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2 years ago

Solve this system of linear equations. Separate the x- and y- values with a comma.

Mathematics

1 answer:

liubo4ka [24]2 years ago

6 0

Answer:

(-1,4)

Step-by-step explanation:

Using elimination, add the two equations to get rid of the y variable.

17x = 43 - 15y

+8x = -68 + 15y

=25x = -25

Now plug in -1 for x in any of the equations.

17(-1) = 43 - 15y

-17 = 43 - 15y

-60 = -15y

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The measures of the angles of XYZ are in the ratio 1:4:10. What are the measures of the angles?

Elanso [62]

Answer:the angles are 12 degrees, 48 degrees and 120 degrees.

Step-by-step explanation:

The sum of the angles in a triangle is 180 degrees.

The measures of the angles of XYZ are in the ratio 1:4:10. The total ratio is the sum of the proportion of each angle. It becomes

1 + 4 + 10 = 15

Therefore, the measure of the first angle would be

1/15 × 180 = 12 degrees

Therefore, the measure of the second angle would be

4/15 × 180 = 48 degrees

Therefore, the measure of the third angle would be

10/15 × 180 = 120 degrees

6 0

2 years ago

PLEASE HELP ME PLZ!!

vichka [17]

Answer:

1. Formula is A2 : A9 = COUNT( A2: A9 ) = 8

2. Formula is SUM( A2: A9 ) = 36

3. Formula is B2 : B9 = COUNT( B2: B9) = 8

4. Formula is MAX( C2: C9) = 5

5. Formula is MIN( C4: C8) = 3

6. Formula is SUM( C5 - C6) = 0

7. Formula is AVERAGE( C2: C9) = 4

Step-by-step explanation: Have a nice day! ✌️

7 0

2 years ago

HELP ASAP! The number of entertainment websites in 1995 wass 54. By 2004 there were 793 entertainment website..

AleksandrR [38]

<h3>Answer: Choice A. 82 websites per year</h3>

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

How I got that answer:

We have gone from 54 websites to 793 websites. This is a change of 793-54 = 739 new websites. This is over a timespan of 2004-1995 = 9 years.

Since we have 739 new websites over the course of 9 years, this means the rate of change is 739/9 = 82.1111... where the '1's go on forever. Rounding to the nearest whole number gets us roughly 82 websites a year.

----------

You could use the slope formula to get the job done. This is because the slope represents the rise over run

slope = rise/run

The rise is how much the number of websites have gone up or down. The run is the amount of time that has passed by. So slope = rise/run = 739/9 = 82.111...

In a more written out way, the steps would be

slope = rise/run

slope = (y2-y1)/(x2-x1)

slope = (793 - 54)/(2004 - 1995)

slope = 739/9

slope = 82.111....

3 0

3 years ago

How is the series 5+11+17…+251 represented in summation notation?

NISA [10]

Answer:

$\displaystyle \large{\sum_{n=1}^{42}(6n-1)$

Step-by-step explanation:

Given:

Series 5+11+17+...+251

To find:

Summation notation of the given series

Summation Notation:

$\displaystyle \large{\sum_{k=1}^n a_k}$

Where n is the number of terms and $\displaystyle \large{a_k}$ is general term.

First, determine what kind of series it is, there are two main series that everyone should know:

Arithmetic Series

A series that has common difference.

Geometric Series

A series that has common ratio.

If you notice and keep subtracting the next term with previous term:

11-5 = 6
17-11 = 6

Two common difference, we can in fact say that the series is arithmetic one. Since we know the type of series, we have to find the number of terms.

Now that brings us to arithmetic sequence, we know that first term is 5 and last term is 251, we’ll be finding both general term and number of term using arithmetic sequence:

<u>Arithmetic Sequence</u>

$\displaystyle \large{a_n=a_1+(n-1)d}$

Where $\displaystyle \large{a_n}$ is the nth term, $\displaystyle \large{a_1}$ is the first term and $\displaystyle \large{d}$ is the common difference:

So for our general term:

$\displaystyle \large{a_n=5+(n-1)6}\\\displaystyle \large{a_n=5+6n-6}\\\displaystyle \large{a_n=6n-1}$

And for number of terms, substitute $\displaystyle \large{a_n}$ = 251 and solve for n:

$\displaystyle \large{251=6n-1}\\\displaystyle \large{252=6n}\\\displaystyle \large{n=42}$

Now we can convert the series to summation notation as given the formula above, substitute as we get:

$\displaystyle \large{\sum_{n=1}^{42}(6n-1)$

5 0

2 years ago

Find the perimeter and area of the polygon shown below. The polygon is a trapezoid made up of a rectangle and a right triangle.

algol13

Since, the polygon is a trapezoid made up of a rectangle and a right triangle. Therefore, according to the question, the figure of the polygon is attached.

Since, perimeter is the total length of the outer boundary of the figure. Therefore,

Perimeter of the polygon is $=AB+BE+ED+DC+CA$