What is the value of x in the solution to this system of equations? 3x = 2y + 14<br> y = -6x + 18

If it is about 41 miles around how many square miles does it cover

vodka [1.7K]

Answer:

133,7697

Step-by-step explanation:

$C=2*r*\pi 41 = 2*r*\pi r= 6,5253\\S=r^2*\pi = 133,7697$

8 0

2 years ago

Which statements about the graph of the function f(x) = -x2 - 4x + 2 are true? Select three options.

Nady [450]

Answer:

Domain is all real numbers.

The range is $\{y|y\le 6\}$

The function is increasing over $(-\infty,-2)$ .

The function is decreasing over $(-2,\infty)$

The function has a positive y-intercept.

-----------------This is a guess if I had interpreted your choices correctly:

Second option: The range is $\{y|y\le 6\}$

Third option: The function is increasing over $(-\infty,-2)$ .

Last option: The function has a positive y-intercept.

I can't really read some of your choices. So you can read my above and determine which is false. If you have a question about any of what I said above please let me know.

Note: I guess those 0's are suppose to be infinities? I hopefully your function is $f(x)=-x^2-4x+2$ .

Step-by-step explanation:

$f(x)=-x^2-4x+2$ is a polynomial function which mean it has domain of all real numbers. All this sentence is really saying is that there exists a number for any value you input into $-x^2-4x+2$ .

Now since the is a quadratic then it is a parabola. We know it is a quadratic because it is comparable to $ax^2+bx+c$ , $a \neq 0$ .

This means the graph sort of looks like a U or an upside down U.

It is U, when $a>0$ .

It is upside down U, when $a$ .

So here we have $a=-1$ so $a$ which means the parabola is an upside down U.

Let's look at the range. We know the vertex is either the highest point (if $a$ ) or the lowest point (if $a>0$ ).

The vertex here will be the highest point, again since $a$ .

The vertex's x-coordinate can be found by evaluating $\frac{-b}{2a}$ :

$\frac{-(-4)}{2(-1)}=\frac{4}{-2}=-2$ .

So the y-coordinate can be found by evaluate $-x^2-4x+2$ for $x=-2$ :

$-(-2)^2-4(-2)+2$

$-(4)+8+2$

$4+2$

$6$

So the highest y-coordinate is 6. The range is therefore $(-\infty,6]$ .

If you picture the upside down U in your mind and you know the graph is symmetrical about x=-2.

Then you know the parabola is increasing on $(-\infty,-2)$ and decreasing on $(-2,\infty)$ .

So let's look at the intevals they have:

So on $(-\infty,-2)$ the function is increasing.

Looking on $(-4,\infty)$ the function is increasing on (-4,-2) but decreasing on the rest of that given interval.

The function's y-intercept can be found by putting 0 in for $x$ :

$-(0)^2-4(0)+2$

$-0-0+2$

$0+2$

$2$

The y-intercept is positive since 2>0.

8 0

3 years ago

WHICH IS A TRUE STATEMENT BASED ON THE DOT PLOTS BELOW 10 POINTS

Nata [24]

Answer:

C. Set B has the greater range.

Step-by-step explanation:

We can start out with listing out each set of data in a way that makes it easier to work with.

Set A:

20,20,30,30,40,40,40,40,40,50,50,60,60,60

Set B:

10,10,20,20,20,30,30,30,30,40,50,50,60

We can start by trying to eliminate answer options; starting with D.

To get the mean of a set of data, we need to add all numbers in the data set and then divide by the number of dots on the plot.

For Set B: 10+10+20+20+20+20+30+30+30+30+40+50+50+60=420 then divide by number of dots (14) 420/14=30 The mean of Set B is equal to 30.

Solve the mean for Set A to compare. The mean is 41. D is not true so we can eliminate this answer choice.

We can look at the median of both sets so that we can eliminate answer choice B. The median is the middle most point in the set of data.

Set A median: 40

Set B median: 30

We can eliminate B because it does not have the greater median.

On to option C: range.

To find the range of each data set, we subtract the smallest number from the biggest number.

Set A: 60-20=40

Set B: 60-10= 50

Set B does in fact have a greater range than Set A. Answer choice C is the correct option.

6 0

3 years ago

Lin took 75 boxes of carrots and 80 boxes of potatoes to the market. She sold 68 boxes of carrots and 71 boxes of potatoes. How

enot [183]

For this case we have:

x: Represents the number of carrot boxes

y: Represents the number of boxes of potatoes

Initially we have:

$x = 75\\y = 80$

If you sold 68 boxes of carrot we have:

$x = 75-68 = 7$

If you sold 71 boxes of potatoes, we have:

$y = 80-71 = 9$

The number of boxes I take home is given by: $x + y = 7 + 9 = 16$

ANswer:

7 boxes of carrots left

There are 9 boxes of potatoes left

A total of 16 boxes remain

8 0

3 years ago

Read 2 more answers

At the banquet 450 people had chicken and 150 had pasta. What percent of people has pasta?

Liono4ka [1.6K]

25 percent of people had pasta.

First add 450 and 150 (which equals 600)

Next divide 600 by 150 (which equals 4)

Which means 150 is a fourth of six hundred, and a fourth is 25 percent.

Which leads to my answer of 25 percent

5 0

3 years ago

What is the value of x in the solution to this system of equations? 3x = 2y + 14 y = -6x + 18​

What is the value of x in the solution to this system of equations? 3x = 2y + 14 y = -6x + 18