All categories

1 year ago

The table below gives the cost of toys at a toy store. Does this represent a proportional relationship?

Mathematics

1 answer:

Goshia [24]1 year ago

8 0

begin math size 18px style text No, because end text 7 over 12 text is not equivalent to end text 1 half text. end text end style

You might be interested in

A man travels 20 km by car from Town P to Town Q at an average speed of x km/h. He finds that the time of the journey would be s

yuradex [85]

Answer:

x = 20.

Step-by-step explanation:

First, you should remember the relation:

Distance = Speed*Time.

First, we know that a man travels a distance of 20km at a speed of x km/h, in a time T.

We can write this as:

20km = (x km/h)*T

We know that the time is shortened by 12 minutes if the speed is increased by 5km/h

Rewriting these 12 minutes in hours (remember that 60min = 1 hour)

12 min = (12/60) hours = 0.2 hours

Then from this, he can travel the same distance of 20km in a time T minus 0.2 hours if the speed is increased by 5 km/h

We can write this as:

20km = (x + 5 km/h)*(T - 0.2 h)

Then we have a system of two equations, and we want to find the value of x:

20km = (x km/h)*T

20km = (x + 5 km/h)*(T - 0.2 h)

First, we should isolate the variable T in one of the equations, if we isolate it in the first one, we will get:

20km/(x km/h) = T

Replacing that in the other equation we get:

20km = (x + 5 km/h)*(T - 0.2 h)

20km = (x + 5 km/h)*( 20km/(x km/h) - 0.2 h)

Now we can solve this for x.

Removing the units (that we know that are correct) so the math is easier to read, we get:

20 = (x + 5)*(20/x - 0.2)

We only want to solve this for x.

20 = x*20/x - x*0.2 + 5*20/x - 5*0.2

20 = 20 - 0.2*x + 100/x - 1

subtracting 20 in both sides we get:

20 - 20 = 20 - 0.2*x + 100/x - 1 - 20

0 = -0.2*x + 100/x - 1

If we multiply both sides by x we get:

0 = -0.2*x^2 + 100 - x

-0.2*x^2 - x + 100 = 0

This is just a quadratic equation, we can solve it using the Bhaskara's equation, the solutions are:

$x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4*(-0.2)*100} }{2*-0.2} = \frac{1 \pm 9 }{-0.4}$

Then the two solutions are:

x = (1 + 9)/-0.4 = -25

x = (1 - 9)/-0.4 = 20

As x is used to represent a speed, the negative solution does not make sense, so we should use the positive one.

x = 20

then the average speed initially is 20 km/h

3 0

2 years ago

Which expression is equivalent to -8? A=-2^-3 B=(-1/2)^-3 C=(1/2)^-3 D=2^-3

sladkih [1.3K]

Answer:

The answer is option B.

Step-by-step explanation:

$( - \frac{1}{2} ) ^{ - 3} = ( - 2) ^{3} = - 8$

Hope this helps you

4 0

2 years ago

Read 2 more answers

John receives two credit card offers in the mail. Credit Card A: 1% introductory APR, 19.9% APR for purchases after the introduc

musickatia [10]

Answer:

(D) "...because he will not have to pay any interest on his purchases during the introductory APR period."

Step-by-step explanation:

There may be many reasons for John to choose one over the other depending on his future and planned usage patterns. However, answer the (D) is the only correct one in terms of stating a reason that is actually supported by the information in the question. Specifically, there is 0% APR for card B.

What's wrong with the other choices:

Choice A: incorrect statement re APR after intro period (is not 1%); B: incorrect statement re cash advance (is not 0%); C: statement is not supported by anything in the information given (it is an assumption, and is unlikely).

5 0

2 years ago

Read 2 more answers

Solve the equation using the quadratic formula. Enter each solution in simplest form.

sergeinik [125]

For this case we have the following quadratic equation:

$x ^ 2-4x + 23 = 0$

The solutions will be given by:

$x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}$

Where:

$a = 1\\b = -4\\c = 23$

Substituting the values we have:

$x = \frac {- (- 4) \pm \sqrt {(- 4) ^ 2-4 (1) (23)}} {2 (1)}\\x = \frac {4 \pm \sqrt {16-92}} {2}\\x = \frac {4 \pm \sqrt {-76}} {2}\\x = \frac {4 \pm \sqrt {76i ^ 2}} {2}\\x = \frac {4 \pmi \sqrt {76}} {2}\\x = \frac {4 \pmi \sqrt {2 ^ 2 * 19}} {2}\\x = \frac {4 \pm2i \sqrt {19}} {2}\\x = 2 \pm i\sqrt {19}$