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Bill is 2 years older than his brother Will. If the product of their ages is one less than five times the sum of their ages, how

Advocard [28]

Answer:

Will's age = 9 years

Bill's age = 11years

Step-by-step explanation:

Let will age = x

Bill = x +2 since he is 2 years older

x(x+2) = 5( x +x+2) - 1

Opening brackets

x² + 2x = 5(2x + 2) - 1

x² + 2x = 10x + 10 - 1

x² + 2x = 10x + 9

Collect like terms

x² + 2x - 10x - 9 = 0

x² - 8x - 9 = 0

Solve quadratically using factorisation method by finding two factors of +9 that can add up to give -8, the coefficient of x.

The factors are -9 and +1

x² + x - 9x - 9 = 0

x(x + 1) -9( x +1)

x+1) (x -9) =0

x + 1 = 0 or x -9 =0

x = -1 or 9

Age can not be negative

Therefore,

Will's age = 9 years

Bill's age = x+2 = 9+2 = 11years

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6 0

2 years ago

In the figure shown to the right, two angle measurements are given. Determine the others.

creativ13 [48]

The figure is shown below

From the figure

Angle 150 degree and angle p forms angles on a straight

Since the sum of angles on a straight line equals 180 degrees

Hence

$150^{\circ}+p=180^{\circ}$

Solve for p in the equation

$\begin{gathered} p=180^{\circ}-150^{\circ} \\ p=30^{\circ} \end{gathered}$

Hence, p = 30

From the figure

Angle p and angle q are vertically opposite angles

Since vertically opposite angles are equal then

$p=q=30^{\circ}$

Hence, q = 30

Applying the rule of angles on a straight line

This implies

$q+w+60=180$

Substitute q = 30 into the equation

$30+w+60=180$

Solve for w

$\begin{gathered} w+90=180 \\ w=180-90 \\ w=90 \end{gathered}$

Hence, w = 90

8 0

1 year ago

Two fair dice, one blue and one red, are tossed, and the up face on each die is recorded. Define the following events:

ZanzabumX [31]

Answer:

Step-by-step explanation:

Given that two fair dice, one blue and one red, are tossed, and the up face on each die is recorded.

a) P(E) = P(the difference of the numbers is 3 or more}

Favourable events are (1,4) (1,5)(1,6) (2,5) (2,6) (3,6) (4,1) (5,1) (5,2) (6,1) (6,2)(6,3)

P(E) = $\frac{12}{36} =\frac{1}{3}$

b)P(F)

Favourable events for F = (1,1) (2,2)...(6,6)

P(F) = $\frac{6}{36} =\frac{1}{6}$

c) P(EF)

There is no common element between E and F

P(EF) =0

4 0

2 years ago

Read 2 more answers

A correlation of r = 0.85 is found between weekly sales of firewood and cough drops over a 1-year period. Which of the following

jolli1 [7]

Answer:

A) There is a pretty strong positive linear relationship between sales of firewood and cough drops.

Explanation:

Correlation coefficient: It is used to analyze the relationship between two variables, the greater it is the stronger the relationship will be.

Sales of firewood affects cough drops, they have a direct and strong positive relationship.

5 0

2 years ago

Calcuate the distance Tom rides his bike if he rides 5\6 mile of each 5 days

defon

The multi-stage fitness test (MSFT), also known as the beep test, bleep test, PACER (Progressive Aerobic Cardiovascular Endurance Run), Pime, they are cautioned. A second caution ends the test for that runner. The number of shuttles completed successfully is recorded as the score of that runner. The score is recorded in Level.Shuttles format (e.g. 9.5).

8 0

3 years ago

Read 2 more answers

Please help me!!!! Thank you!!!