a.)Which two points should you use to find the equation of the model? Explain.
B.) Use the two points you chose in part a to find the slope of the linear model, rounded to three decimal places. Show your work.
c.) What is the equation of the linear model in point-slope form?
d.) Rearrange the equation you wrote in part c into slope-intercept form. Show your work.

The speed of the boat in still water is 8 miles per hour.

To find the speed of the boat in still water, we can use the formula:

Speed of the boat in still water = (speed downstream + speed upstream) / 2

Given that it takes the same amount of time for the boat to travel 36 miles downstream and 12 miles upstream, we can set up the following equation:

36 / (v + 4) = 12 / (v - 4)

Where v is the speed of the boat in still water. Cross multiplying and solving the equation, we get:

36(v - 4) = 12(v + 4)

36v - 144 = 12v + 48

24v = 192

v = 8

Therefore, the speed of the boat in still water is 8 miles per hour.

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The department store sold 20 short-sleeved shirts and 14 long-sleeved shirts. Calculations were made by setting up a system of equations and solving for the variables representing the number of shirts sold.

To solve how many short-sleeved and long-sleeved shirts were sold given the total sales and price per shirt, we can set up a system of equations. Let x represent the number of short-sleeved shirts and y represent the number of long-sleeved shirts. We have two equations: x + y = 34 (since a total of 34 shirts were sold) and 11x + 21y = 514 (representing the total sales from the shirts).

First, we can solve for x in terms of y from the first equation: x = 34 - y. Substituting this expression for x into the second equation gives us 11(34 - y) + 21y = 514. Simplifying this, we get 374 + 10y = 514, which simplifies down to y = 14.

Substituting y = 14 back into the original first equation x = 34 - y, we find that x = 34 - 14, so x = 20. Therefore, the store sold 20 short-sleeved shirts and 14 long-sleeved shirts.

Answer:

Solution: All real numbers.

Step-by-step explanation:

[tex]3(4g+6)=2(6g+9)\qquad|\text{use distributive property}\\\\(3)(4g)+(3)(6)=(2)(6g)+(2)(9)\\\\12g+18=12g+18\qquad|\text{subtract 12g from both sides}\\\\18=18\qquad TRUE[/tex]

It's an identity equation.

Answer : The expression for the given statement is [tex]a-25[/tex]

Step-by-step explanation :

We are given a statement :

"your aunt's age a minus 25"

Let the age of aunt be considered as 'a'

From the given statement, we conclude that

'Minus' in the above statement means subtract (-) operation.

Thus, the expression for the given statement is [tex]a-25[/tex]

4x19=76 tada there ya go pally!

When a number is raised to the power of 2, it is squared. This means the number is multiplied by itself once.

When a number is raised to the power of 2, it is squared. Squaring a number means multiplying it by itself. For example, if you have the number 4 and you square it (raise it to the power of 2), you would multiply 4 by 4, which equals 16. Therefore, 4 squared (or 4 to the power of 2) equals 16.

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These are all division problems.

1)   9 ÷ [tex]\frac{3}{4}[/tex]

= [tex]\frac{9}{1} * \frac{4}{3} = \frac{9(4)}{3}= 3(4) = 12[/tex]

3)   [tex]3\frac{1}{2} = \frac{2(3) + 1}{2} = \frac{7}{2}[/tex]

7 ÷ [tex]\frac{7}{2}[/tex]

= [tex]\frac{7}{1} * \frac{2}{7} = \frac{7(2)}{2}= 7[/tex]

5)   6 ÷ [tex]\frac{1}{8}[/tex]

= [tex]\frac{6}{1} * \frac{8}{1} = 6(8) = 48[/tex]

ANSWER

[tex]x=\frac{13}{62}[/tex]

and

[tex]y= \frac{-9}{62}[/tex]e have

EXPLANATION

[tex]17x-3y=4---(1)[/tex]

[tex]2x-4y=1[/tex]

Let us make y the subject and call it equation (2)

[tex]2x=1+4y[/tex]

[tex]x=\frac{1}{2}+2y--(2)[/tex]

We put equation (2) in to equation (1)

[tex]17(\frac{1}{2}+2y)-3y=4[/tex]

[tex]\frac{17}{2}+34y-3y=4[/tex]

[tex]34y-3y=4- \frac{17}{2} [/tex]

Simplify to get,

[tex]31y= \frac{8-17}{2} [/tex]

[tex]31y= \frac{-9}{2} [/tex]

Divide both sides by 31,

[tex]y= \frac{-9}{2} \div 31[/tex]

[tex]y= \frac{-9}{2} \times \frac{1}{31}[/tex]

[tex]y= \frac{-9}{62}[/tex]

We put this value in to equation (2) to get,

[tex]x=\frac{1}{2}+2\times -\frac{9}{62}[/tex]

[tex]x=\frac{1}{2} -\frac{18}{62}[/tex]

We collect LCM to obtain,

[tex]x=\frac{31-18}{62}[/tex]

[tex]x=\frac{13}{62}[/tex]

To solve the equation 12(m + 3x) = 18(x - 3m), we can start by distributing the coefficients and collecting like terms. Finally, m = -3x/11.

The given equation is 12(m + 3x) = 18(x - 3m).

Therefore, the solution to the equation is m = -3x/11.

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To write an expression in function notation, you must solve it for the dependent variable.

Assuming that you want the expression to be written in the form [tex] y = f(x) [/tex] (i.e., assuming that x is the independent variable), we have to solve the expression for y, which means that we want y to remain alone on the left hand side, and move everything else to the right hand side.

