Christy went on a round-trip bicycle ride starting at her house. When she left, she traveled downhill at a rate of 24 kilometers per hour (kph). She rested for 30 minutes, and then returned to her house. Since the return trip was partly uphill, it took half an hour longer and Christy averaged only 20 kph. How long did the return trip take?

Hey there!!

Fill in the blanks :-

⇒ First graph the line. Locate the value of x on the x-axis. Draw a vertical line from point plotted on the x-axis to the graph of the function and a horizontal line segment from the graph of the function to the y-axis.

Find the value of f(x) when x is -2.

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

Remember :- f(x) is basically the y-value. It is just denoted as _f(x), it stands for function of x. Which means, the value of y, depends upon the value of x or the function of x.

Given : x = - 2

Plugging in the values :

... [tex]f(-2) = \frac{3*(-2)}{2}-4[/tex]

... [tex]f(-2) = \frac{-3}{1} - 4[/tex]

... [tex]f(-2) = -7[/tex]

The last fill in the blank :

The value of y on the y-axis is the value of the function. Therefore, the value of f(x) is -7 when x is -2.

Hope it helps!!

Here we are given the information that an insurance agent receives 16% commission on every premium paid.

Now we are given that a premium of $497.69 is paid.

Let us say $x is the commission paid on the policy with a premium of $497.69.

Let us try to find the amount x here.

So we have to find 16% of 497.69 to get the commission amount x.

So finding 16% of 497.69.

x= 16% of 497.69 = 0.16*497.69 = 79.63

Answer: Commission of $79.63 is paid on a policy with a premium of $497.69.

Answer:

$ 79.6304 of commission was paid on policy with a premium of $497.69.

Step-by-step explanation:

Percentage on amount received on every premium = 16% of the premium

So, when the premium of the $ 497.69 was paid , the commission received by an agent will be: 16% of the $497.69 .

[tex]\$497.69\times \frac{16}{100}=\$79.6304[/tex]

$ 79.6304 of commission was paid on policy with a premium of $497.69.

Since each shelf holds 9 books and the teacher has 55, you'll need to divide 55 ÷ 9 to find the number of shelves used. After dividing, you'll get 6.11. Round up the 6.11 to 7 since the teacher is using 6 shelves and a part of the seventh one.

The teacher fills 7 shelves with 55 books.

To find out how many shelves can be filled with 55 books where each shelf holds 9 books, simply divide 55 by 9. This gives approximately 6.11, but since you can't have a part of a shelf, we round down to 6.

The subject of this question is Mathematics, specifically division. To determine the number of shelves filled by the teacher, we should divide the total number of books by the number of books every shelf can hold. As given, the teacher has 55 books and each shelf holds 9 books.

So, you carry out the division: 55 ÷ 9. The answer is 6.111... Since we can't have a fraction of a shelf, we round this down to the nearest whole number. So, the teacher fills 6 shelves fully with books. Remember, this means there are some books that don't fill up a seventh shelf completely.

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You can solve this using long division. The answer should end up being 2.3.

Answer:

2.3

Step-by-step:

60 divided by 10 =6

3x6=18

Raul would ride 18 miles.

Hope this helped :)

Raul would ride 18 miles for 60 minutes at the same speed.

To find out how many miles Raul would ride for 60 minutes at the same speed, we can set up a proportion. If Raul rides 3 miles for 10 minutes, then we can say that 3 miles is to 10 minutes as x miles is to 60 minutes. Setting up this proportion, we get: 3/10 = x/60. To solve for x, we can cross multiply and then divide both sides by 10. This gives us: x = (3/10) * 60 = 18 miles.

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a.) [tex]769-362 = 407[/tex]

Checking: Since, [tex]407+362 = 769[/tex]

Therefore, our answer is correct.

b.) [tex]502+17 = 519[/tex]

Checking: Since, [tex]519-17 = 502[/tex]

Therefore, our answer is correct.

c.) [tex]7802-3461 = 4341[/tex]

Checking: Since, [tex]4341+3461 = 7802[/tex]

Therefore, our answer is correct.

d.) [tex]1432+2568 = 4000[/tex]

Checking: Since, [tex]4000-2568 = 1432[/tex]

Therefore, our answer is correct.

