For question 1 and 2, you should keep in mind that the sum of all angles in a triangle is 180°.
1. If the measure of one angle of a triangle is 90 degrees, you can assume that the sum of the other two triangles should be 90 degrees. Because
180 - 90 = 90
They do not necessarily have to be both 45 degrees. So your answer would be C, their measure should add up to 90 degrees.
2. There are two angles measured: 100° and 30°. Remember the sum of all angles of a triangle is 180°.
180° = 100° + 30° + X
To get X, you transpose the 100° and 30° to the other equation and it will look like this:
180° - 100° - 30 °= X
Remember when you transpose, you use the opposite operation used.
By following the steps, you can now solve for the missing angle. So your answer to this question is A.
As for number 3, without the figure, it is not possible to solve.
For number 4, just remember that trapezoid angles should sum up to 360°.
Given that m∠A = ?; m∠B = 25°; m∠C = 155°; and m∠D = 117° these should all add up to 360°. Let's write an equation for it:
m∠A + m∠B + m∠C + m∠D = 360°
X + 25° + 155° + 117° = 360°
Add up what you know first then we can derive the missing from what is given:
X + 297° = 360°
Transfer the 297° to the other side of the equation and subtract.
X = 360° - 297°
= 63°
Your answer is then B.
For number 5, without the figure, it cannot be answered.
For number 6, 7 and 8 we can use the Triangle Inequality theorem to determine if the given sides form a triangle. It states that the sum of 2 sides of a triangle should be greater than the other side.
a + b > c b + c > a a + c > b
If all three conditions are met rule then you have a triangle. Now let's use your given.
6. a = 13in b=16in and c= 24 in
Let's do this one after the other:
a + b > c b + c > a a + c > b
13 + 16 > 24 16 + 24 > 13 13 + 24 > 16
29 > 24 30 > 13 37 > 16
Because all three conditions were met, then we can say that a triangle can be found. The answer is A.
7. a = 24.3m b = 7.4m c=5.9m
a + b > c b + c > a
24.3 + 7.4 > 5.9 7.4 + 5.9 > 24.3
31.7 > 5.9 13.3 > 24.3 False
Because b+c is less than a, we can say that the given does not make a triangle. Your answer is B.
8. Using the same theorem and use trial and error to determine which is not plausible.
a = 8 b = 25
if c = 18 if c = 21 if c = 27 if c = 35
8 + 25 > 18 True 8 + 25 > 21 True 8 + 25 > 27 True 8 + 25 > 35 False
25 + 18 > 8 True 25 + 21 > 8 True 25 + 27 > 35 True
8 + 18 > 25 True 8 + 21 > 25 True 8 + 27 > 25 True
18 is possible 21 is possible 27 is possible 35 is not possible
Your answer is then D.
As for questions 9 and 10, it cannot be answered without the figure given.
But just remember that complementary angles are two angles that have a sum of 90° . Supplementary angles are two angles that sum up to 180°.
Answer:
2(x² - 2)(x² - 8)
Step-by-step explanation:
Given
2
- 20x² + 32 ← factor out 2 from each term
= 2( - 10x² + 32)
let u = x², then
- 10x² + 32 = u² - 10u + 32 = (u - 2)(u - 8)
change u back to x²
- 10x² + 32 = (x² - 2)(x² - 8) and
2 - 20x² + 32 = 2(x² - 2)(x² - 8) ← in factored form
Answer:
0.75 could be a 25% discount. 1.06 could be a sales tax.
Step-by-step explanation:
If p is the original price, then 1.06p could be the amount after a 6% tax is include. Then multiplying by 0.75 could indicate a 25% discount (if you <u>don't</u> pay 25% = 0.25, then you <u>do</u> pay 75% = 0.75).
In case you're wondering about discounting <u>first</u> then charging tax, the result is the same because the multiplication can be done in either order.
0.75(1.06p) = 1.06(0.75p)
an equation is undefined, when its denominator is 0, or turns to 0, because we can't divide anything by 0.
so let's simply set the denominator of this one = 0.
![\bf x^2-7x+10=0\implies (x-2)(x-5)=0\implies x= \begin{cases} 2\\ 5 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(2)^2-9}{(2)^2-7(2)+10}\implies \cfrac{-5}{-10+10}\implies \cfrac{-5}{0}\leftarrow und efined \\\\\\ \cfrac{(5)^2-9}{(5)^2-7(5)+10}\implies \cfrac{16}{-10+10}\implies \cfrac{16}{0}\leftarrow und efined](https://tex.z-dn.net/?f=%5Cbf%20x%5E2-7x%2B10%3D0%5Cimplies%20%28x-2%29%28x-5%29%3D0%5Cimplies%20x%3D%20%5Cbegin%7Bcases%7D%202%5C%5C%205%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7B%282%29%5E2-9%7D%7B%282%29%5E2-7%282%29%2B10%7D%5Cimplies%20%5Ccfrac%7B-5%7D%7B-10%2B10%7D%5Cimplies%20%5Ccfrac%7B-5%7D%7B0%7D%5Cleftarrow%20und%20efined%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B%285%29%5E2-9%7D%7B%285%29%5E2-7%285%29%2B10%7D%5Cimplies%20%5Ccfrac%7B16%7D%7B-10%2B10%7D%5Cimplies%20%5Ccfrac%7B16%7D%7B0%7D%5Cleftarrow%20und%20efined)
9 and 7 are the numerators. The greatest common factor between 3 and 7 is 21. Whatever u multiply the bottom by u have to multiply the top by as well
