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3 years ago

1. Triangle ABC with coordinate points A(-2,3); B(-1,0); C(5,-4) is rotated 90 degrees clockwise. What

Mathematics

1 answer:

Reil [10]3 years ago

6 0

Answer: A'(3,2), B'(0,1) and C'(-4, -5).

Step-by-step explanation:

When we rotate (a,b) 90 degrees clockwise, the new point will be (b,-a).

i.e. rotation rule for 90 degrees clockwise : (x,y) → (y,-x)

Given: Triangle ABC with coordinate points A(-2,3); B(-1,0); C(5,-4) is rotated 90 degrees clockwise.

Then, the new image points for triangle A'B'C' will be :

A(-2,3) → A'(3,-(-2)) =A'(3,2)

B(-1,0)→ B'(0,-(-1)) = B'(0,1)

C(5,-4) → C'(-4, -5)

Hence, the new image points for triangle A'B'C' are A'(3,2), B'(0,1) and C'(-4, -5).

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Panzettis owner purchased 6 tables for $186.How much would 9 additional tables cost?

Wittaler [7]

It would be 279 dollars
$186 divided by 6 equals 31
so 31 times 9 equals $279

4 0

3 years ago

Read 2 more answers

the alexander family and jenkins family each used their sprinklers last summer. the water output rate for the alexander familys

Mumz [18]

Answer:
Alexanders family sprinkler used for 35.25 hours
And the Jenkins family sprinkler was used for 29.75 hours.

Step-by-step explanation:

Lets start with 2 assumptions, what if we only used the Alexander's family sprinklers, We can define X as the variable
$20x=1450$
$x= 72.5$
If we just used the Alexanders it would of took 72 hours and 30 minutes.

Now lets look at the Jenkins family sprinkler, lets define it as Y.
$25y=1450$
$y = 58$
With only the Jenkins it would of took 58 hours.

Now, if they just of shared the work equally among the two sprinklers, the Alexanders family doing 725 L and the Jenkins with the other half.
It would of took the Alexanders
$20x= 725$
$x=36.25$

Jenkins
$25y=725$
$y=29$

Making it a combined time of 65.25 hours. 15 minutes long of our 65 hour time.

Now the Jenkins sprinkler generates 5 more L than Alexanders per hour. Which means it would only take the Jenkins family 1 hours to make 25 liters but Alexanders would take $\frac{5}{4}$ hours. We know that 1 hour contains 60 minutes, which means $\frac{1}{4}$ of a hour contains 15 minutes.

So it would take Alexanders family sprinkler 15 minutes more to produce the same amount per hour that the Jenkins does.

So from this we can conclude that if the Jenkins family sprinkler was used more we can cut the extra 15 minutes off, making the answer That the

Alexanders family sprinkler used for 35.25 hours
And the Jenkins family sprinkler was used for 29.75 hours.

7 0

2 years ago

Whose solution is correct and why? Nico is correct because he knew that Negative four-fifths = StartFraction negative 4 over neg

yan [13]

This question is incomplete

Complete Question

Nico and Lorena used different methods to determine the product of three fractions.

Nico’s Method =

(one-sixth) (Negative four-fifths)(2) = (StartFraction 2 over 1 EndFraction) (one-sixth) (negative four-fifths) = StartFraction (2) (1) (negative 4) over (1) (6) (5) EndFraction = Negative StartFraction 8 over 30 EndFraction

Lorena’s Method

= Negative StartFraction 4 over 15 EndFraction (2) (one-sixth) (Negative four-fifths) = (StartFraction 2 over 1 EndFraction) (one-sixth) (negative four-fifths) = StartFraction (2) (1) (negative 4) over (1) (6) (5) EndFraction = Negative StartFraction 8 over Negative 30 EndFraction = StartFraction 4 over 15 EndFraction

Whose solution is correct and why?

a) Nico is correct because he knew that Negative four-fifths = StartFraction negative 4 over negative 5 EndFraction.

b) Nico is correct because he knew that Negative four-fifths = StartFraction negative 4 over 5 EndFraction.

c) Lorena is correct because she knew that Negative four-fifths = StartFraction negative 4 over 5 EndFraction

d) Lorena is correct because she knew that Negative four-fifths = StartFraction negative 4 over negative 5 EndFraction

Answer:

b) Nico is correct because he knew that Negative four-fifths = StartFraction negative 4 over 5 EndFraction.

