standard form 1.03 expanded notation​

Answer:

Options (C) and (F)

Step-by-step explanation:

Polynomial function is,

f(x) = x³ - x² - 5x - 3

Possible rational roots of the given function will be = \(\frac{\pm1, \pm3}{\pm1}\)

By putting x = -1

f(-1) = (-1)³ - (-1)² -5(-1) - 3

     = -1 - 1 + 5 - 3

     = 0

Therefore, x = -1 will a root of the given function.

Now we apply synthetic division to get the other roots,

-1 |  1       -1       -5      -3

      ↓      -1         2      3

     1       -2       -3      0

Therefore, factored form of the polynomial will be (x + 1)(x² - 2x - 3).

Now we will find the roots of (x² -2x - 3).

x² - 2x - 3 = x² - 3x + x - 3

                = x(x - 3) + 1(x - 3)

                = (x + 1)(x - 3)

For roots of the function, f(x) = 0

(x + 1)(x - 3) = 0

x = -1, 3

Therefore, roots of the function are x = -1, 3

Options (C) and (F) are the answers.

Answer:

The correct answer is true.

Answer:

53\(x_{123}\) == 134 cf

Step-by-step explanation:

A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a​

The height of the building is approximately 78.63 meters.

The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.

Therefore, the height of the building is approximately 78.63 meters.

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Answer:

60

Step-by-step explanation:

puppies : adult dogs

          3:2

total =150

then,  150/5*2

=60

The resulting true inequality from -2 < 3 is 10 > -15

From the question, we have the following parameters that can be used in our computation:

Inequality

-2 < 3

Also, we have

Multiply each side by -5

Using the above as a guide, we have the following:

-5 * -2 < 3 * -5

Evaluate

10 > -15

Hence, the inequality is 10 > -15

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Answer: 1/4 of 70,000,000

Step-by-step explanation: 17,500,000 / 70,000,000 = 0.25

Answer:

\(25\%\)

Step-by-step explanation:

\(\frac{17,500,000}{70,000,000}\)

\(\frac{1}{4}=0.25=25/100=25\%\)

Yes, the expression (64+28+76)/6 makes sense as it represents the average quantity of juice per unit when combining all the shown juices.

To determine whether the expression (64+28+76)/6 makes sense, we need to evaluate the components of the expression and consider whether the mathematical operations are valid.

The expression (64+28+76)/6 represents the sum of three numbers (64, 28, and 76), divided by 6. Let's break it down step by step:

Addition: We have three numbers being added together: 64, 28, and 76. The sum of these numbers is 168 (64 + 28 + 76 = 168).

Division: The sum of the three numbers, 168, is then divided by 6. Division is a valid mathematical operation.

Now, let's analyze whether the expression makes sense in the context of Stephen combining all the juice to make fruit punch. The numbers 64, 28, and 76 may represent quantities of juice (in some units) that Stephen is combining. However, without further information or context, we cannot determine if the expression accurately represents the combination of these juices.

If the numbers 64, 28, and 76 represent quantities of juice in the same units (such as milliliters or liters), then the expression (64+28+76)/6 would represent the average quantity of juice per unit. The result, 168/6, would be 28. This would imply that each unit (e.g., glass or serving) of the fruit punch contains an average of 28 units of juice.

In summary, mathematically, the expression (64+28+76)/6 is valid. However, without additional context regarding the units or quantities being represented, it is not possible to determine whether the expression accurately describes the process of combining the juices to make fruit punch.

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The reason that the point (3, 5) is not a solution to the given inequality is given below.

We are given that;

y > 2x + 1

Now,

The inequality y > 2x + 1 can be graphed by first graphing the boundary line y = 2x + 1. Since the inequality is strict (y >), we draw a dashed line to indicate that points on the line are not solutions to the inequality. Then, we shade the region above the line to indicate all points that satisfy the inequality.

If we have (3,5) as a point, we can see that it lies on the boundary line

y = 2x + 1.

Since the inequality is strict (y >), points on this line are not solutions to the inequality

Therefore, by the inequality the answer will be given above.

