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3 years ago

2.1.4. The surm of two numbers is 4 and teir difference is 6. Determine the numbers

Mathematics

2 answers:

Georgia [21]3 years ago

8 0

Answer:

5 and -1.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Terms/Coefficients
Solving systems of equations by substitution/elimination

Step-by-step explanation:

Step 1: Define

Identify

Let x be one number and y be the other.

x + y = 4

x - y = 6

Step 2: Solve for x

Elimination

Combine 2 equations: 2x = 10
[Division Property of Equality] Divide 2 on both sides: x = 5

Step 3: Solve for y

Substitute in x [1st Equation]: 5 + y = 4
[Subtraction Property of Equality] Subtract 5 on both sides: y = -1

Mama L [17]3 years ago

7 0

Answer:

5 and -1

Step-by-step explanation:

Let the two numbers be x and y

x+y =4

x-y = 6

Add the two equations together

x+y =4

x-y = 6

--------------

2x = 10

Divide by 2

2x/2 =10/2

x=5

x+y = 4

5+y = 4

y = 4-5

y = -1

The numbers are 5 and -1

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Solve 5y^2+20=80, where y is the real number

soldi70 [24.7K]

Answer:

2√3

Step-by-step explanation:

5y2+20=80

Step 1: Subtract 20 from both sides.

5y^2+20−20=80−20

5y^2=60

Step 2: Divide both sides by 5.

5y^2 /5 = 60/5

y2=12

Step 3: Take square root.

y=√12

y=2√3

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3 years ago

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 parallel 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>Segment BC:</h3>

The y-intercept 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 slope-intercept form (y = mx + b) to solve for the y-intercept, b.

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 y-intercept of segment BC is: b = 2.

Therefore, the linear equation in slope-intercept form of segment BC is:

⇒ y = -x + 2.

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

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

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 y-intercept of segment BC is: b = 8.

Therefore, the linear equation in slope-intercept form of segment EF is:

⇒ y = -x + 8.

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2.1.4. The surm of two numbers is 4 and teir difference is 6. Determine the numbers​

2.1.4. The surm of two numbers is 4 and teir difference is 6. Determine the numbers