Step-by-step explanation:
-10x+8x=22
-2x=22
x=22/-2
...x=-11.ans
Answer:
1/24
Step-by-step explanation:
The probability of drawing a diamond is 1/4 and the prob. of rolling a 5 is 1/6. Multiply the two together
9514 1404 393
Answer:
one solution (11, 4)
Step-by-step explanation:
Both equations describe curves with positive slope. The y-intercept of the line (-7) is less than that of the root function (-2), so the line must intersect the root function in exactly one place. There is one solution.
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Solved in the conventional way, the equation would become a quadratic, with two solutions. One of them is extraneous. (That is why I prefer a graphical solution.)
Given ...
x -y = 7
y = √(3x +3) -2
We can substitute for y to get ...
x -7 = √(3x +3) -2
x -5 = √(3x +3)
x^2 -10x +25 = 3x +3 . . . . . . square both sides
x^2 -13x +22 = 0 = (x -11)(x -2) . . . . . gives solutions x=11, x=2
The value x=2 does not satisfy the equation ...
x -7 = √(3x +3) -2 ⇒ 2 -7 = √(3·2 +3) -2 ⇒ -5 = 1 (false)
We have 2 different equations with which we need to work to find the answer to this. First off, the area formula is A = L * W. Our area is 12, so 12 = L * W. Then we have the Pythagorean's theorem we have to worry about, which says that . We are going to solve the area equation for L to get . What we are going to do now is sub that into the other formula in place of L to get and . In order to solve for w, we need to multiply all those terms by w^2 to get rid of the denominator. That leaves us with this then: . We need to factor that now to solve for w. We will bring everything over to the one side of the equation and set it equal to 0. . We are going to use a u substitution here to make the factoring easier. We are going to let so . Now we will factor . When we factor that we get (u - 16)(u - 9). By the Zero Product Property, either u - 16 = 0 or u - 9 = 0. u = 16 and u = 9. But remember that u = w^2, so what we really have, after we make the replacement, is so w = 4, and and w = 3. Now it just so happens that if the length is 4 and the width is 3, the product of those is 12 (the area), and if you remember, in a right triangle with a hypotenuse of 5, the side lengths will be 3 and 4. So your dimensions of the rectangle are that the length is 4 and the width is 3. There you go!