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A railroad tunnel is shaped like a semi-ellipse, as shown below. A semiellipse is shown on the coordinate plane with vertices on the x axis and one point of intersection with the positive y axis. The height of the tunnel at the center is 35 ft, and the vertical clearance must be 21 ft at a point 8 ft from the center. Find an equation for the ellipse.

Answer:

y = 5

Step-by-step explanation:

The given equation to us is

⇒ -4y = -20

⇒ y = -20/-4

⇒ y = 5

Therefore this line will pass 5 units away from y axis. For graph refer to the attachment .

More Information :-

Step-by-step explanation:

their mean is....

6+3+2+1+3+2+1+3+0+1/10=2.1

3+2+1+1+4+0+1+2+0/10=1.4

1+1+2+2+2+4+3+1+1+1/10=1.8

2+3+3+1+2+2+2+1+7+1/10=2.4

the means are 2.1,1.4,1.8,2.4

the average mean is

21+14+18+24/40

32+45/40

77/40=1.925

the average mean is 1.925

Answer:

[tex]4x-8+4y[/tex]

Step-by-step explanation:

We are given that an expression

[tex]4(x-2+y)[/tex]

We have to find an equivalent expression using distributive property .

Distributive property:

[tex]a\cdot (b+c)=a\cdot b+a\cdot c[/tex]

Using the property

[tex]4(x-2+y)=4(x-2)+4\cdot y[/tex]

[tex]4(x-2+y)=4x+4(-2)+4y[/tex]

[tex]4(x-2+y)=4x-8+4y[/tex]

Hence, the equivalent expression  of the given expression is given  by

[tex]4x-8+4y[/tex]

Step-by-step explanation:

Therefore, the factors are x + 6 and 2x − 9.

The factors of the polynomial are (2x-9)(x+6)

Factors are the numbers that can divide a number exactly. Hence, after division, there is no remainder left. Factors are the numbers you multiply together to get another number. Thus, a factor is the divisor of another number.

Given is a polynomial 2x²+3x-54, we need to find its factors,

So,

Factors :-

= 2x²+3x-54

= 2x²+12x-9x-54

= 2x(x+6)-9(x+6)

= (2x-9)(x+6)

Hence, the factors of the polynomial are (2x-9)(x+6)

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Answer:

B-10% discount on price

Step-by-step explanation:

A - $1050 - 80 = $970

B - $900 + $45 = $945

C - $1000

D - $1025 - $985

Answer:

store b

Step-by-step explanation:

Answer:

1.5m + 1 ≤ 25

Step-by-step explanation:

Given:

Total amount of gift card Miguel have = $25

Cost of each song = $1.50

Account activation fee = $1

Find:

Inequality

Computation:

Assume;

Number of song Miguel have = m

So,

Total amount of gift card Miguel have ≥ (Cost of each song)(Number of song Miguel have) + Account activation fee

1.5m + 1 ≤ 25

Answer:

Multiplication

Amount Tom earns per hour = $7

Step-by-step explanation:

Amount Jeff earns per hour = $14

Amount Tom earns per hour = 1/2 × $14

Note: 1/2 = 0.5

Amount Tom earns per hour = 1/2

× $14

= 0.5 × $14

= $7

Amount Tom earns per hour = $7

Answer:

sin o = opposite/hypotenuse

sin o= 7/12

Answer:

[tex]q = 3[/tex]

Step-by-step explanation:

[tex]3q−2=7[/tex]

[tex]3q=7+2[/tex]

[tex]3q=9[/tex]

[tex]q = 3[/tex]

Answer:

760

Step-by-step explanation:

25%= 190

100 = 25 × 4

100% (total number of people) = 190 × 4 = 760

The line passes through the y-axis at point (0,4).

Step-by-step explanation:

On a coordinate plane, line DF goes through points (-1,-3) and (2,3).

So, the slope of the line DF is \frac{- 3 - 3}{- 1 - 2} = 2

−1−2

−3−3

=2

Then the straight line which is parallel to DF will be given by

y = 2x + c.

