Given the rectangle below with length 8 and width 6
a) construct the midpoints of all four sides of the rectangle.
b) connect the midpoints to form another quadrilateral. What type of quadrilateral is formed? Justify your answer.
c) find the area of the quadrilateral you formed.
( There is a picture of a rectangle below. I'm willing to give all my points away.)

Answer: Sin45 = x/4

x = 4Sin45

x = 2.83miles

Step-by-step explanation:

Final answer:

The horizontal distance of the ship from the bottom of the lighthouse is equal to the direct distance from the lighthouse to the ship, which is 4.00 miles, because the angle of depression is 45 degrees forming an isosceles right-angled triangle.

Explanation:

The student is asking how to calculate the horizontal distance of a ship from the bottom of a lighthouse when the angle of depression from the top of the lighthouse to the ship is 45° and the direct distance from the lighthouse to the ship is 4 miles. This is a trigonometry problem involving right-angle triangles.

Since the angle of depression is 45°, we can establish that the lighthouse height and the horizontal distance will be equal due to the properties of an isosceles right-angled triangle. Thus, the horizontal distance from the bottom of the lighthouse to the ship is the same as the distance from the top of the lighthouse directly to the ship, which is given as 4 miles. Therefore, the horizontal distance is 4.00 miles.

Step-by-step explanation:

4. 4+11=15

to find the length of The first piece

4/15*75=20

to find the length of the second one

11/15*75=55

5. 4+1=5

to find the length of the first one

4/5*180=144

to find the length of the second one

1/5*180=36

7. 5+7+8=20

to find the length of the first one

5/20*40=10

to find the length of the second one

7/20*40=14

to find the length of the third one

8/20*40=16

4. The lengths of the two pieces are 20 inches and 55 inches.

5. The measures of the two angles are 144 degrees and 36 degrees.

6. The measures of the angles are 36 degrees, 60 degrees, and 84 degrees.

7. The lengths of the sides are 10 inches, 14 inches, and 16 inches.

4: A string that is 75 inches long will be cut into two pieces in the ratio of 4:11. Find the lengths of the two pieces of string.

The total length of the string is 75 inches.

The ratio given is 4:11.

First, find the total parts in the ratio by adding the two numbers: [tex]4 + 11 = 15[/tex].

Now, to find the length of each piece:

5: The ratio of two supplementary angles is 4:1. Find the measures of the two angles.

Supplementary angles add up to 180 degrees.

The given ratio is 4:1.

Find the total parts in the ratio: [tex]4 + 1 = 5[/tex].

Now, calculate the measures of the angles:

6: The ratio of the measures of the angles in a triangle is 3:5:7. Find the measure of each angle.

The sum of the angles in a triangle is 180 degrees.

The given ratio is 3:5:7.

Total parts in the ratio: [tex]3 + 5 + 7 = 15[/tex].

Now, calculate each angle's measure:

7: The ratio of the measure of the sides of a triangle is 5:7:8 and its perimeter is 40 inches. Find the measure of each side.

The perimeter of the triangle is 40 inches.

The given ratio is 5:7:8.

Total parts in the ratio: [tex]5 + 7 + 8 = 20[/tex].

Now, calculate the length of each side:

Answer:

m∠C = 115°

Step-by-step explanation:

DE≈DF

ΔDEF is an isosceles triangle ∴ m∠DEF = m∠DFE = 1/2 (180-50) = 65

∴ m∠DFB = 180 -65 = 115

∵ DCBF is a parallelogram m∠DFB = m∠DCB = 115°

Answer:

see explaination

Step-by-step explanation:

the diagram shows two equal parts being the divided by two in the equations. The parts are worth 8 meaning if you divide 16 by 8 it is 2 because there are two parts.

Answer:

8x2 = 16

Step-by-step explanation:

8x2 = 16

16/2 = 8

Answer:

2 packs

Step-by-step explanation:

Since there is 10 packs just divided it by how many notebooks were in the pack.

Answer:

y=3/2 x + 5

Step-by-step explanation:

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

Firstly, find m (gradient).

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

m= 8-(-1)/ 2-(-4)

m= 9/ 6

m= 3/2

Please leave gradient in improper fraction if its value is not a whole number.

