Three vertices of a rectangle are located at (1,4),(1,2), and (5,2).What are the coordinates of the fourth vertex of the rectangle.

Answer:

The trigonometric equation  (sin Θ − cos Θ)^2 − (sin Θ + cos Θ)^3 can be simplified by:Using x for Θ: (sinx - cosx)^2 - (sinx + cosx)^2 = (sin^2 x - 2sinxcosx + cos^2 x) - (sin^2 x + 2sinxcosx + cos^2 x) = - 2 sinx cosx - 2 sinx cosx = - 4 sinx cosx = - 2sin(2x)

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Expand (sinΘ + cosΘ)²

= sinΘ - cosΘ - (sin²Θ + 2 sinΘcosΘ + cos²Θ)

= sinΘ - cosΘ - sin²Θ - 2sinΘcosΘ - cos²Θ

= sinΘ - cosΘ - 2sinΘcosΘ - (sin²Θ + cos²Θ)

= - 2sinΘcosΘ - cosΘ + sinΘ - 1 → D

ANSWER

Step 3

EXPLANATION

The given polynomial expression is:

[tex]2 {p}^{2} - 3p - 7 - (3 {p}^{2} + p - 5)[/tex]

Fatau correctly expanded the parenthesis in the first step.

[tex]2 {p}^{2} - 3p - 7 - 3 {p}^{2} - p + 5[/tex]

Fatau also correctly grouped the like terms to obtain:

[tex](2- 3) {p}^{2} + (- 3 - 1)p + (- 7 + 5)[/tex]

Fatau committed a mistake at the third step.

Instead of obtaining,

[tex] - {p}^{2} - 4p - 2[/tex]

He mistakenly got:

[tex]{p}^{2} - 2p +2[/tex]

Answer:

31.8 in^2

Step-by-step explanation:

The area of a circle is pi×radius^2.

r=.5d=18/2=9

A=(3.14159)(9^2)=(3.14159)(81)=254.5

And if each peice is of equal area, the area of one peice will equal:

254.5/8=31.8

The area of single slice is 31.7925  inch².

The area of a circle is pi times the radius squared (A = π r²). Learn how to use this formula to find the area of a circle when given the diameter.

Given:

diameter= 18 inches

radius= 9 inches

Area of pizza

=πr²

=3.14*9*9

=254.34 inch²

Now, area of  8 equal slices=254.34 inch²

area of 1 equal slices=254.34 /8

                                     = 31.7925  inch²

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Answer:

hope it helps you!!!!!!!!

The volume of a cylinder with a height of 8 and a radius of 3.8 is 115.52π cubic units, and with a height of 14 and a radius of 5, it is 350π cubic units.

The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height of the cylinder.

For question 4 with a height of 8 and a radius of 3.8, the volume would be: V = π(3.8)²(8) = 115.52π cubic units.

For question 5 with a height of 14 and a radius of 5, the volume would be: V = π(5)²(14) = 350π cubic units.

These calculations illustrate how to determine the volume of cylinders using their respective dimensions, providing a fundamental understanding of geometric principles and applications.

Answer:

[tex]y=-\frac{1}{2}+7\frac{1}{2}[/tex]

Step-by-step explanation:

Let

x ----> the time in hours

y ----> the height of the candle in inches

we have the points

(1,7) and (4,5.5)

step 1

Find the slope m

[tex]m=(5.5-7)/(4-1)\\ m=-1.5/3=-0.5[/tex]

step 2

Find the equation of the line into slope point form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=-0.5\\ (x1,y1)=(1,7)[/tex]

substitute

[tex]y-7=-0.5(x-1)\\ y-7=-0.5x+0.5+7[/tex]

[tex]y=-0.5+7.5[/tex]

[tex]y=-\frac{1}{2}+7\frac{1}{2}[/tex]

Answer:

The graph of [tex]y=cos(x)[/tex] is:

*Stretched vertically by a factor of 3

*Compressed horizontally by a factor  [tex]\frac{1}{10}[/tex] .

*Moves horizontally [tex]\pi[/tex] units to the rigth

The transformation is:

[tex]y=3f(10(x-\pi))[/tex]

Step-by-step explanation:

If  the function [tex]y=cf(h(x+b))[/tex]  represents the transformations made to the graph of [tex]y= f(x)[/tex]  then, by definition:

If  [tex]0 <c <1[/tex] then the graph is compressed vertically by a factor c.