Where, c is any constant and we have to evaluate it if this line passes through the point (-4,-4).

So, - 4 = 2(- 4) + c

⇒ c = 4

So, the straight line which is parallel to DF and passes through the point (-4,-4) is y = 2x + 4.

Now, putting x = 0, we get, y = 4.

Therefore, the line passes through the y-axis at point (0,4). (Answer)

Answer:

The answer would be D

Step-by-step explanation:

Answer:

Option number B

Step-by-step explanation:

As per the statement:

Pieter wrote and solved an equation that models the number of hours it takes to dig a well to a level of 72 feet below sea level.

Given the equation as:

7h - 5 ( 3h -8 ) = -72

Using distributive property, 

a ⋅ ( b + c ) = a ⋅ b + a ⋅ c

7h - 15h + 40 = - 72

Combine like terms;

-8h + 40 = -72

Subtract 40 from both sides we have;

-8h 8= -112

Divide both sides by -8 we have;

h = 14 hours

Therefore, the statement is true about Pieter’s solution is, It must be a positive number since it represents a number of hours.

Answer:

d

Step-by-step explanation:

o

Step-by-step explanation:

There's on;ly one way I know of that this can be done.You must start at a1 and work your way up to a5

a1 = -3n that's given

a2 =

ok this is answer any questions

Answer:

Kenji is wrong

Step-by-step explanation:

3⁵ · 4⁵ = (3 · 4)⁵ = 12⁵

but 12¹⁰ ≠ 12⁵

so , kenji is wrong

Answer:

1 and 2.....then 3 is a different question

Answer:

2.56 * 10^11 L

Step-by-step explanation:

1 body has 40 L

Thus, the amount in 6.4 billion would be;

40 * 6.4 * 10^9

= 256 * 10^9

= 2.56 * 10^2 * 10^9

= 2.56 * 10^11 L

Answer:

Approximately 2

Step-by-step explanation:

103 divided by 53 is 1.94

Round 1. 94 up to a whole number is approximately 2 wood pieces.

Answer:

The triangles are similar.

Step-by-step explanation:

They are similar because they have the same angles. They may be the same size, but it would be best to refer to whatever definition you were given.

The correct descriptions from the list accurately describe the relationship between QRS and TUV is,

⇒ Similar

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

Two triangles are shown in figure.

Here, All the corresponding angles are same in both triangles.

And, The ratio of their corresponding sides are,

In triangle TUV;

⇒ 90 / 108 = 30 / 36

In triangle QRS;

⇒ 30 / 36

Hence, The correct descriptions from the list accurately describe the relationship between QRS and TUV is,

⇒ Similar

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[tex]( - \frac{3}{4} )( \frac{7}{8} )[/tex]

[tex] = \frac{ - 3}{4} \times \frac{7}{8} [/tex]

[tex] = \frac{ - 21}{32} [/tex]

_______________________________________

[tex]( \frac{2}{3} )( - 4)(9)[/tex]

[tex] = \frac{2}{3} \times - 4 \times 9[/tex]

[tex] = \frac{ - 72}{3} [/tex]

[tex] = - 24[/tex]

_______________________________________

[tex]( \frac{5}{16} )( - 2)( - 4)( - \frac{4}{5} )[/tex]

[tex] = \frac{5}{16} \times - 2 \times - 4 \times \frac{ - 4}{5} [/tex]

[tex] = \frac{ - 160}{80} [/tex]

[tex] = \frac{ - 16}{8} [/tex]

[tex] = - 2[/tex]

_______________________________________

[tex](2 \frac{3}{5} )( \frac{7}{9} )[/tex]

[tex] = \frac{13}{5} \times \frac{7}{9} [/tex]

[tex] = \frac{91}{45} [/tex]

Answer:

The temperature at the start is 35F

The temperature of the room is 74F

Step-by-step explanation:

Given

[tex]T(m) = 74 - 39(0.87)^m[/tex]

Solving (a): The temperature at the start.

To do this, we set: [tex]m = 0[/tex]

So, we have:

[tex]T(0) = 74 - 39(0.87)^0[/tex]

[tex]T(0) = 74 - 39*1[/tex]

[tex]T(0) = 74 - 39[/tex]

[tex]T(0) = 35[/tex]

Hence, the temperature at the start is 35F

Solving (b): The room temperature

We have:

[tex]T(m) = 74 - 39(0.87)^m[/tex]

To get the temperature of the room, we simply remove the exponential function.

So, we have:

[tex]Initial = 74[/tex]

Hence, the temperature of the room is 74F

The initial temperature of the liquid is 35 F and the room temperature is 74 F.

The melting point is the temperature at which the solid starts converting into liquid.

Given here,

[tex]T_m = 74- 39(0.87)^m[/tex]

Leat the [tex]m = 0,[/tex]

So,

[tex]T_0 = 74- 39(0.87)^0\\\\T_0 = 35 \rm \ F[/tex]

Thus the initial temperature is 35 F.

Now remove the exponential to get the room temperature,

So,

[tex]T_{RT} = 74[/tex]

Therefore, the initial temperature of the liquid is 35 F and the room temperature is 74 F.

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Answer:

Option D, 140 sq. units

Step-by-step explanation:

Area of the rectangle part, 11*5 = 55 sq. units

Area of the pentagon part (3.4*5)*5/2 = 42.5 sq. units

Total area,

55+2*42.5 sq. units (since there are two pentagons)

= 55+85 sq. units

= 140 sq. units

Answer:

D.6b C.v B.8squared 7b<9

Step-by-step explanation:

we don't see a picture, and you don't not give us any detailed information (all specific numbers like the scale factor are missing in your text). so, it is impossible to calculate anything.

but you can do it yourself very easily.

let's call the same factor "f".

that means you have to multiply the side lengths of every side of ABC by that factor f to get the cushions side lengths is the sides in DEF.

that's it.

that's all that has to be done.

so, assuming that A -> D, B -> E, C -> F

then

AB × f = DE

BC × f = EF

CA × f = FD

as I said - that's it. just use the actual numbers and multiply.

All the lengths of DE, EF, and DF are, 4 , 8 and 12 respectively.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Triangle ABC and DEF are similar.

And, the scale factor from ABC to DEF is 2.

Now, We get;

This means that each side of the triangle ABC were multiplied by the scale factor 2 in order to get the triangle DEF.

Based on the above, you can set up the following equations;

⇒ DE = 2AB

⇒ EF = 2BC

⇒ DF = 2CA

Finally, substituting the corresponding lengths of the triangle ABC into the equations, and then evaluating, you get the following result:

⇒ DE = 2 x 2 = 4

⇒ EF = 2 x 4 = 8

⇒ DF = 2 x 6 = 12

Thus, All the lengths of DE, EF, and DF are, 4 , 8 and 12 respectively.

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Answer:

178m squared

Step-by-step explanation:

make 3 rectangular shapes

shape 1 ) 18×5=90

shape 2) 13×6= 78

shape 3) 5×2=10

Add up all the answers and that's the ans

90+78+10=178

Answer:

-1/35

Step-by-step explanation:

* means multiply

because of pemdas you should do three multiplication parts first

(1/4×2/5)+(-1/6×3/2)+(3/7×2/5)

1/20 - 3/12 + 6/35

3/60 - 15/60 + 6/35

-12/60 + 6/35

-1/5 + 6/35

-7/35 + 6/35

-1/35

Answer:

3/140

Step-by-step explanation:

1/4 × 2/5 + (-1/6) × 3/2 + 3/7 × 2/5 ​=

= 2/20 - 3/12 + 6/35

**********************************************

We need the LCD of 20, 12, 35.

20 = 2^2 * 5

12 = 2^2 * 3

35 = 5 * 7

LCD = 2^2 * 3 * 5 * 7 = 420

**********************************************

= 42/420 - 105/420 + 72/420

= 9/420

= 3/140