if the area of a parallelogram is 86cm and the height is 12cm write an equation that relates the height,base and area of the parallelogram

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut-off point with the y axis

We have two points that belong to the AB line:

[tex](x_ {1}, y_ {1}) :( 2,1)\\(x_ {2}, y_ {2}): (- 1, -8)[/tex]

We can find the slope:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-8-1} {- 1-2} = \frac {-9} {- 3} = 3[/tex]

By definition, if two lines are parallel then their slopes are equal. Thus, a line parallel to AB will have slope [tex]m = 3[/tex], then the equation will be of the form:

[tex]y = 3x + b[/tex]

We substitute the given point and find b:

[tex](x, y) :( 0,2)\\2 = 3 (0) + b\\2 = b[/tex]

Finally, the equation is:

[tex]y = 3x + 2[/tex]

Answer:

[tex]y = 3x + 2[/tex]

Answer:

  (-1/4)(2x +5y)

Step-by-step explanation:

Multiply and divide by -1/4:

  [tex]-\frac{1}{2}x-\frac{5}{4}y=\dfrac{(-\frac{1}{4})(-\frac{1}{2}x-\frac{5}{4}y)}{-\frac{1}{4}}=\left(-\dfrac{1}{4}\right)(-4)\left(-\dfrac{1}{2}x-\dfrac{5}{4}y\right)\\\\=\left(-\dfrac{1}{4}\right)\left(2x+5y)[/tex]

A point B is (1 , -9)

Step-by-step explanation:

The formula of the slope of a line is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

where [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are two points

lie on the line

We need to find a point B that makes that true

Assume that point B is (x , y)

∵ Point A = (5 , 3)

∵ Point B = (x , y)

∴ [tex]x_{1}=5[/tex] and [tex]x_{2}=x[/tex]

∴ [tex]y_{1}=3[/tex] and [tex]y_{2}=y[/tex]

- Substitute these values in the formula of m

∴ [tex]m=\frac{y-3}{x-5}[/tex]

∵ m(A , B) = 3

- Equate the formula of the slope by 3

∴ [tex]\frac{y-3}{x-5}=3[/tex]

- By using cross multiplication

∴ y - 3 = 3(x - 5)

- Simplify the right hand side

∴ y - 3 = 3x - 15

- Add 3 for both sides

∴ y = 3x - 12

To find point B chose any value for x and substitute it in the

equation to find y

∵ x = 1

∴ y = 3(1) - 12 = 3 - 12

∴ y = 9

∴ Point B = (1 , -9)

V.I.N: You can find many values of point B by chose different values of x and find the corresponding values of y

A point B is (1 , -9)

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Answer:

The corresponding answers to the questions are  9.625 cm² , 459, 304.5m², 1 : 3 , 3:4 , 10,000 pounds , 36 inches.

Step-by-step explanation:

1.

Area of triangle = 0.5 x base length x height

Here base length = 5.5cm and height = 3.5cm

So area will be 0.5 x 5.5 x 3.5 cm² = 9.625 cm²

2.

919/2 rounding off to nearest whole

We know that the value of 919/2 = 459.5 .

So the nearest whole number value to which it can be rounded off is 459.

3.

We know that area of parallelogram is base length x height

Here, base length =14.5m and height = 21m

So area = 14.5 x 21 m² = 304.5m²

4.

No. of grilled cheese sandwiches sold = 200

No. of tacos sold                                     = 100

No. of grilled chicken salads sold          = 150

Total lunches sold                                   = 200 + 100 + 150 = 450

So, ratio of chicken salads to lunches sold is 150 : 450 = 1 : 3

5.

Given number : 7,208,631

Odd digits here - 7,3,1 - 3 digits

Even digits here - 2,0,8,6 - 4 digits

So, ratio of odd digits to even digits is 3:4

6.

One ton = 2000 pounds

So 5 tons = 5 x ( 1 ton) = 5 x 2000 pounds = 10,000 pounds

7.