If  [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor c

If [tex]c <0[/tex]  then the graph is reflected on the x axis.

If [tex]b> 0[/tex] The graph moves horizontally b units to the left

If [tex]b <0[/tex] The graph moves horizontally b units to the rigth

If [tex]0 <h <1[/tex] the graph is stretched horizontally  by a factor [tex]\frac{1}{h}[/tex]

If [tex]h> 1[/tex] the graph is compressed horizontally by a factor [tex]\frac{1}{h}[/tex]

In this problem we have the function [tex]y=3cos(10(x-pi))[/tex] and our parent function is [tex]y = cos(x)[/tex]

The transformation is:

[tex]y=3f(10(x-\pi))[/tex]

Then [tex]c =3>1[/tex]  and [tex]b =-\pi < 0[/tex] and [tex]h=10 > 1[/tex]

Therefore the graph of [tex]y=cos(x)[/tex] is:

Stretched vertically by a factor of 3.

Also as [tex]h=10[/tex] the graph is compressed horizontally by a factor  [tex]\frac{1}{10}[/tex] .

Also, as [tex]b =-\pi < 0[/tex] The graph moves horizontally [tex]\pi[/tex] units to the rigth

Answer:

V = 3408 pi  unit^3

Step-by-step explanation:

Volume  of a cone is given by

V = 1/3 pi r^2 h

We know the radius is 12 and the height is 71

V = 1/3 * pi * (12)^2 *71

V = 1/3 * pi * 144 *71

V = 3408 pi  unit^3

Answer:

[tex]Volume=3408 \pi[/tex] [tex]units^3[/tex]

Step-by-step explanation:

Given that radius of the cone is r = 12 units

Given that height of the cone is h = 71 units

Now question says to find the volume of the given cone.

So plug these values into formula of volume of the cone.

[tex]Volume=\frac{1}{3}\pi r^2h[/tex]

[tex]Volume=\frac{1}{3}\pi (12)^2(71)[/tex]

[tex]Volume=\frac{1}{3}\pi (144)(71)[/tex]

[tex]Volume=\frac{1}{3}\pi (10224)[/tex]

[tex]Volume=\frac{10224 \pi}{3}[/tex]

[tex]Volume=3408 \pi[/tex] [tex]units^3[/tex]

Hence correct choice is D.

Answer:  d) Easton

Step-by-step explanation:

Let's evaluate Round 1 (blue) for each bowler:

Jimmy --> the lowest score is 0.5 SD below the mean

Claudia --> the lowest score was the mean

Easton --> the lowest score is 0.75 SD below the mean

Cynthia --> the lowest score was the mean

The person that had the worst game is: Easton

Answer:

easton

Step-by-step explanation:

I did the test

Explanation:

One formula for the area of a triangle is ...

Area = (1/2)ab·sin(C)

This presumes you know the measures of two sides and the angle between them. The Law of Sines is typically used where you know all the angles and only one side measure.

You would use the law of sines to find an additional side measure, then make use of the above formula for area.

To find the area of a triangle using the Law of Sines, you need to determine the lengths of two sides and the measure of the angle opposite one of those sides. Plug those values into the Law of Sines formula and solve for the missing side or angle.

The area of a triangle can be found using the Law of Sines by following these steps:

Answer: Derrick’s mean test score= 74.4

Derrick’s median test score = 81.5

Better picture of his scores is given by Median.

Step-by-step explanation:

The given data : 25, 40, 68, 85, 95, 98, 70, 78, 85, 100

[tex]\text{Mean}=\dfrac{\text{Sum of all observations}}{\text{Number of observations}}\\\\\Rightarrow\ \text{Mean}=\dfrac{744}{10}=74.4[/tex]

For Median , Arrange the data in order

25, 40, 68, 70, 78, 85, 85, 95, 98, 100

Median = Mean of two middle most value

[tex]\text{Median}=\dfrac{78+85}{2}=81.5[/tex]

Since the data set has outlier (25) and mean is affected by outlier.

So the better picture of his scores given by median value.

