Charlotte wants to use a sheet of fiberboard 34 inches long to create a skateboard
ramp with a 20° angle of elevation from the ground. How high will the ramp rise
from the ground at its highest end? Round your answer to the nearest tenth of an
inch if necessary.

Answer: [tex]2tan(theta)[/tex]

Step-by-step explanation:

I know this is pre-calculus, but I want to let you know what this is actually used for in real calculus. This is a method of integration called "u-substitution" which tranforms the function of 'x' into a function of 'theta'. If we allow the value of 'x' to equal 2sec(theta), we can plug this into the function to get:

[tex]\sqrt{x^2-4} =\sqrt{(2sec(theta)^2-4} =\sqrt{4sec^2(theta)-4}[/tex]

Factor out a 4 to get:

[tex]\sqrt{4(sec^2(theta)-1)}[/tex]

Take the square root of 4 to get a 2 on the outside of the radical:

[tex]\sqrt{4(sec^2(theta)-1)}=2\sqrt{sec^2(theta)-1}[/tex]

Use the trig identity below to convert the secant to tangent:

[tex]tan^2(theta)+1=sec^2(theta)[/tex]

[tex]tan^2(theta)=sec^2(theta)-1[/tex]

Therefore our expression becomes:

[tex]2\sqrt{sec^2(theta)-1}=2\sqrt{tan^2(theta)}[/tex]

The square root of tangent is simply tangent:

[tex]2\sqrt{tan^2(theta)} =2tan(theta)[/tex]

Answer

276 square inches.

Step-by-step explanation:

Area of rectangular prism = 2(lb + bh + lh)

2(10*7 + 7*4 + 10*4)

2( 70 + 28 + 40)

2 * 138

276 square inches
please give me Brainliest

Answer:

answer is b

Step-by-step explanation:

Answer: $7 change remains

Step-by-step explanation: When doing rounding in word problems, in most situations you will have to round up regardless of numbers. Rounding to the nickel then means that the cents on the cash amounts must be .00 or .05 Following this pattern:

0.87 is rounded to 0.90

2.66 is rounded to 2.70

3.90 is rounded to 3.90

1.63 is rounded to 1.65

2.53 is rounded to 2.55

1.30 is rounded to 1.30

Then just add together the rounded amounts, which is $13

Simply subtract with the formula, 20-13=7

Answer:

4

Step-by-step explanation: If this regarding the splitting of two polynomials put through the pyth theorem.

Answer:B

Step-by-step explanation:I hope it help

Answer:

white paint

Step-by-step explanation:

i took this test last week :)

Answer:

128 ft³

Step-by-step explanation:

given the scale factor of 2 similar solids is a : b , then

ratio of volumes = a³ : b³

here a : b = 3 : 4

then 3³ : b³ = 3³ : 4³ = 27 : 64

let x be volume of larger solid then by proportion

[tex]\frac{27}{54}[/tex] = [tex]\frac{64}{x}[/tex] ( cross- multiply )

27x = 3456 ( divide both sides by 27 )

x = 128

the volume of the larger solid is 128 ft³

Answer:

Given: Volume of cone = 2464 cm3 Height of cone = 12 cm

Step-by-step explanation:

Answer:

Hope it helps you.

Answer:

x = 1/4

Step-by-step explanation:

To solve, we need to find the constant of proportionality (k) which is defined by the equation:

yx = k

[tex](68)(1/17) = k\\k = 4[/tex]

Therefore when y= 16,

[tex]16x = 4\\x= \frac{1}{4}[/tex]

When y varies inversely with x that means mathematically

  [tex]y = \frac{k}{x}[/tex]

We know for one, that when y = 68 and x = 1/17, that means

  [tex]68 = \frac{k}{\frac{1}{17} } \\68 = 17k\\k = 4[/tex]

Therefore we get the equation of the relationship between y and x as

  ⇒ [tex]y = \frac{4}{x}[/tex]

So when y = 16, then

 [tex]16 = \frac{4}{x} \\4 = 16x\\x = \frac{1}{4}[/tex]

Thus the value of x when y = 16 is 1/4 or the third choice.

