Which one is it, I need help

Mathematics

1 answer:

Y_Kistochka [10]2 years ago

7 0

Answer:

Their y-intercepts are equal

Step-by-step explanation:

The y-intercept is the y-value where the function crosses the y-axis. In this problem, functions are presented in 2 ways: algebraically and in a table.

1) Fortunately, the algebraic equation is written in slope-intercept form; this means that intercept is easy to find. The slope-intercept form is y=mx+b, where b is the y-intercept. In function 1, the b value is 10.

2) Another way to describe the y-intercept is the y-value when x=0. So, the y-intercept on a table is wherever the x-value is 0. In this case, the first row represents when x=0. The table says that when x=0, y=10. This means that the y-intercept for function 2 is 10.

Since the y-intercept for both of the functions is 10, it can be said that the 2 functions have equivalent y-intercepts.

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The line x = k intersects the graph of the parabola x = -2y^2 - 3y + 5 at exactly one point. What is k? Thank you! :)

bearhunter [10]

Answer:

49/8 is the value of k

Step-by-step explanation:

We have the system

x = -2y^2 - 3y + 5

x=k

We want to find k such that the system intersects once.

If we substitute the second into the first giving us k=-2y^2-3y+5 we should see we have a quadratic equation in terms of variable y.

This equation has one solution when it's discriminant is 0.

Let's first rewrite the equation in standard form.

Subtracting k on both sides gives

0=-2y^2-3y+5-k

The discriminant can be found by evaluating

b^2-4ac.

Upon comparing 0=-2y^2-3y+5-k to 0=ax^2+bx+c, we see that

a=-2, b=-3, and c=5-k.

So we want to solve the following equation for k:

(-3)^2-4(-2)(5-k)=0

9+8(5-k)=0

Distribute:

9+40-8k=0

49-8k=0

Add 8k on both sides:

49=8k

Divide both sides by 8"

49/8=k

6 0

3 years ago

The diagonals of a square are 4 meters long. The side of this square is equal to the diagonal of a second square. Find the side

jok3333 [9.3K]

Check the picture below.

since the second figure is also a square, then the sides touching the diagonals have to be all equal, and that'd only happen if those sides bisects the larger square's diagonal.