Now substitute m into the equation:

y= 3/2 x + c

Then substitute a coordinate to find c:

When y= 8, x= 2,

8= 3/2 (2) + c

8= 3 + c

c= 8 - 3 = 5

Thus, the equation of the line is y= 3/2 x + 5.

3c - 7

3 times c = 3c

7 less than is subtraction

Answer:

3c - 7

Step-by-step explanation:

less than = flip the equation

Answer:

A = 2πr2 + 2πrh is the final answer

Step-by-step explanation:

Answer:

h = (x-2πr²)/2πr

Step-by-step explanation:

Given the surfaces area of a cylinder by the formula

SA = 2πr²+2πrh

To solve for h means making h the subject of the formula from the equation.

Let x be the surface area of the cylinder. The formula can be rewritten as;

x = 2πr²+2πrh

Subtracting 2πr² from both sides of the equation will give;

x-2πr² = 2πr²+2πrh-2πr²

x-2πr²= 2πrh

Dividing both sides by 2πr wikk results into;

(x-2πr²)/2πr = 2πrh/2πr

h = (x-2πr²)/2πr where x is the surface area of the cylinder.

Answer:

[tex]\$833.97[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=10\ years\\ P=\$650\\ r=2.5\%=2.5/100=0.025\\n=4[/tex]  

substitute in the formula above

[tex]A=650(1+\frac{0.025}{4})^{4*10}[/tex]  

[tex]A=650(1.00625)^{40}[/tex]  

[tex]A=\$833.97[/tex]  

Answer:in Spanish: su calificación debe ser 60 para aprobar esta clase

Step-by-step explanation:

Answer:

That mean you must have 60 and above to pass and anything below that is failure

Step-by-step explanation:

Answer:

[tex]x=5[/tex]

Step-by-step explanation:

we know that

In a parallelogram opposite sides are parallel and congruent

In this problem

AB and CD are opposite sides

so

AB=CD

substitute the given values

[tex]6x-10=3x+5[/tex]

solve for x

[tex]6x-3x=10+5[/tex]

[tex]3x=15[/tex]

[tex]x=5[/tex]

Answer:

c

Step-by-step explanation: first part of the equations.

[tex]-8x+3\geq 27\\-8x\geq 24\\x\leq -3[/tex]

so first you will subtract 3 from both side of the inequality. The divide by -8 on both side which will flip the inequality sign.

second equation

[tex]-13x+5\geq 57\\-13x\geq 52\\x\leq -4[/tex]

So you subtract 5 from both side then divide by -13 on both side and you need to flip the inequality sign because you divide by a negative.

now you will write the expression for it.

[tex]-4\leq x\leq -3[/tex]

we put x in the middle because it an and statement so that is why you would put x in the middle.

Answer:

I am not agree with him. Because -2 is the leading coefficient of this  polynomial.

Step-by-step explanation:

Pat multiplied the polynomials for a math assignment.

Then he found the product is [tex]-4x+8x^2-2x^3+5[/tex]

Now Pat wants to find the leading coefficient to this polynomial.

Pat's answer was -4.

But I am not agree with him.

Because for a given polynomial we can calculate the leading coefficient when comparing with degrees of the polynomial.

Leading coefficient means that the coefficient whose degree is the highest.

When compared with the given polynomial we have [tex]x^3[/tex] is the highest degree, so that -2 is the leading coefficient to this polynomial.

Answer:

there is not a triangle

Step-by-step explanation:

but if is has all 3 sides the same it is sss, if there is two sides and an angle in between them it is sas, and if there is a hypotenuse and then a leg then it is hl, or if it is none it is d

The method that can be used to prove the triangles below are congruent is the SAS (Side-Angle-Side) criterion. To prove that two triangles are congruent using the SAS criterion, you need to show that two pairs of corresponding sides are congruent and the included angles between them are congruent. In the given options, B. SAS is the correct answer.

The method that can be used to prove the triangles below are congruent is the SAS (Side-Angle-Side) criterion.

To prove that two triangles are congruent using the SAS criterion, you need to show that two pairs of corresponding sides are congruent and the included angles between them are congruent.

