express the fractions 2/3,3/4 and 5/6 as equivalent with denominator of 12

\(\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ f(x)= 2x^2 + x -3 \qquad \begin{cases} x_1=0\\ x_2=2 \end{cases}\implies \cfrac{f(2)-f(0)}{2 - 0} \\\\\\ \cfrac{[2(2)^2 + (2) -3]~~ - ~~[2(0)^2 +(0) -3]}{2}\implies \cfrac{7-(-3)}{2}\implies \cfrac{7+3}{2}\implies \text{\LARGE 5}\)

The rate of change for the interval between 0 and 2 for the quadratic equation will be 5. Then the correct option is C.

It is the average amount by which the function varied per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph depicting the function.

Average rate = [f(x₂) - f(x₁)] / [x₂ - x₁]

The function is given below.

f(x) = 2x² + x - 3

The rate of change of the function for the interval between 0 to 2 is calculated as,

Average rate = [f(2) - f(0)] / [2 - 0]

Average rate = [(2(2)² + 2 - 3) - (2(0)² + 0 - 3)] / 2

Average rate = 10 / 2

Average rate = 5

The rate of change for the interval between 0 and 2 for the quadratic equation will be 5. Then the correct option is C.

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Answer Im not exactly sure

Step-by-step explanation:

Answer:

3.94

Step-by-step explanation:

3.944     rounded to nearest hundredth  = 3.94    becuase the thousandth digit is <5  you do not change the hundredth

Answer:

3

Step-by-step explanation:

27^1/3

= 3√27

=3 is the collect option

Answer:

9.7

Step-by-step explanation:

97/10= 9.7

formula for rectangle= length x width

area divided by width= 97/10

97/10=9.7

length=9.7

9.7x10=97

Answer:

I wish I could help but I don't know

Answer:

D is correct

Step-by-step explanation:

Step-by-step explanation:

\( = ( \frac{3}{5} {)}^{2} \)

\( = \frac{ {3}^{2} = 3 × 3 }{ {5}^{2} = 5 × 5 } \\ \)

\( = \frac{9}{25} \\ \)

☘️☘️☘️...

Answer:

\( \frac{9}{25} \)

Step-by-step explanation:

\( { ( \frac{3}{5} )}^{2} \\ = ( \frac{ {3}^{2} }{ {5}^{2} } ) \\ = \frac{9}{25} \)

Answer:

1 : 2

Step-by-step explanation:

First situation

sides of triangle:-

a=x, b=2x, c=3x

then perimeter = a+b+c

perimeter = x + 2x + 3x

Perimeter = 6x

Second situation(sides are doubled)

sides of triangle:-

a=2x, b=4x, c=6x

then perimeter = a+b+c

perimeter = 2x + 4x + 6x

Perimeter = 12x

Ratio of first situation to second

Perimeter of first situation : Perimeter of second situation

6x : 12x

1 : 2

Answer: 36 m, 144 m

Step-by-Step Explanation:

a = 14 m

b = 12 m

c = 10 m

Perimeter = a + b + c

Therefore,

= a + b + c

= 14 + 12 + 10

= 26 + 10

=> 36

Perimeter = 36 m

Length of Fence required for Fencing 4 times = Perimeter * 4

Therefore,

= Perimeter * 4

= 36 * 4

= 144

Length of Fence required for Fencing 4 times = 144 m

Answer:

lol the answer is the second one

Answer:

90 different ways

Step-by-step explanation:

30 people can finish first, 30 people can finish 2nd, 30 people can finish 3rd. Ends up being 90 different outcomes.

Answer:

12 inches

Step-by-step explanation:

PART A

We can see that the domain is: [-π , π] and the range is: [-1,1].

PART B

We see that the x-intercept is at x=0.

We see that the y-intercept is at y=0.

The expression can be used to represent a French sharing one six of a gallon of lemons equally is 1/6g.

It should be noted that expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them

The expression can be used to represent a French sharing one six of a gallon of lemons equally will be:

= 1/6 × g

= 1/6g

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Complete question

Which expression can be used to represent a French sharing one six of a gallon of lemons equally?

