MTR Apply Mathematics During a drought, the water level of a lake
decreases 3 inches every week. What will be the change in the water level
of the lake if the drought lasts for 7 weeks?

The solution of the system of equations are;

⇒ x = - 6 , y = 44 and z = 2

What is substitution method?

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The system of the equations are,

3x + y - 2z = 22    .... (i)

x + 5y + z = 4       .... (ii)

x = - 3z                .... (iii)

Now,

Solve the equations as;

Substitute x = - 3z in both equations, we get;

⇒ 3x + y - 2z = 22

⇒ 3 × -3z + y - 2z = 22

⇒ - 9z + y - 2z = 22

⇒ - 11z + y = 22   .... (iii)

And, x + 5y + z = 4

- 3z + 5y + z = 4

5y - 2z = 4     ... (iv)

Solve equation (iii) and (iv) we get;

⇒ y = 44 and z = 2

So, x = - 3z    

⇒ x = - 3 × 2

⇒ x = - 6

Thus, The solution of the system of equations are;

⇒ x = - 6 , y = 44 and z = 2

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Given a table represents a relation between x and y

As shown, the change of (x) and (y) vary with a constant rate

So, the table represents a linear function

The general equation will be: y = m * x + b

where (m) is the slope, (b) is the value of y when (x=0)

So, from the table, when x = 0 , y = 25

The slope will be as follows:

So, the equation will be:

When the input = 200, x = 200

So, substitute with (x) to find the output (y)

So, the answer will be:

For an input 200, the output is 1025

===================================================

Another method to solve using the arithmetic sequence.

As shown in the table consider (x) represents the number of terms

So, (y) will be an arithmetic sequence

The first term = a = 30

The common difference = d = 35 - 30 = 5

the general rule of the arithmetic sequence is:

substitute with (a) and (d)

When x = 200

So, for an input 200, the output = 1025

Let's start by completing the first table.

The questions gives the depth in two times:

- 2 hours after start -> 64 inches of water

- 4 hours after start -> 48 inches of water

From this, we can identifythe units:

- for time, we will use hours

- for depth, we will use inches

The first given values are:

- for time, 2

- for depth, 64

The second given valuesa are:

- for time, 4

- for depth, 48

So, the table is:

Quantity Name | Time | Depth of Pool

Unit | hour | inch

Given Value 1 | 2 | 64

Given Value 2 | 4 | 48

Now, we need to calculate the slope, which can be done using the given points and the equation:

So, the slope is -8 inches per hour.

The interceptwe the b in the equation:

Where y is the depth and x is the time. So, using the first given values and the slope, we can find b:

Thus, the intercept is 80 inches.

So, the formula we have for the pump is:

Using it, we can answer questions 1 and 2:

1. After 6 hours means x = 6, so:

So, y = 32, thus, the depth of the water will be 32 inches.

2. The level 24 inches mean y = 24, so:

Thus, x = 7, and the water will be at 24 inches after 7 hours.

The effect on the graph replacing f(x) by f(x)+k is a vertical shift k units.

According to the graph the resulting function is 2 units higher from the original one. This means k has a value of 2.

The value of x in the given quadratic equation are; +9 and -9.

A quadratic equation is the second-order degree algebraic expression in a variable. An equation of degree 2 containing a single variable is known as the quadratic equation. Its general form is  ax² + bx + c = 0 , where variables are x and constants are a, b, and c.

As equation is  x²= 81

Taking square root on both sides;

⇒ √x² = √81

⇒ X = ± 9

Thus the value of X is  ± 9

Hence, The roots of the given quadratic equation are; +9 and -9.

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Answer:

Step-by-step explanation:

Substitute a and b with 1/4 and 6

5b/ 32a^2

5(6)/ 32(1/4)^2

30/32(1.96)

30/62.72

0.5102 Answer

From the question

By the bunkers rule

P = 18,000

R = 17.25% = 0.1725

For the time

Since the year is a leap year then

February has 29 days

Hence

From Feb.4 to Apr 21 implies

The number of days left in Feb. = 25

Number of days in March = 31

Number of days for April = 21

Therefore, Total number of days = 25 + 31 + 21 = 77

By Bankers rule, total days for the year will be 360

Hence the interest is

Therefore, the interest is 664.16

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line.

From point A, point B is observed with an angle of 45 down from the top of the tree to the ground.

