MATHEMATICS HIGH SCHOOL

What is an equation of the line that passes through the points (3,4) and (−4,−3)? Put your answer in fully reduced form

Answers

Answer 1

Answer:

Answer:

The equation of the line is y = x + 1

Step-by-step explanation:

The equation of the line is y = m x + b, where

m is the slope of the line

b is the y-intercept

The rule of the slope of the line is m = $(y2-y1)/(x2-x1)$ , where

(x1, y1) and (x2, y2) are two points on the line

∵ The line passes through points (3, 4) and (-4, -3)

∴ x1 = 3 and y1 = 4

∴ x2 = -4 and y = -3

→ Substitute them in the rule of the slope above to find it

∵ m = $(-3-4)/(-4-3)$ = $(-7)/(-7)$ = 1

∴ m = 1

→ Substitute it in the form of the equation above

∴ y = 1(x) + b

∴ y = x + b

→ To find b substitute x by 3 and y by 4 in the equation

∵ 4 = 3 + b

→ Subtract 3 from both sides

∵ 4 - 3 = 3 - 3 + b

∴ 1 = b

→ Substitute it in the equation

∴ y = x + 1

∴ The equation of the line is y = x + 1

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Answers

two numbers if you multiple them give you 24
and if you add them gives 11
so the numbers are 3, 8
(x+3)(x+8)

Your portfolio has provided you with returns of 8.6 percent, 14.2 percent, -3.7 percent, and 12.0 percent over the past four years, respectively. what is the geometric average return for this period?

Answers

First you have to add all four of your numbers, 8.6+14.2+ -3.7+ 12=31.1. Then you divide your answer by 4, the number of numbers you added, and you get your answer of 7.775.

Can someone help me and let me know if my answer is correct?A large emerald with a mass of 764.3 grams was recently discovered in a mine. If the density of the emerald is 2.76grams over centimeters cubed, what is the volume? Round to the nearest hundredth when necessary and only enter numerical values, which can include a decimal point.

276.92

Answers

The answer is 276.92

The density (D) of is quotient of mass (m) and volume (V):
$D = (m)/(V)$

It is given:
m = 764.3 g
D = 2.76 g/cm³
V = ?

Since:
$D = (m)/(V)$
⇒ $V= (m)/(D)= (764.3g)/(2.76g/cm^(3) ) = 276.92 cm ^(3)$

Therefore, the volume of the emerald is 276.92 cm² and your answer is correct.

Answer:

276.92 cubic cm.

Step-by-step explanation:

Given :

A large emerald with a mass of 764.3 grams was recently discovered in a mine.

The density of the emerald is $2.76gm/cm^3$