Which of the following statements must be true based on the diagram below?
Select all that apply. (Diagram is not to scale.)

Answer: This system of equations can be represented in matrix form as

| -1 | 650 | 175 |

| 75 | -120 | -25080 |

This matrix is called the augmented matrix of the system of equations. The first and second column of this matrix represent the coefficients of the variables x and y, respectively, in the system of equations. The third column represents the constant terms of the equations.

You can use a method such as Gaussian elimination or Gauss-Jordan elimination to solve the system of equations.

The Gaussian elimination method, you would use elementary row operations to transform the matrix into an echelon form or reduced row echelon form. Then you can back-substitute the variables with their values.

Also, the Gaussian-Jordan elimination is similar to Gaussian elimination, but it keeps continuing the elimination process until the matrix becomes an Identity matrix(A matrix with 1 on diagonal and 0 everywhere else) The values on the diagonal of the matrix will give you the solution of the variables.

Step-by-step explanation:

Answer:

2/5

Step-by-step explanation:

To find the fraction that is sugar,

part sugar/ total

The total is sugar + flour = 8+12 = 20

8/20

We can simplify

Divide the top and bottom by 4

8/4 =2

20/4 = 5

The fraction is 2/5

Answer:

[tex]\sf\frac{8}{20}[/tex]

Step-by-step explanation:

First let us find the total.

Total = Flour + Sugar

Total = 12 + 8

Total = 20

Now we know that, there are 8 tablespoons of sugar in the whole mixture.

So, write it as a fraction, you have to divide the number of tablespoons of sugar by the total.

Sugar = 8/20

Answer: To solve the quadratic equation 8x^2 + 16x + 3 = 0, Patel could use the following steps:

Divide both sides of the equation by 8 to obtain x^2 + 2x + 3/8 = 0.

Rewrite the equation in the form (x + a)^2 = b by completing the square: x^2 + 2x + (1/2)^2 = (1/2)^2 - (3/8).

Rewrite the equation as (x + a)^2 - b = 0. In this case, a = 1/2 and b = -3/8.

Use the quadratic formula to solve for x:

x = (-1/2) +/- sqrt((1/2)^2 - (-3/8))

= (-1/2) +/- sqrt(5/8)

= (-1/2) +/- sqrt(40/64)

= (-1/2) +/- sqrt(10/16)

= (-1/2) +/- (5/8)

= -1 +/- 5/8

= -1 + 5/8 or -1 - 5/8

= -7/8 or 1/8

Therefore, the solutions to the quadratic equation are x = -7/8 or x = 1/8.

Step-by-step explanation:

Answer: option b), option c), and option e) are correct options.

Step-by-step explanation:

Given:

The area of a rectangular room= 750 square feet

The width of the room = 5 feet less than the length of the room

The length of the room = Y

To find:

Equations that can be used to solve the value of Y i.e. the length of the rectangular room.

Solution:

The equation can be derived from using the following formula:

Area of rectangle = length * width

According to the question,

Length of the rectangular room = Y

Width of the rectangular room = 5 feet less than the length of the room

                                                       = (Y-5)

Since, Area of rectangle = length * width

Area of the rectangular field = length of the room* width of the room

                          750             = Y (Y – 5)                         ………..eqn. (1)

Or, the above equation can be solved a step further and written as

                          750             = Y2 – 5Y                          ………..eqn. (2)

                         750- Y2 + 5Y= 0                                    ………..eqn. (3)

                         750-Y (Y- 5) =0                                    ………..eqn. (4)

Apart from the above equations, if we solve eqn. (2) we get the following equation:

                          750             = Y2 – 5Y

                           Y2 – 5Y- 750= 0

                          Y2 – 30Y + 25Y- 750 = 0

                          Y (Y- 30) + 25 (Y- 30) = 0

                                                                   take Y- 30 common from L.H.S.

                           (Y -30) (Y+ 25)   = 0                            …………….eqn. (5)        

Hence, the correct options are option b), option c), and option e).

In algebra, the vertex form of a quadratic equation is a way of expressing the equation in the form:[tex]y = a(x - h)^2 + k[/tex]

where (h, k) is the vertex of the parabola defined by the equation. The value of 'a' determines whether the parabola opens up or down and the value of 'h' and 'k' determine the position of the vertex on the coordinate plane.

For example, the standard form of a quadratic equation is:

[tex]y = ax^2 + bx + c[/tex]

To convert this to vertex form, you would first complete the square to get all the terms of x on one side of the equation and a constant on the other side. Then, you would put the equation in the form shown above.

So, given the equation [tex]y = 3x^2 + 6x - 4[/tex], we can complete the square to get:

[tex]y = 3(x^2 + 2x) - 4[/tex]

then rearrange it to

[tex]y = 3(x^2 + 2x + 1) -7 = 3(x+1)^2-10[/tex] which is in vertex form with vertex (-1,-10)

The vertex form of a quadratic function provides a convenient way to quickly identify the vertex of the parabola without having to complete the square every time.

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The correct question is:

Explain vertex form.

The product of f(x) and g(x) is always a polynomial. By the definition of

polynomials the product of polynomials is always a polynomial because

the coefficient are real numbers and the exponents are whole

numbers. Real numbers and whole numbers are closed under addition

and subtraction.

A polynomial is a mathematical expression involving a sum of powers in one or more variables (indeterminates) with coefficients, that is either a constant or the indeterminates (also called variables or x's). The most common examples are the quadratic equation, cubic equation, and so on. The degree of a polynomial is the highest power of the indeterminate in the polynomial. For example, a polynomial with three indeterminates to the power of 2 is said to have a degree of 2.

Here f(x) and g(x) are two given polynomial,

let f(x) = x+1 ang g(x) = x-1

f(x).g(x) = (x+1)(x-1).

f(x).g(x) = x²-1.

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Answer: The statement you've provided describes the economic concept of elasticity. Elasticity is a measure of how responsive the quantity demanded or supplied of a good or service is to a change in its price. It measures the responsiveness of the consumers' and producers' behaviors to changes in price, in other words, how sensitive the consumers or producers are to changes in the good or service prices.

There are different types of elasticity, such as price elasticity of demand and price elasticity of supply. Price elasticity of demand measures how much the quantity demanded of a good changes in response to a change in its price. If a good has a high price elasticity of demand, then a small change in its price will result in a large change in the quantity demanded of the good. On the other hand, price elasticity of supply measures how much the quantity supplied of a good changes in response to a change in its price. A good with a high price elasticity of supply will see a large increase in the quantity supplied in response to a small price increase.

Elasticity is a very important concept in economics because it helps to understand how consumers and producers will react to changes in prices and how it would affect the overall economy.

Step-by-step explanation:

Solution

 16 dm=160 cm

50 cm* 160 cm= 8000 cm²= 0,8 m²

odp C

The slope of the line, given the point on the line and the y - intercept, is - 5. 33

The slope of a line tells us the relationship between the dependent variable and the independent variable. In other words, it tells us what a change in the independent variable leads to in the dependent variable.

The slope can be found in the slope - intercept formula form of :

y = mx + b

m is the slope

b is the y - intercept

We have the y - intercept and a y and x value in ( -3, 6 ) so the slope is:

6 = - 3 ( m ) + ( - 10 )

6 = - 3m - 10

- 3m = 6 + 10

- 3 m = 16

m = 16 / - 3

m = - 5. 33

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The maximum value considering DP of a and b is 9.52.

The decimal places of a number are the number of digits to be considered after the decimal point. E.g Round 4.7583 to 2 dp, we have;

4.76 3 dp

The maximum value of a sum of numbers is the highest value obtained when these numbers are added one to each other. The decimal places of each number is put into consideration in the process.

From the given question;

a = 8.7 and b = 0.82

Thus,

a + b = 8.7 + 0.82

        = 9.52

a + b = 9.52

Therefore, the maximum of a + b = 9.52

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Answer: Congruent by AAS

Step-by-step explanation:

FG and EH are congruent because they are given.

EH is perpendicular to EG because of the definition of perpendicular lines. Lines are perpendicular if they create right angles when they intersect.

FG is perpendicular to EG because of the definition of perpendicular lines. Lines are perpendicular if they create right angles when they intersect.

Angle G is congruent to Angle E because they are both right angles, and right angles are congruent.

Angle EIH and Angle FIG are congruent because of the vertical angles theorem.

Triangle EHI and Triangle GFI are congruent by the Angle-Angle-Side Theorem, or AAS.

Answer:

Step-by-step explanation:

$4.50 + $4.50(0.15) = $5.18

$2.25 + $2.25(0.15) = $2.59

$3.00 + $3.00(0.15) = $3.45

Answer:

45ft is the missing length j.

Answer:

y > X/2 - 3

I think that's the answer.

The time to build the fence will be 10 hours.

The fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since construction company is building a fence that is 1 1/3 miles long and they can building the fence 1/6 Mile every hr.

The time to build the fence will be:

= 1 1/3 ÷ 1/6

= 5/3 × 6/1

= 30 / 3

= 10 hours.

