Full question attached
Answer and explanation:
Since x = number of true or false questions correct
And y = number of multiple choice questions correct
And each question for x =2 points
each question for y=3 points
since she then needs a total score of more than 93 to pass, we add up total correct questions and
Inequality equation = 2x +3y >93
First, find the area of the base (the triangle) and then multiply it by the height
to find the area of the triangle you need to know the height. cut the triangle in half and you get a right triangle, from there you can use the Pythagorean theorem. remember since you cut the triangle in half you have to divide one of the sides by 2
a^2 + b^2 = c^2 (plug in known information)
a^2 + (7.5)^2 = (15)^2 (solve, first solve the exponents)
a^2 + 56.25 = 225 (subtract 56.25 on both sides)
a^2 = 168.75 (solve for a, put 168.75 under the square root)
then once you find the area multiply by the known height
183891 is the answer but you have to subtract it
Answer:
B) 24
Step-by-step explanation:
Hw = 20% = 0.2
120(0.2) = 24
Whenever you multiply a binomial by itself twice, the resulting trinomial is called a perfect square trinomial
For example, (x + 1) × (x + 1) = x2<span> + x + x + 1 = x</span>2<span> + 2x + 1 and x</span>2<span> + 2x + 1 is a perfect square trinomial</span>
Another example is (x − 5) × (x − 5)
(x − 5) × (x − 5) = x2<span> + -5x + -5x + 25 = x</span>2<span> + -10x + 25 and x</span>2<span> + -10x + 25 is a perfect square trinomial </span>
Now, we are ready to start factoring perfect square trinomials
The model to remember when factoring perfect square trinomials is the following:
a2<span> + 2ab + b</span>2<span> = (a + b)</span>2<span> and (a + b)</span>2<span> is the factorization form for a</span>2<span> + 2ab + b</span>2
Notice that all you have to do is to use the base of the first term and the last term
In the model just described,
the first term is a2<span> and the base is a</span>
the last term is b2<span> and the base is b</span>
Put the bases inside parentheses with a plus between them (a + b)
Raise everything to the second power (a + b)2<span> and you are done </span>
<span>Notice that I put a plus between a and b. </span>You will put a minus if the second term is negative!
a2<span> + -2ab + b</span>2<span> = (a − b)</span>2
Remember that a2<span> − 2ab + b</span>2<span> = a</span>2<span> + -2ab + b</span>2<span> because a minus is the same thing as adding the negative ( − = + -) So, a</span>2<span> − 2ab + b</span>2<span> is also equal to (a − b)</span>2
Example #1:
Factor x2<span> + 2x + 1</span>
Notice that x2<span> + 2x + 1 = x</span>2<span> + 2x + 1</span>2
Using x2<span> + 2x + 1</span>2, we see that... the first term is x2<span> and the base is x</span>
the last term is 12<span> and the base is 1</span>
Put the bases inside parentheses with a plus between them (x + 1)
Raise everything to the second power (x + 1)2<span> and you are done </span>
Example #2:
Factor x2<span> + 24x + 144</span>
But wait before we continue, we need to establish something important when factoring perfect square trinomials.
<span>. How do we know when a trinomial is a perfect square trinomial? </span>
This is important to check this because if it is not, we cannot use the model described above
Think of checking this as part of the process when factoring perfect square trinomials
We will use example #2 to show you how to check this
Start the same way you started example #1:
Notice that x2<span> + 24x + 144 = x</span>2<span> + 24x + 12</span>2
Using x2<span> + 24x + 12</span>2, we see that...
the first term is x2<span> and the base is x</span>
the last term is 122<span> and the base is 12</span>
Now, this is how you check if x2<span> + 24x + 12</span>2<span> is a perfect square</span>
If 2 times (base of first term) times (base of last term) = second term, the trinomial is a perfect square
If the second term is negative, check using the following instead
-2 times (base of first term) times (base of last term) = second term
Since the second term is 24x and 2 × x × 12 = 24x, x2<span> + 24x + 12</span>2<span> is perfect and we factor like this</span>
Put the bases inside parentheses with a plus between them (x + 12)
Raise everything to the second power (x + 12)2<span> and you are done </span>
Example #3:
Factor p2<span> + -18p + 81</span>
Notice that p2<span> + -18p + 81 = p</span>2<span> + -18p + 9</span>2
Using p2<span> + -18p + 9</span>2, we see that...
the first term is p2<span> and the base is p</span>
the last term is 92<span> and the base is 9</span>
Since the second term is -18p and -2 × p × 9 = -18p, p2<span> + -18p + 9</span>2<span> is a perfect square and we factor like this</span>
Put the bases inside parentheses with a minus between them (p − 9)
Raise everything to the second power (p − 9)2<span> and you are done </span>
Example #4:
Factor 4y2<span> + 48y + 144</span>
Notice that 4y2<span> + 48y + 144 = (2y)</span>2<span> + 48y + 12</span>2
(2y)2<span> + 48y + 12</span>2, we see that...
the first term is (2y)2<span> and the base is 2y</span>
the last term is 122<span> and the base is 12</span>
Since the second term is 48y and 2 × 2y × 12 = 48y, (2y)2<span> + 48p + 12</span>2<span> is a perfect square and we factor like this</span>
Put the bases inside parentheses with a plus between them (2y + 12)
Raise everything to the second power (2y + 12)2<span> and you are done </span>
