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15 days ago

Line GH contains points G(–2, 6) and H(5, –3). What is the slope of ?

Mathematics

2 answers:

lawyer [4K]15 days ago

6 0

Answer:

Calculate the slope between points G(–2, 6) and H(5, –3).

The slope formula for two points is:

$m = \frac{y_{2} -y_{1}}{x_{2} - x_{1}}$

where m denotes the slope.

Given points are G(–2, 6) and H(5, –3).

$m = \frac{-3-6}{5+2}$

Solving the expression gives:

$m = \frac{-9}{7}$

Hence, the slope between points G(–2, 6) and H(5, –3) is

$m = \frac{-9}{7}$

PIT_PIT [3.9K]15 days ago

5 0

We apply the slope formula by substituting the given points.

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Here, x2 equals 5 and x1 equals -2; y2 equals -3 and y1 equals 6.

$m=\frac{-3-6}{5-(-2)}=\frac{-9}{7}$

Thus, the line's slope is -9 divided by 7.

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Sanjit drives the 45 km distance between York and Leeds he then drives a further 42 km from Leeds to Blackpool

Leona [4166]

The average speed for his entire journey from York to Blackpool is about 61.41 km/h.

Here’s a breakdown of how we arrive at this:

$\text{ The average speed}=\frac{\text{Total distance covered}}{\text{Total time taken}}$

The distance he travelled from York to Leeds is 45 km,

and the speed during that section was 54 km/h.

Therefore, the time taken to travel from York to Leeds is 45/54 hours (since Time = Distance/Speed).

Next, the distance from Leeds to Blackpool is 42 km,

and the time for that leg of the journey is 35 minutes, which is 35/60 hours.

This leads to the total duration for his trip as

$=\frac{45}{54}+\frac{35}{60}=\frac{450+315}{540}=\frac{765}{540}=\frac{17}{12}$ hours.

The cumulative distance covered equals 45 + 42 = 87 km.

Thus, his average speed is calculated as:

$=\frac{87}{17/12}= \frac{12\times 87}{17}=\frac{1044}{17}=61.4117647\approx 61.41\text{ km per hour}$

3 0

4 days ago

Read 2 more answers

A solid oblique cone with a slant length of 17 units is placed inside an empty cylinder with a congruent base of radius 8 units

PIT_PIT [3919]

Step $1$

Calculate the volume of a cylinder

We understand that

the volume of a cylinder can be expressed as

$V1=\pi r^{2} h$

In this scenario

$r=8\ units \\ h=15\ units$

Insert the values

$V1=\pi 8^{2} 15$

$V1=960\pi\ units^{3}$

Step $2$

Calculate the volume of a cone

We are aware that

the volume of a cone equals

$V2=\frac{1}{3}\pi r^{2} h$

In this example

$r=8\ units \\ l=17\ units \\ h=?$

Use the Pythagorean Theorem to determine the height h

$h^{2} =l^{2}-r^{2}\\ h^{2} =17^{2}-8^{2}\\ h^{2}=225\\ h=15\ units$

$V2=\frac{1}{3}\pi 8^{2} 15\\ \\ V2=320\pi \ units^{3}$

Step $3$

Calculate the empty volume inside the cylinder

$V1-V2=960\pi -320\pi =640\pi \ units^{3}$

Thus

the final result is

the empty volume inside the cylinder is $640\pi \ units^{3}$

6 0

8 days ago

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“The perimeter P of a triangle is equal to the sum of the lengths of sides a,b, and c”

AnnZ [3877]

Answer:

1. Calculate the sum of "a", "b" and "c".

2. The perimeter equation is: $P=a+b+c$

Step-by-step explanation:

In this case, P denotes the triangle's perimeter while a, b, and c are the triangle's sides.

The definition states that the sum results from an addition operation. Thus, the statement "The perimeter P of a triangle equals the total of sides a, b, and c" means that the perimeter is determined by aggregating the lengths of the triangle's sides.

Consequently, you can express this in the following equation:

$P=a+b+c$

5 0

4 days ago

Ten liters of pure water are added to a 50-liter pot of soup that is 50% broth. Fill in the missing parts of the table.

Zina [3914]

Answer:

c= 25

d= 60

Step-by-step explanation:

C: This is because 25+0 is simply 25. Essentially, you are not adding anything, so it remains unchanged!:)

D: 50 + 10 = 60. That’s straightforward addition!