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3 years ago

In a 30°- 60° - 90° right triangle, the longer leg has a length of 10 square root of 3. what is the length of the shorter leg?

Mathematics

1 answer:

shutvik [7]3 years ago

3 0

In a 30°-60°-90° triangle, the longer leg is √3 times the shorter leg. In your triangle, ...
the shorter leg is 10.

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Suppose that $p$ and $q$ are positive numbers for which \[\log_9 p = \log_{12} q = \log_{16} (p + q).\] what is the value of $q/

SVEN [57.7K]

Given $p,q>0$ and $\log_9p=\log_{12}q=\log_{16}(p+q)=x$ (say).

Then,

$p=9^x\\ q=12^x\\ p+q=16^x$

From the above 3 equations,

$\frac{q}{p} =(\frac{12}{9} )^x\\ \frac{q}{p} =(\frac{4}{3} )^x\\ \frac{p+q}{p} =(\frac{16}{9} )^x\\ \frac{p+q}{p} =(\frac{4}{3} )^{2x}\\$

From the equations, we get

$\frac{p+q}{p}=(\frac{q}{p})^2\\ 1+\frac{q}{p}=(\frac{q}{p})^2\\ (\frac{q}{p})^2-\frac{q}{p}-1=0\\ \frac{q}{p}=\frac{1 \pm \sqrt{5}}{2}$

Since $p,q>0$ , the negative value is rejected.

$\frac{q}{p}=\frac{1 + \sqrt{5}}{2}$

3 0

3 years ago

Parallel to y = 3x − 2 and passes through (1, 4)

4vir4ik [10]

Answer:

y=3x + 1

Step-by-step explanation:

slope is same

insert coordinates into x and y values

determine y-intercept

4 0

3 years ago

Simplify by using the distributive property:

lesya692 [45]

12. 4(s+5)
4s+20

15. 2(3r-12)
6r-24

18. -3(16-3d)
9d-48

3 0

3 years ago

If log_3(x)=4.5 and log_3(y)=3, what is log_3(x^2/y)? a. 3 b. 6.75 c. 6 d. 1.5

astraxan [27]

There all log base 3, the base won't matter as long as they're all the same.

log(x^2/y)=2log(x)-log(y)=2(4.5)-3=6

Answer: c. 6

4 0

3 years ago

Write an expression equivalent to (7x + 5) - (3x - 5)

KiRa [710]

Answer:

= 2(2x + 5)

Step-by-step explanation:

Given that:

= (7x + 5) - (3x - 5)

By simplifying

"-" sign before bracket will alter the inner signs

= 7x + 5 - 3x + 5

Adding like terms

= 4x + 10

By taking 2 common we get:

= 2(2x + 5)

i hope it will help you!

6 0

3 years ago