the volume of cube is 64 x6 + 144x4 + 108x2 + 27.

Step-by-step explanation: As given in the problem statement the volume

V = s3----- (1)

And

s = 4x2 + 3--------(2)

Hence,

the volume is obtained by substituting (2) in (1).

We get,

V = (4x2 + 3)3

= 64 x6 + 144x4 + 108x2 + 27

Therefore,

the volume of cube is 64 x6 + 144x4 + 108x2 + 27.

Answer:

Step-by-step explanation:

The side length, s, of a cube is 4x2 + 3. If V = s3, what is the volume of the cube?

Volume = s³

s = 4×2+3

so

(4 × 2  + 3)² =                 (remember PEMDAS)

(8 + 3)² =

11² =

121 units²

Answer:

135

Step-by-step explanation:

If 3x = 5, x = 5/3

3^4 = 81

3^4 x = 81x = 81 x 5/3 = 135

The distance between the peter's house and John's house is found as √116 units.

For the given question;

Let the coordinates of the John's house be (x₁, y₁).

Let the coordinates of Paul's house M be (x, y) = ( 3, -5).

Let the coordinates of Peter's house be (x₂, y₂) = (5, -4).

Then, by the formula of mid point.

x = (x₁ + x₂)/2

Put the values and simplifying.

x₁ = (2×3) - 5

x₁ = 1

Similarly for the y coordinates.

y = (y₁ + y₂)/2

Put the values and simplifying.

y₁ = (2×-5) - 4

y₁ = -14

Thus, the coordinates of the John's house is found as (1, -14).

Now, the distance between peter's house and john's house is;

d = √(x₁ - x₂)² + (y₁ - y₂)²

Put the values;

d = √(5-1)² + (-4+14)²

d = √(4)² + (10)²

On simplification,

d = √116 units.

Thus, the distance between the peter's house and John's house is found as √116 units.

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The slope of line segment XZ in triangle XYZ is: -1/3.

Given a line segment on a coordinate plane, we can find the slope of the line by using two points on the line to find the ratio of change in y / change in x = (y2 - y1)/(x2 - x1).

The coordinates of the two points of line segment XZ in triangle XYZ are:

Plug the values into the formula used for finding the slope of a line:

Slope of line segment XZ = change in y / change in x = (5 - 3)/(1 - 7)

Slope of line segment XZ = 2/-6

Slope of line segment XZ = -1/3

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