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Readme [11.4K]
3 years ago
12

a) John is 3 years older than his brother Brian, the product of their ages is 54 i) Express this information in equation form ii

) Show this information as a quadratic equation iii) Hence, solve the equation to find their individual ages.
Mathematics
1 answer:
bekas [8.4K]3 years ago
5 0

Answer:

John is 9, Brian is 6.

Step-by-step explanation:

I)

Let J represent John's age and B represent Brian's age.

John is three years older than Brian. In other words:

J=B+3

The product of their ages is 54. Or:

JB=54

II)

Write this as a quadratic by substituting:

JB=54\\(B+3)B=54\\B^2+3B-54=0

III)

Solve the quadratic:

B^2+3B-54=0\\B^2-6B+9B-54=0\\B(B-6)+9(B-6)=0\\(B+9)(B-6)=0\\B=-9, 6

Since age cannot be negative, Brian must be 6 years old right now.

John is three year older, so John is 9.

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Suppose M is the midpoint of line FG.
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3 years ago
Calculate, to four decimal places, the first ten terms of the sequence. an = 1 +(−4/9)^n
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The first ten terms of the sequence a_n=1 + (-\frac{4}{9} )^n is<em> 0.5556, 1.1975, 0.9122, 1.039, 0.9827, 1.0077, 0.9966, 1.0015, 0.9993 and 1.0003</em>

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more variables and numbers.

Given that:

a_n=1 + (-\frac{4}{9} )^n\\\\When\ n=1:a_1=1 + (-\frac{4}{9} )^1=0.5556\\\\When\ n=2:a_2=1 + (-\frac{4}{9} )^2=1.1975\\\\When\ n=3:a_3=1 + (-\frac{4}{9} )^3=0.9122\\\\When\ n=4:a_4=1 + (-\frac{4}{9} )^4=1.039\\\\When\ n=5:a_5=1 + (-\frac{4}{9} )^5=0.9827\\\\When\ n=6:a_6=1 + (-\frac{4}{9} )^6=1.0077\\\\When\ n=7:a_7=1 + (-\frac{4}{9} )^7=0.9966\\\\When\ n=8:a_8=1 + (-\frac{4}{9} )^8=1.0015\\\\When\ n=9:a_9=1 + (-\frac{4}{9} )^9=0.9993\\\\

When\ n=10:a_{10}=1 + (-\frac{4}{9} )^{10}=1.0003\\

The first ten terms of the sequence a_n=1 + (-\frac{4}{9} )^n is<em> 0.5556, 1.1975, 0.9122, 1.039, 0.9827, 1.0077, 0.9966, 1.0015, 0.9993 and 1.0003</em>

Find out more on equation at: brainly.com/question/2972832

#SPJ1

3 0
2 years ago
Please help me out! I keep getting the wrong answer
Tamiku [17]

The total amount of people who ordered a large is 5 + 12 + 8 = 25 people.

The amount of customers who bought a large cold drink is 5.

The probability that someone bought a large cold drink is 5 out of 25 people.

This is 5/25 which is 1/5 which is .2

Convert the decimal to a fraction by multiplying by 100 and adding a percent sign at the end.

.2 x 100 = 20%

Edit:

The probability was supposed to be if the customer ordered a cold drink based on people who ordered large.

The amount of people who ordered a large drink is 22 + 5 = 27.

The amount of people who ordered a cold large is 5.

To find the percent, divide the people who ordered cold large by the total people who ordered large.

This would be 5/27 which in decimal form is .185185

To convert to a percent, multiply by 100 and add a percent sign after it.

.185185 x 100 = 18.5185%

The question says to round to the nearest percent so your answer is:

19%

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