simplify the expression below: 3(7x) -2(4-x)

a. 12-2x
b. 13+2x
c. 23x-8
d. 20x-8

A) Proportional

y is 1/2 times x

B) Not proportional

y is 3/2 times x

C) Proportional

y is 1/2 times x

Graph a and Graph b are not proportional and Graph c is proportional and for graph c y is 1/2 times of x

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

A proportional relationship graph between two variables is a relationship where the ratio between the two variables is always the same.

(a) Not proportional

(0,0),(2,1)(4,4)

The relationship between these is not same.

The graph a is not proportional.

(b) Not proportional

(2,0)(4,3)(6,6)

The relationship between these is not same.

The graph b is not proportional.

(c)Proportional

(0,0)(2,1)(4,2)

y is 1/2 times of x

The graph c is proportional.

Hence Graph a and Graph b are not proportional and Graph c is proportional and for graph c y is 1/2 times of x

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Answer:

Expand the polynomial using the FOIL method.

a ^2 + a − 6

Hope This Helps!     Have A Nice Day!!

Answer: The answer will be .... a^2 + a - 6

Use the foil method.

F. irst

O. utside

I. nside

L. ast

Answer:

20%

Step-by-step explanation:

What we are looking for is 125*x = 25, where x is the percentile (represented as a decimal)

By dividing both sides by 125, we get that x = 0.2, which means that 25 is 20% of 125, as in percentile, 1 = 100%.

To find out '25 is what percent of 125', you divide 25 by 125, and then multiply by 100. The result is 20. Thus, 25 is 20% of 125.

To find out 25 is what percent of 125, you need to understand the concept of percentage. The term percentage means 'per 100', or 'out of 100'. In your case, you're trying to find out how much 25 is out of 125 in terms of per 100. The formula to find a percentage is:

(Part / Whole) * 100

In your case, the part is 25 and the whole is 125. So, you substitute these values into the formula:

(25 / 125) * 100

That calculation results in 20. Therefore, 25 is 20 percent of 125.

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Let x= the distance that Jana lives from school. Then, x < 2/3

Answer:

Step-by-step explanation:

Let the current display rate be f (in frames per second).  If the new computer is 40% faster, then the new display rate will be 1.40f (frames per second).

" The exact number of additional frames per second that can be displayed on the faster computer cannot be determined without specific information about the software's performance on the current computer. However, if the software's performance scales linearly with the computer's speed, the faster computer could potentially display 40% more frames per second than the slower one.

To solve this problem, we need to understand the relationship between the speed of a computer and the number of frames per second (FPS) it can display. The term ""faster"" in the context of computers generally refers to the processing speed, which can be influenced by factors such as the central processing unit (CPU) clock speed, efficiency of the software code, and the performance of other hardware components.

If we assume that the software's performance is directly proportional to the computer's speed (which is a simplification and may not hold true in all cases due to various bottlenecks and limitations in real-world scenarios), then a computer that is 40% faster should be able to perform 40% more operations in the same amount of time.

Let's denote the number of frames per second that the current computer can display as \( F \). If the new computer is 40% faster, it should be able to display \( F \) frames in[tex]\( 1 - 0.40 = 0.60 \)[/tex] of the time it takes the current computer. To find out how many frames the new computer can display in the original time frame (1 second), we would divide 1 second by 0.60 seconds and then multiply by \( F \):

[tex]\[ \text{New FPS} = \frac{1}{0.60} \times F = \frac{5}{3} \times F \][/tex]

To find the additional frames per second, we subtract the original FPS from the new FPS:

[tex]\[ \text{Additional FPS} = \text{New FPS} - F = \left( \frac{5}{3} \times F \right) - F \][/tex]

[tex]\[ \text{Additional FPS} = \frac{5F}{3} - \frac{3F}{3} \][/tex]

[tex]\[ \text{Additional FPS} = \frac{5F - 3F}{3} \][/tex]

[tex]\[ \text{Additional FPS} = \frac{2F}{3} \][/tex]

This represents a 40% increase in the number of frames per second. However, without knowing the exact value of \( F \) (the FPS on the current computer), we cannot provide a specific number for the additional frames per second.

