Find Sn for the given arithmetic series.

a1 = –74, d = –3, n = 20

Answer:

The distance she walks is 5 km

Step-by-step explanation:

Let

x -----> the distance in kilometers

y ----> the time in hours

we know that the speed is equal to divide the distance by the time

Average speed of 5 km/h

[tex]5=\frac{x}{y}[/tex]

[tex]y=\frac{x}{5}[/tex] -----> equation A

Average speed of 6 km/h

convert 10 minutes to hours

[tex]10\ min=10/60=1/6\ h[/tex]

[tex]6=\frac{x}{y-\frac{1}{6}}[/tex] ----> equation B

Solve the system by graphing

The solution is the intersection point both graphs

The solution is the point (5,1)

see the attached figure

therefore

The distance she walks is 5 km

Verify

Average speed of 5 km/h

[tex]y=\frac{5}{5}=1\ h=(1)*60=60\ min[/tex]

Average speed of 6 km/h

[tex]y=\frac{5}{6}\ h=\frac{5}{6}*60=50\ min[/tex]

The difference is the time she will save

[tex]60\ min-50\ min=10\ min[/tex] ----> is correct

To find the distance Ms. Handler walks, we can set up a proportion and solve for the variable d. The distance is found to be 5 kilometers.

To solve this problem, we can set up a proportion between the distance Ms. Handler walks and the time it takes her at each speed.

Let's say the distance she walks is d kilometers. At a speed of 5 km/h, the time it takes her to walk the distance is d/5 hours. At a speed of 6 km/h, the time it takes her is d/6 hours.

We can then set up the following proportion:

d/5 = d/6 + 10/60

To simplify the equation, we can multiply both sides by 30 to get rid of the denominators:

6d = 5d + 5

Simplifying further, we get:

d = 5

Therefore, the distance Ms. Handler walks is 5 kilometers.

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Answer:

The answer would be B.

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Answer:

First choice.

Step-by-step explanation:

You could plug in the choices to see which would make all the 3 equations true.

Let's start with (x=2,y=-6,z=1):

2x+y-z=-3

2(2)+-6-1=-3

4-6-1=-3

-2-1=-3

-3=-3 is true so the first choice satisfies the first equation.

5x-2y+2z=24

5(2)-2(-6)+2(1)=24

10+12+2=24

24=24 is true so the first choice satisfies the second equation.

3x-z=5

3(2)-1=5

6-1=5

5=5 is true so the first choice satisfies the third equation.

We don't have to go any further since we found the solution.

---------Another way.

Multiply the first equation by 2 and add equation 1 and equation 2  together.

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

4x+2y-2z=-6 is the first equation multiplied by 2.

5x-2y+2z=24

----------------------Add the equations together:

9x+0+0=18

9x=18

Divide both sides by 9:

x=18/9

x=2

Using the third equation along with x=2 we can find z.

3x-z=5 with x=2:

3(2)-z=5

6-z=5

Add z on both sides:

6=5+z

Subtract 5 on both sides:

1=z

Now using the first equation along with 2x+y-z=-3 with x=2 and z=1:

2(2)+y-1=-3

4+y-1=-3

3+y=-3

Subtract 3 on both sides:

y=-6

So the solution is (x=2,y=-6,z=1).

Answer:

4,320 dollars. Expression is 60 × 12(6)

Answer:The trip will cost 132$

can i get brainlyest

Step-by-step explanation:60(to join) + 12(per hike)x6(hikes)

12 x 6 = 72 + 60 =132

Answer:

14b^5

Step-by-step explanation:

4b^ 5 +10b^5   (factor out common factor b^5)

= (4+10) b^5

= 14b^5

Answer:

The expression of that is y/8

Step-by-step explanation:

Quotient always refers to division, so we know we are dividing.

This is the expression:

y÷8

Area of a triangle is 1/2 x base x height.

You are given the area and the height, solve for the base:

600 = 1/2 x base x 20

Multiply both sides by 2:

1200 = base x 20

Divide both sides by 20:

Base = 1200/20

Base = 60 feet.

Answer: 60

A= 1/2BH

600=1/2b*20

20 / 2= 10

600/10=60

Answer:

93

Step-by-step explanation:

PEMDAS

parenthesis, exponents, multiplication, division, addition, subtraction

34 x 3 - 9

102 - 9

93

Answer:

93

Step-by-step explanation:

First we have to use pemdas

so we multiply

34*3=102

the we subtract

102-9=93

so 93 is your answer.

THE Answer is 67

Step-by-step explanation:

Answer:

The Correct Answer Is 57

Step-by-step explanation:

According To Research

=113+(-56)

=113-56

=57

Get photomath it can help with problems like that :)

Answer:

3/4

Step-by-step explanation:

because if he has 3 lemons and 1 lime add 3 + 1= 4 and there is 3 lemons it will be 3/4

Answer: yes

Step-by-step explanation: In this problem, we are asked to determine if the relation shown here is a function. The easiest way to determine if a relation is a function is by looking at the x-coordinates. Notice that none of the coordinates repeat so this relation is a function.

