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3x + 2y = 18

2x + 5y = 14 are both linear equations

The system of linear equations in two variables is an equation with two different variables. Any equation with different variables can be in this system.

The solution for this type of equation by solving and getting two different values for both x and y but the same values are used in both equations.

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Answer:

Step-by-step explanation:

You want to know if David's solution of -2x for (5x-4) -(3x) is correct, and what David should have done.

David's solution is correct up to Step 4.

At that point, it appears as though David treated -4 as if it were -4x. The constant cannot be combined with x terms. Step 4 should have been ...

  Step 4: (5 -3)x -4 = 2x -4

David's incorrect solution should have been 2x -4.

Comparing the √17 and 29/7 using <, > or = , we have √17 < 29/7.

Mathematical number comparison is the process or method of comparing two numbers to determine whether one is less, bigger, or equal to the other. The comparison symbols for numbers are "=", which stands for "equal to," "=", which stands for "greater than," and " ", which stands for "less than." Comparing amounts is a technique for figuring out how much to compare units in relation to a different standard or reference unit. A common reference point is necessary for two comparing units to be compared; otherwise, they cannot be compared.

Given,

Comparing the following using <, > or = ,

Numbers:

√17 and 29/7

For √17

Simplifying,

√17 = 4.123

For 29/7

29/7 = 4.14

√17 < 29/7

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The expression that represents Eddie's pay for the week including overtimes are  34.5x + 638.25.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Assuming the no. of extra work hours to be 'x'.

He has a regular work hour of 37 which pays him $(17.25×37) = $638.25.

And his overtime rate is twice his regular rate which is $(2×17.25)

= $34.5.

Therefore, His total pay for the week including his overtime is,

= 34.5x + 638.25 and we can replace x with the given values in the chart

to find his pay for the week.

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The value of the secant angle will be equal to 60°.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given that the secant angle secθ is equal to 2. The value of the angle will be calculated as,

secθ = 2

θ = sec⁻¹(2)

θ = 60°

The secant angle will have a value of 60°.

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Answer: 12 Chaperones, 80 Students

Step-by-step explanation:

92 total - 12 chaperones = 80 students

3 Chaperones per 20 students, sizing that up by 4 you get 12 and 80.

Answer: 2 cm

Step-by-step explanation:

2 x 3 = 6

Answer: julia dog is 300% bigger than jake's

Step-by-step explanation:

The volume of liters equivalent to a 2/3 serving shown using the proportional relationship displayed on a double number line is 4 liters

A number line consists of numbers spread in equal increments or spacing on an horizontal or vertical line.

The volume equivalent to 1/4 serving = 3/2 liters

A volume of 3/2 liters = 1.5 liters

If 3/2 liters = 1/4 serving, therefore;

1 serving = 4 × (3/2) liters = 6 liters

2/3 serving = (2/3) × 6 liters = 4 liters

Similarly: 0.5 liters = (1/4)/3 = 1/12

Expressing the above information on a double number line, we get;

[tex]{}[/tex]                                1.5      2.0     2.5         3.0           3.5            4.0

Vol. in Liters <--------|----------|----------|-----------|-------------|--------------|------------->

[tex]{}[/tex]                               (1/4)    (1/3)        (5/12)    (1/2)        (7/12)        (2/3)

Serving        <---------|----------|-----------|-----------|-------------|-------------|------------->

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Answer:

Step-by-step explanation:

Divide 9 on both sides and you'd get y=3

Answer:

Each boy earned $88.50.

Step-by-step explanation:

Jordan and Ronald each earned $88.50 since they each earned the same amount after Jordan was reimbursed the $20 he spent for gas. This means that the total earnings they received was $177, and since they each earned the same amount, they each earned $177/2 = $88.50.

Answer:

4/6 and 1/6

Step-by-step explanation:

6 is the least common denominator found by multiplying 3 by 2

To find the number of successes x, we need to first find the total number of defective shoes. To do this, we can multiply the total number of shoes selected for quality assurance by the percentage of defective shoes, expressed as a decimal: 386 shoes * 0.0312 = 12.0736. Since we cannot have a fraction of a shoe, we can round down to the nearest whole number to find the number of successes x: 12.0736 rounded down = 12. Therefore, the number of successes x is 12, and the answer is 12.

The slope of the line in the function is 1

The slope of a line is defined as the change in y-coordinate with respect to the change in x-coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx. So the change in y coordinate with respect to the change in x coordinate can be written as,

m = y₂ - y₁ / x₂ - x₁

Taking two points;

Substituting the values into the formula;

m = -2 - 0 / 3 - 5

m = -2 / - 2

m = 1

The slope is calculated as 1

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Answer: 18/24 and 10/24

Step-by-step explanation:

Answer:

x = 19

Step-by-step explanation:

So cos and sin are closely related, but they are not equal. In order for these two to be equal to each other, the angles (in the parenthesis by the cos and by the sin) have to be complementary. That is, they have to add up to 90°

Use this idea to set up an equation.

x + 16 + 3x - 2 = 90

Combine like terms.

4x + 14 = 90

Subtract 14.

