If you dig a 6ft hole, how deep is it?

By elimination, the solution of the system of equations, x + 2y = 10 and x + y = 6, is (2 , 4).

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.

Subtracting the two equations will eliminate the variable x.

x + 2y = 10     (equation 1)

x +   y = 6     (equation 2)

0x + y = 4

y = 4

Substitute the value of y to any of the two equation and solve for x.

x + 2y = 10     (equation 1)

x + 2(4) = 10

x = 10 - 8

x = 2

Hence, the solution of the system of equations is (2 , 4).

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Answer:

8

Step-by-step explanation:

Answer:

The answer is 470(32-n).

Step-by-step explanation:

Given:

There were 32 volunteers to donate blood. Unfortunately, n of the volunteers did not meet the health requirements, so they couldn't donate. The rest of the volunteers donated 470 milliliters each.

Now, to find milliliters of blood the volunteers donate.

Total volunteers = 32.

The number of volunteers couldn't donate = n

The rest of volunteers who donated = 32 - n

Milliliters of blood the rest of each volunteers donated = 470 milliliters.

Now, to get the milliliters of blood the volunteers donate, we multiply the number of rest of volunteers who donated blood by the milliliters of blood they donated: 470(32 - n)

Therefore, the answer is 470(32-n).

The relation is a function because it is a one-to-one relation

The relation is given as

y = -3x

The inputs are given as

x = 0, x = 1 and x = 2

Substitute the values of x i.e. x = 0, x = 1 and x = 2 in the equation of the function y = -3x

So, we have

y = -3(0) = 0

y = -3(1) = -3

y = -3(2) = -6

From the above computations, we can see that the y values are different for the inputs

Hence, the relation is a function because it is a one-to-one relation

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Answer: 106.6 is the correct answer

Step-by-step explanation:

The equation [tex]A(x)=\frac{18+0.15x}{x}[/tex] represents the correct expression for the Average cost.

What is a mathematical expression?

In mathematics, an expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. Mathematical symbols can represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to aid in determining the sequence of operations and other features of logical grammar.

The store charges $18 for design setting and $0.15 per print out of business card.

Let the number of cards be [tex]x[/tex]

Then, total cost of printing of [tex]x[/tex] cards = $ [tex]0.15x[/tex]

Thus, the expression for the average cost [tex]A(x)[/tex] is given as,

[tex]A(x)=\frac{18+0.15x}{x}[/tex]

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Answer: 2124 dollars

Step-by-step explanation:

4.5% of 1800 is 81. As it is simple interest and not compound, it does not change each year. Therefore, 81 x 4 is 324. 1800+324 = 2124 dollars

Answer:

102

Step-by-step explanation:

Let x equal the unknown number

x/2 = 17 + x/3

3x = 102 + 2x

x = 102

The ratio of the area of circle X to the area of circle Y is  0. 11

The formula for area of a circle is expressed as;

Area = πr²

Where; 'r' is the radius

For circle X, radius = 1/ 3 meter

Let's find the area

Area = 3. 142 × (1/3)²

Area = 3. 142 × 1/ 9

Area = 0. 35 square meters

For circle Y, radius = 1

Area = 3. 142 × 1²

Area = 3. 142 × 1

Area = 3. 142 square meters

Ratio of circle X to circle Y

= 0.35/ 3. 142

= 0. 11

Thus, the ratio of the area of circle X to the area of circle Y is  0. 11

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The value of the algebraic expression is a 5.

According to the statement

We have to find that the value of the algebraic expression.

So, For this purpose, we know that the

Algebraic expression is an expression obtained by a finite number of the fundamental operations of algebra upon symbols representing numbers.

From the given information:

The function is a

g(x) = 3x - 1

Then

we have to put the value of the x is a 2 to find the value of the g(2) in the expression.

Then

g(x) = 3x - 1

g(2) = 3(2) - 1

g(2) = 5.

The value becomes 5.

So, The value of the algebraic expression is a 5.

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There are 13 diamonds in the deck (as well as other colors). Since there are 52 cards, the probability of getting a diamond on the first draw is 13/52. After the first card is drawn, all that's left are his 12 diamonds. Therefore, the probability of drawing a diamond is 12/51 (note that he has only 51 cards left after pulling/removing the first card since there are no replacement cards). The overall probability is the product of two possibilities. The odds of drawing diamonds from the original deck are 13/52 times the odds of drawing diamonds from his remaining 51 cards. Assuming the first card drawn is a diamond, 12/51.

P=13/52*12/51=1/4*4/17=1/17.

