In a video game, Shar has to build a pen shaped like a right triangle for her animals. If she needs 16 feet of fence for the shortest side and 20 feet of fence for the longest side, how many feet of fencing is needed for the entire animal pen?

The rewritten equation to represent the resistance of resistor 2, R₂, in terms of [tex]R_T[/tex] and R₁ is [tex]R_2 = \frac{R_TR_1}{R_1-R_T}[/tex].

Hence, the 3rd option is the right choice.

To rewrite any equation, in terms of the other variable, we just need to change the isolation of the variable by rearranging it.

In the question, we are given the equation for the total resistance [tex]R_T[/tex] for a circuit with two resistance R₁ and R₂ connected in parallel as:

[tex]R_T = \frac{R_1R_2}{R_1+R_2}[/tex]

We are asked to rewrite the equation to represent the resistance of resistor 2, R₂, in terms of [tex]R_T[/tex] and R₁.

To rewrite the equation, we do as follows:

[tex]R_T = \frac{R_1R_2}{R_1+R_2}\\\Rightarrow R_T(R_1 + R_2) = R_1R_2\\\Rightarrow R_TR_1 + R_TR_2 = R_1R_2\\\Rightarrow R_1R_2 - R_TR_2 = R_TR_1\\\Rightarrow R_2(R_1-R_T) = R_TR_1\\\Rightarrow R_2 = \frac{R_TR_1}{R_1-R_T}[/tex]

Thus, the rewritten equation to represent the resistance of resistor 2, R₂, in terms of [tex]R_T[/tex] and R₁ is [tex]R_2 = \frac{R_TR_1}{R_1-R_T}[/tex].

Hence, the 3rd option is the right choice.

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For the complete question, refer to the attachment.

The equation of the line that is parallel and passes through the point (2,3) is; x +2y =8.

If follows from the task content that the slope of the first line is; (-4-0)/(4-(-4)) = -1/2.

Hence, since the lines are parallel, they have the same slope and the equation of the second line is;

-1/2 = (y-3)/(x-2)

-x+2 = 2y -6

x +2y =8.

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Answer: b on edg

Step-by-step explanation:

The equation which best represents the graph shows the amount of money that Janice saves each week from her summer job is option A which is  y=200x.

Given a graph showing the amount of money that Janice saves each week from her summer job.

Equation is relationship between two or more variables expressed in equal to form. Equation of two variables look like ax+by=c. It may be linear equation, quadratic equation and cubic equation.

Equation can be formed from any two points present on the graph with the help of following formula:

[tex](y-y_{1})=(y_{2} -y_{1} ) /(x_{2} -x_{1} )*(x-x_{1} )[/tex] where [tex](x_{1} ,y_{1} ),(x_{2} ,y_{2} )[/tex]are the points.

So,we have to find points first which are (6,1200),(7,1400)

Put the values in the formula:

(y-1200)=(1400-1200)/(7-1)*(x-1200)

y-1200=200/1(x-6)

y-1200=200(x-6)

y-1200=200x-1200

y=200x-1200+1200

y=200x

Hence the equation shows the amount of monet that Janice saves each week from her summer job is option A which is y=200x.

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This question is asking to create 5 of your own questions, so here are mine with the process on how I got each:

Question 1: Given c(x) = 8x + 32, find the range of c for the domain {1, 3, 5}.

Answer w/ Process:

For each equation, I am plugging in each domain value for x in the function, multiplying by 8, and adding by 32.

c(1) = 8(1) + 32 = 8 + 32 = 40

c(3) = 8(3) + 32 = 24 + 32 = 56

c(5) = 8(5) + 32 = 40 + 32 = 72

Range: {40, 56, 72}

Question 2: Given d(x) = x - 7, find the range of d for the domain {-2, 3}.

Answer w/ Process:

For each equation, I am plugging in each domain value for x in the function, and subtracting 7.

d(-2) = -2 - 7 = -9

d(3) = 3 - 7 = -4

Range: {-9. -4}

Question 3: Given f(x) = 7x + 738, find the range of f for the domain {1.5, 11}.

Answer w/ Process:

For each equation, I am plugging in each domain value for x in the function, multiplying by 7, and adding 738.

f(1.5) = 7(1.5) + 738 = 10.5 + 738 = 748.5

f(11) = 7(11) + 738 = 77 + 738 = 815

Range: {748.5, 815}

Question 4: Given g(x) = -2804x + 7268, find the range of g for the domain {50, 75, 256}.

