A tunnel is constructed with a semielliptical arch. The width of the tunnel is 60 feet, and the maximum height at the center of the tunnel is 25 feet. What is the height of the tunnel 5 feet from the edge? Round your answer to the hundredths place.

9.99 feet
13.82 feet
24.65 feet
25.01 feet

There are 245 gallons of antifreeze solution required.

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.

Here, Let 60% antifreeze solution  volume = x

15% antifreeze solution volume = 15%

Final concentration 50%

Process

             0.6x + 0.15(70) = 0.5(70 + x)

Simplification

                 0.6x + 10.5 = 35 + 0.5x

                 0.6x - 0.5x = 35 - 10.5

                          0.1x = 24.5

                             x = 24.5/0.1

                            x = 245 gallons

Thus, There are 245 gallons of antifreeze solution required.

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Answer:

6n+1

Step-by-step explanation:

Eliminate the parenthesis by changing the symbol of each term inside

3+[5n-2+n]

Eliminate the bracket and group similar terms

5n+n+3-2

Simplify terms

6n+1

Answer:

80

Step-by-step explanation:

when you do the math you get two answers, -90 and 80

we dont use -90 because -90 units cannot be manufactured

We know immediately that the line must pass through (-4, 3).

Answer:

width=11/2

length=8

Step-by-step explanation:

44=(2w-3) x w area for a rectangle (44) = the length (2w-3) times the width (w)

44=2w^2 - 3w  distribute

2w^2-3w-44 = 0 subtract 44 from both sides

(w+4)(2w-11) factor

width=11/2

(11/2 x 2) - 3

length = 8

Answer:

Slope: 10

Y-intercept: +9

Step-by-step explanation:

An equation written in slope-intercept form is y=mx+b. "m" is your slope and b is your y-intercept.

Option (B) FR and NR, option (C) NO and NM, and option (D) RC and RO are correct.

The measurements of the sides and angles of two or more geometrical figures determine their congruence. For example triangle's size is determined by its three sides, and its shape is determined by its three angles.

We have:

The diagram represents an unfolded paper kabuto, a samurai warrior's helmet.

Unfolded paper can be seen in the provided figure. The sheet is square.

The diagonals, in this case, are FN and AK, and the midline is CM and OI. At point R, all of these lines converge.

FR ≅ NR

AO ≅ ON

RC ≅ RO

NO ≅ NM

DV ≅ HV

Thus, option (B) FR and NR, option (C) NO and NM, and option (D) RC and RO are correct.

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Answer:

y = 1 - x

Step-by-step explanation:

9x + 9y = 9 ( divide through by 9 )

x + y = 1 ( subtract x from both sides )

y = 1 - x

Answer:

y = 1 - x

Step-by-step explanation:

9x + 9y = 9

First, take 9x to the right side.

9y = 9 - 9x

9y = 9 ( 1 - x )

Divide both sides by 9.

y = 1 - x

The area of wafer required to make the ice cream cone 68.75 cm²

The area is the amount of space within the perimeter of a 2D shape. It is measured in square units, such as cm², m², etc.

Given:

r= 2cm, l=9 cm

Surface area,

=πr(l +r)

=3.14*2(9 + 2)

= 6.25*11

=68.75 cm²

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Answer:

Step-by-step explanation:

Comment

I'm going to assume that this is not a closed figure. The top is open like a water trough for horses.

There are 2 semicircular ends which add up to 1 whole circle.

There is 1 base area. The base area has a width of one of the semicircles. It has a length of 15 cm.

Solution

2 semi circles

r = d / 2

r = 20/2

r = 10

Area = pi r^2    This area is for 2 semicircles which = 1 circle.

Area = 3.14 * 10^2

Area = 3.14 * 100

Area =                                                  314

Trough

r = d / 2  

d= 20

r = 20/2

r= 10

w = 2*pi*r / 2

w = 2*3.14 *10/2

w = 31.4 cm

L = 15 cm

Area = 15 * 31.4

Area =                                                   471

Total Area =                                         785                              

Answer:

x = 1

Step-by-step explanation:

To solve an equation for a variable, we need to isolate (get the variable alone on one side)

(the order of the following was determined by PEMDAS)

5x + 5 = 5 (10 ÷ 5)   [simplify inside parentheses]

5x + 5 = 5 (2)

5x + 5 = 10

     - 5    -5             [subtract 5 from both sides to isolate x]

5x = 5

÷5    ÷5     [divide both sides to get x]

x = 1

hope this helps!!

