Answer:
Only choices C and D are solutions
Step-by-step explanation:
6x + 3y = -15
y = -2x - 5
6x + 3y = -15
6x + 3(-2x - 5) = -15
6x - 6x - 15 = -15
0 = 0
Since 0 = 0 is a true statement, both equations of this system are the same equation and represent a single line on the coordinate plane.
We need to check each choice in just one equation.
Let's use the second equation.
y = -2x - 5
A.
(2, 7)
7 = -2(2) - 5
7 = -4 - 5
7 = -9 False
Not a solution
B.
(5, 0)
0 = -2(5) - 5
0 = -10 - 5
0 = -15 False
Not a solution
C.
(-3, 1)
1 = -2(-3) - 5
1 = 6 - 5
1 = 1 True
Solution
D.
-13 = -2(4) - 5
-13 = -8 - 5
-13 = -13 True
Solution
Answer: Only choices C and D are solutions
4(x + 9) + 5x = 9x - 36
=> 4x + 36 + 5x = 9x - 36
=> 9x + 36 = 9x - 36
=> 9x - 9x = -36 - 36
=> 0 = -72
You can see that the equation doesn't hold true.
So there is no solution for this equation.
Answer is C. no real solutions
Answer:
1.) Yes
2.) Yes
Step-by-step explanation:
Given that
n = k(k + 7)
If k is a positive integer and n = k(k + 7), is n divisible by 6 ?
(1) k is odd. Yes.
Let assume that k = 3
Then, n = 3(3 + 7)
n = 3 × 10
n = 30.
30 is divisible by 6.
(2) When k is divided by 3, the remainder is 2. That is,
Let k = 5
Then,
5/3 = 1 remainder 2
Substitute k into the equation
n = k(k + 7)
n = 5(5 + 7)
n = 5 × 12
n = 60
And 60 is divisible by 6.
Therefore, the answer to both questions is Yes.
Answer: The answer is spinner B. There are 8 sections on the spinner and 4 of them have letter A, so P(A)= 1/2.
Answer: The two roots are x = 3/2 and x = -2
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Explanation:
You have the right idea so far. But the two numbers should be 3 and -4 since
The -1 being the coefficient of the x term.
This means you need to change the -3x and 4x to 3x and -4x respectively. The other inner boxes are correct.
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Refer to the diagram below to see one way to fill out the box method, and that helps determine the factorization.
If we place a 2x to the left of -2x^2, then we need an -x up top because 2x*(-x) = -2x^2
Then based on that outer 2x, we need a -2 up top over the -4x. That way we get 2x*(-2) = -4x
So we have the factor -x-2 along the top
The last thing missing is the -3 to the left of 3x. Note how -3*(-x) = 3x in the left corner and -3*(-2) = 6 in the lower right corner.
We have the factor 2x-3 along the left side.
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The two factors are (2x-3) and (-x-2) which leads to the factorization (x+3)(-x+2)
The last thing to do is set each factor equal to 0 and solve for x
- 2x-3 = 0 solves to x = 3/2 = 1.5
- -x-2 = 0 solves to x = -2
The two roots are x = 3/2 and x = -2
