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3 years ago

Samantha buys a shirt that costs $28.50. She uses a

Mathematics

1 answer:

Gre4nikov [31]3 years ago

7 0

Samantha buys a shirt that costs $28.50. She uses a
30% coupon. What will Samantha pay for the shirt?
ANSWER IS 8.55

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Find the equation of the line that is perpendicular to y=5 through the point (-4,-6)

Nikolay [14]

Answer:

$x=-4$

Step-by-step explanation:

we know that

The given equation y=5 is a horizontal line (is parallel to the x-axis)

The slope of the given line is equal to zero

A perpendicular line to the given line is a vertical line (parallel to the y-axis)

The equation of a vertical line is equal to the x-coordinate of the point that passes through it

The point that passes through it is (-4,-6)

therefore

The equation of the perpendicular line is

$x=-4$

4 0

3 years ago

Which is the inverse of the function a(d)=5d-3? And use the definition of inverse functions to prove a(d) and a-1(d) are inverse

Drupady [299]

Answer:

$a'(d) = \frac{d}{5} + \frac{3}{5}$

$a(a'(d)) = a'(a(d)) = d$

Step-by-step explanation:

Given

$a(d) = 5d - 3$

Solving (a): Write as inverse function

$a(d) = 5d - 3$

Represent a(d) as y

$y = 5d - 3$

Swap positions of d and y

$d = 5y - 3$

Make y the subject

$5y = d + 3$

$y = \frac{d}{5} + \frac{3}{5}$

Replace y with a'(d)

$a'(d) = \frac{d}{5} + \frac{3}{5}$

Prove that a(d) and a'(d) are inverse functions

$a'(d) = \frac{d}{5} + \frac{3}{5}$ and $a(d) = 5d - 3$

To do this, we prove that:

$a(a'(d)) = a'(a(d)) = d$

Solving for $a(a'(d))$

$a(a'(d)) = a(\frac{d}{5} + \frac{3}{5})$

Substitute $\frac{d}{5} + \frac{3}{5}$ for d in $a(d) = 5d - 3$

$a(a'(d)) = 5(\frac{d}{5} + \frac{3}{5}) - 3$

$a(a'(d)) = \frac{5d}{5} + \frac{15}{5} - 3$

$a(a'(d)) = d + 3 - 3$

$a(a'(d)) = d$

Solving for: $a'(a(d))$

$a'(a(d)) = a'(5d - 3)$

Substitute 5d - 3 for d in $a'(d) = \frac{d}{5} + \frac{3}{5}$

$a'(a(d)) = \frac{5d - 3}{5} + \frac{3}{5}$

Add fractions

$a'(a(d)) = \frac{5d - 3+3}{5}$

$a'(a(d)) = \frac{5d}{5}$

$a'(a(d)) = d$

Hence:

$a(a'(d)) = a'(a(d)) = d$

7 0

3 years ago

Which set of numbers does -5 belong

tester [92]

Is there any more to this question? Because-5 doesn’t belong anywhere

3 0

3 years ago

Ross chose a card at random from a deck of 52 cards. Ross replaced the card and then chose a second card. What is the probabilit

DaniilM [7]

Answer:

$\frac{1}{208}$

Step-by-step explanation:

We have been given that Ross chose a card at random from a deck of 52 cards. Ross replaced the card and then chose a second card.

Let us find probability of getting a club.

$\text{ Probability of getting a club}=\frac{13}{52} =\frac{1}{4}$

Now let us find probability of getting the ace of spades.

$\text{ Probability of getting ace of spades}=\frac{1}{52}$

Now let us multiply these to find probability of getting a club and ace of spades.

$\text{ Probability of getting a club and then ace of spades}=\frac{1}{4}*\frac{1}{52}=\frac{1}{208}$

Therefore, probability of getting a club and then the ace of spades $\frac{1}{208}$ .

8 0

3 years ago

What statements are true about the ordered pair (7,19) and the system of equations?

Tju [1.3M]

Answer:C

Step-by-step explanation:

3 0

3 years ago