Table length = 3 feet

We know that 1 foot = 12 inches

So table length = 3 foot = 3 X 12 inches = 36 inches

Answer: 204 teddy bears

Step-by-step explanation:

Answer:

17 x 12 = 204 teddy bears

Step-by-step explanation:

17 cases, 12 bears in each case

You could round 17 --> 20

You could round 12 --> 10

20×10=200

A, D & E

Cells store energy in the form ATPs. These molecules power al the biochemical activities that would not occur spontaneously. Examples of these bioactivities are the contraction of actin filaments, glycolysis cycle, replication of DNA, cell division, gene expression, cell repair and etcetera.

Step-by-step explanation:

All ATPs are not spent at the same time, and futhermore, they are constantly replaced by the continuous process of cellular respiration that captures the chemical energy in the glucose molecules and stores them in ATP. During the release of this energy to power the biochemical reactions, much of it is lost as heat energy and this is why living organisms are always warm.

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Answer: The multiple choice answers would be, A, D, and E.

Step-by-step explanation:

Answer: perpendicular

Step-by-step explanation:

Final answer:

The slopes of the two lines given by the equations 3x-6y=2 and 18x+9y=8 are 1/2 and -2 respectively. Since these slopes are neither equal nor negative reciprocals, the lines are neither parallel nor perpendicular.

Explanation:

To decide whether the pair of lines is parallel, perpendicular, or neither, we need to find the slopes of the lines. The lines are given by the equations 3x-6y=2 and 18x+9y=8. To find the slope of each line, we must rewrite the equations in slope-intercept form (y=mx+b), where m represents the slope

For the first line, 3x-6y=2, we isolate y:

So the slope of the first line is 1/2.

For the second line, 18x+9y=8, we isolate y:

The slope of the second line is -2.

Since the slopes of the two lines are not equal and not negative reciprocals of each other, the lines are neither parallel nor perpendicular.

Answer:

-3

Step-by-step explanation:

2(x+-3)=1/2x

2x+6=1/2x

6=-1/2x

x=-3

Answer:

-3 is the write answer

Step-by-step explanation:

2(x+3)=1/2x

2x+6=1/2x

6=-1/2x

x=-3

Answer:

44°

Step-by-step explanation:

The sum of the angles in a triangle = 180°

In an isosceles triangle the base angles are equal, thus

base angle = [tex]\frac{180-92}{2}[/tex] = [tex]\frac{88}{2}[/tex] = 44°

Answer:

The answer is 19 feet or B.

Step-by-step explanation:

First you should know that a square has equal sides.

Then it tells you to add 5 feet on the original field. So you add 5 to 19 and you get 24. After that, you multiply the 24 by itself to get 576 feet.

Answer:

no solution

Step-by-step explanation:

well first you gotta distribute

-5(-3 - w) + 4 = -5/6(24 - 6w)

15 + 5w + 4 = -20 + 5w

19 + 5w = -20 + 5w

+20           +20

39 + 5w = 5w

      -5w    -5w

39 ≠ 0

therefore there is no solution (which is the answer)

Answer:

80cents per pound

Step-by-step explanation:

24 divided by 30 is .8

Answer:

[tex]\large\boxed{\dfrac{3x+6}{x-4}\div\dfrac{2x^2+9x+10}{x^2+4x}=\dfrac{3x(x+4)}{(x-4)(2x+5)}}[/tex]

Step-by-step explanation:

Just like that

[tex]\dfrac{3x+6}{x-4}\div\dfrac{2x^2+9x+10}{x^2+4x}=\dfrac{3x+6}{x-4}\cdot\dfrac{x^2+4x}{2x^2+9x+10}\\\\=\dfrac{3(x+2)}{(x-4)}\cdot\dfrac{x(x+4)}{2x^2+4x+5x+10}=\dfrac{3(x+2)}{(x-4)}\cdot\dfrac{x(x+4)}{2x(x+2)+5(x+2)}\\\\=\dfrac{3(x+2)}{(x-4)}\cdot\dfrac{x(x+4)}{(x+2)(2x+5)}\qquad\text{cancel}\ (x+2)\\\\=\dfrac{3x(x+4)}{(x-4)(2x+5)}[/tex]

Answer:

There were 120 events planned.

