Assume f(x) = 2x + 8 and g(x) = 5 5. What is the value of (f + g)(3)

Answer:

a) Domain: All real numbers

b) Domain: -4<x<=4

a) Range: All real numbers greater than 2

b) Range: 0<=y<=4

Step-by-step explanation:

Domain is the possible x values

Range is the possible y values

Open circle means not included

Close circle means included

Answer: a) Domain: x = (-∞, ∞)              b) Domain x = (-4, 4]

                  Range y = [2, ∞)                        Range y = [0, 4]

Step-by-step explanation:

Domain represents the x-values. Range represents the y-values.

a) the graph doesn't end so every x-value is possible

  x = All Real Numbers       x = (-∞, ∞)

The lowest y-value (minimum) is at y = 2.  All other y-values are greater than that. y ≥ 2      y = [2, ∞)

b) The graph starts at x = -4 with an open dot so it doesn't include -4.  It ends at x = +4 with a closed dot so it does include +4.

     -4 < x ≤ 4           x = (-4, 4]

The lowest y-value (minimum) is at y = 0.  All other y-values are greater than that up to y = 4. 0 ≤ y ≤ 4      y = [0, 4]

Answer:

32

Step-by-step explanation:

Lets work it out.

First we combine the two equations to get 5x-10. That is equal to 70 so we get out x = 16 we put that into the equation 3x-10 and get 32

Answer:

it would take about 4.2 years for her debt to double.

Step-by-step explanation:

With a principal of $3000, and an annual interest rate of 18%, the equation for accumulated debt as a function of time in years, would be given by the expression:

[tex]A(t)=3000\,(1+0.18)^t[/tex]

now, if we want to find when the debt would double, we replace A(t) with $6000, and solve for the time 't' using logarithms to bring down the unknown (t) that resides in the exponent:

[tex]A(t)=3000\,(1+0.18)^t\\6000=3000\,(1.18)^t\\2=(1.18)^t\\log(2)=t\, \, log(1.18)\\t=\frac{log(2)}{log(1.18)} \\t=4.1878\,\,years[/tex]

which we can round to approximately 4.2 years

Answer:

Length of AD is 8.4 units.

Step-by-step explanation:

Given that:

There are two similar rectangles ABCD and DEFG.

AB = 6 units

DE = 15 units

DG = 21 units

To find:

AD = ?

Solution:

Please refer to the attached image for having a look at the two given rectangles.

First of all, let us learn about the similar rectangles.

If two rectangles are similar, then the ratio of their corresponding sides are always equal.

i.e.

[tex]\dfrac{AB}{AD} = \dfrac{DE}{DG}[/tex]

Putting values of AB, DE and DG to find out AD:

[tex]\dfrac{6}{AD} = \dfrac{15}{21}\\\Rightarrow \dfrac{6}{AD} = \dfrac{5}{7}\\\Rightarrow \dfrac{1}{AD} = \dfrac{5}{7\times 6}\\\Rightarrow \dfrac{1}{AD} = \dfrac{5}{42}\\\Rightarrow AD = \dfrac{42}{5}\\\Rightarrow AD = 8.4\ units[/tex]

So, value of AD is 8.4 units.

Answer:

12 adults and 4 kids were there that the fair

Step-by-step explanation:

Replace f with 190, replace P with 4148 and solve for  s:

4148 = 1.85s + 4.2(190)

Simplify:

4148 = 1.85 + 798

Subtract 798 from both sides:

3350 = 1.85s

Divide both sides by 1.85:

s = 1,810.81

Rounded to nearest square foot = 1811 square feet.

Answer:

d

Step-by-step explanation:

double check your answer

Answer:

  C.  Add a radical term to both sides and square both sides twice

Step-by-step explanation:

We suppose you want to solve ...

  [tex]\sqrt{b+20}-\sqrt{d}=5\\\\\sqrt{b+20}=5+\sqrt{d}\qquad\text{add a radical term}\\\\b+20=25+10\sqrt{d}+d\qquad\text{square both sides once}\\\\b-d-5=10\sqrt{d}\qquad\text{subtract right-side non-radical terms}\\\\(b-d-5)^2=100d\qquad\text{square both sides a second time}[/tex]

__

We note that the solution summary (choice C) doesn't mention the fact that you need to separate the remaining radical term from the others after the first squaring.

The result is a quadratic function that produces extraneous solutions. This is shown in the attached graph. The red function is the original relation between b (x) and d (y). The blue function includes the red function and another branch that is all extraneous solutions.

Answer:

8 questions.

Step-by-step explanation:

100 - 2x = 84

-2x + 100 = 84

-x + 50 = 42

x - 50 = -42

x = 8

Trevor answered 8 questions incorrectly.

Hope this helps!

