The roots of the equation are 2 and k
substituting x=2 in the equation
(x+4)(x-p) = 2-x
(2+4)(2-p) = 2-2
6(2-p) = 0
dividing 6 both side, the answer is
p = 2
substituting x in the equation we
(x-4)(x-p) = 2-x
x² - 2x + 4x- 8 = 2-x
x² - 2x + 4x -8 -2 -x = 0
x² + 3x - 10 = 0
x² + 5x -2x - 10 = 0
x(x + 5) -2( x + 5) = 0
(x + 5)( x - 2) =0
(x + 5) = 0 or (x - 2) = 0
x = -5 and x = 2
therefor k = -5 and p = 2
Answer:
![\boxed{x=73.74}](https://tex.z-dn.net/?f=%5Cboxed%7Bx%3D73.74%7D)
![\boxed{y=16.26}](https://tex.z-dn.net/?f=%5Cboxed%7By%3D16.26%7D)
![\boxed{z=25}](https://tex.z-dn.net/?f=%5Cboxed%7Bz%3D25%7D)
Step-by-step explanation:
Hello there!
<u>Algebra 1</u>
The first thing we should find is the missing angle
Because this is a right triangle we can solve it using the Pythagorean Theorem
The Pythagorean theorem states that the sum of the two legs squared equal the hypotenuse squared
the formula...
where a and b = legs and c = hypotenuse
we are given two legs so we plug in a and b and solve for c
![7^2+24^2=c^2\\7^2=49\\24^2=576\\576+49=625\\625=c^2\\\sqrt{c^2} =c\\\sqrt{625} =25\\c=25](https://tex.z-dn.net/?f=7%5E2%2B24%5E2%3Dc%5E2%5C%5C7%5E2%3D49%5C%5C24%5E2%3D576%5C%5C576%2B49%3D625%5C%5C625%3Dc%5E2%5C%5C%5Csqrt%7Bc%5E2%7D%20%3Dc%5C%5C%5Csqrt%7B625%7D%20%3D25%5C%5Cc%3D25)
so we can conclude that the missing side length ( or z) equals 25
now to solve for the angles
<u>Trigonometry</u>
We can solve for y using sin
sin = opposite side divided by the hypotenuse
the opposite of y is 7 and the hypotenuse is 25
so we set up an equation ![sin(y)=\frac{7}{25}](https://tex.z-dn.net/?f=sin%28y%29%3D%5Cfrac%7B7%7D%7B25%7D)
now we solve for y
![\frac{7}{28} =.28\\arcsin(y)=y\\arcsin(.28)=16.26020471](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B28%7D%20%3D.28%5C%5Carcsin%28y%29%3Dy%5C%5Carcsin%28.28%29%3D16.26020471)
then we round to the nearest hundredth
so we can conclude that angle labeled y = 16.26
<u>basic geometry</u>
Remember all of the angles in a triangle add up to equal 180 so we can find x by subtract the known angles from 180
180 - 90 - 16.26 = 73.74 so we can conclude that x = 73.74
Answer:
B. ![(200+400)-250=p](https://tex.z-dn.net/?f=%28200%2B400%29-250%3Dp)
Step-by-step explanation:
Let p be number of points Michael needs to score in 2nd game to catch up.
We have been given that Janet scored 200 and 400 points in the first 2 rounds of a computer game. So the total points scored by Janet in two games will be:
points.
We are also told that Michael had scored 250 points in the first round and he want to get the same total score as Janet.
So we can find the number of points Michael needs to score to catch up Janet by subtracting the number of points scored by Michael in 1st game from total number of points scored by Janet in two games. We can represent this information in an equation as:
![(200+400)-250=p](https://tex.z-dn.net/?f=%28200%2B400%29-250%3Dp)
Therefore, the equation
will help Michael to find the number of points he need to catch up Janet and option B is the correct choice.
Answer:
x=−3 when y=−27
Step-by-step explanation:
Hope it's help, study well and goodluck!!!