Step-by-step explanation:

We are given the following information in the question:

f(x) represents the total monthly expenses for planning x events.

[tex]f(x) = 50(2x+1) + 300[/tex]

Cost of expenses for the company at the end of one month = $12,350

We have to find the number of events planned that is we have to find the value of x.

[tex]f(x) = 50(2x+1) + 300 = 12350\\50(2x+1) + 300 = 12350\\100x + 50 + 300 = 12350\\100x + 350 = 12350\\100x = 12350-350\\100x = 12000\\\\x = \displaystyle\frac{12000}{100} =120[/tex]

Thus, there were 120 events planned.

Answer:

120

Step-by-step explanation:

i actually did just guess on that answer i didnt know what to put

Answer:

1.  45/482 of the students are in grade 4.

2.  5/9 of the students of the grade 4 are boys.

3. 7/15 of the grade 4 students are in Ms. Ashley's class

4. 3/4 of the students in Mr. Ben's class do not have siblings in the same school.

5. There are 14 students with glasses and 7 without glasses.

Step-by-step explanation:

1. Let's review the information given to us for solving the questions:

Number of students in the school = 482

Ms. Ashley's Grade 4 class = 21 students

Ms. Ashley's Grade 4 class boys = 15 students

Ms. Ashley's Grade 4 class girls = 6 students

Ms. Ashley's Grade 4 class with glasses = 2/3 * 21 = 42/3 = 14 students

Mr. Ben's Grade 4 class = 24 students

Mr. Ben's Grade 4 class boys = 10 students

Mr. Ben's Grade 4 class girls = 14 students

Mr. Ben's Grade 4 class with siblings in the school = 1/4 * 24 = 24/4 = 6 students

2. Let's answer all the questions:

1. What fraction of the students in the school are in grade 4?

(Ms. Ashley's Grade 4 class + Mr. Ben's Grade 4 class)/ Number of students in the school

21 + 24 / 482 = 45/482

2. What fraction of the grade 4 students are boys?

(Ms. Ashley's Grade 4 boys + Mr. Ben's Grade 4 boys)/ (Ms. Ashley's Grade 4 class + Mr. Ben's Grade 4 class)

15 + 10 / 21 + 24

25 / 45 = 5/9

3. What fraction of the grade 4 students are in Ms. Ashley's class?

Ms. Ashley's Grade 4 class / (Ms. Ashley's Grade 4 class + Mr. Ben's Grade 4 class)

21 / 21 + 24

21 / 45 = 7/15

4. What fraction of the students in Mr. Ben's class that do not have siblings in the same school?

(Mr. Ben's Grade 4 class - Mr. Ben's Grade 4 class with siblings in the school)/ Mr. Ben's Grade 4 class

24 - 6 / 24

18 / 24 = 3/4

5. In Ms. Ashley's class, are there more students that wear glasses or do not wear glasses?

There are 14 students with glasses and 7 without glasses.

Note: Same answer to question 14038475, answered by me.

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}4x=-3y-10&\text{add}\ 3y\ \text{to both sides}\\9x+2y=6\end{array}\right\\\\\left\{\begin{array}{ccc}4x+3y=-10&\text{multiply both sides by 2}\\9x+2y=6&\text{multiply both sides by (-3)}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}8x+6y=-20\\-27x-6y=-18\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-19x=-38\qquad\text{divide both sides by (-19)}\\.\qquad\dfrac{-19x}{-19}=\dfrac{-38}{-19}\\.\qquad \boxed{x=2}[/tex]

[tex]\text{Put the value of}\ x\ \text{to the second equation:}\\\\9(2)+2y=6\\18+2y=6\qquad\text{subtract 18 from both sides}\\2y=-12\qquad\text{divide both sides by 2}\\\dfrac{2y}{2}=\dfrac{-12}{2}\\\boxed{y=-6}[/tex]

Answer:

$9.40

Step-by-step explanation:

well since you work 37.5 hours and you earn $352.50 you divide them to get your hourly wage

352.5 ÷ 37.5 = 9.4

so your hourly wage is $9.40

Final answer:

To calculate the hourly wage, the total earnings of $352.50 should be divided by the total work hours of 37.5. The hourly wage comes out to be $9.40.

