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3 years ago

Eexpres -25/60 as a rational number whose denominator is -12

1 answer:

5 0

Answer: 5/-12

Explanation

Divide both the denominator and the numerator by -5 to obtain the denominator of -12 and the numerator of 5.

5/-12

Hope this helps :)

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The green triangle is a dilation of the red triangle with a scale factor of s=1/3 and the center of dilation is at the point (4,

klasskru [66]

Given:

The scale factor is $s=\dfrac{1}{3}$ and the center of dilation is at the point (4,2).

Red is original figure and green is dilated figure.

To find:

The coordinates of point C' and point A.

Solution:

Rule of dilation: If a figure is dilated with a scale factor k and the center of dilation is at the point (a,b), then

$(x,y)\to (k(x-a)+a,k(y-b)+b)$

According to the given information, the scale factor is $\dfrac{1}{3}$ and the center of dilation is at (4,2).

$(x,y)\to (\dfrac{1}{3}(x-4)+4,\dfrac{1}{3}(y-2)+2)$ ...(i)

Let us assume the vertices of red triangle are A(m,n), B(10,14) and C(-2,11).

Using (i), we get

$C(-2,11)\to C'(\dfrac{1}{3}(-2-4)+4,\dfrac{1}{3}(11-2)+2)$

$C(-2,11)\to C'(\dfrac{1}{3}(-6)+4,\dfrac{1}{3}(9)+2)$

$C(-2,11)\to C'(-2+4,3+2)$

$C(-2,11)\to C'(2,5)$

Therefore, the coordinates of Point C' are C'(2,5).

We assumed that point A is A(m,n).

Using (i), we get

$A(m,n)\to A'(\dfrac{1}{3}(m-4)+4,\dfrac{1}{3}(n-2)+2)$

From the given figure it is clear that the image of point A is (8,4).

$A'(\dfrac{1}{3}(m-4)+4,\dfrac{1}{3}(n-2)+2)=A'(8,4)$

On comparing both sides, we get

$\dfrac{1}{3}(m-4)+4=8$

$\dfrac{1}{3}(m-4)=8-4$

$(m-4)=3(4)$

$m=12+4$

$m=16$

And,

$\dfrac{1}{3}(n-2)+2=4$

$\dfrac{1}{3}(n-2)=4-2$

$(n-2)=3(2)$

$n=6+2$

$n=8$

Therefore, the coordinates of point A are (16,8).

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3 years ago

The number of gallons of carbonated soft drink consumed per person annually is normally distributed with mean 47.5 and standard

8_murik_8 [283]

Answer:

$P(45$

And we can find this probability with the following difference:

$P(-0.714$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(-0.714$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the number of gallons of a population, and for this case we know the distribution for X is given by:

$X \sim N(47.5,3.5)$

Where $\mu=47.5$ and $\sigma=3.5$

We are interested on this probability

$P(45$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(45$

And we can find this probability with the following difference:

$P(-0.714$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(-0.714$

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3 years ago

Please help!! (Will give brainy!) (Geometry) (look at picture)

stiv31 [10]

Answer:

First ones 90 and the second one is 48

Step-by-step explanation:

please brainliest me

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3 years ago

Please help.<br> If you could put your work in the answer that would<br> Be greatly appreciated.

AleksandrR [38]

Answer:

38°

because it is equal.

GJ=21

JH=21

GJ=JH

∠GFJ =∠HFJ

∠GFJ =38°

∠HFJ=38°

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3 years ago

Whitch of the given systems is equivalent to the given system? In math

tensa zangetsu [6.8K]

Answer:

Two systems of equations are equivalent if they have the same solution(s).

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3 years ago

Eexpres -25/60 as a rational number whose denominator is -12​

Eexpres -25/60 as a rational number whose denominator is -12