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2 years ago

A line passes through the two points (-4,6) and (2,-5). Calculate the following parts:

Mathematics

1 answer:

Viktor [21]2 years ago

8 0

A line passes through the two points (-4,6) and (2,-5). 11x +6y - 80 = 0 is the given line equation.

<h3>What is the slope of a line which passes through points ( p,q) and (x,y)?</h3>

Its slope would be:

$m = \dfrac{y-q}{x-p}$

The slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.

The slope m of the line is given as

$m = \dfrac{y-q}{x-p}\\\\ m = \dfrac{-5-6}{2+4}\\\\ m = \dfrac{-11}{6}$

The equation of a line is

$( y -y_0) = m (x - x_0)\\\\( y -6) = \dfrac{-11}{6} (x+4)\\\\6( y -6) = (-11) (x+4)\\\\6y -36 = (-11x +44)\\\\11x +6y - 80 = 0$

Hence, the equation is 11x +6y - 80 = 0

Learn more about slopes here:

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3 years ago

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Cassie has test grades of 62, 85 and 89 on the first three tests in herpre-algebra class. What are the possible scores she can m

Vsevolod [243]

Explanation:

The test grade for 1st three tests = 62, 85, 89

Let the fourth test score = x

The result we hoping to get is grade B.

Let's find the average of the four test score

$\text{Average = }\frac{Su\text{ m of all test score}}{nu\text{mber of test score}}$ $\begin{gathered} s\text{ um of test scores = 62 + 85 + 89 + x} \\ nu\text{mber of test score = 4} \\ \frac{\text{62 + 85 + 89 + x}}{4}=\text{ Average} \end{gathered}$ $\begin{gathered} A\text{ grade B represents atleast 80} \\ \text{Atleast represents }\ge \\ \frac{\text{62 + 85 + 89 + x}}{4}\text{ }\ge\text{ 80} \\ \frac{\text{236 + x}}{4}\text{ }\ge\text{ 80} \end{gathered}$ $\begin{gathered} \text{236 + x }\ge\text{ }80(4) \\ \text{236 + x }\ge\text{ }320 \\ \text{subtract }236\text{ from both sides:} \\ 236\text{ - 236 + x }\ge\text{ }320\text{ - 23}6 \\ x\text{ }\ge\text{ 84} \end{gathered}$

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In ineq

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1 year ago

What is the solution to |x − 4| ≥ 7?

Snowcat [4.5K]

9514 1404 393

Answer:

(x ≤ -3) ∪ (11 ≤ x)

Step-by-step explanation:

The given equation resolves to two equations:

x -4 ≥ 7 ⇒ x ≥ 11

x -4 ≤ -7 ⇒ x ≤ -3

The solution is (x ≤ -3) ∪ (11 ≤ x).

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3 years ago

Carly drove 617.3 miles his car get about 41 miles per gallon which is the best estimate of how many gallons of gas Carly used

Lerok [7]

Answer:

He used about 15 gallons

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3 years ago

observe as seguintes situações e sua representação em linguagem matematica dois numeros x e y são tais 2x y=6 x-y=3

agasfer [191]

Answer:

The value of x any y are "-5.29 and 0.79" and "3.79 and -2.29"

Step-by-step explanation:

Given values:

$2xy =6.....(a)\\\\x-y= 3.....(b)\\\\$

After solve equation (a) we get

$\ equation: \\\\2xy= 6\\\\xy =\frac{6}{2} \\\\xy = 3.....(x)\\\\$

After solve equation (b) we get

$\ equation: \\\\x-y =3\\\\x= 3+y....(x1)\\$

put the value of x in to equation (x)

$(3+y)y = 3\\$

$y^2+3y-3=0\\\\\ compare \ the \ value \ with \ ay^2+by+c=0\\a= 1\\b=3\\c=-3\\\ Formula: \\y= \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\y= \frac{-3\pm \sqrt{9+12}}{2}\\y= \frac{-3\pm \sqrt{21}}{2}\\$

The value of y is = -5.29 and 0.79, put the value of y in x1 equation so, we get: 3.79 and -2.29

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