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3 years ago

The sum of two numbers is 30 and their difference is 6

1 answer:

Studentka2010 [4]3 years ago

4 0

I'm going to assume that you are trying to find the two numbers. Based on the information in the problem, we can create the following equations (where $a$ and $b$ are the two numbers):

$a + b = 30$

$a - b = 6$

We have a systems of equations. In this case, it would be easier to use elimination by adding vertically. This produces the result:

$2a = 36$

$a = 18$

To find $b$ , substitute the value for $a$ into one of the earlier equations:

$18 + b = 30$

$b = 12$

The two numbers are 12 and 18.

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LOTS OF POINTS GIVING BRAINLIEST I NEED HELP PLEASEE

Sidana [21]

Answer:

Segment EF: y = -x + 8

Segment BC: y = -x + 2

Step-by-step explanation:

Given the two similar right triangles, ΔABC and ΔDEF, for which we must determine the slope-intercept form of the side of ΔDEF that is parallel to segment BC.

Upon observing the given diagram, we can infer the following corresponding sides:

$\displaystyle\mathsf{\overline{BC}\:\: and\:\:\overline{EF}}$

$\displaystyle\mathsf{\overline{BA}\:\: and\:\:\overline{ED}}$

$\displaystyle\mathsf{\overline{AC}\:\: and\:\:\overline{DF}}$

We must determine the slope of segment BC from ΔABC, which corresponds to segment EF from ΔDEF.

<h2>Slope of Segment BC:</h2>

In order to solve for the slope of segment BC, we can use the following slope formula:

$\displaystyle\mathsf{Slope\:(m)\:=\:\frac{y_2 \:-\:y_1}{x_2 \:-\:x_1}} }$

Use the following coordinates from the given diagram:

Point B: (x₁, y₁) = (-2, 4)

Point C: (x₂, y₂) = ( 1, 1 )

Substitute these values into the slope formula:

$\displaystyle\mathsf{Slope\:(m)\:=\:\frac{y_2 \:-\:y_1}{x_2 \:-\:x_1}}\:=\:\frac{1\:-\:4}{1\:-\:(-2)}\:=\:\frac{-3}{1\:+\:2}\:=\:\frac{-3}{3}\:=\:-1}$

<h2>Slope of Segment EF:</h2>

Similar to how we determined the slope of segment BC, we will use the coordinates of points E and F from ΔDEF to find its slope:

Point E: (x₁, y₁) = (4, 4)

Point F: (x₂, y₂) = (6, 2)

Substitute these values into the slope formula:

$\displaystyle\mathsf{Slope\:(m)\:=\:\frac{y_2 \:-\:y_1}{x_2 \:-\:x_1}}\:=\:\frac{2\:-\:4}{6\:-\:4}\:=\:\frac{-2}{2}\:=\:-1}$

Our calculations show that segment BC and EF have the same slope of -1. In geometry, we know that two nonvertical lines are <u>parallel</u> if and only if they have the same slope.

Since segments BC and EF have the same slope, then it means that $\displaystyle\mathsf{\overline{BC}\:\: | |\:\:\overline{EF}}$ .

<h2>Slope-intercept form:</h2><h3><u>Segment BC:</u></h3>

The <u>y-intercept</u> is the point on the graph where it crosses the y-axis. Thus, it is the value of "y" when x = 0.

Using the slope of segment BC, m = -1, and the coordinates of point C, (1, 1), substitute these values into the <u>slope-intercept form</u> (y = mx + b) to solve for the y-intercept, <em>b. </em>

y = mx + b

1 = -1( 1 ) + b

1 = -1 + b

Add 1 to both sides to isolate b:

1 + 1 = -1 + 1 + b

2 = b

Hence, the <u><em>y-intercept</em></u> of segment BC is: <em>b</em> = 2.

Therefore, the linear equation in <u>slope-intercept form of segment BC</u> is:

⇒ y = -x + 2.

<h3><u /></h3><h3><u>Segment EF:</u></h3>

Using the slope of segment EF, <em>m</em> = -1, and the coordinates of point E, (4, 4), substitute these values into the <u>slope-intercept form</u> to solve for the y-intercept, <em>b. </em>

y = mx + b

4 = -1( 4 ) + b

4 = -4 + b

Add 4 to both sides to isolate b:

4 + 4 = -4 + 4 + b

8 = b

Hence, the <u><em>y-intercept</em></u> of segment BC is: <em>b</em> = 8.

Therefore, the linear equation in <u>slope-intercept form of segment EF</u> is:

⇒ y = -x + 8.

8 0

2 years ago

Guys, please help me with this question.

Elodia [21]

Answer:

Step-by-step explanation:

We are asked to perform the subtraction

x² + xy - 3y² - (5x² - xy + y²) ← distribute the parenthesis by - 1

= x² + xy - 3y² - 5x² + xy - y² ← collect like terms

= (x² - 5x²) + (xy + xy) + (- 3y² - y² )

= - 4x² + 2xy - 4y²

6 0

3 years ago

the table shows how the number of sit-ups Maria does each day has changed over time. At this rate, how many sit-ups will she do

tresset_1 [31]

Answer:

Step-by-step explanation:

a = 17

d = 21 - 17 = 4

12th day: 17 + 4(12 - 1)

17 + 44

8 0

3 years ago

Andre and Diego were each trying to solve 2+6=3−8. Describe the first step they each make to the equation.The result of Diego’s

Fiesta28 [93]

Step-by-step explanation:

2+6=3-8

2+6=8

3-8=-5

8=-5

4 0

3 years ago

Are 4e and 4 like or unlike? *

Finger [1]

I think they are unlike

6 0

3 years ago

Read 2 more answers