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Answer:

y > 1/3 x - 3

Step-by-step explanation:

First, we need to find the equation of the dashed line.

The y-intercept, b, is -3.

The slope, m = rise/run = 1/3.

The equation of the line is

y = 1/3 x - 3

The line is dashed, not solid, so we will use < or >, but not ≥ or ≤.

The shading is above the line, so we use >.

Answer: y > 1/3 x - 3

Answer:

True

Step-by-step explanation:

Angles 1 and 5 match each other; they are congruent and in the same positions. There are therefore corresponding.

HERE IS THE ANSWER!!

Answer: (5 , 1)

Step-by-Step explanation:

hihi your problem is a system of question y = x-4 and  y = -x+6 okay so  graph them both normally and then find the point where they intersect which is gonna be a coordinate point, and that's your solution !!

y = x-4
the y intersect is going to be 4
the slope is a positive 1 , going up to the right, through the positive quadrant, line is facing to the right

y = -x+6
the y intersect is going to be -6
the slope is going to be a -1 , following up the opposite way the line is going to face the left

once you graph them both you'll see the point of intersection, the solution
make sure you drew your lines very clearly !!!!

the solution is  x = 5 and y = 1 which is also (5 , 1)

hopefully this was helpful !

Answer:

6

Step-by-step explanation:

Answer:

2750M

Step-by-step explanation:

2km=2000M

1/2km=500M

1/4km=250M

2000+500+250=2750

Answer:

2750 metres

Step-by-step explanation:

1/4 km= 0.25 km

1/2 km= 0.5 km

2+0.25+0.50= 2.75 km

1 km= 1000 m

2.75*1000= 2750 m

Answer:

option a: -120

Step-by-step explanation:

Answer:

10,800

Step-by-step explanation:

9,000+ 20%= 10,800

The addition of the given fraction expression is 7/8.

In mathematics, an expression is a combination of numbers, symbols, and/or operators that represents a mathematical quantity or relationship. It can be a simple combination of numbers or a more complex combination involving variables, functions, or other mathematical constructs.

When adding fractions with the same denominator, you simply add the numerators and keep the denominator the same.

In this case, both fractions have a denominator of 8, so we can add their numerators:

5/8 + 2/8 = (5 + 2)/8 = 7/8

Thus, the sum of 5/8 and 2/8 is 7/8.

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Answer:

The statements that can be used to compare the characteristics of the functions are:

1. g(x) has the greatest maximum value.

2. All three functions share the same domain.

Explanation:

- The table shows the values of three functions - f(x), g(x), and h(x) - evaluated at different values of x.

- We cannot determine the domain of f(x) or h(x) from the given table but we can see that g(x) has a domain of all real numbers.

- We can see that g(x) has the highest maximum value among the three functions, which is 8.

- We cannot determine the range of f(x) or g(x) from the given table but we can see that h(x) has a range of all negative numbers.

- We cannot say anything about the domain or range of f(x) based on the given table.

- Therefore, the two statements that can be used to compare the characteristics of the functions are: g(x) has the greatest maximum value and all three functions share the same domain.

Total number of rabbits produced in 9 years will be 45.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is a rabbit can produce 5 new rabbits per year

Total number of rabbits produced in 9 years will be -

n = 5y = 5 x 9 = 45 new rabbits

Therefore, total number of rabbits produced in 9 years will be 45.

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Answer:

1. y = 2x + 7

Step-by-step explanation:

The equation of a linear function is y = mx + b. The "x" has to be a first-degree polynomial (no exponents).

The linear relationship illustrated in the provided table can be effectively described by the equation Y = -4x + 2. Option D.

To determine the equation that represents the given table with the values of x and y, we can observe the pattern and find the equation of the line that fits these points.

Given the table:

X: 2 0 4

Y: -4 3 1

We can plot these points on a graph and see that they form a straight line.

Plotting the points (2, -4), (0, 3), and (4, 1), we can see that they lie on a line that has a negative slope.

Based on the given options, we can now evaluate each equation to see which one represents the line:

Y = 1/2x + 5

When we substitute the x-values from the table into this equation, we get the following corresponding y-values: -3, 5, and 6. These values do not match the given table, so this equation does not represent the table.

