Help please and thank you!
Answers
Answer:
25. (x, y) = (5, 11)
26. (x, y) = (-1, 1)
Step-by-step explanation:
Both equations are of the form y=( ), so you can set the expressions for y equal to each other. Or, you can subtract the equation with the smaller y-coefficient from the other one.
25.
x +6 = y = 2x +1 . . . . . equate expressions for y
5 = x . . . . . . . . . . . subtract x+1
y = 5+6 = 11 . . . . . using the first equation to find y
(x, y) = (5, 11)
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26.
(y) -(y) = (3x +4) -(x+2) . . . . subtract the first equation from the second
0 = 2x +2 . . . . . . . . . . . . . . simplify
0 = x + 1 . . . . . . . . . . . . . . . . divide by the x-coefficient
x = -1 . . . . . . . . . . . . . . subtract the constant
y = -1 +2 = 1 . . . . . . . . . use the first equation to find y
(x, y) = (-1, 1)
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Of course, when we say "subtract ..." or "divide ..." we mean that you should do the same operation to both sides of the equation. That way the equal sign remains valid. You can always use an expression or variable in place of its equal (this is the substitution property of equality).
The expression (x+1) that we subtract in problem 25 is the smaller x-term plus the constant on the opposite side of the equal sign. That way, we eliminate both the unwanted x-term and the unwanted constant. You can do these operations one at a time (and you were probably taught to do it that way). That is, subtract x; subtract 1.
For 26, the method of solution that puts both the variable and the constant on the same side of the equation and 0 on the other side has certain advantages. Subtracting one side of the equation from both sides (to make an expression equal to zero) will always work, regardless of the expressions involved. After simplification, you can divide by the coefficient of the variable to get the form x+constant=0, and the answer is always x = -constant. These simple instructions require no judgment. You may find it easier to choose to subtract the side with the smaller coefficient, so the result has a positive coefficient. That's not necessary, but it can reduce anxiety and errors.
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Select the correct difference. -3z^7 - (-5z^7)
Answers
(the same number)^(A - B) power
If 'A' = 'B', then the numerator and the denominator are both
(the same number)^to the same power,
and since (A - B = 0) , the quotient is (the same number)^to the ( 0 ) power.
But a fraction with the same thing in the numerator and the denominator is '1 '.
qed
Its undefined DUH like why would it be 1 or 0
X
(-1,-5)
What is the y-intercept of this graphed line?
PLEASE HELP!!!!!!
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The y-intercept is when a point passes through the y-axis. Hope this helps:)
Final answer:
To find the y-intercept of the given linear function, first, the slope of the function is calculated using the provided points. Then, the slope and one pair of coordinates are substituted into the y = mx + b equation to solve for 'b', which is the y-intercept.
Explanation:
In mathematics, specifically in the context of linear functions, the y-intercept is the point at which the line crosses the y-axis. From the provided points, however, it's not immediately clear what the y-intercept is.
To find the y-intercept, we need to determine the line's equation first. The equation of a line can be represented in the form y = mx + b, where 'm' is the slope of the line and 'b' is the y-intercept. To find the slope, we use the formula (y2 - y1) / (x2 - x1), substituting the given points. After calculating the slope, we can plug one pair of the given coordinates into the equation y = mx + b, and solve for 'b', which gives us the y-intercept.
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f(5) for the function -2x² + 2x - 3
usually the value enclosed in a parenthesis in a function is the value of x.
f(x) = -2x² + 2x - 3
So if x = 5 ; then, we simply substitute x by its value
f(5) = -2(5²) + 2(5) - 3
f(5) = -2(25) + 10 - 3
f(5) = -50 + 10 - 3
f(5) = 10 - 50 - 3
f(5) = 10 - 53
f(5) = -43
To find f(5) for the function –2x^2 + 2x – 3, substitute 5 in place of x and evaluate the expression. The value of f(5) is -43.
To find f(5) for the function –2x2 + 2x – 3, simply substitute 5 in place of x in the function.
So, f(5) = –2(5)2 + 2(5) – 3.
Calculating further, f(5) = –2(25) + 10 – 3 = –50 + 10 – 3 = –40 – 3 = -43.
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a).100 b).150 c).175 d).200 e).250
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Answers
mass1 * karat1 + mass2*karat = total mass * total carat
Total mass = 200g.
Total karat = 14.
Let the 9 karat gold to be mixed be x. The 18 karat would weight (200 - x). Since the total = 200g.
9*x + 18*(200 -x) = 14*200
9x + 18*200 - 18*x = 14*200
18*200 + 9x - 18x = 14*200
3600 - 9x = 2800
3600 - 2800 = 9x
800 = 9x
9x = 800
x = 800/9
x ≈ 88.89
Therefore 88.89 grams of 9 karat gold must be mixed.