16. Describe the type of solution for the linear system of
equations given below.
2x + 3y = 15
6y=-4x + 12
F.
no solution
G. infinite solutions
H.
one solution
J. two solutions

Answer:

u = -5

Step-by-step explanation:

Isolate the variable, u. Note the equal sign, what you do to one side, you do to the other.

First, combine like terms. Like terms are terms that have the same amount of the same variables:

23 = -8u - 7 + 2u

23 = (-8u + 2u) - 7

23 = -6u - 7

Next, isolate the variable, u. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponsnts (& Roots)

Multiplications

Divisions

Additions

Subtraction

~

First, add 7 to both sides of the equation:

23 = -6u - 7

23 (+7) = -6u - 7 (+7)

23 + 7 = -6u

30 = -6u

Next, divide -6 from both sides of the equation:

-6u = 30

(-6u)/-6 = (30)/-6

u = 30/-6

u = -5

u = -5 is your answer.

~

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Answer:

Step-by-step explanation:

[tex]23= -8u-7+2u[/tex]

[tex]-8u-7+2u=23[/tex]

[tex]-8u+2u-7=23[/tex]

[tex]-6u-7=23[/tex]

[tex]-6x-7+7=23+7[/tex]

[tex]-6u=30[/tex]

[tex]\cfrac{-6u}{-6}=\cfrac{30}{-6}[/tex]

[tex]u=-5[/tex]

f(h(x)) = -2x^2 + 12x + (-12) in terms of x.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range.

To find f(h(x)), we first need to substitute h(x) into f(x).

f(h(x)) = f(4(x-3)²)

Now we can substitute 4(x-3)^2 into f(x)

f(h(x)) = 6 - 1/2(4(x-3)^2)

= 6 - 2(x-3)^2

= 6 - 2(x^2 - 6x + 9)

= 6 - 2x^2 + 12x - 18

Hence, f(h(x)) = -2x^2 + 12x + (-12) in terms of x.

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Answer:16.98$

Step-by-step explanation:

A pound of roast beef costs 8.49

2 pounds of roast cost?

2x8.49=16.98

3.76 many times large is 7.9 x 10⁴ than 2.1 x 10³. This can be solved using scientific notation method.

A method of writing numbers that combines a power of 10 with a number between 1 and 10. Using scientific notation, one may express extremely big or extremely small values. Once a number between 1 and 10 has been multiplied by such a power of 10, it is then expressed in scientific notation. For instance, 6.9 × 10⁸ can be used to represent the number 690,000,000.

The main goal of scientific notation is to simplify computations using numbers that are abnormally big or tiny. When a number is written in scientific notation, all of the digits are important since zeros are no longer utilized to set the decimal point.

For: 7.9 x 10⁴

= (79/10) x 10⁴

= 79 x 10³

on the other hand for: 2.1 x 10³

Thus, 3.76 many times large is 7.9 x 10⁴ than 2.1 x 10³.

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The domain is discrete, and point (5, 10) lies on the graph. Then the correct option is C.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

You download a digital soccer game for $2.50. You can add new players for $1.50 each to upgrade your team.

The number of players will be in a whole number. Then the function is given by the greatest integer function.

Let 'y' be the total cost and 'x' be the number of players. Then the equations are given as,

y = 1.50 [x] + 2.5

The total cost for 5 new players will be given as,

y = 1.50 [5] + 2.5

y = 7.5 + 2.5

y = 10

The domain is discrete, and point (5, 10) lies on the graph. Then the correct option is C.

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Answer:

multiple everything by three so say 3×-9x is -27x and 3 ×8 is 24 and you would then divide -27x by 24 and you would get -27x+24 I think

The area of shaded figure rectangle is 7.5m²

The amount of space occupied by a flat surface with a particular shape is referred to as the area. It is calculated using the "number of" square units (square centimeters, square inches, square feet, etc.) The amount of unit squares that can fit inside a rectangle is its area. The flat surfaces of laptop monitors, blackboards, canvas, etc. are a few examples of rectangular shapes.

step1:

The formula for the area of the Rectangle  is:

A= a+ b/2*h= 3+3/2*7=31.5

step2:

The formula for the area of the rectangle is:

A=w l=3*8=24

Now you rest 31.5 -24 and it gives you 7.5

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if in ΔXYZ, y = 500 inches, mm∠Y=117° and mm∠Z=10° then length of z is 97.64 inches.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given that ΔXYZ, y = 500 inches, mm∠Y=117° and mm∠Z=10°.

