Lines and care parallel
What is the measure of _22
m_2 = 31°
m_2 = 50°
m22 = 120
56
m_2 = 130

Answer:

7x + 2y = - 6

Step-by-step explanation:

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

given

y = - \(\frac{7}{2}\) x - 3 ( multiply through by 2 to clear the fraction )

2y = - 7x - 6 ( add 7x to both sides )

7x + 2y = - 6 ← in standard form

-9x − 6y = -6

3x + 2y = 2.

I will use elimination

Multiply the second equation by 3

3(3x + 2y = 2.)

9x + 6y = 6

Add this to the first equation

-9x − 6y = -6

9x + 6y = 6

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

0 = 0

This means that they are the same line

The system will have infinite solutions

infinite solutions

(3,5) is the answer i think

hope it helpss

The compound amount after 3 years is $2275.22.

In this case, you are given:

Principle = $2,000

rate = 0.0353

time = 3

You need to find A, the compound amount after 3 years.

To do this, you need to plug in the values of P, r and t into the formula and use a calculator:

A=P×e^rt

A=2000×(e)^0.0353×3

A≈2275.22

Therefore, by the compound interest the answer will be $2275.22.

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Answer: a popcorn is $9

Step-by-step explanation:

soda is $6

As per the given variables, Victor jumped a total of 4 yards.

Total yards jumped = 6 feet high

Additional yards = 2

A yard is one linear yard. "Yd" is the yard symbol. The standard of measurement has always been derived from either a natural item or a portion of the human body, such as a foot, an arm's length, or the width of a hand.

Converting the initial jump of 6 feet to yards, as the additional distance given is also in yards.

There are 3 feet in a yard, therefore -

6 feet = 6/3  

= 2

Thus, Victor jumped 2 yards initially, and then 2 more yards as given in the problem.

Calculating, the total distance Victor jumped in yards -

= 2 + 2

= 4

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it has the correct conditions and the correct formula for calculating the cost. \(C(x) = 3.25x + 5 if x > = 6\) Thus, option C is correct.

The correct function that models this scenario is:

\(C(x) = 3.75x if x < 6\)

\(C(x) = 3.25x + 5 if x > = 6\)

This is because for rentals less than 6 hours, the cost is simply $3.75 per hour, so the function is  \(C(x) = 3.75x\)  . For rentals of 6 hours or more, there is a discounted hourly rate of $\(3.25\) per hour, but there is also a $5 processing fee, so the function is \(C(x) = 3.25x + 5\)  .

Option (a) is incorrect because it does not include the $5 processing fee for rentals of 6 hours or more.

Option (b) is incorrect because it has the wrong conditions for the hourly rate discounts. It specifies that the discount starts at x = 6, but the correct condition is \(x > = 6.\)

Option (c) is correct, as it has the correct conditions and the correct formula for calculating the cost.

Option (d) is incorrect because it has the wrong condition for the hourly rate discounts (x < 5 instead of x < 6), and it does not include the $5 processing fee for rentals of 6 hours or more.

Therefore, it has the correct conditions and the correct formula for calculating the cost. \(C(x) = 3.25x + 5 if x > = 6\)

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"97.72% of the female students have scores above," seems to be a misinterpretation as the correct statement is that approximately 99.72% of the female students have scores between the lower and upper limits

To calculate the scores that are three standard deviations above and below the mean, we use the formula:

Lower limit = Mean - (Standard Deviation * 3)

Upper limit = Mean + (Standard Deviation * 3)

Given:

Mean = 269

Standard Deviation = 33

Using the formula, we can calculate the limits:

Lower limit = 269 - (33 * 3) = 269 - 99 = 170

Upper limit = 269 + (33 * 3) = 269 + 99 = 368

Therefore, the lower limit is 170 and the upper limit is 368.

To calculate the probability that a female student will have a score between these limits, we need to find the area under the normal distribution curve between the lower and upper limits. This can be calculated using a standard normal distribution table or calculator.

Since the distribution is assumed to be normal, approximately 99.72% of the scores will fall within three standard deviations from the mean. Therefore, the probability that a female student will have a score between these limits is approximately 99.72%.

For a score of 302, which is above the mean of 269, we can calculate the percentage of female students with scores below 302:

Percentage = (1 - Probability) * 100

= (1 - 0.9972) * 100

= 0.0028 * 100

= 0.28%

Therefore, approximately 0.28% of the female students have scores below 302.

It's important to note that the value mentioned, "97.72% of the female students have scores above," seems to be a misinterpretation as the correct statement is that approximately 99.72% of the female students have scores between the lower and upper limits

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Answer:

  1.6 times   or   60% more than

Step-by-step explanation:

The question seems to be asking about the growth factor in the given exponential function.

A generic exponential function will have the form ...

  quantity = (initial value) × (growth factor)^(number of intervals)

Comparing this form to the given formula ...

  f(x) = 58 × 1.6^x

we see the "growth factor" is 1.6. This is the multiplier from one interval (year) to the next.

Each year the expected number of birds is 1.6 times the number the year before.

__

Additional comment

A growth factor is sometimes expressed in terms of a growth rate, usually a percentage.

  growth factor = 1 + growth rate

  1.6 = 1 + 0.60 = 1 + 60%

The growth rate of this bird population is 60% per year. Each year, the population is 60% more than the year before.

Answer: 1.6

Step-by-step explanation:

Answer:

C. the sum of 4 and the product of 3 and X

Answer:

I would assume C

Step-by-step explanation:

The equation is the sum of 4 plus the product of 3 and x

Answer:

1 hour and 50 minutes

Step-by-step explanation:

Time Connie takes to clean the house: 210 minutes

Time takes for both of them at the same time: 100 minutes.
210 - 100 = 110 minutes

Therefore, Alvaro takes one hour and 50 minutes to clean the house by himself.

Answer:Alvaro can clean the house alone in approximately 3.89 hours.

Step-by-step explanation:

If Connie can clean her house in 3.5 hours, then her rate of work is 1/3.5 of the house per hour. Together, Connie and Alvaro can clean the house in 1 hour and 40 minutes, or 1.67 hours.

To find how long it would take Alvaro to clean the house alone, we can use the formula:

combined rate of work = sum of individual rates of work

So, (1/3.5 + 1/a) * 5/3 = 1, where "a" is the time it takes Alvaro to clean the house alone.

Simplifying the equation, we get 1/a = 9/35, which means that Alvaro can clean the house alone in approximately 3.89 hours (or 3 hours and 53 minutes).

Answer:

Step-by-step explanation:

-- there is an equation to find this: (2n + 1) + (2n + 3) = (whatever number is given as their sum)

use the equation: 2n + 1 is an odd interger, 2n + 3 is the next odd integer.

(2n + 1) + (2n + 3) = 88

add like terms.

4n + 4 = 88

4n = 84

n = 21

now plugin.

2(21) + 1

42 + 1

= 43 (the first odd integer)

this means the second one would be 45.

answer: 43 and 45

add them to check:

43 + 45 = 88

The population grow by 24.7% between the years 2004 and 2009

from the question, we have the following parameters that can be used in our computation:

Population in 2004 = 2122

Population in 2009 = 2647

The growth of the population between the years is calculated as

Percentage = Population in 2009/Population in 2004  - 1

Substitute the known values in the above equation, so, we have the following representation

Percentage = 2647/2122 - 1

Evaluate

Percentage = 24.7%

Hence, the population grow between the years by 24.7%

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The statement that "σ(n) < 2n holds true for all n of the form n = p²" has been proved.

Let p be any prime number, and let σ(n) be the sum of all positive divisors of the integer n.

As p is a prime number, and 2 is the smallest prime number, so, p\(\geq\)2

So, the positive divisors of the integer n are: 1,p,p².

As σ(n) represents the sum of all positive divisors of the integer n.

σ(n)=1+p+p²

In order to prove that σ(n) < 2n,for all n of the form n = p².

1+p+p²<2p²

p²-p-1>0

It is know that, p\(\geq\)2.

So, p²-p-1\(\geq\)1

Thus, σ(n) < 2n holds true for all n of the form n = p².

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Answer:

19

Step-by-step explanation

Answer:

19

Step-by-step explanation:

16-14÷2+(3+2)2

16-14÷2+5×2

16-7+5×2

16-7+10

16+10-7

26-7

19

Answer:

7.7 pounds = 3.5 kilograms

Step-by-step explanation:

Given that,

Weight of a gallon of liquid = 7.7 pounds

We need to find weight in kilograms.

We must know the relation between pounds and kilograms and it is as follows :

1 kilogram = 2.20 pounds

or

1 pounds = (1/2.2) kilograms

7.7 pounds = (7.7/2.2) kilograms

= 3.5 kilograms

Hence, 7.7 pounds is equal to 3.5 kilograms.

Answer:

A) h= 201-6t

B) Candle B is 290 millimeters tall and burns at 5 millimeters per hour

C) Candle A burns faster because it has a rate of burning that is 1 millimeter faster per hour than Candle B (coefficient in front of t)

D) 58 hours

Step-by-step explanation:

Candle A Went down 24 in 4 hours so thats 6 millimeters per hour.

A) h= 201-6t

Candle A Went down 24 in 4 hours so thats 6 millimeters per hour (how i found the coeffiecient in front of t.)

B) Candle B is 290 millimeters tall and burns at 5 millimeters per hour

(Just interpreted the given equation)

C) Candle A burns faster because it has a rate of burning that is 1 millimeter faster per hour than Candle B, although candle B is still 50% larger than candle A at the beginning of burning.

D) 290=5t

t=58 hours

It would take 58 hours for Candle B to burn down completely, from the given equation.

Answer:

15227707.5

More info

Step-by-step explanation:

45x676787 the divide it by 2

Answer: C

Step-by-step explanation:

Point D is at -14 on the number line.

In Mathematics, the midpoint of a line segment with two end points can be calculated by adding each end point on a line segment together and then divide by two (2).

Since E is the midpoint of line segment CD, we can logically deduce the following relationship:

Line segment CD = Line segment C + Line segment D

Midpoint E = (point C + point D)/2

By substituting the given points into the equation above, we have the following:

-3 = (8 + D)/2

-6 = 8 + D

D = -6 - 8

D = -14

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Answer:

area should be 84

Step-by-step explanation:

Answer:

84 units squared

Step-by-step explanation:

calculate the width and height if this were a normal rectangle

w = 6 + 3 + 6 = 15

l = 6

use that to calculate the area

15 * 6 = 90

subtract the smaller rectangle

90 - (2 * 3) = 84

Answer:

64°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

let the third angle be x , then

x + 90° + 26° = 180°

x + 116° = 180° ( subtract 116° from both sides )

x = 64°

the other angle is 64°

Answer:

The system of linear equations that can be used to determine the time that each of the trains has been traveling is:

E + W = 4 ....... Equation 1

95 E + 110W = 400  ......Equation 2

Hence,

An Eastbound train has been travelling for =  (E) = 2.67 hours

A Westbound train has been travelling for =  (W) = 1.33 hours

Step-by-step explanation:

An Eastbound train (E) traveling 95 mph and a Westbound train (W) traveling 110 mph leave the same train station at different times. After 4 hours, they are 4 00 miles apart. Which system of linear equations can be used to determine the time that each of the trains has been traveling?

Speed = Distance/Time

Distance = Speed × Time

Let the time

An Eastbound train =  (E)

A Westbound train =  (W)

E + W = 4 hours ....... Equation 1

95mph × E + 110mph × W = 400 miles

95 E + 110W = 400 miles ......Equation 2

The system of linear equations that can be used to determine the time that each of the trains has been traveling is:

E + W = 4 ....... Equation 1

95 E + 110W = 400  ......Equation 2

E = 4 - W

We substitute 4 - W for E in Equation 2

95 (4 - W) + 110W = 400  

380 - 95W + 110W = 400

Collect like terms

95W - 110W = 400 - 380

15W = 20

W = 20/15

W = 1.3333333333 hours

≈ 1.33 hours

E = 4 - W

E = 4 - 1.33 hours

E = 2.67 hours

Therefore,

An Eastbound train has been travelling for =  (E) = 2.67 hours

A Westbound train has been travelling for =  (W) = 1.33 hours

Answer:

5/2

Step-by-step explanation:

1/2 + 6/2 + 5/2 = 12/2 or 6

Answer:

5/2

Step-by-step explanation:

1/2+6/2= 5/2

12/2=6

1/2+6/2+5/2= 6

The lateral surface area and total surface area of the given triangular prism are 252cm² and 348 cm² respectively.

The entirety of an object's sides, excluding its base and top, are referred to as the lateral surface. The size of the lateral surface is referred to as the lateral surface area. The total surface area, which includes the lateral surface area as well as the areas at the base and top, should be distinguished from this.

Total surface area of this prism = 3 × l × b + 2 × h × b

= 3 × 14 × 6 + 2 × 8 × 6

= 348 cm²

And lateral surface area =  3 × l × b

= 3 × 14 × 6

= 252cm²

Thus, the lateral surface area and total surface area of the given triangular prism are 252cm² and 348 cm² respectively.

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Answer:

380 seconds

Step-by-step explanation:

Convert 6 minutes to seconds by multiplying 6 times 60, because there are 60 seconds per minute.
6 x 60 = 360

Now add the 20 seconds.
360 + 20 = 380

6 minutes and 20 seconds are equal to 380 seconds.

Its a function composed, with other function y=x+3

Then

f(x+3) = - (x+3) + 6

f(x+3) = -x -3 + 6 = -x + 3.

then answer is -1, add sign, 3