An architect has designed two tunnels. Tunnel A is modeled by x2 + y2 + 28x + 52 = 0, and tunnel B is modeled by x2 – 36x + 16y + 68 = 0, where all measurements are in feet. The architect wants to verify whether a truck that is 8 feet wide and 13.5 feet high can pass through the tunnels.

Part A: Write the equation for Tunnel A in standard form and determine the conic section. Show your work. (4 points)

Part B: Write the equation for Tunnel B in standard form and determine the conic section. Show your work. (4 points)

Part C: Determine the maximum height of each tunnel. Is the truck able to pass through either tunnel without damage? If so, which tunnel(s) and why? Show your work. (7 points)

Based on the calculations, the angle (θ) of the grade to the nearest hundredth is equal to 3.38 degrees.

An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.

In Science, grade resistance simply refers to force in pounds and can be modeled by the following equation:

F = Wsinθ

Where:

Making theta (θ) the subject of formula, we have:

θ = sin⁻¹(F/W)

Substituting the given parameters into the formula, we have;

θ = sin⁻¹(160/2710)

θ = sin⁻¹(0.0590)

Theta, θ = 3.38 degrees.

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Answer: $72

Step-by-step explanation:

Oddly worded question but if I understand it correctly we need to find the marked down price and subtract $360 from it.

It is 10% off so an easy way to do the math is to find what 90% of $480 dollars is.

.90 * 480 = $432

Then we subtract $360 from this sale price.

$432 - $360 = $72

Answer:

I know that the inequality is 85-4x<40

but im not sure on how to solve it, i think the answer is  12

becuase

85-4(12)< 40

85-48<40

37<40

Step-by-step explanation:

Answer:  85 - 4x < 40; 11

Step-by-step explanation:

85 - 4x < 40

-85          -85

    - 4x < -45  

[When dividing a negative number, change the inequality sign to the opposite sign.]

         x >  11.25  

The the cars was integer, and x is greater than 11.25, therefore, Mr.Schwantz will need to order more wheels after building 11 cars.

Answer:

A

Step-by-step explanation:

x + 2 + [ 4x - [tex]\frac{x^2+6x+8}{x+4}[/tex] ] ← factorise the quadratic on the numerator

= x + 2 + [ 4x - [tex]\frac{(x+4)(x+2)}{x+4}[/tex] ] ← cancel (x + 4) on numerator/denominator

= x + 2 + (4x - (x + 2)

= x + 2 + 4x - x - 2 ← collect like terms

= 4x

Answer:

  14

Step-by-step explanation:

You want the greatest common factor of the terms {98ab^3, 84a, 140b, 112ab​}.

There are no variables that are common to all terms. 'a' and 'b' are each common to 3 of the 4 terms, but not all.

The greatest common factor of the constants cannot be larger than the smallest difference of the constants. That difference is ...

  98 -84 = 112 -98 = 14

Since 14 is a divisor of all of the constants, 14 is the greatest common factor.

__

Additional comment

Factoring out the greatest common factor, we have ...

  = 14{7ab³, 6a, 10b, 8ab}

Answer: 12x+17

Step-by-step explanation:

(hog)(x)=

h(g(x))=

h(4x+5)=

3(4x+5)+2=

12x+15+2=12x+17

Answer:

honestly, I don’t think I’m right

Step-by-step explanation:

This simplifies to

[tex]|(6-x)-9|\\\\\boxed{|-x-3|}[/tex]

So the best actor's age deviates from the mean, he receives the award at the most extreme age.

In response to this question:

Whichever z-score does have the highest absolute value, such that, the one that deviates the most from the mean, has a most extreme age.

Best actor: 31 years old, so.

The mean age of the best actors is 42.2 years, with a standard deviation of 8.2 years.

z = (x - μ)/σ

Put the values;

z = (31 - 42.2)/ 8.2

z = -1.36

Best actress:

So, at the age of 42,

The mean of the best actresses is 31.6 years, with a standard deviation of 10.3 years.

z = (x - μ)/σ

Put the values;

z = (42 - 31.6)/10.3

z = 1.01

Thus, Because the best actor's age is further from the mean, he has the most extreme age when receiving the award.

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Answer:

c) 5

Step-by-step explanation:

Solving for the value of x,

→ 3x + 9 = 24

→ 3x = 24 - 9

→ x = 15/3

→ [ x = 5 ]

Hence, option (c) is correct.

Answer:

Turn the 2 1/2 into the improper fraction which is 5/2. Now you can do 5/2 divided by 1/2. when diving turns the 1/2 to 2/1 and multiply. so 5/2 x 2/1= 1.25. 1.25 as a fraction is 1 1/4

The dimensions of the original rectangle is a length of 56.66 meter and width of 23.33 meter.

Perimeter is the sum of all the sides of a two dimensional polygon or shape.

For first rectangle let x represent width:

Length = 2x + 10; width = x

Perimeter = 2(length + width)

Perimeter = 2(2x + 10 + x) = 6x + 20

For second rectangle:

Length = 2x + 10 + 100 = 2x + 110; width = x - 20

Perimeter = 2(length + width)

Perimeter = 2(2x + 110 + x - 20) = 6x + 180

the perimeter of the new rectangle would be twice the perimeter of the original rectangle. Hence:

6x + 180 = 2(6x + 20)

x = 23.33 m, length = 2x + 10 = 56.66

The dimensions of the original rectangle is a length of 56.66 meter and width of 23.33 meter.

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According to the solving the LHS = RHS this shows the equality symmetric property.

52 = 52.

LHS is an informal shorthand again for the left-hand side of the an equation in mathematics. Likewise, RHS refers to the right-hand side. Because equality is symmetric, both sides share the same value, expressed differently.

Given the "equality" (=) relation and a = b, if b = a holds true for all a and b, equality is said to be symmetric. For all of a and b, the assertion is TRUE (no counterexample can be found). This is known as the equality symmetric property.

-21-17+25+65=52

Proving that both LHS = RHS :

-21-17+25+65=52

-21-17+25+65=52

- 38 + 90 = 52

52 = 52

So,

LHS = RHS

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The measure of AM and BM from the given coordinate points are 8.37 units respectively

The formula for calculating the distance between coordinate points is expressed according to the equation

D = √(x₂-x₁)²+(y₂-y₁)²

Given the coordinate points A (-3, -12) and M(-5, -4). The measure of the distance AM is expressed as:

AM = √(-4+12)²+(-5+3)²

AM = √(8)²+(-2)²

AM =  √70

AM = 8.37 units

Similarly;

Given the coordinate points B(-7, 4). and M(-5, -4). The measure of the distance AM is expressed as:

BM = √(-4-4)²+(-5+7)²

BM = √(-8)²+(2)²

BM =  √70

BM = 8.37 units

Hence the measure of AM and BM from the given coordinate points are 8.37 units respectively

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The operation used in the problem is Multiplication property of equality and the value of x is -14

-3.5 = x/4

- 3.5 × 4 = x

-14 = x

Check:

-3.5 = x/4

- 3.5 = -14 / 4

-3.5 = -3.5

Therefore, the operation used in the problem is Multiplication property of equality and the value of x is -14

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Weighted vote is the policy of law-making where each representative has a variable voting power.

A policy- or law-making body may use weighted voting, where each representative has a variable voting power (weighted vote) based on the number of principals who have designated them as their proxy or the size of the electorate they represent.

The challenge of distributing resources fairly among a group of individuals is to ensure that each person is given their fair share. This is fair division.

Representatives are apportioned among the states in order to create a fair split or distribution. This is apportionment.

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The quotient of the given fraction 45/9 is 5.

Quotient:

So, the quotient of 45/9 is 5 as:
45 ÷ 9 = 5

(Refer to the picture given below for working)

Therefore, the quotient of the given fraction is 5.

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Answer:

every angle equals 60°

Step-by-step explanation:

the sum of angles of any triangle is 180 so the equilateral triangle have all angles equal so 180 ÷ 3 = 60

A library's design is scaled at  [tex]\frac{1}{3}[/tex] inch = 1 feet. The library in the drawing is 12 inches height. The library's true height is 432 inches, or 36 feet.

