42/12 - 85/25 + 117/30

Answer:

Step-by-step explanation:

If the lines l1 and l2 are parallel, then the slope of line l2 is the same as the slope of line l1.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

m is the slope, representing the rate of change of the function.

b is the intercept, representing the value of y when x = 0.

When two lines are parallel, they have the same slope.

Hence, If the lines l1 and l2 are parallel, then the slope of line l2 is the same as the slope of line l1.

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complete question:

In the graph shown below, if lines l 1 l 1 ​ and l 2 l 2 ​ are parallel, then the slope of line l 2 l 2 ​ is

Complete question :

At Alan's auto shop, it takes him 9 minutes to do an oil change and 12 minutes to do a tire change. Let x be the number of oil changes he does. Let y be the number of tire changes he does. Using the values and variables given, write an inequality describing how many oil changes and tire changes Alan can do in less than an hour ( minutes).

Answer:

9x + 12y < 120

Step-by-step explanation:

Given that:

Time taken for oil change = 9 minutes

Time taken for tire change = 12 minutes

x = number of oil changes ; y = number of tire changes

Total hours = 1 hour = 60 minutes

Number of oil and Tyre changes possible in less than an hour

(Number of oil changes * time taken) + (number of tire changes * time taken) less than 60 minutes

9x + 12y < 120

Answer:

9x + 12y < 120

Step-by-step explanation:

Answer:

The number which should be added  with 49x square + 4y square to get a perfect square is 28xy

Step-by-step explanation:

We need to find the number which is to be added with 49x square + 4y square to get a perfect square.

The expression given is: [tex]49x^2+4y^2[/tex]

For the expression to be perfect square it should be of form: [tex]a^2+2ab+b^2=(a+b)^2[/tex]

Now, we are given [tex]49x^2+4y^2[/tex] and we need to find the middle term

So, solving:

[tex]49x^2+4y^2\\=(7x)^2+(2y)^2+2(7x)(2y)-2(7x)(2y)\\=7x^2+28xy+(2y)^2-28xy\\=(7x+2y)^2-28xy[/tex]

The number which should be added  with 49x square + 4y square ([tex]49x^2+4y^2[/tex]) to get a perfect square is 28xy

Answer:

$1200

Step-by-step explanation:

Let the initial amount that you invested be $ x.

We are told that the new balance after investing $500 is $1760.

Thus, the balance you had before the deposit $500 us;

$1760 - $500 = $1260

So, when the amount invested was $x, the balance was $1260.

Since this money earned 5% interest on the amount you initially

Thus;

$1260 = initial deposit + (5% of inital deposit)

Thus;

x + (5% * x) = 1260

x + (0.05x) = 1260

1.05x = 1260

x = 1260/1.05

x = $1200

Answer: 4,000

Step-by-step explanation:

The solution is Option A.

The rate at which the swimming pool is being filled is 66.6 gallons per hour

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the number of gallons be = y

Let the time taken be = x

The total volume of the pool = 15000 gallons

The pool is filled at constant rate

Now ,

The coordinate data is given as

The value of A = A ( 15 , 1000 )

The value of B = B ( 30 , 2000 )

The value of C = C ( 45 , 3000 )

Now , the rate at which the swimming pool is filled is given by the slope of the points in the line

So , the slope of the 2 points is given by the formula

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 2000 - 1000 ) / ( 30 - 15 )

On simplifying the equation , we get

Slope m = 1000 / 15

Slope m = 66.66 gallons per hour

Therefore , the value of A is 66.6 gallons per hour

Hence ,

The rate at which the swimming pool is being filled is given by the slope of the line where slope m = 66.6 gallons per hour

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Answer:

x=3

Step-by-step explanation:

Answer:

1.) 6 football tickets for $24

Step-by-step explanation:

The situation which leads to a unit cost of $6 per football ticket is; 6 football tickets for $24.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Multiplication is the mathematical operation is used to determine the product of two or more numbers.

We have been given a condition as; a unit cost of $6 per football ticket.

Meaning that;

The cost of one football ticket is 6 dollar

Then The cost of 12 football ticket  = 12 x 6 dollar

                                                  = 72

Therefore, the situation which leads to a unit cost of $6 per football ticket is; 12 football tickets for $72.

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Answer:

x=−6 and y=7

Step-by-step explanation:

Step: Solve8x+5y=−13for x:

8x+5y=−13

8x+5y+−5y=−13+−5y(Add -5y to both sides)

8x=−5y−13

8x

8

=

−5y−13

8

(Divide both sides by 8)

x=

−5

8

y+

−13

8

Step: Substitute

−5

8

y+

−13

8

forxin3x+4y=10:

3x+4y=10

3(

−5

8

y+

−13

8

)+4y=10

17

8

y+

−39

8

=10(Simplify both sides of the equation)

17

8

y+

−39

8

+

39

8

=10+

39

8

(Add 39/8 to both sides)

17

8

y=

119

8

17

8

y

17

8

=

119

8

17

8

(Divide both sides by 17/8)

y=7

Step: Substitute7foryinx=

−5

8

y+

−13

8

:

x=

−5

8

y+

−13

8

x=

−5

8

(7)+

−13

8

x=−6(Simplify both sides of the equation)Step: Solve8x+5y=−13for x:

8x+5y=−13

8x+5y+−5y=−13+−5y(Add -5y to both sides)

8x=−5y−13

8x

8

=

−5y−13

8

(Divide both sides by 8)

x=

−5

8

y+

−13

8

Step: Substitute

−5

8

y+

−13

8

forxin3x+4y=10:

3x+4y=10

3(

−5

8

y+

−13

8

)+4y=10

17

8

y+

−39

8

=10(Simplify both sides of the equation)

17

8

y+

−39

8

+

39

8

=10+

39

8

(Add 39/8 to both sides)

17

8

y=

119

8

17

8

y

17

8

=

119

8

17

8

(Divide both sides by 17/8)

y=7

Step: Substitute7foryinx=

−5

8

y+

−13

8

:

x=

−5

8

y+

−13

8

x=

−5

8

(7)+

−13

8

x=−6(Simplify both sides of the equation)

Answer: The intersection between these 2 lines are (-6,7)

Source: Desmos Graphing Calculator (look it up its very helpful and gives answers)

Answer:

q = -2

Step-by-step explanation:

when solving 12q >= -24 you get

q >= -2 (12 divides 24 by 2)

therefore q is greater or equal to -2.