4x = 76

Divide by 4.

x = 19

x = 19

If you are kooking for the angles:

x + 16

= 19 + 16

= 35

and

3x - 2

= 3(19) - 2

= 57 - 2

= 55

Check: 35 + 55=90

Also,

cos35 = sin55

Answer:

It is not possible to determine the dimensions of a rectangle with only the information that its area is 2/9. The area of a rectangle is calculated by multiplying its length by its width, so a rectangle with an area of 2/9 could have many different combinations of length and width. For example, a rectangle with dimensions of 1/3 by 2/3 would have an area of 2/9, as would a rectangle with dimensions of 2/9 by 1.

Answer: sin

Step-by-step explanation:

We can consider that table (A) shows a proportional relationship of 7/1.

Relationships between two variables that are proportional occur when their ratios are equal.

Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value.

The "constant of proportionality" is the name of this constant.

So, consider the tables as follows:

Table A:

7/1

14/2 = 7/1

28/4 = 7/1

35/5 = 7/1

Proportional relationship: 7/1

Now, we don't need to calculate further.

Therefore, we can consider that table (A) shows a proportional relationship of 7/1.

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Answer:5 days.w<0.5*34x

Step-by-step explanation:

2/3 is the probability of selecting silver coin from Urn III.

It is a branch of mathematics that deals with the occurrence of a random event.

Urn I: 5 gold coins

Urn II: 2 gold coins and 2 silver coins

Urn III: 3 silver coins

The probabilities of choosing an urn are calculated as shown below:

P(Urn1)+P(Urn2)+P(Urn3)=1/3

First, calculate the probability of choosing a silver coin from the first urn.

P(S1)=0/5

Now, calculate the probability of choosing a silver coin from the second urn.

P(S2)=2/4=1/2

Now, calculate the probability of choosing a silver coin from the third urn.

P(S3)=3/3=1

Now, calculate the probability that the silver coin is selected from Urn III.

P(Silver coin chosen from urn III)=Favorable outcome/Total outcome

=1/3×1/1/3×0+1/3×1/2+1/3×1

=1/3/(1/6+1/3)

=2/3

Hence, the probability of selecting silver coin from Urn III is 2/3.

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The value of 3M + 7N will be;

⇒ 3M + 7N   = [tex]\left[\begin{array}{ccc}-29&-16\\14&81\\\end{array}\right][/tex]

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The values are;

⇒ M = [tex]\left[\begin{array}{ccc}2&-3\\0&6\\\end{array}\right][/tex]

⇒ N = [tex]\left[\begin{array}{ccc}-5&-1\\2&9\\\end{array}\right][/tex]

Now,

The value of 3M + 7N will be;

⇒ 3M + 7N = [tex]\left[\begin{array}{ccc}6&-9\\0&18\\\end{array}\right] + \left[\begin{array}{ccc}-35&-7\\14&63\\\end{array}\right][/tex]

                 = [tex]\left[\begin{array}{ccc}-29&-16\\14&81\\\end{array}\right][/tex]

Thus, The value of 3M + 7N after simplification is;

⇒ 3M + 7N   = [tex]\left[\begin{array}{ccc}-29&-16\\14&81\\\end{array}\right][/tex]

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By using the concept of fraction, it can be calculated that

I will get 64 meals

What is a fraction?

Suppose there is a collection and a part of a collection has to be taken. The part which is taken is called fraction. In other words, part of a whole is called fraction. The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.

This is a word problem on fraction

Weight of 1 meal = [tex]\frac{3}{8}[/tex] pounds

Total weight of meal = 24 pounds

Number of meals I will get = [tex]24 \div \frac{3}{8}[/tex]

                                            = [tex]24 \times \frac{8}{3}[/tex]

                                            = 64

I will get 64 meals

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The value of the expression ((-1/3)^3)^-3 is option (D)  -19683

The given expression is

((-1/3)^3)^-3

The exponent is defined as the number of times the number is multiplied by its self. If the exponent is a^m, then the number a is multiplied m times

According to the power of the power rule is

(a^m)^n = a^(m×n)

We have to apply the power of the power rule in this question

((-1/3)^3)^-3 = (-1 / 3)^(3 × -3)

Multiply the numbers

=(-1 / 3)^-9

We know

(1/a)^-b = a^b

Then the terms will become

= -3^9

Find the power of the number

= -19683

Therefore, the result is -19683

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The main characteristics of a correct diet are those mentioned below:

A correct diet is a diet that is characterized by having the following elements:

Having a correct diet is important for the care of our health in general.

¡Hope this helped!

Slope of the line having passing points (6,-5) and (-6,-5) is 0.

What do you mean by slope of the line?

A line's slope is defined as the ratio of the change in y coordinate to the change in x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.

Hence, the change in y-coordinate with regard to the change in x-coordinate is given by,

m =  change in y/change in x

Given passing points :

(6,-5) and (-6,-5)

Slope of the line having passing points (x,y) and (a,b) is given by [tex]\frac{b-y}{a-x}[/tex]

Slope of the line become , [tex]\frac{-5+5}{-6-6}[/tex] = [tex]\frac{0}{-12}=0[/tex]

Therefore, slope of the line having passing points (6,-5) and (-6,-5) is 0.

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Answer:

42

Step-by-step explanation: