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3 years ago

A relation is a function if _____.

Mathematics

2 answers:

allsm [11]3 years ago

8 0

The answer is d. there is exactly one input for each output

erastova [34]3 years ago

7 0

I believe the answer to your question is D. there is exactly one input for each output.

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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

Which table shows a proportional relationship between x and y? please help and answer quick plz

gavmur [86]

The answer is c.

(a)

x * 2 = y
2 * 2 = 4
3 * 2 = 6
4 * 2 = 8 not 9

(b)

unknown formula

(c)

x * 3 = y
4 * 3 = 12
5 * 3 = 15
6 * 3 = 18

(d)

x * 4
1 * 4 = 4
2 * 4 = 8
3 * 3 = 9 not 15

3 0

3 years ago

Which expression is equivalent to 1/2 (2n+6)?

Fynjy0 [20]

Multiply the bracket by 1/2

1/2(2n +6)

cross out 2 and 2n and divide by 2.

cross out 6 and 2 and divide by 2

n+3

Answer is n+3

7 0

3 years ago

Read 2 more answers

Ben's age is currently twice of his sister, Emma. 8 years ago, Ben's age was 2 and a half times that of Emma's age at that time.

Yakvenalex [24]

Emma is now 24 years old then Ben would be 2E, or 48 years old.

<h3>What is a system of equations?</h3>

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Let B and E be Ben's and Emma's current ages, respectively.

We have given that;

Ben's age is currently twice of his sister, Emma.

B = 2E

and

8 years ago, Ben's age was 2 and a half times that of Emma's age

B-8 = 2.5(E-8)

We can substitute the value of B from the first equation into the last one

B-8 = 2.5(E-8)

(2E)-8 = 2.5(E-8)

2E-8 = 2.5E- 20

-0.5E = -12

E = 24

Thus, Emma is now 24 years old then Ben would be 2E, or 48 years old.

Learn more about equations here;

brainly.com/question/10413253

#SPJ1

8 0

2 years ago

Read 2 more answers

Can you please answer the question?

Sliva [168]

Answer:

I think its 21 im not sure tho! Sorry if im wrong! :(

Step-by-step explanation:

6 0

3 years ago