Answer:

Parallel

Step-by-step explanation:

The two lines y+7x=14 and y+5=-7x are parallel to each other

The two lines y + 7x=14 and y+5=-7x are parallel to each other.

Parallel lines have the same slope since the slope is like a measure of steepness and since parallel lines are of the same steepness,

thus, are on the same slope.

Since the given parallel line has equation y = 2x + 2, thus its slope is 2 and thus, the slope of the needed line is 2 too.

Given lines is y + 7x=14 and y+5=-7x.

The slope of the given line;

y + 7x=14

y =  -7x + 14

Thus, the slope m = -7.

The slope of the given line;

y+5=-7x

y = -7x - 5

Thus, the slope m = -7.

We can see that the slope are the same.

Thus, The two lines y + 7x=14 and y+5=-7x are parallel to each other.

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Answer: He is 0 cm with respect to the surface of the water.

Step-by-step explanation:

Since we have given that

Length of plastic toy submarine below the water surface = 15 cm

Length of plastic toy submarine above the water surface = 15 cm

For below the surface, we would use negative sign i.e. (-) 15 cm

for above the surface, we would use positive sign i.e. (+) 15 cm

So, now he is

[tex]-15+15=0\ cm[/tex]

Hence, he is 0 cm with respect to the surface of the water.

If a plastic toy submarine is held 15 centimeters below the water surface in a bath tub. The integer that represents the toy submarine's position with respect to the surface of the water is 0.

The toy submarine rose 15 centimetres after initially being 15 centimetres below the water's surface. So, the whole shift in position is upward, or 15 centimetres.

The submarine's net position change is 0 centimetres because it began 15 centimetres below the surface and then rose 15 centimetres (returning to the surface level).

Therefore the integer that represents the toy submarine's position with respect to the surface of the water is 0.

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Answer:

y = ¼x + 2

Step-by-step explanation:

x - 4y = -8

-x - x

__________

-4y = -x - 8

___ _____

-4 -4

y = ¼x + 2

I am joyous to assist you anytime.

Answer:

Step-by-step explanation:

I'm not sure if the right side is [tex]\frac{a + b}{2}[/tex] or [tex]a + \frac{b}{2}[/tex], so I'll provide an answer for both:

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

[tex]2A = a + b[/tex]

[tex]2A - a = b[/tex]

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

[tex]A - a = \frac{b}{2}[/tex]

[tex]2(A - a) = b[/tex]

[tex]2A - 2a = b[/tex]

Step-by-step explanation:

Don't let the variables scare you. they are just an unknown value, that we can call anything we want. So, we can say y=6-0.6x. If you want an easier equation, just use communitive property to change it to

[tex] y = - \frac{3}{5} x + 6[/tex]

Answer:

[tex]\large\boxed{\dfrac{7}{20}=0.35}[/tex]

Step-by-step explanation:

[tex]\bold{METHOD\ 1}\\\\\dfrac{7}{20}=7:20=0.35\\\\\text{Use a calculator or long division}\\\\.\qquad\underline{0.35}\\.\ \ 20|7\\.\ \ \ \ \ \underline{\ 0}\\.\qquad70\\.\ \ \ \ \ \underline{\ 60}\\.\qquad100\\.\qquad\underline{100}\\.\qquad==[/tex]

[tex]\bold{METHOD\ 2}\\\\\dfrac{7}{20}=\dfrac{7\cdot5}{20\cdot5}=\dfrac{35}{100}=0.35[/tex]

Answer is  24 divided by 2/3

Answer:

24 ÷ 2/3

Step-by-step explanation:

Answer:

LCD = 20

Step-by-step explanation:

1/10 = 2/20

2/4 = 10/20

The least common denominator (LCD) of fractions 1/10 and 2/4 (which simplifies to 1/2) is 10. We obtain this by finding the smallest multiple of the largest denominator, 10, that the other denominator (2) can divide.

Looking to find the least common denominator of the fractions 1/10 and 2/4, we first need to simplify the fractions to their lowest terms. The fraction 2/4 can be simplified to 1/2. So now we are finding the least common denominator of 1/10 and 1/2.

Define the least common denominator (LCD): It's the smallest multiple that is exactly divisible by every denominator of the set of fractions.

Start from the largest denominator, which is 10 in this case, and list its multiples: 10, 20, 30, etc. Select the smallest multiple that the other denominator(s) (i.e. 2) can divide. You notice that 2 can divide 10, so the least common denominator of these fractions is 10.

So, the answer is that the least common denominator of the fractions 1/10 and 2/4 (or 1/10 and 1/2 in simplest form) is 10. This step-by-step explanation should provide you with an understanding of how to find the least common denominator of two fractions.

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Answer:5n

Step-by-step explanation:

Final answer:

The weight of a 500g parcel, with a gravitational field strength of 10 N/kg, can be calculated using the formula w = mg, giving a weight of 5 N.

Explanation:

To calculate the weight of a parcel with a mass of 500g (0.5 kg), we will use the formula for weight, which is w = mg, where w is the weight in newtons (N), m is the mass in kilograms (kg), and g is the gravitational field strength in newtons per kilogram (N/kg). Given that the gravitational field strength is 10 N/kg, the weight of the parcel can be calculated as follows:

Therefore, the weight of the parcel is 5 N.

