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3 years ago

The diagonal of a square has length 10√2. Find the area of the square.

Mathematics

1 answer:

alex41 [277]3 years ago

3 0

Answer: $A = 100$ square unit

Step-by-step explanation:

The formula for calculating the area of a square when the diagonal is given is :

$Area = d^{2} / 2$

That is :

$A = \frac{(10\sqrt{2})^{2}}{2}$

$A = \frac{100(2)}{2}$

$A = 100$ square unit

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9 + 6r - 4 <br> simplify the algebraic expression

denpristay [2]

6r+5 I’m pretty sure :))

6 0

3 years ago

Find the missing side length. and how do i set up to solve?

nikitadnepr [17]

Answer:

its 6 because the lines show they are parellel so it has to be equal to 18 and 12 plus 6 is 18

Step-by-step explanation:

6 0

3 years ago

A simple random sample of 100 8th graders at a large suburban middle school indicated that 81% of them are involved with some ty

Sophie [7]

Answer:

The interval is $0.7187 < p < 2.421$

Step-by-step explanation:

From the question we are told that

The sample size is $n = 100$

The population proportion is $p = 0.81$

The confidence level is C = 98%

The level of significance is mathematically evaluated as

$\alpha = 100 -98$

$\alpha = 2%$ %

$\alpha = 0.02$

Here this level of significance represented the left and the right tail

The degree of freedom is evaluated as

$df = n-1$

substituting value

$df = 100 - 1$

$df = 99$

Since we require the critical value of one tail in order to evaluate the 98% confidence interval that estimates the proportion of them that are involved in an after school activity. we will divide the level of significance by 2

The critical value of $\frac{\alpha}{2}$ and the evaluated degree of freedom is

$t_{df , \alpha } = t_{99 , \frac{0.02}{2} } = 2.33$

this is obtained from the critical value table

The standard error is mathematically evaluated as

$SE = \sqrt{\frac{p(1-p )}{n} }$

substituting value

$SE = \sqrt{\frac{0.81(1-0.81 )}{100} }$

$SE = 0.0392$

The 98% confidence interval is evaluated as

$p - t_{df , \frac{\alpha }{2} } * SE < p < p + t_{df , \frac{\alpha }{2} }$

substituting value

$0.81 - 2.33 * 0.0392 < p < 0.81 +2.33 * 0.0392$

$0.7187 < p < 2.421$

4 0

3 years ago

Which graph represents Y as a function of X ?

inna [77]

Answer:

Which graph represents Y as a function of X ?

step-by-step explanation:

a. The graph of y = 2x represents a transformation of the parent function, y = x, which makes the graph twice as steep.

b. The graph of y = 2x represents a transformation of the parent function, y = x, which makes the graph half as steep.

c. The graph of y = x represents a transformation of the parent function, y = 2x, which makes the graph half as steep.

d. The graph of y = x represents a transformation of the parent function, y = 2x, which makes the graph twice as steep.

5 0

3 years ago

What is the area of a regular hexagon (6 sides) whose

Ganezh [65]

Step-by-step explanation:

With reference to the regular hexagon, from the image above we can see that it is formed by six triangles whose sides are two circle's radii and the hexagon's side. The angle of each of these triangles' vertex that is in the circle center is equal to 360∘6=60∘ and so must be the two other angles formed with the triangle's base to each one of the radii: so these triangles are equilateral.

The apothem divides equally each one of the equilateral triangles in two right triangles whose sides are circle's radius, apothem and half of the hexagon's side. Since the apothem forms a right angle with the hexagon's side and since the hexagon's side forms 60∘ with a circle's radius with an endpoint in common with the hexagon's side, we can determine the side in this fashion:

tan60∘=opposed cathetusadjacent cathetus => √3=Apothemside2 => side=(2√3)Apothem

As already mentioned the area of the regular hexagon is formed by the area of 6 equilateral triangles (for each of these triangle's the base is a hexagon's side and the apothem functions as height) or:

Shexagon=6⋅S△=6(base)(height)2=3(2√3)Apothem⋅Apothem=(6√3)(Apothem)2

=> Shexagon=6×62√3=216

8 0

3 years ago