Hope that helps!

Answer:

Hello Camila Sofia Pazos Motta, you have to divide by pi, not 3.

Step-by-step explanation:

Answer:

182

Step-by-step explanation:

We need to find 3/4 of 242.  To do this, multiply 3/4 by 242:

[tex]\sf \implies \dfrac34 \times 242=\dfrac34 \times \dfrac{242}{1}=\dfrac{3 \times 242}{4 \times 1}=\dfrac{726}{4}=181.5[/tex]

181.5 rounded is 182.

Therefore, approximately 182 students went on the field trip.

Answer:

1)  [tex]y=x^2+2[/tex]

2)  [tex]y=x^2-4[/tex]

3)  [tex]y=x^2[/tex]

4)  [tex]y=x^2+6x+14[/tex]

Step-by-step explanation:

Question 1

Given points:  (-2, 6)  (-1, 3)  (0, 2)  (1, 3)

This is likely to be a quadratic equation with a vertex of (0, 2) since the points (-1, 3) and (1, 3) are symmetrical about x = 0

Vertex form of quadratic equation: [tex]y=a(x-h)^2+k[/tex]

(where (h, k) is the vertex)

[tex]\implies y=a(x-0)^2+2[/tex]

[tex]\implies y=ax^2+2[/tex]

To find a, input one of the points into the equation:

[tex](1, 3)\implies a(1)^2+2=3\implies a=1[/tex]

Therefore, the equation of the graph is [tex]y=x^2+2[/tex]

Question 2

If the parabola intersects the x-axis at (-2, 0) and (2, 0) then

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

We are told that the y-intercepts if (0, -4).  Input this into the equation to find a:

[tex]\implies a(0+2)(0-2)=-4[/tex]

[tex]\implies -4a=-4[/tex]

[tex]\implies a=1[/tex]

Therefore,

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

[tex]\implies y=x^2-4[/tex]

Question 3

Given points: (-2, 4)  (-1, 1)  (0, 0)  (1, 1)

This is likely to be a quadratic equation with a vertex of (0, 0) since the points (-1, 1) and (1, 1) are symmetrical about x = 0

Vertex form of quadratic equation: [tex]y=a(x-h)^2+k[/tex]

(where (h, k) is the vertex)

[tex]\implies y=a(x-0)^2+0[/tex]

[tex]\implies y=ax^2[/tex]

To find a, input one of the points into the equation:

[tex](-2,4)\implies a(-2)^2=4\implies a=1[/tex]

Therefore, the equation of the graph is [tex]y=x^2[/tex]

Question 4

[tex]f(x) = x^2 + 5[/tex]

If we wish to move the function to the left by 3 units, we substitute x for [tex]x+3[/tex]:

[tex]\begin{aligned}\implies f(x+3) & =(x+3)^2+5\\ & = x^2+6x+9+5\\ & = x^2+6x+14\end{aligned}[/tex]

[tex]\implies y=(x+3)^2+5[/tex]

Answer: 123 and 125.

Step-by-step explanation:

Answer:

1) SAS

2) ASA

3) SSS

4) AAS

Answer:

a) Team C - lowest average/mean

b) Team A - greatest variability/range

Step-by-step explanation:

Hope this helps!

Answer:

D

Step-by-step explanation:

The equation is 4πr²

The radius is half the diameter so divide the diameter by 2

40÷2=20

4π(20)²=5026.55mm

Rounds to 5027

Answer:

103

Step-by-step explanation:

103.3's 3 is closer to 0 than 5

Answer:

1036 in.²

hope that will help you

Answer: C. A cross section parallel to the base of a right rectangular prism is congruent to the base.

Step-by-step explanation: Cross sections that are parallel to the base will give the shape of the base.  That means that when you do a cross section that's parallel to the base, you're making a horizontal line that goes left to right that is the same as the base.  Therefore, C is your answer.