We have to find the length of z.

By using sine rule we find the length of z.

sin117/500=sin10/z

0.891/500=0.174/z

Apply cross multiplication

0.891z=0.174×500

0.891z=87

z=87/0.891

z=97.64 inches

Hence, if in ΔXYZ, y = 500 inches, mm∠Y=117° and mm∠Z=10° then length of z is 97.64 inches.

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Answer:

97

Step-by-step explanation:

we determined median = 140 and lower quartile = 105.

Median is the middle value of a set of data. Median is determined by the formula, median = 2/4 (N+1)th term, where N is the number of data set.

Quartile is a statistics terms defines that a list of data is divided into four parts. There are three quartiles in the statistics data such as lower quartile, middle quartile and upper quartile.

lower quartile = 1/4(N+1)th term

upper quartile = 3/4(N+1)th term

the median is called the middle quartile.

From the histogram we obtain the data below

80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200

number of data, N = 13

median = 2/4 (N+1)th term= 1/2 ×14 = 7th term

we find 7th term is 140.

median = 140

lower quartile= 1/4× (N+1)th = 1/4 × 14 = 3.5 th term

that means average of 3 and 4th term.

lower quartile = (100 + 110) /2 = 105

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Answer:

Question 8: (-4,7)

Question 10: (5,2)

Step-by-step explanation:

What are equations?:

What is Substitution Method?:

y = -2x - 1

3x - 4y = -40

Question 8:

3x - 4(-2x-1) = -40

3x + 8x + 4 = -40

11x + 4 = -40

11x = -44

x = -4

To find y we can substitute x into the equation.

y = -2(-4) -1

y = 8 -1

y = 7

(-4,7)

Question 8 Solution - (-4,7)

Question 10:

2x - y = 8

x = 5

Since this equation already given x we can substitution to find y.

2(5) - y = 8

10 - y = 8

-y = -2

y = 2

(5,2)

Question 10 Solution - (5,2)

Lenvy~

Answer:

-5x+5

Step-by-step explanation:

That would be the answer

Answer:

-87

Step-by-step explanation:

y=2

3y(2-7)-3(y-4)-63 
3(2)(2-7)-3(2-4)-63 

6(2-7)-3(2-4)-63

6(-5)-3(-2)-63

-30+6-63=-87

Answer:

50,000+30,000+13852=93,852

Answer:

(x+2)(4x-1)

For this problem, use the FOIL (first, outside, inside, last) method

You have x, 2, 4x, and -1. Start by multiplying x by 4x and -1. Then multiply 2 by 4x and -1. You should have four separate values to add together.

(x*4x)+(x*(-1))+(2*4x)+(2*(-1)) = 4x^2+(-x)+8x+(-2)

Once you have this, order each value by their exponents and combine like terms. The highest exponents always go to the left and lowest exponents go to the right.

4x^2+7x-2

The algebraic expression 15(2 + r) by the distributive property can be written as 30 + 15r.

This property states that multiplying the sum of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the algebraic expression is 15(2 + r). The expression by using the distributive property can be written as:-

E = 15(2 + r)

E = 30 + 15r

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Journalize the adjustment entries on August 31 for the $500 in golf income during the three-month period from June 1 to August 31.

By dividing the principal by the interest rate, the passage of time, and other factors, simple interest is determined. Simple return equals principal plus interest plus hours is the formula used in marketing. The easiest way to compute interest is by using this method. The most typical method for calculating interest is as a portion of the principal amount. For example, if he borrows $100 from a buddy and agrees to pay back the loan at 5% interest, he will only pay his share of the 100% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and you must charge interest when you lend it. Typically, interest is determined as an annual percentage of the loan total. The loan's interest is the name given to this percentage.

given

First FMA Assignment

Jornal 1.

