MATHEMATICS HIGH SCHOOL

A decorative steel frame is shown below it is made of a circular section and and 6 stems the length of each stem is 45 cm work out the total length of Steel used in the frame

Answers

Answer 1
Answer:

A total of 552.86 cm of steel is used in the frame development.

What is Equation Modelling?

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have a decorative steel frame is shown below it is made of a circular section and and 6 stems the length of each stem is 45 cm.

Assume that the total length of the steel used is [x] cm. Then -

x = 2πr + 6r

x = 2 x 22/7 x 45 + 6 x 45

x = 282.86 + 270

x = 552.86 cm

Therefore, a total of 552.86 cm of steel is used in the frame development.

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Answer 2
Answer:

Answer:

552.78

Step-by-step explanation:

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Han has 130$ if she saved 25$ per week in how many weeks will she have 600$

Answers

In 19 weeks this would mean she would have 5 dollars over the amount needed but there can't be half of a week.
She would have 5 dollars over the amount

Six years ago Anita was P times as old as Ben was. If Anita is now 17 years old, how old is Ben now in terms of P ?

Answers

Ben is (P)/(11)+6 old now in terms of P .

What is linear equation?

A linear equation in two variables is of the form Ax + By + C = 0, in which A and B are the coefficients, C is a constant term, and x and y are the two variables, each with a degree of 1. For example, 7x + 9y + 4 = 0 is a linear equation in two variables. If we consider two such linear equations, they are called simultaneous linear equations.

According to the question

Six years ago Anita was P times as old as Ben was.

Let Ben's age now be B.

Anita's age now is A.

Writing linear equation in two variables

(A-6) = P(B-6)

But A is 17 and therefore

17 - 6 = P(B - 6)

11 = P(B - 6)

(11)/(P) = (B-6)

B = (P)/(11)+6

Hence,

Ben is (P)/(11)+6 old now in terms of P .

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Anita is  17 years old now
6 years ago she was    17- 6 years  =  11 years
 thus 6 years ago Ben is    P 11 years old
therefore Ben will be     P 11 + 6 years old now

The sum of two numbers is 100, their difference is 56, what are the two numbers?

Answers

\large\bf{\underline{\underline{\mathfrak{Question}:}}}

The sum of two numbers is 100, their difference is 56, what are the two numbers?

\large\bf{\underline{\underline{\mathfrak{Solution}:}}}

Let'sassume that,

:{\Longrightarrow{\small{\rm{The\:one\:number\:=a}}}}

:{\Longrightarrow{\small{\rm{The\:other\:number\:=b}}}}

Now,accordingto thequestion,

:{\Longrightarrow{\small{\rm{a+b=100\:\:....(i)}}}}

:{\Longrightarrow{\small{\rm{a-b=56\:\:....(ii)}}}}

Here, substitution method must be applied.

Now,use the first equation

:{\Longrightarrow{\small{\rm{a+b=100}}}}

:{\Longrightarrow{\small{\rm{a=100-b}\:\:....(iii)}}}

Putthevalueofequation(iii)inequation(ii)

:{\Longrightarrow{\small{\rm{a-b=56}}}}

:{\Longrightarrow{\small{\rm{100-b-b=56}}}}

:{\Longrightarrow{\small{\rm{100-2b=56}}}}

:{\Longrightarrow{\small{\rm{2b=56-100}}}}

:{\Longrightarrow{\small{\rm{2b=-44}}}}

:{\Longrightarrow{\small{\rm{b=(-44)/(-2)}}}}

:{\Longrightarrow{\small{\rm{b=\frac{\cancel{-44}}{\cancel{-2}}}}}}

:{\Longrightarrow{\small{\rm{b=(22)/(1)}}}}

{\therefore{\small{\rm{b=22}}}}

Now,putthisvalueinequation(iii)forgettingtheanswer.

:{\Longrightarrow{\small{\rm{a=100-22}}}}

{\therefore{\small{\rm{a=78}}}}

For verification:

Put the value of a and b in the equation (i)and(ii)

Wehave,

:{\Longrightarrow{\small{\rm{a=78}}}}

:{\Longrightarrow{\small{\rm{b=22}}}}

Incase1:

:{\Longrightarrow{\small{\rm{78+22=100}}}}

:{\Longrightarrow{\small{\rm{100=100}}}}

:{\Longrightarrow{\small{\rm{L.H.S=R.H.S}}}}

Incase2:

:{\Longrightarrow{\small{\rm{78-22=56}}}}

:{\Longrightarrow{\small{\rm{56=56}}}}

:{\Longrightarrow{\small{\rm{L.H.S=R.H.S}}}}

Hence,verified!

Answer: X = 78 and Y = 22.