Using translation concepts, the correct statement is given by:

If function f was translated down 4 units, the f(x) values would be subtracted by 4. A point in the table for the transformed function would be (1,9).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

A translation down 4 units means that the output values are subtracted by 4, hence the table would be given by:

x    1  2  3   4    5

f(x) 9 15 33 87 249

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Answer:

The CORRECT answer is:

1. f(x)

2. decreased by 4

3. (4, 87)

Step-by-step explanation:

Took the test

Answer:

12pi cm

Step-by-step explanation:

The Perimeter of the full shape is the sum of the lengths of the edges of the parts.  For convenience in referencing them, we'll call the large curve "[tex]curve_{big}[/tex]" and the three smaller curves "[tex]curve_1[/tex]" "[tex]curve_2[/tex]" "[tex]curve_3[/tex]" in order from left to right.

Thus, the Perimeter of the full shape can be written as an equation:

[tex]P_{overall} = Length(curve_{big})+Length(curve_1)+Length(curve_2)+Length(curve_3)[/tex]Since all of those edge lengths are curves, and the question states that all of the curves are made from parts of circles, then we need to know how to find the length of the edge of a circle.

Parts of a circle

Since values in the diagram are diameters, use the formula for the Perimeter of a circle [tex]P=\pi d[/tex] (where d is the diameter).

Let's call the diameters of each of our curves "[tex]d_{big}[/tex]"  "[tex]d_1[/tex]"  "[tex]d_2[/tex]"  "[tex]d_3[/tex]", with the subscripts denoting which curve we're referring to.

Note that for each curve, the curve only represents half of a circle.  So, to find the length of each curve, we'll need half of the full perimeter of each circle.

So for instance: [tex]Length(curve_{big})=\frac{1}{2} \pi d_{big}[/tex]

Substituting back into the main equation above:

[tex]P_{overall} = Length(curve_{big})+Length(curve_1)+Length(curve_2)+Length(curve_3)[/tex][tex]P_{overall}=\frac{1}{2} \pi d_{big} + \frac{1}{2} \pi d_{1} + \frac{1}{2} \pi d_{2} + \frac{1}{2} \pi d_{3}[/tex]

Note that all terms have common factors of "one-half" and "pi" in them.  These can be factored out:

[tex]P_{overall}=\frac{1}{2} \pi (d_{big} + d_{1} + d_{2} +d_{3})[/tex]

The diameter for the large Curve, is the sum of the three small diameters, so [tex]d_{big}=12cm[/tex], and [tex]d_{1}=d_{2}=d_{3}=4cm[/tex]

Substituting and simplifying (in terms of pi):

[tex]P_{overall}=\frac{1}{2} \pi ( (12cm) + (4cm) + (4cm) + (4cm) )\\P_{overall}=\frac{1}{2} \pi ( 24cm)\\P_{overall}=12 \pi cm[/tex]

Additional Understanding

Interesting for this problem, since the diameters of the 3 small curves formed the diameter of the large curve [tex]d_{1} + d_{2} + d_{3} =d_{big}[/tex], one could make a different substitution into one of our formulas above:

[tex]P_{overall}=\frac{1}{2} \pi (d_{big} + d_{1} + d_{2} +d_{3})[/tex]

[tex]P_{overall}=\frac{1}{2} \pi (d_{big} + (d_{big}))[/tex]

[tex]P_{overall}=\frac{1}{2} \pi (2d_{big})[/tex]

[tex]P_{overall}=\pi d_{big}[/tex]

Notice that [tex]\pi d_{big}[/tex] is just the full perimeter of a circle with the big diameter.  

So, if one imagined starting with a full circle with the big diameter, even though the bottom half of the circle was turned into a bunch of smaller half circles, since they were in a line along the diameter of the large circle, the full perimeter of the new shape didn't change.

The number of smaller circles doesn't need to be 3 either... as long as it goes the full distance across, right along the diameter.

The intersection between the complement of set A and the complement of set B is 7.

A Venn diagram is a visual representation that shows mathematical sets as circular curves inside of a rectangle (known as the universal set).

From the Venn diagram, we are to find the intersection between the complement of set A and the complement of set B.

[tex]\mathbf{A^c = \{ 7,6,11 \}} \\ \\ \\ \mathbf{B^c = \{7,9,13 \}}[/tex]

Therefore, the intersection between the two sets is the set of elements that exists in both of them. Therefore, we have:

[tex]\mathbf{n(A^c \cap B^c) = \{7\}}[/tex]

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Answer:

g(x) = sin(x)

f(x) = e^x

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]f(x)=e^x\\g(x)=sin~x\\y=f(g(x))=f(sin~x)=e^{sin~x}[/tex]

Answer:

140km

Step-by-step explanation:

Distance = Speed x Time

= 70km/h x 2 hours

= 140km

The length of the box made by Mr. Baker is 10-inch

Mr. Baker has strip of 48- inch long  oak, by this strip he is making the rectangle box of width 14-inch.