In the given options, B. SAS is the correct answer.

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Answer:

x = 8

Step-by-step explanation:

If NO is parallel to KJ then the sides LK and LJ are in proportion, that is

[tex]\frac{KN}{NL}[/tex] = [tex]\frac{JO}{OL}[/tex], substitute values

[tex]\frac{x+2}{x-3}[/tex] = [tex]\frac{x}{x-4}[/tex] (cross- multiply )

x(x - 3) = (x + 2)(x - 4) ← expand factors on both sides

x² - 3x = x² - 2x - 8 ( subtract x² - 2x from both sides )

- x = - 8 ( multiply both sides by - 1 )

x = 8

Answer:

8

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

1+8=9

Answer:

9

Step-by-step explanation:

1+8=9

Answer:

They have 18 vegetable plants.

Step-by-step explanation:

Given:

Emily's family loves to work together  in the garden.

They have a. preference for flowers as 80% of  their plants are flowers and the rest  are vegetables.

They have 90 plants  in the garden.

Now, to find the number of vegetable plants.

Total plants in the garden = 90.

80% of the plants are flowers.

So, number of plants which are flowers = 80% of 90.

[tex]=\frac{80}{100} \times 90[/tex]

[tex]=\frac{7200}{100}[/tex]

[tex]=72\ plants.[/tex]

The number of flower plants = 72.

Total plants = 90 (given)

So, to get the number of vegetable plants we subtract:

[tex]90-72=18\ plants.[/tex]

Thus, vegetable plants = 18.

Therefore, they have 18 vegetable plants.

Step-by-step explanation:

There are certain methods for solving a system of equations. Some of which are:

Substitution Method

Substitution method to solve a system of equations is suitable if a variable of a any equation seems isolated or could comfortably be isolated without any ration/fraction resulting.

For example, for the following system of equations

x - 2y = 11....[A]

x = 5 - y....[B]

substituting the value of x = 5 - y from equation [B] into equation [A], so that

(5 - y) - 2y = 11

5 - y - 2y = 11

3y = -6

y = -2

Elimination Method

Elimination method to solve a system of equations is suitable if both equation are in standard form, and just adding or subtracting the equations to determine an equation in one variable.

For example, for the following system of equations

2x + 7y = -5....[C]

5x - 7y = 12....[D]

Adding Equation [C] and Equation [D].

7x + 0 = 7

x = 1

Graphing Method

Sometimes graphing method may be used to solve the system of the equation and visualize the solution.

For example,

y = -2....[E]

y = 3x + 1....[F]

The solution for this system of equation is the point of intersection of both the lines, which is shown in attached figure. The point of intersection is (-1, -2).

Hence, the solution of this system of equations is (-1, -2), as shown in attached figure.

Keywords: system of equations, elimination method, substitution method, graphing method

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x=y+3 and 30x+80y=640 is the system of equations for given statement where x represents the number of commercials and y represent the number of movies on which Anna's songs were played.

Step-by-step explanation:

Given,

Earning for song played in commercial one time= $30

Earning for song played in movie one time = $80

Let,

x represent the number of  commercials Anna's song played.

y represent the number of movies Anna's song played.

According to given statement;

Anna's songs were played on 3 more commercials than movies

x=y+3    

her total earnings on the royalties from all commercials and movies was $640.

30x+80y=640

x=y+3 and 30x+80y=640 is the system of equations for given statement where x represents the number of commercials and y represent the number of movies on which Anna's songs were played.

Keywords: linear equation, substitution method

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Final answer:

To solve the question, two variables are defined: c for commercials and m for movies. The system of equations is $30c + $80m = $640 and c = m + 3, representing Anna's royalties from commercials and movies.

Explanation:

The student's question involves creating a system of equations to determine the number of commercials and movies on which Anna, a songwriter who collects royalties, had her songs played. We are given that Anna earns $30 from each commercial and $80 from each movie her songs are played in. It is also known that her songs were played in 3 more commercials than movies, and she earned a total of $640. To formulate the system of equations, we introduce two variables: let c represent the number of commercials and m represent the number of movies.

