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3 years ago

Distance between (5, -3) and (9, 2).

Mathematics

1 answer:

Mashutka [201]3 years ago

6 0

Step-by-step explanation:

Using distance formula:

√(5 - 9)² + (-3 - 2)²

√(-4)² + (-5)²

√16+25

√41

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Consider a parallelogram in which one side is 3 inches long, another side measures 4 inches, and the measurement of one angle is

Musya8 [376]

9514 1404 393

Answer:

(a) one parallelogram

(b) opposite sides are 3 inches and 4 inches. Opposite angles are 45° and 135°

Step-by-step explanation:

Opposite sides of a parallelogram are the same length, so if one side is 3 inches, so is the opposite side. Similarly, if one side is 4 inches, so is the opposite side. If sides have different lengths, they must be adjacent sides. The given numbers tell us the lengths of all of the sides.

The 4 inch sides are adjacent to the 3 inch sides. Thus the angle between a 4 inch side and a 3 inch side must be 45°. Opposite angles are congruent, and adjacent angles are supplementary, so specifying one angle specifies them all.

Only one parallelogram can be formed with these sides and angles. (The acute angle can be at the left end or the right end of the long side. This gives rise to two possible congruent orientations of the parallelogram. Because these are congruent, we claim only one parallelogram is possible. Each is a reflection of the other.)

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3 years ago

A group of artists is selling small prints to raise money for charity. They sell p prints, and make a profit of f(p) on the sale

liraira [26]

The correct answer is is D) If the group sells 15 prints they will loose $85.

To figure out which statement is true, we have to evaluate the function ,

$p(x)=17x-340$ for all the values given in options (A)-(D). A negative output represents a loss and a positive output will represent a profit.

In A $p=12$ so $f(12)=17\times 12-340=-136$ . In this case we gather that if they sell 12 prints, they will make a loss of $136. This tells us that option A is wrong.

In B, $p=28$ so $f(28)=17\times 28-340=136$ . In this case we gather that if they sell 28 prints, they make a profit of $136. This tells us that option B is wrong.

In C, $p=35$ so $f(35)=17\times 35-340=225$ . In this case we gather that if they sell 35 prints, they make a profit of $225. This tells us that option C is wrong.

Lastly, $p=15$ so $f(15)=17\times 15-340=-85$ . In this case we gather that if they sell 28 prints, they make a loss of 85 dollars. From this we gather that D is the correct option.

5 0

4 years ago

Find all the zeroes of the equation(with simple steps).

uysha [10]

Answer-

The zeros are, $5,\ -5,\ 4i,\ -4i$

Solution-

$\Rightarrow -3x^4+27x^2+1200=0$

$\Rightarrow -3(x^2)^2+27(x^2)+1200=0$

Here,

a = -3, b = 27, c = 1200

So,

$x^2=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

$=\dfrac{-27\pm \sqrt{-27^2-4\cdot (-3)\cdot 1200}}{2\cdot (-3)}$

$=\dfrac{-27\pm \sqrt{729+14400}}{-6}$

$=\dfrac{-27\pm 123}{-6}$

$=\dfrac{-27+123}{-6},\ \dfrac{-27- 123}{-6}$

$=\dfrac{96}{-6},\ \dfrac{-150}{-6}$

$=-16,\ 25$

So,

$\Rightarrow x^2=25,\ -16$

$\Rightarrow x=\sqrt{25},\ \sqrt{-16}$

$\Rightarrow x=5,\ -5,\ 4i,\ -4i$

8 0

3 years ago

A researcher collected data on the hours of TV watched per day from a sample of five people of different ages. Here are the resu

frozen [14]

Answer:

1. The least squares regression is y = -0.1015·x + 6.51

2. The independent variable is b) age

Please see attached table

Step-by-step explanation:

The least squares regression formula is given as follows;

$\dfrac{\sum_{i = 1}^{n}(x_{i} - \bar{x})\times \left (y_{i} - \bar{y} \right ) }{\sum_{i = 1}^{n}(x_{i} - \bar{x})^{2}}$

We have;

$\bar x$ = 24

$\bar y$ = 4

$\Sigma (x_i - \bar x) (y_i - \bar y)$ = -79

$\Sigma (x_i - \bar x)^2$ = 778

$\therefore \hat \beta =\dfrac{\sum_{i = 1}^{n}(x_{i} - \bar{x})\times \left (y_{i} - \bar{y} \right ) }{\sum_{i = 1}^{n}(x_{i} - \bar{x})^{2}} = \frac{-79}{778} = -0.1015$