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nadezda [96]
3 years ago
7

How is the function shown below related to y=x? Graph the function by translating the parent function y=x+5

Mathematics
2 answers:
zalisa [80]3 years ago
8 0

Just took the quiz, the correct answer is,

B. Each output of y=x-5 is five less than the corresponding output for y=x.

AveGali [126]3 years ago
7 0

Consider x=0.

The output of the function y=x is y=0.

The output of the function y=x+5 is y=0+5, or y=5.

The value 5 is not 5 less than 0, not 1/5 of 0, and not 5 times 0. Rather, it is 5 more than 0, corresponding to selection ...

... C. Each output of y=x+5 is 5 more than the corresponding output of y=x.

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Jane took 15 min to drive her boat upstream to​ water-ski at her favorite spot. Coming back later in the​ day, at the same boat​
s344n2d4d5 [400]

Answer:

The speed of the boat in still water = 8 Km/hr

Step-by-step explanation:

Let the speed of the boat be x

According to question

(x-4)15 = (x+4)5

3x-12 = x+4

⇒x = 8 km/hr

7 0
3 years ago
-2x^2 + 4x + 16 in vertex form​
Reil [10]

Answer:

y = - 2(x - 1)² + 18

Step-by-step explanation:

- 2x² + 4x + 16 ← factor out - 2 from the first 2 terms

= - 2(x² - 2x) + 16

using the method of completing the square

add/subtract ( half the coefficient of the x- term)² to x² - 2x

= - 2(x² + 2(- 1)x + 1 - 1) + 16

= - 2(x - 1)² + 2 + 16

= - 2(x - 1)² + 18 ← in vertex form

6 0
2 years ago
Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false:
kondaur [170]
\text{Proof by induction:}
\text{Test that the statement holds or n = 1}

LHS = (3 - 2)^{2} = 1
RHS = \frac{6 - 4}{2} = \frac{2}{2} = 1 = LHS
\text{Thus, the statement holds for the base case.}

\text{Assume the statement holds for some arbitrary term, n= k}
1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2} = \frac{k(6k^{2} - 3k - 1)}{2}

\text{Prove it is true for n = k + 1}
RTP: 1^{2} + 4^{2} + 7^{2} + ... + [3(k + 1) - 2]^{2} = \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2} = \frac{(k + 1)[6k^{2} + 9k + 2]}{2}

LHS = \underbrace{1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2}}_{\frac{k(6k^{2} - 3k - 1)}{2}} + [3(k + 1) - 2]^{2}
= \frac{k(6k^{2} - 3k - 1)}{2} + [3(k + 1) - 2]^{2}
= \frac{k(6k^{2} - 3k - 1) + 2[3(k + 1) - 2]^{2}}{2}
= \frac{k(6k^{2} - 3k - 1) + 2(3k + 1)^{2}}{2}
= \frac{k(6k^{2} - 3k - 1) + 18k^{2} + 12k + 2}{2}
= \frac{k(6k^{2} - 3k - 1 + 18k + 12) + 2}{2}
= \frac{k(6k^{2} + 15k + 11) + 2}{}
= \frac{(k + 1)[6k^{2} + 9k + 2]}{2}
= \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2}
= RHS

Since it is true for n = 1, n = k, and n = k + 1, by the principles of mathematical induction, it is true for all positive values of n.
3 0
3 years ago
Terry is buying water. He needs 22 liters. A half-liter of water costs $2.11. A 200 -milliliter container of water costs $1.01.
Dvinal [7]

Answer: Terry should buy the half-liter of water that costs $2.11 because buying 200 litres here is cheaper.

Step-by-step explanation:

Terry is buying water and needs 22 liters. A half-liter of water costs $2.11. Using this information, 22 litres will cost:

= 22 ÷ 1/2 × 2.11

= 22 × 2 × 2.11

= $92.84

Also, A 200 -milliliter container of water costs $1.01. Using this information, 22 litres will cost:

= 22 × 1.01 ÷ 200/1000

= 22 × 1.01 × 1000/200

= 22 × 1.01 × 5

= $111.1

Based on this information, Terry should buy the half-liter of water that costs $2.11 because buying 200 litres here is cheaper.

3 0
3 years ago
Fill in the circle with the correct inequality statement. - 1.5O - 1.3 AIV
Ivanshal [37]

Answer:

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4 0
2 years ago
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