Answer:

(A) 74.4 (B) 81.5 (C) Median  (Look below or dont)

Step-by-step explanation:

Answer:

yes these functions are inverse

Step-by-step explanation:

so heisjsksbKjsbkaosbdjskms

Answer:

The area of each section of the circle is [tex]A=25\pi\ m^{2}[/tex]

Step-by-step explanation:

we know that

Each section represent a quarter of circle

The area of a quarter of circle is equal to

[tex]A=\frac{1}{4}\pi r^{2}[/tex]

we have

[tex]r=10\ m[/tex]

substitute

[tex]A=\frac{1}{4}\pi (10)^{2}[/tex]

[tex]A=25\pi\ m^{2}[/tex]

Answer:

Step-by-step explanation:

By my definition, no. There's a continuity up to and including just before 1 approaching from the left, and there's a continuity just after 1 going to the right. But 1 itself has a special definition h(x) = 4 when x = 1 and that makes it discontinuous.

Answer:

24 π

Step-by-step explanation:

First step is to determine the radius of the base.  We have the area, so we can easily determine the radius.  The base is a circle, and the area of a circle is given by A = π * r² , so r² = A / π

r² = (36 π) / π = 36

So, r = 6

The lateral surface of a cylinder is given by the following:

L = 2* π * r * 2

Now that we have r, we can easily calculate it:

L = 2 * π * 6 * 2 = 24π, second choice listed

Answer:

The probability that exactly one switch is good is

[tex]P(x) =0.0392[/tex]

Step-by-step explanation:

The probability that a switch is defective is:

[tex]P(D) = \frac{2}{100} =0.02[/tex]

The probability that a switch is not defective is

[tex]P(D') = 1-P(D)=0.98[/tex]

Therefore, if two switches are selected, the probability that exactly 1 is good is:

[tex]P(1=1)=P (D) P (D ') + P (D') P (D)[/tex]

[tex]P(x)=(0.02)(0.98) + (0.98)(0.02)[/tex]

[tex]P(x) =0.0392[/tex]

Answer:

P (exactly one good switch) = 0.0392

Step-by-step explanation:

We know that 2% of all switches are defective.

P (defective) = [tex]\frac{2}{100} =0.02[/tex]

So P (not defective) = 1 - P (defective) = [tex]1-0.02=0.98[/tex]

Now we have to find the probability of one good switch out of 2 that are used in a device.

P (exactly one good switch) = [tex] (0.02 \times 0.95) + (0.02 \times 0.95) [/tex] = 0.0392

Answer:

The correct answer is 12.5.

Step-by-step explanation:

When looking at the x axis, you locate the 2. After 2 minutes, the point connects at (2,12.5). Therefore, the correct answer is 12.5.

Answer:

At t = 2 minutes, remaining quantity of the radioactive element is 12.5 mg.

Step-by-step explanation:

To get the answer of this question we will solve this further with the help of the equation [tex]A_{t}=A_{0}e^{-kt}[/tex]

where k = decay constant

t = time for decay

[tex]A_{0}[/tex] = Initial quantity taken

From the graph attached we can say that 50 mg of a radioactive element remained half in 1 minute.

So the equation becomes

[tex]50=25e^{-k(1)}[/tex]

Now we take natural log on both the sides of the equation

ln50 = ln[25.[tex]e^{-k}[/tex]

3.912 = ln25 + [tex]ln(e^{-k})[/tex]

3.912 = 3.219 + (-k)lne

3.912 - 3.219 = -k [since lne = 1]

0.693 = -k

k = -0.693

Now we will calculate the remaining quantity of the element after 2 minutes

[tex]A_{t}=50.e^{-(0.693)(2)}[/tex]

              = [tex]50.e^{-1.386}[/tex]

              = [tex]\frac{50}{e^{1.386}}[/tex]

              = [tex]\frac{50}{3.9988}[/tex]

              = 12.50 mg

Now we confirm this value from the graph.

At t = 2 minutes, remaining quantity of the radioactive element is 12.5 mg.

roughly 1.5

since it says the limit as x approaches 2- it means that you are going from the left (from the negative ie 2-). If it said 2+ you would go from the right. So you should start on the left at the end of that line and follow it until it gets essentially at where 2 is. Then record that value which in this case about 1.5

The limit of the function as x approaches 2 is 3.

In mathematics, a limit is a value that a function 'approaches' as the input (or variable) 'approaches' some value. To find the limit using the given graph, we need to examine the behavior of the function as it approaches a particular value. In this case, we look for the value the function approaches as x approaches a specific number.

