John cuts 3 lawns in 5 hours, and Taylor cuts 5 lawns in 8 hours. Who cuts lawns at a faster rate?

9514 1404 393

Answer:

  a. n² +10n +25 = 0

  b. 0

  c. 1 real solution

Step-by-step explanation:

a. Add 25 to put the equation in standard form.

  n² +10n +25 = 0

__

b. The discriminant is d = b²-4ac.

  d = 10² -4(1)(25) = 0

The discriminant is 0.

__

c. A discriminant of 0 means there is 1 real solution.

Answer:

1. Couples tickets: $8

   Individual tickets: $4

2. Song download cost: $2

    Movie download cost: $15

Step-by-step explanation:

You can solve both of these questions by doing system of equations.

Let's start with question 1.

There are 2 variables in this equation:

- Couples tickets price: let's represent these with the letter C

- Individual tickets price: let's represent these with the letter K

Writing the two equations would look this these:

5c + 2k = 48

3c + 2k = 32

Next, isolate a variable. I am going to isolate K in the first equation.

[tex]2k = -5c + 48 \\k = -\frac{5}{2}c + 24[/tex]

Now that we isolated a variable we can plug that back in to the second equation:

[tex]3c + 2(-\frac{5}{2}c + 24) = 32\\3c - \frac{10}{2}c + 48 = 32\\3c -5c + 48 = 32\\-2c + 48 = 32\\-2c = -16\\c = 8[/tex]

We found that c is equal to 8 so we can put that back in to an equation to solve for k.

5(8) + 2k = 48

40 + 2k = 48

2k = 8

k = 4

Therefore, the price for couples tickets is $8 and the price for individual tickets is $4.

Check #1:

5(8) + 2(4) = 48

40 + 8 = 48

48 = 48

3(8) + 2(4) = 32

24 + 8 = 32

32 + 32

Now, let's go on to question 2.

There are 2 variables in this equation:

- Price of songs downloaded: let's represent these with S

- Price of movies downloaded: let's represent these with M

Writing the two equations would look like this:

15s + 11m = 195

15s + 8m = 150

There is a simple way to answer this system, however.

If you change the bottom equations signs to negative you can minus the second equation from the first equation like this:

15s + 11m = 195

-(15s +8m = 150)

Minus them to get this equation:

3m = 45

Solve

m = 15

We have found that each movie download costs $15, now let's plug this back into an equation:

15s + 11(15) = 195

15s + 165 = 195

15s = 30

s = 2

Each song costs $2 to download.

Check #2:

15(2) + 11(15) = 195

30 + 165 = 195

195 = 195

15(2) + 8(15) = 150

30 + 120 = 150

150 = 150

I hope this helps!!

- Kay :)

The temperature in Celsius will be 25.5556 °C and he temperature in degree Fahrenheit will be 105.8 °F, respectively.

A function assigns the value of each element of one set to the other specific element of another set.

Given the function to convert temperature from Celsius to Fahrenheit is F=(9/5)C+32.

A.) Given that If the temperature is 78 degrees Fahrenheit. Therefore, the temperature in degree Celsius will be,

F = (9/5)C + 32

78 = (9/5)C + 32

78 - 32 = (9/5)C

46 = (9/5)C

C = (46 × 5)/9

C = 25.5556

Hence, the temperature in Celsius will be 25.5556 °C.

B.) Given that  the temperature is 41 degrees Celsius. Therefore, the temperature in degree Celsius will be,

F = (9/5)C + 32

F = (9/5)41 + 32

F = 73.8 + 32

F = 105.8

Hence, the temperature in degree Fahrenheit will be 105.8 °F.

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Answer:

hats

Step-by-step explanation:

The value of (f-g)(x) is 2x³ + 7x²-7x-3.

As we know that, the composition of functions is the criteria of combining two or more functions into a single function. A function represents some work. The combination of two or more function always results in a new function.

Given that, f(x) = 2x³ + 7x² - 4x - 5 and g(x) = 3x - 2 and we have to calculate the value of  (f - g)(x).