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       Round 98984 to 1 significant figure.

       100000.

The arithmetic sequence AP's 32nd term is calculated to be 225.

An arithmetic progression (AP) in mathematics is a list and maybe sequence of numbers with each term is obtained by adding a sequence to the term before it.

Finally, the solution to the question is as follows:

The numbers in the displayed sequence are as follows:

101,105,109,113, ...........

We must explore the 32nd number in the series because it contains 32 terms.

The common difference with both two consecutive terms of an AP which are equal is denoted by 'd.'

Let's assume the first term is'a₁' = 101.

Let's assume 'a₂' = 105 is the second term.

Let's assume the third term is 'a₃' = 109

Substitute the values the preceding equation; the 32nd term is-

d = a₂ - a₁  

Obtain the common difference;

d = 105 - 101

d = 4

Put the values in the preceding formula; the 32nd term is

The formula finds the nth term equation;

Put the given values in nth term formula;

a₃₂ = a + (n - 1) d

a₃₂ = 101 + (32 - 1)(4)

a₃₂ = 101 + 128 - 4

a₃₂ = 225

Thus, the 32nd term value of the arithmetic sequence is calculated to be 225.

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Answer: A and E

Step-by-step explanation:

A. 21/25 × 50/63=

(21*50)/(25*63)=

21/63 * 50/25 =

1/3 * 2 =2/3

B. 7/8×9/25=

(7*9)/(8*25)=

63/200 [tex]\neq[/tex] 2/3

C. 1/30×2/3=

(1*2)/(30*3)=

2/90=

1/45 [tex]\neq[/tex] 2/3

D. 3/25×7/12=

(3*7)/(12*25)=

3/12 * 7/25 =

1/4 * 7/25 =

(1*7)/(4*25)=

7/100 [tex]\neq[/tex] 2/3

E. 20/27×27/30=

(20*27)/(27*30)=

27/27 * 20/30=

1 * 2/3 = 2/3

A and E

Step-by-step explanation:

=

[tex](m + 6)(m - 4)[/tex]

HOPE THIS HELPS

The location on the number line to plot the sum will be between -1 1/2 and -2.

It should be noted that the number line is a straight line that is a visual representation of the numbers. It can be used for addition and subtraction.

In this case, the addition of 3/4 + (-2 1/2) will be:

= 3/4 - 2 1/2

= - 1 3/4

Therefore, the location on the number line to plot the sum will be between -1 1/2 and -2.

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Arithmetic mean and geometric mean of a and b are equal when a = b

Arithmetic mean

Arithmetic mean of two numbers is their sum divided by 2. Generally, arithmetic mean is the sum of the values divided by the total value. It gives the average of two or numbers. It is accurate when the data values are not much skewed.

For two numbers a and b, arithmetic mean = a + b /2

Geometric mean

Geometric mean of two numbers is the square root of its product. It is also used for the calculation of averages. For more than two numbers, the geometric mean is the 1/n th power of the product of the numbers. The skewness of the data values does not affect the accuracy in calculating the geometric mean.

For two numbers a and b, geometric mean = [tex]\sqrt{ab}[/tex]

Always arithmetic mean is larger than the geometric mean.

Arithmetic mean = Geometric mean

⇒ (a+b)/2 =  [tex]\sqrt{ab}[/tex]

⇒ a+b = 2 [tex]\sqrt{ab}[/tex]

On squaring,

⇒ [tex]a^2 +2ab+b^2[/tex] = 4ab

⇒  [tex]a^2 -2ab+b^2[/tex] = 0

⇒  [tex](a-b)^2[/tex] = 0

⇒ a -b = 0

⇒ a = b

Arithmetic mean is equal to the geometric mean if the two numbers are equal.

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The two possible locations of the point C are (1, 1) and (- 2, - 5).

According to the statement, we find the coordinates of the ends of a line segment and a partition ratio. There are two possible solutions concening the location of the point B:

Thus, we have the corresponding expressions for each case:

Case 1

C(x, y) = A(x, y) + (4 / 5) · [B(x, y) - A(x, y)]

C(x, y) = (- 3, - 7) + (4 / 5) · [(2, 3) - (- 3, - 7)]

C(x, y) = (- 3, - 7) + (4 / 5) · (5, 10)

C(x, y) = (- 3, - 7) + (4, 8)

C(x, y) = (1, 1)

Case 2

C(x, y) = A(x, y) + (1 / 5) · [B(x, y) - A(x, y)]

C(x, y) = (- 3, - 7) + (1 / 5) · [(2, 3) - (- 3, - 7)]

C(x, y) = (- 3, - 7) + (1 / 5) · (5, 10)

C(x, y) = (- 3, - 7) + (1, 2)

C(x, y) = (- 2, - 5)

The two possible locations of the point C are (1, 1) and (- 2, - 5).

