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BOOKMARK
Simplify each of the following expressions:
-5 - 2 + 8 =

Answer:

17x + 37

Step-by-step explanation:

looked it up

Answer:

Y=KX so its 10=K2

Step-by-step explanation:

Plug in the Number OR K=y/x

By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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Answer:

5n(2n^2-7n+5)

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

They are between integers so they can't be a whole number nor the integer

~~~Hope this helps~~~

Answer: C

Step-by-step explanation:

The statement that is false is no integers are irrational numbers.

Every single integer is a rational number because they do not go on forever.

The answer to the question is option C. Hope this helps!

The smallest number of students who go to one of these clubs is 21.

A stem-and-leaf diagram is a quantitative assessment of a collection of data in which the data values are divided into a "stem" (the first digit of the number) and a "leaf" (the remainder of the number) (the last digit of the number).

Based on the given stem and leaf diagram, the smallest number of students who go to one of these clubs is represented by the leaf value "1" in the stem "2."

Therefore, the smallest number of students who go to one of these clubs is 21.

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Answer:

Step-by-step explanation:

i think that its by 10 percent so sorry if im wrong!

Answer:

20%

Step-by-step explanation:

100/20 (the number of questions) = 5 (how much each question is worth)

16(the number of questions she got correct) times 5 is 80

She got 80 percent correct

That means that she missed 20 percent

A total of 7 Cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.

A line plot is drawn with the cyclists' names plotted on the x-axis and their corresponding distances covered plotted on the y-axis.

The dots are then joined to form a line, revealing the relationship between the cyclist's names and their corresponding distance traveled. The cyclist names and their corresponding distances are given in the table below.

Name Distance (in miles) Gina 40 1/2 Rey 50 Faye 35 3/4 Mark 60 John 45 1/2 James 40 1/2 Albert 40 1/4 William 54 1/4 Nathan 40 Kate 40 1/4 Mary 60 Risa 40 Abi 35 3/4 Joan 50 1/2 1. The number of cyclists is 14. 2. The longest distance covered by a cyclist is 60 miles.

Mary and Mark both covered this distance.3. A total of 7 cyclists traveled less than 50 miles. 4. The most common distance traveled by cyclists is 40 1/2 miles. Gina, James, and Albert covered this distance. 5. 2 more cyclists traveled 45 miles than 55 1/4 miles. Only William traveled 55 1/4 miles, while John and James both traveled 45 1/2 miles.6.

A total of 7 cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.

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Answer: y= 3x+22

70=3x+22

70-22=3x

58=3x

58/3=x

19.33

He needs to buy at least 19 GB

Step-by-step explanation:

At 6 minutes the two airplanes will be at the same altitude and 16200 be will that altitude. When  An airplane is preparing to land at an airport. It is 34,200 feet above the ground and is descending at the rate of 3,000 feet per minute. At the same airport, another airplane is taking off and will ascend at the rate of 2,700 feet per minute.

A triangle's altitude is determined by drawing a perpendicular line from its vertex to its opposite side. The altitude, sometimes referred to as the triangle's height, forms a right-angle triangle with the base.

Given

An airplane is preparing to land at an airport. It is 34,200 feet above the ground and is descending at the rate of 3,000 feet per minute. At the same airport, another airplane is taking off and will ascend at the rate of 2,700 feet per minute.

Altitude equation:

y = 34200 - 3000x

y = 2700x

2700x = 34200 - 3000x

2700x + 3000x = 34200

5700x = 34200

x = 6

For altitude,

y = 2700x

y = 2700(6)

y = 16200

At 6 minutes the two airplanes will be at the same altitude and 16200 be will that altitude.

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The solution is -2x^2 - 20x - 53 is the standard form of the given vertex form.

Here, we have,

Vertex and standard form of an equation

Given the vertex form of a quadratic equation expressed as:

y = -2(x+5)^2 - 3

The standard form is in the form y = ax^2 + bx + c

Expand the given vertex form

y = -2(x+5)^2 - 3

y = -2(x^2+ 10x + 25) - 3

y = (-2x^2 - 20x - 50) - 3

y = -2x^2 - 20x - 53

Hence the standard form of the given expression is -2x^2 - 20x - 53

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complete question:

Convert the following from vertex to standard form

The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).

To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.

1. Find the derivative of the function:

  y' = 3x² - 6x - 9

2. Set the derivative equal to zero and solve for x:

  3x² - 6x - 9 = 0

3. Factorize the quadratic equation:

  3(x² - 2x - 3) = 0

4. Solve the quadratic equation by factoring or using the quadratic formula:

  (x - 3)(x + 1) = 0

  This gives us two possible values for x: x = 3 and x = -1.

5. Substitute these critical points back into the original function to find the corresponding y-values:

  For x = 3:

  y = (3)³ - 3(3)² - 9(3) + 4

    = 27 - 27 - 27 + 4

    = -23

  For x = -1:

  y = (-1)³ - 3(-1)² - 9(-1) + 4

    = -1 - 3 + 9 + 4

    = 9

6. Therefore, the turning points are (3, -23) and (-1, 9).

Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.

