the perimeter of a rectangle garden is 330 feet. If the length of the garden is 94 feet , what is its width ?

The equation of the hyperbola is,

(x/12)² - 4y²/(527) = 1

The standard equation of the hyperbola is

(x/a)² - (y/b)² = 1

Here (a, 0) and (-a, 0) are vertices and asymptotes y = ± √(b/a)x

Foci are (c, 0) & (-c, 0)

Then a² + b² = c²

Here we have to give that.,

2a = 24

a = 12

And 2c = 7

c = 7/2

Therefore a = 12 and c = 3.5

Substituting a and c in Pythagorean identity;

b² = 527/4

Then, the equation of the hyperbola is

(x/12)² - 4y²/(527) = 1

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We have b = 0, which implies that the foci coincide with the vertices, making the hyperbola a degenerate case. In this scenario, the equation of the border would be a vertical line passing through the vertices/foci, given by the equation x = ±a.

To find the equation of the hyperbolic border created by the shadow on the wall, we can start by understanding the properties of a hyperbola. A hyperbola is defined as the set of all points such that the difference of the distances from any point on the hyperbola to two fixed points, called the foci, is constant.

Let's label the vertices of the hyperbola as A and B, and the foci as F1 and F2. The distance between the vertices is given as 2a inches, and the foci are located at a distance c inches from the vertices.

Using the given information, we can find the value of a and c. Since the center of the hyperbola is at the origin, the coordinates of the vertices are (±a, 0), and the coordinates of the foci are (±c, 0).

The distance between the foci is given by the equation:

c = √(a^2 + b^2)

We know that the distance between the foci is given as 2c inches, so:

2c = 2√(a^2 + b^2)

Since c is given as a distance from the vertices, we can substitute c = a - b to simplify the equation:

2(a - b) = 2√(a^2 + b^2)

Squaring both sides to eliminate the square root:

4(a - b)^2 = 4(a^2 + b^2)

Expanding the equation:

4(a^2 - 2ab + b^2) = 4a^2 + 4b^2

Simplifying the equation:

4a^2 - 8ab + 4b^2 = 4a^2 + 4b^2

Canceling out the common terms:

-8ab = 0

Dividing by -8:

ab = 0

This implies that either a = 0 or b = 0. However, since a represents the distance between the vertices and b represents the distance between the foci and vertices, we can rule out a = 0 as it would result in a degenerate hyperbola.

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Answer: 14 cm

Step-by-step explanation:

Rectangle:

x + x + (x - 2) + (x - 2) = 52

2x + 2(x - 2) = 52

2x + 2x - 4 = 52

4x = 52 + 4

4x = 56

x = 14

9514 1404 393

Answer:

  x = 1, x = 7

Step-by-step explanation:

You can see from the graph that the x-intercepts of f(x) are ...

  0 = f(-3)

  0 = f(3)

To find the corresponding values of x for f(x-4), we can solve ...

  0 = f(x -4)

  x -4 = -3   ⇒   x = 1

  x -4 = 3   ⇒   x = 7

The x-intercepts of the function after translation 4 units right are ...

  x = 1, x = 7

__

Your sketch will be the same curve moved 4 units to the right. (Add 4 to every x-value shown.)

no. of right answers = 60

no. of wrong answers = 40

Answer:

16 years

Step-by-step explanation:

Given that :

Earth's distance from sun = 93 million miles

Number of years to complete an orbit = 1 year

Average orbiting distance of new asteroid = 1488 million miles

Number of years to complete an orbit = x

93,000,000 Miles = 1

1488000000 miles = x

Cross multiply :

93000000x = 1488000000

x = 1488000000 / 93000000

x = 16 years

Period taken to orbit the sun = 16 years

Answer: 64 Earth years...

Answer:

20

Step-by-step explanation:

Answer:

n>2 2/3

Draw a filled dot at a little more than 2 1/2 and continue the line to the right.

