Answer:
Step-by-step explanation:
the solution is right
x^2-6x-7=0:
x^2-6x-7=0
(add 7 to both sides)
x^2-6x=7
x^2-6x+9=7+9 (the coefficient of x² will be used to divide all sides)for here its 1, it will remain same ,
then we get the coefficient of x, divide it by 2 and square it and add it to both sides
which is like these
x²-6x=7
the coefficient of x is -6
-6/2 = -3, square it (-3)² = 9
then add 9 to both sides
x^2-6x+9=7+9
simplifiy the squares on the left hand side
x²+9 = (x-3)²
(x-3)^2=16
√(x-3)^2 )=±√16
x-3=± 4
x=-3±4
then simplify each sign
x=-3+4 x=-3-4
x=1 x=-7
Answer:
8/17
General Formulas and Concepts:
<u>Trigonometry</u>
- [Right Triangles Only] cos∅ = adjacent over hypotenuse
Step-by-step explanation:
<u>Step 1: Define</u>
We are given a right triangle. We can use trig to find the ratio.
<u>Step 2: Identify</u>
<em>POV from angle S</em>
Adjacent = 8
Hypotenuse = 17
<u>Step 3: Write</u>
- Substitute [cosine]: cos(s) = 8/17
Answer: 0.25g<2.50.... g<10
Step-by-step explanation: Let us say that the number of gumballs bought is represented by the variable g. In this case, the question is asking how many gumballs can be bought without surpassing the price of $2.50. We know that each gumball is $0.25, therefore the number of gumballs we buy times $0.25 has to be less than $2.50. Hence, the inequality would be 0.25g<2.50. If we were to solve this then g<2.50/0.25-----> g<10. In conclusion, the number of gumballs you can buy has to be less than 10. Thank you!
Answer:
- 50 ft by 75 ft
- 3750 square feet
Step-by-step explanation:
Let x represent the length of the side not parallel to the partition. Then the length of the side parallel to the partition is ...
y = (300 -2x)/3
And the enclosed area is ...
A = xy = x(300 -2x)/3 = (2/3)(x)(150 -x)
This is the equation of a parabola with x-intercepts at x=0 and x=150. The line of symmetry, hence the vertex, is located halfway between these values, at x=75.
The maximum area is enclosed when the dimensions are ...
50 ft by 75 ft
That maximum area is 3750 square feet.
_____
<em>Comment on the solution</em>
The generic solution to problems of this sort is that half the fence (cost) is used in each of the orthogonal directions. Here, half the fence is 150 ft, so the long side measures 150'/2 = 75', and the short side measures 150'/3 = 50'. This remains true regardless of the number of partitions, and regardless if part or all of one side is missing (e.g. bounded by a barn or river).
<h3>
Answer: y = (3/4)x + 13/4</h3>
This is the same as writing y = 0.75x + 3.25
slope is 3/4 = 0.75
y intercept is 13/4 = 3.25
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Explanation:
One marked point on this line is (-3,1)
Another point is at (1,4)
Let's find the slope of the line through these two points.
m = (y2-y1)/(x2-x1)
m = (4-1)/(1-(-3))
m = (4-1)/(1+3)
m = 3/4
m = 0.75
Now let's use point slope form to find the equation of the line
y - y1 = m(x - x1)
y - 1 = 0.75(x - (-3))
y - 1 = 0.75(x + 3)
y - 1 = 0.75x + 2.25
y = 0.75x + 2.25 + 1
y = 0.75x + 3.25
If you wanted, you can convert those decimal values to fraction form
- 0.75 = 75/100 = 3/4
- 3.25 = 325/100 = 13/4
That means the equation
y = 0.75x + 3.25
is the same as
y = (3/4)x + 13/4
