Answer:
x = - 2 ±
Step-by-step explanation:
Given
x² = - 4x + 3 ( add 4x to both sides )
x² + 4x = 3
To complete the square
add (half the coefficient of the x- term)² to both sides
x² + 2(2)x + 2² = 3 + 2²
(x + 2)² = 3 + 4 = 7 ← take the square root of both sides
x + 2 = ± ← subtract 2 from both sides
x = - 2 ± ← exact values
Answer:
8.760 x 10^3
Step-by-step explanation:
There are 8760 hours in 1 year. So, you can convert this to scientific notation by moving the decimal from 8760 three times to the left: 8760. → 8.760 And since it was moved three times, put an exponent of 3 to the 10: 10^3 So, you get 8.760 x 10^3 hours in a year.
Hope this helps! :)
The letters of each proposed conguency statement need to be in corresponding positions of the original congruency statement
For example, consider the first answer selection. The letters on the left (CBA) are the 3rd, 2nd, and 1st letters of the original congruency statement. The letters on the right (MNL) are the 2nd, 3rd, and 1st letters of the original. The order 321 is not the same as the order 231, so the first choice is <em>incorrect</em>.
Appropriate choices are
∆BAC ≅ ∆MLN . . . . 3rd choice
∆ACB ≅ ∆LNM . . . . 4th choice
So to solve for this, we need to set up proportional fractions, which I will help show you how to do.
First, if we are given an amount out of a total, we need to put it over x (if we are looking for the total). It looks like this:
12/x, 12 being the given number and x being the total.
If we are given the total but are looking for an amount, put the total at the bottom of the fraction (aka the denominator). It looks like this: x/16, 16 being the total amount and x being the amount out of the total.
We have a total of 40 test problems, so we can put our total at the bottom, x/40.
X is the amount of questions answered correctly (we are looking for x in the question).
We have answered 80% correct, so put 80% over 100 (100 being the total). It should look like this: 80/100.
Now we have our two fractions: x/40 & 80/100.
Set these up as an equation.
x/40 = 80/100.
Now this is where things may get tricky if you don't pay attention.
Multiply the numerator (the top number of a fraction) of x/40 by the denominator (the bottom number of a fraction) of 80/100.
Your product equation should look like this:
x times 100. This will give is 100x. Leave it at that.
Now, multiply the denominator of x/40 (the bottom number of the fraction) by the numerator (the top number of a fraction) of 80/100. It should look like this:
80 x 40. This will give us 3200.
Now set up our products as an equation.
100x = 3200.
To solve for x, divide both sides by 100.
3200/100 = 32.
x = 32.
I hope this helps and has taught you something!
The given expression is : p - 21 = 34
Smplify the equation for p :
p - 21 = 34
Add 21 on both side :
p - 21 + 21 = 34 + 21
p = 55
p = 55
Answer : p = 55