The ratio of Mr Lim's age to his son's age is 5:2. Four years ago, the ratio of their ages was 3:1. How old will Mr Lim be in 6 years time?

Answer: 37 degrees

Hope this helps :)

Step-by-step explanation:

(The box in the corner tells you this is a right angle)

A right angle is 90 degrees

90 - 53 = 37

Answer:

37 degrees

Step-by-step explanation:

Angle a is equivalent to 37 degrees because the picture signifies a right angle; all right angles are equal to 90 degrees. The equation to solve this would be: 53+x=90, you would solve this by subtracting 90-53=x; x=37

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The slope of the linear function in this problem is given as follows:

m = -4.

The slope of a linear function represents the rate of change of the linear function, hence it is calculated as the change in y divided by the change in x, taking two points.

From the graph of the function, when x increases from 0 to 3, y decays from 5 to -7, hence the slope is calculated as follows:

m =(-7 -5)/3

m = -4.

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With a volume of 700 cubic feet and a height of 9 feet , the radius of cylinder is 3.49 feet after rounding to nearest hundredth.

To find the radius of a right cylinder, you need to know its volume and height. The formula for the volume of a cylinder is given by:

V = πr^2h

Where r is the radius, h is the height, and π is approximately equal to 3.14.

Given that the volume is 700 cubic feet and the height is 9 feet, we can substitute these values into the formula:

700 = πr^2 * 9

Dividing both sides by π * 9:

700 / (π * 9) = r^2

Taking the square root of both sides:

√(700 / (π * 9)) = r

Using a calculator and rounding to the nearest hundredth, we find that:

r ≈ 3.49

So the radius of the cylinder is approximately 3.49 feet.

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The average speed of whole trip was 6.7 mile per hour.

Average speed is calculated by dividing a quantity by the time required to obtain that quantity. Meters per second is the SI unit of speed. The formula S = d/t, where S is the average speed, d is the total distance, and t is the total time, is used to determine average speed.

Given that, the total distance =6+6=12 miles and total time

=58+49= 107 minutes

So, number of hours = 107/60

= 1.8 hours

Now, the average speed = 12/1.8

= 6.7 mile per hour

Therefore, the average speed is 6.7 mile per hour.

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Answer:

7 packs of floorboards

Step-by-step explanation:

total area of floor= (4.5×2)+(2×3)

= 9+6

= 15m2

15÷2.25= 6.6666666

~7 packs (rounded up to the nearest whole no.)

Answer:

[tex]\huge\boxed{\sf 10s + 93}[/tex]

Step-by-step explanation:

= 10 (s + 9) + 3

= 10s + 90 + 3

[tex]\rule[225]{225}{2}[/tex]

Answer:

Step-by-step explanation:

10(s + 9) +3

10s + 90 + 3

10s + 90 +3

10s + 93

Solution 10s + 93

Step-by-step explanation:

It is translated up 6 units, with the y value is vertical (up and down). The y value is 5, (x, y). Because it only moves up you would keep the x value, -3, and add 6 to the y value. So 5+6=11

The new coordinates are now (-3,5)

Hope this helps :)

Answer:

Below

Step-by-step explanation:

3/4 (1/6 x +16) = 3/7 (4 3/8 - 21)      expand L side and compute R side

3/24 x + 12 =  - 7.125        Subtract 12 from both sides of the equation

3/24 x = -19.125             Multiply both sides by 24/2

x = -153

THIS EQUATION DOES SHOW x = -153

PERHAPS you MEANT this :

3/4 (1/(6x) +16) = 3/7 (4 3/8 - 21)       Expand L side  and compute R side

3/(24x) + 12 = - 7.125       subtract 12 from both sides

3/(24x) = -19.125      re-arrange

3 / (-19.125)    = 24 x      divide both sides by 24

3/ (-19.125 * 24) = x = - 1/153      

     Don't know how to find a different answer......check the equation you posted......

Answer:

60

good luck!

The major plate motion rates range from less than 10 mm/y to more than 100 mm/y. The fastest plate is the Pacific Plate, followed by the Australian and Nazca Plates. The North American Plate is one of the slowest, with average rates ranging from around 1 cm/y in the south to nearly 4 cm/y in the north.

Plates move as rigid bodies, it may appear surprising that the North American Plate can move at different rates in different locations. Plates move in a rotational fashion, as explained. For example, the North American Plate rotates counter-clockwise, while the Eurasian Plate rotates clockwise.

There are three types of plate boundaries: divergent, convergent, and transform (moving side by side). Before we discuss processes at plate boundaries, it is critical to note that there are no gaps between plates.

The plates are made up of crust and the lithospheric part of the mantle, and despite moving in different directions all the time, there is never a significant amount of space between them.

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The expression which is equivalent is 2x + 5y - 3.

The equivalent expressions to 3x + 5y - x + 2 - 5 are:

2x + 5y - 3

3x + 5y - 3x + 2 - 5 = 3x - 3x + 5y + 2 - 5 = 2x + 5y - 3

So, both options are equivalent to 3x + 5y - x + 2 - 5.

Equivalent expressions" refer to mathematical expressions that have the same value for all values of the variables involved, regardless of the order or the grouping of the operations. For example, the expressions "2 + 3" and "3 + 2" are equivalent because they both equal 5.

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In linear equation, the store will get $468.72 from the sale of the couch.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                           Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

a.

Commission can be referred to as the reward given by the company on goods for the employee to sell products in order to make more sales and more money.

Commission is calculated as follows:

Total commission = Total Sales * Commission Percentage

Given

Total Sales = $495

Commission Percentage = 5½%

Substitute in, the above values

Total Commission = $496 * 5½%

Total Commission = $496 * 5.5%

Total Commission = $496 * 0.055

Total Commission = $27.28

Hence, the total commission is calculated as $27.28

b. The amount remitted to the store is calculated as

Amount = Total Sales - Total Commission

Where Total Sales = $496

Total Commission = $27.28

Amount = $496 - $27.28

Amount = $468.72

Hence, the store will get $468.72 from the sale of the couch.

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The complete question is -

Lin is shopping for a couch with her dad and heard him ask the salesperson “how much is your commission?” The salesperson says that her commission is 5½% of the selling price.

A.How much commission will the salesperson earn by selling a couch for $495?

B.How much money will the store get from the sale of the couch?

Answer:

a. The total commission is $27.28

b. The store will get $468.72 from the sale of the couch

Answer:

Step-by-step explanation:

The formula of volume is length x width x height.

Step-by-step explanation:

The pool is 10 feet long and 4 feet deep. This means the pool has a volume of 40 cubic feet (10 feet x 4 feet x 1 foot). To calculate the width of the pool, divide the total volume (40) by the length (10) to get 4 feet. Therefore, the width of the pool is 4 feet.

According to the given data, Ryan walked 12 small dogs.

Let x be the number of small dogs that Ryan walked.

The number of large dogs that Ryan walked would then be y = 4 - x.

Using the information given, we can set up the following equation:

x * 2 + (4 - x) * 5 = 40

Expanding and solving for x, we get:

2x + 4 - 5x = 40

-3x = 36

x = 12

So, Ryan walked 12 small dogs.

In this problem, we used a system of equations to solve for the unknown variable, x, which represents the number of small dogs that Ryan walked. By substituting this value back into the equation for the number of large dogs, we were able to confirm that Ryan walked 4 - x = 4 - 12 = 4 large dogs.

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Answer:

Below

Step-by-step explanation:

a)  DIRECT variation    y = k  x

                                    10 = k (4)

                                      10/4 = k = 2.5

                y = 2.5 x

b)    y = 2.5 x

       y = 2.5 (10) = 25

a) The sine and the cosine are given as follows:

b) The tangent is given by the sine divided by the cosine, as follows:

tan(Φ) = sin(Φ)/cos(Φ) = (8/17)/(15/17) = 8/15.

The three trigonometric ratios are defined as follows:

Applying the Pythagorean Theorem, the length of the hypotenuse is given as follows:

h² = 8² + 15²

h = sqrt(8² + 15²)

h = 17.

Considering that 8 is the opposite side and 15 is the adjacent side to the angle, the sine and the cosine are given as follows:

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The sales tax of the car is $1960

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

Price of car = $28000

Given that the sales tax on the new car is 7%, we have

Sales tax amount = 7% * Cost of new car

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

Sales tax amount = 7% *  $28000

Evaluate

Sales tax amount = $1960

Hence. the Sales tax amount is $1960

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The expected time (also known as the expected value or the mean) Is approximately 12.5 days.

The expected time for an activity is the average time it is likely to take, taking into account its optimistic, most likely, and pessimistic estimates. The three-point estimate formula is used to calculate the expected time by weighting the most likely estimate four times as much as the optimistic and pessimistic estimates. In this case, the optimistic time is 15 days, the most likely time is 18 days, and the pessimistic time is 27 days. By plugging these values into the formula, the expected time is calculated to be 12.5 days. This means that, on average, the activity is likely to take 12.5 days to complete.

The expected time (also known as the expected value or the mean) can be calculated using the three-point estimate formula, which is:

Expected time = (Optimistic time + 4 * Most likely time + Pessimistic time) / 6

Plugging in the values, we get:

Expected time = (15 + 4 * 18 + 27) / 6 = (75) / 6 = 12.5

So the expected time for this activity is 12.5 days.