The first equation represents the total earnings based on the number of plays:
$30c + $80m = $640.

The second equation represents the relationship between the number of commercials and movies:
c = m + 3.

Combining these two equations gives us a system that can be solved to find the values of c and m.

By substituting the second equation into the first equation, we can create a system of equations:

30(M + 3) + 80M = 640

30M + 90 + 80M = 640

110M + 90 = 640

110M = 550

M = 5

Now that we have found the number of movies (M = 5), we can substitute this value back into the equation C = M + 3 to find the number of commercials:

C = 5 + 3

C = 8

Answer:

Around 39.2

Step-by-step explanation:

To do this question, you use the pythag theorem, a^2 + b^2 = c^2. You have the hypotenuse of the triangle, 40 feet in length, and you have a because it's 8 feet from the wall. You now have b^2 = 1600-64. b^2 = 1536. Take the square root, and you have the height of the latter on the wall is equal to 39.1918 or 39.2 rounded

Answer:

the building is 90 feet tall

Step-by-step explanation:

each floor is 9 feet, there are 10 floors,

9 x 10 = 90 feet

Answer:

1 1/18 kilograms

Step-by-step explanation:

First add 3/8 + 11/8, which equals to 11/8. Then add 5/8, which equals to 19/8. Change the improper fraction to a mixed number, and the sum is 1 1/18.

ans is 19/8 kilogram.......

Answer:

Monthly sales = $15000

Step-by-step explanation:

Let x be the monthly sale.

Given:

The monthly salary of a show room attendant is the sum of a fixed  salary of $600 plus 8% of all monthly sales.

8% of monthly sale = [tex]\frac{8}{100}\times mothly\ sale[/tex]

8% of monthly sale = [tex]\frac{8}{100}\times x[/tex]

So, the monthly salary of attendant is.

[tex]Monthly\ salary = 600+8\ percent \ of\ monthly\ sales[/tex]

[tex]Monthly\ salary = 600+\frac{8}{100}\times x[/tex]

Monthly salary is given.

[tex]1800 = 600+\frac{8}{100}\times x[/tex]

[tex]1800 - 600 = \frac{8}{100}\times x[/tex]

[tex]1200 = \frac{8}{100}\times x[/tex]

[tex]x=\frac{1200\times 100}{8}[/tex]

[tex]x=\frac{120000}{8}[/tex]

[tex]x=15000[/tex]

Therefore, the monthly sale is $15000

Answer:

C

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - [tex]\frac{5}{3}[/tex] x + 5 ← is in slope- intercept form

with slope m = - [tex]\frac{5}{3}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular }[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{5}{3} }[/tex] = [tex]\frac{3}{5}[/tex]

Answer:

5/3

Step-by-step explanation:

Answer:

Lucey reads 10 pages fewer than Carey.

Answer:

Median

Step-by-step explanation:

Median, in geometry, is a line segment that is drawn from the vertex or the corner of the shape that extends to the middle or the midpoint of the side opposite of that corner.

When you say opposite the corner, that means it is the one across it. Look at the attached picture for emphasis.

Answer: fifty-two hundredths

Step-by-step explanation:

Answer:

Writing 6(3x + 8) + 32 + 12x in 3 different ways:

∵ 6(3x + 8) = 18x +48 as distribute law suggests that  a(b + c) = ab + ac

Step-by-step explanation:

As the expression is 6(3x + 8) + 32 + 12x, and we have to write it in three different ways. Using the properties of operations we can write it in three different ways,

Let way one be denoted as w₁

Let way two be denoted as w₂

Let way three be denoted as w₃

So, lets write 6(3x + 8) + 32 + 12x in 3 different ways:

∵ 6(3x + 8) = 18x +48 as distribute law suggests that  a(b + c) = ab + ac

Keywords: operation properties, distributive law

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Equations are generally in the form of:

y = mx + c

where m is the gradient and c is the y intercept

As you can see, in this equation, the y intercept is 5

Thus, your answer is C. 5

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Answer: 0.236 Liters.

Step-by-step explanation:

First you multiply 1.3 and 0.8 you get 1.064.

You subtract 1.3 and 1.064 and you get your answer 0.236 Liters.