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2 years ago

Find the equation of a line that passes through the point (-2,3) and has a gradient of 3.

Mathematics

1 answer:

nadya68 [22]2 years ago

5 0

Answer:

y = 3x+9

Step-by-step explanation:

The standard form of equation of a line is in the form y = mx + c

m is the gradient

c is the y intercept

Get the y-intercept

Substitute m = 3 and the point (-2, 3) into the formula y = mx+c

3 = 3(-2) + c

3 = -6+c

c = 3+6

c = 9

Get the required equation;

y = 3x + 9

Hence the required equation is y = 3x+9

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One reading an Antarctic research station showed that the temperature was -35 degrees Celsius what is this temperature in degree

Musya8 [376]

It is very simple it would be positive but would remain 35

4 0

2 years ago

The corners of a meadow are shown on a coordinate grid. Ethan wants to fence the meadow. What length of fencing is required?

Nuetrik [128]

Answer:

34.6 units

Step-by-step explanation:

The lenght of fencing required is the total distance between point A to B, B to C, C to D, and D to A. That is the distance between all 4 corners of the meadow.

The coordinates of the corners of the meadow is shown on a coordinate plane in the attachment. (See attachment below).

Let's use the distance formula to calculate the distance between the 4 corners of the meadow using their coordinates as follows:

Distance between point A(-6, 2) and point B(2, 6):

$AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$A(-6, 2)) = (x_1, y_1)$

$B(2, 6) = (x_2, y_2)$

$AB = \sqrt{(2 - (-6))^2 + (6 - 2)^2}$

$AB = \sqrt{(8)^2 + (4)^2}$

$AB = \sqrt{64 + 16} = \sqrt{80}$

$AB = 8.9$ (nearest tenth)

Distance between B(2, 6) and C(7, 1):

$BC = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$B(2, 6) = (x_1, y_1)$

$C(7, 1) = (x_2, y_2)$

$BC = \sqrt{(7 - 2)^2 + (1 - 6)^2}$

$BC = \sqrt{(5)^2 + (-5)^2}$

$BC = \sqrt{25 + 25} = \sqrt{50}$

$BC = 7.1$ (nearest tenth)

Distance between C(7, 1) and D(3, -5):

$CD = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$C(7, 1) = (x_1, y_1)$

$D(3, -5) = (x_2, y_2)$

$CD = \sqrt{(3 - 7)^2 + (-5 - 1)^2}$

$CD = \sqrt{(-4)^2 + (-6)^2}$

$CD = \sqrt{16 + 36} = \sqrt{52}$

$CD = 7.2$ (nearest tenth)

Distance between D(3, -5) and A(-6, 2):

$DA = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$D(3, -5) = (x_1, y_1)$

$A(-6, 2) = (x_2, y_2)$

$DA = \sqrt{(-6 - 3)^2 + (2 - (-5))^2}$

$DA = \sqrt{(-9)^2 + (7)^2}$

$DA = \sqrt{81 + 49} = \sqrt{130}$

$DA = 11.4$ (nearest tenth)

Length of fencing required = 8.9 + 7.1 + 7.2 + 11.4 = 34.6 units

8 0

2 years ago

When results from a scholastic assessment test are sent to test-takers, the percentiles associated with their scores are also gi

hram777 [196]

Answer:

The correct option is (D).

Step-by-step explanation:

Percentiles are statistical measures that are used to interpret data. It represents the data value which is more that a specific percentage of the data set.

The nth percentile of a data set is the value that is more that n% of the data set.

⇒ It is provided that a test-taker's score was at the 94th percentile for their verbal grade.

This statement implies that the test taker scored a mark more than 94% of the other test-takers, i.e. he\she performed better than 94% of the other test-takers in the verbal grade.

⇒ Also the test-taker's score was at the 16th percentile for their quantitative grade.

This implies that the test taker scored a mark more than 16% of the other test-takers, i.e. he\she performed better than 16% of the other test-takers in the quantitative grade.

Thus, the correct option is (D).

8 0

3 years ago

Find the domain of the function. y = <img src="https://tex.z-dn.net/?f=%5Csqrt%7Bx%7D%20%2B%201" id="TexFormula1" title

Step2247 [10]

Answer:

[0, infinity)

Step-by-step explanation:

A square root can only use positive numbers, otherwise it becomes imaginary. A function needs to be real to output real values. Therefore, the domain is everything from 0 onwards.

5 0

3 years ago

Darnell has 8 coins worth $1.80. If the coins are all quarters and nickels, how many quarters and nickels does he have?

Rudiy27

Answer:

7 quarters 1 nickel

Step-by-step explanation:

7 x.25= 1.75

1.75+ .05= 1.80

3 0

2 years ago