I need the answer and explanation for this geometry problem. (this is not a live quiz, test, or exam question, just to clarify)

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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Katy traveled more distance than Roger by 84.9 miles.

Subtraction is a basic arithmetic operation that involves finding the difference between two numbers, by taking away one number from another. It is denoted by the minus (-) sign and is the inverse operation of addition

To find out who traveled more distance, we need to calculate the difference between the distance traveled by Roger and Katy.

So, Katy traveled 205.65 miles and Roger traveled 120.75 miles.

To find out who traveled more, we subtract the distance traveled by Roger from the distance traveled by Katy

= 205.65 miles - 120.75 miles

Subtract the numbers

= 84.9 miles

Therefore, Katy traveled 84.9 miles more than Roger.

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The function that is shown in the graph is y = √(2x - 6) + 1

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

The graph

The parent function of the graph is

y = √2x

The graph is shifted right by 6 units

So, we have

y = √(2x - 6)

The graph is shifted up by 1 unit

So, we have

y = √(2x - 6) + 1

hence, the function is y = √(2x - 6) + 1

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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: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

Answer:

Step-by-step explanation:

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:

[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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Answer:

The cost is $115.20

Step-by-step explanation:

The locker is 8ft by 12ft by 9ft.

The volume is:

V = 8 × 12 × 9

V = 864 cubic feet

But the price is given by cubic yards so we need to find that first. (we have cubic feet)

A cubic yard is

1yd × 1yd × 1yd

And a yard is 3 feet, so that is the same as:

3ft × 3ft × 3ft

= 27cubic feet

Divide:

864/27

= 32

The locker is 32 cubic yards.

The price is $3.60 per cubic yard. Multiply.

32 × 3.60

= 115.2

The cost of the locker will be $115.20.

Answer:

-3+0i

Step-by-step explanation:

have a good day :)

Answer:

25ft

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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To find the limit of ln(5x)/√5x as x approaches infinity, we can use l'Hospital's Rule since it is an indeterminate form of ∞/∞.

Taking the derivative of the numerator and denominator separately, we get: lim [(1/5x) / (1/2√5x)] x→[infinity]

Simplifying this expression, we get: lim 2/5√5x x→[infinity]

Since the denominator approaches infinity as x approaches infinity, the limit is equal to 0.

Therefore: lim ln(5x)/√5x = 0 x→[infinity]

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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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Equations in the system are accurate and coincident.

Solve the system using any approach, such as elimination or substitution, and then categorize the equations as consistent independent, inconsistent, or coincident.

Using the substitution technique:

x - 2y = -4 => x = 2y - 4

Substituting x = 2y - 4 into the first equation:

3x - 6y = -12

3(2y - 4) - 6y = -12

6y - 12 - 6y = -12

-12 = -12

Identity -12 = -12 is a constant. Since the two equations represent the same line and have an infinite number of solutions, the system of equations is consistent and coincident.

Any value of y can be chosen, and x = 2y - 4 can be used to calculate the equivalent value of x.

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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.

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:

This can be figured out from the equation:

2n = 11

If he walks 2 miles/hour, then you can just say "2n" to say the miles in the unknown variable for hours.  Set it to equal 11, the number of miles he will walk in n hours.

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Lakeside Olds should expect to have approximately 3 automobiles lined up at opening time on a typical day based on the probability distribution provided.

To find the expected number of automobiles lined up at the Lakeside Olds dealer at opening time, we use the concept of expected value. The expected value is the average value we would expect to see if we repeated the experiment many times. In this case, the experiment is the number of automobiles lined up at the dealer at opening time.

We are given the probability distribution for the number of automobiles, which tells us the probability of each possible outcome. We use these probabilities to calculate the expected value as the weighted average of all possible outcomes.

Expected number of automobiles = (1 x 0.05) + (2 x 0.30) + (3 x 0.40) + (4 x 0.25)

= 0.05 + 0.60 + 1.20 + 1.00

= 2.8

≈ 3

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The given question is incomplete, the complete question is:

The probability distribution for the number of automobiles lined up at a Lakeside Olds dealer at opening time (7:30 a.m.) for service is:

how many automobiles should Lakeside Olds expect to be lined up at opening time?

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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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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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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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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Answer:

The surface area of the square pyramid is approximately 28.2 square units.

Explanation:

The base area and the areas of each triangle face must be determined to calculate the surface area of a square pyramid.

Since the base is a square with four units for each edge, its area is:

The base area equals 42 to 16 square units.

We must determine the length of the slant height, which is the height of each triangular face, to get the area of each triangle.

The Pythagorean theorem may be used to get the slant height: a2 + h2 = s2,

where an equals half the base's length (2 units), h is similar to the pyramid's size (3 units), and s is the slant height.

Inputting the values, we obtain:

2^2 + 3^2 = s^2

4 + 9 = s^2

13 = s^2 s = √13

Using the following formula, we can now get the area of each triangle face:

The area of the triangular face equals 0.5 base height, where the base is the slant height (13 units), and the size is the square base's edge length (4 units).

The triangular face area equals 0.5 x 4 x 13 = 213 square units.

Given that there are four triangular faces, their combined area is:

Units of area: 4 x 2 x 13 = 8 x 13

The total surface area is then calculated by summing the base and triangle face areas:

Base area plus triangle face area equals total surface area.

Surface area total = 16 + 8 x 13

28.2 square units total surface area (rounded to the nearest decimal point)

Therefore, the square pyramid's surface area is around 28.2 square units.

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Answer: 288

Step-by-step explanation:

2 × 6 × 2 × 4 × 3=288

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 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:

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 :)