Answer:

Consider the numbers:

a) 769 - 362 = ?

Subtract the numbers.

769 - 362 = 702

Therefore, the value is 702.

Now, check using the inverse operation.

407 + 362

Add the numbers.

407 + 362 = 769

Thus, the answer is correct.

Consider the numbers:

b) 502 + 17 = ?

Add the numbers.

502 + 17 = 519

Therefore, the value is 519.

Now, check using the inverse operation.

519 - 17

Subtract the numbers.

519 - 17 = 502

Thus, the answer is correct.

Consider the numbers:

c) 7802 - 3461 = ?

Subtract the numbers.

7802 - 3461 = 4341

Therefore, the value is 4341.

Now, check using the inverse operation.

4341 + 3461

Add the numbers.

4341 + 3461 = 7802

Thus, the answer is correct.

d) 1432 + 2568 = ?

Add the numbers.

1432 + 2568 = 4000

Therefore, the value is 4000.

Now, check using the inverse operation.

4000 - 2568

Subtract the numbers.

4000 - 2568 = 1438

Thus, the answer is correct.

To find (f+g)(x), add f(x) and g(x) together. (f + g)(x) is calculated as (5x - 2) + (2x + 1), which simplifies to 7x - 1. Therefore, the correct answer is C. 7x - 1.

The question asks to find the sum of two functions, f(x) and g(x).

To find (f+g)(x), we add the two functions together.

Here's how we calculate it:
First, we take the function f(x) = 5x - 2 and the function g(x) = 2x + 1.
Then, we add them together: (f + g)(x) = f(x) + g(x).
So, (f + g)(x) = (5x - 2) + (2x + 1).
Combining like terms, we get (f + g)(x) = 5x + 2x - 2 + 1.
This simplifies to (f + g)(x) = 7x - 1.

Therefore, the correct answer is C. 7x - 1.

Final answer:

To find (f+g)(x), we need to add the functions f(x) and g(x) together. The function f(x) is given as f(x) = 5x-2 and the function g(x) is given as g(x) = 2x+1. To add the functions, we simply add the coefficients of the variable and the constant terms. So, (f+g)(x) = (5x-2) + (2x+1) = 7x-1. Therefore, the correct answer is C. 7x-1.

Explanation:

To find (f+g)(x), we need to add the functions f(x) and g(x) together. The function f(x) is given as f(x) = 5x-2 and the function g(x) is given as g(x) = 2x+1.

To add the functions, we simply add the coefficients of the variable and the constant terms. So, (f+g)(x) = (5x-2) + (2x+1) = 7x-1. Therefore, the correct answer is C. 7x-1.

Answer:

291 - 5y

Step-by-step explanation:

x- a measure of the fourth angle

The equation

[tex]x+60+(2y+8)+(3y+1)=360\qquad|\text{combine like terms}\\\\x+(2y+3y)+(60+8+1)=360\\\\x+5y+69=360\qquad|\text{subtract 5y and 69 from both sides}\\\\x=291-5y[/tex]

Comparing the probability values for each Container, Hence, both containers give equal chances of winning .

Complete question:

Container __ Red ___ Blue

A ________ 6 ______ 4

B ________ 60 _____ 40

Using the probability formula:

For Container A :

For Container B :

Since the probability values are the same, then both Container gives equal Chances of winning.

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Answer:

a) [tex]0.4[/tex] grams

b) [tex]0.053[/tex] grams

c) [tex]5.4[/tex] decigrams

d) [tex]2300[/tex] milligrams

Step-by-step explanation:

a)

To convert centigrams to grams you have to divide by 100.