Let me know if this is right! :)

Step-by-step explanation:

I am always available to help, post your worry

Answer:

[tex]\boxed{\dfrac{y}{x}}[/tex]

Step-by-step explanation:

[tex]\dfrac{\dfrac{1}{x} }{\dfrac{1}{y} } \ \text{can also be written as} \ \dfrac{1}{x} \div \dfrac{1}{y}[/tex]

-------------------------------------------

[tex]\rightarrow \dfrac{1}{x} \div \dfrac{1}{y}[/tex]

Simplifying the expression using "a ÷ b = a x 1/b"

[tex]\rightarrow \dfrac{1}{x} \times y[/tex]

[tex]\rightarrow \boxed{\dfrac{y}{x}}[/tex]

Supplementary angles are angles that sum up to 180 degrees

∠A and ∠B are supplementary angles

Find ∠B

Therefore ∠B is 138 degrees

Answer:

∠B = 138

Step-by-step explanation:

Suplementary means = 180 soooo

180=(2x-24)+(5x-27)

180=7x-51

231=7x

x=33

B=5x-27

5(33)-27= 138

Using scientific notation, it is found that the value that is equals to 6 x 10^5 is given by:

A (3 x 10^8) (2 x 10^-3)

A number in scientific notation is given by:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex].

When two numbers are multiplied, we multiply the bases and add the values of the exponents, hence:

[tex](3 \times 10^8) \times (2 \times 10^{-3}) = 6 \times 10^5[/tex]

More can be learned about scientific notation at https://brainly.com/question/16394306

#SPJ1

Answer:

The first part is perfect. Fix the second inequality.

Step-by-step explanation:

The second inequality is:

4x - y > -3

Subtract 4x.

-y > -4x - 3

Multiply by -1 remember when multiplying (or dividing) by a negative number you must REVERSE the inequality symbol.

y < 4x + 3

Your line looks great, but make it dashed. And then the shading will be below the dashed line. This creates the solution set in the triangular area in the middle bottom of the graph. The point they are asking for is not the point of intersection, it is any point in the bottom triangle, which is the doubly shaded solution set area. Use (0, -5) for example.

Answer:

I'm sorry I don't know

Step-by-step explanation:

hopefully someone solves this!

The 9th term of the geometric sequence will be 41,990,400.

A series of non-zero integers where every term after the first is obtained by increasing the one before it by a constant, non-zero value known as the scale factor.

Let a₁ be the first term and r be the common ratio. Then the nth term of the geometric sequence is given as,

aₙ = a₁ · (r)ⁿ⁻¹

The sequence is given below.

25, 150, 900, .....

The first term is 25 and the common ratio is calculated as,

r = 150 / 25

r = 6

Then the 9th term of the sequence is given as,

a₉ = 25 · (6)⁹⁻¹

a₉ = 25 · (6)⁸

a₉ = 25 · 1,679,616

a₉ = 41,990,400

The 9th term of the geometric sequence will be 41,990,400.

More about the geometric sequence link is given below.

https://brainly.com/question/11266123

#SPJ7

Answer:

Step-by-step explanation:

You have a cloth:

____________

|                        |

|                        |

|___________|

and you cut it in half.

There are three sides

Answer:

Step-by-step explanation:

The cut pieces will each have three sides:  two that are equal and one that is the hypotenuse.

If the original square had sides of length s, then the cut pieces would each have two of that length:  s and s; the third side would have length h = √(s² + s²), or h = s√2.

Answer:

I think 4 years

(not sure)

Answer: 7.1 years

Step-by-step explanation:

Lets write a simple interest expression for this:

SI = P(1 + rt)

10,000 = 1,000(1 + 0.065[t])

This model is not quite complete yet, since he is adding 1200 every year. To fix this, we simply add a constant term, 1200t, where t is the number of years that have passed.

10,000 = 1,000(1 + 0.065[t]) + 1200t

Now we just need to evaluate this:

10,000 = 1,000 + 65t + 1200t

9,000 = 1265t

.: t ≅ 7.115

It will take about 7.1 years