Who to square root a decimal

The point of intersection for lines (m) and (n) is (3.5, -1.5). Line (m) equation: (y = x - 5). Line (n) equation: (y = -3x + 9).

To find the point of intersection of two lines, you can use the point-slope form of a line and set the equations of the lines equal to each other. Let's first find the equations of the lines ( m ) and ( n ) using the given points.

Line ( m ) passes through the points ( (6,1) ) and ( (2,-3) ). Let's find the slope of line ( m ) first:

[tex]\[ \text{Slope of } m = \frac{{y_2 - y_1}}{{x_2 - x_1}} \][/tex]

[tex]\[ \text{Slope of } m = \frac{{-3 - 1}}{{2 - 6}} = \frac{{-4}}{{-4}} = 1 \][/tex]

Now we can use the point-slope form of a line to find the equation of line ( m ):

y - y_1 = m(x - x_1)

Let's use the point ( (6,1) ) to find the equation of line ( m ):

y - 1 = 1(x - 6)

y - 1 = x - 6

y = x - 6 + 1

y = x - 5

So, the equation of line ( m ) is ( y = x - 5 ).

Now let's find the equation of line (m and  n) passing through the points

( (2,3) ) and ( (5,-6) ):

[tex]\[ \text{Slope of } n = \frac{{-6 - 3}}{{5 - 2}} = \frac{{-9}}{{3}} = -3 \][/tex]

Using the point ( (2,3) ) to find the equation of line ( n ):

y - 3 = -3(x - 2)

y - 3 = -3x + 6

y = -3x + 6 + 3

y = -3x + 9

So, the equation of line ( n ) is ( y = -3x + 9 ).

Now, we'll set the equations of ( m ) and ( n ) equal to each other to find the point of intersection:

x - 5 = -3x + 9

Now, solve for ( x ):

x + 3x = 9 + 5

4x = 14

[tex]\[ x = \frac{{14}}{4} \][/tex]

x = 3.5

Now, substitute ( x = 3.5 ) into either equation to find ( y ). Let's use the equation of line ( m ):

y = 3.5 - 5

y = -1.5

So, the point of intersection of lines ( m ) and ( n ) is ( (3.5, -1.5) ).

Final answer:

Joan completed 13 free throws. This was determined by solving the equation derived from the information that Tabitha's 6 completed shots were a third of 5 more than Joan's completed shots.

Explanation:

Tabitha completed 6 free throws, which is stated to be a third of 5 more than Joan completed. This means that if J represents the number of shots Joan completed, then 6 is one-third of J plus 5. Therefore, we can express this relationship in an equation: 6 = (J + 5) / 3.

To find out how many shots Joan completed, we solve for J as follows:

Multiply both sides of the equation by 3 to eliminate the fraction: 18 = J + 5.

Subtract 5 from both sides to solve for J: J = 18 - 5.

Calculate the result: J = 13.

Hence, Joan completed 13 free throws.

Final answer:

To find the selling price of a scrapbook kit with a markup rate of 65% on a cost of $20, calculate the markup amount ($20 * 0.65 = $13) and add it to the original cost, resulting in a selling price of $33.

Explanation:

To determine the selling price of a scrapbook kit with a markup rate of 65%, we first need to calculate the amount of markup. The cost of the scrapbook kit to the retailer is $20. The markup amount is found by multiplying this cost by the markup rate expressed as a decimal (65% = 0.65).

The markup amount is: $20 × 0.65 = $13. To find the final selling price, we add this markup to the original cost of the item:

$20 (original cost) + $13 (markup) = $33 (selling price).

Therefore, the selling price of the scrapbook kit is $33.

When you draw a line through each point with a slope of 1/2, the two lines you create will be parallel to each other because they both have the same slope and increase at the same rate.

In mathematics, a slope of 1/2 means that for every 2 units you move to the right (horizontally), you will move up 1 unit (vertically). When you draw a line through each point using this slope, you'll notice that the two lines will be parallel to each other. That's because they both have the same slope, which means they're increasing at the same rate. Therefore, they never intersect and remain an equal distance apart from each other at all points.

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Answer:

8

Step-by-step explanation:

Step 1

Convert mixed numbers to an improper fractions

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

[tex]1\frac{3}{4} =\frac{1*4+3}{4}= \frac{7}{4}[/tex]

Step 2

Find the total cost

we know that

the total cost is equal to the cost of the gallons of white paint  plus the cost of the gallons of blue paint

the cost of the gallons of white paint is equal to

[tex]\frac{7}{2}*17.50= \$61.25[/tex]

the cost of the gallons of blue paint is

[tex]\frac{7}{4}*19.00= \$33.25[/tex]

The total cost is

[tex]\$61.25+\$33.25=\$94.50[/tex]

therefore

the answer is

the total cost is [tex]\$94.50[/tex]

To find the starting amounts of cranberry and orange punch, we equate 2/3 of the cranberry punch to 5/6 of the orange punch. After setting up the equation 2/3 * C = 5/6 * O, we can solve for either C or O given a specific amount for one.