Answer w/ Process:

For each equation, I am plugging in each domain value for x in the function, multiplying by -2804, and adding 7268.

g(50) = -2804(50) + 7268 = -140200 + 7268 = -132932

g(75) = -2804(75) + 7268 = -210300 + 7268 = -203032

g(256) = -2804(256) + 7268 = -717824 + 7268 = -710556

Range: {-132932, -203032, -710556}

Question 5: Given h(x) = -3x - 4, find the range of h for the domain {1, 2, 3}.

Answer w/ Process:

For each equation, I am plugging in each domain value for x in the function, multiplying by -3, and subtracting by 4.

h(1) = -3(1) - 4 = -3 - 4 = -7

h(2) = -3(2) - 4 = -6 - 4 = -10

h(3) - -3(3) - 4 = -9 - 4 = -13

Range: {-13, -10, -7}

b(-3)

b(5)

b(9)

Range

Rest questions

#1

k(x)=2x²-5

Find the range of k for domain {1,2,6}

#2

h(x)=9x³

Find the range of h for domain {9,0,8}

#3

o(x)=6x-7

find the range of o for domain {0,1,9}

#4

p(x)=23x²-5x

Find the range of p for domain {3,4,8}

Answer:

Option (1)

Step-by-step explanation:

From the unit circle, we see that y, which represents sin(x) when x is 0 or pi.

Answer: A

Step-by-step explanation:

Each value of x maps onto only one value of y.

Answer:

no solution

Step-by-step explanation:

y = (1/3)x - 4

3y - x = -7

put the first equation into the second

3(1/3)x - (3)4 - x = -7

x - 12 - x = -7

-12 = -7 can never be true so this is no solution

Answer: C: [tex]D\cap F = \{2, 4, 6, 8\}[/tex]

Step-by-step explanation:

Let's first find the specific numbers that are in sets D and F.

[tex]D=\{0,1,2,\ldots\}[/tex], as D has all whole numbers.

[tex]F=\{2,4,6,8\}[/tex], as all of these numbers are even, greater than or equal to two, and less than nine.

Since all the numbers in F are whole numbers, all of them would be in D. Hence, the intersection of both would just be {2, 4, 6, 8}.

[tex]D\cap F = \{2, 4, 6, 8\}[/tex]

Answer: 1/2

Step-by-step explanation:

Scale factor = (image)/(preimage) = 6/12 = 1/2

180-180=100

2+3=5

100÷5= 20

x = 20

Answer:

[tex]5x+80=180[/tex]
I hope this helps and that you can give a brainliest!

Step-by-step explanation:

This is a straight line which is always 180°.

Here there are 3 angles adding up to the total 180°.

So the initial equation is [tex]3x+80+2x =180[/tex].

But there are coefficients that share the same variable.
So by simplifying the equation, you end up with:

[tex]5x+80=180[/tex]

Using the relation between velocity, distance and time, it is found that his jogging rate was of 4.5 mph.

Velocity is distance divided by time, hence:

[tex]v = \frac{d}{t}[/tex]

Jogging, his velocity was of v, while the time was of t + 2, for a distance of 10 miles, hence:

[tex]v = \frac{10}{t + 2}[/tex]

Riding, his velocity was of 16, while the time was of t, also for a distance of 10 miles, hence:

[tex]v + 16 = \frac{10}{t}[/tex]

Then, considering the first equation and replacing in the second:

[tex]\frac{10}{t + 2} + 16 = \frac{10}{t}[/tex]

[tex]\frac{10}{t} - \frac{10}{t + 2} = 16[/tex]

[tex]\frac{10t + 20 - 10t}{t(t + 2)} = 16[/tex]

16t² + 32t - 20 = 0 -> t = 0.5.

Then his jogging rate in mph was:

[tex]v = \frac{10}{0.5 + 2} = 4.5[/tex]

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The package has a surface area of 4520cm². The area of the package is less than the area of the wrapping paper. So, dayson  can cover the package with the wrapping paper.

According to the question,

The first step is to determine the surface area of the package.

