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3 years ago

△R′S′T′ is the image of △RST under a dilation through point C. RS=5 and R′S′=8 . What scale factor was used in the dilation?

Mathematics

2 answers:

Rudiy273 years ago

7 0

Answer:

1.6

Step-by-step explanation:

To find the scale factor, we compare the image size to the pre-image size.

R'S' = 8 and RS = 5; this makes the scale factor 8/5, which is 1.6.

antoniya [11.8K]3 years ago

4 0

1.6 is the scale factor. 8÷5=1.6
1.6×5=8 hope that helps.

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At 3 a.M. The temperature is -5 degrees Fahrenheit between 3 a.M. And 6 a.M. The temperature dropped by 12 degrees Fahrenheit be

LuckyWell [14K]

What I would do is subtract 12 from -5. Then you would have -17. Then you would add 4 and it would be -13. So your answer is:

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4 years ago

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Find the volume of a pyramid with a square base, where the perimeter of the

lianna [129]

Answer:

$42.7\,\,cubic\,\, meters$

Step-by-step explanation:

Given: Perimeter of base of a pyramid = 12.8 m

Height of the pyramid = 12.5 m

To find: volume of a pyramid

Solution:

Perimeter of base of a pyramid = 12.8 m

As base of the pyramid is a square,

12.8 = $4(side\,\,of\,\,a\,\,square)$

side of a square = $\frac{12.8}{4}=3.2\,\,m$

Area of a square (A) = $(side\,\,of\,\,a\,\,square)^2=(3.2)^2=10.24\,\,m^2$

Height of the pyramid (h) = 12.5 m

Volume of the pyramid = $\frac{Ah}{3}=\frac{1}{3}(10.24)(12.5)=42.7\,\,cubic \,\,meters$

6 0

4 years ago

your drawer contains 6 black socks and 8 white socks. what is the probability that both socks are black

Nimfa-mama [501]

$\displaystyle |\Omega|=\binom{14}{2}=\dfrac{14!}{2!12!}=\dfrac{13\cdot14}{2}=91\\ |A|=\binom{6}{2}=\dfrac{6!}{2!4!}=\dfrac{5\cdot6}{2}=15\\\\ P(A)=\dfrac{15}{91}\approx16\%$

8 0

4 years ago

Ida needs to hire a singer for her wedding. Singer A is offering his services for an initial $95 in addition to $12.95 per hour.

Ludmilka [50]

Answer:

The answer is 3.6

Step-by-step explanation:

Step one:

Singer A is offering his services for an initial $95 in addition to $12.95 per hour

let the number of hours be x and the total charge be y

the expression for the total for singer A is

y=12.95x+95----------2

Singer B is offering her services for an initial $99 in addition to $11.85 per hour

let the number of hours be x and the total charge be y

the expression for the total for singer A is

y=11.85x+99----------2

Step two:

Equating 1 and 2 we have

12.95x+95=11.85x+99

collect liker terms

12.95x-11.85x=99-95

1.1x=4

divide both sides by 1.1

x= 4/1.1

x=3.63

to the nearest tenth it is 3.6

6 0

3 years ago

The square of the sum of two numbers is 144 and the sum of of their square is 180, find the number... Please I really need the a

mr Goodwill [35]

Answer:

The numbers are either ±13.35 and ±1.35 or ±1.35 and ±13.3

Step-by-step explanation:

Let the two numbers be 'x' and 'y'.

Given:

The squares of the sum of two numbers = 144

The sum of their squares = 180

The sum of the numbers = $x+y$

The square of the sum of numbers = $(x+y)^2$

Square of first number = $x^2$

Square of second number = $y^2$

The sum of their squares = $x^2+y^2$

Now, as per question:

$(x+y)^2=144---(1)\\\\x^2+y^2=180---(2)$

Expanding equation (1) using the formula $(a+b)^2=a^2+b^2+2ab$

This gives,

$(x+y)^2=144\\\\x^2+y^2+2xy=144\\\\\textrm{Plug in the value of }x^2+y^2\textrm{ from equation (2)}\\\\180+2xy=144\\\\2xy=144-180\\\\2xy=-36\\\\xy=-\frac{36}{2}\\\\xy=-18\\\\y=-\frac{18}{x}---(3)$

Plug in the value of 'y' from equation (3) in equation (1). This gives,

$x^2+(-\frac{18}{x})^2=180\\\\x^2+\frac{324}{x^2}=180\\\\x^4+324=180x^2\\\\x^4-180x^2+324=0\\\\\textrm{On solving, we get:}\\\\x^2=178.2\ or\ x^2=1.8\\\\\textrm{Square root both sides, we get:}\\\\x=\pm13.35\ or\ x=\pm1.35$

Therefore,

$y=-\frac{18}{x}=-\frac{18}{\pm13.35} = \pm1.35\ or\\\\y=-\frac{18}{x}=-\frac{18}{\pm1.35}=\pm13.3$

Therefore, the numbers are either ±13.35 and ±1.35 or ±1.35 and ±13.3

6 0

3 years ago