All categories

3 years ago

What is the scale factor of the dilation?

Mathematics

2 answers:

LenaWriter [7]3 years ago

5 0

Answer:

1/3

Step-by-step explanation:

To find the scale factor write a ratio from the side length of the small triangle to a corresponding side length of the large triangle.

C'B' has the distance 3 units and CB has the distance 9 units.

The ratio then is 3/9 = 1/3. So the scale factor is 1/3 because it is shrinking the larger triangle to the smaller as shown by the ' marks on the letters.

vovikov84 [41]3 years ago

3 0

Answer: C. $\dfrac{1}{3}$

Step-by-step explanation:

The coordinates of vertices of any figure(pre-image) (x,y) after dilation with scale factor 'k' will become : (kx,ky)→ Image.

such that $k=\dfrac{\text{coordinate of x in image}}{\text{coordinate of x in pre-image}}$

From the given figure, the coordinates of point C (in pre-image)=(-6,-6)

And the coordinates of image = (-2,-2)

$\\\\\Rightarrow\ k=\dfrac{-2}{-6}=\dfrac{1}{3}$

Hence, the scale factor of the dilation = $\dfrac{1}{3}$

You might be interested in

The vertex of y=x^2+12x+32

ollegr [7]

Answer:

The vertex is y=-4

Step-by-step explanation:

The vertex is the minimum point of the graph of the quadratic equation.

Let's first find the like of symmetry.

dy/dx=2x+12

2x+12=0

2x=-12

x=-6

Now plug -6 into the quadratic equation

y=(-6)²+12(-6)+32

y=-4

7 0

2 years ago

Suppose you have 60 red marbles and 40 blue marbles in a

andrew-mc [135]

Answer: The required probability is 0.26.

Step-by-step explanation: Given that there are 60 red marbles and 40 blue marbles in a box 10 marbles are picked without replacement.

We are to find the probability of selecting 6 red marbles.

Since the marbles are picked up without replacement, so it is a situation of combination.

Let S denote the sample space of the experiment of drawing 10 marbles and E denote the event that 6 marbles are red.

So,

$n(S)=^{100}C_{10}=\dfrac{100!}{10!(100-10)!}=\dfrac{100!}{10!90!}=17310309456440,\\\\\\n(E)=^{60}C_6\times^{40}C_4=\dfrac{60!}{6!54!}\times\dfrac{40!}{4!36!}=50063860\times91390.$

Therefore, the probability of event E is given by

$P(E)=\dfrac{n(E)}{n(S)}=\dfrac{50063860\times91390}{17310309456440}=0.26.$

Thus, the required probability is 0.26.

6 0

3 years ago

Line a is parallel to line b, m 6=85 and m 3=2x. Find m 1.

FromTheMoon [43]

The sum of the angles <6 and <3 must be 180. Since <3 and <1 are opposed to the top, their measure are equal. We need then to calculate the measure of angle >3 = 180 - <6 = 180-85=95

m(<1) = 95

8 0

3 years ago

A ____________________ is a measurement of the change in variables over a specific period of time.

Montano1993 [528]

Answer:

rate of change

Step-by-step explanation:

The rate of change (ROC) is the speed at which a variable changes over a specific period of time.

5 0

3 years ago

John has two jobs. For daytime work at a jewelry store he is paid

djyliett [7]

Given Information:

John's mean monthly commission = μ = $10,000

Standard deviation of monthly commission = σ = $2,000

Answer:

$P(9,000 < X < 11,000) = 0.383\\\\P(9,000 < X < 11,000) = 38.3 \%$

The probability that John's commission from the jewelry store is between $9,000 and $11,000 is 38.3%

Step-by-step explanation:

What is Normal Distribution?

We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.

We want to find out the probability that John's commission from the jewelry store is between $9,000 and $11,000?

$P(9,000 < X < 11,000) = P( \frac{x - \mu}{\sigma} < Z < \frac{x - \mu}{\sigma} )\\\\P(9,000 < X < 11,000) = P( \frac{9,000 - 10,000}{2,000} < Z < \frac{11,000 - 10,000}{2,000} )\\\\P(9,000 < X < 11,000) = P( \frac{-1,000}{2,000} < Z < \frac{1,000}{2,000} )\\\\P(9,000 < X < 11,000) = P( -0.5 < Z < 0.5 )\\\\P(9,000 < X < 11,000) = P( Z < 0.5 ) - P( Z < -0.5 ) \\\\$

The z-score corresponding to 0.50 is 0.6915

The z-score corresponding to -0.50 is 0.3085

$P(9,000 < X < 11,000) = 0.6915 - 0.3085 \\\\P(9,000 < X < 11,000) = 0.383\\\\P(9,000 < X < 11,000) = 38.3 \%$

Therefore, the probability that John's commission from the jewelry store is between $9,000 and $11,000 is 38.3%

How to use z-table?

Step 1:

In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 1.4, 2.2, 0.5 etc.)

Step 2:

Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 0.50 then go for 0.00 column)

Step 3:

Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.

4 0

3 years ago