 In summary, if the software's performance scales perfectly with the computer's speed, a 40% faster computer should be able to display [tex]\( \frac{2F}{3} \)[/tex]additional frames per second. However, in practice, the actual increase in FPS may be less due to various factors such as software limitations, hardware bottlenecks, and the complexity of the tasks being performed."

The answer is: The first graphic representation.

We are given a quadratic equation, meaning that it could be two possible solutions for the exercise, however, we are talking about time, so we have to consider only the obtained positive values.

Let's make the equation equal to 0 in order to find the values of "t"

[tex]h(t)=-16.1t^2 + 150\\0=-16.1t^2 + 150\\16.1t^2=150\\t^2=\frac{150}{16.1}=9.32\\t=+-\sqrt{9.32}=+-3.05\\t1=3.05\\t2=-305[/tex]

So, discarding the negative value, we can use the possitive value to find the correct graphic representation.

To find the correct graphic representation we must take into consideration the following:

- We must remember that the sign of the coefficient of the quadratic term (t^2) will define if the parabola opens downward or upward.

From the given quadratic (or parabola) equation we have:

[tex]a=-1\\b=0\\c=150[/tex]

So, since the coefficient of the quadratic term is negative, the parabola opens downward.

- Since we are looking for a graphic that represents the change in height over time, we need to look for a graphic that shows only positive values for the x-axis (time)

- We are looking for a parabola which y-axis intercept is equal to 150.

Therefore, the graphic representation of the quadratic function that models a ball's height over time is the first graphic representation.

Have a nice day!

Answer: A

Step-by-step explanation:

Answer:

option B

Elia multiply the dividend by 100 instead of 10.

Step-by-step explanation:

Given that,

divisor  = 0.6

dividend = 1.848

Elia decided to multiply each by 10 to get

but unfortunately she multiply the dividend by 100

As,

1.848 x 100 = 184.8

So,

Elia's error was that she multiply the dividend by 100 instead of 10.

recall that the reference angle, is the angle made by the terminal point with the x-axis.

Check the picture below.

The amount to which $500 will grow to is $881.17.

From the question, we have the following parameters that can be used in our computation:

Principal = 500

Rate = 12%

Time = 5 years

The future value is calclated as

FV = P * (1 + r)ⁿ

substitute the known values in the above equation, so, we have the following representation

FV = $500 * (1 + 0.12)⁵

Evaluate

FV = $881.17

Hence, the amount is $881.17

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The equation would look like this: -3(x + 6) = 4. Then solve to find x.

-3x -18 = 4 → -3x = 22 → x = -7.3

You can substitute this number into the equation to check.

-3(-7.3 + 6) = 4 → 3.9 = 4. As you can see the number isn't exact becuase -7.3 is a repeating decimal.

Answer:

-7 1/3

Step-by-step explanation:

ANSWER

[tex]h = - 4,k = - 6[/tex]

Minimum value: y=-6

Occurs at: x=-4

EXPLANATION

Given

[tex]f(x) = {x}^{2} + 8x + 10[/tex]

We need to write the equivalent of this function in vertex form:

[tex]f(x) = ({x - h)}^{2} + k[/tex]

where (h,k) is the vertex.

We must complete the square to get the function to this form.

We add and subtract the square of half the coefficient of x.

[tex]f(x) = {x}^{2} + 8x +( \frac{8}{2}) ^{2} - ( \frac{8}{2}) ^{2} + 10[/tex]

This gives us;

[tex]f(x) = {x}^{2} + 8x +16- 16 + 10[/tex]

The first three terms form a perfect square quadratic trinomial.

[tex]f(x) =( x + 4) ^{2} - 6[/tex]

or

[tex]f(x) =( x - - 4) ^{2} - 6[/tex]

Therefore we compare to

[tex]f(x) = ({x - h)}^{2} + k[/tex]

h=-4 and k=-6

The minimum value of the function is

[tex]y = - 6[/tex]

and this occurs at;

[tex]x = - 4[/tex]

b. Any two negative numbers when multiplying gives positive answers which are never between negative numbers. -9*-3=27

c. same logic, positive answer so never less than either negative number.