Explanation:

To find out your hourly wage, you need to divide your total earnings by the number of work hours. In this instance, you worked 37.5 hours (since 1/2 an hour is equivalent to 0.5 hours) and earned $352.50. So, your hourly wage would be calculated as follows:

Hourly Wage = Total Earnings ÷ Number of Work Hours

Hourly Wage = $352.50 ÷ 37.5 hours

Hourly Wage = $9.40 per hour

Therefore, your hourly wage is $9.40.

The product of 3 factorial is 6.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

We have to find the value of 3 factorial.

By the definition of factorial, factorial of any natural number can be defined as,

a factorial = 1 × 2 × ....... × (a - 1) × a

Here we have to find 3 factorial.

3 factorial can be written as,

3 factorial = 3 × 2 × 1 = 6 × 1 = 6

Hence the required product of 3 factorial is 6.

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Answer:

Step-by-step explanation:

[tex]3x+2=x+4(x+2)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\3x+2=x+(4)(x)+(4)(2)\\\\3x+2=x+4x+8\qquad\text{combine like terms}\\\\3x+2=(x+4x)+8\\\\3x+2=5x+8\qquad\text{subtract 2 from both sides}\\\\3x+2-2=5x+8-2\\\\3x=5x+6\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\3x-5x=5x-5x+6\\\\-2x=6\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2x}{-2}=\dfrac{6}{-2}\\\\x=-3[/tex]

Answer:

The radius of the circle is 12.006 m.

Step-by-step explanation:

Let us assume the radius of the circle = r

Circumference  = 75.4 m

Now, CIRCUMFERENCE OF A CIRCLE = 2 π r

⇒ 75 .4 m = 2 π r

Now, putting  π = 3.14, we get:

75 .4 m = 2 (3.14)  r

⇒ 75.4 = 6. 28 r

or, r = 75.4/6.28 =  12.006

or, r  = 12.006 m

Hence, the radius of the circle with circumference 75.4 m is 12.006 m.

The volume of the silo is 461.81 m³

Step-by-step explanation:

A barn silo, excluding the top, is a cylinder

We need to find the volume of the silo

∵ The silo is shaped a cylinder

∵ The volume of a cylinder = base area × height

∵ The base is shaped a circle

∵ Area a circle = π r², where r is the radius of the circle

∴ The volume of the silo = π r² × h

∵ The diameter of the silo = 7 m

∵ The radius of a circle is half the diameter

∴ The radius of the silo = [tex]\frac{1}{2}[/tex] × 7 = 3.5 m

∵ The height of the silo = 12 m

- Substitute the values of r and h in the rule of volume

∴ The volume of the silo = π (3.5)² × 12

∴ The volume of the silo = 147 π = 461.81 m³

The volume of the silo is 461.81 m³

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Final answer:

The volume of a barn silo that is shaped like a cylinder with a diameter of 7 meters and a height of 12 meters is approximately 461.7 cubic meters.

Explanation:

To calculate the volume of the silo which is in the shape of a cylinder, we use the formula V = πr²h, where V is the volume, r is the radius, and h is the height. The diameter of the silo is given as 7 meters, so the radius is half of that, which is 3.5 meters. The height of the silo is 12 meters. Plugging these values into the formula gives:

V = π × (3.5 m)² × 12 m

V = π × 12.25 m² × 12 m

V = π × 147 m³

Assuming π to be approximately 3.14159, the calculation results in:

V = 3.14159 × 147 m³ = 461.7 m³ (approx)

So, the volume of the silo is approximately 461.7 cubic meters.

Answer:

If you were asking how many miles in total: 290 miles.

