Solve the equation 3(x-3)=6x+3

Find the distance between the origin and the points (-8,4)

Papessa [141]

Hi, I'm happy to help!

To solve this, we need to find the distance from the origin to the y coordinate value, x coordinate value, then use the Pythagorean Theorem.

The origin of a graph (center) has the coordinates (0,0), so this will be our other coordinates.

First, let's find the x coordinate distance change. We move from the x coordinate 0, to the x coordinate -8, so we move 8 x units.

Next, let's find the y coordinate distance change. We move from the y coordinate 0, to the y coordinate 4, so we move 4 y units.

Now that we have these two leg lengths, let's imagine this as a right triangle. Moving from the origin, we draw a line from (0,0), to (-8,0). Then, we draw a line from (-8,0) to (-8,4). Now, draw a direct line from (0,0), to (-8,4). We have the length of the first(8) and second(4) lines, and we need to find the third line length to find our answer. To do this, we use the Pythagorean Theorem, which states that a²+b²=c². This says that, in a right triangle, the square of the two shorter lengths equals the square of the longest length. The longest length is what we are solving for.

Let's say x distance is a, and y distance is b. Now, apply the values:

8²+4²=c²

64+16=c²

80=c²

Now, we need to find the value of c, so we need to find the square root of 80.

√80=c

8.9442...=c

Since the number goes on forever, we need to round it. For this example, let's round it to the nearest tenth, which would be 8.9.

To summarize the distance between the origin and the coordinates (-8,4), is about 8.9.

I hope this was helpful, keep learning! :D

8 0

3 years ago

At a lemonade stand, pink lemonade costs $2.50 and sweet tea lemonade costs $4. In one morning, the stand sells 21 drinks for $6

snow_tiger [21]

Answer:

lemonade = 11

Step-by-step explanation:

let p = pink lemonade

let t = sweet tea

create a system of equations -- one with quantity, one with associate costs

p + t = 21

2.5p + 4t = 67.5

substitution method: let t = 21 - p

2.5p + 4(21 - p) = 67.5

2.5p + 84 - 4p = 67.5

-1.5 p = -16.5

p = 11

t = 21 - 11

t = 10

4 0

3 years ago

In a certain school district, it was observed that 32% of the students in the element schools were classified as only children (

kipiarov [429]

Answer:

We conclude that the proportion of only children in the special program is significantly different from the proportion for the school district.

Step-by-step explanation:

We are given that in a certain school district, it was observed that 32% of the students in the element schools were classified as only children (no siblings).

However, in the special program for talented and gifted children, 135 out of 347 students are only children.

Let p = population proportion of only children in the special program.

So, Null Hypothesis, $H_0$ : p = 32% {means that the proportion of only children in the special program is equal to the proportion for the school district}

Alternate Hypothesis, $H_A$ : p $\neq$ 32% {means that the proportion of only children in the special program is significantly different from the proportion for the school district}

The test statistics that would be used here One-sample z proportion statistics;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of only children in the special program = $\frac{135}{347}$ = 0.39

n = sample of students = 347

So, test statistics = $\frac{0.39-0.32}{\sqrt{\frac{0.39(1-0.39)}{347} } }$

= 2.673

The value of z test statistics is 2.673.

Now, at 0.02 significance level the z table gives critical value of -2.3263 and 2.3263 for two-tailed test. Since our test statistics does not lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the proportion of only children in the special program is significantly different from the proportion for the school district.

4 0

3 years ago

1.84repeating as a mixed number in simplest form

Dennis_Churaev [7]

Hello!

I'm assuming you're looking for 1.848484.

The first thing we want to do is get rid of the repeating part. The way we can do this is subtract the number we are given from itself multiplied by a power of 10. So, set 1.8484... = x. And based off of that, find 100x. This is because the next time the decimal repeating will become .8484 again is after two numbers pass.

1.848484... = x

184.8484... = 100x

Next, subtract x from 100x. This will get rid of the repeating decimal.

100x - x = 184.8484... - 1.8484

99x = 183

Finally, divide both sides by 99. This leaves us with a fraction.

99x = 183

x = 183 / 99

Simplify this fraction.

183 / 99 -> 61 / 33

Finally, turn it into a mixed number, as this is the form your question is looking for.

61/33 -> 1 28/33

Hope this helps!

7 0

3 years ago

Please help!!! Correct answer will get brainliest and full ratings !!!!

Afina-wow [57]

Many ways to do this.
A, Plot the points and connect them, if it is a straight line you won.

B, A linear function has a set slope. You can calculate this and apply to all points. If it works you won.

4 0

4 years ago