2. Accounts Title Date (Mar) Debit ($) Credit ($)

1 Cash 60,000

60,000 Common Stock

3 Land 23,000

Structures 9,000

6k in equipment

Cash 38,000

5) Marketing Costs 1,600

Cash 1,600

Golf Sales 800

19) Cash (100 x 15) 1,500

1,500 in unearned revenue

25,000 dividends

Cash 1,000

30) salaries and 600 in expenses

Cash 600

30) Payable Accounts 26,000

Cash 26,000

31) Cash 500

500 Golf Revenue

Journalize the adjustment entries on August 31 for the $500 in golf income during the three-month period from June 1 to August 31.

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16 is the number  gives a result of −4 when 8 is subtracted from the quotient of the number and 4.

A division is a process of splitting a specific amount into equal parts.

If it gives a result of -4 then our equation will have ___ = -4

If we subtract 8 from the quotient of a number and 4 we have  x/4 - 8

Our equation is:

x/4 - 8 = -4    

Add 8 to both sides

x/4=-4+8

x/4=4

Multiply both sides by 4

x=16.

Hence, 16 is the number  gives a result of −4 when 8 is subtracted from the quotient of the number and 4.

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Note that where the following values are given: 0, 3, 4, 6, 9, 10, 11, 12, 16, the respective quartile values are:

The minimum = 0

The first quartile (Q₁) is = 3.5

The median (Q₂) = 9

The third quartile (Q₃) = 11.5

The maximum = 16

The IQR = 8 .

The median is the value that separates the upper and lower halves of a data sample, population, or probability distribution in statistics and probability theory.

It is to be noted that sometimes referred to as "the middle" value in data collection.

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A term that means the same as the term "variable" in an ANOVA procedure is a factor.

A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.

There are two methods of finding factors: multiplication and division. In addition, rules of divisibility may also be used.

Let us consider the number 8. 8 can be a product of 1 and 8, and 2 and 4. As a result, the factors of 8 are 1, 2, 4, and 8. Therefore, when finding or solving problems involving factors, only positive numbers, whole numbers, and non-fractional numbers are considered.

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In a party of 300 people, 54% of the people who would have someone to kiss is 162 people.

A percentage is a number or ratio that can be expressed as a fraction of 100 in mathematics. If we need to calculate the percentage of a number, divide it by the whole and multiply by 100. As a result, the percentage denotes a part per hundred.

To determine the percentage of people with partners to kiss at midnight;

300 people present in party

54% will have someone to kiss = 0.54

Number of people that will have someone to kiss = 300 x 0.54 = 162

The 54% of people with someone to kiss are 162 in number.

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Answer: In an experiment, if the probability that event A occurs is 0.2 and the probability that event B occurs is 0.5, then the probability that either event A or event B (or both) will occur is the sum of their individual probabilities, which is 0.2 + 0.5 = 0.7.

It should be noted that the sum of the individual probabilities of two events is less than or equal to 1. If the sum of the probabilities is greater than 1, it means that the events are not mutually exclusive and that means that they can happen at the same time.

It's important to mention that the above answer is based on the assumption that events A and B are mutually exclusive events, which means that they cannot happen at the same time. If they are not mutually exclusive, the probability of both occurring at the same time would have to be calculated using the formula P(A and B) = P(A) * P(B|A) where P(A) is the probability of event A occurring and P(B|A) is the probability of event B occurring given that event A has already occurred.

Step-by-step explanation:

The vertices of the image after transformation is K(5,-2), L(-1,3) and M(4,-5)

A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same.

A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question.

According to the given question,

with respect to the mirror

the vertices of the image of the triangle is

J (2,-5) ---------->! (5,2)

K (-1, -3) --------> K'(-1,3 )

L (-4, 5) --------->"(4,-5 )

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The value of the evaluated iterated integral is = 0.002

As per the given data the iterated integral is, [tex]I[/tex] = [tex]\int\limits^1_0[/tex] [tex]\int\limits^s_0[/tex] cos ([tex]s^{6}[/tex] ) [tex]dt ds[/tex]

Here we have to evaluate the given iterated integral.

The definite integral of a real-valued function f(x) with respect to a real variable x on an interval [a, b] is expressed as,

[tex]\int\limits^a_b f({x} )\, dx[/tex] = f(b) - f(a)

Where,

a = Lower limit

b = Upper limit

f(x) = Integrand

dx = Integrating agent

Thus, [tex]\int\limits^_[/tex] ab f(x) dx is read as the definite integral of f(x) with respect to d x from a to b.

Indefinite integrals are implemented when the boundaries of the integrand are not specified.

[tex]I[/tex] = [tex]\int\limits^1_0[/tex] [tex]\int\limits^s_0[/tex] cos ([tex]s^{6}[/tex] ) [tex]dt ds[/tex]

Integrate the given iterated integral.

We get:

= [tex]\int\limits^1_0[/tex] cos ([tex]s^{6}[/tex] ) ([tex]\int\limits^5_0dt[/tex] ) ds

= [tex]\int\limits^1_0[/tex] cos ([tex]s^{6}[/tex] ) [t][tex]0 to s^{5}[/tex] ds

= [tex]\int\limits^1_0[/tex] cos ([tex]s^{6}[/tex] ) [tex](s^{5} -0)[/tex] ds

= [tex]\int\limits^1_0[/tex] [tex]s^{5}[/tex]cos ([tex]s^{6}[/tex] )ds

Then,

[tex]s^{6}[/tex] = t       when s = 0

[tex]\frac{dt}{ds}[/tex] = 6[tex]s^{5}[/tex]         t = 0  

[tex]\frac{dt}{6}[/tex] = [tex]s^{5}[/tex]  ds      when s = 1.....   t = 1

Replace the assumed terms.

Then we get:

[tex]I[/tex] = [tex]\int\limits^1_0[/tex] cos(t) [tex]\frac{dt}{6}[/tex]

[tex]I[/tex] = [tex]\frac{1}{6}[/tex] [tex]\int\limits^1_0[/tex] cos(t) dt

[tex]I[/tex] = [tex]\frac{1}{6}[/tex] [sin(t)][tex]0to1[/tex]

[tex]I[/tex] = [tex]\frac{1}{6}[/tex] [ sin(1) - sin(0) ]

[tex]I[/tex] = [tex]\frac{sin(1)}{6}[/tex]

[tex]I[/tex] = 0.002

Therefore,

The value of the evaluated iterated integral is = 0.002

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The provided model represents the expression 4x-3.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign.

Here,

You have 4 x's, then you minus 3,

=4x-3

The expression is represented by the model given is 4x-3.

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The correct option is:

d) Median is a better measure of central tendency

When a graph of a distribution of data is symmetric, it means that the left and right sides of the graph are mirror images of each other. This indicates that the data is evenly distributed around the center and that there are no extreme outliers. In such cases, the median is the best measure of central tendency, because it is the middle value of the dataset and it represents the center of the data distribution. The median is not affected by outliers.

The mean, mode, and midrange are also measures of central tendency, but they may not be as representative of the center of the data distribution when the data is symmetric. The mean is sensitive to outliers, the mode is the value that appears most frequently in the data, and the midrange is the average of the maximum and minimum values.

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Answer:

d

Step-by-step explanation:

Answer:

Step-by-step explanation:

∠ADB=360-90=270°

circumference of circle=2πr=2π×3=6π m

length of arc ADB

[tex]=\frac{270}{360} \times 6\pi \\=\frac{3}{4} \times 6\pi \\=\frac{9}{2} \pi \\\approx 14.137~m\\[/tex]

area of circle =πr²=π×3²=9π m²

area of shaded region

[tex]=\frac{270}{360} \times 9\pi \\=\frac{27}{4} \pi ~m^{2} \\\approx 21.206~m^2[/tex]