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victus00 [196]
2 years ago
14

A father’s age is the square of his son’s age (x). In 20 years’ time the father will be 3 times as old as his son. What are the

ages of the father and son?
I am supposed to solve this by writing and solving a quadratic equation but I don't know how. The ages are 64 and 8.
Mathematics
1 answer:
VMariaS [17]2 years ago
6 0

If the current son's age is x, the current age of the father is x^2.

In 20 years they will be, respectively, x+20 and x^2+20 years old, and we know that the father will be 3 times as old as his son:

x^2+20=3(x+20) \iff x^2+20=3x+60 \iff x^2-3x-40=0

The quadratic equation has solutions

x_{1,2}=\dfrac{3\pm\sqrt{9+160}}{2}=\dfrac{3\pm 13}{2}

So, the two solutions are

x_1 = \dfrac{16}{2}=8,\quad x_2 = \dfrac{-10}{2}=-5

We clearly can't accept negative values as solution for a problem involving the age of a person, so the only feasible solution is x=8, and we deduce that the father's age is 8 squared, i.e. 64.

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O DATA ANALYSIS AND STATISTICS Outcomes and event probability A number cube is rolled three times. An outcome is represented by
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ANSWER

EXPLANATION

For each of the three events, there are 8 possible outcomes, so the probability of each event is,

P(event)=\frac{favorable\text{ }outcomes}{possible\text{ }outcomes}=\frac{favorable\text{ }outcomes}{8}

• Event A:, there must be only odd numbers in the last two rolls, which are either ,EOO or OOO,. This event has 2 favorable outcomes, ,so its probability is 1/4,.

,

• Event B,: this is the complementary event to event A. Here the last two rolls must be even numbers - both or only one of the last two: ,OOE, EEO, EOE, OEE, EEE, OEO,. This event has 6 favorable outcomes, so ,its probability is 3/4,.

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• Event C,: this event is when the first and last rolls are even numbers in the same event. This is either ,EOE or EEE,. Since this event has 2 favorable outcomes, ,its probability is 1/4,.

5 0
1 year ago
A school survey of 90 sixth graders showed that 25% of them play basketball and about 17% play soccer. What are the chances that
bogdanovich [222]

Answer:

0.0425

Step-by-step explanation:

probability of  basket player = 0.25

probability of being a soccer player = 0.17

chances that a sixth grader plays basketball AND soccer = 0.25×0.17 = 0.0425

7 0
2 years ago
is vector v with an initial point of (-5,22) and a terminal point of (20,60) equal to vector u with an intintal point of (50,120
marta [7]

Answer:

Yes, vectors u and v are equal.

Step-by-step explanation:

We need to check whether vectors u and v are equal or not.

If the initial point is (x_1,y_1) and terminal point is (x_2,y_2), then the vector is

Vector=(x_2-x_1)i+(y_2-y_1)j

Vector v with an initial point of (-5,22) and a terminal point of (20,60).

\overrightarrow v=(20-(-5))i+(60-22)j

\overrightarrow v=25i+38j       ..... (1)

Vector u with an initial point of (50,120) and a terminal point of (75,158).

\overrightarrow u=(75-50)i+(158-120)j

\overrightarrow u=25i+38j         .... (2)

From (1) and (2) we get

\overrightarrow u=\overrightarrow v

Therefore, vectors u and v are equal.

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Tax she will pay would be $2.04
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5. What would the graph of y= 3/4x -7/8 look like?
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