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Masteriza [31]
3 years ago
11

Why is the image of a figure after a translation is congruent to its preimage

Mathematics
1 answer:
zaharov [31]3 years ago
6 0

"Translation" means "move it to a different place".

When you buy a hula-hoop or a frisbee and take it home from the store,
its shape doesn't change.  And when you leave home in the morning and
move yourself to school, your shape and size don't change.

Translation does not change the shape or the size of a figure.  All of its
sides and angles are still the same as they were in the original location.
Wherever it may go, it's still congruent to the picture of it that you took
before it moved.

You might be interested in
Given that the measure of ∠x is 120°, and the measure of ∠y is 60°, find the measure of ∠z.
Alexxx [7]

Answer:

60 degrees

Step-by-step explanation:

angle y is vertically opposite to angle a, (we can call it.)

angle x is supplementary to the other angle inside the triangle, which we can call angle b.

so, angle a is 60 degrees, as vertically opposite angles are equal

angle b is 60 degrees as supplementary angles = 180

based of the sum of angles in a triangle is 180 theorem;

60+60+unknown= 180

so unknown is 60 degrees

8 0
3 years ago
Use a triple integral to find the volume of the given solid. the solid enclosed by the cylinder x2 + y2 = 9 and the planes y + z
Alexxx [7]
Using cylindrical coordinates, we have

\begin{cases}x=r\cos\theta\\y=r\sin\theta\\z=\zeta\end{cases}

so that the Jacobian gives

\mathrm dV=\mathrm dx\,\mathrm dy\,\mathrm dz=r\,\mathrm dr\,\mathrm d\theta\,\mathrm d\zeta

The volume is given by the triple integral

\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=3}\int_{\zeta=2}^{\zeta=14-r\sin\theta}r\,\mathrm d\zeta\,\mathrm dr\,\mathrm d\theta
=\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=3}r(14-r\sin\theta-2)\,\mathrm dr\,\mathrm d\theta
=\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=3}(12r-r^2\sin\theta)\,\mathrm dr\,\mathrm d\theta
=\displaystyle\int_{\theta=0}^{\theta=2\pi}(54-9\sin\theta)\,\mathrm d\theta
=108\pi
6 0
3 years ago
The area of a square is 72.25 inches squared. Find the length of the side and the perimeter.
Darina [25.2K]

Area of the square = 72.25

side^2 = 72.25

side = \sqrt{72.25}

Side = 8.5 in

Perimeter = 4 × side

Perimeter = 4 × 8.5 in

Perimeter = 34 in

4 0
3 years ago
Click on the length of the pencil
diamong [38]

Answer:

2 and 3/4

Step-by-step explanation:

The tiny lines between each inch is worth 1/4.

The answers would be 2.75 or 2 and 3/4 :)

6 0
2 years ago
Legalization of marijuana, Part I. The 2010 General Social Survey asked 1,578 US res- idents: \Do you think the use of marijuana
mixer [17]

Answer:

Step-by-step explanation:

a) Sample statistics are used to estimate population value. Since 48% is a sample proportion, therefore, it is a sample statistic.

b) For 95% confidence level, z* = 1.96.

\hat{p}\pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}= 0.61\pm 0.61\sqrt{\frac{0.61(1-0.61)}{1578}}=0.61\pm 0.024 \ or (0.586, 0.634).

We are 95% confident that the true proportion of US residents who think marijuana should be made legal lies between 58.6% and 63.4%.

c)

\\np=1578(0.61)=962.58

\\n(1-p)=1578(1-0.61)=615.42

Since both np and n(1-p), are at least 10, the normal model is a good approximation for these data.

d) As the lower limit of confidence interval is less than 0.5, less than 50% population is also a plausible value of true proportion. This means the statement "Majority of Americans think marijuana should be legalized" is not justified.

4 0
3 years ago
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