The scale factor for the reduction is . The length of A = 20 (one-fifth) = 4 feet What is the length of B? B = feet

Answer: 12 1/3

hope this helps.. stay safe and have a great day

Step-by-step explanation:

Answer:

Can give you the example then you have to figure out.

Step-by-step explanation:

We are assuming the center of the tower is at the origin, so we can use the standard form of a horizontal hyperbola centered at the origin: \displaystyle \frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}}=1

​a

​2

​​  

​

​x

​2

​​  

​​ −

​b

​2

​​  

​

​y

​2

​​  

​​ =1, where the branches of the hyperbola form the sides of the cooling tower. We must find the values of \displaystyle {a}^{2}a

​2

​​  and \displaystyle {b}^{2}b

​2

​​  to complete the model.

First, we find \displaystyle {a}^{2}a

​2

​​ . Recall that the length of the transverse axis of a hyperbola is \displaystyle 2a2a. This length is represented by the distance where the sides are closest, which is given as \displaystyle \text{ }65.3\text{ } 65.3  meters. So, \displaystyle 2a=602a=60. Therefore, \displaystyle a=30a=30 and \displaystyle {a}^{2}=900a

​2

​​ =900.

To solve for \displaystyle {b}^{2}b

​2

​​ , we need to substitute for \displaystyle xx and \displaystyle yy in our equation using a known point. To do this, we can use the dimensions of the tower to find some point \displaystyle \left(x,y\right)(x,y) that lies on the hyperbola. We will use the top right corner of the tower to represent that point. Since the y-axis bisects the tower, our x-value can be represented by the radius of the top, or 36 meters. The y-value is represented by the distance from the origin to the top, which is given as 79.6 meters. Therefore,

x

2

a

2

−

y

2

b

2

=

1

Standard form of horizontal hyperbola

.

b

2

=

y

2

x

2

a

2

−

1

Isolate  

b

2

=

(

79.6

)

2

(

36

)

2

900

−

1

Substitute for  

a

2

,

x

,

and  

y

≈

14400.3636

Round to four decimal places

The sides of the tower can be modeled by the hyperbolic equation

\displaystyle \frac{{x}^{2}}{900}-\frac{{y}^{2}}{14400.3636 }=1,\text{or}\frac{{x}^{2}}{{30}^{2}}-\frac{{y}^{2}}{{120.0015}^{2} }=1

​900

​

​x

​2

​​  

​​ −

​14400.3636

​

​y

​2

​​  

​​ =1,or

​30

​2

​​  

​

​x

​2

​​  

​​ −

​120.0015

​2

​​  

​

​y

​2

​​  

​​ =1

The shape of hyperbolic cooling tower is a conic section that can be described with a formula equation.

a = 28.5, b ≈ 52.65

[tex]Equation \ of \ hyperbola;\ \dfrac{x^2}{28.5^2} - \dfrac{(y-155)^2}{56.62^2} = 1[/tex]

Reasons:

The parameters of the hyperbolic cooling tower are;

Minimum diameter = 57 feet

The height at which the diameter occurs = 155 ft.

The diameter of the tower = 175 feet

Total height of the tower = 200 feet

Height at which the center of the hyperbola occurs = 155 feet

Solution:

The equation of a hyperbola is; [tex]\dfrac{(x - h)^2}{a^2} - \dfrac{(y- k)^2}{b^2} = 1[/tex]

The center of the hyperbola = (0, 155)

[tex]a = \dfrac{57}{2} = 28.5[/tex]

At y = 155,  

Therefore;

[tex]\dfrac{x^2}{28.5^2} - \dfrac{(y -155)^2}{b^2} = 1[/tex]

At y = 200 feet [tex]x = \dfrac{75 \ feet}{2} = 37.5 \ feet[/tex]

Therefore;

[tex]\dfrac{37.5^2}{28.5^2} - \dfrac{(200 -155)^2}{b^2} = 1[/tex]

b² = 2769.0340909

b ≈ 52.62

The equation of the hyperbola is therefore;

[tex]\dfrac{x^2}{28.5^2} - \dfrac{(y-155)^2}{56.62^2} = 1[/tex]

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Answer:

a

Step-by-step explanation:

:P

Answer: a.

Step-by-step explanation:

If there is a negative mark next to the whole fraction, that means both of the numbers are negative.

I am not sure if this answer is accurate. Please inform me if I am incorrect. TY.

Answer:

freeeeeeeeeeeeeee  pointtttttttttttt

Step-by-step explanation:

Answer:

y = 8x + 13

Step-by-step explanation:

slope-intercept form: y = mx + b

Given equation: [tex]y = -\frac{1}{8}x -2[/tex]

Second equation: unknown

Slope: unknown

Given point: (-2, -3)

When two lines are perpendicular, their slopes are negative reciprocals. So, since the slope(m) of the given line is [tex]-\frac{1}{8}[/tex], the slope of the line perpendicular to it is 8.