The product of two negative numbers will always be positive, so both cases described in the question are not possible. This is due to the property of real numbers which states that the product of two negative numbers results in a positive number.

b. The product of two negative numbers will always be positive, so the case where the product of two negative numbers falls between the two numbers is not possible.

c. The product of two negative numbers is always positive, which is larger than their negatives. Therefore, the scenario of two negative numbers having a product that is less than both numbers cannot occur.

These conclusions are based on the property of real numbers which specifies that the product of two negative numbers is a positive number. For example, if you multiply -3 by -2, the result is 6, which is a positive number and larger than both -3 and -2.

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sqrt(4x) / 2x + 1 = 3

Set domain :

2x + 1 cannot equal 3

2x cannot equal 2 | :2

x cannot equal 1

sqrt(4x) = 3(2x + 1)

sqrt(4x) = 6x + 3

4x = 36x^2 + 9

36x^2 - 4x + 9 / f(x) = ax^2 + bx + c

16-4*36*9

16-1296 = - 1280

There's no solutions in Real Number set.

See the image for solution

Answer: A,B,C

Step-by-step explanation: I did it on Imagine Math :)

Let x represent the unknown number.

7x - x = -48

Group like terms together.

6x = -48

Divide both sides by 6.

x = -8

Hence, the number is negative eight.

Answer:x=-8

Step-by-step explanation:

What I did was set up my equation and my equation was 7x-x=-48. My second step was to combine like terms and then I had 6x=-48 lastly I divided both sides by 6x then my final answer was x=-8.

[tex]4) \: {x}^{2} + 11x + 28 = 0 \\ \Leftrightarrow {x}^{2} + 7x + 4x + 28 = 0 \\ \Leftrightarrow x(x + 7) + 4(x + 7) = 0 \\ \Leftrightarrow (x + 4)(x + 7) = 0 \\\Leftrightarrow x = - 4 \: \vee \: x = - 7 \\ \\ 5) \: (3a + 8)(3 {a}^{2} - a - 7) \\ = 9 {a}^{3} - 3 {a}^{2} - 21a + 24 {a}^{2} - 8a - 56 \\ = 9 {a}^{3} + 21 {a}^{2} - 29a - 56[/tex]

The answer 5 (1/4) because if you add 1 and a quarter to it then that would make it 6 and a half

Answer:

B, C,and E

Step-by-step explanation:

edge 2020

Answer:

Step-by-step explanation:

c. The point (10,100) reprensents that after 10 business hours, it costs $100 for electricity

d. c=10h

Answer:

(x+1) meters

Step-by-step explanation:

Area is length times width so x^2-x-2 = L * (x-2)

factor and divide x-2 to get x+1

Answer:

Perimeter of the shaded region is 268 m

Step-by-step explanation:

In this diagram a semi circle is drawn inside a rectangle of length 150m.

Length of diameter of a semicircle = 150 m

So radius of the semicircle = [tex]\frac{150}{2}=75 m[/tex]

We have to find the perimeter of the shaded region.

Perimeter of the shaded region = length of tangents drawn on the circle at A and B + m(arc AB)

Length of tangents = radius of the semi circle = 75 m

and m(arc AB) = [tex]\frac{\text{Perimeter of the circle}}{4}=\frac{2\pi r}{4}[/tex]

= [tex]\frac{2\pi (75)}{4}[/tex]

= [tex]\frac{2(3.14)(75)}{4}[/tex]\

= [tex]\frac{471}{4}[/tex]

= 117.75 m

Now Perimeter of the shaded region = 75 + 75 + 117.75

P = 267.75 ≈ 268 m

Given the image showing a rectangle that is 150 cm long with a semicircle inside of it, the perimeter of the shaded region is:  267.8 m

Recall:

Perimeter of a circle = [tex]2 \pi r[/tex]

Thus, given the semicircle in the diagram below, where:

Length of rectangle = 150 m

Radius of semi circle = half of 150 m = 75 m

Thus,

The width of the circle = 75 m

The shaded region is bounded by the circumference of a quarter circle (AB) and two sides measuring 75 m each.

