Through:(-2,-5) , slope=5

What is the length of the hypotenuse of the triangle?<br>7 cm<br>З cm

siniylev [52]

Answer:

8

Step-by-step explanation:

Fourmla:

a^2+b^2=c^2

7^2=49

3^2=9

49+9=58

square root of 58 is about 8.

7 0

3 years ago

Please help! I’m having trouble in this class:(

allochka39001 [22]

Only GOD can help you god bless you AMEN

4 0

4 years ago

A square park measures 170 feet along each side. Two paved paths run from each corner to the opposite corner and extend 3 feet i

Cerrena [4.2K]

Answer:

The total area, in square feet, taken by the paths is 2,004

Step-by-step explanation:

see the attached figure with lines to better understand the problem

I can divide the figure into four right triangles, one small square and four rectangles

step 1

Find the area of the right triangle of each corner of the path

The area of the triangle is

$A=(1/2)(b)(h)$

substitute the given values

$A=(1/2)(3)(3)=4.5\ ft^2$

step 2

Find the hypotenuse of the right triangle

Applying Pythagoras Theorem

Let

d -----> hypotenuse of the right triangle

$d^{2}=3^{2}+3^{2}$

$d^{2}=18$

$d=\sqrt{18}\ ft$

simplify

$d=3\sqrt{2}\ ft$

The hypotenuse of the right triangle is equal to the width of the path

step 2

Find the area of the small square of the path

The area is

$A=b^{2}$

we have

$b=3\sqrt{2}\ ft$ ----> the width of the path

substitute

$A=(3\sqrt{2})^{2}$

$A=18\ ft^2$

step 3

Find the length of the diagonal of the square park

Applying Pythagoras Theorem

Let

D -----> diagonal of the square park

$D^{2}=170^{2}+170^{2}$

$D^{2}=57,800$

$D=\sqrt{57,800}\ ft$

simplify

$D=170\sqrt{2}\ ft$

step 4

Find the height of each right triangle on each corner

The height will be equal to the width of the path divided by two, because is a 45-90-45 right triangle

$h=1.5\sqrt{2}\ ft$

step 5

Find the area of each rectangle of the path

The area of rectangle is $A=LW$

we have

$W=3\sqrt{2}\ ft$ ----> width of the path

Find the length of each rectangle of the path

$L=(D-2h-d)/2$

where

D is the diagonal of the park

h is the height of the right triangle in the corner

d is the width of the path (length side of the small square of the path)

substitute the values

$L=(170\sqrt{2}-2(1.5\sqrt{2})-3\sqrt{2})/2$

$L=(170\sqrt{2}-3\sqrt{2}-3\sqrt{2})/2$

$L=(164\sqrt{2})/2$

$L=82\sqrt{2}\ ft$

Find the area of each rectangle of the path

$A=LW$

we have

$W=3\sqrt{2}\ ft$

$L=82\sqrt{2}\ ft$

substitute

$A=(82\sqrt{2})(3\sqrt{2})$

$A=492\ ft^2$

step 6

Find the area of the paths

Remember

The total area of the paths is equal to the area of four right triangles, one small square and four rectangles

so

substitute

$A=4(4.5)+18+4(492)=2,004\ ft^2$

therefore

The total area, in square feet, taken by the paths is 2,004

3 0

3 years ago

the group hiked a total of 17.4 miles on the first day. on the second day that group Heights a distance 12% more than the total

Leto [7]

Let x be the number of miles on the second day
X/17.4=1.12
X=17.4*1.12
X=19.5 miles
Hope this helps!

7 0

3 years ago

Each pants leg on page 8 has an opening with a circumference of 8.5 inches. It took 15 stitches to make 3 inches in width. How m

lord [1]

Answer:

43 stitches.

Step-by-step explanation:

We have been given that each pant's leg has an opening with a circumference of 8.5 inches. It took 15 stitches to make 3 inches in width. We are asked to find the number of stitches required to make up the circumference.

Let us find stitches needed to make 1 inch by dividing 15 by 3.

$\text{Stitches needed to make 1 inch}=\frac{15}{3}$

$\text{Stitches needed to make 1 inch}=5$

Since 5 stitches make 1 inch, so to find stitches needed to make 8.5 inches, we will multiply 8.5 by 5 as:

$\text{Stitches needed to make 8.5 inches}=5\times 8.5$

$\text{Stitches needed to make 8.5 inches}=42.5$

Upon rounding to nearest stitch, we will get:

$\text{Stitches needed to make 8.5 inches}\approx 43$

Therefore, 43 stitches will make up the circumference.

8 0

3 years ago