Thus, the angle of depression is 45°

A rotation of 270 degrees about the origin would transform the figure as follows:

Which does not maps the A to A'.

Now, one sequence of transformations that take A to A' is:

1)First, a reflection over the x-axis would transform the figure as follows:

2) We translate the figure 3 units up and 4 units to the right:

Answer: Reflection over the x-axis, translation 3 units up and 4 units to the right.

Given:

1 mile = 1.6 km

So, 8 miles per hour in kilometers per hour is given by:

Where x = # of kilometers

So, solve for x:

This is 12.8 km per hour

Next, the distance traveled in 2 hours is:

Substitute the values:

Answer:

Rate: 12.8 km/h

Distance traveled in 2 hours: 25.6 km

By working with inequalities, we will see that:

Let's define:

We know that Mrs. Smith spent $50 more at a store than Mrs. Jones, then:

S = J + 50

And together they spent at most $250, then:

S + J ≤ 250

Now, replacing the equation in the inequality, we get:

(J + 50) + J  ≤ 250

2*J + 50  ≤ 250

2*J  ≤ 250 - 50

2*J  ≤ 200

J  ≤ 200/2

J  ≤ 100

So Mrs. Jones spent at most 100 dollars.

And Mrs Smith spent $50 more than that, so we can write the inequality.

50  ≤ S ≤ 150

She spends between $50 and $150.

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Explanation: First of all we need to know if our triangle is a right triangle (has one 90° inner angle) to be able to use the law of sines to calculate the distance between Amanda and the helicopter.

Step 1: Once we know that the sum of all inner angles of a triangle is equal to 180° we can calculate the unknown angle as follows

As we can see above the missing inner angle is 90° which means it is a right triangle.

Step 2: Now we can use the law of sines as follows

once sin (90°) = 1 and sin (30°) = 0.5, let's calculate "x" below

Final answer: As we can see above, the final answer is 2000 ft

Total number of cards: 52

Number of face cards: 12

To calculate the percentage that the face cards represent we need to divide the number of face cards by the total number of cars, and then multiply by 100%:

The first division 12/52 will give us the proportion that the face cards represent, and by multiplying that by 100 we find the percentage.

Solving the operations:

-solving the division

-solving the multiplication:

The face cards represent 23.08%.

Rounding to the nearest tenth of a percent (one decimal place):

Answer: 23.1%

Measure of ∠B = 16°

∠A and ∠B are Vertical angles with ∠A = x+12° and ∠B = 6x-8°.

Vertical angles are angles formed between two lines at the intersection of them and are opposite to each other.

Also measures of Vertical angles are equal.

Now to find the measure of ∠B, we need to find x.

So here,  ∠A = ∠B

⇒ x+12° = 6x-8°

⇒ 6x - x = 12 + 8

⇒ 5x = 20

⇒ x = 4

Hence, ∠B = 6x-8° = 6 x 4 -8 = 16°

So measure of ∠B = 16°

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Answer:

3

Step-by-step explanation:

Hello!

A simple way to find if the number is a multiple of 9 is if the sum of the digits in the number is a multiple of 9, then the number itself is a multiple of 9.

So that means: 7 + 2 + b + 3 + 8 + 4 is a multiple of 9

If we add it up we should get: 24 + b

The multiples of 9 include 9,18,27,36,45,54....., and the closest multiple of 9 to 24 is 27. Therefore, the missing digit should be 3, as 27 - 24 is 3.

The next closest numbers would be 18 and 36, but you would need to add a negative number to get 18, and a two-digit number to get 36.

The dimension of the brick is given 110 cm x 655 cm x 1330 cm.

We know that 1 cm = 10^-2 m.

So, the dimensions of brick in meters will be 1.10 m x 6.55 m x 13.30 m.

The volume of the brick is calculated below:

Thus, the volume of the brick in cubic meters is 95.8265 m^3.

The scientific notation of the expression is as follows:

The proper format for scientific notation is a x 10ᵇ where a is a number or decimal number such that the absolute value of a is greater than or equal to one and less than ten or, 1 ≤ |a| < 10.

Scientific notation is a special way of writing numbers.

