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3 years ago

The parabola y=x^2 is scaled vertically by a factor of 1/10

Mathematics

1 answer:

Andre45 [30]3 years ago

4 0

Answer:

Step-by-step explanation:

We want to scale by a factor of 1/10 so |a| = 1/10. This means that the graph is compressed vertically.

We do not reflect across the x axis so a = 1/10.

The new parabola is: y = 1/10 x^2

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If y varies directly as the x^2 and y = 200 when x = 5, what is the value of y when x = -3?

gayaneshka [121]

As the variation is direct we have:
$y = kx ^ 2
$
We must find the value of k.
For this, we use the following data:
y = 200 when x = 5
Substituting values we have:
$200 = k5 ^ 2
$
Clearing k:
$k = 200/5 ^ 2

k = 200/25

k = 8$
Then, the function is:
$y = 8x ^ 2
$
We evaluate the function for x = -3
$y = 8 (-3) ^ 2

y = 8 (9)

y = 72$
Answer:
the value of y when x = -3 is:
c.
72

6 0

4 years ago

According to the National Education Association (NEA), teachers generally spend more than 40 hours each week working on instruct

abruzzese [7]

Answer:

The median number of hours worked per week for the sample of 13 high school science teachers is 52.

Step-by-step explanation:

Median of a data set:

The median of a data set is the element that separates the lower 50% of the set from the upper 50%.

If the cardinality n of the set is odd, the median is the element at the position (n+1)/2 of the sorted sed.

If the cardinality n of the set is even, the median is the mean between the elements at the position n/2 and (n/2)+1 of the sorted sed.

In this question:

Hours worked for the sample of 13 high school science teachers:

55, 58, 52, 52, 56, 59, 48, 63, 52, 52, 50, 52, 56

Sorting in an ascending way:

48, 50, 52, 52, 52, 52, 52, 55, 56, 56, 58, 59, 63

Cardinality of 13, so odd, the median is the element at the 13+1/2 = 7th position of the sorted set, which is 52.

The median number of hours worked per week for the sample of 13 high school science teachers is 52.

8 0

3 years ago

The weight of tigers follow a normal distribution with a mean of 220 kg and a SD of 30 kg. 1) If we randomly select a tiger, wha

mylen [45]

Answer:

0.89736

Step-by-step explanation:

We solve this question using z score formula

Z score = x - μ/σ

x = raw score

μ = population mean

σ = population standard deviation

Hence,

x = 258, μ = 220, σ = 30

Z = 258 - 220/30

=1.26667

Probability value from Z-Table:

P(x<258) = 0.89736

Therefore, the probability that his weights is less than 258 kg is 0.89736

6 0

3 years ago

25 Points ! Write a paragraph proof.<br> Given: ∠T and ∠V are right angles.<br> Prove: ∆TUW ∆VWU

vladimir2022 [97]

Answer:

Δ TUW ≅ ΔVWU ⇒ by AAS case

Step-by-step explanation:

* Lets revise the cases of congruent for triangles

- SSS ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ

- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and

including angle in the 2nd Δ

- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ

≅ 2 angles and the side whose joining them in the 2nd Δ

- AAS ⇒ 2 angles and one side in the first triangle ≅ 2 angles

and one side in the 2ndΔ

- HL ⇒ hypotenuse leg of the first right angle triangle ≅ hypotenuse

leg of the 2nd right angle Δ

* Lets solve the problem

- There are two triangles TUW and VWU

- ∠T and ∠V are right angles

- LINE TW is parallel to line VU

∵ TW // VU and UW is a transversal

∴ m∠VUW = m∠TWU ⇒ alternate angles (Z shape)

- Now we have in the two triangles two pairs of angle equal each

other and one common side, so we can use the case AAS

- In Δ TUW and ΔVWU

∵ m∠T = m∠V ⇒ given (right angles)

∵ m∠TWU = m∠VUW ⇒ proved

∵ UW = WU ⇒ (common side in the 2 Δ)

∴ Δ TUW ≅ ΔVWU ⇒ by AAS case

7 0

3 years ago

Read 2 more answers

Could someone check this again

ANTONII [103]

Answer:

yeah your right

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers