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The value of x that would make triangle ABC a right triangle is x= 2. The justification is that the product of the slopes of two perpendicular lines is -1/2, and when the points are plugged into the distance formula, the sides satisfy the Pythagorean theorem.

To determine a value of x that would make triangle ABC a right triangle, we need to check if the square of the length of any two sides equals the square of the length of the third side.

We can use the distance formula to find the lengths of the sides of the triangle

AB = √((x + 3)² + 4²)

BC = √(2² + 3²)

CA = √((x + 1)² + 1²)

To make triangle ABC a right triangle, we need to find a value of x that satisfies the Pythagorean theorem

AB² + BC² = CA²

[(x + 3)² + 4²] + [2² + 3²] = [(x + 1)² + 1²]

Simplifying this equation yields

x² + 2x - 8 = 0

Solving for x, we get

x = 2 or x = -4

So, if x = 2 or x = -4, then triangle ABC is a right triangle.

To justify this, we can find the slopes of the line segments connecting the vertices of the triangle

mAB = (3 - (-1)) / (x - (-3)) = 4 / (x + 3)

mBC = (-4 - (-1)) / (-1 - (-3)) = -3/2

mCA = (3 - (-4)) / (x + 1 - (-1)) = 7 / (x + 2)

When x = 2, we get

mAB = 4/5

mBC = -3/2

mCA = 7/3

mAB * mBC = -2/5

mBC * mCA = -7/6

mCA * mAB = 14/15

when x = 2, triangle ABC is right triangle.

When x = -4, we get

mAB = 4/(-1) = -4

mBC = -3/2

mCA = 7/(-3) = -7/3

mAB * mBC = 6

mBC * mCA = 14/3

mCA * mAB = 7/2

when x = -4, triangle ABC is not a right triangle.

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Using the distributive property, the filled expression is 2 X (1+6) = (2 X 1) + (2 X 6)

From the question, we have the following parameters that can be used in our computation:

2 X (1+6) = (2 X _) + (2 X _)

The distributive property states that

a * (b + c) = ab + ac

So, we have

2 X (1+6) = (2 X 1) + (2 X 6)

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Answer:

Angle BAC

Step-by-step explanation:

The actual angle letter (in this case A) is ALWAYS in the center. The first and last letters are the ends of the lines that make the angle (B and C). You can put the first and last letters as BAC OR CAB, because either way you are describing the same angle.

I hope this helps :)

Using unit conversions, the height of  the International Space Station in kilometers is 400 kilometers.

Unit conversion enables the conversion of one unit to another.

Division and multiplication operations are heavily deployed in unit conversions.

These two basic mathematical operations help create the conversion factors for unit conversions.

The orbiting height of the International Space Station = 250 miles

5 miles = 8 kilometers

250 miles = 250 x 8/5 kilometers

= 400 kilometers

Thus, a height of 250 miles is the same as a height of 400 kilometers.

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Answer:

The answer for the radius is approximately 18ft

Step-by-step explanation:

23.6ft=0/360×2pir

23.6=150/360×22/7×r

23.6=3300r/2520

cross multiply

23.6×2520=3300r

59472=3300r

divide both sides by 3300

3300r/3300=59472/3300

r=18.02

r≈18ft

Answer:

-3+0i

Step-by-step explanation:

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The reflection of D (-1, 6) over the x - axis D' is(-1, -6)

A reflection is a transformation representing a flip of a figure. Figures may be reflected in a point, a line, or a plane.

When reflecting a figure in a line or in a point, the image is congruent to the preimage.

A reflection maps every point of a figure to an image across a fixed line.

We have the coordinates of D is (-1, 6)

(x, y) => (x, -y)

We apply this reflection, we get:

and the reflection will be D' (-1 , -6)

Hence, The reflection of D (-1, 6) over the x - axis D' is (-1, -6)

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The given question is incomplete, complete question is:

The point D (-1, 6) is plotted on the coordinate grid below. Plot the point D’, the reflection of D over the y-axis

The piecewise function in the graph is:

f(x) = 3   if -8 < x < - 2

f(x) = -0.5x + 5 for -2 < x - 6

First we can see a constant segment at y = 3 that starts at x = -8 and ends at x = -2

So we have:

f(x) = 3   if -8 < x < - 2

Then we have a line that starts at x = -2, and ends at x = 6

We can see that the y-intercept is 5, then we can write:

y = ax + 5

It also passes through (4, 3), replacing that:

3 = a*4 + 5

3 - 5 = a*4

-2 = a*4

-2/4 = a

-0.5 = a

Then the second part is:

f(x) = -0.5x + 5 for -2 < x - 6

The piecewise function is:

f(x) = 3   if -8 < x < - 2

f(x) = -0.5x + 5 for -2 < x - 6

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Answer:

The Clean & Bright box holds more detergent than the Soapy Suds box.

