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2 years ago

Give one word problem involving Pythagorean Theorem and solve the problem completely with steps

1 answer:

3 0

Sam wants to build a fence splitting her square garden down the middle, diagonally. the width of the original square is 3 yards, and the length is 4 yards. how long should the separating fence be?

answer: 5 yards, as 3^2 + 4^2 = 5^2

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66 bats were sold. Some were sold for $42 each the rest were sold for $30 each. The total sales were$2,460. Write and solve a sy

Phoenix [80]

Answer:

40 bats sold for $42

26 bats sold for $30

Step-by-step explanation:

x + y = 66

42x + 30y = 2460

solve first equation for y and plug in for y in second equation

42x + 30 (66 - x) = 2460

x = 40

y = 66- 40 = 26

5 0

3 years ago

Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. n^2-4n/3

ololo11 [35]

Answer:

(n- 2/3)²

Step-by-step explanation:

Perfect square trinomial is: a²+2ab+b²= (a+b)²

We have:

n² - 4n/3

It can be put as:

n² -2×n×2/3

Here we consider n = a and -2/3 = b, then

b²= (-2/3)²= 4/9

Now we add 4/9 to a given binomial to make it perfect square:

n² - 2×n×3/2 + 4/9= (n- 2/3)²

So, added 4/9 and got a perfect square (n- 2/3)²

7 0

3 years ago

Please, Help. the answer isn't 30°

vagabundo [1.1K]

The missing angle of the right triangle ABC has a measure of 30°. (Correct answer: A)

<h3>How to find a missing angle by triangle properties</h3>

Triangles are geometrical figures formed by three sides and whose sum of internal angles equals 180°. There are two kind of triangles existing in this question: (i) Right triangles, (ii) Isosceles triangles.

Right triangles are triangles which one of its angles equals 90° and isosceles triangles are triangles which two of its sides have equal measures.

According to the statement, we know that triangle BQR is an isosceles triangle, whereas triangles ABC, ANB and NBC are right triangles. Based on the figure attached below, we have the following system of linear equations based on right triangles ABC and NBC:

2 · x + 90 + θ = 180 (1)

(90 - x) + 90 + θ = 180 (2)

By equalizing (1) and (2) we solve the system for x:

2 · x = 90 - x

3 · x = 90

x = 30

And by (1) we solve the system for θ:

θ = 180 - 2 · x - 90

θ = 30

The missing angle of the right triangle ABC has a measure of 30°. (Correct answer: A) $\blacksquare$

To learn more on right triangles, we kindly invite to check this verified question: brainly.com/question/6322314

8 0

2 years ago

Evaluate the following double integral where a = 2y

Keith_Richards [23]

Change the order of integration.

$\displaystyle \int_0^1 \int_{2y}^2 \cos(x^2) \, dx \, dy = \int_0^2 \int_0^{x/2} \cos(x^2) \, dy \, dx \\\\ ~~~~~~~~ = \int_0^2 \cos(x^2) y \bigg|_{y=0}^{y=x/2} \, dx \\\\ ~~~~~~~~ = \frac12 \int_0^2 x \cos(x^2) \, dx$

Substitute $u=x^2$ and $du=2x\,dx$ .

$\displaystyle \frac12 \int_0^2 x \cos(x^2) \, dx = \frac14 \int_0^4 \cos(u) \, du = \frac14 \sin(u) \bigg|_{u=0}^{u=4} = \boxed{\frac{\sin(4)}4}$

4 0

11 months ago

Which properties justify the steps taken to solve the system?

Nutka1998 [239]

Answer:

X=-1

Y=1

Step-by-step explanation:

6x-12y

-18

) 6x + 4y

-2

Subtract the two equations

6x - 12y - (6x + 4y) = -18 - (-2)

Determine the sign

6x- 12y - 6x- 4y

=-18 + 2

Simplify

-12y

- Ay

=-18 + 2

Solve the equation

Substitute

6×+4

-2

Solve the equation

6 0

2 years ago