MATHEMATICS MIDDLE SCHOOL

David is the president of the his student council. When the leadership team met for the first time,he asked each person to shake everyone else's hand if there were six people at this meeting how many handshakes were made

Answers

Answer 1
Answer:

Answer:

There will be 15 handshakes.

Step-by-step explanation:

David is the president of the his student council. He asked each person to shake everyone else's hand.

Total number of people in the meeting = 6

Let us assume that no two people shake hands if they've already shaken them once.

The first person will shake hands with 5 persons.

The second will hand shake with 4 persons.

The third will shake hands with 3 persons and so on.

So, total handshakes will be = 5+4+3+2+1 = 15

Therefore, there will be 15 handshakes.
Answer 2
Answer: I believe it would be 30 total handshakes because there's 6 people and they all must shake hands with 5 other people (they can't give themselves a handshake) and 5 multiplied by 6 is 30

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Answer:

-3 5/6

Step-by-step explanation:

Please help! Its for my big test tomorrow!

Answers

Answer:

# The solution x = -5

# The solution is x = 1

# The solution is x = 6.4

# The solution is x = 4

# The solution is 1.7427

# The solution is 0.190757

Step-by-step explanation:

* Lets revise some rules of the exponents and the logarithmic equation

# Exponent rules:

1- b^m  ×  b^n  =  b^(m + n) ⇒ in multiplication if they have same base

  we add  the power

2- b^m  ÷  b^n =  b^(m – n) ⇒  in division if they have same base we

   subtract  the power

3- (b^m)^n = b^(mn) ⇒ if we have power over power we multiply

   them

4- a^m × b^m = (ab)^m ⇒ if we multiply different bases with same  

   power then we multiply them ad put over the answer the power

5- b^(-m) = 1/(b^m)  (for all nonzero real numbers b) ⇒ If we have

   negative power we reciprocal the base to get positive power

6- If  a^m  =  a^n  ,  then  m  =  n ⇒ equal bases get equal powers

7- If  a^m  =  b^m  ,  then  a  =  b    or    m  =  0

# Logarithmic rules:

1- log_(a)b=n-----a^(n)=b

2- loga_(1)=0---log_(a)a=1---ln(e)=1

3- log_(a)q+log_(a)p=log_(a)qp

4- log_(a)q-log_(a)p=log_(a)(q)/(p)

5- log_(a)q^(n)=nlog_(a)q

* Now lets solve the problems

# 3^(x+1)=9^(x+3)

- Change the base 9 to 3²

∴ 9^(x+3)=3^(2(x+3))=3^(2x+6)

∴ 3^(x+1)=3^(2x+6)

- Same bases have equal powers

∴ x + 1 = 2x + 6 ⇒ subtract x and 6 from both sides

∴ 1 - 6 = 2x - x

∴ -5 = x

* The solution x = -5

# ㏒(9x - 2) = ㏒(4x + 3)

- If ㏒(a) = ㏒(b), then a = b

∴ 9x - 2 = 4x + 3 ⇒ subtract 4x from both sides and add 2 to both sides

∴ 5x = 5 ⇒ divide both sides by 5

∴ x = 1

* The solution is x = 1

# log_(6)(5x+4)=2

- Use the 1st rule in the logarithmic equation

∴ 6² = 5x + 4

∴ 36 = 5x + 4 ⇒ subtract 4 from both sides

∴ 32 = 5x ⇒ divide both sides by 5

∴ 6.4 = x

* The solution is x = 6.4

# log_(2)x+log_(2)(x-3)=2

- Use the rule 3 in the logarithmic equation

∴ log_(2)x(x-3)=2

- Use the 1st rule in the logarithmic equation

∴ 2² = x(x - 3) ⇒ simplify

∴ 4 = x² - 3x ⇒ subtract 4 from both sides

∴ x² - 3x - 4 = 0 ⇒ factorize it into two brackets

∴ (x - 4)(x + 1) = 0 ⇒ equate each bract by 0

∴ x - 4 = 0 ⇒ add 4 to both sides

∴ x = 4

OR

∵ x + 1 = 0 ⇒ subtract 1 from both sides

∴ x = -1

- We will reject this answer because when we substitute the value

 of x in the given equation we will find log_(2)(-1) and this

 value is undefined, there is no logarithm for negative number

* The solution is x = 4

# log_(4)11.2=x

- You can use the calculator directly to find x

∴ x = 1.7427

* The solution is 1.7427

# 2e^(8x)=9.2 ⇒ divide the both sides by 2

∴ e^(8x)=4.6

- Insert ln for both sides

∴ lne^(8x)=ln(4.6)

- Use the rule ln(e^(n))=nln(e) ⇒ ln(e) = 1

∴ 8x = ln(4.6) ⇒ divide both sides by 8

∴ x = ln(4.6)/8 = 0.190757

* The solution is 0.190757

QUESTION 1

{3}^(x + 1) = {9}^(x + 3)

This is the same as:

{3}^(x + 1) = {3}^(2(x + 3))

Equate the exponents.

x+1=2(x+3)

Expand:

x+1=2x+6

Group similar terms;

2x-x=1-6

x=-5

QUESTION 2

log(9x - 2) = log(4x + 3)

Equate the arguments.

9x-2=4x+3

Group similar terms;

9x-4x=3+2

5x=5

Divide through by 5

x=1

QUESTION 3

log_(6)(5x + 4) = 2

Take antilogarithm to obtain,

5x + 4 = {6}^(2)

This implies that,

5x+4=36

5x=36-4

5x=32

x=32/5

or

x = 6 (2)/(5)

QUESTION 4

log_(2)(x) + log_(2)(x - 3) = 2

Use the product rule of logarithms:

log_(2)x(x - 3) = 2

Take antilogarithm,

{x}^(2) - 3x = {2}^(2)

{x}^(2) - 3x - 4 = 0

Factor:

(x + 1)(x - 4) = 0

This implies that,

x = - 1 \: or \: x = 4

But the domain is x>0, therefore the solution is

x=4

QUESTION 5

x=\log_(4)(11.2)

x=\log_(4)((56)/(5))

x=\log_(4)(56)-\log_(4)(5)

x=1.7 to the nearest tenth.

QUESTION 6

2e^(8x)=9.2

Divide both sides by 2.

e^(8x)=4.6

Take natural log of both sides

{8x}=\ln(4.6)

{x}=\ln(4.6)/ 8

x=0.2 to the nearest tenth.

What is the solution to the system?-2x + y + 6z = 1
3x + 2y + 5z = 16
7x + 3y – 4z = 11

Answers

Answer:

x = 4, y = -2, z = 3

Step-by-step explanation:

\left\{\begin{array}{ccc}-2x+y+6z=1&(1)\n3x+2y+5z=16&(2)\n7x+3y-4z=11&(3)\end{array}\right\n\n(1)\n-2x+y+6z=1\qquad\text{add}\ 2x\ \text{to both sides}\ny+6z=2x+1\qquad\text{subtract}\ 6z\ \text{from both sides}\ny=2x-6z+1\n\n\text{Substitute it to (2) and (3):}\n\n\left\{\begin{array}{ccc}3x+2(2x-6z+1)+5z=16\n7x+3(2x-6z+1)-4z=11\end{array}\right\qquad\text{use the distributive property}\n\n

\left\{\begin{array}{ccc}3x+4x-12z+2+5z=16&\text{subtract 2 from both sides}\n7x+6x-18z+3-4z=11&\text{subtract 3 from both sides}\end{array}\right\n\left\{\begin{array}{ccc}7x-7z=14&\text{divide both sides by 7}\n13x-22z=8\end{array}\right\n\left\{\begin{array}{ccc}x-z=2&\text{multiply both sides by (-13)}\n13x-22z=8\end{array}\right

\underline{+\left\{\begin{array}{ccc}-13x+13z=-26\n13x-22z=8\end{array}\right}\qquad\text{add both sides of the equations}\n.\qquad\qquad-9z=-18\qquad\text{divide both sides by (-2)}\n.\qquad\qquad \boxed{z=2}\n\n\text{Put it ot the equation}\ x-z=2:\nx-2=2\qquad\text{add 2 to both sides}\n\boxed{x=4}\n\n\text{Put the values of}\ x\ \text{and}\ z\ \text{to the equation}\ y=2x-6z+1:\n\ny=2(4)-6(2)+1\ny=8-12+1\n\boxed{y=-3}

How many square feet of outdoor carpet will we need for this hole?

