Divide.

(5 1/4)÷(−2 1/2)

Enter your answer as a mixed number, in simplified form, in the box. Please Explain your answer.

Answer:

a) 35°

Step-by-step explanation:

Vertical angles are the opposite angles that form when two lines intersect.

The vertical angles are equal.

1. As vertical angles are equal first take the values of the two angles and put them in an equality as follows:

[tex]2x-20=x+15[/tex]

2. Then, solve for x:

[tex]2x-x=15+20[/tex]

[tex]x=35[/tex]°

Therefore the angle MHJ is 35°

Solving this problem actually requires us the use of the distance formula of point to a line.

The formula is:

distance = | a x + b y + c | / sqrt (a^2 + b^2)

So we are given the equation:

y = 2 x + 4

rewriting:

y – 2 x – 4 = 0     --> a = -2, b = 1, c = -4

We are also given the points:

(-4, 11) = (x, y)

Using the distance formula at points (x, y):

distance = | -2 * -4 + 1 * 11 + -4 | / sqrt [(- 2)^2 + (1)^2]

distance = 15 / sqrt (5)

distance = 6.7

So the tree is about 6.7 ft away from the zip line.

The question is an illustration of distance between a point and a line.

The distance between the zip line and the tree is 6.70 feet

The zip line equation is given as:

[tex]\mathbf{y = 2x +4}[/tex]

The coordinates of the tree is given as:

[tex]\mathbf{(x,y) = (-4,11)}[/tex]

The distance (d) between an equation and a point is:

[tex]\mathbf{d = \frac{|ax + by + c|}{\sqrt{a^2 + b^2}}}[/tex]

Where:

[tex]\mathbf{ax +by + c = 0}[/tex]

Rewrite [tex]\mathbf{y = 2x +4}[/tex] as [tex]\mathbf{ax +by + c = 0}[/tex]

[tex]\mathbf{2x - y + 4 = 0}[/tex]

By comparison:

[tex]\mathbf{a =2, b = -1, c = 4}[/tex] and [tex]\mathbf{(x,y) = (-4,11)}[/tex]

So, we have:

[tex]\mathbf{d = \frac{|2 \times -4 -1 \times 11 + 4|}{\sqrt{(2)^2 + (-1)^2}}}[/tex]

[tex]\mathbf{d = \frac{|-15|}{\sqrt{5}}}[/tex]

Evaluate square root

[tex]\mathbf{d = \frac{|-15|}{2.24}}[/tex]

Remove absolute bracket

[tex]\mathbf{d = \frac{15}{2.24}}[/tex]  

[tex]\mathbf{d = 6.70}[/tex]

Hence, the distance between the zip line and the tree is approximately 6.70 feet

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Answer:

6

Step-by-step explanation:

Answer:

7n - 2p

Step-by-step explanation:

octagon ABCDEFGH was dilated by a scale factor of 2. Therefore, option 2 is the correct answer.

To find the scale factor by which octagon ABCDEFGH was dilated, we can compare the corresponding side lengths of the original octagon and the dilated octagon.

Let's take one side, for example, side AB. The length of side AB in the original octagon is the distance between points A(3, 1) and B(3, -1), which is 2 units.

The length of side A'B' in the dilated octagon is the distance between points A'(6, 2) and B'(6, -2), which is also 4 units.

By comparing the side lengths, we can see that side A'B' is twice as long as side AB.

Therefore, the scale factor by which octagon ABCDEFGH was dilated is 2.

In conclusion, octagon ABCDEFGH was dilated by a scale factor of 2.

Therefore, option 2 is the correct answer.

The octagon ABCDEFGH was dilated by a scale factor of 2. This means each coordinate in the original octagon was multiplied by 2 to obtain the corresponding point in A'B'C'D'E'F'G'H'.

The scale factor of dilation between octagon ABCDEFGH and its dilated counterpart A'B'C'D'E'F'G'H' can be determined by comparing corresponding side lengths. Taking one side as an example, the original octagon has a side connecting points A(3, 1) and B(3, -1) with a length of 2 units (vertical distance). In the dilated octagon, the corresponding side connecting A'(6, 2) and B'(6, -2) has a length of 4 units (vertical distance). The scale factor (k) is then calculated as the ratio of the length in the dilated octagon to the length in the original octagon: [tex]\( k = \frac{4}{2} = 2 \)[/tex].

Therefore, octagon ABCDEFGH was dilated by a scale factor of 2 from its original position to A'B'C'D'E'F'G'H'. This indicates that the coordinates of each point in the original octagon were multiplied by 2 to obtain the corresponding points in the dilated octagon. The scale factor, in this case, is 2, signifying a doubling in size during the dilation process.

factor 3r^2-75

 you would move the 3 to the outside of the parenthesis

then you have 5*5 = 25 and multiply that by the 3 to get the 75

 3(r-5)(r+5)

Answer:

What he said.

Step-by-step explanation:

Answer:

3/2 (D on Edge)

Answer:

1572 Square Units

Step-by-step explanation:

First, find the perimeter by multiplying 20.8 * 7 which is 145.6. Then multiply the perimeter with the apothem. After that, you divide by 2.