Perimeter of Quarter circle = [tex]\frac{1}{4} \times 2 \pi r[/tex]

Perimeter of Quarter circle = [tex]\frac{1}{4} \times 2 \times \pi \times 75 = 117.8 m[/tex]

Perimeter of the shaded region = 117 + 75 + 75 = 267.8 m

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Answer:

d. 64

Step-by-step explanation:

x^1/2 = 8

Square each side

(x^1/2 )^2=( 8)^2

x = 64

Answer:

(d) 64

Step-by-step explanation:

Please write either x^(1/2) or x^0.5 or √x, to reduce the chances of misinterpreting your input.

√x = 8 becomes x = 64 when both sides are squared.

This corresponds to answer (d).

The median is the moddle number of a data set. If the number of numbers is even add the 2 middle numbers and divide by 2.

Median = (7+7)÷2 = 7

The mean is the averagw value in a data set. You find it be adding all the numbers and then divide the answer by the number of numbers.

Mean: (6+6+6+7+7+7+8+8+8+9) ÷ 10

= 72 ÷ 10 = 7.2

Happy to help! Marking my answer as the Brainliest would really be aprreciated.

Answer: the first one, second, third, and fourth.

I advise you to get a scientific calculator to do these.

Answer: 45 DVDs

Step-by-step explanation:

45 is the least common multiple of 3, 5, and 9.

45 can be equally divided by 3, 5, and 9:

45 ÷ 3 = 15

45 ÷ 5 = 9

45 ÷ 9 = 5

Answer:

B

Step-by-step explanation:

*cough cough*

Answer:

7

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

here [ a, b ] = [ 4, 6 ]

f(b) = f(6) = 6² - 3(6) - 10 = 36 - 18 - 10 = 8

f(a) = f(4) = 4² - 3(4) - 10 = 16 - 12 - 10 = - 6, hence

average rate of change = [tex]\frac{8-(-6)}{6-4}[/tex] = [tex]\frac{14}{2}[/tex] = 7

Answer:

[tex]y=-222[/tex]

Step-by-step explanation:

When "y varies directly with x" this means that:

[tex]y=k\times x[/tex]

where k is a number we need to find out (called the constant of proportionality if you care about that).

We can figure out what k is because they tell us when y= -252, x=84. Substituting those values into our equation we get:

[tex]-252 = k \times 84[/tex]

and therefore:

[tex]k=-3[/tex].

So our equation or formula between y and x is:

[tex]y= -3x[/tex].

So when x = 74, then:

[tex]y=-3 \times 74 = -222[/tex]

Answer:

3/24 or 1/8

Step-by-step explanation:

1. convert 1/4 and 2/3 into fractions with common denominators of 24 (since there are 24 pieces.

2. find the multiples of 4 and 3

    4, 8, 12, 16, 20, 24  = 5

    3, 6, 9, 12, 15, 18, 21, 24 = 8

3. convert the fractions

    1/4 * 5/5 = 5/24

    2/3*8/8 = 16/24

4. add the fractions.

    5/24 + 16/24 = 21/24

5. subtract 21/24 from 24/24 = 3/24

6. reduce by dividing both terms by 3 = 1/8

Will and Tommie ate a total of 22 pieces from the 24-piece candy bar. Therefore, 2 pieces remain.

Will and Tommie bought a giant candy bar composed of 24 pieces. Will ate 1/4 of the bar, which equals 6 pieces (since 1/4 of 24 is 6). Tommie ate 2/3 of the bar, which is 16 pieces (since 2/3 of 24 is 16). To find out how many pieces are left, we subtract the amount eaten by both from the total number of pieces:

Total candy bar pieces = 24

Pieces eaten by Will = 1/4 of 24 = 6

Pieces eaten by Tommie = 2/3 of 24 = 16

Pieces remaining = Total - (Pieces eaten by Will + Pieces eaten by Tommie)

Pieces remaining = 24 - (6 + 16) = 2 pieces.

Therefore, there are 2 pieces of the giant candy bar left.