Ivan likes ice-cream cones. At the ice-cream parlor,a single-scoop cone costs 75 cents .
Each additional scoop of ice cream costs 50 cents . Ivan earns 25 cents each time he takes out the trash. How many times does Ivan have to take out the trash to buy a
double-scoop cone?

Answer:

6 quarters, 9 dimes, and 18 nickels

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

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.

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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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.

The decimal point should be to the left of the 6.

A division is a process of splitting a specific amount into equal parts.

A is INCORRECT because Lucita's estimate is about right and if the decimal point was to the left of 2, then the answer would be -0.26 which is still too small.

B is CORRECT because again Lucita's estimate is about right and if the decimal is to the left of six the number would be -2.6 which is close to her estimate (-3)

C is INCORRECT because it is saying that -0.026 is the correct answer and Lucita's estimate was just too small which is incorrect since we know -0.026 is actually what is too small.

D is INCORRECT because it is saying that -0.026 is correct and if her estimate (-3) was too high, it would be bigger than the number she got which was -0.026 and regardless of anything we know -3 is not bigger that -0.026.

Hence the decimal point should be to the left of the 6. Option C is correct.

To learn more on Division click:

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