Answers

Answer:

6 square feet of outdoor carpet will be needed for the given hole.

Step-by-step explanation:

We need to find how many square feet of outdoor carpet will be needed for the hole.

So, to find the required outdoor carpet we need to calculate the area of the hole.

Now, from the diagram, the hole is in the shape of a rectangle.

So, Area or rectangle = Length × width

Length = 3 feet and Width = 2 feet

⇒ Area = 3 × 2 = 6 feet²

Hence, 6 square feet of outdoor carpet will be needed for the given hole.

The area of the outdoor carpet given in the image is gotten as; 36 ft²

What is the required area of the shape?

We can see the shape of the outdoor carpet is a triangle. However, a rectangular shape is cut out of it. Thus;

Area of outdoor carpet = (Area of triangle) - Area of rectangle

Area of triangle = ½ × base × height

Area of triangle = ½ × 7 × 12

Area of triangle = 42 ft²

Area of rectangle = 3 * 2

Area of rectangle = 6 ft²

Thus;

Area of outdoor carpet = 42 - 6

Area of outdoor carpet = 36 ft²

Read more about Area of a triangle at; brainly.com/question/17335144

Nine less than four times a number equals fifteen

Answers

nine less means minus 9 
four times a number equals 4x
and equals fifteen is this = 15 
lets put all our knowledge together to make an equation:)
 4x - 9 = 15

merry christmas:)
9-4x3=15 it is 3 and 3️⃣

A ladybugs length measures 2 cm express this measurement in meters. explain your thinking. include an Equation with an exponent in your explanation

Answers

Answer:

Length of lady bug in meters is:

0.02

Step-by-step explanation:

A ladybugs length measures 2 cm.

We have to express this measurement in meters.

We know that 1 m=100 cm

1 cm= 1/100 m

      =0.01 m

2 cm=2×0.01 m

      =0.02 m

Hence, Length of lady bug in meters is:

0.02

The measurement 2\text{ centimetre} in meters is \boxed{\bf 0.02\text{\bf\ metre}}.

Further explanation:

The centimetre and metre are the units of measurement to calculate the length of an object.

“Centi” is first introduced in metric system that means one hundredth of a unit.

Therefore, 1 meter is 100\text{ cm} or we can say a centimetre is one-hundredth of a meter.

It can be mathematically expressed as follows:

\boxed{1\text{ m}\rightarrow 100\text{ cm}}

Procedure used:

Conversion from centimetre to metre.

1) First divide the unit (cm) by 100.

2) Now represent the resultant fraction into decimal form by moving the decimal two times to the left.

Given:

The length of ladybug is 2\text{ cm}.

Calculation:

Step 1:

The length of ladybug is 2\text{ cm}.

Use the above procedure to convert 2\text{ cm} into meters.

First divide the number 2 by 100.

\boxed{2\text{ cm}=(2)/(100)\text{ m}}  

Step 2:

Now follow the second step of the procedure.

The first digit on the right of decimal known as tenths or can say (1)/(100).

The second digit on the right of decimal known as hundredth or can say (1)/(100).

The resultant fraction (2)/(100) can be convert into decimal form as follows:

\boxed{(2)/(100)=0.02}

Here, we shifted the decimal two times to the left in the digit 2.

Therefore, the unit of 2\text{ cm} in meters is 0.02\text{ m}.    

Thus,  the measurement 2\text{ centimetre} in meters is \boxed{\bf 0.02\text{\bf\ metre}}.

Learn more:  

1. Learn more about the representation of the graph brainly.com/question/2491745

2. Learn more about the graph of the quadratic function brainly.com/question/2334270

3. Learn more about graphed below of the function brainly.com/question/9590016

Answer details:

Grade: Junior school

Subject: Mathematics

Chapter: Units and measurement

 

Keywords: Measurement, unit, decimal, fractions, ones tens, tenth, hundredth, position, numbers, centimetres, meters, numbering system, denominator, conversion, rational number, whole numbers, left side, ladybug, length.
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