Step-by-step explanation:

In the above question

We start from Nico's method

Nico’s Method =

Step 1 : (one-sixth) (Negative four-fifths)(2)=

(1/6)(-4/5)(2)

Step 2 : (StartFraction 2 over 1 EndFraction) (one-sixth) (negative four-fifths) =

= (2/1)(1/6)(-4/5)

Step 3: StartFraction (2) (1) (negative 4) over (1) (6) (5) EndFraction

= (2)(1)(-4)/(1)(6)(5)

Step 4: Negative StartFraction 8 over 30 EndFraction

= (-8/30)

Step 5 : Negative StartFraction 4 over 15

EndFraction

= -4/15

Nico is correct

For Lorena’s Method

Step 1: Negative StartFraction 4 over 5 EndFraction (2) (one-sixth)

= -4/5(2)(1/6)

Step 2: (Negative four-fifths) = (StartFraction 2 over 1 EndFraction) (one-sixth) (negative four-fifths) =

(2/1)(1/6)(-4/-5)

Step 3: StartFraction (2) (1) (negative 4) over (1) (6) (negative 5) EndFraction

(2)(-1)(-4)/(1)(6)(-5)

Step 4: Negative StartFraction 8 over Negative 30 EndFraction =

-8/-30

Step 5: StartFraction 4 over 15

EndFraction

= 4/15

Lorena is wrong because

that Negative four-fifths ≠StartFraction negative 4 over negative 5 EndFraction

Mathematically

-4/5 ≠ -4/-5

Therefore,option b) Nico is correct because he knew that Negative four-fifths = StartFraction negative 4 over 5 EndFraction.

4 0

3 years ago

Read 2 more answers

I need the answer for a & b

Licemer1 [7]

Answer:

a. 2.14% should have IQ scores between 40 and 60

b. 15.87% should have IQ scores below 80

Step-by-step explanation:

* Lets explain how to solve the problem

- For the probability that a < X < b (X is between two numbers, a and b),

convert a and b into z-scores and use the table to find the area

between the two z-values.

- Lets revise how to find the z-score

- The rule the z-score is z = (x - μ)/σ , where

# x is the score

# μ is the mean

# σ is the standard deviation

* Lets solve the problem

- IQS are normally distributed with a mean of 100 and standard

deviation of 20

∴ μ = 100 and σ = 20

- The IQS is between 40 and 60

∴ 40 < X < 60

∵ z = (x - μ)/σ

∴ z = (40 - 100)/20 = -60/20 = -3

∴ z = (60 - 100)/20 = -40/20 = -2

- Use the z table to find the corresponding area

∵ P(z > -3) = 0.00135

∵ P(z < -2) = 0.02275

∴ P(-3 < z < -2) = 0.02275 - 0.00135 = 0.0214

∵ P(40 < X < 60) = P(-3 < z < -2)

∴ P(40 < X < 60) = 0.0214 = 2.14%

* 2.14% should have IQ scores between 40 and 60

- The IQS is below 80

∴ X < 80

∵ z = (x - μ)/σ

∴ z = (80 - 100)/20 = -20/20 = -1

- Use the z table to find the corresponding area

∵ P(z < -1) = 0.15866

∵ P(X < 80) = P(z < -1)

∴ P(X < 80) = 0.15866 = 15.87%

* 15.87% should have IQ scores below 80

6 0

4 years ago

2) Given: lines a and b are parallel Prove: m<1 = m<8

monitta

Explanation:

* Demonstrate that the related angles are the same.

* Demonstrate that different interior angles are equivalent.

* Demonstrate the adjacent interior angles are supplementary.

* Demonstrate the adjacent external angles are not mutually exclusive.

* Show that the lines in a plane are perpendicular to the same axis.

<1 and <8 are the same because they are alternate exterior angles that means that they are

Opposite sides of the transversal.

And that they are on the exterior side of the parallel lines.

Now because of that they have the same measures no matter what so would

<2 and <7

<3 and <6

<4 and <5

6 0

3 years ago