Total surface area of a cuboid = 2 (l w + w h + l h)

where:

• l = length

• w = width

• h = height

2[(50 x 20) + (50 x 18) + (20 x 18)] = 4520cm²

The second step is to convert 1 square meter to cm

1m² = 100 cm²

100 x 100 = 10,000

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Answer:

336 mangoes

Step-by-step explanation:

If 320 mangoes = 100%

Increasing them by 5% means that we will need to work out 105%

32 mangoes = 10%

3.2 mangoes = 1%

336 mangoes = 105%

Our final answer is 336 mangoes

Hope this helped and have a good day

The value of x in the trapezoid is 11.

Therefore, the angle 9x and 7x + 4 are supplementary.

Hence,

9x + 7x + 4 = 180

16x + 4 = 180

16x  = 180  - 4

16x = 176

x = 176 / 16

x = 11

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Answer:11

Step-by-step explanation:Easy

[tex]\frac{97}{100}[/tex] probability that a randomly chosen college student either has a job or lives on campus.

What is probability?

To find the probability that a randomly chosen college student either has a job or lives on campus:

Given: 85% of college students have a job, 54% live on campus, and 42% have a job and live on campus.

So, out of 100 students, 42 students either has a job or live on campus.

43 college students have a job and 12  live on campus.

So, 43 + 42 + 12 = 85 + 54 - 42

85 + 12 = 139 - 42

97 = 97

Therefore, [tex]\frac{97}{100}[/tex] probability that a randomly chosen college student either has a job or lives on campus.

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The solution to the questions are:

1) Generally, the equation for  m∠ACB is  mathematically given as

CA= CB

CA = radius of the circle

Therefore,

∠CAB =

[tex]\angle CBA = 60 \textdegree[/tex]

the sum of all the angles of a triangle

the sum of all the angles of a triangle is 180°

[tex]< CAB + < CBA + < ACB = 180 \textdegree[/tex]

[tex]60\textdegree + 60\textdegree + < ACB = 180\textdegree[/tex]

[tex]120\tetxtdegree + < ACB = 180\tetxtdegree[/tex]

[tex]< ACB = 60\textdegree[/tex]

The value of [tex]< ACB\ is\ 60\textdegree[/tex].

2. What is the length of segment AB?

In the same manner, as in ACB, all of the angles are the same. As a result, we may say that the triangle has equal sides.

In a triangle with equilateral sides, each of the triangle's three sides has the same length.

AB = BC =CA = R

As a consequence, the radius of the circle is equal to the length of the segment AB.

The formula for calculating the hexagon's perimeter is 6a, where an is the number of sides in the hexagon.

The circumference of the hexagon is equal to 6 times a.

The circumference of the hexagon is equal to six times each side (AB)

The perimeter of the hexagon is equal to r times 6.

As a result, the number 6r represents the hexagon's perimeter.

4. The perimeter of the hexagon is  6r the circumference of the circle.

[tex]P=2*\pi*r[/tex]

P=2*3.14*r

P=6.28r

As a consequence of this, the hexagon's perimeter is less than the diameter of the circle.      

5. The circumference of the circle is 6.28r.

the perimeter of the circle = [tex]2 \pi r[/tex]

[tex]P=2*\pi*r[/tex]

P=2*3.14*r

P=6.28r

As a result, the diameter of the circle is a fraction of a unit bigger than.

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Answer:

1. 60 degrees

2. r

3. 6r

4. slightly less than

5. slightly greater than 6r

Step-by-step explanation: I just did it on edge 2023. Hope this helps!

The first error in the proof is the fourth reason

Mathematical proofs are statements or collections of statements that are used to prove or disprove a statement, proof or theory

To determine the first error in the proof, we simply read through the statements and the given reason

From the table in the question, we have the following conclusions

Hence, the first error in the proof is the fourth reason

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The Slope of the line :

[tex]m=-\frac{1}{5} \approx-0.2[/tex]

Using small, whole integer coordinates, it is simple to manually determine a line's slope. The formula becomes more effective if the coordinates are given greater or decimal values.

Because all horizontal lines have the same y-coordinates, it is important to note that all of them have a gradient of zero. In the slope formula's numerator, this will produce a zero. A vertical line, on the other hand, will have an arbitrary slope because the x-coordinates are constant. When applying the formula, this will lead to a division by zero error.

slope = (y₂ - y₁) / (x₂ - x₁)

Using the two points P=(2,3) and Q=(-3,4) as your input, determine the slope.