Answer:

8

8Step-by-step explanation:

100-2x=84

subtract 84 from both sides

16-2x=0

add 2x to both sides

16=2x

divide both by 2 to get x

x=8

hope this helped

Answer:

60

Step-by-step explanation:

Answer:

[tex]10\frac{2}{3}\pi[/tex]

Step-by-step explanation:

First find the area of the whole thing. It is 8^2π = 64π. Then the blue part is 60/360 = 1/6 of the area. This is 64/6π=32/3π=10.66π

Answer:

False

Step-by-step explanation:

it has more than one dot in the same row, which means it has the same number more than once in the x - axis.

Answer:

False

Step-by-step explanation:

You can check whether a graph represents a function by using the vertical line test.

Draw a vertical line on the graph, the vertical line intersects the graph at many points, therefore the graph does not represent a function.

Answer:

Step-by-step explanation:

7x² - 3 = 60

7x² - 3 - 60 = 0

7x² - 63 = 0

Simplify the terms

Divide both terms by 7

That's

x² - 9 = 0

Solve the quadratic equation

Use difference of two squares

That's

a² - b² = ( a + b)(a - b)

x² - 9 = 0

(x + 3)(x - 3) = 0

x + 3 = 0 x - 3 = 0

x = - 3 x = 3

Hope this helps you

Answer:

the third one 5(4-x)<3x+1

Answer:

number 3 hope this helps one year later

Step-by-step explanation:

Answer:

8 1/3

Step-by-step explanation:

Step 1: Simplify

50/6 = 8 2/6

Step 2: Simplify fraction

2/6 = 1/3

Step 3: Add it up

8 1/3

Answer:

[tex]8 \frac{1}{3}[/tex]

Step-by-step explanation:

[tex]50/6\\25/3\\25 \div 3\\= 8- remainder-1\\= 8 \frac{1}{3}[/tex]

Answer:  123.6 units²

Step-by-step explanation:

Since it is an isosceles triangle, we can draw a median from the ap ex (b) to the base (ac) to create a right triangle at point (d). Then we can use the Pythagorean Theorem to find the height (bd) of the triangle.

(dc)² + (b d)² = (bc)²

 7²  +  (b d)² =  19²

          (b d)²  = 19² - 7²

          (b d)² = 312

           b d  = 17.66

A = (1/2) base x height

  = (1/2) ac x b d

  = (1/2) 14 x (17.66)

   = 7(17.66)

   = 123.6

Answer:

C

Step-by-step explanation:

3|x-2|=18-6

3|x-2|=12

|x-2|=4

Ther are two options.

First;

x-2=-4

x=-2

Second;

x-2=4

x=6

If you don't understand, you can ask :)

Given that,

Speed of first bicycle = 9 mph

Speed of second bicycle = 5 mph

Suppose the length of the circle 24 miles.

We need to find the relative velocity

Using formula of relative velocity

[tex]v=v_{1}-v_{2}[/tex]

Put the value into the formula

[tex]v=9-5[/tex]

[tex]v=4\ mph[/tex]

We need to calculate the time

Using formula of time

[tex]t=\dfrac{d}{v}[/tex]

[tex]t=\dfrac{24}{4}[/tex]

[tex]t=6\ hr[/tex]

We need to calculate the distance of the points where the two bicycles meet

Using formula of distance

For first bicycles,

[tex]d=9\times6[/tex]

[tex]d=54\ miles[/tex]

For second bicycles,

[tex]d'=5\times6[/tex]

[tex]d'=30\ miles[/tex]

Hence, The points where the two bicycles meet after every 6hr at 30 miles and 54 miles.

Answer:

Step-by-step explanation:

Hello,

[tex]g(n)=80*(\dfrac{3}{4})^n \ So\\g(1)=80*\dfrac{3}{4}=20*3=60 \\\\ and \\\\\dfrac{g(n)}{g(n-1)}=\dfrac{80*(\dfrac{3}{4})^n}{80*(\dfrac{3}{4})^{n-1}}=\dfrac{3}{4} \ so \\\\g(n)=g(n-1)*\dfrac{3}{4}[/tex]

do not hesitate if you have any question

Answer:

Step-by-step explanation:

[tex]A(-3,-2) and B(1,6).\\\\x_1 = -3\\y_1 = -2\\x_2 = 1\\y_2 =6\\\frac{y-y_1}{x-x_1} =\frac{y_2-y_1}{x_2-x_1} \\\frac{y -(-2)}{x -(-3)} =\frac{6-(-2)}{1-(-3)}\\\frac{y+2}{x+3} = \frac{6+2}{1+3} \\\frac{y+2}{x+3} = \frac{8}{4} \\Cross-multiply\\4(y+2) =8(x+3)\\4y +8 =8x+24\\4y = 8x +24-8\\4y = 8x+16 \\OR\\ y = 2x+4[/tex]

Answer:

x = 8

Step-by-step explanation:

Step 1: Subtract 5x from both sides

-1 = x - 9

Step 2: Add 9 to both sides

x = 8

Answer:

The length of AC = 4 and the length of A'C' = 1 so the scale factor is 1/4.

