Find the distance between the given points.

W(0, 8) and X(0, 12)

Distance =

4
4√(13)
10

Answer:

A

Step-by-step explanation:

The equation of a circle is:

(x - h)² + (y - k)² = r²

where (h, k) is the center and r is the radius.

Here, the center is (2, 1) and the radius is 1.

(x - 2)² + (y - 1)² = 1²

The equation of the given circle is Option(A)  [tex](x-2)^{2} + (y - 1)^{2} = 1[/tex] .

The standard equation of any circle is given as -

[tex](x-h)^{2} + (y - k)^{2} = r^{2}[/tex]  

where (h,k) is the coordinate of the center of the given circle and r is the length of radius of the circle.  

In the diagram given aside, we can see that the circle has its center at (2,1) and also the radius of the circle measures 1 units.

Thus, we have h = 2 , k = 1 and r = 1 in the standard representation.

The equation of the circle is -

⇒ [tex](x-2)^{2} + (y - 1)^{2} = 1^{2}[/tex]

∴  [tex](x-2)^{2} + (y - 1)^{2} = 1[/tex]

Therefore, the equation of the given circle is Option (A) [tex](x-2)^{2} + (y - 1)^{2} = 1[/tex] .

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Answer: -1

Step-by-step explanation:

3x − y − 3z           if x = −2      y = 1     z = −2

Step 1: 3(-2)-1-3(-2)

Step 2: -6-1+6

Step 3: -7+6

Step 4: -1

Answer:

$114.99

Step-by-step explanation:

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sorry if there is random numbers and letters i am glitchy

Answer:

97.45 • 0.18 = 17.54. 97.45 + 17.54 = 114.99. I think this is right.

Step-by-step explanation:

This is a quick sketch of the problem

the answer is about 235.31 ft

you have to use this equation to get the length of the other side, which is roughly 213 ft:

[tex]100 \div \sin(28) [/tex]

then it's just Pythagorean Theorem to get the end result:

[tex] {100}^{2} + {213}^{2} = {c}^{2} [/tex]

To find the distance from the car to the base of the pole, use the tangent function. Plug in the values and solve for the adjacent side.

To find the distance from the car to the base of the pole, we can use trigonometry. Since the observer is looking down at an angle of depression, we can use the tangent function. Tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the pole (100 ft) and the adjacent side is the distance from the car to the base of the pole.

So, using the formula tan(angle) = opposite/adjacent, we can plug in the values and solve for the adjacent side:

tan(28 degrees) = 100 ft/adjacent

adjacent = 100 ft / tan(28 degrees)

Using a calculator, we find that the distance from the car to the base of the pole is approximately 169.38 ft.

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Answer:

(x - 1)

Step-by-step explanation:

Given

8x² - 15x + 7

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 8 × 7 = 56 and sum = - 15

The factors are - 8 and - 7

Use these factors to split the x- term

8x² - 8x - 7x + 7 ( factor the first/second and third/fourth terms )

= 8x(x - 1) - 7(x - 1) ← factor out (x - 1) from each term

= (x - 1)(8x - 7) ← in factored form

The missing factor is (x - 1)

Answer:

The correct answer is B. point

Step-by-step explanation:

We know that a line has a length so option a cannot be correct.

A point is represented by a dot which has no length, width and height.

A ray is formed by a collection of points which altogether make its length.

Similarly an angle is formed by two rays.

So, angle, ray and line, all of them have length, width or height.

Hence, B. Point is the right answer ..

Answer:

1 and 4 should be the answer since 1 is 4 just angled differently

^-^

Answer:

0 Siblings: 4 Students

3 or more siblings: 5 students

Step-by-step explanation:

The numbers at the bottom represents how many siblings they have and the dots represent the number of studens so using this we know:

0 Siblings: 4 Students

1 Sibling: 3 Students

2 Siblings: 3 Students

3 Siblings: 1 Student

4 Siblings: 0 Students

5 Siblings: 2 Students

6 Siblings: 1 Student

7 Siblings: 1 Student

3 or more: 1 + 0 + 2 + 1 + 1 = 5

3 or more siblings: 5 students

Answer:

0 Siblings: 4 Students3 or more siblings: 5 students

Step-by-step explanation:

Answer:

Statements 1, 2, 4, and 5.