P=(x1,y1) and Q=(x2,y2) are two points on a line, and the slope of that line is given by :

                                 [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

we have that:

                        [tex]x_{1}=2, y_{1}=3, x_{2}=-3, y_{2}=4[/tex]

Fill in the blanks in the slope calculation,

                                    [tex]m=\frac{(4)-(3)}{(-3)-(2)}\\\\=\frac{1}{-5}\\\\=-\frac{1}{5}[/tex]

Reaction:  the slope of the line is =[tex]m=-\frac{1}{5} \approx-0.2[/tex]

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Answer:

  (a)  3

Step-by-step explanation:

The fundamental theorem of algebra tells you a polynomial has a number of roots equal to its degree.

The degree of a polynomial is the largest exponent of the variable. Here, the degree is 3. That means there are three roots.

In general, the roots of a polynomial with real coefficients will be real or pairs of complex roots. The attached graph shows the roots of this cubic function are all real (and irrational).

Answer:

[tex]x^2+7x-8-\frac{3}{x-7}[/tex]

Step-by-step explanation:

I think this question is a bit hard to explain by typing, so I'll add an image down below.  

I used long division for this question, and the final answer is: [tex]x^2+7x-8-\frac{3}{x-7}[/tex]

We conclude that the odds of hitting the ball are 0.158

The odds (like the probability) are given by the quotient between the number of attempts in which you hit the ball and the total number of attempts.

Here we know that out of 19 attempts, in 3 you hit the ball. Then the odds of hitting the ball are:

P = 3/19 = 0.158

We conclude that the odds of hitting the ball are 0.158

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The triangles are similar by SAS principle.

Similar triangles have the same shape but may have different sizes.

In similar triangles, corresponding sides are always in the same ratio.

The corresponding angles are congruent.

Therefore, using SAS ratio,

6 / 8 = 8 × 3 / 32

6 / 8  = 24 / 32 = 3 / 4

Therefore, the corresponding sides are a ratio of each other.

Therefore, the triangles are similar by SAS principles because the two triangles have two pairs of sides in the same ratio and the included angles are also equal

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The number of ways in which the name 'ESTABROK' can be made with no restrictions is 40, 320 ways.

Given the word:

ESTABROK

Then n = 8

p = 6

The formula for permutation without restrictions

P = n! ( n - p + 1)!

P = 8! ( 8 - 6 + 1) !

P = 8! (8 - 7)!

P = 8! (1)!

P = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 × 1

P = 40, 320 ways

Thus, the number of ways in which the name 'ESTABROK' can be made with no restrictions is 40, 320 ways.

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The probability of picking a red counter is therefore; 8/25.

Since the ratio of red to green is 2 :3 and there are 24 green counters, it follows that the number of red counters is;

x = (2/3)× 24 = 16 red.

The total of red and green is; 16 +24 = 40 which constitutes 80% of the total counters.

The total number of counters is therefore; 40/0.8 = 50 counters.

The probability of picking a red counter is therefore; 16/50 = 8/25.

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Students who receive a grade of at least a C must have a minimum score of 50.38.

We may assume that the cut-off will be below 67.66 % because that percentage is more than 50%.

To get the value of 67.66 - 50 = 17.66, we must search in a regular normal table.

Hence, A z value of 0.458 will cause that value to occur.

Next, increase the standard deviation of 9 by 0.458.

The result is 4.122.

This indicates that the threshold for a student earning a C or higher is the mean minus 4.122.

So, the final result is 54.50-4.122 = 50.38.

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The probability of hitting the black circle inside the target is close to 0, and the probability of hitting the white portion is close to 1.

Given:

The square's length is 10 units.

The circle's diameter is equal to two units.

To Determine:

It is necessary to determine the probability that the target's white section and black circle will both be hit.

Solution:

The square's area is 10 x 10 or 100 units.

The shaded circle's area is given by  πr² = 3.14 (1)² = 3.14 units.

The white area has a surface area of (100 - 3.14) = 96.86 units.

Probability of an event = The number of favorable events /Total number of events

The probability that it will occur in the shaded area = 3.14/100 = 0.0314  (The probability is close to 0).

The probability of hitting the white section is equal = 96.86/100= 0.9686.

(The probability is quite near to 1)

Hence, the probability of hitting the black circle inside the target is close to 0, and the probability of hitting the white portion is close to 1.

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Answer:

12.8 m.

Step-by-step explanation:

The length of the wire on the shorter pole (AC)

= √(6^2+8^2)

= √100

= 10 m.

The 2 triangles are similar so

10/16 = 8/x      where x is height of taller pole.

10x = 128

x = 12.8m