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The y-coordinate is 4 and the y-intercept is (0,4)

The given equation is 4x + 3y = 12

Comparing the equation with the equation of line ax + by = c

where a = 4, b = 3, c = 12

The y-intercept is the point where the graph intersects the y-axis. To graph, any function that is of the form y = f(x) finding the intercepts is really important. There are two types of intercepts that a function can have. They are the x-intercept and the y-intercept. An intercept of a function is a point where the graph of the function cuts the axis.

for y-intercept,

x coordinate is 0

that is x=0

4(0) + 3y = 12

3y = 12

y = 12/3

y = 4

Hence the y-coordinate is 4 and the y-intercept is (0,4)

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The value of x makes the triangle a right triangle is 15 .

Pythagoras Theorem states that sum of square of two sides of triangle  is equal to the square of longest side of the right angle triangle.

In the given question

the length of longest side = 25.

length of other two side= x and x+5.

By Pythagoras Theorem

[tex]x^{2} +(x+5)^{2} =25^{2}[/tex]

[tex]x^{2} +x^{2} +25+10x=625[/tex]

[tex]2x^{2} +10x-600=0[/tex]

[tex]2x^{2} +40x-30x-600=0[/tex]  ( By Splitting the middle term)

[tex]2x(x+20)-30(x+20)=0\\ \\ (2x-30)(x+20)=0\\[/tex]

solving 2x-30=0   and  x+20=0

we get x=15 and x= -20 ( not possible as distance can't be negative)

x=15.

Therefore , the value of x makes the triangle a right triangle is 15 .

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Square feet of cardboard are used to make each barrel = 23.4558 sq. ft.

The recycling barrels are cylindrical.

Height of the cylinder, h = 3ft

Diameter of the base circle of the cylinder = 30 inches

So radius, r = 15 inches = 15 x 0.083 ft = 1.245 ft

The total surface area of the cylinder is the sum of its lateral surface area and the area of the base and lid circles.

Here the base and lid of the cylinder is made of plastic and sides made of cardboard. So to find the square feet of cardboard required, we need only to find the lateral surface area of the cylinder.

Lateral surface area of the cylinder = 2πrh

                                                           = 2 x 3.14 x 1.245 x 3

                                                           = 23.4558 square feet

So 23.4558 square feet of cardboard is used to make each barrel

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The sum of finite arithmetic series 10+20+30+ . . . . . +110+120 is 780

Suppose we are given an arithmetic series:

   a(1) + a(2) + a(3) + ... + a(n)

The sum of the first nth terms is given by:

S(n) = n/2 [a(1) + a(n)]

Where:

a(1) is the first term and a(n) is the nth term.

The given series is:

    10+20+30+ . . . . . +110+120

We get, then,

a(1) = 10

a(n) = 120

To find n, recall the formula of the nth term of an arithmetic sequence:

a(n) = a(1) + (n-1) . d

where d is the common difference.

From the given series, we get:

d = 20 - 10 = 10

Substitute a(1) =10, d = 10, and a(n) = 120 into the formula:

120 = 10 + (n-1) . 10

120 = 10 n

n = 12

Substitute n = 12 into the sum formula:

S(n) = n/2 [a(1) + a(n)]

S(12) = 12/2 (10 + 120)

         = 6. 130 = 780

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Pressure is defined as the force applied perpendicular to an object's surface per unit area across which that force is dispersed. The proof for calculating water pressure can be given as shown below.

Pressure is defined as the force applied perpendicular to an object's surface per unit area across which that force is dispersed. Gauge pressure is the pressure in relation to the surrounding atmosphere. Pressure is expressed using a variety of units.

The formula given for pressure under water is P=ρgh, where ρ is the density of water, g is gravity, and h is the height of the water.

Now, if the fomula is solved for h it can be written as,

P=ρgh

Divide both the sides of the equation by ρg, therefore, we can write,

P/ρg = ρgh/ρg

h = P/ρg

Now, the value of ρ for water and g is 997 kg/m³ and 9.81 m/sec², respectively. Therefore, we can write,

h = P/(ρg)

h = P/(997kg/m³ × 9.81 m/sec²)

Now, just with the pressure known we can calculate the height of the water column.

Hence, proved.

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Answer:

Step-by-step explanation: