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3 years ago

Given triangles ABC and DEF. What is the simplest transformation that could produce triangle DEF from triangle ABC?

Mathematics

2 answers:

WARRIOR [948]3 years ago

7 0

Answer:

Step-by-step explanation:

ABC is transformed into DEF.

We find from the pictures given that

when ABC is transformed in to DEF, there are three steps of transformations involved

I transformation is Triangle ABC is rotated by 90 degrees about Vertex A

Then we would get a right triangle with AC horizontal on top and AB vertically down with vertex A same as (-5,-4)

Next is simple transformation of shifting A to D i.e. vertex (-5,-4) to (2,2)

For this, first shifting of 7 units to the right is done to make A as (2,-4)

Now next is vertically up by 6 units so that A becomes (2,2)

Thus we have a series of 3 transformations

i) rotation about A 90 degrees

ii) Shifting to right by 7 units

iii) shifting up by 6 units

Wewaii [24]3 years ago

3 0

Answer:

Rotation

Step-by-step explanation:

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The square root of 1521 = 39, evequate 390 to the 2nd power

ki77a [65]

Answer:

390 to the second power is 152100

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3 years ago

Which is the value of the expression (StartFraction (10 Superscript 4 Baseline) (5 squared) Over (10 cubed) (5 cubed)) cubed?

Flura [38]

Answer:

The value to the given expression is 8

Therefore $\left[\frac{(10^4)(5^2)}{(10^3)(5^3)}\right]^3=8$

Step-by-step explanation:

Given expression is (StartFraction (10 Superscript 4 Baseline) (5 squared) Over (10 cubed) (5 cubed)) cubed

Given expression can be written as below

$\left[\frac{(10^4)(5^2)}{(10^3)(5^3)}\right]^3$

To find the value of the given expression:

$\left[\frac{(10^4)(5^2)}{(10^3)(5^3)}\right]^3=\frac{((10^4)(5^2))^3}{((10^3)(5^3))^3}$

( By using the property ( $(\frac{a}{b})^m=\frac{a^m}{b^m}$ )

$=\frac{(10^4)^3(5^2)^3}{(10^3)^3(5^3)^3}$

( By using the property $(ab)^m=a^mb^m$ )

$=\frac{(10^{12})(5^6)}{(10^9)(5^9)}$

( By using the property $(a^m)^n=a^{mn}$ )

$=(10^{12})(5^6)(10^{-9})(5^{-9})$

( By using the property $\frac{1}{a^m}=a^{-m}$ )

$=(10^{12-9})(5^{6-9})$ (By using the property $a^m.b^n=a^{m+n}$ )

$=(10^3)(5^{-3})$

$=\frac{10^3}{5^3}$ ( By using the property $a^{-m}=\frac{1}{a^m}$ )

$=\frac{1000}{125}$

$=8$

Therefore $\left[\frac{(10^4)(5^2)}{(10^3)(5^3)}\right]^3=8$

Therefore the value to the given expression is 8

3 0

2 years ago

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If r = 10 units and x = 14 units, then what is the volume of the cylinder shown above?

Agata [3.3K]

Answer:

4398.23 is the volume

5 0

3 years ago

Read 2 more answers

Select the correct answer from each drop-down menu.

serious [3.7K]

Answer:

Center: (4,8)

Radius: 2.5

Equation: $(x-4)^2+(y-8)^2=6.25$

Step-by-step explanation:

It was given that; the endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5).

Note that the longest chord is the diameter;

The midpoint of the ends of the diameter gives us the center;

Use the midpoint formula;

$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2} )$

The center is at; $(\frac{4+4)}{2} ,\frac{5.5+10.5}{2}=(4,8)$

To find the radius, use the distance formula to find the distance from the center to one of the endpoints.

The distance formula is;

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$r=\sqrt{(4-4)^2+(10.5-8)^2}$

$r=\sqrt{0^2+(2.5)^2}$

$r=\sqrt{0^2+(2.5)^2}=2.5$

The equation of the circle in standard form is given by;

$(x-h)^2+(y-k)^2=r^2$

We substitute the center and the radius into the formula to get;

$(x-4)^2+(y-8)^2=2.5^2$

$(x-4)^2+(y-8)^2=6.25$

6 0

3 years ago

For f (x) = 9 * 81^x evaluate f(-1/2)

LekaFEV [45]

Step-by-step explanation:

f(x) = 9 * 81^x

When x = -1/2,

f(-1/2) = 9 * 81^(-1/2) = 9 * (1/9) = 1.

8 0

2 years ago