the temperature (in degrees Fahrenheit) x hours after 5 p.m. is represented by t(x)=-4+72. The temperature x hours after 10 a.m. is represented by d(x)=4x+72. Describe the transformation from the graph of t to the graph of d.

Given:

Required:

We need to graph the given step function.

Explanation:

From the given data we have, -5,-1, and 2 are the respective values of y.

The draw annulus to denote the points do not lie on the line since there is a symbol '<'.

Final answer:

Answer: f(h) = (2 pi (5x + 2)^2)

Step-by-step explanation:

1) Set the area of the circle in an equation

f(h) = pi r ^2

2) Set r to the rate that the circle is growing

The rate is 5x +2 because its starting value is two, and the 5x because it is growing 5 inches per hour.

f(h) = (2 pi (5x + 2)^2)

Let X be the number, then we know that

If we isolate X by moving 10 to the right hand side, we obtain

that is, the answer is 30,000

Given:

Vertical asymptotes are when the denominator is 0 but the numerator isn't 0.

[tex]x-36=0 \implies x=36[/tex]

Since this value of x does not make the numerator equal to 0, the vertical asymptote is [tex]x=36[/tex].

Horizontal asymptotes are the limits as [tex]x \to \pm \infty[/tex].

[tex]\lim_{x \to \infty} \frac{6x}{x-36}=\lim_{x \to \infty}=\frac{6}{1-\frac{36}{x}}=6\\\\\lim_{x \to -\infty} \frac{6x}{x-36}=\lim_{x \to -\infty}=\frac{6}{1-\frac{36}{x}}=6\\\\[/tex]

So, the horizontal asymptote is [tex]y=6[/tex].

End behavior:

we have

f(x)

and

g(x)=-2f(x)+5

so

step 1

First transformation

Reflection about the x-axis

so

f(x) -----> -f(x)

step 2

Second transformation

A vertical dilation with a scale factor of 2

so

-f(x) ------> -2f(x)

step 3

Third transformation

A translation of 5 units up

so

-2f(x) -------> -2f(x)+5

Answer:

1500$

Step-by-step explanation:

Answer: -1500

Step-by-step explanation: yes it is

A package of 3 pairs of insulated socks costs $15.87, thus the unit price of the pair of socks can be calculated as $5.29 via the unitary method.

A unit price is the cost of a single object or unit of measurement, such as a pound, a kilogram, or a pint, and it is used to compare the prices of similar products offered in various weights and quantities.

Selling more than one unit of the same product at a discount from its unit price is known as multiple pricing.

A price stated in terms of a certain amount per predetermined or standard unit of good or service agreed to purchase the gravel for 50 cents per yard.

Frequently a price that is quoted that includes both the base unit of the good or service and any additional costs (such as shipment or installation).

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Answer:

[tex]58.29[/tex] cm

Step-by-step explanation:

So the area of a trapezium follows this equation/formula:  [tex]\frac{a+b}{2} h[/tex]

So we pretty much just substitute the numbers given into this equation

[tex]\frac{a+b}{2} h[/tex]

[tex](\frac{7+10.4}{2} )6.7[/tex]

[tex](\frac{17.4}{2} )6.7[/tex]

[tex](8.7) 6.7[/tex]

[tex]58.29[/tex] cm

√54²-43.8² +2(7)

54-1918.44+14

-1850.44

Given the functions:

f(x)=1/4x+5

g(x)=4x-20​

The functions g and f are said to commute with each other if g ∘ f = f ∘ g.

Let's check the functions if they are commutative.

a.) f ∘ g = f(g(x))

b.) g ∘ f = g(f(x))

Conclusion:

g ∘ f = f ∘ g

Therefore, the functions are commutative.

x represents the number of packages of coffee sold

y represents the number of packages of pastry sold

We were the cost of a package of coffee is $6 and the cost of a package of pastry is $4. If the total amount made from selling x packages of coffee and y packages of pastry is $72, then the equation representing this scenario is

6x + 4y = 72

Also, we were told that she sold 2 more packages of coffee than pastries. This means that

x = y + 2

Thus, the system of linear equations is

6x + 4y = 72

x = y + 2

We would plot these equations on the graph. The graph is shown below

The red line represents x = y + 2

The bu line represents x = y + 2

[tex]k=4[/tex].

[tex]20 +7k = 8(k + 2)[/tex]

[tex]20 +7k = 8k+16[/tex]

[tex]-20+20 +7k = 8k+16-20\\ \\7k = 8k-4[/tex]

[tex]7k-8k = 8k-4-8k\\ \\-k = -4[/tex]

[tex](-1)-k = -4(-1)\\ \\k=4[/tex]

[tex]20 +7(4) = 8((4) + 2)\\ \\20 +28 = 8(6)\\ \\48=48[/tex]

[tex]k=4[/tex].

Answer:

k = 4

Step-by-step explanation:

a) Simplify both sides of the equation.

20 + 7k = 8(k + 2)

20 + 7k = (8)(k) + (8)(2)

20 + 7k = 8k + 16

7k + 20 = 8k + 16

b) Subtract 8k from both sides.

7k + 20 − 8k = 8k + 16 − 8k

−k + 20 = 16

c) Subtract 20 from both sides.

−k + 20 − 20 = 16 − 20

−k = −4

Divide both sides by -1.

