All categories

2 years ago

Solve the system of equations using substitution or graphing.

Mathematics

2 answers:

Lerok [7]2 years ago

4 0

Answer: A

Step-by-step explanation:

We can use substitution to solve this problem. Since we are given y=-x²+4x+5 and y=x+1, we can set them equal to each other.

-x²+4x+5=x+1 [subtract both sides by x]

-x²+3x+5=1 [subtract both sides by 1]

-x²+3x+4=0

Now that we have the equation above, we can factor it to find the roots.

-x²+3x+4=0 [factor out -1]

-1(x²-3x-4)=0 [factor x²-3x-4]

-1(x+1)(x-4)=0

This tells us that x=-1 and x=4.

We can narrow down our answer to A, but let's plug in those values to be sure it is correct.

-(-1)²+4(-1)+5=(-1)+1 [exponent]

-1+4(-1)+5=-1+1 [multiply]

-1-4+5=-1+1 [add and subtract from left to right]

0=0

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

-(4)²+4(4)+5=(4)+1 [exponent]

-16+4(4)+5=4+1 [multiply]

-16+16+5=4+1 [add and subtract from left to right]

5=5

Therefore, we can conclude that A is the correct answer.

Gelneren [198K]2 years ago

3 0

Step-by-step explanation:

I think substitution would be the easiest since you already have one of the variables solved for.

$y=-x^2+4x+5\\y=x+1\\x+1=-x^2+4x+5\\x^2-3x-4=0\\(x-4)(x+1)=0\\x-4=0\\x=4\\x+1=0\\x=-1$

(You can just set the equations equal to each other since they both equal y).

Now, to get the points, plug in x = 4 and x = -1 into one of the equations (I'm going to plug them into y = x+1 because that one is much simpler)

$y(4)=4+1\\y(4)=5\\y(-1)=-1+1\\y(-1)=0$

So, your final points are:

(4,5) and (-1,0)

You might be interested in

Whats 10 percent higher than 39

creativ13 [48]

It will be 49% out of 100

3 0

3 years ago

Abigail and Mason are saving money to buy a CD that costs

maw [93]

Answer:

abigail

Step-by-step explanation:

abigail is correct because she has 30 dimes a dime is worth 30 cents and if 30 times ten equals 300 it would be 3 dollars so all together they have 6 dollars so now all they need is 3 dollars

I hope that made it easier for you good luck

6 0

3 years ago

In an examination of purchasing patterns of shoppers, a sample of 16 shoppers revealed that they spent, on average, $54 per hour

Lesechka [4]

Answer:

$54-1.64\frac{21}{\sqrt{16}}=45.39$

$54 +1.64\frac{21}{\sqrt{16}}=62.61$

So on this case the 90% confidence interval would be given by (45.39;62.61)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=54$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=21$ represent the sample standard deviation

n=16 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.90 or 90%, the value of $\alpha=1-0.9=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=1.64$