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2 years ago

This diagram shows a pre-image △ABC , and its image, △A′′B′′C′′ , after a series of transformations.

Mathematics

2 answers:

MrMuchimi2 years ago

5 0

Answer:

△ABC is first reflected across the line y=x, then reflected across the x-axis. Since the transformations are rigid, △ABC ≅ △A''B''C''.

Step-by-step explanation:

Comparing △ABC and △A'B'C', we see that the x- and y-coordinates have been switched. This describes a reflection across the line y=x.

Comparing △A'B'C' and △A''B''C'', we see that the y-coordinates have been negated. This describes a reflection across the x-axis.

Reflections are called rigid transformations. This is because they preserve congruence and shape. Since congruence is preserved, △ABC ≅ △A''B''C''.

Serhud [2]2 years ago

4 0

Hello there,

This diagram shows a pre-image △ABC , and its image, △A′′B′′C′′ , after a series of transformations.

Select from the drop-down menus to correctly complete the statements.

△ABC is reflected across the line y = x

to become △A′B′C′ . Then △A′B′C′ is reflected across the x-axis

△A′′B′′C′′ . Because the transformations are both rigid

, the pre-image and image are congruent.

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A force of 500.0 is represented graphically with its tail at the origin and the tip pointed in a direction 30.0° above the posit

trapecia [35]

Answer:

$F^{'}=(250\sqrt{3},250 })$

Step-by-step explanation:

We have F´ =500 and $\alpha$ =30º, so x and y components:

F´ = $(F_{x} , F_{y})$ this is

$F_{x} = F^{'} *Cos\alpha$

$F_{y} = F^{'} *Sin\alpha$

$F_{x} = F`*Cos\alpha =500*Cos30=500*\frac{\sqrt{3} }{2} =250\sqrt{3}$

$F_{y}=F*Sin\alpha =500*Sin30=500*\frac{1}{2}=250$ ;

Finally

F' = $(250\sqrt{3} , 250)$

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2 years ago

Describe the transformation f(x) = √x + 1 − 5 in words. The parent function f(x) = √x has been shifted 1 unit and 5 units.

KATRIN_1 [288]

Answer:

The translation is $1$ unit to the left and $5$ units down

Step-by-step explanation:

we have

$g(x)=\sqrt{x+1}-5$

$f(x)=\sqrt{x}$ -----> parent function

we know that

The transformation

f(x)-----> g(x) has the following rule

$(x,y)-------> (x-1,y-5)$

That means

The translation is $1$ unit to the left and $5$ units down

see the attached figure to better understand the problem

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2 years ago

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Estimate the indicated probability by using normal distribution as an approximation to the binomial distribution. Estimate P(6)

lianna [129]

Answer:

P(6) = 0.6217

Step-by-step explanation:

To find P(6), which is the probability of getting a 6 or less, we will need to first calculate two things: the mean of the sample (also known as the "expected value") and the standard deviation of the sample.

Mean = np

Here, "n" is the sample size and "p" is the probability of the outcome of interest, which could be getting a heads when a tossing a coin, for instanc

So, Mean = n × p = (18) ×(0.30) = 5.4

Next we we will find the standard deviation:

Standard Deviation = $\sqrt{npq}$

n = 18 and p = 0.3 "q" is simply the probability of the other possible outcome (maybe getting a tails when flipping a coin), so q = 1 - p

Standard Deviation = $\sqrt{npq} = \sqrt{(18)(0.3)(0.7)}$

= 1.944

Now calculate the Z score for 6 successes.

Z = ( of successes we're interested in - Mean) ÷ (Standard Deviation)

=(6-5.4) ÷ (1.944) = 0.309

we have our Z-score, we look on the normal distribution and find the area of the curve to the left of a Z value of 0.309. This is basically adding up all of the possibilities for getting less than or equal to 6 successes. So, we get 0.6217.

5 0

2 years ago

The health benefits Tom receives from his employer cover 43% of the total monthly premium of $345.00. How much does Tom have to

Elza [17]

Answer:

The Amount tom has to pay is $196.65 therefore, Option b is correct

Step-by-step explanation:

Tom recieves 43% of total monthly premium

That means out of 100% he is getting 43% he has to pay (100%-43%)= 57% of $345.00

The amount Tom has to pay each month is $57\%\cdot 345.00$ it will become $.57 \cdot 345.00=196.65$