Suppose h(x) =  (f - g)(x)

Now, we simply have to solve (f - g)(x), let's proceed to solve

=  (f - g)(x)

= f(x)-g(x)

= 2x³ + 7x² - 4x - 5-(3x-2)

= 2x³ + 7x² - 4x - 5-3x+2

= 2x³ + 7x²-7x-3

h(x) = (f - g)(x) = 2x³ + 7x²-7x-3

∴ (f - g)(x) = 2x³ + 7x²-7x-3

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Answer:

5 hours for priya   4 of yard mowing and 1 bag moving and they will both earn 42 dollars

Step-by-step explanation:

The addition of the 7 / 4 + 1 / 2 + 5 / 3 + 1 / 3 + 1 / 4 + 1 / 2 is 5.

A fraction represents a portion of a total. This entire may refer to a place or a group of places. The Latin word "fraction," which means "to break," is the source of the English term "fraction."

The distribution of food and supplies as well as the lack of a metal currency were among the mathematical issues that the Egyptians utilized fractions to solve because they were the first civilization to understand fractions.

Given:

7 / 4 + 1 / 2 + 5 / 3 + 1 / 3 + 1 / 4 + 1 / 2

Rearrange the number as shown below,

7 / 4 + 1 / 4 + 1 / 2 + 1 / 2 + 5 / 3 + 1 / 3

Add the like terms as shown below,

(7 + 1) / 4 + (1 + 1) / 2 + (5 + 1) / 3

8 / 4 + 2 / 2 + 6 / 3

Divide the terms as shown below,

2 + 1 + 2

5

Thus, the addition is 5.

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Hello!

[tex]\large\boxed{m = 1}[/tex]

Use the slope formula to determine the slope between the points:

m = (y2 - y1) / (x2 - x1)

Plug in the values:

m = (7 - 2) / (10 - 5)

m = 5 / 5

m = 1

Answer:

y = 14.5x + 5

Step-by-step explanation:

x = Number of tickets for the concert

y = Price of the order of x tickets

y = 14.5x + 5

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Order of 4 tickets has a price of $63

Order of 6 tickets has a price of $92

2. Write an equation to find the price of any amount of tickets.

Let's find out the price of a ticket to understand if there's a service fee and how much is it, this way:

Price of a ticket = (Order of 6 tickets - Order of 4 tickets)/2

Price of a ticket = (92 - 63)/2

Price of a ticket = 29/2 = 14.50

If a ticket costs $ 14.50, 4 tickets will cost $ 58 and 6 tickets will cost $ 87, therefore there is a service or delivery fee of $ 5.

Order of 4 tickets - Price of 4 tickets = Service or delivery fee

Replacing, we have:

63 - 58 = 5

Order of 6 tickets - Price of 6 tickets = Service or delivery fee

Replacing, we have:

92 - 87 = 5

Now, we can write the equation to find the price of an order of any amount of tickets, this way:

x = Number of tickets for the concert

y = Price of the order of x tickets

y = 14.5x + 5

Answer:

I'm positive its C

Step-by-step explanation:

Answer:

6.6%

Step-by-step explanation:

If the distance in space is often written using a light year and a light year is the distance light travels in one year. It is equal to about 6,000,000, 0 0 0, 0 0 0 miles. This measurement in scientific notation is: C. 6 x 10¹2 miles.

Given:

Measurement = 6,000,000,000,000 miles

Since the given measurement in mile is 6 trillion, now let convert the measurement in mile to scientific notation.

6 trillion = 6,000,000,000,000 miles

Hence,

6,000,000,000,000 miles = 6 × 10^12

Therefore the correct option is C.

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Answer:

You cannot add two numbers that have different variables.

Step-by-step explanation:

You can multiply them, but since 3 is multiplied by "a" or a different number than "b" then the answer would be incorrect.

Answer:

because 3a and 3b have different variables. You can't add "unlike terms" to each other because the variables have different values. by writing 3a+2b as 5ab, you're completely changing the meaning of the problem. You would get a totally different answer than you would by just adding the two terms together.

