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3 years ago

The point that is not on the straight line y= 2x-1

1 answer:

7 0

-2 is the x coordinate and 7 is the y coordinate. If you plug them into the equation y= 2x - 1, you end up with 7 = 2(-2) - 1; 7 = -4 -1; 7 = -5 which isn’t true so you know that point isn’t on the line.

For example, let’s say you have an x coordinate for a point on the line but need to figure out what the y coordinate is. Let’s say x = 3. You plug 3 in for x in the equation y = 2x -1 and solve for y.

So y = 2(3) -1 which is y = 6-1 which is y = 5 So the answer would be (3,5) (x-coordinate, y-coordinate). You can check your answer by plugging 5 into the equation for y and solving for x.

If you take (3,5) and plug them into the equation, y = 2x - 1, 5 = 2(3) - 1 which is 5 = 6 - 1 which is 5 = 5. You know the coordinates (3,5) belong to a point on the line because the equation matches.

I went the long way around on the explanation and I hope I didn’t confuse you!

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A boy has 3 red , 2 yellow and 3 green marbles. In how many ways can the boy arrange the marbles in a line if: a) Marbles of the

Ilya [14]

Answer:

The total number of different arrangements is 560.

Step-by-step explanation:

A multiset is a collection of objects, just like a set, but can contain an object more than once.

The multiplicity of a particular type of object is the number of times objects of that type appear in a multiset.

Permutations of Multisets Theorem.

The number of ordered n-tuples (or permutations with repetition) on a collection or multiset of $n$ objects, where there are $k$ kinds of objects and object kind 1 occurs with multiplicity $n_1$ , object kind 2 occurs with multiplicity $n_2$ , ... , and object kind $k$ occurs with multiplicity $n_k$ is:

$\begin{equation*}\frac{n!}{n_1!*n_2!*\dots * n_k!}\end{equation*}$

We know that a boy has 3 red, 2 yellow and 3 green marbles. In this case we have n = 8.

If marbles of the same color are indistinguishable, then the total number of different arrangements is

${8 \choose 3, 2, 3} = \frac{8 !}{3 ! 2 ! 3 !} = \frac{8\cdot \:7\cdot \:6\cdot \:5\cdot \:4}{2!\cdot \:3!}=\frac{6720}{2!\cdot \:3!}=\frac{6720}{12}=560$

8 0

3 years ago

Add or subtract. Write the result in the form a+bi

STALIN [3.7K]

Number 1: (-1+2i)+(6-9i)

$Group\:the\:real\:part\:and\:the\:imaginary\:part\:of\:the\:complex\:number\\\left(a+bi\right)\pm \left(c+di\right)=\left(a\:\pm \:c\right)+\left(b\:\pm \:d\right)i\\=\left(-1+6\right)+\left(2-9\right)i\\=5-7i$

Number 2: (3-3i)-(4+7i)

Number 3: (-5+2i)+(-2+8i)

8 0

3 years ago

Nick and eddie are both thinking of a number. Eddies number is 3/7 of nicks number. There is a difference of 52 between their tw

joja [24]

Answer:

nick's number = 91

eddie's number = 39

Step-by-step explanation:

n = nick's number

$\frac{3}{7}$ n = eddie's number

$\frac{7}{7}$ n - $\frac{3}{7}$ n = 52

$\frac{4}{7}$ n = 52

cross-multiply: 4n = 52(7)

4n = 364

n = 364/4 = 91

eddie's number: $\frac{3}{7}$ · 91 = 273/7 = 39

3 0

3 years ago

Here is a right cone:

11111nata11111 [884]

Answer:

Choice B: A triangle

Choice C : A shape with two edges, one straight and one curved

Step-by-step explanation:

When a cone is cut by a plane that runs exactly through its vertex, and perpendicular to its base, the shape that is obtained is an isosceles triangle, when the section is viewed.

When a cone is cut through a plane that runs perpendicularly to its base, but not through its vertex, we can get two different shapes which have parabolas or hyperbolas as their curved edge, and a straight edge which is formed from the base of the cone

3 0

4 years ago

The length of a rectangular garden is three times the width if the perimeter is 32 meters, what are the dimentions of the garden

yanalaym [24]

Length (L): 3w

width (w): w

Perimeter (P) = 2L + 2w

32 = 2(3w) + 2(w)

32 = 6w + 2w

32 = 8w

4 = w

Length (L): 3w = 3(4) = 12

Answer: width = 4 meters, length = 12 meters

5 0

3 years ago