A parallelogram is cut out of a 12-inch by 8-inch sheet of paper. There are four right triangle remnants. Two have the dimensions 2 inches by 9 inches, and the other two have the dimensions 3 inches by 6 inches.

A parallelogram is shown. An altitude is drawn from one point to the opposite side to form a right angle. The length of the base is 9.22 inches.

The resulting parallelogram has a base of approximately 9.22 inches.

Complete the following steps to calculate the altitude of the parallelogram using area methods.

The area of the sheet of paper is
square inches.

The combined area of the triangle cutouts is
square inches.

The area of the parallelogram is
square inches.

The altitude of the parallelogram rounded to two decimals is
square inches.

Answers

Answer 1

The area of a shape is the amount of space it occupies.

The area of the paper is 96 square inchesThe combined area of the triangle cutouts is 36 square inchesThe area of the parallelogram is 60 square inchesThe altitude of the parallelogram is 6.51 inches

The area of the paper

The dimension of the paper is given as: 12-inch by 8-inch

So, its area is:

[tex]Area = 12 * 8[/tex]

[tex]Area = 96[/tex]

Hence, the area of the paper is 96 square inches

The area of the triangles

The dimensions of the 4 right triangles are: Two 2 inches by 9 inches, and two 3 inches by 6 inches

So, the combined area is:

[tex]Area = 0.5(2 * 2 * 9 + 2 * 3 * 6)[/tex]

[tex]Area = 36[/tex]

Hence, the combined area of the triangle cutouts is 36 square inches

The area of the parallelogram

The area of the parallelogram is the difference between the areas of the paper and the four right triangles.

So, we have:

[tex]Area = 96 - 36[/tex]

[tex]Area = 60[/tex]

Hence, the area of the parallelogram is 60 square inches

The altitude of the parallelogram

The base is given as 9.22

So, we have:

[tex]Area = Base * Altitude[/tex]

This gives

[tex]60 = 9.22* Altitude[/tex]

Divide both sides by 9.22

[tex]Altitude = 6.51[/tex]

Hence, the altitude of the parallelogram is 6.51 inches

Read more about parallelograms at:

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Answer 2

Answer:    The area of the paper is 96 square inches

   The combined area of the triangle cutouts is 36 square inches

   The area of the parallelogram is 60 square inches

   The altitude of the parallelogram is 6.51 inches

Step-by-step explanation:


Related Questions

₹7,000 is borrowed at 3.5% rate of interest p.a. borrowed for 2 years. Find the
amount to be paid at the end of the second year

Answers

The answer would be 7498.575

Hope this helps (:

Find the slope of the graph

Answers

Answer:

(1,3), (2,1

Step-by-step explanation:

Answer:

1. m = -3

2. m = 4

Step-by-step explanation:

1. m = -3

2. m = 4

slope intecept form is y = mx + b

The ratio of boys to girls is 4:5 calculate the number of boys if there are 1080 learners

Answers

Answer:

480 Boy

Step-by-step explanation:

The ratio of Boys =  4x

The ratio of  Girls =  5x

The Number of Boys in the School = 4x + 5x = 1080

=         9x = 1080

=        x  = 1080/9

=         x  = 120

The ratio of Boys = 4x  = 4 x 120 = 480

The ratio of  Girls =  5x = 5 x 120 = 600

Hence, Number of Boys = 480

Ratio Boys to Girls = 480:600

[RevyBreeze]

help me please !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

B) [tex]-38[/tex]

Step-by-step explanation:

[tex]\frac{4}{(-1.6+3.6)}+\frac{0.8(9+11)}{-0.4}\\\\=\frac{4}{2}+\frac{0.8(20)}{-0.4}\\\\=2+-2(20)\\\\=2-40\\\\=-38[/tex]

One equation in a system of equations is given in the graph. Which equation below would have to be the second equation so that the system has no solutions?

Answers

Solution:

To classify the system of equations as no solutions, the lines must be parallel (Not intersect).

First, let's identify the equation forming the line.

Slope = Rise/Run = 2/-3 = -0.66Y-intercept = 0Equation formed: y = -2/3

We also know that the slope of the equation must be -1.5.