[tex]40[/tex] centigrams = [tex]\frac{40}{100}[/tex] grams

                                        =[tex]0.4[/tex] grams

b)

To convert milligrams to grams you have to divide by 1000.

[tex]53[/tex] milligrams = [tex]\frac{53}{1000}[/tex] grams

                                        =[tex]0.053[/tex] grams

c)

To convert grams to decigrams you have to multiply by 10.

[tex]0.54[/tex] grams = [tex]0.54*10[/tex] decigrams

                                        =[tex]5.4[/tex] decigrams

d)

To convert grams to milligrams you have to multiply by 1000.

[tex]2.3[/tex] grams = [tex]2.3*1000[/tex] milligrams

                                        =[tex]2300[/tex] milligrams

Part A.

You spend $6 per lawn and charge $35 per lawn, so the profit per lawn is $35 - $6 = $29. Let the number of lawns you mow be n. You earn a profit of $29 pewr laun, so you earn a profit of 29n for mowing n lawns.

29n = 450

Divide both sides by 29.

n = 450/29 = 15.517...

You must mow 16 lawns to make profit.

Part B.

3 lawns per day for 5 days per week means 15 lawns per week. Since you make a profit of $29 per lawn, you will make a profit of 15 * $29 for 15 lawns in each week. 15 * $29 = $435.

You want to make $2500 profit, but you must spend $450 on the lawn mower, so you need to earn a total of $2500 + $450 = $2950.

Let n be the number of weeks. In one week, you make $435 in profit. In n weeks, you make 435n in profit.

435n = 2950

Divide both sides by 435.

n = 6.7816...

If you work for 7 weeks, you will make at least $2500 in profit.

Since the summer vacation is longer than 7 weeks, it is a reasonable goal, but you must take into account the time it takes to mow three lawns in one day.

Answer: its 4.6

just took test

The y-coordinate for point A is approximately 4.6.

To find the y-coordinate of point A, we can use the Pythagorean theorem since we know the x-coordinate (-2) and the radius of the circle (5). The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the radius of the circle and the other two sides are the x and y coordinates. So we have:

x^2 + y^2 = r^2

Substituting the given values, we get:

(-2)^2 + y^2 = 5^2

Simplifying the equation, we have:

4 + y^2 = 25

y^2 = 21

Taking the square root of both sides, we get:

y ≈ ± 4.6

Since the point A lies in the upper half of the circle, the y-coordinate is positive. So the nearest tenth of the y-coordinate for point A is 4.6.

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Answer:

[tex]10x-6[/tex]

Step-by-step explanation:

[tex]f(x) = 5x+2x\\g(x)=3x-6[/tex]

[tex](f+g)(x)\\f(x)+g(x)[/tex]

[tex]5x+2x+3x-6\\10x-6[/tex]

The value of (f+g)(x) is 10x - 6

We are taking into consideration the following two functions f(x) and g(x). The sum of these functions can be written f(x) + g(x) or as (f + g)(x). . The sum of the two functions is the sum of the two polynomials. Or in other words, the sum of any two functions gives us the addition of the terms present inside the function.

Given functions,  f(x) = 5x + 2x

and g(x) = 3x - 6

Sum of the two functions -

∴ (f+g)(x) = f(x) + g(x) = 5x + 2x + 3x - 6 = 10x - 6

Therefore (f+g)(x) = 10x - 6

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Method 1: By Listing Multiples

List out all multiples of each number, and find the first common one.

Multiples of 2

: 2, 4, 6 ... 26, 28, 30, ...

Multiples of 5

: 5, 10, 15, 20, 25, 30, ...

Multiples of 6

: 6, 12, 18, 24, 30, ...

Therefore, the LCM is 303030.

Method 2: By Prime Factors

List all prime factors of each denominator, and find the union of these primes.

Prime Factors of 2

: 2

Prime Factors of 5

: 5

Prime Factors of 6

: 2, 3

Therefore, the LCM is 2×3×5=30.

