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Functions can be represented using equations and graphs

The key features are (1) both f(x) and g(x) include domain values of [3, ∞) and range values of (0, ∞), and both functions are positive for the entire domain.

The functions are given as:

[tex]f(x) = 3^x[/tex]

[tex]g(x) = \sqrt{ x - 3}[/tex]

Using a graphing calculator:

By comparing the above highlights, the true statement between functions g(x) and f(x) is option (1)

Read more about function domain and range at:

https://brainly.com/question/10197594

Answer:

120 miles

Step-by-step explanation:

A proportion is a ratio that equals a ratio. I'm going to use cm/miles when I setup the proportion.

[tex]\frac{2.5}{10} =\frac{30}{x}[/tex]

Cross multiply

2.5x = 300

divide

2.5x/2.5 = 300/2.5

x = 120 miles

Answer:

20 out of 28 games.

Step-by-step explanation:

28 divided by 7 is 4.

5 times 4 is 20.

20 out of 28 games.

(This is simple math honestly.)

Answer:

$3863.17

Step-by-step explanation:

This is simple adding and subtracting.

3000.00

   345.97

   567.20

+ 150.00

4063.17

  -200.00

 $3863.17

Step-by-step explanation:

9.

the first we see when going from left to right : the line goes down, so it has a negative slope (factor of x).

then we look at the y-intercept (the point where the line crosses the y-axis) : negative y and around -5.

with all that we have eliminated B and D.

and not only does the line go down, it goes sharply down. so, the absolute value of the slope must be bigger.

therefore, C is the right answer.

and a quick check confirms, as the slope -10/3 means that for a change of x by +3 units causes y to change by -10, and that is what we are seeing on the chart.

at x = -3 it looks like y is about +5.

and at x = 0 (change by +3) it looks like y is about -5 (change by -10).

10.

the y-intercept does not give us a clue here, it is 1 for all 4 options, and the graph confirms it.

but this line goes up, so the slope is positive.

it is rather "flat" and by far not even diagonally, so the absolute value of the slope must be a small value (much smaller than 1, as a slope of 1 means "diagonally").

therefore, D is the right answer.

a quick check confirms, as the slope 1/5 means that for a change in x by +5 would lead to a change in y by +1.

and that is what we are seeking on the chart.

at x = -5 it looks like y is about 0.

at x = 0 (change by +5) it looks like y is about +1 (change by +1) - the y-intercept.

Answer:

y=1/5x-4

Step-by-step explanation:

Hi there!

We want to write the equation of the line, and we're given that the line has a slope of 1/5, and the y intercept of the line is (0, -4)

There are multiple ways to write the equation of the line, the most popular being slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

We are already given the slope (1/5), so we can plug it in as m in the equation.

y=1/5x+b

Now for b, we are also given the y intercept; the value of b is the value of y at the point of the y intercept

In this case, b would equal -4

So substitute -4 as b into the equation:

y=1/5x-4

This is the equation of the line.

Hope this helps!

Take a look here for a similar problem to practice if you wish: https://brainly.com/question/21717067

Answer:

[tex]n= 5 \sqrt{3} [/tex]

Step-by-step explanation:

[tex]n = \sqrt{15 \times 5} = \sqrt{75} \\ \\ \huge n=\boxed{ 5 }\sqrt{\boxed{3}} [/tex]

What is the percent​ increase from $200 to $280?

There was 40% increase from $200 to $280

What would be the percent increase if the airline charges an additional​ $50 baggage fee with the new ticket​ price?

There was 65% increase with the baggage fee.

#1

Rate of increase (Percent increase)

[tex]\\ \tt\hookrightarrow \dfrac{80}{200}\times 100[/tex]

[tex]\\ \tt\hookrightarrow 40\%[/tex]

#2

Percent increase:-

[tex]\\ \tt\hookrightarrow \dfrac{130}{200}(100)[/tex]

[tex]\\ \tt\hookrightarrow 65\%[/tex]

Locate 6 in the x row. Directly below this is 96

This means f(6) = 96

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

Now locate 3 in the f(x) row. Directly above this is 7

You are correct in stating that f(7) = 3

Answer:

13. (B). False

Explanation

in the image

Answer:

It should be <AFB

Step-by-step explanation:

The reason is that supplementary angels add up to 180 degrees which is a flat line and <AFB and <CFA do that

Answer:

302.33

Step-by-step explanation:

Answer:

302.333... Its a repeating number.

Step-by-step explanation:

Step-by-step explanation:

area of ∆ = .5*pq*qr* sin q

= 23.63

Answer:

Figure D

Step-by-step explanation:

15/10 can be simplified to 3/2. Figure D represents a consistent rate of 3/2

what do you mean by that?

Answer:

➢ The multiplication property of equality states that when we multiply both sides of an equation by the same number, the two sides remain equal. Example 1 : Lisa and Linda have got the same amount of money. ... Multiply both sides by 4.

