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2 years ago

What is the distance between point A (-2 , -1) and point B (3, 2)?

Mathematics

1 answer:

lana [24]2 years ago

4 0

Answer:

Distance = √34

Step-by-step explanation:

Using the formula for distance

d = √(x_2 - x_1)^2 + ( y_2 - y_1)^2

Using what we are provided with

Two points

( -2, -1)(3, 2)

x_1 = -2

y_1 = -1

x_2 = 3

y_2 = 2

Inserting the values

d = √ ( 3 -(-2)^2 + (2-(-1)^2

= √ (3+2)^2 + (2+1)^2

= √ 5^2 + 3^2

= √25 + 9

= √34

= 5.83

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Triangle ABC with vertices A(2, 4) , B(4, 0) , and C(6, 6) is dilated about the origin to be triangle A′B′C′ .

natka813 [3]

Answer:

Triangle ABC is dilated by a scale factor of 1.5

Step-by-step explanation:

The general rule for the dilation about the origin with a factor of k is

$(x,y)\rightarrow (kx,ky)$

You are given two triangles ABC and A'B'C'.

In triangle ABC:

A(2,4)
B(4,0)
C(6,6)

From the diagram, in triangle A'B'C':

A'(3,6)
B'(6,0)
C'(9,9)

As you can see

$A(2,4)\rightarrow A'\left(\dfrac{3}{2}\cdot 2,\ \dfrac{3}{2}\cdot 4\right)=A'(3,6)$
$B(4,0)\rightarrow B'\left(\dfrac{3}{2}\cdot 4,\ \dfrac{3}{2}\cdot 0\right)=B'(6,0)$
$C(6,6)\rightarrow C'\left(\dfrac{3}{2}\cdot 6,\ \dfrac{3}{2}\cdot 6\right)=C'(9,9)$

So, triangle ABC is dilated by a scale factor of $\dfrac{3}{2}=1.5$

8 0

3 years ago

Read 2 more answers

Let (8,−3) be a point on the terminal side of θ. Find the exact values of cosθ, cscθ, and tanθ.

denis23 [38]

Answer:

$\text{Cos}\theta=\frac{\text{Adjacent side}}{\text{Hypotenuse}}=\frac{x}{R}=\frac{8}{\sqrt{73}}$

$\text{Csc}\theta=-\frac{\sqrt{73}}{3}$

$\text{tan}\theta =\frac{\text{Opposite side}}{\text{Adjacent side}}=\frac{y}{x}=\frac{-3}{8}$

Step-by-step explanation:

From the picture attached,

(8, -3) is a point on the terminal side of angle θ.

Therefore, distance 'R' from the origin will be,

R = $\sqrt{x^{2}+y^{2}}$

R = $\sqrt{8^{2}+(-3)^2}$

= $\sqrt{64+9}$

= $\sqrt{73}$

Therefore, Cosθ = $\frac{\text{Adjacent side}}{\text{Hypotenuse}}=\frac{x}{R}=\frac{8}{\sqrt{73}}$

Sinθ = $\frac{\text{Opposite side}}{\text{Hypotenuse}}=\frac{y}{R}=\frac{-3}{\sqrt{73} }$

tanθ = $\frac{\text{Opposite side}}{\text{Adjacent side}}=\frac{y}{x}=\frac{-3}{8}$

Cscθ = $\frac{1}{\text{Sin}\theta}=\frac{R}{y}=-\frac{\sqrt{73}}{3}$

6 0

3 years ago

Michelle is building shelves for her room. She has a plank 137 inches long that she wants to cut into 7 shelves of equal length.

ipn [44]

I think that each shelf will be 19 inches. Because 137 divided by 7 is 19 with the remainder of 4. Half of 4 is 2. Take 2 inches off of each end and that is the 4. So each shelf is 19 inches.

4 0

2 years ago

Read 2 more answers

Please help, marking brainleist, show work

Stels [109]

Answer:

Perimeter: 16x + 16

Area: 40x + 15

Step-by-step explanation:

Remember, the perimeter is the sum of all the sides of a figure, it can be found by adding up all the sides. The area is the space within the figure, in the case of a quadrilateral can be found by multiplying the length by the width. Finally, in a rectangle, the opposite sides are congruent, parallel, and intersect in 90degree (right) angles.

Using this,

1. Find the perimeter

Since opposite sides are congruent, there will be two sides with a measure of ( 8x + 3 ), and two sides with the measure of 5. Hence the sum of all the sides would be

8x + 3 + 8x + 3 + 5 + 5

Add them together,

16x + 16.

The perimeter of the figure is 16x + 16

2. Find the area,

To find the area of a rectangle, multiply the length by the width.;

( 8x + 3 ) * 5

Distribute:

40x + 15

The area of the figure is 40x + 15

4 0

2 years ago

I will give brainly!!!!<br><br>±sqrt-38=± <br><br>simplify plz

vichka [17]

I think it’s 1,2,19,38

3 0

3 years ago