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On solving the provided question, we can say that - by the help of unitary method the value of 9 units will be

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

here,

cost for the 12 classes = $72

cost of 1 unit = $6

cost of 9 units = $54

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Answer:

Step-by-step explanation:

Answer:

Option A) [tex]3\frac {1}{2}[/tex]

Step-by-step explanation:

In order to find the diameter you need to multiply the radius x 2

Over here the radius is given as 7/4cm

But the diameter is

[tex]\frac{7}{4} X\frac{2}{1}[/tex] = [tex]\frac{7}{2}[/tex]

And when we simply the mixed fractions we only get one possible answer

which is [tex]3\frac{1}{2} = \frac{7}{2}[/tex] Option A)

Answer:

B

Step-by-step explanation:

Center of the distributions -> mean/median (preferably mean)

The option with range is eliminated

Median might not be accurate as median is the center person, not the center result.

Based on the graphs, identify the graph with the intervals of greatest frequency.

For North Heights -> between 30 and 32 (right-skewed, some higher values)

For Southview -> between 28 and 30 (most concentrated there)

Hence, mean of Southview is lower than North Heights.

The United States' entry into World War I led to a rise in nationalism and patriotism, as well as a shift towards a more interventionist foreign policy. This had a lasting impact on the culture and international political policies of the country.

The United States' entry into World War I marked a significant shift in the culture of the country. Prior to the war, the United States had maintained a policy of isolationism, with a focus on avoiding involvement in foreign conflicts. However, the country's entry into the war marked a shift towards a more interventionist foreign policy, as the United States began to take a more active role in international affairs.

Unit rate is the quantity of an amount of something at a rate of one of another quantity.

The rate at which the oil burns.

1 hour = 2/3 ounce

At 12 noon = 193/3 = 64.33 ounces

At 2 pm = 63 ounces

At 5 pm = 61 ounces

The amount of oil at 12 noon is 64.33 ounces.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

A camper lights an oil lantern at 12 noon and lets it burn continuously. Once the lantern is lit, the lantern burns oil at a constant rate each hour.

At 2 p.m., the amount of oil left in the lantern is 63 ounces.

At 5 p.m., the amount of oil left in the lantern is 61 ounces.

This means,

Amount of oil burnt in the lantern from 2 pm to 5 pm.

= 63 ounces - 61 ounces

= 2 ounces

Now,

3 hours = 2 ounces

2 hours = 1.33 ounces

1 hour = 0.67 ounces

Now,

The number of hours from 12 noon to 2 pm.

= 2 hours

So,

The amount of oil at 12 noon.

= 63 + 4/3

= (189 + 4) / 3

= 193/3 ounces

Thus,

The amount of oil at 12 noon is 65 ounces.

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On solving the provided question, we can say that - the value the exponent [tex]10^n\\[/tex] will be 100000

Exponentiation, often known as "b raised to the nth power," is a mathematical operation denoted by the symbol bn that involves two numbers: a base number, b, and an exponent, or power, n. Exponents show how many times a number has been multiplied by itself. As an illustration, 2-3 (written as 23) denotes: 2 x 2 x 2 = 8. 23 is not equivalent to 2 + 3 = 6. Recall that an integer raised to the power of one equals itself. A approach to express huge numbers as powers is through the use of exponents. Exponent, then, is the quantity that indicates how many times a number has been multiplied by itself. As an illustration, 6 is multiplied by 4 to provide 6 x 6 x 6 x 6. It may be expressed as 64. 4 is where

from the given exponents we have

[tex]10^n[/tex]

where n = 5

so [tex]10^5 = 100000[/tex]

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Answer:

Step-by-step explanation:

-140

The answer to |-14| is 14

In the graph of a quadratic function with vertex (2, -4) is shown in the figure, the Domain: -∞ < x < ∞ and Range: -4 ≤ x < ∞.

When a polynomial function has one or more variables and the highest exponent of any one of the variables is two, the function is said to be quadratic function.

A polynomial of degree 2 is referred to as such because the highest degree term in a quadratic function is of second degree. There must be at least one second-degree term in a quadratic function. This function is algebraic.

Domain for this quadratic function is all possible values of x where function is defined.

Thus, Domain: -∞ < x < ∞

Range is the set of value functions that correspond to the value 'x.'

Range: -4 ≤ x < ∞

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Answer:

In the form of y=mx+b:

y = -5/6x-5

Step-by-step explanation:

I'm not that good at explaining, but I'll try:

Slope intercept is y=mx+b, M is the slope of the line which is rise over run, the rise is -5 (distance traveled along y-axis) and the run is 6 (distance traveled along x-axis) found from two points: (-6, 0) and (0, -5). Using this data -5/6 can be plugged in for M, and b is the y variable at (0, _) in this case the y variable is -5. The final answer after plugging everything in is y=-5/6x-5, I hope this wasn't too confusing.

Answer:

1/2

Step-by-step explanation:

Slope(m)

= (y2 - y1)/(x2 - x1)

= (8 - 1)/(7+7)

= 7/14

= 1/2