Y = -1/2x + 3

When we substitute the x-values from the table into this equation, we get the corresponding y-values: 4, 3, and 2. These values also do not match the given table, so this equation does not represent the table.

Y = 2x - 3

When we substitute the x-values from the table into this equation, we get the corresponding y-values: -4, -3, and 5. These values do not match the given table, so this equation does not represent the table.

Y = -4x + 2

When we substitute the x-values from the table into this equation, we get the corresponding y-values: -6, 2, and -14. Interestingly, these values match the y-values in the given table. Therefore, the equation Y = -4x + 2 represents the table.

In conclusion, the equation Y = -4x + 2 represents the linear relationship described by the given table. So Option D is correct.

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The formula for determining slope is expressed as

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

y2 and y1 are the final and initial coordinates of y

x2 and x1 are the final and initial coordinates of x

From the information given,

x1 = 1, y1 = - 7

x2 = - 7, y2 = - 10

Slope = (- 10 - - 7)/(- 7 - 1)

Slope = (- 10 + 7)/- 8

Slope = - 3/- 8

Slope = 3/8

Answer:

Step-by-step explanation:

\(6 \frac{4}{5}=\frac{34}{5}\)

\(3 \frac{2}{9} = \frac{29}{9}\)

\(\frac{34}{5} : \frac{29}{9} = \frac{34}{5}*\frac{9}{29} = \frac{306}{145} \\\)

\(\frac{306}{145}=2\frac{16}{145} \\\)

Answer:

3 is an odd number, so we need an even number of sets of 3 cards because 18 is an even number.

So we need 0, 2, 4 or 6 sets of three.

0 2-card + 6 3-card, 3 2-card+4 3-card, 6 2-card+2 3-card, 9 2-card+0 3-card. There are only 4 combinations:

(2-card, 3-card)=(0,6), (3,4), (6,2), (9,0).

A rectangle that could have a perimeter of 52 feet is a 12 feet by 14 feet rectangle.

The symbols W and L are variables.

The symbol P is a constant.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(L + W)

52 = 2(12 + 14)

52 = 2(26)

52 feet = 52 feet.

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Answer:

I believe  D is the answer to the question above.

Step-by-step explanation:

Answer: pretty sure its D

Step-by-step explanation:

Answer:

The 99% confidence interval for estimating the population mean μ is ($60,112.60, $68087.40).

Step-by-step explanation:

The complete question is:

Salaries of 42 college graduates who took a statistics course in college have a​ mean, \(\bar x\) of, $64, 100. Assuming a standard​ deviation, σ of ​$10​,016 construct a ​99% confidence interval for estimating the population mean μ.

Solution:

The (1 - α)% confidence interval for estimating the population mean μ is:

\(CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\)

The critical value of z for 99% confidence interval is:

\(z_{\alpha/2}=z_{0.01/2}=z_{0.005}=2.57\)

Compute the 99% confidence interval for estimating the population mean μ as follows:

\(CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\)

     \(=64100\pm 2.58\times\frac{10016}{\sqrt{42}}\\\\=64100+3987.3961\\\\=(60112.6039, 68087.3961)\\\\\approx (60112.60, 68087.40)\)

Thus, the 99% confidence interval for estimating the population mean μ is ($60,112.60, $68087.40).

Answer:

Okay so!

Step-by-step explanation:

33, 34, 38, 42, 47, 47, 48, 49, 51.

The median is 47 because it turns up twice.

Answer:

No, because sides JM and KL have different slopes from sides AD and BC.

Step-by-step explanation:

Quadrilateral ABCD is dilated by 2 to form Quadrilateral JKLM. Then the correct option is A.

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

On a coordinate plane, 2 quadrilaterals are shown.

Quadrilateral ABCD has points (2, -2), (4, -2), (3, -4), and (1, -4).

Quadrilateral JKLM has points (4, -4), (8, -4), (6, -9), and (2, -9).

The quadrilaterals are shown below.

Yes, because sides JK and ML are twice as long as sides AB and DC.

The scale factor will be 2.

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