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3 years ago

Consider the following system of equations:

Mathematics

1 answer:

erma4kov [3.2K]3 years ago

8 0

Answer:

Line 2

Step-by-step explanation:

(x = 2, y = 4)

When we input it into Line 1:

2 + 6 = -2; not true

When we input it into Line 2:

3*2 - 4 = 2; true

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1.How many combinations are possible from the letters HOLIDAY if the letters are taken?

Lesechka [4]

Using the combination formula, it is found that:

1. A. 7 combinations are possible.

B. 21 combinations are possible.

C. 1 combination is possible.

2. There are 245 ways to group them.

<h3>What is the combination formula?</h3>

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by:

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Exercise 1, item a:

One letter from a set of 7, hence:

$C_{7,1} = \frac{7!}{1!6!} = 7$

7 combinations are possible.

Item b:

Two letters from a set of 7, hence:

$C_{7,2} = \frac{7!}{2!5!} = 21$

21 combinations are possible.

Item c:

7 letters from a set of 7, hence:

$C_{7,7} = \frac{7!}{0!7!} = 1$

1 combination is possible.

Question 2:

Three singers are taken from a set of 7, and four dances from a set of 10, hence:

$T = C_{7,3}C_{10,4} = \frac{7!}{3!4!} \times \frac{10!}{4!6!} = 245$

There are 245 ways to group them.

More can be learned about the combination formula at brainly.com/question/25821700

6 0

2 years ago

What is the value of 5 in 5,708

poizon [28]

Answer:

5000

Step-by-step explanation:

The 5 is in the "thousand" place, so it would be 5000

4 0

3 years ago

Write in slope intercept form an equation of the line that passes through (-2,5),(-1,1)

Juliette [100K]

Answer:

y=-4x-3

Step-by-step explanation:

Hi there!

We are given the following two points: (-2,5) and (-1,1)

We want to write the equation of the line that passes through these two lines in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

First, let's find the slope

The formula for the slope (m) calculated from 2 points is $\frac{y_2-y_1}{x_2-x_1}$ , where $(x_1, y_1)$ and $(x_2, y_2)$ are points

We have everything we need to calculate the slope, but let's label the value of the points to avoid any confusion

$x_1=-2\\y_1=5\\x_2=-1\\y_2=1$

Now substitute into the formula

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

m= $\frac{1-5}{-1--2}$
Simplify

m= $\frac{1-5}{-1+2}$

Subtract

m= $\frac{-4}{1}$

Divide

m=-4

Now substitute -4 as m into the equation:

y=-4x+b

Now we need to find b

As the equation passes through both (-2, 5) and (-1, 1), we can use either point to help solve for b.

Taking (-2,5) for example:

Substitute -2 as x and 5 as y:

5=-4(-2)+b

Multiply

5=8+b

Subtract 8 from both sides

-3=b

Substitute -3 as b.

y=-4x-3

Hope this helps!

See more on this topic here: brainly.com/question/27304092

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2 years ago

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The answer is 2.22 if you divide it. Add the ingredients then divide on how many servings.

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3 years ago

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