Step-by-step explanation:

(Follow along with the diagram)

The first thing we should do is figure out the measure of every angle. We know immediantly that CED is 90 degrees, and consequently CEA is too. This verifies the first two statements. We are told that EB bisects AEC (AEC = CEA).  This means that EB splits AEC into two congruect angles, BEA and CEB. If BEA = CEB, and BEA + CEB = CEA, then BEA and CEB both equal 45 degrees. This verfies statement 4, and helps us start statement 5. Statement 5 says that DEB = 135 degrees. We can see that the angle DEB is made up of angles CEB and CED. We already know that CEB = 45, and CED = 90. 90 + 45 = 135. So, statement 5 is true.

Regarding the incorrect statements, I will explain why they are false. We deduced that BEA = 45, so statement 6, stating that AEB (same as BEA) is 35, is not true. Statement 3 says that CEA = 1/2 of CEB. This equation regards the angles' measurements. If we plug in their known measurements, the equation reads 90 = 1/2 of 45. Through logic, we know this is not true. So, statement 3 is also false.

Statements are true regarding the given statement and diagram1, 2, 4, and 5.

1: ∠CED is a right angle.

2: ∠CEA is a right angle.

3: m∠CEB = m∠BEA

5 : m∠DEB = 135°

The first thing we should do is figure out the measure of every angle. We know immediately that CED is 90 degrees, and consequently, CEA is too. This verifies the first two statements. We are told that EB bisects AEC (AEC = CEA).  

This means that EB splits AEC into two congruent angles, BEA and CEB. If BEA = CEB and BEA + CEB = CEA, then BEA and CEB both equal 45 degrees.

This verifies statement 4 and helps us start statement 5. Statement 5 says that DEB = 135 degrees. We can see that the angle DEB is made up of angles CEB and CED.

We know that CEB = 45, and CED = 90. 90 + 45 = 135. So, statement 5 is true.

Congruent angles are two or more angles that are identical to each other. Thus, the measure of these angles is equal to each other.

Congruent angles have the same angle measure. For example, a regular pentagon has five sides and five angles, and each angle is 108 degrees. Regardless of the size or scale of a regular polygon, the angles will always be congruent.

In general, all congruent angles are not supplementary angles. For angles to add up to 180, they must be supplementary angles. So only right angles are congruent as well as supplementary angles because they have the same measure and they add up to 180.

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Answer:

1. 702 square centimeters

2. m∠YWX = 63°

Step-by-step explanation:

1.

The total surface area is area of all the sides.

Adding all these up  154 + 120 + 120 + 168 + 140 = 702 centimeters square.

2.

Angle WYX is equal to 46° (vertical angles are equal).

Now looking at triangle XWY, we know all three angles will add up to 180°. Given x =71° and Y = 46°, we can figure out W (Angle YWX)

71 + 46 + Angle YWX = 180

Angle YWX = 180 - 71 - 46 = 63°

Second answer choice is correct.

The length of the sunken ship is 28.56m

To calculate the length of the sunken ship , we have to calculate the distance between the beneath of the ship to the front and to the back.

distance between the beneath of the ship to back of the sunken ship

Tan 62 = 200/x

x = 200/tan 62

x = 106.34m

distance between the beneath of the ship to front of the sunken ship

Tan 56 = 200/y

y = 200/tan 56

y = 134.90m

The length of the sunken ship = 134 .90 - 106.34

= 28.56m

Answer:

D

Step-by-step explanation:

f(2)=4(2)-12

=8-12

=-4

Answer:

D. -4

Step-by-step explanation:

We have the following function:

[tex]f(x)=4x-12[/tex]

and we are asked to find the value of the function [tex]f(x)[/tex] when the variable [tex]x[/tex] is equal to 2:  [tex]f(2)[/tex].