LCM = 30

we are given

[tex]f(x)=e^x sin(x)[/tex]

(a)

Firstly, we will find critical numbers

so, we will find derivative

[tex]f'(x)=e^x sin(x)+e^x cos(x)[/tex]

now, we can set it to 0

and then we can solve for x

we get

[tex]x=\frac{3\pi }{4} ,x=\frac{7\pi }{4}[/tex]

now, we can draw a number line and then locate these values

and then we can find sign of derivative on each intervals

increasing intervals:

[tex][0,\frac{3\pi}{4} )U(\frac{7\pi}{4} , 2\pi][/tex]

Decreasing interval:

[tex](\frac{3\pi}{4} ,\frac{7\pi}{4} )[/tex]

(b)

Local maxima:

It is the value of x where function changes from increasing to decreasing

so, local maxima is at

[tex]x=\frac{3\pi}{4}[/tex]

Local minima:

It is the value of x where function changes from decreasing to increasing

so, local minima is at

[tex]x=\frac{7\pi}{4}[/tex]

now, we will plug critical numbers and end values into original function

and we get

At x=0:

[tex]f(0)=e^0 sin(0)[/tex]

[tex]f(0)=0[/tex]

At [tex]x=\frac{3\pi}{4}[/tex]:

[tex]f(\frac{3\pi}{4})=e^{\frac{3\pi}{4}} sin(\frac{3\pi}{4})[/tex]

[tex]f(\frac{3\pi}{4})=7.46049[/tex]

At [tex]x=\frac{7\pi}{4}[/tex]:

[tex]f(\frac{7\pi}{4})=e^{\frac{7\pi}{4}} sin(\frac{7\pi}{4})[/tex]

[tex]f(\frac{7\pi}{4})=-172.640[/tex]

At [tex]x=2\pi [/tex]:

[tex]f(2\pi)=e^{2\pi} sin(2\pi )[/tex]

[tex]f(2\pi )=0[/tex]

Global maxima:

It is the largest value among them

so, we get

[tex]f(\frac{3\pi}{4})=7.46049[/tex]

Global minima:

It is the largest value among them

so, we get

[tex]f(\frac{7\pi}{4})=-172.640[/tex]

(c)

now, we can find second derivative

[tex]f'(x)=e^x sin(x)+e^x cos(x)[/tex]

[tex]f''(x)=\frac{d}{dx}\left(e^x\sin \left(x\right)+e^x\cos \left(x\right)\right)[/tex]

[tex]=\frac{d}{dx}\left(e^x\sin \left(x\right)\right)+\frac{d}{dx}\left(e^x\cos \left(x\right)\right)[/tex]

[tex]=e^x\sin \left(x\right)+\cos \left(x\right)e^x+e^x\cos \left(x\right)-e^x\sin \left(x\right)[/tex]

[tex]f''(x)=2e^x\cos \left(x\right)[/tex]

now, we can set it to 0

and then we can solve for x

[tex]f''(x)=2e^x\cos \left(x\right)=0[/tex]

so, we get

[tex]x=\frac{\pi}{2} ,x=\frac{3\pi}{2}[/tex]

now, we  can draw number line and locate these values

and then we can find sign of second derivative on each intervals

concave up intervals:

[tex][0,\frac{\pi}{2})U(\frac{3\pi}{2}, 2\pi][/tex]

Concave down intervals:

[tex](\frac{\pi}{2} ,\frac{3\pi}{2})[/tex]

Turning points:

All values of x for which concavity changes

so, we get turning points at

[tex]x=\frac{\pi}{2} ,x=\frac{3\pi}{2}[/tex]

fff

[tex]f(x) = e^x sin (x)[/tex]

To find increasing and decreasing intervals we take derivative

[tex]f'(x) = e^xsin(x)+e^x(cosx)= e^x(sinx+cosx)[/tex]

