All categories

2 years ago

Which statement explains how the lines x + y = 2 and y = x + 4 are related?

1 answer:

8 0

Answer: X = -1 and Y = 3
—————————————
X + Y = 2
X = 2 - Y
————————
Y = x + 4
Y = 2 - Y + 4
2Y = 2 + 4
2Y = 6
Y = 3
————————
X + Y = 2
X + 3 = 2
X = -1

You might be interested in

What is the mean, median, mode, and range from this data?

Zinaida [17]

Answer: The mean is 4, median is 4, no mode, range is 4

Step-by-step explanation:

mode is adding all the numbers and subtracting by the total amount of whole numbers

median is putting the numbers in a line ex.( 2, 6, 4, 5, 3) and crossing out left to right until theres one number left

mode is which ever number is repeated the most

range is the biggest number subtracted by the smallest number

7 0

3 years ago

Given a function <img src="https://tex.z-dn.net/?f=f%28x%29%3D3x%5E4-5x%5E2%2B2x-3" id="TexFormula1" title="f(x)=3x^4-5x^2+2x-3"

Levart [38]

Answer:

$\huge\boxed{f(-1) = -7}$

Step-by-step explanation:

In order to solve for this function, we need to substitute in our value of x inside to find f(x). Since we are trying to evalue f(-1), we will substitute -1 in as x to our equation.

$f(-1) = 3(-1)^4 - 5(-1)^2 + 2(-1) - 3$

Now we can solve for the function by multiplying/subtracting/adding our known values.

Starting with the first term to the last term:

$3(-1)^4 = 3$

WAIT! How is this possible? $-1^4 = -1$ (according to my calculator), and $3 \cdot -1 = -3$ , not 3!

It's important to note that taking a power of a negative number and multiplying a negative number are two different things. Let's use $-2^2$ as an example.

What your calculator did was follow BEMDAS since it wasn't explicitly told not to.

BEMDAS:

- Brackets

- Exponents

- Multiplication/Division

- Addition/Subtraction

Examining the equation, your calculator used this rule properly. Note that exponents come over multiplication.

So rather than being "-2 squared" - it's "the negative of of 2 squared."

Tying this back into our problem, the squared method would only be true if it looks like $-1^4$ . However, since we're substituting in -1, it looks like $(-1)^4$ , so the expression reads out as "-1 to the fourth."

MULTIPLYING -1 by itself 4 times results in $-1\cdot-1\cdot-1\cdot-1=1$ .

Applying this logic to our original term, $3(-1)^4$ :

$3(-1\cdot-1\cdot-1\cdot-1)$
$3(1)$
$3$

Therefore, our first term is 3.

Let's move on to our second and third terms.

Second term: $-5x^2$

$-5(-1)^2$

Applying the same logic from our first term:

$-5(-1 \cdot -1)$
$-5(1)$
$-5$

Third term: $2x$

$2(-1) = -2$

-3 is just -3, no influence of x.

Combining our terms, we have $3-5-2-3$ .

This comes out to be -7, hence, the value of $f(-1)$ for our function $f(x)=3x^4-5x^2+2x-3$ is -7.

Hope this helped!

4 0

3 years ago

Read 2 more answers

The dot plot shows the number of hours, to the nearest hour, that a sample of 5th graders and 7th graders spend watching televis

Black_prince [1.1K]

Answer:

is the median for both of them .

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

What is 5000 rounded to the nearest hundred

Vlada [557]

The next larger hundred is 5,100 .
The next smaller hundred is 4,900 .
5,000 is exactly midway between 4,900 and 5,100.
Neither of them is closer to 5,000 than the other one is.
So 5,000 is already rounded to the nearest hundred.

4 0

3 years ago

Read 2 more answers

Food inspectors inspect samples of food products to see if they are safe. This can be thought of as a hypothesis test with the f

Molodets [167]

Answer:

b. type II

Step-by-step explanation:

given that food inspectors inspect samples of food products to see if they are safe. This can be thought of as a hypothesis test with the following hypotheses.

H0: the food is safe

Ha: the food is not safe

It was concluded from the hypothesis test that the food is safe while it was not actually safe.

This is a case of false acceptance of null hypothesis when it is false.

In hypothesis test, there are two errors. a type I error is the rejection of a true null hypothesis while a type II error is the non-rejection of a false null hypothesis

So this is type II error because we did not reject a false null hypothesis.

8 0

3 years ago