Question 2 2.1. Rewrite 92 and 146 as products of their prime factors. 2.2. Write down the LCM and HCF of 92 and 146. 2.3. 2.4. 2.7. The price of petrol is increased from R12,58 per litre to R13,28 per litre. Determine the percentage increase in the price. [1 Divide 240g in the ratio 5 : 3: 4. Thoriso can either walk to school at 5 km/h or ride her bicycle at 15 km/h. If she rides her bicycle, it takes her 10 minutes to get to school. 2.4.1. How long will it take her if she walks to school? (2) 2.4.2. Is this direct or indirect proportion? Give a reason for your answer. (2) 2.5. Brian wants to exchange South-African rand for British pound. If R1 is worth 0,075199 pound, how many pounds will he get for R2 100 if he must pay an agent commission of 1,5%? 2.8. (2 (2 (3 (3) (2) A motor car drives at an average speed of 106 km/h for 2 hours 45 minutes. At which constant speed must the car drive to travel the same distance in 2 hours 35 minutes? (4 [20​

The solution is, For job- A will Des earn the most money per week.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

Job A pays £3.80 per hour for 40 hours per week,

Job B pays £4.50 per hour for 32 hours per week.

for, job A - he earns =  £3.80 * 40

                                 = £ 152 pe week

and, for job B - he earns = £4.50 * 32

                                        =£ 144 per week.

Hence, The solution is, For job- A will Des earn the most money per week.

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Answer:

Step-by-step explanation:

To determine if the triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Let's label the sides of the triangle as follows:

a = 4 inches

b = 5 inches

c = 7 inches

Using the Pythagorean theorem, we can calculate:

c^2 = a^2 + b^2

7^2 = 4^2 + 5^2

49 = 16 + 25

49 = 41

Since 49 does not equal 41, this means that the triangle is not a right triangle.

Therefore, the answer is no, the triangle is not a right triangle.

The possible combination of cereal and milk the shopper can buy and still stay in their budget is:

12 ≤ 2.99x + 4.99y ≤  25      (x , y ∈ N)

The relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.

"Information available from the question"

A store sells cereal for $2.99 and milk for $4.99.

A shopper wants to spend at least $12 but no more than $25 on groceries.

To find the possible combination of cereal and milk the shopper can buy and still stay in their budget.

Now, According to the question:

Let x represents the shopper buy and y represent the milk.

Then represents the inequality according to the information.

A store sells cereal for $2.99

It write 2.99x

And for the milk is 4.99y

So,

12 ≤ 2.99x + 4.99y ≤  25      (x , y ∈ N)

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The length of the hypotenuse of the isosceles right triangle is 2.8 inches.

An isosceles right triangle is a right triangle with two equal sides. In this case, the two equal sides are each 7 8 inches long.

To find the length of the hypotenuse, we can use the Pythagorean theorem:

a^2 + b^2 = c^2, where c is the length of the hypotenuse

In this case, a = b = 7/8 inches, so:

(7/8)^2 + (7/8)^2 = c^2

(49/64) + (49/64) = c^2

98/64 = c^2

c = sqrt(98/64) inches

To the nearest tenth, c = 2.8 inches, so the length of the hypotenuse of the isosceles right triangle is 2.8 inches.

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The matching is as follow:

x²³ / x³ -->  [tex]x^{20[/tex]

[tex]x^{14}/ x^{17}[/tex] --> 1/x³

[tex]x^{19}/ x^{33}[/tex] --> 1/[tex]x^{14[/tex]

[tex]x^{16}/ x^7[/tex] -->  [tex]x^9[/tex]

Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward fashion.

Given:

We will use the Property of exponent and power

[tex]x^m/ x^n[/tex] = [tex]x^{m-n[/tex]

1. x²³ / x³

Using the property

x²³ - ³ = [tex]x^{20[/tex]

2. [tex]x^{14}/ x^{17}[/tex]

Using the property

= [tex]x^{14- 17}[/tex]

= [tex]x^{-3[/tex]

= 1/x³

3. [tex]x^{19}/ x^{33}[/tex]

Using the property

= [tex]x^{19-33}[/tex]

= [tex]x^{-14}[/tex]

= 1/[tex]x^{14[/tex]

4. [tex]x^{16}/ x^7[/tex]

Using the property

= [tex]x^{16-7}[/tex]

= [tex]x^9[/tex]

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The probability that you draw a sphere given that it is blue is given as follows:

5/7.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

The total outcomes in this problem are the blue shapes, hence the number is given as follows:

6 + 15 = 21 shapes.

The desired outcomes are the blue spheres, hence the number is given as follows:

15.

Hence the probability that you draw a sphere given that it is blue is given as follows:

p = 15/21

p = 5/7. (simplify numerator and denominator by 3).

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Answer:

x³ - 3x² + 5x - 6

Step-by-step explanation:

      1) (2x + y)(4x - 9) = 2x*(4x - 9) + y(4x - 9)

                                 = 2x*4x - 2x*9 + y*4x - y *9

                                = 8x² - 18x + 4xy - 9y

2) (3x + 5y)²

Identity : (a + b)² = a² + 2ab + b²

a = 3x and b = 5y

(3x +5y)² = (3x)² + 2 * 3x *5y + (5y)²

               = 9x² + 30xy + 25y²

3) (x -2)(x² - x + 3) = x*(x² - x + 3) - 2(x² - x + 3)

                             =x*x² - x*x + x*3 -2*x² + 2*x - 2*3

                            = x³ - x² + 3x - 2x² + 2x - 6

                            =x³ - x² - 2x² + 3x + 2x - 6

Combine like terms. Like terms have same variable with same exponent.

                           = x³ - 3x² + 5x - 6

The Expected value is the long-term average position of any variable. The anticipated value will be$5.18

The predicted value is the long-run average of all variables. It also shows the loaded normal probabilities for all possible values. Investors use expected value to estimate an investment's return, often in relation to its risk.

Given the data in detail

Pupil Lunch check Bones spent Probability

2$10 20/50.

1$8 8/50.

12$6 72/50.

23$5 115/50.

8$4 32/50.

4$3 12/50

The sum will be

aggregate = 20+ 8 +72 +115 +32 +12

                           50

= 259/50

= $5.18

The anticipated value a pupil would spend on lunch each day will be $5.18

Question

From the following data, calculate the expected  value a pupil can spend on lunch each day?

Students & Amount spent

2$ 10

1$ 8

12$ 6

23$ 5

8$ 4

4$ 3

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The value of 9/10  divided by 3/5 is 3/2.

How to multiply two fractions?

When multiplying fractions, you first start with the two fractions you want to multiply. You multiply the numerators (the top numbers) together, and then multiply the denominators (the bottom numbers) together. After putting the two results together as a new fraction, you may need to simplify the fraction in order to express it in its lowest terms.

Firstly , let's find the reciprocal of the divisor

Reciprocal of

3/5 is 5/3

Now, multiply it with the dividend

So,

9/10 ÷ 3/5

= 9/10 × 5/3

=  45/30

After reducing the fraction, the answer is

3/2

Hence , the value of 9/10  divided by 3/5 is 3/2.

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The high temperature increased by 15.38% from yesterday to today.

First, you must find the actual increase in temperature. by using this formula:

Percentage increase = (Today's temperature - Yesterday's temperature) / Yesterday's temperature * 100

Percentage increase = (75 - 65) / 65 * 100 = 15.38%

Temperature is a physical quantity that indicates hot and cold. It is the manifestation of thermal energy, present in all matter, which is the inception of the occurrence of heat, a flow of energy when a body is in contact with another that is colder or hotter.

Temperature is measured with a thermometer.

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Answer:

$3.30

Step-by-step explanation:

6 x 1.50 = 9

12.30 - 9 = $3.30

$9.10 in all nickels is how many nickels

9.10 / 0.05

how many 5 cent pieces add up to that

182 nickels

a penny is one cent

just move the decimal place over twice

9.10

910.0

910 pennies

Hope this helps

- Jeron :- )

If a back-to-school sale offered a laptop for $379 and this sale price reflected a 15% discount, after using the equation the cost of the computer before the reduction in price is, $446.47.

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

Let's call the original cost of the laptop "x".

The equation to find the cost after a discount is:

x - x * (discount rate) = sale price

In this case, the discount rate is 15%, or 0.15. Plugging in the given values:

x - x * 0.15 = 379

Expanding the equation:

x - 0.15x = 379

0.85x = 379

Dividing both sides by 0.85:

x = 379 / 0.85

x = 446.47

So, the cost of the laptop before the reduction in price was $446.47.

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The cost of each balloon and each banner is $2 and $1 respectively.

Let

cost of balloon= x

cost of banner= y

6x + 3y = 15

4x + y = 9

Multiply equation (2) by 3

12x + 3y = 27

6x + 3y = 15

12x + 3y = 27

Subtract the equations to eliminate y

12x - 6x = 27 - 15

6x = 12

divide both sides by 6

x = 12/6

x = $2

Substitute into

4x + y = 9

4(2) + y = 9

8 + y = 9

y = 9 - 8

y = $1

Therefore, each balloon cost $2 and each banner cost $1

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The chance at least one of the alarms will wake her up is 0.96.

If the probability of one event does not affect the probability of another event, the events are independent.

Given

Probability that Alarm clock 1 is reliable = 60% = 0.60

Probability that Alarm clock 2 is reliable = 90% = 0.90

P of alarm clock 1 not reliable = 0.40

P of alarm clock 2 not reliable = 0.10

Therefore,

The chance at least one of the alarms will wake her up is;

=p1.p2' + p1'. p2 + p1.p2

so, calculating we get,

= 0.96

Hence, the chance at least one of the alarms will wake her up is 0.96.

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Answer:

3.19

Step-by-step explanation:

5.5% of 58 is 3.19

and is you need it,

58 - 3.19 = 54.81

I believe this is right

the sales tax on $58 at a rate of 5.5% is $3.19

How to find the tax on $58 at a rate of 5.5%?

Taxes are a mandatory contribution to the state. So sales must pay taxes, and it is stated that the rate of tax that must be paid is 5.5%

The way to calculate tax from sales is to multiply the tax rate by the income from sales.

the income = $58

the rate of tax = 5.5%

the tax to be paid by sales = the income x the tax

                                             = $58 x 5.5%

                                             = $3.19

so the answer to the question is $3.19

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The table that represents a linear relationship is the one in option 3.

A linear relationship can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If we add 1 to the input we get:

y = a*(x + 1) + b

y = (a*x + b) + a

So for each increase of 1 unit on the input we have a constant increase on the value of y.

The table that represents a line is the number 3, where you can see that the increases in the f(x) values are constants.

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Step-by-step explanation:

Hi joolin

Hyvwzzaetu =g m eet co de

Co me get free answers

Or give me the in sta id

Answer:

this equation is always true

Step-by-step explanation:

Solve the equation and check your solution: -2(x - 1) = 2 - 2x

-2(x - 1) = 2 - 2x

-2x + 2 = 2 - 2x

-2x + 2x = 2 - 2

0 = 0

(this equation is always true)

------------------------------

check

whatever value you give to x the equation is always true, let's take 2 as an example

-2(2-1) = 2 - 2 * 2

-4 + 2 = 2 - 4

-2 = -2

a. The total of the two sides of the right triangle using Algebraic expression is 3x²+7x-4.

b. The length of the missing side of the triangle is 3x³-4x²-15x+5.

c. If the value of x=2, then the length of the three sides of the triangle is

   a=11, b=11 and c= -17.

d. No, it is not possible to have these side lengths for a right triangle.

Algebra is a discipline of mathematics that studies symbols and the mathematical operations that can be applied to them. These symbols are referred to as variables because they don't have predetermined values. These values are usually represented in algebra by variables, which are symbols like x, y, z, p, or q. These symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations in order to ascertain the values.

a. Let the sides of the right triangle be a, b and c.

Given, one side of the triangle is 2x² + 2x - 1 and

another side is 5x + x² -3.

So, let a = 2x²+2x-1 and b = 5x+x²-3

Now, the total of the two sides= a+b

          a+b

         =2x²+2x-1 + 5x+x²-3

         = 3x²+7x-4

Therefore, the total of the two sides of the right triangle = 3x²+7x-4.

b. Now the perimeter of the triangle is given= 3x³-x²-8x+1.

Given, a+b+c=3x³-x²-8x+1.

We already have a+b, so by simplifying the equation a+b+c=3x³-x²-8x+1

we can find the length of the third side, c.

a+b+c= 3x³-x²-8x+1

⇒3x²+7x-4 +c= 3x³-x²-8x+1

⇒c= 3x³-x²-3x²-8x-7x+1+4

⇒c= 3x³-4x²-15x+5.

Therefore, length of the missing side is 3x³-4x²-15x+5.

c. We have the three sides of the triangle with us which are:

a = 2x²+2x-1

b = 5x+x²-3

c = 3x³-4x²-15x+5

Now putting the value of x as 2 in the equations as follows:

a= 2(2²) +2(2)-1

 = 8+4-1

 =11

b=5(2) +2²-3

 = 10+4-3

 =11

c=3(2³)- 4(2²) -15(2) +5

 =24-16-30+5

 = -17

Therefore, the length of the three sides of the right triangle

are 11, 11 and -17.

d. The sides of the right triangle are.

a = 11

b = 11

c = -17

We know as per the Pythagorean theorem c² = a² + b².

Accordingly, c²= 289 & a² = 121 and b²= 121, a² + b²= 242

which shows that c² is not equal to a² + b².

As, the sides of the triangle does not follow the Pythagorean theorem, so these are not the sides of a right-angle triangle.

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The bearing of the lighthouse from the fishing boat is 242

From the question, we have the following parameters that can be used in our computation:

The bearing of a fishing boat from a lighthouse is 118°.

The bearing of the lighthouse from the fishing boat is calculated as

The bearing of the lighthouse from the fishing boat = 360 - The bearing of a fishing boat from a lighthouse

Substitute the known values in the above equation, so, we have the following representation

The bearing of the lighthouse from the fishing boat = 360 - 118

Evaluate

The bearing of the lighthouse from the fishing boat = 242

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The area of the new rectangle is 9 times the previous area and the perimeter of the new rectangle is 3 times the previous area

From the question, we have the following parameters that can be used in our computation:

(-1, 2), (-1, -4), (3, -4), and (3, 2).

See attachment for the points, where we have

Length = 4 and width = 6

Using area and perimeter formulas, we have

Area = 4 * 6 = 24

Perimeter = 2 * (4 + 6) = 20

Here, we have

New = (-3, 6), (-3, -12), (9, -12), and (9, 6).

See attachment for the points, where we have

Length = 12 and width = 18

Using area and perimeter formulas, we have

Area = 12 * 18 = 216

Perimeter = 2 * (12 + 18) = 60

The area of the new rectangle is 9 times the previous area

i.e. 216/24 = 9

The perimeter of the new rectangle is 3 times the previous area

i.e. 60/20 = 3

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The number of different sets of three points of this grid can be the three vertices of an isosceles triangle is 36.

An isosceles triangle is one with two equal sides. The two angles that face the two equal sides are also equal. An isosceles triangle, in other words, is a triangle whose two sides are equal in length.

By using the Permutation formula,

Number of isosceles triangle to be formed is,

9!/(7!x2!) = 9x8x7!/7!x2!

= 9x8/2

= 36

So number of isosceles triangle that can be formed of this 3-by-3 grid is 36.

When a square is described as a 3 x 3 Magic square, it has three rows and three columns. An illustration of a 3 by 3 magic square with the magic constant.

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The cash price of the refrigerator is $408.

A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.

Given that, a new refrigerator has a price of $480.00.

The store will discount the price by 15% if the purchaser pays in cash.

Now, the discount is

15% of 480

= 15/100 ×480

= 0.15×480

= 72

Now, 480-72

= $408

Therefore, the cash price of the refrigerator is $408.

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By applying binomial distribution formula, it can be concluded that the probability less than two have a side effect is 56.86%.

Binomial distribution is the discrete probability distribution of the number of successes or failures in n independent trials, where each trial result has a probability p.

P(x) = C(n,x) · pˣ · qⁿ⁻ˣ where:

C = number of combinations

p = probability of success

q = probability of failure

x = number of times for a specific outcome within n trials

n = number of trials

We have the following information:

p = 12% = 0.12, thus:

q = 1 - p

  = 1 - 0.12

  = 0.88

n = 12

We want to find the probability less than two have the side effect, P(x<2):

P(x<2) = P(0) + P(1)

          = (C(12,0) · 0.12⁰ · 0.88¹²)  +   (C(12,1) · 0.12¹ · 0.88¹¹)

          = (1 · 1 · 0.2157)   +   (12 · 0.12 · 0.2451)

          = 0.2157 + 0.3529

          = 0.5686 ≈ 56.86%

Thus, the probability less than two have the side effect is 56.86%.

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Given all sides are right angles, the height of the sides are equal.

left side = 12

right side = x+5

set equation equal to each other and solve for x.

12 = x +5 =>> 12-5 = x =>> x = 7

x = 7 cm

Answer:

[tex]\frac{13}{12}=1\frac{1}{12}[/tex]

Step-by-step explanation:

You have 12/12 + 1/12 so it would end up being 13/12 so you can simplify the 12/12 to 1 and have [tex]1\frac{1}{12}[/tex]

Answer: 720

Step-by-step explanation:

Volume = l x w x h, so 9 x 10 = 90, 90 x 8 = 720.

Hope this helps.