Now we set the derivative =0  and solve for x

[tex]e^x(sinx+cosx)=0[/tex]

sinx + cosx =0

divide whole equation by cos x

[tex]\frac{sinx}{cosx} + \frac{cosx}{cosx} =0[/tex]

tanx +1 =0

tanx = 1

[tex]x=\frac{3\pi }{4}[/tex] and  [tex]x=\frac{7\pi}{4}[/tex]

Now we pick a number between 0 to  [tex]\frac{3\pi }{4}[/tex]

Lets pick  [tex]\frac{\pi }{2}[/tex]

Plug it into the derivative

[tex]f'(x) =e^{\frac{\pi }{2}}(sin(\frac{\pi}{2})+cos(\frac{\pi }{2}))[/tex]

= 4.810 is positive

So the graph of f(x) is increasing on the interval [0, [tex]x=\frac{3\pi }{4}[/tex])

Now we pick a number between   [tex]\frac{7\pi}{4}[/tex] to 2pi

Lets pick  [tex]\frac{11\pi}{6}[/tex]

Plug it into the derivative

[tex]f'(x) =e^{\frac{11\pi}{6}}(sin(\frac{11\pi}{6})+cos(\frac{11\pi }{6}))[/tex]

= 116 is positive

So the graph of f(x) is increasing on the interval [tex](\frac{7\pi }{4}, 2\pi)[/tex]

Increasing interval is [tex](0,\frac{3\pi }{4}) U (\frac{7\pi }{4}, 2\pi)[/tex]

Decreasing interval is [tex](\frac{3\pi}{4}, \frac{7\pi}{4})[/tex]

(b)

The graph of f(x) increases and reaches a local maximum at [tex]x=\frac{3\pi}{4}[/tex]

The graph of f(x) decreases and reaches a local minimum at [tex]x=\frac{7\pi}{4}[/tex]

(c)

f(0) = 0

[tex]f(2\pi)=0[/tex]

[tex]f(\frac{3\pi }{4})=7.46[/tex]

[tex]f(\frac{7\pi}{4})=-172.64[/tex]

Here global maximum at [tex]x=\frac{3\pi}{4}[/tex]

Here global minimum at [tex]x=\frac{7\pi}{4}[/tex]

Hi,

Solution:

Find Common Denominators,

2/5 = 8/20

2 7/20

Turn into improper fractions,

2 7/10 = 47/20

Divide,

47/20 ÷ 8/20 = 5.875/1 = 5 7/8

Answer,

5 7/8

Answer:

[tex]\frac{M}{1-0.8}[/tex] and [tex]5M[/tex]

Step-by-step explanation:

1. Let's imagine that you have 100 e-mails unread. When you read 80% of these e-mails you have the following amount [tex]M[/tex] unread:

[tex]100-(0.8)(100)=20[/tex] e-mails

2. If you substitute 20 e-mails into the equations shown above, you will obtain the original amount:

[tex]\frac{20}{1-0.8}=100\\5(20)=100[/tex]

answer :  option A  and B

After reading 80% of her emails in her inbox, Danette still has M unread emails

M unread emails

Let x be the number of emails before reading

80% of emails are left in the box. So, 0.08x  emails are left in the box

Now we make an equation

number of emails - 80% of unread emails= number of unread mails

x  - 0.08x = M

Now we factor out x

x ( 1- 0.08) = M

So [tex]x = \frac{M}{1-0.8}[/tex]

or [tex]x = \frac{M}{0.2}= 5M[/tex]

-33/5 belongs to the set of

Rational numbers

Real numbers

Complex numbers

(all at the same time)

Hello  Crystalkujawa

41 Fahrenheit is 5 degrees Celsius

EQUATION :

(41°F − 32) × 5/9 = 5°C

:)

Using the formula, C = (F - 32) × 5/9, 41 degrees Fahrenheit is equal to 5 degrees Celsius.

To convert Fahrenheit (F) to Celsius (C), you can use the following formula:

C = (F - 32) × 5/9

In this formula, "F" represents the temperature in Fahrenheit, and "C" represents the temperature in Celsius.