Given that,

A library's design is scaled at  [tex]\frac{1}{3}[/tex] inch = 1 feet.

The library in the drawing is 12 inches height.

We can take  [tex]\frac{1}{3}[/tex] inch = 1 feet

1 inch=3 feet = 36 inches.

36 inches is the actual height .

Now actual height of the library is

Multiplication of the height of the library in the drawing is 12 inches and the new height 36 inches.

12[tex]\times[/tex]36=432 inches

We can say 432 inches is equal to 36 feet.

Therefore, 432 inches or 36 feet is the actual height of the library.

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Answer:

x=7

7-7/7-6=0

0/1=0

Zero divided by anything=0

14  is the perimeter of the rectangle .

What does a rectangular 's perimeter mean?

The answer provided below has been developed in a clear step by step manner.

Step: 1

Given,  A(x) = x(14-x)

Comparing with A = lw , we have

Length , l = x and

Width , w = 14 - x

Step: 2

We know,

Perimeter of rectangle ,

p = 2( l + w )

p = 2 ( x + 14 - x )

p = 28

Hence,

Perimeter of rectangle = 14

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Step-by-step explanation:

f(x) = 4x + 15

6x - 3

if x = -1 (replace x with -1 )

f(-1) = 4(-1) + 15

6(-1) -3

= -4 + 15

-6 -3

= -11

-9

"minus cancel each other when dividing"

Answer = 11

9 or 1.22

Hope this helps ...:⁠-⁠)

Answer: log4=0.60206    log15=1,17579

Step-by-step explanation:

[tex]log4=\\log2^2=\\2log2=\\2(0.30103)=\\0.60206\\\\log15=\\log(3*5)=\\log3+log5=\\0.47712+0.69897=\\1.17579[/tex]

Answer:1,3

Step-by-step explanation: it is reflecting over the x-axis, not the y-axis. when answering these questions, keep in my what axis you're working with. hope this helps.

Answer: AC=15

Step-by-step explanation:

AC=AB+BC

AC=12+3

AC=15

Answer:

[tex]\frac{36}{B^2}[/tex]

Step-by-step explanation:

Given:

[tex]AB=12\\BC=3[/tex]

Find:

[tex]AC[/tex]

First, arrange equation 1 to isolate A by dividing both sides by B:

[tex]AB=12\\A=\frac{12}{B}[/tex]

Then, arrange equation 2 to isolate C by dividing both sides by B:

[tex]BC=3\\C=\frac{3}{B}[/tex]

Now, multiply A and C together and simplify:

[tex]AC=\frac{12}{B}*\frac{3}{B}[/tex]

[tex]AC=\frac{36}{B^2}[/tex]

the value of y for the given circle will be 1 / 50 ( approx).

We are given a unit circle.

So, we get that:

centre = (0, 0)

Equation of the circle will be

x² + y² = 1

Now, we have a point (- 17 / 20, y)

Substituting the values in the equation, we get that:

(- 17 / 20)² + y² = 1

343 / 400 + y² = 1

y² = 57 / 400

y = 1 / 50 ( approx)

Therefore, we get that, the value of y for the given circle will be 1 / 50 ( approx).

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Answer: top one is 111 dont know bottom

Step-by-step explanation:

<3

Answer: f(0)=40/x

Step-by-step explanation:

f(n)=2xf(n-1)-50

f(1)=2xf(1-1)-50

f(1)=2xf(0)-50

30=2xf(0)-50

2xf(0)=80

f(0)=80/(2x)

f(0)=40/x

With the partial product method the multiplication answer is 4725.

According to the statement

We have to find that the by which strategy for multiplying 75 and 63 should result In the correct product.

So, For this purpose, we know that the

The partial product method involves multiplying each digit of a number in turn with each digit of another where each digit maintains its place.

From the given information:

We have to multiply the numbers 75 and the 63.

Then

According to the above written strategy,

75 = 70+5 and

63 = 60+3

Then

75*63 = (70*60) + (70*3) + (5*60) + (5*3)

then solve it

75*63 = (4200) + (210) + (300) + (15)

75*63 =  4410 +  315

75*63 =  4725.

So, With the partial product method the multiplication answer is 4725.

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