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3 years ago

Is y=3x^2-x-1 a function

Mathematics

1 answer:

NARA [144]3 years ago

7 0

Answer: Yes it is a function.

This is because any x input leads to exactly one y output.

The graph passes the vertical line test. It is impossible to draw a single vertical line through more than one point on the parabolic curve.

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-4x-15y=-17<br>-x+5y=-13<br><img src="https://tex.z-dn.net/?f=%20-%204x%20-%2015y%20%3D%20%20-%2017%20%20%5C%5C%20%20-%20x%20%2B

salantis [7]

To solve this system of linear equations we need a little trick called elimination steps are below

we are given the following system of equations
$- 4x - 15y = - 17$
$- x + 5y = - 13$
if you look at the x variables in both equations you can see that we can easily eliminate them by multiplying the bottom equation by -4 as so
$- 4x - 15y = - 17$
$- 4( - x + 5y = - 13)$
simplify and we get
$- 4x - 15y = - 17$
$4x - 20y = 52$
now we can combine like terms on each side with the x's cancelling and get

$- 35y = 35$
now divide off -35
$y = - 1$
great now we can go back to our original system and pick a equation and substitute y back in to find x lets use

$- x + 5y = 13$
so now we substitute y and get
$- x + 5( - 1) = 13$
$- x - 5 = 13$
$- x = 17$
$x = - 17$

now we put x and y into one coordinate (x,y)
so now our FINAL ANSWER IS
(-17,-1)

6 0

3 years ago

Sarah invested $1000 in an account paying 5.5% interest compounded semi-annually. How long will it take for the account balance

NISA [10]

Answer: it will take 43.25 years

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = $1000

A = $10450

r = 5.5% = 5.5/100 = 0.055

n = 2 because it was compounded 2 times in a year.

Therefore,.

10450 = 1000(1 + 0.055/2)^2 × t

10450/1000 = (1 + 0.0275)^2t

10.45 = (1.0275)^2t

Taking log of both sides, it becomes

Log 10.45 = 2t log 1.0275

1.019 = 2t × 0.01178 = 0.02356t

t = 1.019/0.02356

t = 43.25 years

4 0

3 years ago

you have 280 gallons of a solution that is 20% salt. how much water should be added to dilute the solution down to 14% salt

Readme [11.4K]

19.6 gallons of water need to be added.....
I think

5 0

4 years ago

Bernie played 3 rounds of golf, and the mean of his score was 78. If his lowest score was 74, what is the greatest possible valu

zmey [24]

Answer:

85.

Step-by-step explanation:

Let x represent Bernie's highest score.

We have been given that Bernie played 3 rounds of golf, and the mean of his score was 78. His lowest score was 74.

Since Bernie's lowest score is 74, so we can assume that his score on 2nd round would be 75.

Now, we will use mean or average formula to solve our given problem.

$\text{Mean}=\frac{\text{Sum of all data points}}{\text{Number of data points}}$

$78=\frac{74+75+x}{3}$

Let us solve for x.

$78\cdot 3=\frac{74+75+x}{3}\cdot 3$

$234=74+75+x$

$234=149+x$

$x=234-149$

$x=85$

Therefore, the greatest possible value of his highest score would be 85.

5 0

4 years ago

Drag each factor to the correct location on the image. If p(1) = 3, p(-4) = 8, p(5) = 0, p(7) = 9, p(-10) = 1, and p(-12) = 0, d

Dominik [7]

Answer:

Step-by-step explanation:

Recall that when we are factoring a polynomial, we are implicitly finding its roots. By finding a root, we are looking for a value of x (say c) such that p(c) =0. When this happens, our polynomial has the the polynomial (x-c) as a factor.

We are given the values of p at some values of x. We notice that p(5) = 0 and p(-12) =0. So, this means that our polynomial has as a factor the polynomials (x-5) and (x+12).

4 0

3 years ago