Answer:

Third choice, 3/4

Step-by-step explanation:

There's 3 lines in the middle before it's the number 1, if u count 1 into the lines then there's 4, 1 divided by 4 is 0.25 or 1/4, so each small line is going up or down by 1/4. So it's 0 -> 1/4 -> 2/4 -> 3/4 which is A -> 4/4 which is 1

So A is 3/4

Answer:

since equation a has -x on one side just add x to both sides to get rid of the -x and since you do it to both sides you maintain balance

Step-by-step explanation:

Answer:

4x+x=6-2

5x=6-2

5x+2=6

Step-by-step explanation:

Answer:

500

Step-by-step explanation:

Answer:

20$

Step-by-step explanation:

because 20*5 =100 which 20 times 5 is the same thing as adding 20+20

+20+20+20 witch is 20$ per dog he walks. hope this helps!

Answer:

x + 4y ≥ 15; y ≥ 0

Step-by-step explanation:

The solid line signifies it is a ≤ or ≥.

The equation of the line joining 0, 3.75 and 15, 0 is gotten using the formula:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\Substituting:\\\\y-3.75=\frac{0-3.75}{15-0}(x-0)\\\\ y-3.75=-\frac{1}{4}x\\\\y=-\frac{1}{4}x+3.75\\\\4y=-x+15\\\\4y+x=15[/tex]

Since the first and second quadrant are shaded, this represents y ≥ 0.

Also, above the solid line of 4y + x = 15 is shaded, this represents 4y + x ≥ 15.

Hence the inequality modeled is x + 4y ≥ 15; y ≥ 0

Answer: He right

Step-by-step explanation:

The length of the kite string is 16. 984m

A kite is currently flying at an altitude of 9 meters above the ground.

and, the angle of elevation from the ground to the kite is 32 degrees.

To find the length of the kite string to the nearest meter.

Now, According to the question:

Let the length of the kite string be x m.

From the diagram, the length of the kite string x m is hypothesis

The altitude is 9 m is opposite

and, horizontal line is adjacent.

Formula is:

Sin θ = opposite / hypotenuse

where Sinθ = 32 degree

opposite = 9 m

Hypotenuse = x m

Hence, Sin 32 = 9/x

x = 9/ sin 32 , and Sin 32 degree = 0.5299(approx.)

x = 9/ 0.5299

x = 16. 984 (approx.)

Hence, The length of the kite string is 16. 984m

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Answer:

a: 1/7 +2/7

b:1/7 +1/7+1/7

Answer:

The answer to this question is 15.

Step-by-step explanation:

We know that dividing a fraction by another fraction is the same as multiplying a fraction by the other fractions reciprocal, where the numerator and denominator are switched.

5/8 ÷ 1/24 =

5/8 x 24/1 =

120/8

120 ÷ 8 = 15.

Hence, the answer to this question is 15.

Hope this helps! :D

Final Answer:

15

Step-by-step explanation:

5/8 ÷ 1/24

5/8 ÷ 24/1

5/8 × 24/1 = 120/8

120/8 ⇒ 15/1 ⇒ 15

the last one

Hope this helps!      :3

plz mark as brainliest!

Answer:

126°

Step-by-step explanation:

A line is equal to 180°

to find x you would subtract 180° - 54°

The answer is 126°

My work is in the picture below

I hope it helped!

Have a nice day!

In the figure, the angle x° is an alternate angle with angle 54° so the measure of angle x° is 54°.

We have,

From the figure,

Line m and line n are parallel.

Line t is the transversal line.

Now,

Alternate angles are a pair of angles that are formed when a transversal (a line that crosses two other lines) intersects two parallel lines.

When this happens, the alternate angles are on opposite sides of the transversal and are congruent, which means they have the same measure.

Angle 54° and angle x° are alternate angles.

Alternate angles are equal.

So,

x° = 54°

Thus,

The measure of angle x° in the figure is 54°.

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