Can I please get some help on these questions:
1. If , find the value of 2 square root of 17-x = 2x-10, find the value of x/4.
2. If absolute value of 3x+6 < 9, then which of the following is a possible value of x ?
My answer choices are -7, 1, -5, -1, 10. When I solve for x, I get x<1, so can't it be -7, -5, OR -1?
3. If 5<absolute value of 2x+1<11, then which of the following is a possible value of x ?
I get 2<x<5, My answer choices are -6, -4, 2, -3, and 5.
4. If y is inversely proportional to x and y = 8 when x = 1.55, what is the value of x when y = -0.62?
I'm not sure on this
5. Simplify the following expression: 41abc(-1 + z)-41abcz
...
Thanks to anyone who can help me!
#1 is worded wrong, if 2 square root of 17-x = 2x-10, find the value of x/4.
#1 Can't quite parse the problem, but if
2√(17-x) = 2x-10
√(17-x) = x - 5
17-x = x^2 - 10x + 25
x^2 - 9x + 8 = 0
(x-1)(x-8) = 0
x = 1 or 8
but x=1 does not fit the original equation, so x=8, and x/4 = 2
#2 Recall that |n| = n if n>=0 and -n if n<0
|3x+6|<9
if 3x+6>=0, then
3x+6 < 9
x < 1
If 3x+6 < 0,
-(3x+6) < 9
-3x - 6 < 9
-3x < 15
x > -5
so -5 < x < 1
Looks like -1 is the only choice.
Think of the graph of |x|. It is a V-shape. So, if |x| < n you get the pointy part of the v below the line y=n.
#3
5 < |2x+1| < 11
This is just a sneaky way of getting you to solve two inequalities in one problem. You end up with
-6 < x < -3 or 2 < x < 5
Looks like -4 is the only choice.
#4
y = k/x
8 = k/1.55
k = 12.4
so, when y = -.62
-.62 = 12.4/x
x = -20
#5
41abc(-1 + z)-41abcz
ever heard of the distributive property?
41abc(-1) + 41abc(z) - 41abcz
-41abc + 41abcz - 41abcz
-41abc
Thank you!
1. To solve the equation 2√(17-x) = 2x-10, we can start by isolating the square root term by dividing both sides of the equation by 2. This gives us √(17-x) = x-5.
To eliminate the square root, we can square both sides of the equation. This gives us (√(17-x))^2 = (x-5)^2. Simplifying further, we get 17-x = x^2 - 10x + 25.
Rearranging the equation, we have x^2 - 11x + 8 = 0. Now, we can factor this quadratic equation as (x-1)(x-8) = 0. Setting each factor equal to zero, we can find the possible values of x: x-1 = 0 or x-8 = 0.
Solving for x, we get x = 1 or x = 8.
To find the value of x/4, we can substitute the values of x into the expression x/4. The possible values of x are 1 and 8, so x/4 would be 1/4 or 8/4, which simplifies to 1/4 or 2, respectively.
2. Given that |3x+6| < 9, we need to solve for the possible values of x. The absolute value of a number is always non-negative, so |3x+6| < 9 implies -9 < 3x+6 < 9.
By subtracting 6 from all sides of the inequality, we get -15 < 3x < 3. Dividing by 3, we have -5 < x < 1.
From the answer choices, the values of x that satisfy this inequality are -7, -5, and -1.
3. We are given 5 < |2x+1| < 11. To solve this inequality, we need to consider two cases:
Case 1: 2x+1 is positive
In this case, the absolute value of 2x+1 is equal to 2x+1 itself. So, the inequality becomes 5 < 2x+1 < 11.
By subtracting 1 from all sides of the inequality, we get 4 < 2x < 10. Dividing by 2, we have 2 < x < 5.
Case 2: 2x+1 is negative
In this case, the absolute value of 2x+1 is equal to -(2x+1). So, the inequality becomes 5 < -(2x+1) < 11.
Multiplying all sides by -1, the inequality becomes -11 < 2x+1 < -5.
Subtracting 1 from all sides of the inequality, we get -12 < 2x < -6. Dividing by 2, we have -6 < x < -3.
Combining the results from both cases, we find that -6 < x < -3 and 2 < x < 5.
From the list of answer choices, the possible value of x is 2.
4. If y is inversely proportional to x, it means that y = k/x, where k is a constant.
To find the value of k, we can use the given information that y = 8 when x = 1.55.
Plugging these values into the equation, we have 8 = k / (1.55). Solving for k, we get k = 12.4.
Now that we know the value of k, we can find the value of x when y = -0.62.
Substituting these values into the equation k/x = y, we have 12.4 / x = -0.62.
Solving for x, we get x = -20.
5. To simplify the expression 41abc(-1 + z) - 41abcz, we can distribute the term -1 + z to the terms inside the parentheses.
This gives us -41abc + 41abcz - 41abcz, which simplifies to -41abc.