The length of a rectangle is 1 ft more than twice the width, and the area of the rectangle is 66ft. Find the dimensions of the rectangle

Answer:

The foci are located at [tex](0,\pm \sqrt{5})[/tex]

Step-by-step explanation:

The standard equation of an ellipse with a vertical major axis is [tex]\frac{x^2}{b^2}+\frac{y^2}{a^2}=1[/tex] where [tex]a^2\:>\:b^2[/tex].

The given equation is [tex]9x^2+4y^2=36[/tex].

To obtain the standard form, we must divide through by 36.

[tex]\frac{9x^2}{36}+\frac{4y^2}{36}=\frac{36}{36}[/tex]

We simplify by canceling out the common factors to obtain;

[tex]\frac{x^2}{4} +\frac{y^2}{9}=1[/tex]

By comparing this equation to

[tex]\frac{x^2}{b^2}+\frac{y^2}{a^2}=1[/tex]

We have [tex]a^2=9,b^2=4[/tex].

To find the foci, we use the relation: [tex]a^2-b^2=c^2[/tex]

This implies that:

[tex]9-4=c^2[/tex]

[tex]c^2=5[/tex]

[tex]c=\pm\sqrt{5}[/tex]

The foci are located at [tex](0,\pm c)[/tex]

Therefore the foci are [tex](0,\pm \sqrt{5})[/tex]

Or

[tex](0,-\sqrt{5})[/tex] and [tex](0,\sqrt{5})[/tex]

Answer:

Part 1) [tex]f(x)=\frac{2x-1}{x+2}[/tex] -------> [tex]f^{-1}(x)=\frac{-2x-1}{x-2}[/tex]

Part 2) [tex]f(x)=\frac{x-1}{2x+1}[/tex] -------> [tex]f^{-1}(x)=\frac{-x-1}{2x-1}[/tex]

Part 3) [tex]f(x)=\frac{2x+1}{2x-1}[/tex] -----> [tex]f^{-1}(x)=\frac{x+1}{2(x-1)}[/tex]

Part 4) [tex]f(x)=\frac{x+2}{-2x+1}[/tex] ----> [tex]f^{-1}(x)=\frac{x-2}{2x+1}[/tex]

Part 5) [tex]f(x)=\frac{x+2}{x-1}[/tex] -------> [tex]f^{-1}(x)=\frac{x+2}{x-1}[/tex]

Step-by-step explanation:

Part 1) we have

[tex]f(x)=\frac{2x-1}{x+2}[/tex]

Find the inverse  

Let

y=f(x)

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

Exchange the variables x for y and t for x

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

Isolate the variable y

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

Let

[tex]f^{-1}(x)=y[/tex]

[tex]f^{-1}(x)=\frac{-2x-1}{x-2}[/tex]

Part 2) we have

[tex]f(x)=\frac{x-1}{2x+1}[/tex]

Find the inverse  

Let

y=f(x)

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

Exchange the variables x for y and t for x

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

Isolate the variable y

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

Let

[tex]f^{-1}(x)=y[/tex]

[tex]f^{-1}(x)=\frac{-x-1}{2x-1}[/tex]

Part 3) we have

[tex]f(x)=\frac{2x+1}{2x-1}[/tex]

Find the inverse  

Let

y=f(x)

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

Exchange the variables x for y and t for x

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

Isolate the variable y

[tex]x=\frac{2y+1}{2y-1}\\ \\2xy-x=2y+1\\ \\2xy-2y=x+1\\ \\y[2x-2]=x+1\\ \\y=\frac{x+1}{2(x-1)}[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

[tex]f^{-1}(x)=\frac{x+1}{2(x-1)}[/tex]

Part 4) we have

[tex]f(x)=\frac{x+2}{-2x+1}[/tex]

Find the inverse  

Let

y=f(x)

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

Exchange the variables x for y and t for x

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

Isolate the variable y

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

Let

[tex]f^{-1}(x)=y[/tex]

[tex]f^{-1}(x)=\frac{x-2}{2x+1}[/tex]

Part 5) we have

[tex]f(x)=\frac{x+2}{x-1}[/tex]

Find the inverse  

Let

y=f(x)

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

Exchange the variables x for y and t for x

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

Isolate the variable y

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

Let

[tex]f^{-1}(x)=y[/tex]

[tex]f^{-1}(x)=\frac{x+2}{x-1}[/tex]

Answer:

Step-by-step explanation:

Area of a full circle is PI x r^2

Area = 3.14 x 8^2 = 200.96

Area of a sector is area *  central angle / full circle

Area = 200.96 x 5PI/3 / 2PI = 160PI/3

Answer is C.

Answer:[tex]\frac{160\pi }{3} units^2[/tex]

Step-by-step explanation:

Given

Angle subtended by sector is[tex]\frac{5\pi }{3}[/tex]

radius =8 units

[tex]Area of sector=\frac{\theta }{2\pi }\pi r^2 [/tex]

[tex]A=\frac{20\times 8\pi }{3}[/tex]

[tex]A=\frac{160\pi }{3}[/tex]

For this case we have that by definition, the slope of a line is given by:

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

We have the following points:

[tex](x_ {1}, y_ {1}) :( 3,2)\\(x_ {2}, y_ {2}): (- 2,3)[/tex]

Substituting we have:

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

Finally, the slope is:

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

Answer:

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

Answer:

Susanne is 16 years old.

Step-by-step explanation:

You're gonna need three equations.

Key: B = Bob, D = Dakota, s = Susanne

B = 4s

D = s - 3

B + D + s = 93

Now plug in B and D into the third equation:

4s + (s - 3) + s = 93

Now solve it:

4s + s - 3 + s = 93

6s - 3 = 93

+3 +3

6s = 96

6s/6 = 96/6

s = 16

Bob's age is 4 times greater than Susanne's age, and Dakota is 3 years younger than Susanne.

The sum of their ages is 93. Susanne's age is 16.5.

Let's assign variables to represent the ages of the individuals involved:

We are given that Bob's age is 4 times greater than Susanne's age, so we can write the equation B = 4S.

We are also told that Dakota is three years younger than Susanne, so we can write the equation D = S - 3.

The sum of their ages is given as 93, so we can write the equation B + S + D = 93.

Substituting the first equation into the second equation, we get D = 4S - 3.

Substituting the values from the second and third equations into the fourth equation, we have (4S - 3) + S + (S - 3) = 93.

Simplifying this equation, we get 6S - 6 = 93. Adding 6 to both sides, we have 6S = 99. Dividing both sides by 6, we find that S = 16.5.

Therefore, Susanne's age is 16.5.

[tex]5x + 3x -4 = 10\\8x=14\\x=\dfrac{14}{8}=\dfrac{7}{4}[/tex]

one

Answer:0ne

Step-by-step explanation:

Answer:

where is rectangle???

Answer:

10

Step-by-step explanation:

The length of AB is 10 and the length of BC is 13. CD is parallel to AB so its 10.

Answer:

asa only because the two triangles are facing each other like a reflection making them congruent

ΔWZV and ΔWZY are congruent by AAS congruency

Considering    ΔWZV         and        ΔWZY

                      ∠WVZ            =            ∠WYZ  (given)

                        ∠WZV           =           ∠WZY   ( both angles are 90° since it is given that WZ is perpendicular to VY)

                           WZ is common side

So  ΔWZV and ΔWZY are congruent (AAS congruency)

Find more about "Congruency" here: https://brainly.com/question/2938476

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Answer:

the angle Ф is 63.9 degrees.

Step-by-step explanation:

A right triangle describes this situation.  The height of the triangle is 45 ft and the base is 22 ft.  The ratio height / base is the tangent of the angle of elevation and is tan Ф.  We want to find the angle Ф:

                opp

tan Ф = ---------- = 45 / 22 = 2.045.  

               adj

Using the inverse tangent function on a calculator, we find that the angle Ф is 63.9 degrees.

(4 - 7n) – (20+5)

Simplify:

(4 -7n) - 25

Remove parenthesis:

4 - 7n -25

Combine like terms:

4-25 = -21

Now you have:  -21-7n

The term with the variable is usually rearranged to be in front, so it becomes:  -7n-21

Answer:

67.972 ÷ 10 = 6.7972

679.72 ÷ 10 = 67.972

6797.2 ÷ 10 = 679.72

6797200 ÷ 10 = 679720

Answer:

83 square inches

Step-by-step explanation:

Let's find the answer, you can see the attached file for clarity.