The expression can be express in scientific notation as follows:

Therefore,

(7 × 10⁻⁶) (7 × 10⁻⁶)

Hence, we have to multiply the integers and add the exponents as follows:

(7 × 7) × (10⁻⁶. 10⁻⁶)

49 × 10⁻⁶⁻⁶

49 × 10⁻¹²

4.9 × 10⁻¹¹

Hence, the second can be express in scientific notation as follows:

(3.76 × 10⁵) + (7.44 × 10⁵)

(3.76 + 7.44) × 10⁵

11.2 × 10⁵

1.12 × 10⁵⁺¹

1.12 × 10⁶

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Answer: The second ratio in the proportion is set up as ounces over oranges. The units should be in the same place in proportion to the first ratio.

Step-by-step explanation:

The most appropriate choice for cone and total surface area of cone will be given by-

Total surface area of the cone is [tex]198235.71 cm^2[/tex]

What is cone and total surface area of cone?

Cone is a 3 dimensional figure whose base is a circle and upper surface finally converge to a point.

Cone is obtained by revolving a right angled triangle about one of its legs.

Total surface area of the cone is the sum of curved surface area of the cone and the area of the base of the cone.

If r is the radius of the base of the cone and l is the slant height of the cone, then total surface area of the cone will be given by

[tex]\pi r(r+l)[/tex]

Here

Ratio of the slant height and radius of base of the cone = 2:1

Radius = 145cm

Slant height = [tex]145 \times 2[/tex]

                    = 290 cm

Total surface area of cone = [tex]\pi r(r+l)\\[/tex]

                                              = [tex]\frac{22}{7} \times 145\times (145+290)\\[/tex]

                                              = [tex]\frac{22}{7} \times 145 \times 435[/tex]

                                               = [tex]198235.71 cm^2[/tex]

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Complete Question

The slant height and the radius of  base of the cone are in the ratio 2:1. If the radius of the cone is 145cm. What is the total surface area of the cone?​

Answer:  A) moves two places to the right

Example:

[tex]2.567 * 10^2 = 2.567 * 100 = 256.7[/tex]

The positive exponent over the 10 tells us how many places to move to the right. If the exponent was negative, then we'd move to the left. This only works when the base is 10.

The required answer would be (24 -3x - 4x²) / 4x = 0 which is the lcm of the rational algebraic equation 6/x+x-3/4=2.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The given equation below as:

⇒ 6/x + x - 3/4 = 2

We have to determine the lcm of the rational algebraic equation

⇒ 6/x + x - 3/4 = 2

Rearrange the term of 2 in the equation,

⇒ 6/x + x - 3/4 - 2 = 0

Take LCM in the above equation,

⇒ [tex]\dfrac{6\times4+x\times4x-3\times x -2 \times 4x}{4\times x}[/tex]

⇒ (24 + 4x² -3x - 8x²) / 4x = 0

Combine the likewise terms in the numerator,

⇒ (24 -3x - 4x²) / 4x = 0

Therefore, the required answer would be (24 -3x - 4x²) / 4x = 0.

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Answer:-900 feet. I think this is correct so don't use it unless you think its right

Step-by-step explanation:

Answer:

The answer is (1,4,2)

every day she spent $35, if after 1 day she still have $315, the day before that she had $315+$35=$350

Therefore, the initial value was $350

To solve this exercise, we define the following variables:

• j = Japan size of shoes,

• u = United Sates size of shoes,

• k = Korea size of shoes.

From the statement of the problem, we know that:

0. In Japan, shoe size is 16 more than the size in the United States →, j = 16 + u,,

1. In Korea, shoe size is 224 more than the size in Japan →, k = 224 + j.

We must find a function for the U.S. size of a shoe (u) in terms of the shoe size in Korea (k).

1) From point 1, we have:

2) From point 2, we have:

Replacing the expression of j in terms of k in the expression of u, we get:

Replacing the value k = 250 in the last equation, we get:

Answer

The U.S. shoe size of a shoe that is 250 in Korea is equal to 10.

The answer is in my screenshot pic.

[tex] \frac{13}{5} \times - \frac{8}{3} \\ = - \frac{104}{15} [/tex]

ATTACHED IS THE SOLUTION

Answer:

(-104/15)

Step-by-step explanation:

    3              2

2 ------ × -2 -------

    5              3

5 × 2 = 10

10 + 3 = 13

3 × -2 = -6

-6 + -2 = -8

 13        -8            104

------- × ------- = (-) -------

  5          3             15

I hope this helps!

Length of the given arc

So the length of the given arc is 1.57 cm

Answer:

(49.4 - 39) / 4

= 10.4 / 4

= 2.6GB

Step-by-step explanation: