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3 years ago

Which function has a vertex at the origin?

Mathematics

1 answer:

Wewaii [24]3 years ago

6 0

Answer:

f(x) = –x2

Step-by-step explanation:

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Help, I’m a bit confused, what would the coordinates be. The question is in the picture!!!!!

kotykmax [81]

(x+4), (y-1) because the figure is translated 4 units to the right and 1 down.

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3 years ago

Does the point (4, 8) satisfy the equation y = x + 6

Oksanka [162]

It can, it just depends upon the slope

Do you know what the slope is?

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3 years ago

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If the force acting on an object stays the same, then the acceleration of the object is inversely proportional to its mass. If a

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3 years ago

A bridge in the shape of an arch connects two cities separated by a river. The two ends of the bridge are located at (–7, –13) a

sdas [7]

Answer:

$y=-\dfrac{13}{49}x^2$

Step-by-step explanation:

The shape of an arch corresponds to a parabola.

the general equation for a parabola is:

$y=ax^2+bx+c$

we're given three coordinates: (-7,-13),(7,-13) and (0,0)

so we can plug these values in the general equation to make 3 separate equations:

(x,y) = (-7,-13)

$-13=a(-7)^2+b(-7)+c$

$49a-7b+c=-13$

(x,y) = (7,-13)

$-13=a(7)^2+b(7)+c$

$49a+7b+c=-13$

(x,y) = (0,0)

$0=a(0)^2+b(7)+c$

$c=0$

so we have three equations. and we can solve them simultaneously to find the values of a,b, and c.

we've already found c = 0, let's use substitute it to other equations.

$49a-7b+c=-13\quad\Rightarrow\quad49a-7b=-13$

$49a+7b+c=-13\quad\Rightarrow\quad49a+7b=-13$

we can solve these two equation using the elimination method, by simply adding the two equations

$\quad\quad49a-7b=-13\\+\quad49a+7b=-13$

------------------------------

$\quad\quad 98a=-26$

$\quad\quad a=-\dfrac{13}{49}$

Now we can plug this value of a in any of the two equations.

$49a-7b=-13$

$49\left(-\dfrac{13}{49}\right)-7b=-13$

$-13-7b=-13$

$-7b=0$

$b=0$

We have the values of a,b, and c. We can plug them in the general equation to find the equation of the arch.

$y=\left(-\dfrac{13}{49}\right)x^2+0x+0$

$y=-\dfrac{13}{49}x^2$

$49y=-13x^2$

This our equation of the arch!

5 0

3 years ago

Question 2.2. Which ordered pairs make the inequality true?

taurus [48]

<span>Question 2.2. Which ordered pairs make the inequality true?</span><span>2x + y > –4</span>The solutions are (-1, 2) and (1, -5), look at the graph in the attachment.

Question 3.3. What is the slope of the line represented by the equation?

There is no equation

Question 4.4. What is the slope of the line represented by the equation 6x - 3y = 4?

Convert to slope-intercept form:

6x - 3y = 4

Subtract 6x to both sides:

-3y = -6x + 4

Divide -3 to both sides:

y = -6/-3x + 4/-3

Simplify:

y = 2x - 4/3

Now it's in slope intercept form, y = mx + b, where 'm' is the slope. So the slope here is 2.

Question 5.5. What is the simplified form of the expression?

15y - 3(4y + 10)

Distribute -3 into the parenthesis:

15y - 12y - 30

Combine like terms:

3y - 30

8 0

3 years ago