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2 years ago

What is the slope of the line between the points (2,-1) and (5,-3)

Mathematics

1 answer:

Ilya [14]2 years ago

6 0

Answer:

The slope of the line between the points (2,-1) and (5,-3) is $m=-\frac{2}{3}$

Therefore $m=-\frac{2}{3}$

Step-by-step explanation:

Given that the line between the points (2,-1) and (5,-3)

To find the slope of the line between the points (2,-1) and (5,-3) :

The formula for slope is $m=\frac{y_2-y_1}{x_2-x_1}$

Let $(x_1,y_1)$ , $(x_2,y_2)$ be the given points (2,-1) and (5,-3) respectively

Now substitute the values of the points in the formula

$m=\frac{-3-(-1)}{5-2}$

$=\frac{-3+1}{3}$

$=\frac{-2}{3}$

Therefore $m=-\frac{2}{3}$

The slope of the line between the points (2,-1) and (5,-3) is $m=-\frac{2}{3}$

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Answer:

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<h2>Sam will get is £30 (putting the value of x)</h2><h2>and Bethan will get £24</h2>

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2 years ago

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chubhunter [2.5K]

My exact answer is 2.2

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2 years ago

Forensic specialists can estimate the height of a deceased person from the lengths of the person's bones. These lengths are subs

Lera25 [3.4K]

Answer:

$130.2845\leq h\leq 137.7245$

Step-by-step explanation:

Given an inequality that relates the height h, in centimeters, of an adult female and the length f, in centimeters, of her femur by the equation

$|h - (2.47f + 54.10)| \leq 3.72$

If an adult female measures her femur as 32.25 centimeters, we can determine the possible range of her height by plugging f = 32.25cm into the modelled equation as shown:

$|h - (2.47(32.25) + 54.10)| \leq 3.72\\|h - (79.9045 + 54.10)| \leq 3.72\\|h - (134.0045)| \leq 3.72\\$

If the modulus function is positive then:

$h - 134.0045 \leq 3.72\\h \leq 3.71+134.0045\\h\leq 137.7245$

If the modulus function is negative then:

$-(h - 134.0045) \leq 3.72\\-h+134.0045 \leq 3.72\\-h\leq 3.72-134.0045\\-h\leq -130.2845\\$

multiply through by -1

$-(-h)\geq -(-130.2845)\\h\geq 130.2845\\130.2845\leq h$

combining the resulting inequalities, the estimate of the possible range of heights will be $130.2845\leq h\leq 137.7245$

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2 years ago

A box is being created out of a 15 inch by 10 inch sheet of metal. Equal-sized squares are cutout of the corners, then the sides

ivolga24 [154]

Answer:

Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box has largest volume.

Step-by-step explanation:

Given that,

A box is being created out of a 15 inches by 10 inches sheet of metal.

The length of the one side of the squares which are cut out of the each corners of the metal sheet be x.

The length of the metal box be = (15-2x) inches.

The width of the metal box be =(10-2x) inches

The height of the metal box be =x inches

Then, the volume of the metal box= length×width×height

=(15-2x)(10-2x)x cubic inches

=(150x-50x²+4x³) cubic inches

∴ V= 4x³-50x²+15x

Differentiating with respect to x

V'=12x²-100x+15

Again differentiating with respect to x

V''=24x-100

For maximum or minimum value, V'=0

12x²-100x+15=0

Apply quadratic formula $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ , here a=12, b= -100 and c=15

$x=\frac{-(-100)\pm\sqrt{(-100)^2-4.12.15}}{2.12}$

$\Rightarrow x=\frac{100\pm\sqrt{9280}}{2.12}$

$\Rightarrow x=0.1528,8.18$

For x= 8.18, The value of (15-2x) and (10-2x) will negative.

∴x=0.1528 .

Now, $V''|_{x=0.1528}=24(0.1528)-100$

∴At x=0.1528 inch, the volume of the metal box will be maximum.

Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box has largest volume.

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2 years ago

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Westkost [7]

Answer:

The answer is 1/15

I hope it helps

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2 years ago