The answer is:

8 miles

Answer:

A

Step-by-step explanation:

Edge

The trigonometric functions y = arcsinx and y = arccosx have a domain of [–1, 1] option (A) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The domain of a trigonometric function is [-1, 1]

As we know,

The range of the sin x and cos x functions is [-1, 1]

The inverse of the above trigonometric functions are:

arc sin x and arc cos x

The range of sin x and cos x becomes domain.

So the domain of y = arcsinx and y = arccosx is [-1, 1].

Thus, the trigonometric functions y = arcsinx and y = arccosx have a domain of [–1, 1] option (A) is correct.

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Answer:

f=8/3

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

−y+4≥8

Step 2: Subtract 4 from both sides.

−y+4−4≥8−4

−y≥4

Step 3: Divide both sides by -1.

−y

−1

≥

4

−1

y≤−4

Answer:

12

Step-by-step explanation:

| 4-y| ≥8

Separate into two inequalities, one positive and one negative (remembering to flip the inequality)

4-y ≥8 or 4-y≤ -8

Solve

Subtract 4 from all sides

4-y -4 ≥8-4    or 4-y-4≤ -8-4

-y  ≥4    or -y≤ -12

Divide each side by -1, remembering to flip the inequality

y ≤-4  or y ≥12

The smallest positive number is 12

Answer:

3x4/8×4-1x2/16x2

12/32-2/32=10/32

hope it helped

Answer:

the expected population after 3 years is 863.7009

Step-by-step explanation:

The computation of the expected population after 3 years is shown below

P = P_0 × e^rt

where,

r = 21% = 0.21

t = 3 years

P_0 = 460

Now place these values to the above formula

P = 460 × exp(0.21 × 3)

= 863.7009

hence, the expected population after 3 years is 863.7009

We simply applied the above formula so that the correct value could come

And, the same is to be considered

Answer:

Step-by-step explanation:

Here is a guide to help:

Best of luck!

Answer: (9,21)

Step-by-step explanation:

R180 (3,-7) = (-(3),-(-7)) = (-3,7)

D3​ (−3,7) = (3 x −3, 3 x 7) = (−9,21)

Answer:

Below

Step-by-step explanation:

A perfect number is one whose proper divisors add up to that number.

For example, 6 is a perfect number because

Its proper divisors 1, 2 and 3 and 1+2+3 = 6.

First list prime factors:

3364 = 2 * 2 * 29 * 29

Proper divisors are 1, 2, 4, 29, 58, 116, 841, 1682

Sum of these = 2733.

So, 3364 is not a perfect number.

4489 = 67 * 67

Divisors are 1 and 67.

Sum = 68.

So, 4489 is not a perfect number.

4358 =2 * 2179

Divisors are 1 , 2 and 2179.

Sum = 2182.

So, 4358 is not a perfect number.

Answer:

x = 16/5

Step-by-step explanation:

9x – 6 = 4x + 10 <-- Combine like terms on one side

5x = 16 <-- Isolate x

x = 16/5

Answer: 3.2

Step-by-step explanation:

(9x - 6) = 4x + 10

9x - 6 = 4x + 10

9x = 4x + 16

5x = 16

x = 3.2

Answer:

A

Step-by-step explanation:

Total amount of extra money needed to be raised

= $483.62 -$218.25

= $265.37

Since each student raises the same amount and there are 17 students, $265.37 would be shared equally amongst the 17 students.

Amount of money each student must raise

= $265.37 ÷17

= $15.61

Answer: John grew 4 and 3/4 inches in one year.

Step-by-step explanation:

Start by subtracting  64.375 (64 and 3/8) by 59.625 (59 and 5/8).

Type your numbers into a calculator (both ways can be put into your calculator, but decimals are easier for you to type)

Get your final answer of 4.75.

Hope this helps!

Answer:

i think they both scored the same

Answer:

Colton did.

Step-by-step explanation:

Jack's score was 80%.

Colton got a score of 83.33...

I got Colton's score by solving 10/12.

Answer:

1) It has a y-intercept of 4

2) A, the rate of change represents how fast the boys run every hour.

Answer:

Step-by-step explanation:

your answer is A

Answer:

50 degrees

Step-by-step explanation:

vertical angles are the same

angle LPM = 180-60-70

angle LPM = 180-130 = 50

angle LPM = angle KPN

50=angle KPN

Answer:

vegetarians= 28

chickens= 44

Step-by-step explanation:

let the number of vegetarians be x

and chickens be y

So

x+2.7y=119.6----------1

x+y=72--------------2

from 2, x= 72-y

put x= 72-y in 1

72-y+2.7y=119.6

-y+2.7y=119.6-72

1.7y=47.6

divide both sides by 1.7

y=47.6/1.7

y=28

put y=28 in 1

x+28=72

y= 72-28

y=44

Answer:

91

Step-by-step explanation:

   a(n) = a +(n-1)d

   a(n) = 7+(n-1)4

   a(22) = 7+(22-1)4

            =91

hope this helps

Answer:

hum I think it is a bisect