ind the equation of a line perpendicular to y - 3x = – 8 that passes through the point (3, 2). (answer in slope-intercept form)
Answers
Find the equation of a line perpendicular to y - 3x = – 8 that passes through the point (3, 2)
y - 3x = – 8-----> y=3x-8------> the slope m=3
we know that
if two lines are perpendicular
then
m1*m2=-1
m1=3
so
m2=-1/3
with m=-1/3 and point (3, 2) find the equation of the line
y=mx+b
2=(-1/3)*3+b------> 2=-1+b-----> b=3
the equation of the line is
y=(-1/3)x+3
the answer is
y=(-1/3)x+3
see the attached figure
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How can you recognize whether a real-world situation should be represented by an equation or an inequality?PLEASE HELP!!!
Answers
Using division, the thickness of each sheet of paper is 0.005 inches
What is the thickness of each sheet of paper?
To find the thickness of each sheet of paper, divide the total thickness of the telephone book by the number of sheets used.
Thickness of each sheet of paper = Total thickness / Number of sheets
Thickness of each sheet of paper = 2.6 inches / 565 sheets ≈ 0.004602 inches
Rounded to the nearest thousandth of an inch, the thickness of each sheet of paper is approximately 0.005 inches.
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What this means is 2.6 inches is the thickness of 565 sheets of paper.
To find the thickness of each sheet of paper, all we do is:
2.6 ÷ 565
This gives us quite a large answer:
0.0046017699
To round to the thousandth place, we look at the third number past the decimal and look to see if we need to round up or round down.
The number to the right of our digit in the thousandth place lets us know (in this case) to round up.
Therefore, 0.0046017699 rounded to the nearest thousandth is:
0.005
Don't forget to label (inches)
15x + 6y = 21
1.25x +0.5y = 2
6.5x + 3.5y = 9.5
Answers
We can take the coefficient of x as an example.
First, we reduce the coefficient of x of the given equation to 1 to make it simpler. We divide the whole equation by 5 and we get:
x + (2/5) y = 8/5
We do the same to the given options of equations.
We divide equation 1 with 2, equation 2 with 15, equation 3 with 1.25 and equation 4 with 6.5.
Compare the result with the given equation divided by 5 or x + (2/5) y = 8/5 and if it is the same, then the two equation are equivalent.
The third option: 1.25x +0.5y = 2 will give you the same equation.
Answer:
C.)1.25x +0.5y = 2
Step-by-step explanation:
Answers
2.11. Tariff is the cost or charge for a service.
2.2.2. The cost of refilling the pool with 15kl of water is R285.90.
2.2.3. The VAT inclusive cost for 15kl is R328.79.
2.11. Tariff is the cost or charge for a particular service or resource. It can be thought of as a rate or price that is applied to a specific quantity or volume of the resource being used.
2.2.2. To calculate the cost of refilling the pool, we need to determine the amount of water required and then multiply it by the appropriate tariff rate.
In this case, 15 kilolitres of water needs to be refilled, and based on the provided tariffs, the cost would be: 15 kl x R19.06/kl = R285.90.
2.2.3. To calculate the VAT inclusive amount for using 15 kl, we need to include the value-added tax (VAT) to the cost. VAT is calculated as a percentage of the initial cost.
Assuming a VAT rate of 15%, the VAT inclusive cost would be: R285.90 + (15/100 x R285.90) = R328.79.
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Answers
The x-coordinate of the x-intercept in quadrant || for the given function is -1.
x = -1.
What are coordinates?
Coordinates are a set of values that helps to show the exact position of a point in the coordinate plane.
We have,
x-intercept in quadrant ||.
f(x) = x³ - x² - x + 1
x-intercept means y = 0 so,
f(x) = y
0 = x³ - x² - x + 1
We see that,
when x = -1 we get,
f(x) = -1 - 1 + 1 + 1 = 0
When x = 1 we get,
f(x) = 1 - 1 - 1 + 1 = 0
But we can not take x = 1 because in quadrant || x is a negative value.
Thus,
The x-coordinate of the x-intercept in quadrant || for the given function is -1.
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ANSWER
The x-coordinate of the x-intercept of the function is
.
EXPLANATION:
The x-intercept refers to the point where the function meets or cuts the x-axis.
At the x-intercept, .
This means we have to equate the whole function to zero and solve for .
According to the rational roots theorem, the possible rational roots of the equation are
.
We now plug in these possible rational roots to see which of them are real roots.
Since ,
is a root.
By the factor theorem, is a factor of the function.
We now divide the polynomial function, by
to find the remaining roots.
See long division in diagram.
This means that .
Or
Hence the roots are or
In the second quadrant the x-coordinate is negative
Therefore, the x-coordinate of the x-intercept of the function is
.
See graph in attachment
Answers
You did the first step correctly ... even admirably !
You zeroed in on finding 'x' with laser-like precision, and
you knocked it out of the park.
Then, from there ... you fell off the deep end.
There's no reason that (3x + 18) has to be equal to 2(y+6).
In fact, they add up to 180°, so you could have used that
and solved for 'y'.
BUT ... (5x + 2) and 2(y+6) are "vertical angles", and THEY
are equal.
So 2 (y+6) = 5x + 2
2 (y+6) = 102
(y+6) = 51
y = 45 .
But the angle 3x+18 is not equal to the angle with the y variable.
They are supplementary angles (equal 180) but are not necessarily equal.
The angle that equals 2(y+6) is the angle opposite to it, 5x+2 (Vertical angle theorem).
So you should have substituted 20 into 5x+2
B. Yes, because the sum of any two multiples of 4 is also a multiple of 8.
C. No, and a counterexample is –4 + (–8) = –12.
D. No, and a counterexample is 26 + 16 = 42.