Answer:
a. yes
b. no
c. no
d. no
e. yes
Step-by-step explanation:
Here, we want to answer yes or no for each of the numbers
a) Yes
If we compare with the general form
y = mx + b
m
is slope and b is y-intercept
so, 2 is slope and 3 is y intercept; so 3 in y-intercept is (0,3)
b. No
This is the point-slope form we are trying to
get
Evaluating this, we have that
y-3 = 2x - 6
y = 2x-6 + 3
y = 2x-3
c) NO
Just insert the values and check here
-1 = 2(5) + 3
it does not work
d) No
Substitute
-4 = 2(-5) + 3
e) Yes
This is the point-slope form
y + 3 = 2x + 6
y = 2x + 6-3 = 2x + 3
Answer: 3/4
Step-by-step explanation:
The line that is parallel to this line will have the same slope of this line, as the two will never intersect. They will run side by side. The line y = 2x - 5 is written in slope-intercept form, which is y = mx + b. The value of m represents the slope, and in this equation m = 2. Therefore, the line we are looking for will have a slope of 2 also.
That line should also be in slope-intercept form. We now know the value of m, but we also know the value of x and y. The ordered pair (8, 10) is a point on the line, and every ordered pair is in the form (x, y). Therefore, x = 8 and y = 10. We can plug those values into y = mx + b, along with m = 2. That gives us:
10 = 2(8) + b We need to solve for b.
10 = 16 + b
b = -6
Lets write as an equation the info provided in the problem:
original area = 200*300 = 60000 squared meters
Adding x meters to the length is: 300 + x
Adding x meters to the width is: 200 + x
If the area doubles in size we have: 2*<span>60000
Now writing as a single equation all info:
(300 + x)(200 + x) = 120000
We have to make the operations and solve:
60000 + 300x + 200x + x^2 = </span><span>120000
x^2 + 500x - 60000 = 0
This is a squared trinomial, to solve it we need two numbers that subtracted give us 500 and multiplied -60000:
(x + 600)(x -100) = 0
So there are two solutions, x = -600 and x = 100, we choose the positive one:
x = 100
thererefore the value of x is 100 meters</span>
Hi there!
For any 45 45 90 right triangle, the length of the hypotenuse is always the square root of 2 times one of the legs.
To get the lengths of the leg, let's divide the length of the hypotenuse by the square root of 2.
We get the following:
When simplifying fractions like this, we want to avoid having radicals on the bottom. In order to remove the radical from the denominator, let's multiply the numerator and the denominator by the square root of 2.
We get the following:
That's your answer.
Have an awesome day! :)
- collinjun0827, Junior Moderator