Answer:

[tex]b^{\frac{6}{7}}[/tex]  is the required expression.

Step-by-step explanation:

[tex](b^2)^{\frac{3}{7}}\\\\\mathrm{Apply\:exponent\:rule:\:}\left(a^b\right)^c=a^{bc},\:\quad \mathrm{\:assuming\:}a\ge 0\\\\=b^{2\cdot \frac{3}{7}}\\\\=b^{\frac{6}{7}}[/tex]

Best Regards!

Answer:

-4

Step-by-step explanation:

(-2)^2 + (-2)^3

this is right if the 2 and 3 are exponents

Answer:

-4

Step-by-step explanation:

Substitute the value of x:

-8+4 = -4

Plz mark me brainliest!!

Answer:

Brainliest please

Step-by-step explanation:

15 women= 12days

find 10 days,

12÷10×15= 18women in ten days

how many more women, subtract 18 women and 15 women

=3 is the answer

Answer:

The correct answer is 96

Step-by-step explanation:

Answer:

[tex]\frac{1}{4}r[/tex]

Step-by-step explanation:

The amount of red pepper that Harvey has is r red peppers and one fourth as many orange peppers. What this means is that the number of orange pepper that Harvey has is one fourth the number of red peppers. Since the number of red pepper is r, therefore the number of orange pepper is given as:

Number of orange pepper = [tex]\frac{1}{4} \ of\ red\ pepper(r)[/tex]

[tex]Number\ of\ orange\ pepper=\frac{1}{4}r[/tex]

D

Step-by-step explanation:

Probabilities are used to determine the chances of picking a marble

The probability of picking a blue marble is: x/20

The given parameters are:

[tex]\mathbf{Marbles = 40}[/tex]

[tex]\mathbf{Red = x}[/tex]

The probability of picking a red marble is calculated as:

[tex]\mathbf{Pr = \frac{Red}{Marbles}}[/tex]

Substitute values for Red and Marbles

[tex]\mathbf{Pr = \frac{x}{40}}[/tex]

He is twice as likely to randomly pick a blue marble from a bag as she is to pick a red marble

So, the probability of picking a blue marble is:

[tex]\mathbf{P(Blue) = 2 \times \frac x{40}}[/tex]

This gives

[tex]\mathbf{P(Blue) = \frac x{20}}[/tex]

Hence, the probability of picking a blue marble is: x/20

Read more about probabilities at:

https://brainly.com/question/11234923

Answer:

A prism is a polyhedron A prism is a 3-dimensional shape with two identical shapes facing each other. These identical shapes are called “bases”. The bases can be a triangle, square, rectangle or any other polygon.

Step-by-step explanation:

i hope this will help you

Answer:

A triangular prism is a prism whose bases are triangles and whose lateral faces are rectangles.It has 9 edges and 6 vertices.

please see the attached picture.

hope this helps..

Good luck on your assignment..

Answer:

Mean = 25

Median = 23

Mode = 33

Step-by-step Explanation:

First, let's write out all the values represented in the stem and leaf plot. We have the following data sets as follows:

15, 18, 18, 19,

22, 23, 25,

31, 33, 33, 33

=>Mean = sum of all values ÷ no of values

= (15+18+18+19+22+23+25+31+33,+33+33)/11

= 270/11 ≈ 25 (to the nearest whole number)

=>Median is the middle value when the data set is ordered. Since we have 11 values, our median value would be the 6th value in our data set = 23

15, 18, 18, 19, 22, |23|, 25, 31, 33, 33, 33

=>Mode is the most occured value = 33

Answer:

x = 2 and (2, 4 )

Step-by-step explanation:

The equation of a parabola in standard form is

f(x) = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

f(x) = 3(x - 2)² + 4 ← is in vertex form

with vertex = (2, 4 )

This is a vertical parabola, opening upwards and is symmetrical about the vertex.

The axis of symmetry is a vertical line with equation x = 2

According to the equation of the parabola, we have that:

The equation of a quadratic function, of vertex (h,k), is given by:

[tex]y = a(x - h)^2 + k[/tex]

In which a is the leading coefficient.

The axis of symmetry is x = h.

In this problem, the equation is:

[tex]f(x) = 3(x - 2)^2 + 4[/tex]

Hence h = 2, k = 4, thus:

More can be learned about the equation of a parabola at https://brainly.com/question/24737967

Answer:

60

Step-by-step explanation:

5(a + 2) + 6(2a - 3)

Expand the brackets.

5a + 10 + 12a - 18

Add or subtract like terms.

17a - 8

Plug a = 4 and evaluate.

17(4) - 8

68 - 8

= 60