Understanding Proportional Quantities in Punch

To determine how many ounces of cranberry and orange punch might have been at the start of the party, given that guests drank 2/3 of the cranberry punch and 5/6 of the orange punch, and that they drank the same amount of each, we can set up an equation. Let's label the amount of cranberry punch initially as C ounces and the amount of orange punch initially as O ounces. According to the problem, 2/3 of C is equal to 5/6 of O; therefore:

2/3 * C = 5/6 * O

We can find a common multiple of the denominators 3 and 6 to solve the equation. For simplicity, let's assume that the common multiple is 6. If we multiply both sides of the equation by 6 to get rid of the fractions, we have:

4 * C = 5 * O

This means that the amount of cranberry punch is always 5/4 times the amount of orange punch. For example, if there were 20 ounces of orange punch at the start (O = 20), then there would have been 5/4 * 20 = 25 ounces of cranberry punch (C).

Final answer:

The party guests drank equal amounts of 2/3 of cranberry punch and 5/6 of orange punch. By setting up an equation and choosing a common multiple of the denominators (6), we conclude that one possible starting amount for each type of punch is 18 ounces, demonstrating that whenever x is chosen, y will be equal to x.

Explanation:

The student's question involves solving a problem where two quantities are compared to find out how much of each was present initially. Since the guests drank the same amount of cranberry punch and orange punch, with the proportions being 2/3 and 5/6 respectively, we can set up an equation to solve for the initial amounts.

Let x represent the original amount of cranberry punch and y represent the original amount of orange punch. According to the question:

2/3 of cranberry punch = 5/6 of orange punch

To find multiple answers, we could assume a common multiple of both denominators 3 and 6, which is 6. Then, if we let x = 6 and y = 6, we have:

However, these amounts are not equal. We need to find a value for x and y that, when substituted into the proportion, yields an equal amount for both types of punch. Multiply both sides of the equation by 3/2 to isolate y:

Now, we can select any multiple of 6 for x to represent the initial amount. If we choose multiple of 6 such as 18 ounces for x, then y would also be 18 ounces. Thus, the starting amount of both cranberry punch and orange punch could have been 18 ounces each as one of the possible answers.

Keywords:

Water, plant, water, liters, daily, milliliters, divide

For this case we must find the amount of liters of water that students used daily, for 28 days, to water a plant, knowing that they used a total of 23.8 liters of water at the end of 28 days. For this, we must divide and the result convert it to milliliters. So:

Let "x" be the number of liters of water that students used per day:

[tex]x = \frac {23.8\ liters} {28\ days}\\x = 0.85\ liters\ per\ day.[/tex]

Thus, the students used 0.85 liters of water per day.

On the other hand, we know that: 1 liter equals 1000 milliliters. Then, by rule of three:

1 L -------------> 1000 mL

0.85L ---------->?

Where "?" represents the amount of daily water watered in milliliters

[tex]? = \frac {0.85 * 1000} {1}\\? = 850\ mL[/tex]

Thus, the students used 850 milliliters of water per day.

Answer:

850 milliliters of water per day.

They use 0.85 liters = 850 mililiters each day.

Comparison is an effort to compare two or more objects in terms of shape or size, or number

Proportional Comparisons are comparisons of two or more numbers where one number increases, the other numbers also increase

[tex]\frac {x1} {y1} = \frac {x2} {y2}[/tex]

  so that if:

  x = 2

  then

[tex]y =  \frac {y} {x} \times \: 2[/tex]

While the reversal value comparison is the comparison of two or more numbers where one number increases, the other number decreases in value

  Can be formulated

 [tex]\displaystyle \frac {x1} {y2} = \frac {x2} {y1}[/tex]

so that if:

  x = 2

  then

[tex]\displaystyle y = \frac {x} {y} \times \: 2[/tex]

students use a total of 23.8 liters of water over the 28 days

The amount of water used in a day

From this we can make a comparison:

[tex]28~days=23.8~liters[/tex]

[tex]1~day=x~liter[/tex]

[tex]\displaystyle \frac{1~day}{28~day} =\frac{x~liters}{23.8}[/tex]

[tex]\displaystyle x~=~\frac{1~\times~23.8}{28}[/tex]

x = 0.85 liters

From the unit of volume, we convert liters to milliliters

1 liter = 10³ milliliters

0.85 liters we move the comma 3 units to the right becomes:

[tex]\displaystyle 0.85 = 0~\boxed{,}\rightarrow~8~\rightarrow~5~\rightarrow~0~\boxed{,}[/tex]

= 850 mililiters

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Keywords: water a plant, liters, mililiters,students