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3 years ago

Give the equations of 3 lines that are parallel to the line with the equation y=3x+2

Mathematics

1 answer:

horsena [70]3 years ago

4 0

Answer:

y = 3x+5

y = 3x+9

y = 3x+22

There are infinitely many ways to answer this

======================================================

Explanation:

Parallel lines have equal slopes, but different y intercepts.

So the answers will have y = 3x in them. We'll change the +2 to other values.

Pick 3 of your favorite numbers, as long as you don't pick the number 2.

I'll pick the numbers 5, 9 and 22

Three possible answers are:

y = 3x+5

y = 3x+9

y = 3x+22

All of those equations have a slope of 3, but different y intercepts so we are guaranteed to have parallel lines to the original y = 3x+2.

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Simplify the expression- <br> 3k+ -9k+ -6+10k

Nady [450]

Answer:

4k-6

Step-by-step explanation:

$3k+ -9k+ -6+10k=3k-9k-6+10k=4k-6$

8 0

3 years ago

Read 2 more answers

The general solution to the second-order differential equation y′′+10y=0 is in the form y(x)=c1cosβx+c2sinβx. Find the value of

allsm [11]

Answer:β=√10 or 3.16 (rounded to 2 decimal places)

Step-by-step explanation:

To find the value of β :

we will differentiate the y(x) equation twice to get a second order differential equation.
We compare our second order differential equation with the Second order differential equation specified in the problem to get the value of β

y(x)=c1cosβx+c2sinβx

we use the derivative of a sum rule to differentiate since we have an addition sign in our equation.

Also when differentiating Cosβx and Sinβx we should note that this involves function of a function. so we will differentiate βx in each case and multiply with the differential of c1cosx and c2sinx respectively.

lastly the differential of sinx= cosx and for cosx = -sinx.

Knowing all these we can proceed to solving the problem.

y=c1cosβx+c2sinβx

y'= β×c1×-sinβx+β×c2×cosβx

y'=-c1βsinβx+c2βcosβx

y''=β×-c1β×cosβx + (β×c2β×-sinβx)

y''= -c1β²cosβx -c2β²sinβx

factorize -β²

y''= -β²(c1cosβx +c2sinβx)

y(x)=c1cosβx+c2sinβx

therefore y'' = -β²y

y''+β²y=0

now we compare this with the second order D.E provided in the question

y''+10y=0

this means that β²y=10y

β²=10

B=√10 or 3.16(2 d.p)

5 0

3 years ago

A donut store has 11 different types of donuts. You can only buy a bag of 3 of them, where each donut has to be of a different t

MakcuM [25]

Answer:

$165$ .

Step-by-step explanation:

Since repetition isn't allowed, there would be $11$ choices for the first donut, $(11 - 1) = 10$ choices for the second donut, and $(11 - 2) = 9$ choices for the third donut. If the order in which donuts are placed in the bag matters, there would be $11 \times 10 \times 9$ unique ways to choose a bag of these donuts.

In practice, donuts in the bag are mixed, and the ordering of donuts doesn't matter. The same way of counting would then count every possible mix of three donuts type $3 \times 2 \times 1 = 6$ times.

For example, if a bag includes donut of type $x$ , $y$ , and $z$ , the count $11 \times 10 \times 9$ would include the following $3 \times 2 \times 1$ arrangements:

$xyz$ .
$xzy$ .
$yxz$ .
$yzx$ .
$zxy$ .
$zyx$ .

Thus, when the order of donuts in the bag doesn't matter, it would be necessary to divide the count $11 \times 10 \times 9$ by $3 \times 2 \times 1 = 6$ to find the actual number of donut combinations:

$\begin{aligned} \frac{11 \times 10 \times 9}{3 \times 2 \times 1} = 165\end{aligned}$ .

Using combinatorics notations, the answer to this question is the same as the number of ways to choose an unordered set of $3$ objects from a set of $11$ distinct objects:

$\begin{aligned}\begin{pmatrix}11 \\ 3\end{pmatrix} &= \frac{11 !}{(11 - 3)! \times 3 !} \\ &= \frac{11 !}{8 ! \times 3 !} \\ &= \frac{11 \times 10 \times 9}{3 \times 2 \times 1} = 165\end{aligned}$ .

5 0

2 years ago

What is 8.5% of 70 when you multiply

tigry1 [53]

5.95 is your answer. Have a wonderful day

4 0

3 years ago

Read 2 more answers

A table is 2 feet wide it is 6 times as long it is wide

yan [13]

Answer:

Length = 12 feet

Perimeter = 28 feet

Area = 24ft²

Step-by-step explanation:

You didn't ask a question so I don't know what the answer you want is so I assumed it was related to one of the answers shown above.

To calculate the length, you simply do 6*2

which is equal to 12.

The length is 12 feet.

However, if you want to find the perimeter:

12 + 12 + 2+ 2 = 28ft

If you wanted to find the area:

12*2 = 24ft²

I hope this helps!

7 0

3 years ago