Step-by-step explanation:

The volume of the Soapy Suds Box is:

8 x 13 x 9 = 936 cubic inches

The volume of the Clean & Bright Box is:

13 x 12 x 8 = 1248 cubic inches

Therefore, the Clean & Bright box holds more detergent than the Soapy Suds box.

The probability of selecting a person who wears a watch given that they wear a ring is 2/5 or 0.4.

From the Venn diagram, we can see that there are 10 people who wear rings, 2 of whom also wear watches. This means that the probability of randomly selecting a person who wears a ring is 10 out of the total number of people in the class. That is:

P(Ring) = 10 / (10+2) = 10/12

Similarly, we can find the probability of selecting a person who wears both a watch and a ring. From the diagram, we can see that there are 4 such people. Thus,

P(Watch and Ring) = 4 / (10+2) = 4/12

Using the formula for conditional probability, we get:

P(Watch|Ring) = P(Watch and Ring) / P(Ring)

Substituting the values we obtained earlier, we get:

P(Watch|Ring) = (4/12) / (10/12) = 4/10 = 2/5 or 0.4

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Answer:

yes

Step-by-step explanation:

If the graph of a relationship is a line or a ray through the origin, then it is proportional. If it is a line or ray that does not pass through the origin, then it is not proportional. Also, if it is not linear, then it is not proportional.

Answer:

[tex]x = \sqrt{ {28.46}^{2} - {27}^{2} } = \sqrt{80.9716} = 9.00[/tex]

The number of players expect to spin before someone wins $500 in the game is equal to 16.

Number of times each player spin the wheel = once

Expected number of players who would spin the wheel before someone wins $500.

Calculate the probability of winning $500 on a single spin

And then use the formula for the expected value of a geometric distribution.

At the spinner, there are 16 equal sections.

And one of these sections is labeled with $500.

The probability of winning $500 on a single spin is,

P(winning $500) = 1/16

Next, use the formula for the expected value of a geometric distribution,

Expected value = 1 / P(winning)

Here, the probability of winning is 1/16,

so the expected value is equal to,

Expected value = 1 / (1/16)

                           = 16

Therefore, expected number of players spinning the wheel before someone wins $500 in this carnival game is 16.

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According to the information, the view from above would have 8cm on each side and 6cm on each section of the base. On the other hand, the side view would be 4cm high in the roof part and 4cm in the wall part and 8cm in the base.

To identify the correct measurements we must see the measurements in meters that the construction has. In this case the measurements are in meters, to make a scale model we must express each meter in 2cm. So, we must multiply the numbers of each section by 2 and put the expression "cm" to refer to the fact that they are centimeters. According to the above:

The view from above would have 8cm on each side and 6cm on each section of the base. On the other hand, the side view would be 4cm high in the roof part and 4cm in the wall part and 8cm in the base.

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The total number of boxes purchased using $11.40 and the remaining expected changed money received is 28 boxes and $0.20 respectively.

Total amount of money to buy drink boxes = $11.40

Cost of each drink box = $0.40

Number of drink boxes bought

= $11.40 ÷ $0.40/drink box

= 28.5 drink boxes

Since you cannot buy a fractional part of a drink box.

Round down to the nearest whole number.

Here,  28 drink boxes can be bought with the available money.

To determine expect change,

Subtract the total cost of the drink boxes from the amount of money available.

$11.40 − ($0.40/drink box × 28 drink boxes)

= $11.40 − $11.20

= $0.20

The amount of change is $0.20.

Therefore,  the number of boxes bought with given amount is 28 boxes and the remaining expected amount of money received is $0.20 .

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Answer: 288

Step-by-step explanation:

2 × 6 × 2 × 4 × 3=288

Answer: C. 5

Step-by-step explanation:

Neither student's work properly verifies the identity and  csc x = 1/sin x,  sin² x + cos² x = 1 are the  two identities that were used in Student A's verification.

Part A:

Both Student A and Student B did not verify the identity properly. Student A started with the correct expression, but then manipulated it incorrectly.

In Step 1, multiplying cosine x over sine x times cosine x does not equal cosecant x minus sine x.

In Step 2, dividing cosine squared x by sine x also does not equal cosecant x minus sine x. Student B also started with the correct expression, but made a mistake in Step 2.

Subtracting sine squared x over sine x from 1 does not equal 1 over sine x minus sine squared x over sine x.

Therefore, neither student's work properly verifies the identity.

Part B:

Identity 1: csc x = 1/sin x

Student A uses this identity in Step 4 when they rewrite 1/sin x as csc x.

Identity 2: sin² x + cos² x = 1

Student A uses this identity in Step 3 when they rewrite cos² x as 1 - sin²x.

Hence, neither student's work properly verifies the identity and  csc x = 1/sin x,  sin² x + cos² x = 1 are the  two identities that were used in Student A's verification.

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It will take 7.9 years for the lobster to travel 39.5 miles

Word problem is usually made up of a few sentences describing a situation that needs to be solved through mathematics

How to determine this

If a lobster travels 5 miles each year

i.e 5 miles = 1 years

How many years will it take the lobster to travel 39.5 miles

Let x represent the number of years the lobster travel

For lobster to travel 39.5 miles,

i.e 39.5 miles = x years

To calculate the number of years

When 5 miles = 1 year

39.5 miles = x

x = 39.5 miles * 1 year/5 miles

x = 39.5 years/5

x = 7.9 years

Therefore, it will take 7.9 years for the lobster to travel 39.5 miles

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The fraction of cloths which are either black or white is 17/24.

Given that, Regan has 7/12 of the clothes are white and another 1/8 are black.

We need to find the fraction of the clothes are either black or white,

To find the same, we need to simply add both the fractions,

7/12 + 1/8 = 14 + 3 / 24

= 17/24

Hence, the fraction of cloths which are either black or white is 17/24.

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The linear function f with the values f(10) = 5 and f(2) = -3 is f(x) = x - 5.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

hence, to write a linear function f with the values f(10) = 5 and f(2) = -3, we need to find the slope and y-intercept of the function.

The slope of a linear function can be found by using the formula:

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

Using the values of f(10) = 5 and f(2) = -3,

we can find the slope:

Slope m = (5 - (-3)) / (10 - 2)

= 8 / 8

= 1

Now that we have the slope, we can use the point-slope form to find the equation of a line:

y - y1 = m(x - x1)

Where m is the slope and (x1, y1) is one of the points on the line.

Using the point (10, 5) and slope m = 1, we have:

y - y1 = m(x - x1)

y - 5 = 1(x - 10)

Simplifying, we get:

y - 5 = x - 10

y = x - 5

f(x) = x - 5

Therefore, the linear function is f(x) = x - 5.

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Answer:

Step-by-step explanation:

The solution is: y = 30x, is the equation for total pay (y) as a function of total hours worked (x).

Here, we have,

Because we are talking about over 8 hours.

The question states that you get 30$ per hour for overtime hours.

That means if you work over 8 hours your dollars per hour increases to 30.

So because the amount of dollars increases to 30 you can infer that all you have to do is make the same equation as the 20 dollar's per hour equation.

Except you put 30 making it y = 30x.

Hence, The solution is: y = 30x, is the equation for total pay (y) as a function of total hours worked (x).

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complete question:

A company pays $20 per hour for up to 8 hours of work, and $30 per hour for overtime hours (hours beyond 8 hours). For up to 8 hours worked, the equation for total pay (y) for hours worked (x) is y = 20x. For over 8 hours worked, what is the equation for total pay (y) as a function of total hours worked (x)?

The first four terms of the geometric sequence are -1, 11, -121, and -1210.

We have,

To find the first four terms of the geometric sequence, we need to determine the common ratio, r, and then use it to calculate the other terms.