From the graph, we can see that as x approaches 2 from the left side, the y-values approach 3. Similarly, as x approaches 2 from the right side, the y-values also approach 3.

Therefore, the limit of the function as x approaches 2 is 3.

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Answer:

 2 a^4 -2a^2b^2 -6b^4

Step-by-step explanation:

C = 7a^4 + 5a^2b^2 -3b^4

D = 5a^4 +7a^2b^2 +3b^4

C-D = 7a^4 + 5a^2b^2 -3b^4 - ( 5a^4 +7a^2b^2 +3b^4)

Distribute the minus sign

   7a^4 + 5a^2b^2 -3b^4 -  5a^4 -7a^2b^2 -3b^4

I like to line them up vertically

 7a^4 + 5a^2b^2 -3b^4

-  5a^4 -7a^2b^2 -3b^4

--------------------------------------

 2 a^4 -2a^2b^2 -6b^4

its either a half or part of what its worth

Answer:

Step-by-step explanation:

The actual definition of a fractional equation could be:

[tex]\frac{a}{x}+\frac{b}{x+1}=c[/tex]

In words, fractional equations are those which has variables in the denominator of a fractional term, that doesn't mean that all fractions must have a unknown denominator, but at least one of the denominators should have a variable.

Therefore, according to its definition, the right answer is third option.

In addition, other options don't make sense, multiple variables is not necessarily the case for fractional equations. Similarly, not all denominators must have variables. And, having variable only in the numerators don't define the equation as fractional.

Answer:

D. 914 feet

Step-by-step explanation:

We are given the distance that a person can see on a clear day from the upper observation platform of the Eiffel tower in Paris. We are then required to estimate the height of the upper observation platform using the formula;

[tex]d=\frac{5}{6}\sqrt{h}[/tex]

Where d is the distance and h the height of the upper observation platform. The first step would be to solve for h, that is make h the subject of the formula in the above equation;

We multiply both sides of the equation by the reciprocal of 5/6 which is 6/5;

[tex]\sqrt{h}=\frac{6}{5}d[/tex]

The next step is to eliminate the square root on the Left Hand Side of the equation by squaring both sides;

[tex]h=1.44d^{2}[/tex]

Given d is 25.2, h becomes;

[tex]h=1.44*25.2^{2}\\h=914.4576[/tex]

To the nearest whole number, h becomes 914

The correct option is D. The height of the upper observation platform is approximately 914 feet

To estimate the height  h  in feet of the upper observation platform using the given formula  [tex]d = \frac{5}{6} \sqrt{h}[/tex] , follow these steps:

1. Given:

d = 25.2 miles

We need to solve for  h .

2. Substitute the given  d  into the formula:

[tex]25.2 = \frac{5}{6} \sqrt{h}[/tex]

3. Isolate [tex]\sqrt{h}[/tex]:

Multiply both sides by [tex]\frac{6}{5}[/tex] to get rid of the fraction:

[tex]25.2 \times \frac{6}{5} = \sqrt{h}[/tex]

4. Calculate the left side:

[tex]25.2 \times \frac{6}{5} = 25.2 \times 1.2 = 30.24[/tex]

So,

[tex]\sqrt{h} = 30.24[/tex]

5. Square both sides to solve for  h :

[tex](\sqrt{h})^2 = 30.24^2 \\\\h = 30.24^2[/tex]

6. Calculate  30.24^2 :

[tex]30.24 \times 30.24 = 914.0576[/tex]

7. Round to the nearest whole number:

[tex]h \approx 914 \text{ feet}[/tex]

Therefore, the height of the upper observation platform is approximately 914 feet, which matches option D.

Answer: D. 914 feet

Answer:

x ≥ -3

Step-by-step explanation:

Step  1  :

Pulling out like terms :

1.1     Pull out like factors :

  -4x - 12  =   -4 • (x + 3)

Equation at the end of step  1  :

Step  2  :

2.1    Divide both sides by  -4

Remember to flip the inequality sign:

Solve Basic Inequality :

2.2      Subtract  3  from both sides

           x ≥ -3

Inequality Plot :

2.3      Inequality plot for

        -4.000 X  - 12.000  ≥  0

Answer:

5 ≤x

Step-by-step explanation:

3x + 9 ≤7x -11

Subtract 3x from each side

3x-3x + 9 ≤7x-3x -11

9 ≤4x -11

Add 11 to each side

9+11  ≤4x -11+11

20 ≤4x

Divide each side by 4

20/4 ≤4x /4

5 ≤x

Final answer:

The probability that Mark spends a night at Rutgers University, the University of Miami, and Clemson University is 1/720, or approximately 0.00139.

