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3 years ago

Find the gradient of the line segment between the points N(-1,2) and M(-6,3)

Mathematics

1 answer:

siniylev [52]3 years ago

8 0

Answer:

1/5

Step-by-step explanation:

Gradient is another word for slope. To find the gradient, we have to use a formula.

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In the diagram below, we have $ST = 2TR$ and $PQ = SR = 20$. Find the length $UV$.

Maslowich

Answer:

Step-by-step explanation:

1. $ST=2TR$ and $SR=20,$ then by segment addition postulate

$ST+TR=SR\\ \\2TR+TR=SR\\ \\3TR=20\\ \\TR=\dfrac{20}{3}\\ \\ST=2\cdot \dfrac{20}{3}=\dfrac{40}{3}$

2. Consider triangles PQU and TSU. These triangles are similar by AA similarity theorem (triangles have congruent vertical angles PUQ and TUS and congruent alternate interior angles PQU and TSU). Similar triangles have proportional corresponding sides, so

$\dfrac{QU}{US}=\dfrac{PQ}{ST}=\dfrac{20}{\frac{40}{3}}=\dfrac{60}{40}=1.5$

$QU=1.5US$

3. Consider triangles QUV and QSR. These triangles are similar by AA similarity theorem. Similar triangles have proportional corresponding sides, so

$\dfrac{QU}{QS}=\dfrac{UV}{SR}\\ \\\dfrac{QU}{QU+US}=\dfrac{1.5US}{1.5US+US}=\dfrac{1.5}{2.5}=0.6$

$\dfrac{UV}{SR}=0.6\Rightarrow UV=0.6SR=0.6\cdot 20=12$

7 0

3 years ago

Read 2 more answers

what is the answer for this question does this table represent a function? why or why not? hours of training 10,20,30,40,50,60,

Afina-wow [57]

The domain values uniquely map to the dependent variable.
A function that fits these values is f(x)=20x+1020.

3 0

3 years ago

Read 2 more answers

Solve 2x - 11 greater than or equal to 5

ololo11 [35]

2x - 11 >_ 5
To solve for x, we need to get 2x by itself and then simplify.

Add 11 to both sides.

2x >_ 16

Divide both sides by 2 to get x.

x >_ 8 is your solution.

I hope this helps!

5 0

3 years ago

Triangle ABC has vertices at (-3, -1), (-1, 2) and (6, 1). What is the perimeter of triangle ABC, rounded to the nearest tenth?

Marta_Voda [28]

$Perimeter=19.9units$

Why?

We can find the perimeter of any triangle adding the length of its sides. Since we are given 3 points, we need to calculate the length of the three sides of the triangle, and then add them to know the perimeter of the triangle.

Let be the points:

A(-3,-1)

B(-1,2)

C(6,1)

<h3>- Distances</h3>

From A to B:

$d(A,B)=\sqrt{(-1-(-3))^{2}+(2-(-1)^{2}}\\\\d(A,B)=\sqrt{(2)^{2}+(3)^{2}}=\sqrt{4+9}=3.61units$