Step-by-step explanation:

Subtract 1/3 from both sides to get

2 2/3

Flip the inequality

n> 2 2/3

I hope this helps!

Answer:

A. (5, 2)

Step-by-step explanation:

Given

[tex]\begin{cases}x+y=7,\\2x+3y=16\end{cases}[/tex],

Multiply the first equation by 2, then subtract both equations to get rid of any terms with [tex]x[/tex]:

[tex]\begin{cases}2(x+y)=2(7),\\2x+3y=16\end{cases}\\\implies 2x+2y=14,\\2x+3y=16,\\2x-2x+2y-3y=14-16,\\-y=-2,\\y=\boxed{2}[/tex]

Substitute [tex]y=2[/tex] into any equation to solve for [tex]x[/tex]:

[tex]x+y=7,\\x+2=7,\\x=7-2=\boxed{5}[/tex]

Since coordinates are written as (x, y), the solution to this system of equations is (5, 2).

Answer:

A. ( 5 , 2 )

Step-by-step explanation:

In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.

To make x and 2x equal, multiply all terms on each side of the first equation by 2 and all terms on each side of the second by 1.

Simplify.

Subtract 2x+3y=16 from 2x+2y=14 by subtracting like terms on each side of the equal sign.

Add 2x to -2x. Terms 2x and -2x cancel out, leaving an equation with only one variable that can be solved.

Add 2y to -3y.

Add 14 to -16.

Divide both sides by -1.

Substitute 2 for y in 2x+3y=16. Because the resulting equation contains only one variable, you can solve for x directly.

Multiply 3 and 2

Subtract 6 from both sides of the equation.

Divide both sides by 2.

The system is now solved.

x = 5 and y = 2

Answer:

determine the number of miles the car drives in a year.

divide that number by the cars average MPG (miles per gallon) then multiply that number by the average cost of a gallon of gas in your area.

Step-by-step explanation:

Answer:

After 10 years, Julie's account balance will be $ 363.88 and Leah's account balance will be $ 411.75, thus Leah will have more money in her account.

Step-by-step explanation:

Since Julie invests $ 200 per month in an account that earns 6% interest per year, compounded monthly, and Leah invests $ 250 per month in an account that earns 5% interest per year, compounded monthly, to determine the amount of each after 10 years, the following calculations must be performed:

200 x (1 + 0.06 / 12) ^ 10x12 = X

200 x 1.005 ^ 120 = X

200 x 1.8193 = X

363.88 = X

250 x (1 + 0.05 / 12) ^ 10x12 = X

250 x 1.00416 ^ 120 = X

250 x 1.647 = X

411.75 = X

Therefore, after 10 years, Julie's account balance will be $ 363.88 and Leah's account balance will be $ 411.75, thus Leah will have more money in her account.

Answer:

[tex]x < 4368 \frac{8}{19} [/tex]

Step-by-step explanation:

[tex]28x < 83000 + 9x[/tex]

[tex]28x - 9x < 83000[/tex]

[tex]19x < 83000[/tex]

[tex]x < 4368 \frac{8}{19} [/tex]

Answer:

The two lines meet at (-1,1)

Answer:

A = 16 ft^2

P = 20 ft

Step-by-step explanation:

P = perimeter

A = area

STEP 1: divide the shape into rectangles

Rectangle 1: 2ft*3ft

Rectangle 2: 2ft*5ft

STEP 2: Find the area of each rectangle

Equation for area of a rectangle = bh

Rectangle 1: b = 2, h = 3

Rectangle 2: b = 2, h = 5

(2 * 3) + (2 * 5)

6 + 10

16 ft^2

Now, we have to find the perimeter

STEP 1:  Find the unknown side lengths.

To find the lengths of the sides not labeled, you have to use the lengths of the sides we already know.

The length of one parallel side is 5, and the length of another parallel side is 2. The length of the unknown side starts at the same place as the top of the side length that is 5, and ends at the top of the side length that is 2. This means that we have to subtract 2 from 5 in order to find the unknown side length.

STEP 2: Add up all the side lengths

P = 2 + 5 + 5 + 2 + 3 + 3

P = 20 ft

Don't forget to label your answers!!

I hope this made sense, it's is a little hard to explain in simple terms without being able to draw, but I hope it helped.

Answer:

[tex]\boxed{\sf cos2A =\dfrac{\sqrt3}{2}}[/tex]

Step-by-step explanation:

Here we are given that the value of sinA is √3-1/2√2 , and we need to prove that the value of cos2A is √3/2 .

Given :-

• [tex]\sf\implies sinA =\dfrac{\sqrt3-1}{2\sqrt2}[/tex]

To Prove :-

•[tex]\sf\implies cos2A =\dfrac{\sqrt3}{2} [/tex]

Proof :-

We know that ,

[tex]\sf\implies cos2A = 1 - 2sin^2A [/tex]

Therefore , here substituting the value of sinA , we have ,

[tex]\sf\implies cos2A = 1 - 2\bigg( \dfrac{\sqrt3-1}{2\sqrt2}\bigg)^2 [/tex]

Simplify the whole square ,

[tex]\sf\implies cos2A = 1 -2\times \dfrac{ 3 +1-2\sqrt3}{8} [/tex]

Add the numbers in numerator ,

[tex]\sf\implies cos2A = 1-2\times \dfrac{4-2\sqrt3}{8} [/tex]

Multiply it by 2 ,

[tex]\sf\implies cos2A = 1 - \dfrac{ 4-2\sqrt3}{4} [/tex]

Take out 2 common from the numerator ,

[tex]\sf\implies cos2A = 1-\dfrac{2(2-\sqrt3)}{4} [/tex]

Simplify ,

[tex]\sf\implies cos2A = 1 -\dfrac{ 2-\sqrt3}{2}[/tex]

Subtract the numbers ,

[tex]\sf\implies cos2A = \dfrac{ 2-2+\sqrt3}{2} [/tex]

Simplify,

[tex]\sf\implies \boxed{\pink{\sf cos2A =\dfrac{\sqrt3}{2}} } [/tex]

Hence Proved !

Answer:

The correct answer is B.

Step-by-step explanation:

Since a jar contains 4 pieces of gum, 7 pieces of candy, and 3 pieces of mint, and each time you draw out an item, you record the outcome and put the item back in the jar before making another draw, to determine what is the probability that you get exactly the sequence candy-mint-candy, in that order, the following calculation should be performed:

4 + 7 + 3 = 14

7/14 x 3/14 x 7/14 = X

0.5 x 0.2142 x 0.5 = X

0.053 = X

Therefore, the probability that the chosen sequence will be obtained is 0.0530, or 5.3%.

Answer:

1. log3 81 = 4

2. 4 3/2=8

Step-by-step explanation:

1. Convert the exponential equation to a logarithmic equation using the logarithm base (3)(3) of the right side (81)(81) equals the exponent (4)(4).

log3(81)=4

or

you can remember this

loga Y= X

so, a^x =y

2. Use the definition of a logarithm,

log

b

(

x

)

=

y

⟹

b

y

=

x

, to convert from the logarithmic form to the exponential form.

Answer:

Step-by-step explanation:

The formula for arc length is

[tex]AL=\frac{\theta}{360}*2\pi r[/tex] where theta is the measure of the central angle and r is the radius. We have both of those pieces of info; filling in:

[tex]AL=\frac{30}{360}*2(3.14) (4)[/tex] and simplifying a bit:

[tex]AL=\frac{1}{12}(8)(3.14)[/tex] and a bit more:

[tex]AL=\frac{25.12}{12}[/tex] and finally, to

AL = 2.09 m

Answer:

(a) 3178

(b) 14231

(c) 33152

Step-by-step explanation:

Given

[tex]y = \frac{269573}{1+985e^{-0.308t}}[/tex]

Solving (a): Year = 1998

1998 means t = 8 i.e. 1998 - 1990

So:

[tex]y = \frac{269573}{1+985e^{-0.308*8}}[/tex]

[tex]y = \frac{269573}{1+985e^{-2.464}}[/tex]

[tex]y = \frac{269573}{1+985*0.08509}[/tex]

[tex]y = \frac{269573}{84.81365}[/tex]

[tex]y = 3178[/tex] --- approximated

Solving (b): Year = 2003

2003 means t = 13 i.e. 2003 - 1990

So:

[tex]y = \frac{269573}{1+985e^{-0.308*13}}[/tex]

[tex]y = \frac{269573}{1+985e^{-4.004}}[/tex]

[tex]y = \frac{269573}{1+985*0.01824}[/tex]

[tex]y = \frac{269573}{18.9664}[/tex]

[tex]y = 14213[/tex] --- approximated

Solving (c): Year = 2006

2006 means t = 16 i.e. 2006 - 1990

So:

[tex]y = \frac{269573}{1+985e^{-0.308*16}}[/tex]

[tex]y = \frac{269573}{1+985e^{-4.928}}[/tex]

[tex]y = \frac{269573}{1+985*0.00724}[/tex]

[tex]y = \frac{269573}{8.1314}[/tex]

[tex]y = 33152[/tex] --- approximated

Answer:

Amazon

Step-by-step explanation:

Answer:

1/5

Step-by-step explanation:

Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.

For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.

probability that the ticket drawn has a number which is a multiple of 5 =

Number of tickets that are a multiple of 5 / total number of tickets

Multiple of 5 = 5, 10, 15, 20

there would be 4 tickets that would be a multiple of 5

= 4/20

To transform to the simplest form. divide both the numerator and the denominator by 4

= 1/5

9514 1404 393

Answer:

  (a)  QP and SR

Step-by-step explanation:

The congruent central angles intercept congruent arcs QP and SR. Chords of congruent arcs are congruent.

chords QP and SR are congruent

Answer: its A

Step-by-step explanation:

CLB is better than DONDA

Answer:

2. (x,y) → (x+7,-y)

Step-by-step explanation:

Point A:

The original coordinate of point A was (-6,-6).

The coordinate after the transformation is A'(1,6), which eliminates option 3.

Point B:

The original coordinate of point B was (-2,4).

After the transformation, we have B'(5,-4), which eliminates option 1 and option 4. This means that the correct answer is:

2. (x,y) → (x+7,-y)

Answer:

x = 16, or if you didn't want the value for x,

2x + 3 = 35

Step-by-step explanation:

Three more: +3

Twice a number: 2x

Combined:

2x + 3 = 35.

Get rid of the 3 by subtracting it from both sides:

2x = 32

Get rid of the 2 by dividing it from both sides:

x = 16

Answer:

The number is 16.

Step-by-step explanation:

Let the unknown number be x.

Now we translate the sentence into an equation piece by piece.

Three more than twice a number is 35.

2x

Three more than twice a number is 35.

2x + 3

Three more than twice a number is 35.

2x + 3 = 35

Now we solve the equation.

Subtract 3 from both sides.

2x = 32

Divide both sides by 2.

x = 16

Answer: The number is 16.

P.S. Notice that x was a variable that was introduced solely to solve the problem. The original problem is a word problem, not an equation, and has no x in it. The correct answer makes no reference to x since x was used to solve the equation but is not part of the given problem. The person asking the question has no idea what x is. He just wants a number as an answer.

Answer:

Below

Step-by-step explanation:

It is 5 1/4 PERCENT not just 5 1/4.

5 1/4 % = 5.25%

= 5.25/100

= 0.0525.

Answer:

B

Step-by-step explanation:

Let the base of the triangle be b and the height be h.

The sum of the base and height is 14. Thus:

[tex]b+h=14[/tex]

Recall that the area of a triangle is given by:

[tex]\displaystyle A=\frac{1}{2}bh[/tex]

From the first equation, solve for either variable:

[tex]h=14-b[/tex]

Substitute:

[tex]\displaystyle A=\frac{1}{2}b(14-b)[/tex]

Distribute:

[tex]\displaystyle A=\frac{1}{2}(14b-b^2)[/tex]

Distribute:

[tex]\displaystyle A=-0.5b^2+7b[/tex]

Let b = x. Hence:

[tex]A=-0.5x^2+7x[/tex]

Therefore, our answer is B.

Answer:

[tex]x=2[/tex]

Step-by-step explanation:

When given the following equation;

[tex]\frac{x+3}{3x-2}-\frac{x-3}{3x+2}=\frac{44}{9x^2-4}[/tex]

One has to solve for the variable (x). Remember, when working with fractions, one must have a common denominator in order to perform operations. Since the denominators on the left side of the equation are unlike, one must change them so that they are like denominators. Multiply each fraction by the other fraction's denominator on the respective side. Remember to multiply both the numerator and denominator by the value to ensure that the equation remains true.

[tex]=\frac{x+3}{3x-2}*(\frac{3x+2}{3x+2})-\frac{x-3}{3x+2}*(\frac{3x-2}{3x-2})=\frac{44}{9x^2-4}[/tex]

Simplify,

[tex]=\frac{(x+3)(3x+2)}{(3x-2)(3x+2)}-\frac{(x-3)(3x-2)}{(3x+2)(3x-2)}=\frac{44}{9x^2-4}\\\\=\frac{3x^2+11x+6}{9x^2-4}-\frac{3x^2-11x+6}{9x^2-4}=\frac{44}{9x^2-4}[/tex]

Distribute the negative sign to simplify the left side of the equation;

[tex]=\frac{3x^2+11x+6}{9x^2-4}-\frac{3x^2-11x+6}{9x^2-4}=\frac{44}{9x^2-4}\\\\=\frac{3x^2+11x+6-(3x^2-11x+6)}{9x^2-4}=\frac{44}{9x^2-4}\\\\=\frac{3x^2+11x+6-3x^2+11x-6}{9x^2-4}=\frac{44}{9x^2-4}\\\\=\frac{22x}{9x^2-4}{=\frac{44}{9x^2-4}[/tex]

Since the denominators on opposite sides of the equation are like, one can now ignore the denominators,

[tex]=22x=44[/tex]

Inverse operations,

[tex]=22x=44[/tex]

   ÷[tex]2[/tex]       ÷[tex]2[/tex]

     [tex]x=2[/tex]

Answer:

M = 84 , r = 32

Step-by-step explanation:

Given M is directly proportional to r then the equation relating them is

M = kr ← k is the constant of proportion

To find k use the condition when r = 2, M = 14 , then

14 = 2k ( divide both sides by 2 )

7 = k

M = 7r ← equation of proportion

(a)

When r = 12

M = 7 × 12 = 84

(b)

When M = 224 , then

224 = 7r ( divide both sides by 7 )

32 = r

Answer:

75.5

Step-by-step explanation:

First, the picture is not to scale.

The Area of the bottom (2) rectangle is 33

base x height = A

11 x 3 = 33      (where did I get 3? Total height of shape is 8. Trapezoid is 5)

                      (8-5 = 3)

Area of the trapezoid:

A = [tex]\frac{h (B_{1} + B_{2}) }{2}[/tex]

  =  [tex]\frac{(5)(6 + 11)}{2}[/tex]

  =  [tex]\frac{5(17)}{2}[/tex]

  = [tex]\frac{85}{2}[/tex]

  = 42.5

42.5 + 33 = 75.5

Answer:

18

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

Identify

b = 3

y = -3

5b - y

Step 2: Evaluate