Explanation:

To find the probability that Mark spends a night at Rutgers University, a night at the University of Miami, and a night at Clemson University, we assume that these choices are made without replacement from the 10 colleges he is considering. As he can only spend the night at 3 of them, his first choice has a 1 in 10 chance of being Rutgers University, his second choice a 1 in 9 chance of being the University of Miami, given that his first choice was Rutgers, and his third choice a 1 in 8 chance of being Clemson University, given that his first two choices were Rutgers and the University of Miami.

The overall probability is the product of these independent probabilities:

Probability = (1/10) × (1/9) × (1/8) = 1/720

Therefore, the probability is 1/720, or about 0.00139 when rounded to five decimal places.

Answer:

B. False

Step-by-step explanation:

Given an equation of the type x = a(y-x)^2 + h, We know that If the "y" is squared, it is horizontal (opens left or right). If a is positive, the parabola opens up or to the right. If it is negative, it opens down or to the left.

Like the y is squared and the "a" is positive then it opens to the right, so it's false

Well... for starters:

[tex]

\frac{5}{2}=5\times\frac{1}{2} \\

\frac{5}{2}=\frac{5}{1}\times\frac{1}{2}

[/tex]

And the rule is [tex]\frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}[/tex]

Therefore:

[tex]\frac{5}{2}=\frac{5\times1}{1\times2}\Longrightarrow\boxed{\frac{5}{2}=\frac{5}{2}}[/tex]

Answer:

Step-by-step explanation:

There's only 1 '6' on an ordinary die with 6 sides, so the probability of rolling a 6 is 1/6.

That of NOT rolling a 6 is the complementary probability:  1 - 1/6 = 5/6.

Answer:

1) The lateral area is LA=95 cm²

2) The surface area is SA=275  cm²

The answer is the option D) 95 cm² ; 275 cm²

Step-by-step explanation:

we know that

The surface area of the box (rectangular prism) is equal to

SA=2B+LA

where

B is the area of the base

LA is the lateral area of the box

Find the lateral area

LA=PH

where

P is the perimeter of the base

H is the height of the box

substitute

LA=2[15+6](2.26)=94.92 cm²

Round to the nearest whole number

LA=95 cm²

Find the area of the base B

B=(15)(6)=90 cm²

Find the surface area of the box

SA=2B+LA

substitute the values

SA=2(90)+95=275  cm²

1/tan^2(x)=cot^2(x)

csc^2(x)-1=cot^2(x)"trigonometric identity"

ANSWER

96 yd

EXPLANATION

Let the width of the rectangle be w, then, the length of the rectangle will be:

[tex]l = 5w[/tex]

The area of a rectangle is calculated using the formula:

[tex]Area=l \times w[/tex]

[tex]Area=5w \times w[/tex]

[tex]Area=5 {w}^{2} [/tex]

It was given that, the area of the rectangle is 320yd²

[tex]320=5 {w}^{2} [/tex]

Divide both sides by 5.

[tex]64 = {w}^{2} [/tex]

Take square root of both sides to get:

[tex]w = 8yd[/tex]

This means the length is

[tex]l = 5 \times 8 = 40yd[/tex]

The perimeter of a rectangle is given by:

P=2(w+l)

We plug in the values to get:

[tex]P=2(40 + 8) = 2 \times 48 = 96yd[/tex]

The perimeter is 96yd

The opposites of the numbers 5, -2.5, 1.15, and 915 are -5, 2.5, -1.15 and -915 respectively. The opposite of a number is its value, but it is in the opposite direction on a number line.

The opposite of a number is the value that is exactly as far from 0, but in the opposite direction on a number line. Thus, the opposite of a positive number is the same number, but negative. Similarly, the opposite of a negative number is the same number, but positive. So the opposites of the given numbers 5, -2.5, 1.15, and 915 would be -5, 2.5, -1.15, and -915 respectively.

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Answer:what is the table

Step-by-step explanation: