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3 years ago

What is the measure of m? 5 15 E n m = [?]

Mathematics

1 answer:

AlekseyPX3 years ago

7 0

<h3>Answer: 10</h3>

====================================================

Explanation:

The two smaller triangles are proportional, which lets us set up this equation

5/n = n/15

Cross multiplying leads to

5*15 = n*n

n^2 = 75

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Apply the pythagorean theorem on the smaller triangle on top, or on the right.

a^2+b^2 = c^2

5^2+n^2 = m^2

25+75 = m^2

100 = m^2

m^2 = 100

m = sqrt(100)

m = 10

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Given that A varies directly as B and inversely as C and that; A=12 when B=3 and C=2. Find B when A=10 and C=1.5

maria [59]

Answer:

B = 1.875

Step-by-step explanation:

given that A varies directly as B and inversely as C then the equation relating them is

A = $\frac{kB}{C}$ ← k is the constant of variation

to find k use the condition A = 12 when B = 3 and C = 2 , then

12 = $\frac{3k}{2}$ ( multiply both sides by 2 to clear the fraction )

24 = 3k ( divide both sides by 3 )

8 = k

A = $\frac{8B}{C}$ ← equation of variation

when A = 10 and C = 1.5 , then

10 = $\frac{8B}{1.5}$ ( multiply both sides by 1.5 )

15 = 8B ( divide both sides by 8 )

1.875 = B

8 0

2 years ago

Rewrite: 72x3/4 please show how you got answer

Alex_Xolod [135]

We have been given the expression

$72 \times \frac{3}{4}$

We can rewrite the expression as $\frac{72\times 3}{4}$

In order to simplify the given expression, we can check if we have any common terms in the numerator and denominator.

We can write the term 72 which is in the numerator as $18\times 4$

Thus, the expression becomes

$\frac{18\times 4\times 3}{4}$

We can see that 4 is common in both numerator and denominator. Hence, we can cancel 4. Thus, we are left with

$18 \times 3\\
=54$

Therefore, we can rewrite the given expression as 54.

8 0

3 years ago

Eight thousand six and thirty-four thousandths * Write as a decimal

valentinak56 [21]

Answer:

8,006.034

Step-by-step explanation:

eight thousand six = 8,006

and = .

thirty-four thousandths = .034

5 0

3 years ago

. If α and β are the roots of

Lostsunrise [7]

Answer:

$18x^2+85x+18 = 0$

Step-by-step explanation:

Given Equation is

=> $2x^2+7x-9=0$

Comparing it with $ax^2+bx+c = 0$ , we get

=> a = 2, b = 7 and c = -9

So,

Sum of roots = α+β = $-\frac{b}{a}$

α+β = -7/2

Product of roots = αβ = c/a

αβ = -9/2

Now, Finding the equation whose roots are:

α/β ,β/α

Sum of Roots = $\frac{\alpha }{\beta } + \frac{\beta }{\alpha }$

Sum of Roots = $\frac{\alpha^2+\beta^2 }{\alpha \beta }$

Sum of Roots = $\frac{(\alpha+\beta )^2-2\alpha\beta }{\alpha\beta }$

Sum of roots = $(\frac{-7}{2} )^2-2(\frac{-9}{2} ) / \frac{-9}{2}$

Sum of roots = $\frac{49}{4} + 9 /\frac{-9}{2}$

Sum of Roots = $\frac{49+36}{4} / \frac{-9}{2}$

Sum of roots = $\frac{85}{4} * \frac{2}{-9}$

Sum of roots = S = $-\frac{85}{18}$

Product of Roots = $\frac{\alpha }{\beta } \frac{\beta }{\alpha }$

Product of Roots = P = 1

The Quadratic Equation is:

=> $x^2-Sx+P = 0$

=> $x^2 - (-\frac{85}{18} )x+1 = 0$

=> $x^2 + \frac{85}{18}x + 1 = 0$

=> $18x^2+85x+18 = 0$

This is the required quadratic equation.

5 0

3 years ago

Read 2 more answers

Solve the linear equation x + 4 + 3 + 72

elixir [45]

Answer:

x=17

Step-by-step explanation

4x+4=72

-4 -4

4x=68

/4 /4

x= 17

7 0

3 years ago

Read 2 more answers