MATHEMATICS HIGH SCHOOL

XY is dilated by a scale factor of 1.3 with the origin as the center of dilation to create the image X'Y'. If the slope and length of XY are m and l respectively, what is the slope of X'Y'?

Answers

Answer 1

Answer:

Answer: The slope of line X'Y'= m

Step-by-step explanation:

Given: XY is dilated by a scale factor of 1.3 with the origin as the center of dilation to create the image X'Y'.

The slope and length of XY are m and l respectively.

Dilation is a transformation that forms similar shape, but with a different size such that the corresponding sides of image and original shape are parallel to each other.

As the slope of parallel line are equal .

⇒ The slope of XY and X'Y' are equal.

Hence, the slope of X'Y' is m.

Answer 2

Answer: Hello,

Dilatations conserved parallelism

=> slope of X'Y'=m= slope of XY

Dilatations multiply length by the scale factor

==> |X'Y'|=1.3*|XY-=1.3*L

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The volume of a hemisphere is 144 pi. Find the radius and total surface area.

Answers

Formula of the Volume of a hemisphere:
V = $(2)/(3)$ $\pi$ r³
144 $\pi$ = $(2)/(3)$ $\pi$ r³
Multiply by 3 to cancel fraction in the right side
144 $\pi$ × 3 = 2 $\pi$ r³
432 $\pi$ = 2 $\pi$ r³
Divide by 2 $\pi$ on either sides to isolate r³
$(432 \pi )/(2 \pi )$ = $(2 \pi )/(2 \pi )$ r³
2 $\pi$ and $2 \pi$ cancel out
216 = r³
Take cube root to find the radius
$\sqrt[3]{216}$ = $\sqrt[3]{r^3}$
6 = r
Radius is 6 units

The formula of the surface area of a hemisphere is:
S.A = 2 $\pi$ r² + $\pi$ r²
= $2\pi$ (6)² + $\pi$ (6)²
=2 $\pi$ × 36 + 36 $\pi$
= 72 $\pi$ + 36 $\pi$
= 108 $\pi$ units² (in terms of $\pi$ )
≈ 339.12 units²

Surface area = 108 $\pi$ units

A juice pitcher holds 1.5 gallons of liquid. How many 8-ounce glasses of juice can be poured from a full pitcher? (1 gallon = 128 ounces) explain by describing the steps you uses to solve the problem.

Answers

$1gallon=128ounces\nTo\ receive\ volume\ of\ pitcher\ in\ onces\ we\ need\ to\ multiply\ its\nvolume\ in\ gallons\ by\ ounces\ in\ 1\ gallon.\n1,5g=1,5*128=192o\nNow\ to\ receive\ answer\ we\ need\ to\ divide\ volume\ of\ pitcher\ in\nounces\ by\ volume\ of\ glass.\n192:8=24\n\nWe\ need\ to\ 24\ glasses.$

)Line CP is a perpendicular bisector to line segment AB. If

Answers

Answer:

Step-by-step explanation:

Line CP is a perpendicular bisector to line segment AB

two congruent lines are formed when AB is intersected ( bisector forms two equal in measure and congruent parts)

and

a right angle is formed between the line CP and AB ( perpendicular lines form right angles.)

Calculate the average speed of a gazelle that runs 140 meters in 5.0 seconds.

Answers

Answer:

Average speed(S) is given by:

$S =(D)/(t)$ ....[1]

where,

D is the total distance and t is the time.

As per the statement:

A gazelle that runs 140 meters in 5.0 seconds.

⇒D = 140 meters and t = 5 seconds

Substitute in [1] we have;

$S =(140)/(5)$

Simplify:

⇒S = 28 m/sec

Therefore, average speed of a gazelle is, 28 m/sec

You would multiply to find the average meters/minute.
140 x 5.0 = 700.
But, if you're looking for average m/s you would divide.
140/5 = 28.
If you want meters/hour, you have to multiply the average meters/minute by 60.
140 x 5 x 60 = 4,200.

I'm not sure which one you're looking for but I hope something I wrote helps!

What is the area of this triangle?

Answers

area of triangle is 1/2 times base times height
lets say the base is from x1,y2 to x1,y1 the distance is 6 units

1/2 times 6 times height
from x1,y1 to x3,y3 is 7 units to the right
1/2 times 6 times 7=3 itmes 7=21

area=21 square units or
21 units^2

The area of this triangle with three vertices (x₁, y₁) , (x₂, y₂) and (x₃, y₃) is,

A = 1/2 [[(x₁ (y₂ - y₃) + x₂ (y₃ - y₁) + x₃ (y₁ - y₂))]

We have to give that,

The three vertices of the triangle are,

(x₁, y₁) , (x₂, y₂) and (x₃, y₃)

Since a triangle is a three-sided polygon, which has three vertices and three angles it has the sum of 180 degrees.

Hence,

The area of this triangle with three vertices (x₁, y₁) , (x₂, y₂) and (x₃, y₃) is,

A = 1/2 [[(x₁ (y₂ - y₃) + x₂ (y₃ - y₁) + x₃ (y₁ - y₂))]

So, the Formula is,

A = 1/2 [[(x₁ (y₂ - y₃) + x₂ (y₃ - y₁) + x₃ (y₁ - y₂))]

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ6

What is the sum of √-2 and √-18a. 4 √2
b. 4 √2i
c. 5 √2
d. 5 √2i

Answers

First, it is necessary to take out the i from the root. This is done by factoring out -1 as follows, using the relation √(-1) : = i

√-2 = √(-1)(2) = i√2
√-18 = √(-1)(2)(9) = 3i√2

Simplifying by adding the two terms together:
i√2 + 3i√2 = 4i√2

Therefore the answer is B.

Answer:

B. 4 √2i

Step-by-step explanation:

did the test

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