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3 years ago

An angle measures 12 degrees less than three times its supplement. Find the measure of the angle.

Mathematics

1 answer:

Nimfa-mama [501]3 years ago

7 0

Supplementary angles must add up to 180 degrees.

3x-12=180

x=64 degrees

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A rectangular picture frame measures 27 cm by 48 cm. What is the perimeter or distance around the picture frame in meters

Firlakuza [10]

150, you just add the numbers

7 0

3 years ago

What is the determinant of <br><br>15<br><br>18<br><br>154

IgorC [24]

Answer:

The determinant is 15.

Step-by-step explanation:

You need to calculate the determinant of the given matrix.

1. Subtract column 3 multiplied by 3 from column 1 (C1=C1−(3)C3):

$\left[\begin{array}{ccc}-25&-23&9\\0&3&1\\-5&5&3\end{array}\right]$

2. Subtract column 3 multiplied by 3 from column 2 (C2=C2−(3)C3):

$\left[\begin{array}{ccc}-25&-23&9\\0&0&1\\-5&-4&3\end{array}\right]$

3. Expand along the row 2: (See attached picture).

We get that the answer is 15. The determinant is 15.

6 0

3 years ago

Pls help:Find all the missing elements:

Yuliya22 [10]

Answer:

Step-by-step explanation:

In order to find B we must first angle C

To find angle C we use the sine rule

That's

$\frac{ |a| }{ \sin(A) } = \frac{ |c| }{ \sin(C) }$

From the question

a = 15

A = 70°

c = 14

So we have

$\frac{15}{ \sin(70) } = \frac{14}{ \sin(C) }$

$\sin(C) = \frac{14 \sin(7 0 ) }{15}$

$C = \sin^{ - 1} ( \frac{14 \sin(70) }{15} )$

C = 61.288

<h3>C = 61.3° to the nearest tenth</h3>

Since we've found C we can use it to find B.

Angles in a triangle add up to 180°

To find B add A and C and subtract it from 180°

That's

A + B + C = 180

B = 180 - A - C

B = 180 - 70 - 61.3

<h3>B = 48.7° to the nearest tenth</h3>

To find b we can use the sine rule

That's

$\frac{ |a| }{ \sin(A) } = \frac{ |a| }{ \sin(B) }$

$\frac{15}{ \sin(70) } = \frac{ |b| }{ \sin(48.7) }$

$|b| = \frac{15 \sin(48.7) }{ \sin(70) }$

b = 11.9921

<h3>b = 12.0 to the nearest tenth</h3>

Hope this helps you

6 0

3 years ago

PLEEEEEEEAAAAAAASSSSSSSSSSEEEEEEEEEEE help me!!!!!!!!!!

defon

Answer:

$\boxed{\sf \ \ \ \dfrac{18}{(x-7)(x+12)(x+30)} \ \ \ }$

Step-by-step explanation:

hello,

first of all we will study the quadratic expressions

we can write that, (the different answers provide good clues :-) )

$x^2+5x-84=(x-7)(x+12)$

and

$x^2+23x-210=(x-7)(x+30)$

so first of all as we cannot divide by 0 we need to take x different from 7, -12 and -30 and then we can write

$\dfrac{1}{x^2+5x-48}-\dfrac{1}{x^2+23x-210}=\dfrac{1}{(x-7)(x+12)}-\dfrac{1}{(x-7)(x+30)}\\\\=\dfrac{(x+30) -(x+12)}{(x-7)(x+12)(x+30)}=\dfrac{x+30-x-12}{(x-7)(x+12)(x+30)}\\\\=\dfrac{18}{(x-7)(x+12)(x+30)}$

hope this helps

7 0

3 years ago

One uranium atom has a mass of 3.95 x 10^-22 grams.

creativ13 [48]

Remember
(ab)/(cd)=(a/c)(b/d)
and
$\frac{x^n}{x^m}=x^{n-m}$

1kg=1000g=1*10^3g
hmm, I estimate, 4 of them

x=number of attoms
mass of 1 times x=1*10^3
3.95*10^-22 times x=1*10^3
divide both sides by 3.95*10^-22
x= $\frac{1*10^3}{3.95*10^{-22}}= (\frac{1}{3.95} )( \frac{10^{3}}{10^{-22}} )$ = $0.25316*10^{25}$ = $2.5316*10^{24}$
a million has 9 zeroes
so 24 zeroes is alot that is a <span>septillion, so there are 2.5316 septillion uranium atoms in 1kg

a. 4
b. underestimate

</span>

5 0

3 years ago