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svet-max [94.6K]
3 years ago
14

I need help with this question ASAP

Mathematics
1 answer:
IgorLugansk [536]3 years ago
7 0

Answer:

The answer would be 49 I think hehe

Step-by-step explanation:

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Explain algebraically using properties of logs how log(100x) is related to log(x)
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Log(100x)=log(100)+logx
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3 years ago
Can someone help me with this question on Prodigy? ​
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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
The points (1, 3) and (−3, 7) lie on a line. where does the line cross the x-axis?
Anastasy [175]
First, we find the equation of the line...

(1,3),(-3,7)
slope = (7 - 3) / (-3 - 1) = 4/-4 = -1

y = mx + b
slope(m) = -1
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now sub into the formula and find b, the y int
3 = -1(1) + b
3 = -1 + b
3 + 1 = b
4 = b
so the equation for this line is : y = -1x + 4 which is usually written as :
 y = -x + 4

Now...to find where the line crosses the x axis (or the x intercept)...we sub in 0 for y and solve for x

y = -x + 4
0 = -x + 4
x = 4... so ur x intercept (where the line crosses the x axis) is : (4,0)

3 0
3 years ago
Choose all numbers that are divisible by 2 and 5
harina [27]

Step-by-step explanation:

numbers divisible by 2 end with an even number (2,4,6,8,0)

numbers divisible by 5 end with either 5 or 0

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2 years ago
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The length of a rectangle is 2x-7 and the width is 3x+5. Describe the step you would need to take to find the area of the rectan
Kruka [31]

Answer:

A= 6x^2-11x-35

Step-by-step explanation:

Given data

Length=  2x-7

Width= 3x+5.

Area= L*W

substitute

A= (2x-7)* (3x+5)

Open bracket

A= 6x^2+10x-21x-35

collect like terms

A= 6x^2-11x-35

Hence the area is

A= 6x^2-11x-35

6 0
2 years ago
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