Answer:
So a point is (-3,-5) and the vertex is (-4,-3)
Step-by-step explanation:
This is in vertex form. Vertex form is y=a(x-h)^2+k where (h,k) is the vertex.
The vertex here is (-4,-3)... now just use a value of x to plug in (any value besides -4)
I will choice -3. This gives -2(-3+4)^2-3
f(-3)=-2(1)^2-3
f(-3)=-2-3
f(-3)=-5
So a point is (-3,-5) and the vertex is (-4,-3)
The two intersection points are (-2.79, -0.58) and (0.79, 6.58).
<h3>
How to find the points of intersection?</h3>
Here we want to solve the system of equations:
y = 2x + 5
x² + y² = 36
To solve this, we need to replace the first equation into the second one:
x² + (2x + 5)² = 36
Now we can solve this for x:
x² + 4x² + 10x + 25 = 36
5x² + 10x - 11 = 0
This is a quadratic equation, to solve it we use the general formula:

So we have two solutions for x:
x = (-10 - 17.9)/10 = -2.79
x = (-10 + 17.9)/10 = 0.79
To get the y-values of the solutions, we evaluate the linear equation in these values of x:
y = 2*(-2.79) + 5 = -0.58
y = 2*( 0.79) + 5 = 6.58
Then the two intersection points are (-2.79, -0.58) and (0.79, 6.58).
If you want to learn more about intersection points:
brainly.com/question/17206319
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Answer:
The answer is a. 21.
Step-by-step explanation:
We solve this question by using Pythagoras theorem to relate the sides of a right angled triangle.
Here,
Hypotenuse of the given triangle(c)=75
Two sides of right angled triangle are:
a=72
b=?
Then,
for a given right angled triangle abc,
Using Pythagoras theorem,

Squaring on both sides,

or,
or, 
or,
or,
∴
So, the value of b is obtained to 21 by the use of Pythagoras theorem.
<h3>Answer: 32 degrees</h3>
================================
Work Shown:
Inscribed angle theorem
arc measure = 2*(inscribed angle)
arc ABC = 2*(angle D)
arc ABC = 2*(35)
arc ABC = 70 degrees
-------------
break arc ABC into its smaller pieces
(minor arc AB)+(minor arc BC) = arc ABC
(38)+(minor arc BC) = 70
minor arc BC = 70-38
minor arc BC = 32