Use what you learned in the lesson and the online content to answer the following question: Which renewable source of energy should the United States focus its research and development efforts to make this source of energy our country’s main energy source by the year 2050? Why?

To find the base of a trapezoid, you can view the trapezoid as two right triangles joined together. The base of the trapezoid is the sum of the bases of these triangles. Depending on the orientations of the sides of the trapezoid and the height, you might need to use the Pythagorean theorem.

The question asks to find the length of the base for a given trapezoid. In order to do this, we can use concepts from geometry and trigonometry. Consider the trapezoid as two right triangles back to back. The base of the trapezoid is the sum of the bases of the two right triangles.

For example, if you have a trapezoid with sides A and B, and the height is H, you can use these sides and the trigonometric principles to calculate the lengths of the bases. If side A or B is not perpendicular to the base, you would need to use the Pythagorean theorem. That formula is A^2+B^2=C^2, where C is the hypotenuse of the right triangle formed.

In case, the sides A and B are perpendicular to the base, the lengths of the bases would simply be side A + side B. This would give you the total length of the base of the trapezoid.

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The point was reflected over the y -axis and translated up 4 units.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

We have,

A point located at (5, -2) undergoes two transformations.

Its image is located at (-5, 2).

The point was reflected over the y-axis and translated up 4 units, as shown by the coordinates becoming (-5, -2), respectively, when the point was reflected over the y-axis and (-5,2).

So, The point was reflected over the y -axis and translated up 4 units.

Learn more about transformation here:

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Answer: Hello there!

Let's define x = age of parent 1, and y = age of parent 2, and suppose that y is the oldest one.

we know that:

x + y = 92

x*y = 2107

now we have a system of equations that we need to solve:

the first step is isolate one of the variables in one of the equation, let's isolate x in the first equation:

x = 92 - y

now we can replace it in the second equation and find the value of y.

x*y = 2107

y*(92 - y) = 2107

92y - y^2 = 2107

now we need to solve a cuadratic equation!

-y^2 + 92y - 2107 = 0

using the Bhaskara formula, we get:

[tex]y = \frac{-92 +/- \sqrt{92^{2} -4 *(-1)*(-2107) } }{-2} = \frac{-92 +/- \sqrt{36} }{-2} = \frac{-92 +/- 6}{-2}[/tex]

so we have two solutions:

y = (-92 + 6)/(-3) = 43

y = (-92 - 6)/(-2) = 49

because y is the oldest one, we need to take the biggest solution, this is y = 49.

so the oldest parent has 49 years.

if you want to find the age of the other parent, replace this in the first equation:

y + x = 92

49 + x = 92

x = 92 - 49 = 43

Final answer:

The total surface area for the 4 cylindrical coasters, each with a height of 0.5 inches and a radius of 2.5 inches, is approximately 188.4956 square inches.

Explanation:

Deena has a set of 4 coasters, each shaped like a cylinder.

To calculate the surface area of one coaster, we need to find the area of the two circular bases and the area of the side that wraps around the cylinder (the lateral surface area).

The formula for the surface area of a cylinder is SA = 2πr(h+R), where r is the radius, h is the height, and R is the radius of the bases.

Given a height of 0.5 inches and a radius of 2.5 inches:

SA = 2π(2.5)(0.5+2.5)

SA = 2π(2.5)(3)

SA = 2π(7.5)

SA = 15π

The result is the surface area for one coaster. As we have 4 coasters, we multiply this result by 4:

Total surface area for 4 coasters = 4 × 15π ≈ 4 × 47.1239 ≈ 188.4956 square inches.

Answer:

16

Step-by-step explanation:

if 2/3 is used by one scarf, then we can divide 2/3 into 12

12/1 × 2/3

12/1 ×3/2= 36/2

36/2= 16

Christopher can create a total of 12 scarves with the 12 balls of yarn he buys, based on the ratio of 2/3 of a ball needed for one scarf.

Christopher can make scarves from yarn, where it takes 2/3 of a ball of yarn to make one scarf. If he buys 12 balls of yarn, we need to calculate the total number of scarves he can make.

Let's find out how many scarves he can create with 12 balls:

Therefore, Christopher can make 12 scarves with 12 balls of yarn.

7 9/10 is the correct answer. I use the wonderful world of google to help me with questions like that one

Answer:

A. Length of PQ = Length of P′Q′

Step-by-step explanation:

We are given,

Figure PQRS is rotated by 180° counter-clockwise about the origin to obtain P'Q'R'S'.

Since, we know that, 'Rotation' is a transformation that turns the figure around a fixed point to a certain degree.

We get that, rotation does not affect the length of the figure.

So, the length of PQ = length of P'Q' and length of RS = length of R'S'

Thus, according to the options, we get that option A i.e. Length of PQ = Length of P′Q′ is correct.