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Aleonysh [2.5K]
3 years ago
15

What is the equation of the line that passes through the point (- 1, 5) and is parallel to the line y = - 3x + 5

Mathematics
1 answer:
Harlamova29_29 [7]3 years ago
5 0

Answer:

<h2>          y - 5 = -3(x + 1)</h2>

Step-by-step explanation:

Parallel lines has the same slope.

The equation of a line that passing through point (x₁, y₁) with a slope of m is:

y - y₁ = m(x - x₁)

m = -3

(-1, 5)   ⇒  x₁ = -1,  y₁ = 5

Therefore the equation:

y - 5 = -3(x + 1)

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Isolate the variable by dividing each side by factors that don't contain the variable.

6 0
2 years ago
What is the area of a rectangle with a base of 28 and a width of 42
OverLord2011 [107]
Area = base x height
28 x 42 = 1176
5 0
3 years ago
Angela and Jayden were at track practice. The track is 2/5 kilometers around. Angela ran 1 lap in 2 Minutes. Jayden ran 3 laps i
I am Lyosha [343]

Answer:

Step-by-step explanation:

Angel ran 1 lap in 2 minutes.

Jayden ran 3 laps in 5 minutes.

How many minutes does it take Angel to run one kilometer? What about Jayden?

How far does Angel run in one minute? What about Jayden?

Who is running faster? Explain your reasoning.

IM Commentary

Parts (a) and (b) of the task ask students to find the unit rates that one can compute in this context. Part (b) does not specify whether the units should be laps or km, so answers can be expressed using either one.

The purpose of part (c) is to give students an opportunity to make use of the unit rates that they found in parts (a) and (b). While it is possible for students to solve part (c) in other ways, the solution shown represents the kind of reasoning with unit rates that 7th graders should be able to do. It is important to note that the answer can be determined using different unit rates as long as the reasoning behind it is correct.

Solution

We can create a table that shows how far each person runs for a certain number of laps:

Number of laps Number of km

1 25

2 45

3 65

We can see from the table that 1 km is exactly half way between 2 and 3 laps. So it will take 2.5 laps to run 1 km.

Since it takes Angel 2 minutes to run 1 lap, she will take

2.5 laps1 km⋅2 minutes1 lap=5 minutes1 km.

So it takes Angel 5 minutes to run 1 km.

Since it takes Jayden 5 minutes to runs 3 laps, she runs 1 lap in 53 minutes. Thus, it takes Jayden

2.5 laps1 km⋅5 minutes3 laps=52⋅53 minutes/km=256 minutes/km=416 minutes/km.

So it takes Jayden 416 minutes to run 1 km.

Angel runs 1 lap in 2 minutes so she runs 12 lap in 1 minute. Since 1 lap is 25 km, 12 lap is 15 km. So she also runs 15 km in one minute.

Since Jayden runs 1 lap in 53 minutes, she will run 35 laps in 1 minute. Since Jayden runs 1 km in 256 minutes, she will run 625 km in 1 minute.

Jayden runs the same distance in less time than Angel (alternatively, Jayden runs farther in the same time than Angel), so Jayden is running faster than Angel.

4 0
2 years ago
In the △ABC, the height AN = 24 in, BN = 18 in, AC = 40 in. Find AB and BC.
strojnjashka [21]

Answer:

AB = 30 inch

BC = 14 inch or BC = 50 inch

Step-by-step explanation:

Make a drawing. Please see the attachment. All measurements are in inches.

Consider the two triangles:

∆ ABC and ∆ AB'C

1. Looking only at ∆ ABC. Since this is <em>not</em> a rectangular triangle, let's first consider ∆ ANC, so we can calculate NC.

AN is the height and there fore is perpendicular to NC and thus also to BC.

In ∆ ANC

AN² + NC² = AC²

We want to calculate NC, so:

NC² = AC² - AN²

Given: AC = 40 and AN = 24

NC² = 40² + 24²

NC² = 1600 + 576

NC² = 1024

NC = +-SQRT(1024)

NC = 32

NC = NB + BC

We want to know BC

BC = NC - NB

Given: NB = BN = 18 and we just calculated NC to be 32 so...

BC = 32 - 18

BC = 14

2. Looking only at ∆ AB'C

AN is the height and there fore is perpendicular to B'C. Let's consider ∆ AB'N, so we can calculate AB'.

AN is the height and there fore is perpendicular to B'N, which means it has an angle of 90° in ∆ AB'N.

In ∆ AB'N

c² = a² + b²

AB'² = AN² + B'N²

Given: AN = 24 and B'N = 18

AB'² = 24² + 18²

AB'² = 576 + 324

AB'² = 900

AB' = +-SQRT(900)

AB' = 30

In ∆ AB'C

with AB' = 30 and AC = 40

c² = a² + b²

B'C² = AB'² + AC²

B'C² = 30² + 40²

B'C² = 900 + 1600

B'C² = 2500

B'C = +-SQRT(2500)

B'C = 50

Now we have our answers.

Extra:

Please look at the picture again, but now concentrate on the indicated 50 and - 50...

I am trying to explain something about the meaning of the outcome of mathematical calculations like:

c² = 2500

c = +- SQRT(2500)

c = 50 or c = - 50

Depending on where you want to start from, you can "move" 50 inch in one direction or 50 inch in the opposite direction, hence the -50 inch. Please let me explain why I am making a fuss...

1). Let's consider ∆ AB'C. Going from B' to C, you "move" -50 inch form B' towards C. This 50 inch is what we calculated earlier, but the we neglected to explain why we discarded the minus value of the SQRT... We just stated it to be only the positive value! Normally we give no meaning to the negative variant of it... Well, is this true in this case?

2). Let's consider ∆ ABC'. Going from B to C', you "move" 50 inch form B towards C'. Please understand that the direction is opposite that of - 50 inch in 1).

It is important to understand that a negative sign means the 180° in the direction of the other way.

In general. When calculating a square side by using the SQRT, you carefully need to consider if you can discard the -

minus value of your calculated outcome.

Not always, but <em>usually</em> there is some sort of meaning to the negative part of the SQRT, you just need to be willing to understand what it possibly could mean.

I hope this has made some sense to you :-).

6 0
3 years ago
A cone-shaped table centerpiece has a diameter of 14 cm and a slant height that measures 31 cm. What is the surface area of the
neonofarm [45]

Answer:

i think it's C hope that helps

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
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