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Answer: To solve the inequality, we start by isolating the variable n:

-6(n-1) < 3

-6n + 6 < 3

-6n < -3

n > 1/2

And for the other inequality:

2(n+1) > 0

2n + 2 > 0

2n > -2

n > -1

Now, we can plot these solutions on a number line:

[-----1/2-----][-------------n > 1/2----------------]

[-----n > -1-----][-------------]

So, the solution set for the inequality is n > -1 and n > 1/2, which means that n belongs to the interval (1/2, +∞).

Step-by-step explanation:

Answer: To happen before

Step-by-step explanation:

Answer:

40 to 60 is the answer of this question

Answer:

I only

Step-by-step explanation:

any point and its coordinates is an ordered pair of (x, y).

in other words, we get the x value used for the function and the resulting y value.

if the equation is true for such a pair, then the point is on the line. if it is false, then not.

y = (-5/4)x + 5

(4, 0)

0 = (-5/4)×4 + 5 = -5 + 5 = 0

true.

(0, 5)

5 = (-5/4)×0 + 5 = 0 + 5 = 5

true.

y + 5 = (-5/4)(x - 4)

(4, 0)

0 + 5 = (-5/4)(4 - 4)

5 = (-5/4)×0 = 0

false.

so, II is not containing (4, 0).

therefore, only I is contains both points.

Los intervalos numéricos para la recta numérica en el punto x=2, con 2>x<7, son: (2,7) e (2,∞).

Esto significa que los valores de x pueden oscilar entre 2 y 7, o bien entre 2 y el infinito.

Por ejemplo, el intervalo numérico (2,7) incluiría todos los números entre 2 y 7, incluyendo 2 y 7, pero excluyendo los números menores que 2 y mayores que 7. El intervalo numérico (2, ∞) significa que todos los números mayores que 2 están incluidos, mientras que los números menores que 2 no están incluidos.

Versión en inglés:

The numerical intervals for the number line at the point x=2, with 2>x<7, are: (2,7) and (2,∞).

This means that the values of x can range from 2 to 7, or from 2 to infinity.

For example, the numerical interval (2,7) would include all numbers between 2 and 7, including 2 and 7, but excluding numbers less than 2 and greater than 7. The numerical interval (2, ∞) means that all numbers greater than 2 are included, while numbers less than 2 are not included.

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13. a. To the ones: 26. 5

b. To the tenths: 26. 52

c. To the hundredths: 26. 519

14. 7x + 5 - 1. Terms = 3. coefficients: 1, constants: 1, variables: 1

3a - 5c + 9 - 1. Terms = 4, coefficients = 2 , constants = 2 , variables = 2

15. Collecting like terms;

a. 2b + 6

b. 9c + 3b + 7

16a. 2(8 - 7) = 2(1) = 2

16 - 14 = 2

b. 10(8 + 4) = 10(12) = 120

80 + 40 = 120

They are defined as expressions comprising of terms, coefficients, variables, constants and factors.

They are also composed of mathematical operations.

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The skier's displacement from his starting point is 127.179 m and makes an angle of 33.78°.

The law of cosines, commonly referred to as the cosine rule or the cosine formula, in trigonometry essentially connects the length of the triangle to the cosines of one of its angles. It claims that we can determine the length of the third side of a triangle if we know the length of the first two sides and the angle between them.

Given A skier moves 100.0 m horizontally, and then travels another 35.0 m uphill at an angle of 35.0º

base distance = 100 m

We will utilize the cosine rule to determine the magnitude of displacement because the triangle formed by the starting point, where he begins to ascend, and the ending point does not have a 90-degree angle. Cosine law requires a triangle with two sides and an angle between them, both of which are present.

a² = b² + c² - 2.b.ccos(α)

here a is the length of the third side,

b = base = 100m

c = 35 m

and α = 180 - 35 = 135°

so a² = b² + c² - 2.b.ccos(α)

a² = 100² + 35² - 2(100)(35)cos(135)

a² = 10000 + 1225 + 4949.74

a² = 16174.74

a = 127.179 m

and the angle between sides 100m and 127.179 m is given by

cosβ = (a² + c² - b²)/2a.c

cosβ = (127.179² + 35² - 100²)/2(127.179)(35)

cosβ = 0.831

β = cos⁻¹(0.831)

β = 33.78°

Hence displacement from the starting point is 127.179 m and forms an angle of 33.78°.

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A direct variation equation that shows the relationship between x and y is,

y = 8x.

A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.

Given:

In a direct variation, y=16 when x=2.

The proportional relationship between x and y:

y ∝ x.

y = kx, where k is constant.

When x = 2,

16/2 = k

k = 8.

Therefore, the relationship is y = 8x.

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Answer: mass of silver is 75g

Step-by-step explanation:

Check the picture below.

let's recall that on an isosceles triangle, twin sides make twin angles.

Answer:

0.7619047619≈0.76

Step-by-step explanation: