All categories

3 years ago

What is the value of x?

Mathematics

1 answer:

Nat2105 [25]3 years ago

5 0

This is a 30-60-90 triangle, meaning that x is 1/2 (the square root of 3) * 10

1/2 * 10 = 5

x would equal 5 root 3

You might be interested in

The sum of first three terms of a finite geometric series is -7/10 and their product is -1/125. [Hint: Use a/r, a, and ar to rep

Alchen [17]

Ooh, fun

geometric sequences can be represented as
$a_n=a(r)^{n-1}$
so the first 3 terms are
$a_1=a$
$a_2=a(r)$
$a_2=a(r)^2$

the sum is -7/10
$\frac{-7}{10}=a+ar+ar^2$
and their product is -1/125
$\frac{-1}{125}=(a)(ar)(ar^2)=a^3r^3=(ar)^3$

from the 2nd equation we can take the cube root of both sides to get
$\frac{-1}{5}=ar$
note that a=ar/r and ar²=(ar)r
so now rewrite 1st equation as
$\frac{-7}{10}=\frac{ar}{r}+ar+(ar)r$
subsituting -1/5 for ar
$\frac{-7}{10}=\frac{\frac{-1}{5}}{r}+\frac{-1}{5}+(\frac{-1}{5})r$
which simplifies to
$\frac{-7}{10}=\frac{-1}{5r}+\frac{-1}{5}+\frac{-r}{5}$
multiply both sides by 10r
-7r=-2-2r-2r²
add (2r²+2r+2) to both sides
2r²-5r+2=0
solve using quadratic formula
for $ax^2+bx+c=0$
$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$
so
for 2r²-5r+2=0
a=2
b=-5
c=2

$r=\frac{-(-5) \pm \sqrt{(-5)^2-4(2)(2)}}{2(2)}$
$r=\frac{5 \pm \sqrt{25-16}}{4}$
$r=\frac{5 \pm \sqrt{9}}{4}$
$r=\frac{5 \pm 3}{4}$
so
$r=\frac{5+3}{4}=\frac{8}{4}=2$ or $r=\frac{5-3}{4}=\frac{2}{4}=\frac{1}{2}$

use them to solve for the value of a
$\frac{-1}{5}=ar$
$\frac{-1}{5r}=a$
try for r=2 and 1/2
$a=\frac{-1}{10}$ or $a=\frac{-2}{5}$

test each
for a=-1/10 and r=2
a+ar+ar²= $\frac{-1}{10}+\frac{-2}{10}+\frac{-4}{10}=\frac{-7}{10}$
it works

for a=-2/5 and r=1/2
a+ar+ar²= $\frac{-2}{5}+\frac{-1}{5}+\frac{-1}{10}=\frac{-7}{10}$
it works

both have the same terms but one is simplified

the 3 numbers are $\frac{-2}{5}$ , $\frac{-1}{5}$ , and $\frac{-1}{10}$

6 0

3 years ago

The measured weights of 1,000 men in a certain village follow a normal distribution with a mean of 150 pounds and a standard dev

Hitman42 [59]

Z = (X-Mean)/SD
z1 = (165 - 150)/15 = +1 
z2 = (135 - 150)/15 = - 1 
According to the Empirical Rule 68-95-99.7 
Mean +/- 1SD covers 68% of the values 
100% - 68% = 32% 
The remaining 32% is equally distributed below z = - 1 and z = +1 
32%/2 = 16%

Therefore,

a) Number of men weighing more than 165 pounds = 16% of 1000 = 160 
b) Number of men weighing less than 135 pounds = 16% of 1000 = 160

3 0

3 years ago

Read 2 more answers

. Question 1.1. What is the first step in solving x2 + 2x + 3 = 0 by completing the square?. (Points : 1). Factor the left side.

Assoli18 [71]

U r going to subtract 3 from each side of the equation....leaving you with :
x^2 + 2x = -3

6 0

4 years ago

Read 2 more answers

Can anyone help me on this? also pls use step by step thank you

Lisa [10]

Answer:

1000 = 125 /65536

Step-by-step explanation:

Rewrite the expression using the negative exponent rule and then Raise

2 to the power of 21 . Cancel the common factor of 32. Combine 125 and 1 /65536

7 0

3 years ago

Read 2 more answers

This is due today, someone pls help!

Alex

The answer should be 32,890!

Move the decimal 4 places to the right
3.289 —> 32890

Jesse moved it 7 places to the right!

I’m not great at explaining but I hope it’ll help!

6 0

3 years ago

Read 2 more answers