which are the perfect square numbers from the given list: 1,2,3,4,5,6,7,8,9,10,12,14,15,16,18,20,21,24

Answers

Answer 1

Answer: Answer: The perfect square numbers in the list, are: 1, 4, 9, 16.

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What is the common ratio of the geometric sequence whose second and fourth terms are 6 and 54, respectively?

(Picture Attached)20 Pts:

Which of the following completes the proof? (6 points)

By the midpoint formula

By definition of congruence

Given

By construction

Answers

by the mid point formula is my best guess

Find the surface area of the following figures 16 ft 13 ft 12ft 19ftPlease help me solve number 3! And if i got #2 incorrect, please help me fix that one too.

Answers

Answer:

1192 ft²

Step-by-step explanation:

Figure 3 is a trapezoidal prism.

The total surface area of a trapezoidal prism is made up of 2 congruent trapezoid bases and 4 rectangular faces connecting the bases.

The formula for the area of a trapezoid is:

$\boxed{S.A.=(1)/(2)(a+b)h}$

where a and b are the bases, and h is the height.

From observation of the given diagram, the bases are 16 ft and 19 ft, and the height is 12 ft. Therefore, the area of each trapezoid base is:

$\begin{aligned}\textsf{Area of trapezoid base}&=(1)/(2)(16+19)\cdot 12\n\n&=(1)/(2)(35)\cdot 12\n\n&=17.5\cdot 12\n\n&=210\; \sf ft^2\end{aligned}$

To calculate the areas of all the rectangular faces, we first need to calculate the slant (s) of the trapezoid base by using the Pythagoras Theorem:

$\begin{aligned}s^2&=(19-16)^2+12^2\ns^2&=3^2+12^2\ns^2&=9+144\ns^2&=153\ns&=√(153)\end{aligned}$

The area of a rectangle is the product of its width and length.

Therefore, the sum of the areas of the rectangular faces is:

$\begin{aligned}\textsf{Area of rectangular faces}&=16\cdot13+12\cdot13+19\cdot13+√(153)\cdot13\n&=208+156+247+13√(153)\n&=771.801119...\n&=772\; \sf ft^2\;(nearest\;foot)\end{aligned}$

To find the total surface area of the given trapezoidal prism, sum the area of the two trapezoid bases and the area of the rectangular faces:

$\begin{aligned}\textsf{Total S.A.}&=2 \cdot 210+772\n&=420+772\n&=1192\; \sf ft^2\end{aligned}$

Therefore, the total surface area of the given trapezoidal prism is 1192 ft², rounded to the nearest foot.

the perimeter of a rectangle is 58. The length is 1 more than 2 1/2 times the width. Find the dimensions of the rectangle

Answers

The formula of the perimeter of a rectangle is given as

P=2L+2W

where L is the length and W is the width. Substitution of the given values will yield,

58=2L+2W (1)

The next thing that we have to do is to translate the relationship between the two variables, L and W, into a mathematical equation.

So we have

L=2.5W+1 (2)

Now we have two equations, we also have two unknowns, so this problem is solvable. Substitution of equation (2) in (1) yields

58=2(2.5W+1)+2W
58=5w+2+2w
58=7W+2
56=7W
8=W

Substitution of this value to equation (2) yields

L=2.5(8)+1
L=21

So, the dimensions of the rectangle are:, specifically, width is equal to 8 while length is equal to 21.

The rectangular vegetable garden in 6 feet longer than 2 times its width. If the perimeter is 48 feet, what is the garden's width? Remember, the perimeter of a rectangle is the sum of all its sides.

Answers

Since there are 4 sides in a rectangle, we'll divide 48 by 4

$(48)/(4)$ = 12

We know that the length is 6 feet longer than 2 times it width.

12 + 6 = 18

The length of one side of a rectangle is 18.

The total length of both sides is 36 because 18 + 18 = 36

48 - 36 = 12

The width of both sides of a rectangles is 12. Now if we divide 12 by 2 we'll get the width of one side of a rectangle..

$(12)/(2)$ = 6

The width of one side of the rectangle is 6.
The length of one side of the rectangle is 18.

Let's check and see if our answer is correct. We need to get a 48 as an answer since that's the perimeter of the rectangle.

2 × ( length + width )
2 × ( 18 + 6 ) = 48

Yay! We got it right!! Hope you understood this :)

Final answer:

The width of the garden is 6 feet. We found this by expressing the length in terms of width, substituting into the perimeter equation, simplifying to find the value of width.

Explanation:

In solving this problem, we will follow a few simple steps. First, we know that the perimeter of a rectangle is given by the formula: Perimeter = 2*length + 2*width. We know from the problem that the perimeter is 48 feet and the length of the garden is 6 feet longer than 2 times its width.

Let's denote the width as 'w'. Then, the length would be 2w + 6. Substituting these into the perimeter equation, we have: 48 = 2*(2w+6) + 2*w. Simplifying this equation gives 48 = 4w + 12 + 2w, which further simplifies to 48 = 6w + 12. If we now deduct 12 from both sides, we have: 36 = 6w. Finally, dividing by 6 gives us the width: w = 6 feet.

Learn more about Perimeter here:

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Solve each quadratic equation. Show your work.

14. (2x – 1)(x + 7) = 0

Answers

(2x – 1)(x + 7) = 0

2x-1=0
2x=1
x=1/2
x=0.5

x+7=0
x= -7

solve your equation step-by-step.

(2x−1)(x+7)=0

Simplify both sides of the equation.

2x2+13x−7=0

Factor left side of equation.

(2x−1)(x+7)=0

Set factors equal to 0.

2x−1=0 or x+7=0

x=1/2 or x=−7

What is the intersection of plane WZVS and plane STUV?

Answers

Answer: The required intersection is the line 'VS'.

Step-by-step explanation: We are given to find the intersection of the planes WZVS and plane STUV.

We know that,

If two planes intersect each other, then their intersection is a straight line.

As shown in the given figure, the point 'V' and 'S' lie on both the planes WZVS and STUV.

So, the line joining these two points, i.e., the line VS also lie on both the planes.

Therefore, the intersection of both the planes is the line 'VS'.

Thus, the required intersection is the line 'VS'.

An easy way to find this is to look at the cross section, and see where the lines meet

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