Answer:
Slope is -3, y-intercept is 30
Step-by-step explanation:
You take the two points (11,-3) and (7,9), plug them into the formula y2-y1/x2-x2=m. Now, you have 9-(-3)/7-11 which gives you 12/-4, 12/-4 can be simplified into -3 which is your slope. To find y-intercept you must use the formula y=mx+b. Plug -3, your slope, into m, and any of the coordinates on your line into the y and x; I used (7,9). You solve for b from 9=-3*7+b. -3*7 gives you -21, now you have 9=-21+b, to get b by itself, you add 21 to both sides, 30=b. B is your y-intercept.
Answer:
measure of angle 2 and angle 3 are both 97
Step-by-step explanation:
angle 2 and angle 3 are vertical angles
We are given the following:
- parabola passes to both (1,0) and (0,1)
<span> - slope at x = 1 is 4 from the equation of the tangent line </span>
<span>First, we figure out the value of c or the y intercept, we use the second point (0, 1) and substitute to the equation of the parabola. W</span><span>hen x = 0, y = 1. So, c should be equal to 1. The</span><span> parabola is y = ax^2 + bx + 1 </span>
<span>Now, we can substitute the point (1,0) into the equation,
</span>0 = a(1)^2 + b(1) + 1
<span>0 = a + b + 1
a + b = -1 </span>
<span>The slope at x = 1 is equal to 4 which is equal to the first derivative of the equation.</span>
<span>We take the derivative of the equation ,
y = ax^2 + bx + 1</span>
<span>y' = 2ax + b
</span>
<span>x = 1, y' = 2
</span>4 = 2a(1) + b
<span>4 = 2a + b </span>
So, we have two equations and two unknowns,<span> </span>
<span>2a + b = 4 </span>
<span>a + b = -1
</span><span>
Solving simultaneously,
a = 5 </span>
<span>b = -6</span>
<span>Therefore, the eqution of the parabola is y = 5x^2 - 6x + 1 .</span>
Answer:32mm
Step-by-step explanation:
area of triangle = 1/2 *base * height
192mm2 = 1/2 *b* 12mm
192 =6b
base=192/6
base= 32mm