A) 2x + 3y = 0

3y = 0 - 2x=> 3y = -2x=> (y = -2x/3) ∦ (y = -2x/3)

B) 2x + 3y = 6

=> 3y = -2x + 6=> (y = -2x/3 + 2) ║ (y = -2x/3)

C) 2x - 3y = 9

=> -3y = -2x + 9=> y = -2x/-3 + 9/-3=> (y = 2x/3 - 3) ∦ (y = -2x/3)

D) y = 3x + 2

(y = 3x + 2) ∦ (y = -2x/3)

Option B is correct.

help on 5 . find the value of x

Answers

Answer:

The choice B. 5°

Step-by-step explanation:

The angle in the figure is 90°

[tex]36 + (11x - 1) = 90 \\ 36 + 11x - 1 = 90 \\ 11x + 35 = 90 \\ 11x = 90 - 35 \\ 11x = 55 \\ \\ x = \frac{55}{11} \\ \\ x = 5[/tex]

To find the value of x, we can set an equation like: 36 + 11x - 1 = 90
Combining like terms gets us to 35 + 11x = 90
Subtract 35 from both sides and divide by 11 to get
x = 5

The larger of two numbers is 10 less than twice the smaller number. If the sum of the two numbers
is 38, find the two numbers.



Answers

Answer:

16,22

larger number=22

smaller number=16

Step-by-step explanation:

let 2x-10=larger number

let x=smaller number

x+2x-10=38

Simplify

3x-10=38

   +10  +10

Add 10 to both sides of the equation

3x=48

divide both sides by 3

x=16

First answer.

2x-10=22

2nd answer

Check your work:

16+22=38

It is correct.

Answer:

66 & -28

Step-by-step explanation:

x > y

x + y = 38

x = 10 - 2y

10 - 2y + y = 38

-y + 10 = 38

-y = 28

y = -28

x + (-28) = 38

x = 66

Evaluate. Write your answer in simplified, rationalized form. Do not round.

cos

45°

=

Answers

Answer:

  cos(45°) = (√2)/2

Step-by-step explanation:

The cosine of 45° is the x-coordinate of the point on the unit circle where the line y=x intersects it. That is, it is the positive solution to the equation ...

  x^2 +x^2 = 1

  x^2 = 1/2 = 2/4 . . . . . collect terms, divide by 2, express the fraction with a square denominator

  x = √(2/4) . . . . . . take the square root

  x = (√2)/2 . . . . . simplify

The cosine of 45° is (√2)/2.

Based on data from 2011-2012, the percentage of 6- to 11-year-olds who were obese was about _____ than the percentage of two- to five-year-olds who were obese.

Answers

Using the percentage concept, it is found that the percentage of 6- to 11-year-olds who were obese was about 17.76% more than the percentage of two- to five-year-olds who were obese.

What is a percentage?

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

[tex]P = \frac{a}{b} \times 100\%[/tex]

Researching on the internet, we find that:

The percentage of two-to-five year old who are obese is of a = 15.2%.The percentage of 6-to-11 year old who are obese is of b = 17.9%.

Hence:

[tex]P = \frac{17.9}{15.2} \times 100\% = 117.76\%[/tex]

117.76% - 100% = 17.76%.

Hence the percentage of 6- to 11-year-olds who were obese was about 17.76% more than the percentage of two- to five-year-olds who were obese.

More can be learned about percentages at https://brainly.com/question/24372153

A ship has an island directly in the path of the destination port, so it has to travel 11.5 miles west and then 8.4 miles north to get to the port. To the nearest tenth,how much shorter would the trip be if the ship could go directly to port?

Answers

Answer:

Step-by-step explanation:

The direct distance there (without the island in the way) is found using the Pythagorean Theorem

c^2 = a^2 + b^2

a = 8.4

b = 11.5

c = ?

c^2 = 8.4^2 + 11.5^2              Square the length of the legs.

c^2 = 70.56 + 132.25            Combine  

c^2 = 202.81                          Take the square root.

c = 14.24

But the island is there. The distance travelled = 8.4 + 11.5 = 19.9 miles

So the additional distance = 19.9 - 14.24 = 5.66 miles.

Find the slope of the graph

Answers

Answer:

Step-by-step explanation:

m=26 when u as u go as down as {{6-2} -13

Answer:

2

Step-by-step explanation:

By definition, the slope or gradient of a line describes its steepness, incline, or grade.

m = y2 - y1 / x2 - x1

Where

m — slope

If the 2 Points are Known:

Slope (m) = ΔY/ΔX

= 7-(-1) / 3-(-1)

= 8/4

= 2/1

= 2

θ = arctan (ΔY/ΔX)

= tan¯¹(8/4)

= 63.434948822922°

ΔX = 3 – (-1) = 4

ΔY = 7 – (-1) = 8

Distance (d) = √ΔX2 + ΔY2 = √80

= 8.9442719099992

Equation of the line:

y = 2x + 1

When x=0, y = 1

When y=0, x = -0.5

Mr. Connolly recorded the closing price of a stock each day for a month. Which measure of data did he use to determine that the
closing stock price varied by $20.50 during the month?
A. Mean
C. Mode
B. Median
D. Range

Answers

range, if he calculate all of it and checked the price from beginning to end this would be because he found the range

What is the difference between the LCM and HCF of 8,10,12

Answers

Answer:

118

Step-by-step explanation:

LCM = 12×10 = 120

HCF = 12-10 = 2

Difference = 120-2 = 118

Please mark me as brainliest because i want to be Virtuoso rank

emily bought 4 pounds of grapes for $20 .find the unit price A)$5
c)1
d)20
b)15

Answers

Answer:

$5

Step-by-step explanation:

20/4 = 5

Determine whether a triangle with the given side lengths is a right triangle.

Answers

Step-by-step explanation:

It is possible to determine if a triangle contains a right angle using Pythagoras' theorem . If the squares of the two shorter sides add up to the square of the hypotenuse, the triangle contains a right angle.

Help me please please please please please please

Answers

I think 100 grams per box

Which equation describes the line with a
slope of 2 that contains the point (4, -3)?

Answers

Answer:

y = 2x - 11

                                               Explanation:

using the formula:

[tex]\boxed{y-y1= m(x-x1)}[/tex] .........where m is slope || y1 is y value || x1 is x value

y - -3 = 2( x - 4 )

y + 3 = 2(x -4)

y + 3 = 2x - 8

y = 2x - 8 - 3

y = 2x - 11

HELP ME I DON'T GET IT!!!!!
Kamille is calculating the length of diagonal on a picture board and gets a solution of the square root of 58. She needs to buy the ribbon to put across the diagonal of the board, so she estimates that she will need at least 60 inches of ribbon to cover the diagonal. Is she correct? Explain.

Answers

Answer:

Kamille is wrong

Step-by-step explanation:

Kamille is wrong, because:

√58 is between √49 and √64

or

7 < √58 < 8

She needs about 8 inches ribbon not 60 inches

Simplify 3 - 4y + (-8y) +8.7.
Pls answer

Answers

Answer:

11.7 - 12y

Step-by-step explanation:

1. Open parenthesis

3 - 4y - 8y + 8.7

2. Combine like terms

11.7 - 12y

The answer is 11.7 - 12y

Hope this helps :)

Have an awesome day!


Remove parentheses.
3

4
y

8
y
+
8.7
3
-
4
y
-
8
y
+
8.7
Add
3
3
and
8.7
8.7
.

4
y

8
y
+
11.7
-
4
y
-
8
y
+
11.7
Subtract
8
y
8
y
from

4
y
-
4
y
.

12
y
+
11.7

What is the product of the complex numbers (-3i+4) and (3i+4)?

Answers

Answer: 25

Step-by-step explanation:

Finding the product of complex numbers is not different to finding the product of real numbers

(-3i+4) * (3i+4) = -9i^2 + 12i - 12i + 16 = 25

Answer:

25

Step-by-step explanation:

An easy way to multiply binomials is the FOIL(first, outer, inner, last) method. Multiply the first terms of each binomial, -3i×3i=-9i^2. Then do the outer terms, -3i×4=-12i. Then do the inner terms 4×3i=12i. Then do the last terms, 4×4=16. Lastly combine like terms, the -12i and 12 cancel out, and you're left with -9i^2+16. i^2=1, so then you get -9(-1)+16. -9×-1=9. 9+16=25

1: 18 is __ % of 30
2: 56 is 80% of
3: a pack of cinnamon scented penclis sells for 4:00$ what is the sales tax rates if the total cost of the pencils is 4:32?

Answers

Answer:

1.  60%

2. 70

3. 8%

Step-by-step explanation:

I attached pictures to show my work (sorry if they’re a bit messy)!

Can u help me and give me the solution. I have rsm tomorrow! please and thanks. find x

Answers

Answer: 25°

Step-by-step explanation: Notice that in this figure, we are given two triangles and to find the value of x, we first need to find the missing angle measure in the big triangle.

Since all the interior angles of a triangle add up to 180 degrees, we know that the missing angle of the big triangle is 180° - 94° - 41° or 45°.

Now we know all the angles of the big triangle and we know two of the angles of the smaller triangle, so we can find the value of x.

The missing angle of the smaller triangle will be 180° - 110 - 45° or 25°

So we know that the missing angle is 25°.

please answer correctly

Answers

Answer:

y=2x-1

Step-by-step explanation:

up 2 right 1 for slope

y intercept is -1

Answer:

[tex] \boxed{(b) \: y = 2x - 1}[/tex]

Step-by-step explanation:

Find the gradient

( 2,3 ) and ( 0, -1)

[tex]m = \frac{y2 - y1}{x2 - x1} = \frac{ - 1 - 3}{0 - 2} = \frac{ - 4}{ - 2} = 2[/tex]

Gradient is 2

Find linear equation

y - y1 = m ( x - x1 )

y - 3 = 2 ( x - 2 )

y - 3 = 2x - 4

y = 2x - 4 + 3

[tex] \boxed{y = 2x - 1}[/tex]

2 divided by 4,050. I know the answer from an answer key but I am wondering the step to step using long division.

Answers

Math answers to fraction 4050 divided by 2 can be calculated as follows.

4050/2 math problems division = 2025. Therefore 2025 to 2 decimal places= 2025
(I don’t know if this gonna help, but I hope it help)gdd luck

4050/2 divided by 2 » (4050/2) ÷ 2 » 2025 ÷ 2 = 1012.5 . Check 4050/2 long division below

Find the value of x.
87, x,105,92,135

Answers

Answer:

121

Step-by-step explanation:

(5-2)180

180-135-105-87-92=121

The product of numbers in the circles connected by the different lines must be equal. Use number from 1 to 9 only once.​

Answers

Answer:

you must be so stiupid that you have to use answers ff a website to cheat for school

Step-by-step explanation:

Find the area of each shaded region

Answers

[tex]\bold{\huge{\blue{\underline{ Solution }}}}[/tex]

Given :-

The radius of the circle is 5 units

To Find :-

We have to find the area of shaded region .

Let's Begin :-

The given figure is composed of two figures triangle and circle. In which triangle is enclosed in the circle.

The triangle is the unshaded region of the given figure

We know that,

Area of triangle

[tex]\bold{\red{ = }}{\bold{\red{\dfrac{1}{2}}}}{\bold{\red{\times{ Base }}}}{\bold{\red{\times{ height }}}}[/tex]

Here,

The base of the triangle is equal to the diameter of the circle that is, [tex]\sf{ Base = 5 + 5 = 10 \: units }[/tex]The height of the triangle is equal to the radius of the triangle that is[tex]\sf{ Height = 5 \:units }[/tex]

Subsitute the required values,

Area of the given triangle

[tex]\sf{ = }{\sf{\dfrac{1}{2}}}{\sf{\times{ 10 }}}{\sf{\times{ 5 }}}[/tex]

[tex]\sf{ = 5 }{\sf{\times{ 5}}}[/tex]

[tex]\bold{ = 25\: units }[/tex]

Thus, The area of triangle is 25 units

Now

We have to find the area of the circle

The radius of the circle is 5 units

We know that,

Area of circle

[tex]\bold{\pink{ = }}{\bold{\pink{\pi{r^{2}}}}}[/tex]

Subsitute the required values,

[tex]\sf{ = }{\sf{\pi{(5)^{2}}}}[/tex]

[tex]\sf{ = }{\sf{\dfrac{22}{7}}}{\sf{\times{ 25}}}[/tex]

[tex]\sf{ = }{\sf{\dfrac{550}{7}}}[/tex]

[tex]\bold{ = 78.57\: units }[/tex]

Thus, The area of circle is 78.57 units

Therefore,

Area of shaded region

= Area of circle - Area of triangle

Subsitute the required values,

[tex]\sf{ = 78.57 - 25 }[/tex]

[tex]\bold{\green { = 53.57 \: units }}[/tex]

Hence, The area of shaded region is 53.57 units.

