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3 years ago

Solve each equation by substitution

Mathematics

2 answers:

Artemon [7]3 years ago

5 0

Answer:

(1, 7)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS
Equality Properties

Algebra I

Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define systems

y = 3x + 4

y = 6x + 1

Step 2: Solve for x

Substitute in y: 3x + 4 = 6x + 1
Subtract 3x on both sides: 4 = 3x + 1
Subtract 1 on both sides: 3 = 3x
Divide 3 on both sides: 1 = x
Rewrite: x = 1

Step 3: Solve for y

Define original equation: y = 6x + 1
Substitute in x: y = 6(1) + 1
Multiply: y = 6 + 1
Add: y = 7

Aneli [31]3 years ago

4 0

Answer:

(1, 7)

Step-by-step explanation:

y = 3x + 4

y = 6x + 1

6x + 1 = 3x + 4 ⇒ x = 1

y = 3(1) + 4 = 7

(1, 7)

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You use 4 gallons of water on 30 plants in your garden. At that rate, how much water will it take to water 45 plants?

ICE Princess25 [194]

Answer:

6 gallons

Step-by-step explanation:

6 0

3 years ago

9 cos(sin¯¹(x)) = √81 – 81x²

Ira Lisetskai [31]

The equation 9cos(sin¯¹(x)) = √(81 – 81x²) is true since L.H.S = R.H.S

To answer the question, we need to know what an equation is

<h3>What is an equation?</h3>

An equation is a mathematical expression that show the relationship between two variables.

Given 9cos(sin¯¹(x)) = √(81 – 81x²), we need to show L.H.S = R.H.S

So, L.H.S = 9cos(sin¯¹(x))

= 9[√{1 - sin²(sin¯¹(x)}] (Since sin²y + cos²y = 1 ⇒ cosy = √[1 - sin²y])

9[√{1 - sin²(sin¯¹(x)}] = √9² × √{1 - sin²(sin¯¹(x)}]

= √[9² × {1 - sin²(sin¯¹(x)}]

= √[81 × {1 - sin²(sin¯¹(x)}]

= √[81 × {1 - x²}] (since sin²(sin¯¹(x) = [sin(sin¯¹(x)]² = x²)

= √(81 – 81x²)

= R.H.S

So, the equation 9cos(sin¯¹(x)) = √(81 – 81x²) is true since L.H.S = R.H.S

Learn more about equations here:

brainly.com/question/2888445

#SPJ1

6 0

2 years ago

Find the equations of the following lines

White raven [17]

You need these two basic solutions and facts to find the equation of a line:

If you know the gradient $m$ and one point $(x_0,y_0)$ :

$y-y_0=m(x-x_0)$

If you know the gradient two points $(x_1,y_1),\ (x_2,y_2)$ :

$\dfrac{x-x_2}{x_1-x_2}=\dfrac{y-y_2}{y_1-y_2}$

The slope of a line is the coefficient m when you write it in the $y=mx+q$ form
Parallel lines have the same slope
The slopes of perpendicular lines give -1 when multiplied

We can use this list to solve all the exercises:

Use the first equation to get

$y-1=-4(x-2) \iff y=-4x+9$

Use the second equation to get

$\dfrac{x-4}{2-4}=\dfrac{y-2}{-1-2} \iff \dfrac{x-4}{-2}=\dfrac{y-2}{-3}\iff 3(x-4)=2(y-2) \iff 3x-12=2y-4 \iff 2y = 3x-8 \iff y = \frac{3}{2}x-4$

d) same as c)

e) We derive the slope of the line by writing it as

$5y = -x-15 \iff y = -\dfrac{1}{5}x-3$

So, the slope is -1/5. From here, it's the same as b)

f) same as e)

g) Again we find the slope as

$3x+y+2=0\iff y=-3x-2$

so the slope is -3, and a perpendicular line has slope 1/3. From there, it's the same as b).

6 0

4 years ago

Alan compared the slope of the function y=3x+2 to the slope of the linear function that fits the values in this table. Which cho

Anastaziya [24]

OPTIONS:

*The slope of the graph of the table is 1 more than the slope of the graph of the equation.

*The slope of the graph of the table is 2 more than the slope of the graph of the equation.

*The slope of the graph of the equation is 2 more than the slope of the graph of the table.

*The slope of the graph of the equation is 1 more than the slope of the graph of the table.

Answer:

The slope of the graph of the equation is 1 more than the slope of the graph of the table.

Step-by-step explanation:

The slope in the equation of the function, y = 3x + 2, is identified as 3.

We know this because, the equation for the function was given in the slope-intercept form, y = mx + b, where m represents the slope.

Therefore, the slope of the function is 3.

The slope of the function represented by the table of values can be calculated using any two given pairs on the table.

Using (1, 6) and (3, 10):

$slope (m) = \frac{y_2 - y_1}{x_2 - x_2} = \frac{10 - 6}{3 - 1} = \frac{4}{2} = 2$

Slope of the function represented by the table of values is 2.

Therefore, comparing the slope of both functions, we can conclude that:

✅"The slope of the graph of the equation is 1 more than the slope of the graph of the table."

5 0

3 years ago

What is the range of possible sides for x 8.0 2.5

Vinil7 [7]

Answer:

idk

Step-by-step explanation:

sorry i need more info

4 0

3 years ago