Calculation:

Given temperature in Fahrenheit, F = 41°F

Plug the value of F into the formula:

C = (41 - 32) × 5/9

Now, perform the calculation:

C = 9 × 5/9

The 9 in the numerator and denominator cancel out, leaving us with:

C = 5

So, 41°F is equal to 5°C.

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Lets x and y are the value of two numbers.

x + y = 16

x - y = 2.4

If x + y = 16 then x = 16 - y

Substitute x = 16 - y into x - y = 2.4

16 - y - y = 2.4

16 - 2y = 2.4

2y = 13.6

 y = 6.8

x = 16 - y

x = 16 - 6.8

x = 9.2

Answer:

The value of two numbers are 9.2 and 6.8

Do you need all the coordinates or just A' and B'

[tex]f(x)=3(x+5)+\dfrac{4}{x}\\\\f(a+2)\to\text{put x = a + 2 to the equation of the function f}\\\\f(a+2)=3(a+2+5)+\dfrac{4}{a+2}=3(a+7)+\dfrac{4}{a+2}[/tex]

nickel

cardboard

bubble wrap

steam

not 100% sure though

(1,1)

(5, 3)

(6, 4)

(1, 2)

1

For this, all you need to do is plug in the x and y values.

When adding, add the two x values together to get your final x value, and add your y values to get your final y value.

a + b = (3 + (-2), 2 + (-1))

a + b = (1, 1)

When subtracting, subtract the two x values from each other to get your final x value, and subtract your y values to get your final y value.

a - b = (3 - (-2), 2 - (-1))

a - b = (5, 3)

When multiplying set a by 2, all you need to do is distribute.

2a = (3x2, 2x2)

2a = (6, 4)

For this, all you need to do is multiply the x and y values in set a by 2, and multiply the x and y values in set b by 4. Then add the product of the x value in set a to the product of the x value in set b.

2a + 4b = (2(3) + 4(-2), 2(2)+ 4(-1))

2a + 4b = (6 + (-8), 4 + (-4))

2a + 4b = (-2, 0)

For the last one you just need to find the absolute value.

|a| = (3, 2)

If you have any further questions feel free to ask. Hope this helps.

To solve this you have to first find out how many 1000s are in 14000

There are 14 1000s in 14000 so now you multiply 15.68 by 14

15.68*14=219.52

so the answer is $219.52

Final answer:

Clem's monthly payment is $219.52.

Explanation:

To find Clem's monthly payment, we need to multiply the amount borrowed by the rate per $1000 borrowed. The rate is $15.68 for every $1000 borrowed. Clem borrowed $14000, so we divide $14000 by $1000 to find the number of $1000 increments. There are 14 $1000 increments in $14000.

Multiplying $15.68 by 14 gives us the monthly payment of $219.52.

Therefore his monthly payment is $219.52.

4 yards, 2 feet, and 1 inch

Answer:

9y - 3xy + 2x - 6

= 3y(3 - x) + 2(x - 3)

= -3y(x - 3) + 2(x - 3)

= (2 - 3y)(x - 3)

Answer:

[tex]a_{n}=12n-8[/tex]

Step-by-step explanation:

We have been given a recurrence relation [tex]a_{n+1}=a_{n}+12[/tex] and the first term of the sequence [tex]a_{1}=4[/tex].

We can rewrite the given recurrence relation as: [tex]a_{n+1}-a_{n}=12[/tex]

We know that if difference between two consecutive terms is always constant, the sequence is called an arithmetic sequence. So we are dealing with an arithmetic sequence with first term as 4 and common difference as 12.

We can therefore, write an explicit formula for nth terms of the sequence as.

[tex]a_{n}=a_{1}+(n-1)d\\a_{n}=4+(n-1)(12)\\a_{n}=4+12n-12\\a_{n}=12n-8\\[/tex]

This is the required explicit function rule for the given sequence.