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3 years ago

Write the coordinates for the given dilation

Mathematics

1 answer:

Olegator [25]3 years ago

5 0

<u>Answer:</u>

D $_o$ of Y = (-3/2, -1)

<u>Step-by-step explanation:</u>

We are given three points on the graph:

X (4, 0)

Y (3, 2)

Z (2, 2)

and the scale factor of dilation which is $-\frac{1}{2}$ .

Given that, we are to find the coordinates of Y after dilation. To find that, we will multiply the coordinates of the point Y with the scale factor.

Y = $(-\frac{1}{2}$ × $3$ , (-\frac{1}{2}[/tex] × $2)$

Y = $(-\frac{3}{2} , -1)$

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A metalworker has a metal alloy that is 30% copper and another alloy that is 55% copper. How many kilograms of each alloy shou

Ilya [14]

<h3>Answer:</h3>

32 kg of 30% copper
48 kg of 55% copper

<h3>Step-by-step explanation:</h3>

Let x represent the mass of 55% copper alloy that is to be used in the mix. Then 80-x is the mass of 30% copper alloy to be used. The total amount of copper in the mix is then ...

... 0.55x + 0.30(80-x) = 0.45·80

... 0.25x = 12 . . . . . . simplify, subtract 24

... x = 48 . . . . . . . . . divide by the coefficient of x

... 80-x = 32 . . . . . . the mass of 30% copper alloy required

The metalworker should combine 32 kg of 30% copper alloy with 48 kg of 55% copper alloy to make 80 kg of 45% copper alloy.

4 0

3 years ago

The equation of circle having a diameter with endpoints (-3, 1) and (5, 7) is

nydimaria [60]

The equation of a circle:
$(x-h)^2+(y-k)^2=r^2$
(h,k) - the coordinates of the center
r - the radius

The center is the midpoint of the diameter.
$(-3,1) \\
x_1=-3 \\ y_1=1 \\ \\
(5,7) \\
x_2=5 \\ y_2=7 \\ \\
\hbox{the midpoint: } (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\
\frac{x_1+x_2}{2}=\frac{-3+5}{2}=\frac{2}{2}=1 \\
\frac{y_1_y_2}{2}=\frac{1+7}{2}=\frac{8}{2}=4 \\
\Downarrow \\
(1,4) \\ h=1 \\ k=4$

The radius is half the diameter, or the distance from one of the endpoints to the center.
$r=\sqrt{(x_1-h)^2+(y_1-k)^2}=\sqrt{(-3-1)^2+(1-4)^2}=\\
=\sqrt{(-4)^2+(-3)^2}=\sqrt{16+9}=\sqrt{25}=5 \\ \Downarrow \\
r^2=5^2=25$

The equation of the circle:
$\boxed{(x-1)^2+(y-4)^2=25}$

8 0

3 years ago

Read 2 more answers

In AGHI, the measure of ZI=90°, the measure of ZG=5°, and IG = 57 feet. Find the

kupik [55]

9514 1404 393

Answer:

57.2 ft

Step-by-step explanation:

The relevant trig relation is ...

Cos = Adjacent/Hypotenuse

cos(G) = IG/GH

GH = IG/cos(G) = (57 ft)/cos(5°)

GH ≈ 57.2 ft

4 0

3 years ago

Find f(x) of |2x-2| if x is -1.

Pavlova-9 [17]

Answer:

Step-by-step explanation:

x = -1

|2x-2| = |2(-1)-2| = |-2-2| = |-4| = 4

4 0

3 years ago

Read 2 more answers

How do you graph Y equals -1/3 X +6 and Y equals 3X +6

elena-s [515]

Step-by-step explanation:

step 1. so you want to graph 2 linear equations?

step 2. y = (-1/3)x + 6. put a dot on the y intercept (0, 6).

step 3. draw the line through (0, 6) with a slope of -1/3 (down 1 and to the right 3).

step 4. y = 3x + 6. put a dot on the y intercept (0, 6).

step 5. draw the line through (0, 6) with a slope of 3/1 (up 3 and to the right 1).

4 0

4 years ago