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Natalka [10]
3 years ago
12

What is the equation of a line that passes through the point (4, 2) and is perpendicular to the line whose equation is y= x/3−1

?
Mathematics
1 answer:
Alex_Xolod [135]3 years ago
6 0
Perpendicular lines have slopes that are opposite and reciprocal. Therefore, the line we are looking for has a -3 slope.
y= -3x+b

Now, we can substitute in the point given to find the intercept.
2= -3(4)+b
2= -12+b
b=14

Finally, put in everything we've found to finish the equation.
y= -3x+14
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Find a polynomial equation that has zeros at x = −2, x = 0, x = 3 and x = 5
VashaNatasha [74]

If a polynomial "contains", in a multiplicative sense, a factor (x-x_0), then the polynomial has a zero at x=x_0.

So, you polynomial must contain at least the following:

(x-(-2)),\quad (x-0),\quad (x-3),\quad (x-5)

If you multiply them all, you get

x(x+2)(x-3)(x-5)=x^4 - 6 x^3 - x^2 + 30 x

Now, if you want the polynomial to be zero only and exactly at the four points you've given, you can choose every polynomial that is a multiple (numerically speaking) of this one. For example, you can multiply it by 2, 3, or -14.

If you want the polynomial to be zero at least at the four points you've given, you can multiply the given polynomial by every other function.

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3 years ago
A storekeeper increased the price of hats by 5%. Write an equation to calculate the increase of the total cost, c, when the pric
Naddik [55]

Answer:

c = 1.05p

Step-by-step explanation:

the price of the hat before the increase was 100%, after the increase it becomes 100 + 5% = 105%. Representing it as a decimal becomes 1.05p

Let illustrate with an example.

The price of a hat was $100, after the 5% increase. the cost of the hat becomes

100 + (0.05 x 100) = 105

To find the percentage increase

divide 105 by 100 and subtract 1

(105/100) - 1 = 1.05

3 0
3 years ago
True or False: Every number has a limited amount of factors, but an unlimited amount of multiples. ​
Irina18 [472]

Answer:

true

Step-by-step explanation:

3 0
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A square dartboard contains a red square and a blue square that overlap. A dart hits a random point on the board.
FinnZ [79.3K]
They want to know the probability of landing in the blue and red section at the same time. In other words, they want to know the probability of landing in the purple section.

We'll need the area of the purple square. This square is 1.5 inches by 1.5 inches. This is because 4 - 2.5 = 1.5

So the purple square has an area of 1.5*1.5 = 2.25 square inches

Divide this over the total area of the largest square (which is 9x9) to get 2.25/81 = 0.02777... where the 7's go on forever

Round that to two decimal places. The final answer is 0.03

Side note: 2.25/81 is equivalent to the reduced fraction 1/36 (express 2.25/81 as 225/8100 and then divide both parts by the GCF 225)
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3 years ago
At the AoPS office, mice vary inversely with cats, that is, $\text{mice}=\frac{k}{\text{cats}}$, for some value of $k$. When the
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Answer:

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Step-by-step explanation:

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