Answer:
f(x) = 4
Step-by-step explanation:
Let us assume that the linear function f(x) = ax + b
Here, we have to find the value of a and b to know the function.
Given that f(-10) = 4 and f(-2) = 4
So, -10a + b = 4 ....... (1) and
-2a + b = 4 .......... (2)
From equations (1) and (2) we get a = 0 and b = 4.
So, the linear function is f(x) = 4. (Answer)
Basically, you have two circles. You are asked to take circle 1 and "move it" so that it is on top of circle 2. This process of moving is called a translation and can be thought of as sliding. You do this by ensuring that the two have the same center. So, starting at (-4,5) how do you have to move to end up at (2,1)?
To do this we need to move right 6 as the x-coordinate goes from -4 to 2. We also need to move down 4 as the y-coordinate goes from 5 to 1. So we add 6 to the x-coordinate and subtract 4 from the y-coordinate. The transformation rule is (x+6, y-4).
Once you do this the circles have the same center. Next you wish to dilate circle 1 so it ends up being the same size at circle 2. That means you stretch it out in such a way that it keeps its shape. Circle 1 has a radius of 2 centimeters and circle 2 has a radius of 6 centimeters. That is 3x bigger. So we dilate by a factor of 3.
Translations and dilations (along with reflections and rotations) belong to a group known as transformations.
Answer:
The proportion that can be used to find x is;
(200-x)/x = 7/6
Step-by-step explanation:
Now, we want to find the proportion which can be used to find x.
From the question, we are told that the father skater traveled 7 ft for every 6 ft of the slower skater;
this means that the ratio of their speed is 7:6
Now, when they passed each other , the slower skater has traveled x ft, what this means is that the faster skater will have traveled a distance of (200-x) ft at that moment they passed each other.
Mathematically, since their time is equal i.e the time they used to pass each other, then, the ratio of their distances is same as the ratio of their speeds;
Hence;
(200-x)/x = 7/6 or x/(200-x) = 6/7
1and2 are supplementary angles is conjecture is false
Answer:
See below
Step-by-step explanation:
<u>Given function</u>
<u>We can find its factors:</u>
- x³ + 3x² - 7x - 21 =
- x²(x + 3) - 7(x + 3) =
- (x² - 7)(x + 3)
We can conclude that the given polynomial function is fully divisible by (x + 3) and the quotient is (x² - 7)
Also one of zeros of the function is -3
