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Marina CMI [18]
3 years ago
13

Write an expression for the sequence of operations described below.

Mathematics
1 answer:
leonid [27]3 years ago
3 0

Answer:

(a+8)/7

Step-by-step explanation:

It says to add a to 8 and THEN divide which means you have to add first.

You might be interested in
Complete the square to write the quadratic expression in vertex form.
Anvisha [2.4K]

Answer:

1. (x - 3)² = 8

2. (x + 2)² = 3

3. (x + 6)² = $ \frac{101}{2} $

4. (x + 3)² = 27

5. (x + 4)² = 13

6.  $ \bigg( x - \frac{15}{9} \bigg) ^2 = \frac{261}{81} = \frac{29}{9} $

Step-by-step explanation:

Completion of Square: $ (x - a) ^2 = x^2 - 2ax + a^2 $

In the following problems the terms in the RHS of the above equation may be missing. We balance the equation. Simplify it and re write it in terms of LHS.

1. x² - 6x + 1 = 0

Taking the constant term to the other side, we get:

x² - 6x = - 1

⇒ x² - 2(3)x = -1

⇒ x² -2(3)x + 9 = - 1 + 9  [Adding 9 to both the sides]

⇒ x² -2(3)x + 3² = 8

⇒ (x - 3)² = 8 is the answer.

2. 3x² + 12x + 3 = 0

Note that the co-effecient of x² is not 1. We make it 1, by dividing the whole equation by 3. And then proceed like the previous problem.

3x² + 12x = -3

Dividing by 3 through out, x² + 4x = - 1

⇒ x² + 2(2) + 4 = -1 + 4

⇒ x² +2(2) + 2² = 3

⇒ (x + 2)² = 3 is the answer.

3. 2x² + 24x = 29

x² + 12x = $ \frac{29}{2} $

⇒ x² + 2(6)x + 36 = $ \frac{29}{2} $ + 36

⇒ x² + 2(6)x + 6² = $ \frac{29 + 72}{2} $

⇒ (x + 6)² = $ \frac{101}{2} $ is the answer.

4. x² + 6x - 18 = 0

x² + 6x = 18

⇒ x² + 2(3)x = 18

⇒ x² + 2(3)x + 9 = 18 + 9

⇒ x² + 2(3)x + 3² = 27

⇒ (x + 3)² = 27 is the answer.

5. x² + 8x + 3 = 0

x² + 8x = -3

⇒ x² + 2(4)x = -3

⇒ x² + 2(4)x + 16 = - 3 + 16

⇒ x² + 2(4)x + 16 = 13

⇒ (x + 4)² = 13 is the answer.

6. 9x² - 30x + 6 = 0

9x² - 30x = - 6

⇒ x² $ - \frac{30}{9} $ x = - 6

$ \implies x^2 -2 \bigg( \frac{15}{9} \bigg )x + \frac{225}{81} = - 6 + \frac{225}{81} $

$ \implies x^2 - 2\bigg( \frac{15}{9} \bigg ) x + \bigg ( \frac{15}{9} \bigg ) ^2 = \frac{261}{81} $

$ \bigg( x - \frac{15}{9} \bigg) ^2 = \frac{261}{81} = \frac{29}{9} $ is the answer.

6 0
3 years ago
Help me, its trigonometry college
prohojiy [21]

4) (a) For these problems, you should take time to familiarize yourself with common fractions that appear on the unit circle.  \frac{\sqrt{3}} {3} does not appear in the unit circle unless you take the quotient 1/2 divided by sqrt(3)/2 which gives you 1/sqrt(3) which is the same as sqrt(3)/3.  So our numerator is 1/2 and our denominator is sqrt(3)/2.

And remember tangent is just sin/cos.  So what degree has sinx as 1/2 and and cosx as sqrt(3)/2?  Well, 30 degrees does, but 30 degrees is not within the range we are given.  That means they are looking for a sinx that gives us -1/2 and a cosx that gives us -sqrt(3)/2 and that is 210 degrees.

And 210 degrees in radians is 7pi/6.

I hoped that made sense.

(b) This is a lot easier. What angle gives us a cos x of -sqrt(3)/2?  According to the unit circle, 150 degrees and 210 degrees does.  They usually want these in radians, so the answer is 5pi/6 and 7pi/6, respectively.

5) What quadrant is radian measure 5 in?

Well 2pi or roughly 6.28 is a full circle. And 5 is slightly less than 6.28, so it is probably in quadrant IV.

But to be sure let's change 5 radian to degrees:

5 * 180/pi = 900/pi = 286.48 degrees

286.48 degrees is definitely in Q4, so we are correct.




7 0
3 years ago
Answer this please i don't really understand it so help me please lol.
expeople1 [14]

Answer:

11

Step-by-step explanation:

Step 1:

( 9 - 3 ) + 20 ÷ 4   Equation

Step 2:

6 + 20 ÷ 4     Subtract

Step 3:

6 + 5   Divide

Answer:

11    Add

<u>PEMDAS:</u>

<u>1. Parenthesis</u>

<u>2. Exponents</u>

<u>3. Multiplication</u>

<u>4. Division</u>

<u>5. Addition</u>

<u>6. Subtraction</u>

<u />

Hope This Helps :)

<u />

8 0
2 years ago
Read 2 more answers
Solve the system of equations by substitution <br> y= 3x - 10<br> 3x + 2y = 16
Natalija [7]
Y= 3x - 10
<span>3x + 2y = 16

3x+2(3x-10)=16
3x+6x-20=16
9x-20=16
9x=36
x=4

y=3x-10
y=3(4)-10
y=12-10
y=2</span>
5 0
3 years ago
I need both of these help!
marysya [2.9K]
The angle next to the angle 5x is 180 - 5x

All angles sum to 360

(6x - 58) + (2x + 4) + (180 - 5x) = 180
3x + 126 = 180
3x = 54
x = 18

For question 10, sum of angles in pentagon is 540 degrees

x + 105 + 85 + 114 + 126 = 540
x + 430 = 540
x = 110

3 0
3 years ago
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