-k/-1 = -4/-1

k = 4

Answer:

the bread bakes for 45 minutes (yum)

Answer: D

Step-by-step explanation:

0.92 metres =   1 yard

 40 metres  = 43.5 yard [tex](\frac{40 * 1}{0.92})[/tex]

  5 yards   :  3 minutes

43.5 yards :  26.1 minutes [tex](\frac{43.5*3}{5})[/tex]

26.1 mins ≈ 26 mins

Using the average rate of change, it is found that:

A. The average population decline between 1984 and 2018 was of 2.25 thousand deer a year.

B. The population would have reached 225 thousand deer between 2017 and 2018.

C.

The rates are as follows:

Meaning that between 1994 and 2004 there was a increase in the population of deer, and from 2004 to 2014 there was a decrease.

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

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

For 1984 and 2018, we have that:

Hence the rate is:

r = (173.50 - 250)/(2018 - 1984) = -2.25 thousand deer a year.

For item b, the situation is modeled by a linear function, as follows:

D(t) = 230.50 - 1.45t.

The population would be of 225 thousand deer when D(t) = 225, hence:

230.50 - 1.45t = 225

1.45t = 5.5

t = 5.5/1.45

t = 3.79.

Hence between the years of 2017 and 2018.

For item c, the rates are as follows:

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Answer:

105/64 or 1 41/64

Step-by-step explanation:

Math

Make common denominator of 64

:]

You have the following expression:

(37) + (-2) + (-65) + (-8)​

eliminate parenthesis with the required change of signs:

37 - 2 - 65 - 8

sum negative numbers

37 - 75

simplify: rest the numbers and put the sign of the higher number:

-38

Then, you have:

(37) + (-2) + (-65) + (-8)​ = -38

Given data,

For the greatest sum,

We need to add the two large number.

Thus,

For the greatest difference, we need to substract the largest number from the smallest,

Thus,

To find the greatest product,

we should multiply the two great numbers.

To find the greatest quotient,

we need to divide the largerst number by the smallest

We can calculate how much she get for 1/7 of a day by multiplying the daily pay rate by 1/7:

Answer: Ariel will earn $5 for 1/7 of the day.

    Equivalent fractions are those that, despite their visual differences, reflect the same value. For instance, if you take a cake and cut it into two equal pieces, you will have consumed half of the cake.

          When two fractions are expressed in their simplest form, they are said to be equivalent. When broken down into its simplest components, the fraction 26/28 equals 13/14. You only need to multiply the numerator and denominator of the reduced fraction (13/14) by the same natural number, i.e., multiply by 2, 3, 4, 5, 6 to get analogous fractions.

    In decimal form, 13/14 is 0.92857142857143.

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To find the slope of a line that passes through two points, we can use the following formula:

Then, we have:

Line EF

Line GH

Now, when graphing the two lines, we have:

If two lines have equal slopes, then the lines are parallel. As we can see, their slopes are equal, therefore the lines EF and GH are parallel.

Line JK

Line LM

Now, when graphing the two lines, we have:

As we can see, the slopes of these lines are different, so they are not parallel. Let us see if their respective slopes have the relationship shown below:

Since their respective slopes do not have the relationship shown below, then the lines are not perpendicular.

Line NP

Line QR

Now, when graphing the two lines, we have:

Two lines are perpendicular if their slopes have the following relationship:

In this case, we have:

Since the slopes of the lines NP and QR satisfy the previous relationship, then this pair of lines are perpendicular.

Line ST

The line ST has an indefinite slope because it is not possible to divide by zero. Lines that have an indefinite slope are vertical.

Line VW

Line VW has a slope of 0. Lines that have a slope of 0 are horizontal.

Now, when graphing the two lines, we have:

As we can see in the graph, the ST and VW lines are perpendicular.

Answer:

tan t = 7/24

csc t = 25/7

sec t = 25/24

cot t = 24/7

Explanation:

From the question, we're told that sin t = 7/25 and cos t = 24/25. Since we know the identities of sine and cosine to be as follows we can go ahead and determine tan t as shown below;

Let's go ahead and find cosecant t (csc t);

For sec t, we'll have;

For cot t;

Given:

The cost of graduation picnic = $13 for decoration plus an additional $5 for each attendee

Let the number of attendance = x

we need to find x when sam budgets a total of $33 for his graduation picnic

So,

solve for x, subtract 13 from both sides:

divide both sides by 5

So, the answer is:

The number of attendees = 4

Part N 1

Apply property of log

so

the answer is false

Part N 2

we have

applying property of log

so

the answer is false

Part N 3

we have

log1000=3

so

log1000-2=3-2=1

10^1=10 -----> is true

SOLUTION

Now the ground is assumed to be 0, so we have that

So, that means we have

Now, we have found t, which is how long it takes to get to the ground, you can plug it into x(t) to find the horizontal distance travelled, we have

Hence it takes her 2.5 seconds to reach the ground

And she is 20 feet away from the cliff

The rate of change is 65 miles per hour

Given the ordered pairs (1, 65) and (2, 130)

The rate of change is given as:

The rate of change is 65 miles per hour

Solution:

Given that;

To find out if watching a movie and buying a popcorn are independent, the formula is

From the deductions above;

Hence, the answer is

For this question, we use the following formula for compounded interest:

Solving for a we get:

Answer:

To find: After how many months of saving do Sam and Frank have the same amount in their accounts and how much do they have in their accounts at this time

From the graph,

x axis represents number of months,

axis represents Amount saved.

The red graph represents the amount saved by Sam over the number of months

The blue graph represents the amount saved by Frank over the number of months

To find the intersection point of the two graphs.

The intersection point is (4,80)

After 4 months Sam and Frank saved $80.

Hence we get that,

After 4 months, Sam and Frank have the same amount in their accounts. They have $80 in their accounts.

Answer is: After 4 months, Sam and Frank have the same amount in their accounts. They have $80 in their accounts.