Answer:
20 / x = 10
20 / 2 = 10
Step-by-step explanation:
quotient is the result obtained by dividing
Answer:
12 < x < 16
What we know:
- The longest side of the triangle is 20, another side length is 'x + 4'
- Since the triangle is acute, we know that the value of 'x' will have to be <u>greater than its right triangle value</u> because whatever 'x' equals will result in a <em>right </em>triangle, not an acute one
- We must solve for the <em>right </em>triangle first in order to determine the acute triangle
Solving for 'x' in the right triangle:
- a^2 + b^2 = c^2
- (x+4)^2 + x^2 = 20^2
- x^2 + x^2 + 8x + 16 = 400
- 2x^2 + 8x - 384 = 0
- simplify x^2 + 4x - 192 = 0
- factor (x + 16) (x - 12) = 0
- solve for each 'x' x + 16 = 0 & x - 12 = 0
- x = -16 & x = 12
- check the value of 'x' cannot be negative, so it is not -16. this means the value of 'x' is 12
- the value of 12 for 'x' makes a <em>right triangle, </em>so that is not the answer. this means the the value of 'x' needs to be <em>greater</em> than 12
<u>Checking your answer:</u>
- original equation (x + 4)^2 + x^2 = 20^2
- with answer (12 + 4)^2 + (12)^2 = 20^2
- (16)^2 + (12)^2 = 20^2
- 256 + 144 = 400
- 400 = 400 this is true, so the answer of 'x = 12' is <em>correct </em>for making it into a <em>right triangle</em>
<em></em>
Solving for 'x' in the acute triangle:
- x = 12 makes a right triangle
- x > 12 minimum for an acute triangle
- what is the maximum value for 'x' in the acute triangle? take the two other side lengths --> (x + 4) < 20 (longest side, so it will be the greater number)
- simplify x < 16
- x < 16 maximum for an acute triangle
Conclusion:
- if 'x = 12' makes a right triangle, then 'x > 12' and 'x < 16' are the values that will make it acute
- answer 12 < x < 16
Answer:
x=2, -4
Step-by-step explanation:
The equation is 
. The x-intercept is the point(s) where the function intersects the x axis, so this value can be found by plugging in 0 for y. doing so results in 
. Then, solve for x by moving 18 over, dividing by -2, square rooting both sides, and subtracting 1 to find the value of x.
Zero pairs can be (+1)+(-1)=0.
Answer:
Step-by-step explanation:
b. The set of all pairs of line segments c. Congruent pairs of segments have the same measure. 8. ... ZB ZDCA,. 2. Given. ZA. ZDCB. 3. mZB mZDCB,. 3. Definition of. mZA. mZDCB congruent angles .
