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2 years ago

Find the area of a right triangle with side lengths 12 cm, 35 cm, and 37cm

Mathematics

1 answer:

Maurinko [17]2 years ago

7 0

Answer:

210 cm sq

Step-by-step explanation:

Area of a triangle is 1/2bh.

12 cm and 35 cm would be both sides of the triangle, not 37 cm because it is the hypotenuse (largest side).

1/2*12*35=210 cm sq

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Aubrey can run at a pace of six miles per hour. running at the same rate how many miles can she run in ninety minutes

Eddi Din [679]

Aubrey would be able to run 9 miles in ninety minutes.

90 minutes=1.5 hours

6*1.5=9

Hope this helps

7 0

3 years ago

Find the values of the variables, giving brief reasons for your answers.

Yuki888 [10]

Answer:

Step-by-step explanation:

Because of the parallel lines (marked by those arrows) we know that the corner angles are the same:

110 - x = x so

110 = 2x

55 = x

4 0

3 years ago

A group of 15 people are going to run a race. The top 8 will advance to the finals. Determine if the situation is a permutation

LUCKY_DIMON [66]

For the given situation we have a total of 259,459,200 permutations.

<h3>How many permutations are?</h3>

First, how we know that it is a permutation?

Because the order matters, we aren't only selecting 8 out of the 15 people, but these 8 selected also have an order (is not the same thing to finish the race first than fourth, for example).

Then we need to find the number of permutations, to do it, we need to find the numbers of options for each of the 8 positions.

For the first position there are 15 options.
For the second position ther are 14 options (one runner already finished).
For the third position there are 13 options.
And so on.

Then the total number of permutations (product between the numbers of options) is:

P = 15*14*13*12*11*10*9*8 = 259,459,200

If you want to learn more about permutations:

brainly.com/question/11732255

#SPJ1

8 0

3 years ago

The sum of three numbers is 244.84. One of the numbers is 24.6. The other two numbers are equal to each other. What is the value

mamaluj [8]

Answer:

The value of each of the other two numbers is 110.12

Step-by-step explanation:

244.84 - 24.6 = 220.24

220.24 divided by half is 110.12

The value of the other two numbers is 110.12

4 0

2 years ago

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2/3 + y2/3 = 4 (−3 3 , 1)

vovikov84 [41]

Answer with Step-by-step explanation:

We are given that an equation of curve

$x^{\frac{2}{3}}+y^{\frac{2}{3}}=4$

We have to find the equation of tangent line to the given curve at point $(-3\sqrt3,1)$

By using implicit differentiation, differentiate w.r.t x

$\frac{2}{3}x^{-\frac{1}{3}}+\frac{2}{3}y^{-\frac{1}{3}}\frac{dy}{dx}=0$

Using formula : $\frac{dx^n}{dx}=nx^{n-1}$

$\frac{2}{3}y^{-\frac{1}{3}}\frac{dy}{dx}=-\frac{2}{3}x^{-\frac{1}{3}}$

$\frac{dy}{dx}=\frac{-\frac{2}{3}x^{-\frac{1}{3}}}{\frac{2}{3}y^{-\frac{1}{3}}}$

$\frac{dy}{dx}=-\frac{x^{-\frac{1}{3}}}{y^{-\frac{1}{3}}}$

Substitute the value x= $-3\sqrt3,y=1$

Then, we get

$\frac{dy}{dx}=-\frac{(-3\sqrt3)^{-\frac{1}{3}}}{1}$

$\frac{dy}{dx}=-(-3^{\frac{3}{2}})^{-\frac{1}{3}}=-\frac{1}{-(3)^{\frac{3}{2}\times \frac{1}{3}}}=\frac{1}{\sqrt3}$

Slope of tangent=m= $\frac{1}{\sqrt3}$

Equation of tangent line with slope m and passing through the point $(x_1,y_1)$ is given by

$y-y_1=m(x-x_1)$

Substitute the values then we get

The equation of tangent line is given by

$y-1=\frac{1}{\sqrt3}(x+3\sqrt3)$

$y-1=\frac{x}{\sqrt3}+3$

$y=\frac{x}{\sqrt3}+3+1$

$y=\frac{x}{\sqrt3}+4$

This is required equation of tangent line to the given curve at given point.

8 0

4 years ago