This means that we must substitute the value of [tex]x = 2[/tex] wherever there is an [tex]x[/tex] in the function:

[tex]f(2)=4(2)-12[/tex]

[tex]f(2)=8-12[/tex]

[tex]f(2)=-4[/tex]

The answer is D. -4

Answer:

Step-by-step explanation:

1, 2 and 3 are interior angles

4 is the exterior angle

Answer:

Area of rhombus = 126 m²

Explanation:

We are given that the two diagonals of the rhombus are:

D₁ = 14 meters and D₂ = 18 meters

The area of the rhombus using its diagonals can be calculated using the following rule:

[tex]Area = \frac{D_1 * D_2}{2}[/tex]

Substitute with the given values to get the area as follows:

[tex]Area = \frac{14*18}{2}=126 m^2[/tex]

Hope this helps :)

Answer:

2.16m2

Step-by-step explanation:

[tex]\text{Hey there!}[/tex]

[tex]\text{3x}>\text{96}[/tex]

[tex]\text{You have to DIVIDE by 3 on BOTH OF YOUR SIDES.}[/tex]

[tex]\dfrac{3\text{x}}{3}>\dfrac{96}{3}[/tex]

[tex]\text{Cancel out: }\dfrac{3\text{x}}{3}\text{ because it equals to 1}[/tex]

[tex]\text{Keep: }\dfrac{96}{3}\text{ because it helps us solve for our answer, to compare}[/tex] [tex]\text{both numbers.}[/tex]

[tex]\text{96}\div3\text{ = 32}[/tex]

[tex]\boxed{\boxed{\bf{Answer:x > 32}}}\checkmark[/tex]

[tex]\text{It's a}[/tex] [tex]\text{(o)(p)(e)(n)(e)(d) circle shaded to the right side of the number line}[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

x>32

Step-by-step explanation:

Divide by 3 from both sides of equation.'

3x/3>96/3

Simplify, to find the answer.

96/3=32

x>32 is the correct answer.

I hope this helps you, and have a wonderful day!

Answer:

Option A is correct.

Step-by-step explanation:

Distance between two points can be calculated from formula

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

Here x₁ = 6, y₁ = 2,x₂ = -3 and y₂ = -2

Putting the values in the formula

[tex]d = \sqrt{(-3-(6))^2+(-2-(2))^2}\\d = \sqrt{(-3-6)^2+(-2-2)^2} \\d = \sqrt{(-9)^2+(-4)^2} \\d = \sqrt{81+16}\\d = \sqrt{97}\\d= 9.85[/tex]

So, the distance between points (6, 2) and (-3, -2) is 9.85 or ≈ 9.

So, Option A is correct.

ANSWER

[tex] \sqrt{ 97 }[/tex]

EXPLANATION

The formula for calculating the distance between two points is

[tex]d = \sqrt{ {(x_2-x_1)}^{2} +(y_2-y_1)^{2} } .[/tex]

We use this formula to find the distance between (6,2) and (-3,-2)

We plug in the points to get,

[tex]d = \sqrt{ {( - 3-6)}^{2} +( - 2-2)^{2} } .[/tex]

[tex]d = \sqrt{ {( - 9)}^{2} +( - 4)^{2} } .[/tex]

[tex]d = \sqrt{ 81+16}[/tex]

[tex]d = \sqrt{ 97 }[/tex]

The distance between the two given points is

[tex] \sqrt{ 97 }[/tex]

Answer:

[tex]\large\boxed{C)\ \left\{\begin{array}{ccc}y=x\\\\y=\dfrac{-x+10}{x-4}\end{array}\right}[/tex]

Step-by-step explanation:

We have the points

(-2 , -2) → x = -2 and y = -2 → x = y

(5, 5) → x = 5 and y = 5 → x = y

The equation of a line is [tex]y=x[/tex]

The hyperbola has the vertical asymptote x = a and the horizontal asymptote y = -1.

Therefore the second equation is:

[tex]y=\dfrac{a}{x-4}-1=\dfrac{a}{x-4}-\dfrac{x-4}{x-4}=\dfrac{a-(x-4)}{x-4}=\dfrac{a-x+4}{x-4}[/tex]

Where a > 0.

The corresponding equation in the solutions to choose is:

[tex]y=\dfrac{-x+10}{x-4}[/tex]

The correct answer is (D) 1,155 miles (rounded to the nearest whole number).

To find the round trip distance from Kansas City to Denver, we need to calculate the actual distance in miles based on the scale given in the map.

