Plot the line for the equation on the graph. y−2=−2(x+4)

Sales for the first year were 2 millions of dollars

Solving linear equation mean calculating the unknown variable from the equation.

Let the linear equation : y = mx + c

If we draw the above equation on Cartesian Coordinates , it will be a straight line with :

m → gradient of the line

( 0 , c ) → y - intercept

Gradient of the line could also be calculated from two arbitrary points on line ( x₁ , y₁ ) and ( x₂ , y₂ ) with the formula :

[tex]\large {\boxed {m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]

If point ( x₁ , y₁ ) is on the line with gradient m , the equation of the line will be :

[tex]\large {\boxed {y - y_1 = m ( x - x_1 )}}[/tex]

Let us tackle the problem!

Let:

Sales for the first year = s₁

Sales for the second year = s₂

Sales for the third year = s₃

Given:

s₂ = 6 + s₁

s₃ = 3s₂

s₃ = 24

Unknown:

s₁ = ?

Solution:

[tex]s_3 = 3s_2[/tex]

[tex]24 = 3s_2[/tex]

[tex]s_2 = 24 \div 3[/tex]

[tex]s_2 = 8[/tex]

[tex]s_2 = 6 + s_1[/tex]

[tex]8 = 6 + s_1[/tex]

[tex]s_1 = 8 - 6[/tex]

[tex]s_1 = 2[/tex]

Sales for the first year = 2 millions of dollars

Grade: High School

Subject: Mathematics

Chapter: Function

Keywords: Function , Trigonometric , Linear , Quadratic

The sales in the first year is [tex]\boxed{2{\text{million of dollars}}}.[/tex]

Further explanation:

The linear equation with slope m and intercept c is given as follows.

[tex]\boxed{y = mx + c}[/tex]

The standard form of the linear equation can be expressed as follows,

[tex]\boxed{ax + by = c}[/tex]

The formula for slope of line with points [tex]\left( {{x_1},{y_1}} \right)[/tex] and [tex]\left( {{x_2},{y_2}} \right)[/tex] can be expressed as,

[tex]\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}[/tex]

Explanation:

Consider the sale in the first year as [tex]x[/tex].

Consider the sale in the second year as [tex]y[/tex].  

Consider the sale in the third year as [tex]z[/tex].

Sales for a company were 6 million dollars more the second year than the first.

[tex]y = 6 + x[/tex]

Sales for the third year were 24 million dollars.

[tex]z = 24[/tex]

Sales for the third year were tripled the sales for the second year.

[tex]z = 3y[/tex]

Substitute 24 for z in above equation.

[tex]\begin{aligned}24&= 3y\\\frac{{24}}{3} &= y\\8&= y\\\end{aligned}[/tex]

Substitute [tex]8[/tex] for [tex]\text{y}[/tex] in equation [tex]y = 6 + x[/tex]

[tex]\begin{aligned}8&= 6+ x\\8 - 6&= x\\2&= x\\\end{aligned}[/tex]

The sales in the first year is [tex]\boxed{2{\text{million of dollars}}}.[/tex]

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear inequality

Keywords: sales, company, 6 million, dollars, second year, first, sales for second, sales for third year, tripled, first year, 24 million, millions of dollars.

4 [tex]\frac{3}{8}[/tex] is  larger than 4.25 lb.

We'll convert the fraction 4 [tex]\frac{3}{8}[/tex]  to a decimal and compare it to the decimal 4.25.

First,

convert the mixed number 4 [tex]\frac{3}{8}[/tex] to an improper fraction:

4 [tex]\frac{3}{8}[/tex] = 4 + [tex]\frac{3}{8}[/tex]

Next,

convert [tex]\frac{3}{8}[/tex]  to a decimal:

3 ÷ 8

= 0.375.

Add the whole number part and the decimal:

4 + 0.375

= 4.375.

Now, we compare 4.375 with 4.25:

4.375 is clearly larger than 4.25.

So, 4 [tex]\frac{3}{8}[/tex]  is larger than 4.25 lb.

Option 2 is the correct answer because it shows the proper steps for constructing an angle bisector using a compass and a straightedge.

Steps:

Draw the angle to be bisected.

Place the compass point at the vertex of the angle and draw an arc that intersects both sides of the angle.

Without changing the compass radius, place the compass point at each of the arc intersection points and draw two more arcs that intersect each other.

Draw a line from the vertex of the angle through the point of intersection of the two arcs.

This line is the angle bisector.

The other options are incorrect because they do not show all of the necessary steps, or they show the steps in the wrong order.

For example, option 1 shows the steps for constructing an angle bisector using a protractor, but this is not the method that was asked for.

Option 3 shows the steps for constructing an angle bisector using a compass and a straightedge, but it does not show the step of drawing the arc through the vertex of the angle.

Option 4 is incorrect because it shows the steps for constructing an angle bisector using a ruler and a triangle, but this is not the method that was asked for.

For such more question on bisector

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Answer:

The lowest mean temperature was on Friday.

Step-by-step explanation:

TTM Answer

The sentence "9 is less than x is -1" written as an equation is A. 9 - x = -1

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

Now the given sentence is,

9 is less than x is -1

So, since less than means subtraction

Therefore 9 is less than x is written as,

9 - x

And this equal to -1

So we can write,

9 - x = -1

which the required equation of the given sentence.

The sentence "9 is less than x is -1" written as an equation is  9 - x = -1

Thus the correct answer is A. 9 - x = -1.

To learn more about equation:

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Answer:

Step-by-step explanation:

The amount of grapes that he gave away is 3.5 pounds.

Number of grapes with Martin = 7 pounds

Fraction given away = 2/5

In this case, to use compatible numbers, we have to find a fraction that's close to 2/5 which will be 1/2.

Then, we have to multiply 1/2 by 7 and this will be:

= 1/2 × 7

= 3.5

In conclusion, the amount of grapes that he gave away is 3.5 pounds.

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Answer:

7/30

Step-by-step explanation:

2a/b = w

 divide both sides by 2 to get

a/b = w/2

now multiply both sides by b to get

a = bw/2

1. $69.00 * 5 = $345.00

2. $27.75 * 3.5 = $97.13

Answer:

6 quarters, 9 dimes, and 18 nickels

Answer:

How many hours do you spend at the pharmacy each month?

Step-by-step explanation:

A statistical question is a question that will have variable answers. It will not have a single answer. Like - How tall are the students in your class?

So, here the answer is -

How many hours do you spend at the pharmacy each month?

As here, the answer can be variable. Some days it can be 8 hours, some days it can be 12 hours.

Final answer:

Inno's solution of using the square root of 9 and 16 is the best estimate for the square root of ten, as it provides a narrower and more accurate range for the estimate.

Explanation:

To estimate a square root that is not a perfect square, one strategy is to find integers that the number falls between, and then those integers' respective square roots give us a range within which the square root of the number will fall.

Rosa and Inno's approaches are similar and most appropriate because they both use 9 and another square number that is close to 10.

Rosa uses the square roots of 9 and 25. Since the square root of 9 is 3, and the square root of 25 is 5, we know that √10 is a little more than 3, because 10 is closer to 9 than it is to 25. Inno uses the square roots of 9 and 16. Since the square root of 16 is 4, √10 is closer to 3 than 4 because 10 is closer to 9.

Therefore, Inno's solution gives a closer estimate of the square root of 10, as it falls between 3 and 4 (and closer to 3), and this is the best solution among those proposed.