Step-by-step explanation:

Let's call the two numbers X and Y. We are given two pieces of information:

1. The sum of the two numbers is 100, so we can write this as an equation: X + Y = 100.

2. The difference between the two numbers is 56, which can also be written as an equation: X - Y = 56.

Now, you have a system of two equations with two variables:

1. X + Y = 100

2. X - Y = 56

You can solve this system of equations by adding the two equations together to eliminate the Y variable:

(X + Y) + (X - Y) = 100 + 56

This simplifies to:

2X = 156

Now, divide both sides by 2 to solve for X:

2X / 2 = 156 / 2

X = 78

Now that you know the value of X, you can substitute it into one of the original equations to find the value of Y. Let's use the first equation:

X + Y = 100

78 + Y = 100

Subtract 78 from both sides:

Y = 100 - 78

Y = 22

So, the two numbers are X = 78 and Y = 22.

A 1/2 gallon of paint covers 1/6 of a wall. How much paint is needed to cover the entire wall? Could u show me how to do this question?

Answers

"A 1/2 gallon of paint covers 1/6 of a wall."
So a gallon of paint covers 2/6 of a wall.

2/6 = 1/3

a gallon ⇒ 1/3 of a wall
3 gallons ⇒ 3/3 of a wall (entire wall)

Sara travels twice as far as Eli when going to camp. Ashley travels as far as Sara and Eli together. Hazel travels 3 times as far as Sara. In total, all 4 travel a total of 888 miles to camp. How far do each of them travel?

Answers

Eli travels 74 miles

Sara travels 148 miles

Ashley travels 222 miles

Hazel travels 444 miles

Further explanation

Simultaneous Linear Equations could be solved by using several methods such as :

  • Elimination Method
  • Substitution Method
  • Graph Method

If we have two linear equations with 2 variables x and y , then we need to find the value of x and y that satisfying the two equations simultaneously.

Let us tackle the problem!

Let :

Sara's Distance = s

Eli's Distance = e

Ashely's Distance = a

Hazel's Distance = h

Sara travels twice as far as Eli when going to camp.

s = 2e

Ashley travels as far as Sara and Eli together.

a = s + e = 2e + e = 3e

Hazel travels 3 times as far as Sara.

h = 3s = 3(2e) = 6e

In total, all 4 travel a total of 888 miles to camp.

s + a + h + e = 888

2e + 3e + 6e + e = 888

(2 + 3 + 6 + 1)e = 888

12e = 888

e = 888 / 12

e = \boxed {74 ~ \texttt{miles}}

s = 2e = 2(74) = \boxed {148 ~ \texttt{miles}}

a = 3e = 3(74) = \boxed {222 ~ \texttt{miles}}

h = 6e = 6(74) = \boxed {444 ~ \texttt{miles}}

Learn more

Answer details

Grade: High School

Subject: Mathematics

Chapter: Simultaneous Linear Equations

Keywords: Simultaneous , Elimination , Substitution , Method , Linear , Equations
Eli travels the shortest distance, so she'll be the main letter for algebra. She can be 'e'.
Sara travels twice as far, so her distance is 2e.
Ashley travels Sara and Eli, so 2e + e, or 3e
Hazel travels 3 times Sara, so 2e * 3, or 6e. Together they all travel 888 miles.
So e + 2e + 3e + 6e = 888
Simply, 12e = 888
Therefore, e = 888/12, or 74
So Eli travels 1*74 (74) miles
Sara travels 2*74 (148) miles
Ashley travels 3*74 (222) miles
Hazel travels 6*74 (444) miles

I need this TONIGHT!!! Three years ago, Jolene bought $750 worth of stock in a software company. Since then the value of her purchase has been increasing at an average rate of 5 1/2% per year. How much is the stock worth now? (Round each money calculation you make to the nearest cent.) The stock is worth $ now.

Answers

Answer:

A\approx\$880.68

Step-by-step explanation:

So, we know that Jolene bought an initial $750.

We also know that the purchase is increasing at an average rate of 5 1/2 %or 5.5%. In other words, this is being compounded.

So, we can use the compound interest formula, which is:

A=P(1+(r)/(n))^(nt)

Where A is the total amount, P is the principal value, r is the rate and n is the number of times compounded per year, and t is the amount of years.

So, substitute 750 for P. 5 1/2% is the same as 5.5% or 0.055 (you move the decimal two places to the left and remove the percent symbol) so substitute this for r. Since it's increasing yearly, n is 1. So, our formula is:

A=750(1+0.055)^t

Add:

A=750(1.055)^t

Since the stock was bought 3 years ago, the value now is t=3. So, substitute 3 for t and evaluate:

A=750(1.055)^3

Evaluate. Use a calculator:

A\approx\$880.68

And we're done!

Formula: A = P(1 + r/n)^t

We have these variables:

P = 750

r/n = 0.055

t = 3

Substitute and simplify:

A = 750(1 + 0.055)^3

A = 750(1.055)^3

A = 880.68

Best of Luck!
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