The rectangle is 4 sided geometric shapes whose opposites are equal in lengths and all angles are about 90°.

As Mr. Baker has a strip that is 48-inch long and he made a rectangle box with it.

The width of the  box = 14 inches
now the length of the box = (total length of the strip - 2* width of the box)/2
⇒ length of the box = (48 - 2*14)/2
⇒ length of the box = 10 inches

Thus the Mr. Baker made the box which is 10 inches long.

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The solution of the given quadratic equation is x=-2 or x=-3.

The given quadratic equation is x²+5x+6=0.

The different methods of solving quadratic equations are factoring, completing the square or using the quadratic formula.

By using the splitting middle term method we can solve x²+5x+6=0.

That is, x²+2x+3x+6=0

⇒x(x+2)+3(x+2)=0

⇒(x+2)(x+3)=0

⇒(x+2)=0, (x+3)=0

⇒x=-2 or x=-3.

Therefore, the solution of the given quadratic equation is x=-2 or x=-3.

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[tex]1) \text{ } 2^{1/2}=\sqrt{2}\\\\2) \text{ } 2^{2/3}=\sqrt[3]{2^{2}}\\\\3) \text{ } 3^{3/2}=\sqrt{3^{3}}\\\\4) \text{ } 3^{1/3}=\sqrt[3]{3}[/tex]

Answer: correct radical forms are:

[tex]2^\frac{1}{2} = \sqrt{2}[/tex]

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

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

[tex]3^\frac{1}{3} = \sqrt[3]{3}[/tex]

Step-by-step explanation:

Radical form : If n is a positive integer that is greater than 1 and a is a real number then, [tex]\sqrt[n]{a} =a^\frac{1}{n}[/tex] where n is called the index, a is called the radicand, and the symbol √ is called the radical.

therefore,  

radical form of given values are :

[tex]2^\frac{1}{2} = \sqrt{2}[/tex]

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

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

[tex]3^\frac{1}{3} = \sqrt[3]{3}[/tex]

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Answer:

-3 - false

0 - true

1 - true

2 - false

4 - true

Step-by-step explanation:

the "zeros" of a function are its x-intercepts

(because that is when the function = zero [0])

So, we can look at the x-intercepts of the graph to find the zeros:

at 0, 1, and 4 the function = 0, meaning that those are zeros of the function

hope this helps!! have a lovely day :)

Answer: A. [tex]\frac{12}{13}[/tex]

Step-by-step explanation:

The best way to remember this is SOH-CAH-TOA. For sin, it would be the opposite angle over the hypotenuse. The opposite angle of ∠C is 24 and the hypotenuse is 26. But that isn't in the answer choices, so you'll simplify the fraction.

[tex]\frac{24}{26} =\frac{12}{13}[/tex], therefore, the answer is A.

I hope this helps! Pls mark brainliest!! :)

Remember that for a given angle θ, any point on the unit circle is written as:

(cos(θ), sin(θ)).

And remember that:

cos(45°) = sin(45°) = √2/2

Then the angle θ = 45° is a solution.

To find another positive solution, we just add the period of the circle, which is 360°.

θ = 45° + 360° = 405°

Adding the period again:

θ = 405° + 360° = 765°

So the 3 positive solutions can be:

{45°, 405°, 765°}

To get the negative angles we just subtract the period:

45° - 360° = -315°

We can do that again:

-315° - 360° = -675°

So the two negative angles are:

{-315°, -675°}

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Let the numbers be x and x/7

Now

The numbers are

Answer:

7x+X=824

8X/8=834/8

x=108

Step-by-step explanation:

hope I helped

Answer:

you can buy 98 beds and buy dresses by rest of the money

Answer:

It appears to already be solved. What do you need help with?

Step-by-step explanation:

The time taken for Terick to run one complete mile is determined as 12 minutes

The speed of chad is calculated as follows;

s = distance/time

s = (3.25 miles)/(40)

s = 0.08125 miles/min

2/3 of a mile = 8 mins

1/3 of a mile = ?

1/3 of a mile  =  4mins

1 mile = 8 mins + 4 mins = 12 mins

Thus, the time taken for Terick to run one complete mile is determined as 12 minutes.

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Answer:

7

Step-by-step explanation:

The length of AB is the distance between A and B which is B-A -> 13-6= 7

Answer:

30%

Step-by-step explanation:

First we find out the difference between them:

$654,030 - $457,821 = $196,209

Then we compare it with the original price:

196,209/654,030 = 0.3

Since 0.3 is 30%, that is 30% decrease in value.