The area of the shaded figure is 13.375 square units.

What is the area of the shaded region?

The shaded region is a circle with a triangle inside of it removed.

To get the area, we need to get the area of the circle and remove the area of the triangle.

Remember that for a circle of radius R, the area:

A = 3.14*R^2

In this case, we can see that the diameter of the circle measures 5 units, then the radius (half of the diameter) measures 2.5 units.

A = 3.14*(2.5)^2 = 19.625 square units.

And a triangle of base B and height H has an area:

A' = B*H/2

In this case, the base of the triangle is equal to the diameter of the circle, and the height is equal to the radius of the circle, so we have:

B = 5 units.

H = 2.5 units.

Then:

A' =5*2.5/2 = 6.25 square units.

Then the shaded area is:

shaded area =  19.625 square units -  6.25 square units.

                     = 13.375 square units.

If you want to learn more about areas, you can read:

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10 examples of direct and Inverse variation from our daily life​

Answers

Answer:

Direct Variation:

The number of family members are directly expenditures.  The number of fruit in kg directly proportional to price of fruit.The number of selling products directly proportional to profit. The distance covered by body directly proportional to speed of bodyThe acceleration produce in car directly proportional to change in velocity The income is directly proportional to working hours. The cost of electrical bill directly proportional to number of fans running in    the house. The quantity of water fill in tank is directly to time for which the motor is switch on. The marks in study is directly proportional to hardworking. The bank balance is directly proportional to amount of saving.

Inverse Variation:

1. The bank balance is inversely proportional to expenditures.

2. The number of family members (which not work) are inversely proportional to amount of saving.

3.The working days required to complete the work are inversely proportional to number of labors.

4. The velocity of body is inversely proportional to time.

5. The acceleration is inversely proportional to time.

6.  The acceleration of body is inversely proportional to mass of body.

7. The number of student fail in the class is inversely proportional to number of qualify teachers and hardworking.

8. The battery power is inversely proportional to time for which it used.

9. The ability of do work hard is inversely proportional to age of man after youngness to onward.

10.  The number of mistake in work is inversely proportional to practice.

Explanation:

Direct Variation: A relationship where one quantity is a constant multiplied by another quantity is called direct variation.

Inverse Variation: Inverse variation is defiend as the relationship between two variables in which the resultant product is a constant. If a is inversely proportional to b, the form of equation is a = k/b, where k is constant. Inverse variation is known as the opposite of direct variation. If there an increas ein one variable, the other variable decreases in proportion so that the resultant product remains unchanged.

The house number is a three digit number.it is a multiple of 5. There are no zeros in this number. The number in the hundreds place is two less than the number in the ones place. The sum of the digits is 10

Answers

Answer:

235

Step-by-step explanation:

325( Three digit number)

No zero

5-3=2

3+2+5=10

The house number if the house number is a three-digit number, it is a multiple of 5. There are no zeros in this number, is 235.

What is equation?

A formula known as an equation uses the equals sign to denote the equality of two expressions.

Given:

A house number is a three-digit number.it is a multiple of 5,

The number in the hundreds place is two less than the number in the one's place,

The sum of the digits is 10,

Write the equation as shown below,

x + y + z = 10

Here x is in one place y is in the tens place and z is in the hundred places,

The number will be = 100z + 10y + x

y = x - 2

As we know if the number is a multiple of 5 then its one's place is either 0 or 5 here no zeroes in the number,

x = 5,

y = 5 - 2 = 3

z = 10 - 3 - 5

z = 2

Thus, the number will be,

Room number = 100 × 2 + 10 × 3 + 5

Room number = 200 + 30 + 5

Room number = 235

To know more about equation:

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PLEASE HELP!! Question: Which number line shows the points −125 and –2.8?

Answers

Answer:

you need picture with it

Step-by-step explanation:

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