Which of the following is equivalent to the expression 5x + 15
a. 5( x + 3)
b. x(5 + 15)
c. 5(x + 2)
d. x(1 + 5x)

Answer:

m is your slope. In parallel lines, your slopes are always the same and the y-intercept is always different. so ur slope is also 55.

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Step-by-step explanation:

Answer:

First Option {-2 , 0 , 2}

Step-by-step explanation:

A critical point occurs when the derivative is 0 or undefined.

The function in the question is undefined at x = 2 and at x = -2 because if we put x = 2 or x = -2 the denominator becomes 0 hence anything divided by 0 is undefined, and the derivative equals 0 at x = 0 so the critical points are

{-2 , 0 , 2}

Use the quotient rule to find the derivative of the function then equal it to zero

[tex]y=\frac{x^2-1}{x^2-4}\\\\\frac{dy}{dx}=\frac{(x^2-4)(2x)-(x^2-1)(2x)}{(x^2-4)^2}\\\\0=\frac{(x^2-4)(2x)-(x^2-1)(2x)}{(x^2-4)^2}\\\\0=2x^3-8x-2x^3+2x\\0=-6x\\x=0[/tex]

Answer:

6

Step-by-step explanation:

Answer:

D) 6

Step-by-step explanation:

Assumption method:

Assume all are postcards.

Total cost of postcards = 10 × $1

                                       = $10

Difference between total = $22 - $10

                                          = $12

Difference between subjects = $3 - $1

                                                 = $2

No. of magnets = $12 ÷ $2

                          = 6

Answer:

240 feet per hour

Step-by-step explanation:

Given that:

Submarine is descending for examining the sea floor.

Distance of sea floor from the surface = 2100 feet

Time taken for the descend = 8.75 hours

To find:

The rate of descent in feet per hour = ?

Solution:

Here, we are given the distance traveled in feet and the time taken to travel that distance in hours.

And we have to find nothing but the speed of the submarine.

First of all, let us have a look at the relationship among speed, distance and time.

[tex]Speed = \dfrac{Distance}{Time}[/tex]

Putting the values of distance and time.

[tex]Speed = \dfrac{2100}{8.75}\\\Rightarrow Speed = \bold{240\ feet/hr}[/tex]

Answer:

Therefore, the rate of change of function 2 is 3 more than the rate of change of function 1.

Hence, option C is true.

Step-by-step explanation:

Function 1

A horizontal straight line is drawn joining the ordered pairs (0, 3) and (4, 3).

Given the points

It means

at x = 0, y = 3

at x = 4, y = 3

Since the y-values are same, it means the points lie on a horizontal.

The rate of change or slope of a horizontal line is zero because it does not rise vertically ( i.e. y₁ - y₂ = 0).

Therefore, the rate of change of function 1 = 0

Function 2

y = 3x+1

comparing with the slope-intercept form

y = mx+b      

here m is the rate of change or slope and b is the y-intercept

so the rate of change of the function 2 = m = 3

Conclusion:

Therefore, the rate of change of function 2 is 3 more than the rate of change of function 1.

Hence, option C is true.

9514 1404 393

Answer:

  {0, 1, 2, 3}

Step-by-step explanation:

The domain is the set of function input values. Here, they are labeled x values. The set of the is {0, 1, 2, 3}.

The domain is {0, 1, 2, 3}.

Answer:

size of angle A is 93.19°

Answer:

[tex]2d^{\frac{7}{10}}[/tex] [tex]= \sqrt[10]{2d^7}[/tex]

Step-by-step explanation:

Given

[tex]2d^{\frac{7}{10}}[/tex]

Required

Determine the radical expression

To do this, we apply the following law of indices:

[tex]a^{\frac{m}{n}} = \sqrt[n]{a^m}[/tex]

By comparing the above to [tex]2d^{\frac{7}{10}}[/tex], we have:

[tex]m=7[/tex]

[tex]n = 10[/tex]

So, the solution becomes

[tex]2d^{\frac{7}{10}}[/tex] [tex]= \sqrt[10]{2d^7}[/tex]

Answer:

The unit rate that Jeremy can row is 1.33 miles per hour.

Step-by-step explanation:

Unit rate is defined as the distance over a time period. The distance that Jeremy can row is given and the time period is given.

The distance (miles)=1/3=0.3333333...

time period: 1/4

0.33333/0.25=1.333333

Answer:

[tex]G(x) = 2x^2+6[/tex].

Step-by-step explanation:

The given function is

[tex]f(x) = \frac 2 3 x^2 +2[/tex]

On vertical stretch by a factor of 3, the new function G(x) is

G(x) = 3 f(x)

So, [tex]G(x) = 3 \times ( \frac 2 3 x^2 +2)= 2x^2+6[/tex]

Hence, the required function is [tex]G(x) = 2x^2+6[/tex].

Step-by-step explanation:

As an event planner, you may have noticed the steadily increasing online event registration fees. Moreover, many people are anticipating the next economic crisis is coming soon. It may trigger you to think about looking for a new registration system that’s affordable yet still flexible and easy to use.

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Answer: A=(38*x)-(x*4) (x equals rows)

So the top row consists of 272 boxes of soda.