Because we have a rectangle measuring 8 inches by 5 inches, we can use the area of the rectangle as follows:

A1=base*height=(8 inches)*(5 inches)=40 square inches

Now, because we have a triangle over the square side of 8 inches long, we can divide the triangle into 2 rectangle triangles, each of them with a base of 4 inches and a height of 7 inches, obtaining:

A2=2*(base*height/2)=2*(4 inches)*(7 inches)/2=28 square inches

Doing the same for the other triangle we get 2 triangles with a base of 2.5 inches and a height of 6 inches, obtaining:

A3=2*(base*height/2)=2*(2.5 inches)*(6 inches)/2=15 square inches

The addition of all areas is:

A=A1+A2+A3=40 square inches + 28 square inches + 15 square inches

A=83 square inches.

In conclusion we have an area of 83 square inches.

Answer:

83

Step-by-step explanation:

Your question asks how much money was collected at the toll for a period of 8 hours.

To find the answer, we would need to gather some important information from the question.

Important information:

With the information above, we can solve the problem.

First, let's find how much money the toll makes in one hour. To find this, we need to multiply 1.50 by 160 cars, since the toll costs $1.50 and 160 cars go through it per hour.

[tex]1.50*160=240[/tex]

The toll makes $240 per hour.

Now, since we need to find how much the toll makes in 8 hours, we need to multiply 240 by 8.

[tex]240 * 8=1,920[/tex]

When you're done solving, you should get 1,920.

This means that the toll makes $1,920 in 8 hours.

Answer:

A.  s = 3/10 m.

Step-by-step explanation:

s = km  where k is a constant , s = the length of the string and m = the mass of the object.

Substituting m = 30 and s = 9:

9 = k * 30

k =  9/30 = 3/10

So the equation is s = 3/10 m.

Answer:

60 different votes.

Step-by-step explanation:

This is a permutations question. There are a total of 5 bands to be voted for, and Rafeal has to vote only for 3 of the bands. It is also mentioned that the voting has to be done for the favorite, the second favorite, and the third favorite bands from the list. This means that the order of selection is important. This means that permutations will be used. Thus, 3 bands out of 5 have to be selected in an order. This implies:

5P3 = 5*4*3 = 60 possibilities.

There are 60 different votes!!!

Answer: 60 different votes are possible

Step-by-step explanation:

We have a list of 5 bands and we must choose 3 of them. In this case, the order of the election is important. Therefore this is a problem that is solved using permutations.

The formula for permutations is:

[tex]nPr=\frac{n!}{(n-r)!}[/tex]

Where n is the number of bands you can choose and you choose 3 of them.

Then we calculate:

[tex]5P3 =\frac{5!}{(5-3)!}\\\\5P3=\frac{5!}{2!}\\\\5P3 = 60[/tex]

Finally, the number of possible votes is 60

Answer:

Oops I went too far.

The other point is (9,4).

The average rate of change is 1/5.

Step-by-step explanation:

So I think your function is [tex]f(x)=\sqrt{x}+1[/tex]. Please correct me if I'm wrong.

You want to find the slope of the line going through your curve at the points (4,f(4)) and (9,f(9)).

All f(4) means is the y-coordinate that corresponds to x=4 and f(9) means the y-coordinate that corresponds to x=9.

So if [tex]f(x)=\sqrt{x}+1[/tex], then

[tex]f(4)=\sqrt{4}+1=2+1=3[/tex] and

[tex]f(9)=\sqrt{9}+1=3+1=4[/tex].

So your question now is find the slope of the line going through (4,3) and (9,4).

You can use the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] but I really like to just line up the points vertically and subtract then put 2nd difference over 1st difference. Like this:

( 9  ,   4)

-( 4  ,   3)

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

 5         1

So the slope is 1/5.

The average rate of change of the function f on the interval [4,9] is 1/5.

A function describes the relationship between related variables.

Given that:

[tex]f(x) = \sqrt x + 1,\ 4 \le x \le 9[/tex]

The average rate of change (m) is calculated as:

[tex]m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}[/tex]

[tex]m = \frac{f(9) - f(4)}{9 - 4}\\[/tex]

So, we have:

[tex]m = \frac{f(9) - f(4)}{5}[/tex]

Calculate f(4)

[tex]f(x) = \sqrt x + 1[/tex]

[tex]f(4) = \sqrt 4 + 1[/tex]

[tex]f(4) = 2 + 1[/tex]

[tex]f(4) = 3[/tex]

Calculate f(9)

[tex]f(x) = \sqrt x + 1[/tex]

[tex]f(9) = \sqrt 9 + 1[/tex]

[tex]f(9) = 3 + 1[/tex]

[tex]f(9) = 4[/tex]

So, we have:

[tex]m = \frac{f(9) - f(4)}{5}[/tex]

[tex]m = \frac{4 - 3}{5}[/tex]

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

Recall that:

[tex]f(4) = 3[/tex] --- this represents the coordinate of the start interval

[tex]f(9) = 4[/tex] --- this represents the coordinate of the end interval

Hence, the coordinates of the end interval is (9,4)

Read more about average rates of change at:

https://brainly.com/question/23715190

Answer:

First draw two axes x and y. Then mark all points for which x=4, this is a vertical line. Do the same for the other sides and you will find a square with side length 8.

Answer:

The correct answer is 6-4i

Answer:

6 - 4i .

Step-by-step explanation:

I will assume that (10 - 51) is ( 10 - 5i) since the other number is a complex number.

You add the real parts and the imaginary parts separately.

(-4 + i) + (10 - 5i)

= (-4 + 10) + (i - 5i)

= 6 - 4i .

Answer:

√(3)/2

Step-by-step explanation:

To find the quotient, rationalize the denominator by multiplying both the numerator and denominator by √(6)

3√(8)*√(6)    =     3√(48)

4√(6)*√(6)              24

Next, simplify the top radical

12√(3) =  √(3)/2, This is the answer, it cannot be simplified any further.

 24  

For this case we must find the quotient of the following expression:

[tex]\frac {3 \sqrt {8}} {4 \sqrt {6}} =[/tex]

We combine [tex]\sqrt {6}[/tex] and [tex]\sqrt {8}[/tex] into a single radical:

[tex]\frac {3 \sqrt {\frac {8} {6}}} {4} =\\\frac {3 \sqrt {\frac {4} {3}}} {4} =\\\frac {3 \frac {\sqrt {4}} {\sqrt {3}}} {4} =\\\frac {3 \frac {2} {\sqrt {3}} * \frac {\sqrt {3}} {\sqrt {3}}} {4} =[/tex]

[tex]\frac {3 * \frac {2 \sqrt {3}} {3}} {4} =\\\frac {\frac {6 \sqrt {3}} {3}} {4} =\\\frac {6 \sqrt {3}} {12} =\\\frac {\sqrt {3}} {2}[/tex]

Answer:

[tex]\frac {\sqrt {3}} {2}[/tex]

Answer:

- [tex]\frac{27}{7}[/tex]

Step-by-step explanation:

Given

f(x) = [tex]\frac{3}{x+2}[/tex] - [tex]\sqrt{x-3}[/tex]

Evaluate f(19) by substituting x = 19 into f(x)

f(19) = [tex]\frac{3}{19+2}[/tex] - [tex]\sqrt{19-3}[/tex]

       = [tex]\frac{3}{21}[/tex] - [tex]\sqrt{16}[/tex]

       = [tex]\frac{1}{7}[/tex] - 4

       = [tex]\frac{1}{7}[/tex] - [tex]\frac{28}{7}[/tex] = - [tex]\frac{27}{7}[/tex]

Answer:

It would be 7/2s, however if you want to solve it completely, you do 7 ÷ 2. It would give you 3.5 so, s = 3.5.

5(x - 2) - 3x + 7.

First use the distributive property:

5(x-2) = 5x-10

Now you have:

5x - 10 - 3x +7

Now combine like terms to get:

2x - 3

Answer:

2x -3

Step-by-step explanation:

5(x - 2) - 3x + 7

Distribute the 5

5x -10 -3x+7

Combine like terms

5x-3x   -10 +7

2x -3

Answer:

B. 3

Step-by-step explanation:

First of all we will define rotational symmetry.