Now we know the slope of the line. To find the y-intercept, input the values of the slope and the given point into the equation format and solve for b:

y = mx + b

-3 = 8(-2) + b

-3 = -16 + b

13 = b

The y-intercept is 13.

Now that we know the slope and the y-intercept, we can write the equation:

y = 8x + 13

Hope this helps :)

In 3 hours, one good worker can paint one fourth of your house. Three good workers can thus paint three fourths of your house in three hours, leaving one fourth to be done by bad workers.

One bad worker can paint one twelfth of your house in 3 hours. There are three twelfths in one fourth, so you will need to hire three bad workers to have your house painted on time.

Answer:

117.6 meter per min

Step-by-step explanation:

since the jogger wants to complete the trail in 30 minutes and the total length of the trail is 3528m you just need to divide the length of the trail (3528) by the total amount of time to get the answer

Answer:

117.6m per minute

Step-by-step explanation:

3528:30

588:5

30 divided by 6=5

3528 divided by 6=588

Then

5 divided by 5=1

588 divided by 5=117.6

117.6m:1

Answer:

the last one is an increase of $.22

Step-by-step explanation:

the last one is an increase of $.22

Answer:

There are no partial products to this equation. There is only one product! Okay first we will multiply 4 x 6 to get 4 in our ones place, carry the 2 over the zero put the 2 down 4 x 7 is 28 put the 8 down carry the 2, 4 x 3 is 12 + 2 is 14! So you're final product is 14,824!!!

The partial products of the given expression will be ( 3000 x 4 ) + ( 706 x 4 ).

Multiplication is the process of determining the product of two or more numbers in mathematics. A product, or an expression that specifies factors to be multiplied, is what happens when you multiply two numbers in mathematics.

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

The given product is 3706 x 4 and can be written as:-

3706 x 4 = [ 3000 x 4 + 706 x 4 ]

Therefore, the partial products of the given expression will be ( 3000 x 4 ) + ( 706 x 4 ).

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If we can translate the statement "The ice rink costs $200 plus $4 per person to rent for a birthday celebration and the entire cost of the rental is $324" into an algebraic equation, we get 4x + 200 = 324, where x is the number of people at the birthday party. The solution of this equation i.e. the number of people at the birthday party is 31.

A statement of the equivalence of two expressions created by executing algebraic operations on a set of variables, such as addition, subtraction, multiplication, division, raising to a power, and root extraction, is known as an algebraic equation.

Let the number of people at the birthday party be x.

Given that the ice rink costs $200 plus $4 per person to rent for a birthday celebration. So, the rent is 4x + 200.

Also, given that the entire cost of the rental is $324.

We can write the corresponding algebraic equation as

4x + 200 = 324

Now we have to solve this equation.

So, 4x = 324 - 200 = 124

i.e. x = 124/4 = 31

Therefore the required algebraic equation is 4x + 200 = 324, where x is the number of people at the birthday party. Also, the solution of this equation i.e. the number of people at the birthday party is 31.

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Answer: 1/12

Step-by-step explanation:

Answer:

ez pts tysm

Step-by-step explanation:

Answer:

y = -1/3x + 2

General Formulas and Concepts:

Pre-Algebra

Algebra I

Perpendicular lines have the negative reciprocal slope of the original.

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

y = 3x - 11

Point (-6, 4)

Step 2: Find slope m

Negative Reciprocal of 3 = -1/3

Step 3: Define

y = -1/3x + b

Step 4: Find y-intercept b

Step 5: Write perpendicular linear equation

y = -1/3x + 2

Answer

8

Step-by-step explanation:

16

Using the distance formular, the distance between the coordinate points given is 25

Recall the relation :

Distance = √[(28 - 4)² + (5 - 12)²]

Distance = √[(24)² + (-7)²]

Distance = √(576 + 49)

Distance = √625

Distance = 25

Hence, the distance between the points is 25

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Answer:

Step-by-step explanation:

Leon visited Chicago, which is located on the shore of

Lake Michigan. The lake has a volume of about 4,920

km cubed. Chicago was a major gateway to the west in

1825 when the Erie Canal was completed. When built,

the Erie Canal was 680 long and only 100 or

10 deep. While in Chicago, Leon visited the Sear

Tower. One of the tallest buildings in the world, the

Sears Tower is 443 tall

during Leon's visit was about 7

Answer:

25

Step-by-step explanation:

trust me it's right it might be easier if you use paoer

Answer:

C) 93 r 3

Your Welcome! ^O^

   0 0 9 3

7 2 6 6 9 9

 − 0      

   6 6    

 −   0    

   6 6 9  

 − 6 4 8  

     2 1 9

   − 2 1 6

         3

Answer:

thats wrong the correct answer is 94 r 3

Step-by-step explanation:

Divide 4 wholes by 2/3 pieces to fnd number of pieces.

4 / 2/3

When you divide by a fraction, flip the fraction over then multiply:

4 x 3/2 = (4 x 3)/2 = 12/2 = 6

There are 6 pieces.

Answer:

6

Step-by-step explanation:

lets put this in terms of 3, because of 2/3. the number above the three will be divided by three to get to four. So if we multiply three by four to get twelve, we can put that over 3, and then find our answer. 12/3=4, so we know that is correct. and since we need to find how many 2/3 pieces we need, we divide 12/3 by 2/3 to get 6. so you need 6 2/3 pieces to get four wholes.

Answer:

Ai. Common ratio = 2/3

Aii. First term = 54

B. Sum of the first five terms = 422/3

Step-by-step explanation:

From the question given above, the following data were obtained:

3rd term (T3) = 24

6Th term (T6) = 64/9

First term (a) =?

Common ratio (r) =?

Sum of the first five terms​ (S5) =?

Ai. Determination of the common ratio (r).

T3 = ar²

T3 = 24

24 = ar²....... (1)

T6 = ar⁵

T6 = 64/9

64/9 = ar⁵......... (2)

The equation are:

24 = ar²....... (1)

64/9 = ar⁵......... (2)

Divide equation 2 by equation 1.

64/9 ÷ 24 = ar⁵ / ar²

64/9 × 1/24 = r³

8/27 = r³

Take the cube root of both side

r = 3√(8/27)

r = 2/3

Thus, the common ratio is 2/3

Aii. Determination of the first term (a).

T3 = ar²

3rd term (T3) = 24

Common ratio (r) = 2/3

First term (a) =?

24 = a(2/3)²

24 = 4a/9

Cross multiply

24 × 9 = 4a

216 = 4a

Divide both side by 4

a = 216/4

a = 54

Thus, the first term (a) is 54

B. Determination of the sum of the first five terms.

Common ratio (r) = 2/3

First term (a) = 54

Number of term (n) = 5

Sum of first five terms (S5) =?

Sn = a[1 –rⁿ] / 1 – r

S5 = 54[1 – (⅔)⁵] / 1 – ⅔

S5 = 54 [1 – 32/243] / ⅓

S5 = 54 (211/243) × 3

S5 = 54 × 211/81

S5 = 6 × 211/9

S5 = 2 × 211/3

S5 = 422/3

Thus, the sum of the first five terms is 422/3

The first option is correct.

if we multiply the 34 and 12 so it comes 408

And according to first option, it we add 340 and 68 so it comes 408.

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Answer:

It's C

Step-by-step explanation:

In step 2, he should have divided. Have a great day!

Answer:

C: In step 2 he should divide the equation on both sides by 5.

Step-by-step explanation:

Took the test, got it right.

Answer:

Yes, that's right:  the cross section will be a rectangle (but also a parallelogram).

Step-by-step explanation:

Answer:

y=2

Step-by-step explanation:

y = 26

If you substitute x for -3 in the equation y = 6x + 8, your equation becomes:

y = 6(-3) + 8 now you can simplify it and solve for y

6 x -3 = -18

18 + 8 = 26

y = 26

Answer:

1000000000000000005

Answer:

1000000000000005

Step-by-step explanation:

Let x be -b/2a

x = -193/2•(-16)

x = -193/-32

x = 6.03125

Now, plug this value of x into every x in the function and simplify. The max is the y value.

Can you finish?

The time at which the rocket will hit the ground to the nearest hundredth of seconds is 13 seconds.

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.

As per the given height of tower y in terms of time is seconds x

y = -16x² + 193x + 128

The height of the tower when the rocket hit the ground will be zero.

Thus, y = 0

0 = -16x² + 193x + 128

16x² - 193x - 128=0

By quadratic equation formula,

x = [-(-193) ± √((-193)²-4×16×(-128))]/ 2×16

x = [193 ± 213.168]/32

x = 12.69 and x = -0.63 since time can be never negative thus 12.69 seconds will be correct.

12.69 to the nearest hundred is 13.

Hence "The time at which the rocket will hit the ground to the nearest hundredth of seconds is 15 seconds".

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Answer:

A little over 4 and a half

Step-by-step explanation:

8 divided by 2 (making it one half) is 4 and 7/8 is greater than 1/2

Answer:

Step-by-step explanation:

Given

[tex]Length = 450\ m[/tex]

[tex]Width = 1200\ m[/tex]

Required

Determine the number of hectares  in this dimension

First, we need to calculate the area of the land

[tex]Area = Length * Width[/tex]

[tex]Area = 450m * 1200dm[/tex]

Convert dm to m

[tex]Area = 450m * 120m[/tex]

[tex]Area = 54 000 m^2[/tex]

[tex]1 hectare = 0.0001m^2[/tex]

So, we have:

[tex]1\ hectare = 0.0001m^2[/tex]

Multiply by 54000

[tex]Hectare = 0.0001 * 54000[/tex]

[tex]Hectare = 5.4[/tex]

Hence, there are 5.4 hectares