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yaroslaw [1]
3 years ago
5

How are dilation different from other types of transformations?

Mathematics
1 answer:
krok68 [10]3 years ago
4 0
While rotations, translations and reflexions do not alter the volume of the matter, dilation does increases the volume. 

So the answer would be, dilation increases the volume while other types of transformations do not.


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Find the 12th term of the following geometric sequence.<br> 10, 30, 90, 270,
DanielleElmas [232]

Answer:

<h3>The 12th term is 1771470</h3>

Step-by-step explanation:

Since the above sequence is a geometric sequence

An nth term of a geometric sequence is given by

A(n) = a(r)^{n - 1}

where a is the first term

r is the common ratio

n is the number of terms

From the question

a = 10

To find the common ratio divide the previous term by the next term

That's

r = 30/10 = 3 or 90/30 = 3 or 270/90 = 3

Since we are finding the 12th term

n = 12

So the 12th term is

A(12) = 10( {3})^{12 - 1}

A(12) = 10 ({3})^{11}

<h3>A(12) = 1771470</h3>

Hope this helps you

8 0
3 years ago
CD is perpendicular to AB and passes through point C5, 12).
Aleksandr-060686 [28]

Answer:

x intercept of CD = 17

Step-by-step explanation:

We are given a line AB with its end coordinates. and Another line segment CD which is perpendicular to AB. We have the coordinates of C , and we are asked to find the x intercept of line CD.

For that we need to find the equation of CD

we have coordinates of C , and hence if we have slope of CD we can find equation of CD

Slope of CD can be determine with the help of slope of AB as CD⊥ AB

So, the slope of CD mCD = -\frac{1}{mAB}

Hence we start from determining slope of AB

slope is given as

m= \frac{y_2-y_1}{x_2-x_1}

m= \frac{14-(-3)}{7-(-10)}=\frac{17}{17}=1

Hence mAB=1

There fore mCD=-1

(∵  Product of Slopes of two perpendicular lines is always -1)

Now we find the equation of CD with the help of slope -1 and coordinates of C(5,12)

m=\frac{y-y_1}{x-x_1}

-1=\frac{y-12}{x-5}

-x+5=y-12

y=-x+17

Hence we have our equation , now in order to find the x intercept we keep y = 0 in it and solve for x

0=-x+17

x=17

Hence the x intercept is 17

8 0
3 years ago
What is the product of -3 and 5<br><br>it's on engenuity so I need answer​
Katarina [22]

Answer.........

-15

.______.

8 0
3 years ago
Read 2 more answers
The value of a certain car decreases by 16% each year. What is the 1⁄2-life of the car?
svet-max [94.6K]

Answer:

The half life of the car is 3.98 years.

Step-by-step explanation:

The value of the car after t years is given by the following equation:

V(t) = V(0)(1-r)^{t}

In which V(0) is the initial value and r is the constant decay rate, as a decimal.

The value of a certain car decreases by 16% each year.

This means that r = 0.16

So

V(t) = V(0)(1-r)^{t}

V(t) = V(0)(1-0.16)^{t}

V(t) = V(0)(0.84)^{t}

What is the 1⁄2-life of the car?

This is t for which V(t) = 0.5V(0). So

V(t) = V(0)(0.84)^{t}

0.5V(0) = V(0)(0.84)^{t}

(0.84)^{t} = 0.5

\log{(0.84)^{t}} = \log{0.5}

t\log{0.84} = \log{0.5}

t = \frac{\log{0.5}}{\log{0.84}}

t = 3.98

The half life of the car is 3.98 years.

7 0
3 years ago
9sin(2x) sin (x) = 9cos(x)
nikdorinn [45]

Answer:

\sin(2x)  = 2 \sin(x)  \cos(x)  \\ 9( 2 \sin(x)  \cos(x) ) \sin(x)  = 9 \cos(x)  \\ 18 { \sin}^{2} (x)9 \cos(x)  - 9 \cos(x)  = 0 \\ 9 \cos(x) (2{ \sin}^{2} (x) - 1) = 0 \\ 9 \cos(x) = 0 \: or \: 2{ \sin}^{2} (x) - 1 = 0 \\  \sin(x)  =  \pm \frac{1}{ \sqrt{2} }  \\  \cos(x)  = 0 \\ x =  { \cos}^{ - 1} (0) \\ x =  \frac{ \pi}{2}  = 90 \degree \\ x = \frac{ \pi}{2} + 2\pi \: n \:  \forall \: n \:  \in \:  \Z  \\ = 90 \degree +  360\degree\: n \:  \forall \: n \:  \in \:  \Z \\  =  \pm\frac{ \pi}{4}  \pm2\pi \: n \:  \forall \: n \:  \in \:  \Z \\ x =  \pm45\degree  \pm 360\degree\: n \:  \forall \: n \:  \in \:  \Z

8 0
2 years ago
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