So, first of all, we can add 9x to both sides to get

[tex] 3y = 9x+24 [/tex]

Finally, we divide both sides by 3:

[tex] y = 3x + 8 [/tex]

8 camper in each tent

You have 5/8 remaining of a pizza. You want to divide it into 3 equal slices.

To find the answer, Divide 5/8 with 3, or multiply 5/8 x 1/3

5/8 x 1/3 = 5/24

Each portion is 5/24 of the original slice.

hope this helps

Y intercept (0, 2) so b = 2

Slope = (2 - 0) / (0 + 3) = 2/3

Equation y =  mx + b

In this case slope m = 2/3 and y intercept = b = 2

So equation y = 2/3 x + 2

Answer

A.) Y = 2/3 x + 2

The answer is x  = −2

open the attachment to get the show the explaining.

The number is 4.

[tex]1 + 3*4 = 13\\2 * 4 + 5 = 13[/tex]

The problem is about solving a simple algebraic equation. The given condition can be put into an equation and solved step by step. The number that meets the condition is 4.

The subject of this problem is algebra. We need to find a number that satisfies the given condition. If we define the unknown number as 'x', the given statement can be translated into the following algebraic equation: 1 + 3x = 2x + 5.

To find the number, we solve this equation step by step. First, we can rearrange the equation by subtracting 2x from both sides, which gives us: 1 + x = 5. Then, subtracting 1 from both sides, we have: x = 4.

So, the number that satisfies the given condition is 4.

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I think the answer is 40.  

Hey there!!  

Given equation :

... 2t + 8 > -4 ( t + 1 )

Using the distributive property :

... 2t + 8 > -4t - 4

Adding 4t on both sides :

... 6t + 8 > - 4

Subtracting 8 on both sides :

... 6t > - 12

Dividing by 6 on both sides :

... t > -2

Hence, the number in the blank is -2.

Hope my answer helps!!

The sentence 'four more than the number of weeks in a group of days' is converted into the equation is W = D/7 + 4.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Convert the sentence into an equation or expression.

The sentence is four more than the number of weeks in a group of days.

We know that in a week, there are 7 days. Then the equation will be

Week = (Days / 7) + 4

Simplify the equation, then the equation will be

W = D/7 + 4

The sentence 'four more than the number of weeks in a group of days' is converted into the equation is W = D/7 + 4.

More about the Algebra link is given below.

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when solving sales tax it's pretty simple because all you do is add everything for a subtotal and multiply your sub total by the tax so i'll use the first as an example your subtotal is 19.96 x0.05 to get 0.99 <-- your sales tax and your final total with tax to be 20.96

If you bought a $3 smoothie and your total (with tip) is $3.60, you have to divide 3.6/3. You get 1.2, which means you left a 20% tip, which would be .2 in decimal form.

To find the percent tip, divide the tip amount by the total cost and multiply by 100.

To find the percent tip, we need to first calculate the total cost of the smoothies and the tip. Since the smoothies cost $3 each, the total cost of the smoothies is $3 * 2 = $6. Let's assume the tip amount is x dollars. The split total (including the tip) is $3.60, which is equal to half of the total cost plus the tip: $3 + $3 + x = $6 + x. Solving this equation, we can find the value of x:

The tip amount is $1.20. To find the percent tip in decimal form, we divide the tip amount by the total cost and multiply by 100: $1.20 / $6 * 100 = 20%. Therefore, you and your friend left a 20% tip.

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The answer would be 0.335 because thousandths is the third decimal from zero

Leticia needs to take the 21/8 yards to earn enough to buy a music player that costs $45 and this can be determined by forming the linear equation.

Given :

The following steps can be used to determine the equation that shows how many more times Leticia needs to take the yard to earn enough to buy a music player that costs $45:

Step 1 - Let the number of yards she takes after she earns $24 be 'x'.

Step 2 - The amount she needs to earn to buy a music player is:

= 8x

Step 3 - The linear equation according to the given data is given by:

24 + 8x = 45

Step 4 - Simplify the above equation.

8x = 21

[tex]\rm x = \dfrac{21}{8}[/tex]

Leticia needs to take the 21/8 yards to earn enough to buy a music player that costs $45.

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a) Assuming the problem statement means the edge length of the cubical case is 3w, three times the width of the artifact, the volume of the case is ...

V = s³ . . . . . . volume of a cube with edge length s

V = (3w)³

b) The expression can be simplified by applying the rules of exponents, distributing the exponent to the contents of parentheses.

V = 3³w³

V = 27w³

Solution

Number of weeks in a year = 52 weeks

If in a normal year when each package of flea treatment lasts for 4 weeks, then in a year there Jim's dog will have to be treated for

[tex]\frac{52}{4} =13 times[/tex]

Where as, when the fleas are bad in a year, the treatment lasts for only 3 weeks.

Then in a year Jim's dog would get

[tex]\frac{52}{3} =17 times[/tex]

So Jim's dog will get 17- 13 =4 treatments more.

4 treatments that are made in 3 weeks each will be 4×3 =12 weeks more treatment

The Number treatments is the ratio of the number of weeks in a year and the number weeks per treatment. Hence, Jim's dog would get 4 more treatments due to the bad weather.

Number of weeks in a year = 52

The number of flea treatment he'll get in a year can be calculated thus :

Normal weather = 52 / 3 = 17. 333 = 17 treatments

Bad weather = 52 / 4 = 13 treatments

Difference in treatment = 17 - 13 = 4

Therefore, as a result of the bad weather, Jim's dog would get 4 more treatments than during normal weather.

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