If you were asking how many miles in the 2 hours: 122 miles

Step-by-step explanation:

In the first 168 miles,

[tex]Since \\v_1=168miles/3h=56 miles/h\\\\Thus  \\v_2=v_1+5=56+5=61miles/h\\\\X_1=168miles\\X_2=v_2*2h=61*2=122miles\\X_1+X_2=168+122=290miles\\\\[/tex]

Final answer:

To find the radius of the circular trampoline, we can use the formula for the area of a circle and rearrange it to solve for the radius. The radius of the trampoline is approximately 6.5 ft (rounded to the nearest tenth).

Explanation:

To find the radius of the circular trampoline, we can use the formula for the area of a circle, which is A = πr². In this case, the area is given as 132.2 ft². We can rearrange the formula to solve for the radius:

r² = A/π

r² = 132.2/π

r ≈ √(132.2/π)

r ≈ √(42)

r ≈ 6.5 ft (rounded to the nearest tenth)

Final answer:

To find the radius of the trampoline, we use the formula for the area of a circle and rearrange it to solve for the radius. After substituting the given area and approximating π as 3.14, we find that the radius is approximately 6.5 ft when rounded to the nearest tenth.

Explanation:

The area of a circle is given by the formula A = πr², where A is the area and r is the radius of the circle. Given the area of the trampoline as 132.2 ft², we can solve for the radius using the area formula. We rearrange the formula to solve for the radius: r = √(A/π).

Substituting the given area and the approximate value for π (3.14), we get r = √(132.2/3.14). This simplifies to r = √(42.085...), which is approximately r = 6.487 ft. Rounding to the nearest tenth gives us a radius of 6.5 ft.

Answer:

0.2

Step-by-step explanation:

Absolute values are positive version of any number. So the absolute value of both 0.2 and -0.2 would be 0.2

Answer:

 2[tex]\frac{1}{2}[/tex] cups

Step-by-step explanation:

Given, a recipe uses 8[tex]\frac{3}{4}[/tex] cups of milk for every 3[tex]\frac{1}{2}[/tex] cups of oatmeal.

So, For each 8.75 cups of milk ,3.5 cups of oatmeal is required.

Or,

we can say 3.5 cups of oatmeal require 8.75 cups of milk.

Thus,

1 Cup of oatmeal will require  [tex]\frac{8.75}{3.5}[/tex] cups of milk.

                                              =   2.5 cups of milk .

Thus answer is 2.5 cups, Which we can write 2 + 0.5 cups

                                                                      =  2[tex]\frac{1}{2}[/tex] cups (In mixed form)

Final answer:

The correct statement must be that the slope of the equation is the cost per round of $33.47, and the y-intercept is the initial membership fee of $17.72, since the slope represents the additional cost per round and the y-intercept the initial cost at zero rounds.

Explanation:

In the function T = 33.47r + 17.72, which represents the total cost T of playing miniature golf as a function of the number of rounds played r, the coefficient of r represents the slope and the constant term is the y-intercept. The slope indicates the additional cost for each additional round of golf played, while the y-intercept represents the initial cost when no rounds are played, which can be interpreted as the membership fee. Therefore, the correct statement about the cost structure of the Cape Gerbil City Miniature Golf Club is A: The slope is the cost per round $33.47, and the y-intercept is the membership fee of $17.72.

Answer:

Speed = 39.3 miles/hr

Time = 6.5 hrs.

Distance = Speed x time

= 39.3 x 6.5

= 245.45 miles (approx.)

Hope this helps!

Answer:

Speed = 39.3 miles/hr

Time = 6.5 hrs.

Distance = Speed x time

= 39.3 x 6.5

= 255.45 miles (approx.)

Step-by-step Explanation:

Answer:

D. pyramid (not including the vertex)

E. prism

Step-by-step explanation:

D and E are the answers to this question.

D. pyramid (not including the vertex)

E. prism

Answer:

2x-5

Step-by-step explanation:

(4x-7)-(2x-2)=4x-2x-7-(-2)=2x-7+2=2x-5

Answer:

2x-5

Step-by-step explanation: