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4 years ago

Algebra 2 Math question Grade 11

Mathematics

1 answer:

Paha777 [63]4 years ago

3 0

Answer:

$\displaystyle y=\frac{4}{5}x+\frac{13}{5}$

Step-by-step explanation:

The equation of the line in slope-intercept form is:

y=mx+b

Where m the slope of the line and b the y-intercept.

When two points are given, it's convenient to calculate the slope first.

Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

The points are (3,5) and (-2,1):

$\displaystyle m=\frac{1-5}{-2-3}=\frac{4}{5}$

The equation is now:

$\displaystyle y=\frac{4}{5}x+b$

To calculate b, we use any of the given points and solve for b. Use (3,5):

$\displaystyle 5=\frac{4}{5}3+b$

Operate:

$\displaystyle 5=\frac{12}{5}+b$

Solve:

$\displaystyle b=5-\frac{12}{5}=\frac{13}{5}$

The required equation of the line is:

$\boxed{\displaystyle y=\frac{4}{5}x+\frac{13}{5}}$

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an inlet pipe and a hose together can fill the pond in 10 hours. The inlet pipe alone can complete the job in one hour less time

Annette [7]

Answer:

The hose pipe can fill the pond in 21.465 hours.

The inlet pipe can fill the pond in 20.465 hours.

Step-by-step explanation:

Given that, a inlet pipe and a hose pipe together can fill the pond in 10 hours.

The inlet pipe alone can fill the pond in one hour less time than the hose pipe can fill the pond.

Let the hose pipe can complete the job in x hours.

Then the inlet pipe can fill the pond in (x-1) hours.

The rate of filling of hose pipe is $=\frac{1}{x}$

The rate of filling of inlet pipe is $=\frac{1}{x-1}$

The rate of filling of both pipes is = $\frac 1{10}$

According to the problem,

$\frac{1}{x}+\frac{1}{x-1}=\frac{1}{10}$

$\Rightarrow \frac{x-1+x}{x(x-1)}=\frac1{10}$ [ simplifying the fraction]

$\Rightarrow \frac{2x-1}{x^2-x}=\frac1{10}$

$\Rightarrow 10(2x-1)= x^2-x$ [ Multiplying 10(x²-x) both sides]

$\Rightarrow x^2-x= 20x-10$

$\Rightarrow x^2-x-20x+10=0$ [ simplifying ]

$\Rightarrow x^2-21x+10=0$

$\Rightarrow x=\frac{-(-21)\pm\sqrt{(-21)^2-4.1.10}}{2.1}$ [ applying quadratic formula]

$\Rightarrow x=\frac{21\pm21.93}{2.1}$

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The hose pipe can fill the pond in 21.465 hours.

The inlet pipe can fill the pond in (21.465-1)=20.465 hours.

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The distance between two towns is 120 kilometers. There are approximately 8 kilometers in 5 miles.

Svetlanka [38]

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aliina [53]

Answer: The second proof table is the the proper proof table.

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So far, this eliminates the first proof table because in this table, the last line says "angle c and angle h are supplementary" which is not what we want to end up with. We want the last line to say "angle b and angle h are supplementary".

We can also eliminate the third proof table because of the statement "angle d and angle h are supplementary". They are only supplementary if they are both right angles. Also, the reasoning of "alternate interior angles" is false as they are corresponding angles.

The only thing left is the second proof table which is correctly argued from start to finish.

1. r || s ........................ given

2. angle b = angle c ................ vertical angles

3. c and e are supplementary angles ....... same side interior

4. angle e = angle h ................. vertical angles

5. b and h are supplementary ...... substitution

Note: in line 5, we start with line 3's statement. Then we replace 'c' with 'b', at the same we replace 'e' with 'h'.

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