1/6g

2/3g

6g

1/3g

Answer:

Item price now= 3.95

Step-by-step explanation:

To find out the price now, we will subtract 79 (original price) by 95% of 75. That will equal the discounted price. Finding the percentage of anything, we can use the formula, Total amount•percentage/100. The total amount is 79, and the percentage is 95. 79•95=7505, 7505/100=75.05. Now, 95% of 79 is 75.05, 79-75.05=3.95. $3.95 is the price now of the item. Though, I am unsure what a ALEKS calculator is. Have a nuce time, and joyful day

Answer: -2 and 4

Step-by-step explanation:

\(f(x) = \frac{-2x+2}{2x+4}\)            g(x) = -2x+8

Question asks what the domain is if we had f(x) ÷ g(x)

\(\frac{f(x)}{g(x)} = \frac{-2x+2}{2x+4}\)  ÷                  >When dividing fractions, keep the first

                                                      Change the sign, flip the second fraction

\(\frac{f(x)}{g(x)} = \frac{-2x+2}{2x+4} * \frac{1}{-2x+8}\)        

\(\frac{f(x)}{g(x)} = \frac{-2x+2}{(2x+4)(-2x+8)}\)          

> you can never get a 0 on the bottom of division so that is where the exception of what x cannot be.

2x+4 = 0

2x= -4

x =  -2

and

-2x+8 = =

-2x = -8

x = 4

So x cannot be -2 and 4

The negative relationship between the amount of sugar eaten and happiness level only shows: correlation without causation".

Therefore, the negative relationship between the amount of sugar eaten and happiness level only shows: correlation without causation".

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Answer: yes

Step-by-step explanation: because its a decrease

There isn't a ton of info provided in your question, however, I believe the solution is 1 = 1.

Answer:1.5 inches

Step-by-step explanation:

Total: 499.75

Step-by-step explanation:

4 × 110.5 = 442

3 × 19.25 = 57.75

442 + 57.75 = 499.75

Answer:

1. 160 candidates

2. 2,3,5 (not sure tho)

3. i don think there's any.

The equation thatmodels the movement of the objet is:

where h(t) is equal to the hight and t is the time, so we can replace h(t)=36 so:

now we can use the cuadratic function to find the values of t so:

So the equation become:

Now we operate so:

Now we solve bout solutions:

So he will reach a hight of 36 feets at 0.75 seconds and a time of 3 seconds because the first time is when his is going up and the second time is we he is falling back to the grownd.

Answer:

Negative 5

Step-by-step explanation:

\(10x+5-5=9x-5\)

\(10x+5-5\\= 10x+\left(5-5\right)\\= 5-5\\=0\\=10x+0\\=10x\)

--------------

\(9x-5\\= 9x-5\)

→ \(10x=9x-5\)

\(10x-9x=9x-5-9x\)

\(10x - 9x\\= 1x\\= 1 \times x\\= 1\)

\(9x-5-9x\\=9x\left(-5\right)-9x\\= 9x - 9x\\= 0 - \left(-5\right)\\= -5\\x = -5\)

Hope this helps!

length of the original rectangle is 28.8 inches.

width of the original rectangle is 19.2 inches.

given that the scale factor is

\( \frac{5}{8} \)

multiply the dimensions of original rectangle by 5/8 to obtain the dimensions of the scale drawing.

the following method is useful to find the dimensions of the original rectangle.

length of the original rectangle

\( \frac{8}{5} \times 18 = 28.8 \: inches\)

width of the original rectangle\( \frac{8}{5} \times 12 = 19.2 \: inches\)

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Answer:

180

Step-by-step explanation:

From the table :

Slope :

m = (y2 - y1) / (x2 - x1)

m = (100 - 80) / (5 - 4)

m = 20 / 1

m = 20

y = 20x

Hence, when, x = 12

y = 20 * 12

y = 240

From the graph:

Slope :

m = (y2 - y1) / (x2 - x1)

m = (280 - 70) / (8 - 2)

m = 210 / 6

m = 35

y = 35x

When x = 12

Graph :

y = 35 * 12

y = 420

Difference :

420 - 240

= 180

A) The variable is n, which represents the number of the figure in the pattern.