Step-by-step explanation:

HOPE IT WILL HELP YOU

[tex]kai6417[/tex]

#carry on learning

Answer:

Clear the fraction first which means multiply both side by the reciprocal (2)

2a = bh

Divide both sides by b since you are solving for h

Your answer is 2a/b = h

Answer:

No t-intercept/zero

Step-by-step explanation:

1- Substitute f (t) = 0

Rewrite

2- Calculate

3- The statement is false for any of t

4- there is no t-intercept/zero

The multiplier that would be used to calculate the depreciation of the car is 0.83^y.

Depreciation is when the value of an asset declines due to wear and tear.

The equation that can be used to represent depreciation is:

Value of the asset x (1 - rate of depreciation)^years

$31,000 x 0.83^y.

To learn more about depreciation, please check: https://brainly.com/question/25552427

-5 (3 + 5)

-5 (8)

-5 × 8

= -40

Good luck :)

Answer:

-40

Step-by-step explanation:

First you distribute

-5 · 3 = -15

-5 · 5 = -25

Then you add

-15 + (-25) = -40

Answer:

[tex]\frac{13}{32}[/tex]

Step-by-step explanation:

Answer:

x = 11/7 y = -1/7

Step-by-step explanation:

2x + y = 3

2x + y - 2y = 3 - 2y

y = 3 - 2x

x - 3(3 - 2x) = 2

x - 9 + 6x = 2

x - 9 + 6x + 9 = 2 + 9

x + 6x = 11

7x = 11

7x / 7 = 11/7

x = 11/7

2(11/7) + y = 3

22/7 + y = 3

22/7 + y - 22/7 = 3 - 22/7

y = -1/7

Answer:

(¹¹⁄₇, -⅐)

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}2x+y=3&\\x-3y=2\end{cases}[/tex]

What is the elimination method?

The elimination method is when you rewrite the two equations so that when added together, one of the two variables (x or y) is eliminated.

Step 1: Multiply the first equation by [tex]3[/tex].

[tex]\implies (3)2x+(3)y=(3)3[/tex]

[tex]\implies 6x+3y=9[/tex]

Step 2: Add the above equation to the second equation to eliminate 3y.

[tex]\begin{array}{r l}6x+3y & = 9\\+\ x-3y&=2\\\cline{1-2}7x&=11 \end{array}[/tex]

Step 3: Solve for x (by dividing both sides by 7).

[tex]\implies \dfrac{7x}{7}=\dfrac{11}{7}[/tex]

[tex]\implies \boxed{x=\dfrac{11}{7}}[/tex]

Step 4: Substitute ¹¹⁄₇ as the value of [tex]x[/tex] in any of the given equations and solve for [tex]y[/tex].

[tex]\implies 2\left(\dfrac{11}{7}\right)+y=3[/tex]

[tex]\implies \dfrac{22}{7}+y=3[/tex]

Step 5: Convert [tex]3[/tex] into a fraction and subtract ²²⁄₇ from both sides of the equation.

[tex]\implies \dfrac{22}{7}-\dfrac{22}{7}+y=\dfrac{21}{7}-\dfrac{22}{7}[/tex]

[tex]\implies \boxed{y=-\dfrac{1}{7}}[/tex]

The solution to the given system of equations is (¹¹⁄₇, -⅐).

Learn more here:

brainly.com/question/27868564

Answer:

Step-by-step explanation:

The ratio of males to females at a gym is 4:5. There are 20 females at the gym. How many males are in the gym?​

4 : 5 = x : 20

x = 4 * 20 : 5

x = 16

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

check

4 : 5 = 16 : 20

4 : 5 = 4 : 5

the answer is good

Answer:

[tex]{ \tt{L = 4\pi zt + 5\pi {z}^{2} }} \\ \\ { \tt{L = \pi z(4t + 5z)}} \\ \\ { \tt{ \frac{L}{\pi z} = 4t + 5z}} \\ \\ { \tt{4t = \frac{L}{\pi z} - 5z}} \\ \\ { \tt{t = \frac{L}{4\pi z} - \frac{5z}{4} }} \\ \\ { \boxed{ \tt{t = \frac{L - 5\pi {z}^{2} }{4\pi z} }}}[/tex]

Using the Poisson distribution, it is found that there is a 0.8647 = 86.47% probability of at least one flaw appearing in 300 square feet.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

Flaws in a certain type of drapery material appear on the average of one in 150 square feet, hence, considering 300 square feet, the mean is of:

[tex]\mu = \frac{300}{150} \times 1 = 2[/tex]

The probability of at least one flaw appearing in 300 square feet is given by:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-2}2^{0}}{(0)!} = 0.1353[/tex]

Then:

[tex]P(X \geq 1) = 1 - 0.1353 = 0.8647[/tex]

0.8647 = 86.47% probability of at least one flaw appearing in 300 square feet.

More can be learned about the Poisson distribution at https://brainly.com/question/13971530