All categories

3 years ago

Find the length of the hypotenuse of a right triangle with legs of 5 ft and 12 ft

Mathematics

1 answer:

just olya [345]3 years ago

3 0

Answer:

B. 13

First, use the Pythagorean Theorem

a^2 + b^2 = c^2

5^2 + 12^2 = c^2

25+144=c^2

169=c^2

square root of 169=13

Therefore your answer would be, B. 13

Have a great day!!!!! :D

Sry, it is a week late.... :\

You might be interested in

If every gram of salt is 20.9% chlorine, how much is required to make a 220 ppm chlorine solution with 350 grams of water?

Temka [501]

Answer:

The amount of salt required is 0.3685 grams.

Step-by-step explanation:

20.9% of 1 gram of salt is chlorine, which means the grams of chlorine in 1 gram of salt are

$\dfrac{20.9\%}{100\%} *1\: gram = 0.209g\: \text{chlorine}$

Now, to make 220 ppm solution, it must be that

$\dfrac{220}{10^6} = \dfrac{y}{350+y},$

where $y$ is the grams of chlorine required.

We rearrange the equation and solve for $y:$

$220(350+y) = 10^6y$

$77000+220y =10^6y$

$77000 = (10^6-220)y$

$y = \dfrac{77000}{999780}$

$\boxed{y= 0.07702g}$

since 1 gram of salt has 0.209 grams of chlorine, 0.07702g of chlorine corresponds to

$\dfrac{0.07701}{0.209} = 0.3685g {\text{ of salt. }$

Thus the amount of salt required is 0.3685 grams.

7 0

3 years ago

13 POINTS- please help me

allsm [11]

Answer:

See explanation

Step-by-step explanation:

16. Two parallel lines are cut by transversal. Angles with measures $(6x+20)^{\circ}$ and $(x+100)^{\circ}$ are alternate exterior angles. By alternate exterior angles, the measures of alternate exterior angles are the same:

$6x+20=x+100\\ \\6x-x=100-20\\ \\5x=80\\ \\x=16$

Then

$(6x+20)^{\circ}=(6\cdot 16+20)^{\circ}=116^{\circ}\\ \\(x+100)^{\circ}=(16+100)^{\circ}=116^{\circ}$

17. Two parallel lines are cut by transversal. Angles with measures $(2x+12)^{\circ}$ and $(3x-22)^{\circ}$ are alternate interior angles. By alternate interior angles, the measures of alternate interior angles are the same:

$2x+12=3x-22\\ \\2x-3x=-22-12\\ \\-x=-34\\ \\x=34$

Then

$(2x+12)^{\circ}=(2\cdot 34+12)^{\circ}=80^{\circ}\\ \\(3x-22)^{\circ}=(3\cdot 34-22)^{\circ}=80^{\circ}$

18. Two parallel lines are cut by transversal. Angles with measures $(6x-7)^{\circ}$ and $(5x+10)^{\circ}$ are alternate exterior angles. By alternate interior angles, the measures of alternate exterior angles are the same:

$6x-7=5x+10\\ \\6x-5x=10+7\\ \\x=17$

Then

$(6x-7)^{\circ}=(6\cdot 17-7)^{\circ}=95^{\circ}\\ \\(5x+10)^{\circ}=(5\cdot 17+10)^{\circ}=95^{\circ}$

19. The diagram shows two complementary angles with measures $2x^{\circ}$ and $56^{\circ}$ . The measures of complementary angles add up to $90^{\circ},$ then

$2x+56=90\\ \\2x=90-56\\ \\2x=34\\ \\x=17$

Hence,

$2x^{\circ}=2\cdot 17^{\circ}=34^{\circ}$

Check:

$34^{\circ}+56^{\circ}=90^{\circ}$

20. Angles $\angle 1$ and $\angle 2$ are vertical angles. By vertical angles theorem, vertical angles are congruent, so

$m\angle 1=m\angle 2\\ \\5x+7=3x+15\\ \\5x-3x=15-7\\ \\2x=8\\ \\x=4$

Hence,

$m\angle 1=(5x+7)^{\circ}=(5\cdot 4+7)^{\circ}=27^{\circ}\\ \\m\angle 2=(3x+15)^{\circ}=(3\cdot 4+15)^{\circ}=27^{\circ}$

21. $\angle 5$ and $\angle 8$ are supplementary. The measures of supplementary angles add up to $180^{\circ},$ so

$m\angle 5+m\angle 8=180^{\circ}\\ \\3x-40+7x-120=180\\ \\10x-160=180\\ \\10x=180+160\\ \\10x=340\\ \\x=34$

Therefore,

$m\angle 5=(3x-40)^{\circ}=(3\cdot 34-40)^{\circ}=62^{\circ}\\ \\m\angle 8=(7x-120)^{\circ}=(7\cdot 34-120)^{\circ}=118^{\circ}\\ \\62^{\circ}+118^{\circ}=180^{\circ}$