Answer:

Step-by-step explanation:

2. Both a relation and function

Answer:

2.

Step-by-step explanation:

Per every pound the price is $3.42

So it does have a relation and function.

Alexis spent 2 hours and 45 minutes away from home, which is equivalent to 2.75 hours.

To calculate how long Alexis spent away from home, we need to find the difference between the time she left and the time she returned. She left her house at 7:45 p.m. and returned at 10:30 p.m.

First, we'll convert both times to a 24-hour format to make it easier to compute the time difference. The time Alexis left remains the same as 19:45 (since p.m. times are already in the second half of a 24-hour day), and the time she came back is 22:30.

Next, we subtract the time Alexis left from the time she returned:

22:30
-19:45
______

The difference in the minutes column is 30 - 45, which would be negative, so we need to borrow an hour from the hours column.

22:30
-19:45
______

Convert the borrowed hour into 60 minutes and add to the 30 minutes: 60 + 30 = 90 minutes.

21:90
-19:45
______

Now we can subtract the minutes:

90 - 45 = 45 minutes.

And subtract the hours:

21 - 19 = 2 hours.

Therefore, Alexis spent 2 hours and 45 minutes away from home.

To express this time purely in hours, we convert 45 minutes into hours by dividing by 60:

45 minutes ÷ 60 minutes per hour = 0.75 hours.

Adding this to the 2 hours, we find that Alexis was away from home for 2.75 hours.

Final answer:

Alexis was away from home for 2 hours and 45 minutes, which is equivalent to 2.75 hours. The calculation involves subtracting the time she left from the time she returned and converting minutes to hours for an accurate measure.

Explanation:

The student is asking how to calculate the time Alexis spent away from home while she went shopping for clothes. To solve this, we need to calculate the difference in time between when she left and when she returned.

Alexis left her house at 7:45 p.m. and returned at 10:30 p.m.. To find the number of hours she spent away from home, we can follow these steps:

Convert the times into a 24-hour format if necessary, but here it's not required as both times are in the p.m.

Subtract the start time from the end time.

In this case, 10:30 p.m. is the same as 22:30 in a 24-hour format, and 7:45 p.m. is the same as 19:45. So,

22:30 (End Time)
- 19:45 (Start Time)
----

We have a difference of 2 hours and 45 minutes. To express this time purely in hours, we convert 45 minutes to a decimal by dividing by 60 (since there are 60 minutes in an hour).

45 minutes / 60 = 0.75 hours

Therefore, Alexis was away for 2.75 hours.

Answer:1/4

Step-by-step explanation: divide both numbers by 4

[tex]\huge\boxed{\frac{1}{4}}[/tex]

You can simplify a fraction by dividing its numerator and denominator both by a factor from both of the numbers.

In this case, [tex]4[/tex] is a factor of the numerator and the denominator.

Divide both the numerator and the denominator by [tex]4[/tex].

[tex]\dfrac{4}{16} \div \dfrac{4}{4} = \dfrac{4 \div 4}{16 \div 4} = \boxed{\dfrac{1}{4}}[/tex]

Answer:

The number is 200.

Step-by-step explanation:

12% of a number = 24

Let the number be x.

[tex]\frac{12}{100}[/tex] of x = 24

0.12x = 24

x = [tex]\frac{24}{0.12}[/tex] = 200

So the number (x) is 200.

Answer:

[tex]\frac{20}{3} x=300[/tex]

Step-by-step explanation:

Given that the bag has 300 Gummy Bears and Mr.Smith eats 20 Gummy Bears every 3 minutes, then;

Lets assume x time taken to finish all Gummy Bears in the bag, then

Given in the question that

3 minutes =20 Gummy Bears

? minutes=300 gummy Bears

Perform cross-multiplication

[tex]=\frac{300*3}{20} =45minutes[/tex]

This means after 45 minutes the bag of Gummy Bears will be empty.

The equation to model the number of Gummy Bears in the bag will be;

[tex]\frac{20}{3} x=300[/tex]

Answer:

     [tex]600-\frac{20}{3}\text{x}[/tex]

Step-by-step explanation:

Given: Mr. Smith has a super-sized bag of Gummy Bears. He goes to eat from the bag of Gummy bears which has 300 Gummy Bears in it. Mr. Smith eats 20 Gummy Bears every 3 minutes.

To Do: Write an equation to model the number of Gummy Bears in his bag.

Solution: Total Number of Gummy bears in Mr. Smith's super-sized bag =[tex]300[/tex]

  Number of Gummy bears eaten by Mr. Smith in every 3 minutes = [tex]20[/tex]

Number of Gummy bears eaten  by Mr. Smith in every in minutes= [tex]\frac{20}{3}[/tex]

Now,

The number of Gummy bears in his bag after [tex]\text{x}[/tex] minutes is

                                         =[tex]600-\frac{20}{3}\text{x}[/tex]

The equation for number of gummy bears in Mr. Smith's bag after [tex]\text{x}[/tex] minutes is                

                                              [tex]600-\frac{20}{3}\text{x}[/tex]