Answer:

[tex]Speed = 21.43m/s[/tex]

Step-by-step explanation:

Given

[tex]Distance = 1200m[/tex] -- of the roadworks

[tex]Time\ Recorded = 56s[/tex]

Required

Determine the speed

In this case:

[tex]Speed = \frac{Distance\ of\ Roadword}{Time\ Captured}[/tex]

[tex]Speed = \frac{1200m}{56s}[/tex]

[tex]Speed = 21.43m/s[/tex] --- approximated

Answer and Step-by-step explanation: Area of a right triangle, (as any other triangle), is calculated as:  [tex]A1=\frac{(base)(height)}{2}[/tex]

Area of a rectangle is calculated as: [tex]A2=(side)(side)[/tex]

Area of a right trapezoid is: [tex]A3=\frac{(a+b)h}{2}[/tex], where:

a is short base

b is long base

h is height

1) Expressing areas in terms of x:

Area of triangle S1:

[tex]S1=\frac{(2x-3)(4x-6)}{2}[/tex]

[tex]S1=4x^{2}-12x+9[/tex]

Area of rectangle S2:

[tex]S2 = (4x-6)(3x-2)[/tex]

[tex]S2=12x^{2}-26x+12[/tex]

Area of trapezoid S3:

[tex]S3=\frac{(2x+3+4x+1)(2x-3)}{2}[/tex]

[tex]S3=\frac{(6x+4)(2x-3)}{2}[/tex]

[tex]S3=6x^{2}-5x-6[/tex]

2) a) [tex]S=4x^{2}-12x+9+12x^{2}-26x+12-(6x^{2}-5x-6)[/tex]

[tex]S=4x^{2}-12x+9+12x^{2}-26x+12-6x^{2}+5x+6[/tex]

[tex]S=10x^{2}-33x+37[/tex]

Which is the same as S = (2x-3)(5x-9)

b) For the areas to be the same:

[tex]\frac{(3x-2+3x-2+2x-3)(4x-6)}{2}=\frac{(6x+4)(2x-3)}{2}[/tex]

[tex]\frac{(8x-7)(4x-6)}{2}=\frac{(6x+4)(2x-3)}{2}[/tex]

[tex]32x^{2}-48x-28x+42=12x^{2}+8x-18x-12[/tex]

[tex]20x^{2}-66x+54=0[/tex]

Using Bhaskara to solve the second degree equation:

[tex]\frac{66+\sqrt{(-66)^{2}-(4.20.54)} }{2(20)}[/tex]

[tex]x_{1}=\frac{66+6}{40}[/tex] = 1.8

[tex]x_{2}=\frac{66-6}{40}[/tex] = 1.5

For the areas of AFGC and ADEB to be equal, x has to be 1.5 or 1.8.

c) Expand a polynomial (or equation) is to multiply all the terms, remiving the parenthesis. Reduce a polynomial (or equation) is to combine terms alike,e.g.:

[tex]S=(2x-3)(5x-9)[/tex]

[tex]S=10x^{2}-18x-15x+27[/tex] (expand)

[tex]S=10x^{2}-33x+27[/tex] (reduce)

d) For area of AFCG to be bigger than area of ADEB by 27:

[tex]32x^{2}-48x-28x+42=12x^{2}+8x-18x-12+27[/tex]

[tex]32x^{2}-48x-28x+42=12x^{2}+8x-18x+15[/tex]

[tex]20x^{2}-66x+27=0[/tex]

Solving:

[tex]\frac{66+\sqrt{(-66)^{2}-(4.20.27)} }{2(20)}[/tex]

[tex]\frac{66+46.86}{40}[/tex]

[tex]x_{1}=\frac{66+46.86}{40}=[/tex] 2.82

[tex]x_{2}=\frac{66-46.86}{40}[/tex] = 0.48

According to the enunciation, x cannot be less than 1.5, then, the value of x so that area AFGC exceeds the area ADEB by 27 is 2.82

A = L x W

W = A/L

W = 32/6

W = 5.333

Answer:

Step-by-step explanation:

1km = 100000cm

50 km = 50 x 100000 = 5000000cm

Answer:

[tex]m \times n \\ when \: m = 13 \: and \: n = 12 \\ = 13 \times 12 \\ = 156[/tex]

Answer:

D=6

Step-by-step explanation:

common defence is 6

hope it help you

Answer:

x = 3

Step-by-step explanation:

6.78x - 5.2 = 4.33x + 2.15

6.78x - 4.33x = 5.2 + 2.15

2.45x = 7.35

x = 7.35/2.45

x = 3

Thus, The value of x is 3

-TheUnknownScientist

Answer:

6.9

7.-5

8.-10

Step-by-step explanation:

Answer:

Solution in photo

Step-by-step explanation:

Answer:

2Girls:3Boys

Step-by-step explanation:

gdfgdsfgdsgsdfgdsgdsfgdsfgdsfg

Answer:

38%

Step-by-step explanation:

Is that an answer choice ?

Answer:

<4 = 88

<3 = 92

Step-by-step explanation:

The sum of the angles of a triangle is 180

<4 + 45+ 47 = 180

<4 + 92 = 180

< 4 = 180-92

<4 = 88

We know the <3 and <4 form a line

<3 + <4 = 180

<3 + 88 = 180

< 3 = 180-88

<3 = 92

Given:

The table shown the number of campers, x, at a local campsite and the total amount of money, y, in dollars, earned by the camp site.

To find:

The unit for the rate of change.

Solution:

We know that, rate of change is the change in y-values with respect to x-values, i.e.,

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

In the given problem, y is the total earnings in dollars and x is the number of campers. So, the rate of change represents the change is earnings with respect to number of campers.

Thus, the unit of rate of change is dollars per camper.

Therefore, the correct option is D.

Answer:

1.5 times greater because the ratio of triangle ABC to triangle DEF is 2:3

Step-by-step explanation:

Answer:

1.4 times is the correct answer