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3 years ago

Find the slope of the line that contains the points (3, 2) and (7,5)

Mathematics

2 answers:

DanielleElmas [232]3 years ago

5 0

Answer:

3/4

Step-by-step explanation:

The formula for the slope between any two points is:

$m=\frac{y_2-y_1}{x_2-x_1}$

Let's let (3,2) be x₁ and y₁ and let's let (7,5) be x₂ and y₂. Thus:

$m=\frac{5-2}{7-3}$

Subtract:

$m=3/4=0.75$

So the slope is 3/4 or 0.75.

And we're done!

Ivanshal [37]3 years ago

4 0

Answer:

3/4

Step-by-step explanation:

We can find the slope using the slope formula

m = (y2-y1)/(x2-x1)

= (5-2)/(7-3)

=3/4

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3 years ago

On Thursday, rrr centimeters of rain fell on Deborah's garden. On Saturday, 15\%15%15, percent more rain fell on the garden.

xenn [34]

Answer:

Step-by-step explanation:

Complete question

On Thursday, r centimeters of rain fell on Deborah's garden. On Saturday, 15% more rain fell on the garden.

The expression r+0.15r describes the number of centimeters of rain Deborah's garden got on Saturday. We can also use the expression 1.15r to represent the same quantity.

Match each amount in the situation with the expression that represents it.

Since we have given that

Let amount of rainfall on Deborah's garden on Thursday be 'r'.

According to question, 15% more rainfall on the garden on Saturday.

So, Amount of rainfall on Saturday would be

$r+\dfrac{15}{100}r\\\\=r+0.15r\\\\=1.15r$

Hence, Deborah got 1.15r amount of rainfall on Saturday.

4 0

4 years ago

Read 2 more answers

What is the range of the data below 23,33,25,16,27,43,29,40,35

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3 years ago

Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 181.5 square cen

3241004551 [841]

Answer:

The base and height of the solid is 5.5cm

Step-by-step explanation:

Given

$Surface\ Area = 181.5cm^2$

Required

Determine the dimensions that maximizes the volume

Let the base dimension be x and the height be h

The volume is calculated as:

$Volume =x^2 * h$

$Volume =x^2h$

181.5 =x^2h

The surface area (S) is calculated as this:

$S = 2(x^2 + xh + xh)$

$S = 2(x^2 + 2xh)$

$S = 2x^2 + 4xh$

Substitute 181.5 for S

$181.5 = 2x^2 + 4xh$

Make h the subject:

$4xh = 181.5 - 2x^2$

$h = \frac{181.5 - 2x^2}{4x}$

Substitute $h = \frac{181.5 - 2x^2}{4x}$ in $Volume =x^2h$

$V = x^2(\frac{181.5 - 2x^2}{4x})$

$V = x(\frac{181.5 - 2x^2}{4})$

$V = \frac{1}{4}(x)(181.5 - 2x^2)$

$V = \frac{181.5x}{4} - \frac{2x^3}{4}$

$V = \frac{181.5x}{4} - \frac{x^3}{2}$

To get the maximum, we differentiate V with respect to t and set the differentiation to 0

$dV = \frac{181.5}{4} - \frac{3x^2}{2}$

Set to 0

$0 = \frac{181.5}{4} - \frac{3x^2}{2}$

$\frac{3x^2}{2} = \frac{181.5}{4}$

Multiply through by 4

$4 * \frac{3x^2}{2} = \frac{181.5}{4} * 4$

$2*3x^2 = 181.5$

$6x^2 = 181.5$

$x^2 = \frac{181.5}{6}$

$x^2 = 30.25$

$x = \sqrt{30.25$

$x = 5.5$

Recall that:

$h = \frac{181.5 - 2x^2}{4x}$

$h = \frac{181.5 - 2 * 5.5^2}{4 * 5.5}$

$h = \frac{181.5 - 60.5}{22}$

$h = \frac{121}{22}$

$h = 5.5$

So, we have:

$h = 5.5$

$x = 5.5$

Hence, the base and height of the solid is 5.5cm

7 0

3 years ago