The equation of the line that passes through (−1,3) and is parallel to the line y = 2x + 2 in slope intercept form is y = 2x + 5
<h3><u>Solution</u>:</h3>
Given that line passes through (-1, 3) and parallel to line y = 2x + 2
We have to find the equation of the line
Let us first find the slope of the line
<em><u>The slope intercept form of line is given as:</u></em>
y = mx + c ---- eqn 1
where "m" is the slope of the line and "c" is the y-intercept
Comparing the given line equation y = 2x + 2 with y = mx + c,
We get slope "m" = 2
The slope of parallel lines are equal
Hence slope of the line which is parallel to y = 2x + 2 is also 2
Now let us find the equation of line with slope "m" = 2 and passes through point (-1, 3)
Substitute (x, y) = (-1, 3) in eqn 1 to find value of "c"
3 = 2(-1) + c
3 = -2 + c
c = 5
Now substitute "c" = 5 and m = 2 in eqn 1 to get equation of required line
y = 2x + 5
Thus the equation of line in slope intercept form is y = 2x + 5
By concepts of polynomials and systems of linear equations, the constants c and d of the expression p(x) = x⁴ - 5 · x³ - 7 · x² + c · x + d are 29 and 30.
<h3>How to determine the missing coefficients of a quartic equation</h3>
A value x is a root of a polynomial if and only if p(x) = 0. We must replace the given equation with the given roots and solve the resulting system of <em>linear</em> equations:
(- 1)⁴ - 5 · (- 1)³ - 7 · (- 1)² + (- 1) · c + d = 0
- c + d = 1 (1)
3⁴ - 5 · 3³ - 7 · 3² + 3 · c + d = 0
3 · c + d = 117 (2)
The solution of this system is c = 29 and d = 30.
By concepts of polynomials and systems of linear equations, the constants c and d of the expression p(x) = x⁴ - 5 · x³ - 7 · x² + c · x + d are 29 and 30.
To learn more on polynomials: brainly.com/question/11536910
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Answer:
A. 36
B. 3.5
Step-by-step explanation:
To solve for the first equation, we could represent the hot dogs as h(1.75-.50), since they are losing .50 cents for each hot dog, <em>h,</em> they make.
Since they want to know how many hot dogs they have to sell to equal the amount of money they spent, we can represent it as an equal sign.
Now all we have to do is add the constants. Add 12 to our overall equation and subtract 57, since the <u>received</u> $12 in donations and <u>lost</u> $57.
Our equation is 12+h1.75=57+.5h We can just put all of the negative numbers on one side and the positive numbers on the other to find out when they will be equal.
First, subtract 12 from 57.
h1.75=45+.5h
Now subtract .5h from both sides.
h1.25=45
Finally, divide both sides by 1.25.
h=36.
They will have to sell 36 hot dogs.
If they want to sell halve the hotdogs for the same price, simply multiply the current price by 2.
The hotdogs will have to cost $3.5.
Hope this helps!
Here three sides of a right angled triangle given.
The three sides are b, 8 and 14.
The side with length 14 is the hypotenuse here. We have to find the side of length b.
To get b, we will use Pythagoras theorem here.
By using Pythagoras theorem we can write,
, where c is the hypotenuse.
So here we can write,
To solve it for b, now we have to move 64 to the left side by subtracting it from both sides.
Now to find b, we have to take square root to both sides. We will get,
We have got the required answer for the side b.