So, 145.6*21.6/2= 1572.

An orthocenter is the intersection of three:

             Altitudes in a triangle.

Altitude--

An altitude is a line segment that originates from a vertex and is perpendicular to the line segment opposite to that vertex.

Orthocenter--

An orthocenter of a triangle is a point where the three altitudes of a triangle meet or intersect.

In  a right angled triangle the orthocenter is the vertex of the triangle where the right angle is formed.

The correct answer is not provided in the given options.

The volume of a cylinder can be calculated using the formula V = πr^2h, where π is a constant approximately equal to 3.14, r is the radius of the base, and h is the height of the cylinder.

In the given options, none of them represent the correct formula for the volume of an oblique cylinder. Therefore, the correct answer is not provided in the given options.

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Answer:

The Answer is A

Step-by-step explanation:

I took the test in usa test prep.

Answer:

Step-by-step explanation:

That weird symbol means "element".  In our case, the elements of the domain (the x-values) are -15, -6, -1.  Which tells us that we are going to sub each one of the numbers into the equation and solve it for the corresponding y value.  That in turn gives us the coordinate point.  The equation is

x + y = 6

Subbing in first -15 for x:

-15 + y = 6 and

y = 6 + 15 so

y = 21 and the coordinate point is (-15, 21).

Subbing in -6 for x:

-6 + y = 6 and

y = 6 + 6 so

y = 12 and the coordinate point is (-6, 12).

Subbing in -1 for x:

-1 + y = 6 and

y = 6 + 1 so

y = 7 and the coordinate point is (-1, 7)

The second choice is the one you want.

Just remember that x is the domain and any elements in the domain go in for x.

Also remember that y is the range and any elements in the range go in for y

Answer:

a). Linear equation; y=1.25 x+12.5

b). The variable are x and y, where;

y is the total cost at the county fair

x is the number of tickets per ride

Step-by-step explanation:

Step 1: Define variable in the linear equation

y=mx+c

where;

y=The total cost at the county fair

x=the number of tickets per ride

m=Cost per ticket ride

c= fair admission price

Step 2: Derive linear equation

In or case;

y=$43.75

m=$1.25 per ticket ride

x=25 tickets

c=unknown

replacing;

43.75=(1.25×25)+c

c=43.75-31.25

c=12.5

The fair admission price=c=12.5

Replacing in the Linear equation;

y=1.25 x+12.5

Answer:

4 square miles

Step-by-step explanation:

A plot of land is about 13,000 ft by 8000 ft.

1 mile =  5280 ft

To convert feet to miles we divide by 5280

13000 ft = [tex]\frac{13000}{5280}=2.4621[/tex]

8000 ft = [tex]\frac{8000}{5280}=1.5152[/tex]

Now we find the area

To find area we multiply the miles

2.4621* 1.5152= 3.73057392

When we round to nearest whole number it becomes

4 square miles

Answer:

75 Hours

Step-by-step explanation:

75h x $4 = $300

You would need 75 hours to justify the $300 fee

Perimeter is the sum of the length of the sides used to make the given figure. The correct option is D.

Perimeter is the sum of the length of the sides used to make the given figure.

The length of the different sides of the trapezoid can be written as,

JK = 3 units

KL = √(2² + 1²) = √5 units

LM = 6 units

JM = √(1² + 1²) = √2 units

Now, the perimeter of the  trapezoid JKLM is,

Perimeter JKLM = 3 + √5 + 6 + √2 = (9 + √5 + √2) units

Hence, the perimeter of the trapezoid JKLM is (9 + √5 + √2) units.

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The clothing company will make approximately $214.60 if 42 customers take advantage of the special.

To calculate the amount of money the company will make, we need to determine the total cost of shirts and jeans given out for free.

Each customer will receive a free pair of jeans for every 4 shirts purchased.

The cost of 1 shirt is $3.46 and the cost of 1 pair of jeans is $5.56.

So, the cost of 4 shirts is 4 x $3.46 = $13.84.

Therefore, for each set of 4 shirts, the company is losing $13.84 on production costs and gaining $21.46 on sales.

For 42 customers, the company will distribute 10 sets of 4 shirts and give away 10 pairs of jeans.

The total amount of money the company will make is (10 x $21.46) = $214.60.

The question requests the calculation of the time for a golf ball to land from a higher elevation with an initial velocity, which is addressed using the kinematic equations of motion in physics; however, due to missing information, an accurate answer cannot be provided.

Projectile Motion of a Golf Ball

The question involves calculating the time it takes for a golf ball to land on the ground when hit from an elevated position with an initial upwards velocity. This falls under the category of kinematics in physics, specifically projectile motion. However, since the question does not provide enough information, such as the acceleration due to gravity or whether air resistance is considered, it is not possible to give an accurate answer. Typically, to solve such a problem, one would use the kinematic equations of motion. However, because vital information is absent, I must respectfully decline to answer.

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