We can start by using the formula for the nth term of a geometric sequence:

an = a1 x r^(n - 1)

where an is the nth term, a1 is the first term, r is the common ratio, and n is the position of the term we want to find.

Since we are given a2 and a3, we can use them to form two equations:

a2 = a1 x r

a3 = a1 x r²

We can then solve for a1 and r:

a1 = a2 / r = 11 / r

r = a3 / a2 = -121 / 11

Substituting these values into the formula for the nth term, we get:

an = (11 / r) x (-121 / 11)^(n - 2)

Simplifying this expression, we get:

an = -11 x 11^(n - 2)

Now we can calculate the first four terms:

a1 = 11 / r = 11 / (-121 / 11) = -1

a2 = 11

a3 = -121

a4 = -11 x 11^(4 - 2) = -1210

Therefore,

The first four terms of the geometric sequence are:

-1, 11, -121, -1210

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A 11.544 acre-feet of this ice field will melt from the beginning of day 1 (t = 0) to the beginning of day 4 (t = 3). So, correct option is C.

To solve the problem, we need to integrate the given rate of melting with respect to time over the interval [0,3] to find the total amount of ice that melts during this time.

First, we can simplify the given rate of melting by using the identity: sin³(t) = (3sin(t) - sin(3t))/4

So, M(t) = 4 - (3sin(t) - sin(3t))/4 = 16/4 - 3sin(t)/4 + sin(3t)/4 = 4 - 0.75sin(t) + 0.25sin(3t)

Integrating this expression with respect to t over the interval [0,3], we get:

[tex]\int\limits^3_0[/tex] M(t) dt = [tex]\int\limits^3_0[/tex] (4 - 0.75sin(t) + 0.25sin(3t)) dt

= [4t + 0.75cos(t) - (1/3)cos(3t)]|[0,3]

= (12 + 0.75cos(3) - (1/3)cos(9)) - (0 + 0.75cos(0) - (1/3)cos(0))

= 11.544

Therefore, the answer is (C) 11.544.

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Answer:x= 39 , y= -6

Step-by-step explanation:

we have y = -6 (1)

x = -8y-9 (2)

Let (1) replace (2)

x = -8(-6)-9

x = 48-9 = 39

So x=39 , y=-6

In the triangle the value of JL is 14.

Let us find the value of KJ which is hypotenuse

8²+6²=KJ²

64+36=KJ²

KJ=10

From the triangle KLM

tan 45= opposite side/adjacent side

1=6/ML

ML=6

So JL = 8+6

=14

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The correct conclusions which can we draw from the circle graph is,

⇒ Together, Walk and Streetcar are the preferred transportation for 165 residents.

Given that;

The circle graph describes the distribution of preferred transportation methods from a sample of 300 randomly selected San Francisco residents.

And, Circle graph titled San Francisco Residents Transportation with five sections labeled walk 40 percent, bicycle 8 percent, streetcar 15 percent, bus 10 percent, and cable car 27 percent.

Hence, For Walk and Streetcar;

(40 + 15)% of 300

55% of 300

55/100 x 300

55 x 3

165

Thus, The correct conclusions which can we draw from the circle graph is,

⇒ Together, Walk and Streetcar are the preferred transportation for 165 residents.

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The area of Circle D is 3.36 times greater than the area of Circle A.

What is circle?

A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center.

We are given the following information about the radii of the four circles:

The radius of Circle A is 6 mm.

The radius of Circle B is 3 mm greater than the radius of Circle A, so it is 6 + 3 = 9 mm.

The radius of Circle C is 5 mm greater than the radius of Circle B, so it is 9 + 5 = 14 mm.

The radius of Circle D is 3 mm less than the radius of Circle C, so it is 14 - 3 = 11 mm.

The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius.

Therefore, we can calculate the areas of the four circles as follows:

The area of Circle A = π(6)² = 36π mm².

The area of Circle B = π(9)² = 81π mm².

The area of Circle C = π(14)² = 196π mm².

The area of Circle D = π(11)² = 121π mm².

To find out how many times greater the area of Circle D is than the area of Circle A, we can divide the area of Circle D by the area of Circle A:

Area of Circle D / Area of Circle A = (121π) / (36π) = 3.36

Therefore, the area of Circle D is 3.36 times greater than the area of Circle A.

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