Rotational symmetry is when a shape looks the same after some rotation or less than one rotation.

The order of rotational symmetry is how many times it matches the original shape during the rotation.

So, for the given shape the rotated shape will match the original shape three times so the order for symmetry for the given shape is 3.

Hence,

the correct answer is B. 3 ..

Answer:

.333333... can be expressed as 1/3.

Step-by-step explanation:

A rational number is defined as:

any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.

aka, any number that you can express as a fraction.

Any person who has spent enough time in math should be familiar with the fact that the thirds (aka 1/3, 2/3) are repeating decimals, but are rational numbers as they can be written as whole number fractions.

If you didn't know this, don't worry. You'll get it soon enough.

Hope this helped!

Answer:

Hanan collect [tex]\frac{3}{8}[/tex] of a bag of clothes

Step-by-step explanation:

Let

x ------> amount of clothing bag that Jenny collected

y ------> amount of clothing bag that Hanan collected

we know that

[tex]y=\frac{1}{2}x[/tex] -----> equation A

[tex]x=\frac{3}{4}[/tex] -----> equation B

Substitute equation B in equation A

[tex]y=\frac{1}{2}(\frac{3}{4})[/tex]

[tex]y=\frac{3}{8}[/tex]

therefore

Hanan collect [tex]\frac{3}{8}[/tex] of a bag of clothes

Answer:

[tex]\large\boxed{\dfrac{x^2-1}{x^2-x}=\dfrac{x+1}{x}=1+\dfrac{1}{x}}[/tex]

Step-by-step explanation:

[tex]\dfrac{x^2-1}{x^2-x}=\dfrac{x^2-1^2}{x(x-1)}\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=\dfrac{(x-1)(x+1)}{x(x-1)}\qquad\text{cancel}\ (x-1)\\\\=\dfrac{x+1}{x}=\dfrac{x}{x}+\dfrac{1}{x}=1+\dfrac{1}{x}[/tex]

Answer:

its b on edge 2021

Step-by-step explanation:

Megan can have 7 different values of A for the number of 25c coins she possesses.

Given:

Megan has 25c coins and 10c coins with a total value of $1.95.

To find:

Number of different values of A (number of 25c coins) Megan can have.

Step-by-step solution:

Therefore, Megan can have 7 different values of A for the number of 25c coins she possesses.

Answer:

59.25 cm

Step-by-step explanation:

The perimeter means the sum of all the sides of a figure.

The perimeter of a triangle would be sum of all 3 sides (triangle has 3 sides).

The measure oof 3 sides are given, so we just need to add them to get the perimeter.

Perimeter = 16.3 + 18.75 + 24.2 = 59.25 cm

To find the perimeter of the triangle, add the side lengths of 16.3 cm, 18.75 cm, and 24.2 cm to get a total of 59.25 cm. The formula used is simple addition of all side lengths.

To find the perimeter of a triangle, you need to add up the lengths of all its sides. The side lengths given are 16.3 cm, 18.75 cm, and 24.2 cm.

Therefore, the perimeter of the triangle is 59.25 cm.

Answer:

The vertex is (-2,-17).

Step-by-step explanation:

We have given y=2x²+8x-9

To find the x-coordinates we use:

xv= -b/2a

where a=2 and b=8

Now put the values in the formula:

xv= -(8)/2(2)

xv=-8/4

xv= -2

Now to find the y coordinates, we will simply substitute the value in the given equation:

y=2x²+8x-9

y=2(-2)²+8(-2)-9

y=2(4)-16-9

y=8-16-9

y=-8-9

y= -17

Therefore the vertex is(-2, -17)....

Answer:

2y = 3x

Step-by-step explanation:

general formula for a straight line is given as

y = mx + b

Given 2 points (2,3) and (4,6), we can use the attached formula to calculate the slope, m of the line which connects the 2 points

m = (6-3) / (4-2) = 3/2

hence the general formula becomes

y = (3/2) x + b

Substitute  one of the given points into this equation to find b.

We pick point (2,3)

3 = (3/2) (2) + b

b = 0

hence the equation is

y = (3/2)x

2y = 3x  (answer)