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2 years ago

What is the equation of the line that passes through the points (-3,5) (6,8)

1 answer:

6 0

$(\stackrel{x_1}{-3}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{(-3)}}}\implies \cfrac{3}{6+3}\implies \cfrac{3}{9}\implies \cfrac{1}{3}$

$\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{\cfrac{1}{3}}(x-\stackrel{x_1}{(-3)}) \\\\\\ y-5=\cfrac{1}{3}(x+3)\implies y-5=\cfrac{1}{3}x+1\implies y=\cfrac{1}{3}x+6$

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2. Choose the graph that shows the solution of the inequality on the number line

horsena [70]

Answer:

Number line 3 also known as [C]

Step-by-step explanation:

Given that:

c ≤ -1

Knowing that:

≤ = Less than or equal to

Now substitute into the equation:

C less than or equal to -1

Thus, it going left on a number line.

The only number line with left is [A] and [C]

Since ≤ = Less than or equal to -1

then, it including -1

also known as a closed circle means the number is included and an open circle means it is not.

Hence, it closed circle.

Thus, the answer is [C]

Kavinsky

4 0

1 year ago

Find the angle of depression from the top of a lighthouse, 260 feet above water to a ship that's 270 feet offshore?

expeople1 [14]

Answer: OPTION C.

Step-by-step explanation:

Observe the triangle ABC attached.

Notice that the angle of depression is represented with $\alpha$ .

Knowing that the top of a lighthouse is 260 feet above water and the ship is 270 feet offshore, you can find the value of $\alpha$ by using arctangent:

$\alpha= arctan(\frac{opposite}{adjacent})$

In this case you can identify that:

$opposite=260\\adjacent=270$

Therefore, substuting values into $\alpha= arctan(\frac{opposite}{adjacent})$ , you get that the angle of depression is:

$\alpha= arctan(\frac{260}{270})\\\\\alpha=43.92\°$

4 0

3 years ago

Use the substitution method to solve the system of equations. Choose the correct ordered pair.

motikmotik

Ur gonna have to pick an equation and solve for a variable.

2x - 2y = 6
2x = 2y + 6 ...divide everything by 2 because u want x by itself
x = y + 3

now we sub y + 3 in for x in the other equation
14x - 2y = 78
14(y + 3) - 2y = 78...distribute thru the parenthesis
14y + 42 - 2y = 78...subtract 42 from both sides, cancelling the 42 on the left
-42 -42
-----------------------
14y - 2y = 36 ...simplify
12y = 36...divide by 12 on both sides, cancelling out the 12 on the left
y = 36/12
y = 3

now , we already know that x = y + 3...and we know y = 3...so sub in 3 for y and solve for x
x = y + 3
x = 3 + 3
x = 6

solution is (6,3)

it is always a good idea to check ur answer by subbing it into one or both of the equations to see if it is correct
2x - 2y = 6......(6,3)...x = 6 and y = 3
2(6) - 2(3) = 6
12 - 6 = 6
6 = 6 (correct)

so yes, ur solution is (6,3)

4 0

2 years ago

Read 2 more answers

Represent 240.149 in two different ways

choli [55]

Answer:

240 149/1000, 240149/1000

Step-by-step explanation:

Mixed Number, Improper Fraction

8 0

2 years ago

The value of\[\left( 1-{1\over3} \right)\left( 1-{1\over4} \right)\left( 1-{1\over5} \right)....\left( 1-{1\over n} \right)\]is

Oliga [24]

Example 1

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For most fractions, the beginning is indicated with "start fraction", the horizontal line is indicated with "over", and the end of the fraction is indicated by "end fraction". For the semantic interpretation, most numeric fractions are spoken as they are in natural speech. Also if a number is followed by a numeric fraction, the word "and" is spoken in between.

6 0

2 years ago