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Bumek [7]
2 years ago
8

Help Review of linear pair vertical and complementary

Mathematics
1 answer:
Lera25 [3.4K]2 years ago
7 0

Answer:

x = 15

Step-by-step explanation:

The two angles form a straight line so they add to 180 degrees

3+6x   + 5x+12 = 180

Combine like terms

11x+15 = 180

Subtract 15 from each side

11x+15-15 =180-15

11x = 165

Divide by 11

11x/11 =165/11

x =15

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You push your younger sister on a swing one time and then allow your sister to
Ber [7]

Answer:

My sister will swing the total distance = 40 feet

Step-by-step explanation:

On the first swing my sister travels a distance of 8 feet.

In every successive swing she travels 80% of the distance of the previous distance.

So the sequence formed by the distance traveled in every swing will be a geometric sequence.

First term of the sequence 'a' = 8 feet

common ratio 'r' = 0.80

Since this sequence is an infinite geometric sequence,

Sum of this sequence = \frac{a}{(1-r)}  [Since r < 1]

                                     = \frac{8}{1-0.8}

                                     = \frac{8}{0.2}

                                     = 40 feet

Therefore, my sister will cover the total distance = 40 feet

7 0
2 years ago
Estimate the area of a circle with a radius of 3.1 feet
Aliun [14]

Answer:

Step-by-step explanation:

Area of a circle = pi x square of radius = 30.190 ft

5 0
3 years ago
Can someone help me with this question on Prodigy? ​
lions [1.4K]

Answer:

  8 +(3/8)√53 in² ≈ 10.73 in²

Step-by-step explanation:

Given the net of a triangular pyramid with some of the dimensions filled in, you want to find the total surface area.

<h3>Triangle base</h3>

The triangle bases identified by dashed lines will have a length equal to the hypotenuse of the right triangles with legs shown as solid lines. The legs of each of those right triangles are ...

  a = (3 in)/2 = 1.5 in

  b = 2 in . . . . . . shown as the altitude of the triangle

Then the hypotenuse is found using the Pythagorean theorem:

  c² = a² +b²

  c² = 1.5² +2² = 2.25 +4 = 6.25

  c = √6.25 = 2.5

The dashed lines are 2.5 inches long.

<h3>Triangle altitude</h3>

The altitude from the solid horizontal line to the vertex at the bottom of the figure can be found using the fact that all of the outside edge lengths of the net are the same length. That edge length is found as the length of the hypotenuse of the right triangles in the left- and right-sides of the upper portion of the net. Each of those has a leg that is (2.5 in)/2 = 1.25 in and a leg marked as 2 in.

  c² = a² +b²

  c² = 1.25² +2² = 1.5625 +4 = 5.5625

  c = (√89)/4 ≈ 2.358 . . . in

The unmarked altitude of the bottom triangle is then ...

  b² = c² -a²

  b² = 89/16 -1.5² = 53/16

  b = (√53)/4 ≈ 1.820 . . . in

<h3>Surface area</h3>

The surface area of the figure is the sum of the areas of the four triangles that make up the net. Each triangle has an area given by the formula ...

  A = 1/2bh

The left and right triangles have b=2.5, h=2, so they each have an area of ...

  A = 1/2(2.5)(2) = 2.5 . . . . in²

The center triangle has dimensions of b=3, h=2, so an area of ...

  A = 1/2(3)(2) = 3 . . . . in²

The bottom triangle has dimensions of b=3, h=(√53)/4, so an area of ...

  A = 1/2(3)(√53/4) = (3/8)√53 ≈ 2.730 . . . . in²

The total surface area is the sum of the areas of these triangles, so is ...

  A = 2.5 in² +2.5 in² +3 in² +2.73 in² = 10.73 in²

The surface area of the triangular pyramid is (64+3√53)/8 ≈ 10.73 in².

__

<em>Additional comment</em>

Often we work with pyramids that are rotationally symmetrical about a vertical line through the peak. This one is not. The altitude of the bottom triangle in the net is less than the altitude of the other triangles. This short face of the pyramid will tend to be more vertical than the other two lateral faces.

4 0
1 year ago
La suma de 3 más el doble de un número es igual a ese número pero con signo negativo.llamemos x al número desconocido.
nydimaria [60]

Answer:

x = -1

Step-by-step explanation:

3 + 2x = -x

   - 2x     - 2x

3 = -3x

divides 3 por ambos lados del signo igual

x = -1

4 0
3 years ago
If your car gets 24 miles per​ gallon, how much does it cost to drive 440 miles when gasoline costs ​$2.80 per​ gallon?
mojhsa [17]
This not might be correct (Cause in a middle schooler) but I think is....
440 divides by 24 = 18.3333333
We round it to the neared whole number which is 18.
18 x 2.80 = 50.4
So it is 50.4 altogether...
7 0
3 years ago
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