On the map, 1 inch represents 3 miles. The distance from Kansas City to Denver on the map is given as 192 inches. To find the actual distance in miles:

Actual distance = (Distance on the map) × (Scale factor)

Actual distance = 192 inches × 3 miles/inch

Actual distance = 576 miles

Since the round trip distance includes going from Kansas City to Denver and back, we need to double the actual distance:

Round trip distance = 2 × 576 miles

Round trip distance = 1152 miles

So, the correct answer is (D) 1,155 miles (rounded to the nearest whole number).

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Answer:

2:30 pm

Step-by-step explanation:

In two hours (from 10am), she is 45 * 2 = 90 miles from vacation cabin.

From then on her average is still 45 mph and her husband's is 65 mph. So, husband catches her 20 miles (65-45=20) in every hour.

The husband has to catch up 90 miles. How long would it take if he is catching up at 20 miles an hour?

90/20 = 4.5 hours

So husband starts at 10am and 4.5 hours form that time is 2.30pm

Answer:

x = 95 - 4y

Step-by-step explanation:

Let the pieces he has now be a variable x and the no. of students in his class be y, So the pieces he gave to everyone become 4y (note that 4 here means he had given four to each) and as he had won 95 pieces at the fair in the starting,

therefore the equation becomes:-

x = 95 - 4y

The expression for how many pieces of gum Deshawn has now is 95 - (4 x number of students in his math class).

To find out how many pieces of gum Deshawn has after giving four to every student in his math class, we need to subtract the number of pieces of gum he gave away from the total number he won at the county fair.

We can represent this situation using the expression: 95 - (4 x number of students in Deshawn's math class).

For example, if there were 20 students in Deshawn's math class, the expression would be: 95 - (4 x 20) = 95 - 80 = 15.

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Answer:

Distributive Property.

Step-by-step explanation:

Cos(A-B)= Cos A- Cos B

The variables in the parenthesis gets multiplied into the Cos

Cos A - Cos B

Answer:

Yes, they are parallel.

Step-by-step explanation:

Parallel lines have the same slope. We must find the slopes of the two lines.

When the equation of a line is written in the slope-intercept form,

y = mx + b,

the slope is m.

The first line has equation

[tex] y = \dfrac{2}{3}x - 17 [/tex]

It is already written in the slope-intercept form. Comparing y = 2/3x - 17 with y = mx + b, you see that m = 2/3. The slope of the first line is 2/3.

Now we solve the second equation for y to obtain the slope-intercept form of that equation.

4x - 6y = -6

Subtract 4x from both sides.

-6y = -4x - 6

Divide both sides by -6.

[tex] \dfrac{-6}{-6}y = \dfrac{-4}{-6}x + \dfrac{-6}{-6} [/tex]

[tex] y = \dfrac{2}{3}x + 1 [/tex]

We now compare this form of the second equation with y = mx + b, and we see that m = 2/3.

Both equations have the same slope, 2/3, so the lines are parallel.

Answer:

The answer in the procedure

Step-by-step explanation:

Let

m1 and m2 ----> the slopes of the lines constructed

we know that

If two lines are perpendicular, then the product of their slopes is equal to -1

therefore

To verify if the lines constructed are perpendicular

Multiply their slopes

if m1*m2=-1 ------> the lines are perpendicular

Answer:

C. Check the intersecting lines with the corner of a piece of paper to ensure the lines create 90° angles. Took the test just now and got it right

Step-by-step explanation:

It has 3 zeroes which are

[tex]\frac{-1}{2}, -1, \frac{4}{5}[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

F ................................

Answer:

base= 2 cm

Step-by-step explanation:

A=1/2bh

(1/2x)40=1/2b(10)x(1/2)

20=b(10)/10

2=b

Answer:

base = 8 cm

Step-by-step explanation:

A= 1/2bh

40=1/2*b*10

40/ 1/2= 80

80/10= 8

b=8

Answer:

1. 0.283333333

2. 0.016666667

3. 0.0833333333333333

4.0.0666666666666667

5. 0.1

6. 0.2

7. 0.05

8.0.0333333333333333

Step-by-step explanation:

Simply divide the numerator by the denominator. ex. 17 divided by 60.

Hope this helps :)

Answer:

p^3

--------

n^6

Answer: correct option is C

Step-by-step explanation:

Took test