B) Here is a table for up to 8-figure patterns:

Figure Number of Cheerios

1                      1

2                      3

3                      6

4                     10

5                     15

6                     21

7                    28

8                    36

C) The equation to represent the nth term of the sequence is n(n+1)/2.

D) If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12.

E) It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.

F) Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.

Here is a more detailed explanation of how to answer each question:

A) Identify and label the variable

The variable is n, which represents the number of the figure in the pattern. For example, the first figure is figure 1, the second figure is figure 2, and so on.

B) Make a table for up to 8-figure patterns

Here is a table for up to 8-figure patterns:

Figure Number of Cheerios

1                        1

2                        3

3                        6

4                        10

5                        15

6                        21

7                        28

8                        36

C) Write an equation to represent the nth term of the sequence

The equation to represent the nth term of the sequence is n(n+1)/2. This equation can be derived by looking at the table of values. For example, the number of Cheerios in the first figure is 1, which is equal to 1(1+1)/2. The number of Cheerios in the second figure is 3, which is equal to 2(2+1)/2. And so on.

D) If the pattern continues, what figure number will have 20 whole Cheerios in it?

If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12. This can be found by solving the equation n(n+1)/2 = 20. The solution is n = 12.

E) Is it reasonable to think this pattern would continue forever? If not, explain.

It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.

F) Based on the information provided, what is the largest figure number we can have using a full box of Cheerios?

Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.

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Explanation:

Segment AW bisects angle CAD.

This leads to the smaller pieces (angles CAW and DAW) to be equal to one another. Both are 20 degrees each. That totals to 20+20 = 40 degrees.

Therefore, angle CAD = 40 degrees.

The supplement of this is angle DAX

(angle CAD) + (angle DAX) = 180

angle DAX = 180 - (angle CAD)

angle DAX = 180 - 40

angle DAX = 140 degrees

The value of cost of wall-to-wall carpeting in room is,

⇒ 27.916

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

WE have to given that;

Dimensions of room is,

⇒ 24' x 17'

And, Carpeting is on sale for 9.97 per square yard.

Now, Area of room is,

⇒ A = 24' × 17'

⇒ A = 2 × 17/12 yards²

⇒ A = 2.8 inhces²

Since, Carpeting is on sale for 9.97 per square yard.

Hence, The value of cost of wall-to-wall carpeting in room is,

⇒ 9.97 x 2.8

⇒ 27.916

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The quadratic equation that fits each set of points (0.-8), (2, 0), and (-3, -5) is -3x² + 10x - 8 = 0

Quadratic equation:

Quadratic equation refers algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

Given,

Here we have the set of points (0.-8), (2, 0), and (-3, -5).

Now, we have to find the quadratic equation for this points.

We know that the standard form of the quadratic equation is,

y = ax² +  bx + c

Here we have to use each point value in order to find the value of a, b and c to find the quadratic equation of the points,

First we have to take the point (0, -8) and apply it on the formula, then we get,

-8 = a(0)² +  b(0) + c

-8 = c

Now, use the point (2,0), then we get,

0 = a(2)² +  b(2) + c

0 = 4a + 2b + c --------------------(1)

Finally, take the point (-3, -5), then we get the equations,

-5 = a(-3)² +  b(-3) + c

-5 = 9a - 3b + c --------------------(2)

Now, apply the value of c as -8, then we get,

4a + 2b = 8 ----------------(3)

9a -3b = 3 -----------------(4)

Divide equation (4) by 3 and equation (3) by 2 on both sides then we get,

2a + b = 4

3a - b = 1

When we subtract these equation then we get the value of

a = -3

Then the value of b is

2(-3) + b = 4

b = 4 + 6

b = 10

Therefore, the quadratic equation is -3x² + 10x -8 = 0

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