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The number of inches apart that the four bolts will be along the circumference of the metal plate shown in the figure is 9.425 inches.

The circumference refers to the total distance around a circle.

The circumference can determined using the following formula.

Circumference = 2πr

Diameter of the circle = 12 inches

Radius = 12/2 inches = 6 inches

Circumference = 2 x 22/7 x 6

= 37.7 inches

The number of bolts along the circumference = 4

Distance between the four bolts = 9.425 inches (37.8 ÷ 4)

Thus, using division operation, the distance apart of the four bolts is 9.425 inches.

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The country's area is 117% of Iowa's area, indicating that the country's area is 17% more than Iowa's area.

To find the percentage that represents the country's area in comparison to Iowa's area, we need to calculate the ratio of the country's area to Iowa's area and then express it as a percentage.

Let's assume that the area of Iowa is represented by x. According to the given information, the area of the country is 17% more than the area of Iowa. Therefore, the area of the country can be calculated as 1.17x (x + 17% of x).

To find the percentage of the country's area in comparison to Iowa's, we need to divide the area of the country by the area of Iowa and multiply the result by 100:

[(1.17x) / x] * 100

Simplifying this expression, we get:

(1.17 * 100) = 117

The country's area is 117% of Iowa's area.

The country's area is 117% of Iowa's area, indicating that the country's area is 17% more than Iowa's area.

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Answer: x = 9

Step-by-Step Solution:

Hypotenuse = 15 units

Base = 12 units

Altitude = x units

Using Pythagoras Theorem,

=> Hypotenuse^2 = Base^2 + Altitude^2

(15)^2 = (12)^2 + x^2

225 = 144 + x^2

225 - 144 = x^2

81 = x^2

x^2 = 81

x = √81

=> x = 9

Therefore, Altitude = 9 units

Answer:

D. 5^6

Step-by-step explanation:

\(5^2*5^4\\5^2^+^4\\5^6\)

Answer:

55

Step-by-step explanation:

\(\displaystyle MOE = z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\4=1.96\biggr(\frac{15}{\sqrt{n}}\biggr)\\\\4=\frac{29.4}{\sqrt{n}}\\\\\sqrt{n}=\frac{29.4}{4}\\\\\sqrt{n}=7.35\\\\n=54.0225\\\\n\approx55\uparrow\)

Make sure to always round up the required sample size to the nearest integer!

Answer:

Let x be the other number.

3x+8+x=32

4x=24

x=6

Hence the two numbers are 26 and 6.

To determine the regression equation, we need to fit a line to the data that best describes the relationship between the dependent variable and the independent variable. The equation of the line is typically expressed in the form:

where y is the dependent variable, x is the independent variable, a is the y-intercept (the point at which the line crosses the y-axis), and b is the slope of the line (the rate of change of y with respect to x).

If we determine that a = 10 and b = 0.5, the regression equation would be:

This equation describes the relationship between the dependent variable (days-on-the-market) and the independent variable (price). It tells us that for every unit increase in price, the number of days on the market is expected to increase by 0.5.

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The set (A U B) n (A U C) is {2, 5, 7, 10}. A.

To find the set (A U B) n (A U C), we first need to calculate the union of sets A and B, and then calculate the union of that result with set C. Finally, we find the intersection of these two sets.

Set A U B:

The union of sets A and B, denoted as A U B, is the combination of all elements from both sets without any repetitions.

A contains the elements 2, 5, 7, and 10, while B contains the elements 1, 2, and 3.

A U B consists of the elements {1, 2, 3, 5, 7, 10}.

Set (A U B) U C:

Next, we calculate the union of the set (A U B) with set C, denoted as (A U B) U C. A U B contains the elements {1, 2, 3, 5, 7, 10} and C contains the elements {1, 2, 3, 4, 5}.

Taking the union of these two sets results in {1, 2, 3, 4, 5, 7, 10}.

Finding the intersection:

Finally, we find the intersection of (A U B) U C with A U C. A U C consists of the elements {2, 5, 7, 10}.

The intersection of these two sets is the combination of common elements.

The common elements are {2, 5, 7, 10}.

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Answer:

15.2cm

Step-by-step explanation:

From the given diagram;

KN = SN = 14cm

KL = NT = 6cm

Required

ST

Using the Pythagoras theorem;

ST² = SN² + NT²

ST² = 14² + 6²

ST² = 196 + 36

ST² = 232

ST = √232

ST = 15.2cm

Hence the length of ST is 15.2cm

Answer:

(4,-6)  

Step-by-step explanation:

1) First, let's find the slope of the line between the two points. Use the slope formula \(m = \frac{y_2-y_1}{x_2-x_1}\), substitute the x and y values of (-2,9) and (2,-1) into it, then solve:

\(m = \frac{(-1)-(9)}{(2)-(-2)}\\m = \frac{-1-9}{2+2} \\m =\frac{-10}{4} \\m = -\frac{5}{2}\)

So, the slope of the line is \(-\frac{5}{2}\).

2) Now, using that slope, let's find another point on the line. You can do this by drawing the two points on a graph (picture below). Now, remember that the slope is \(\frac{rise}{run}\). So, starting from any of the two points (I chose (2,-1), as seen below) count 5 units down, then 2 units to the right. This gives an answer, (4,-6).

The width of the rectangular rug is 13 feet and the length of the rectangular rug is 26 feet.

Area of a rectangle formula: A = L * W. A

rectangle's length and width are multiplied to produce its area.

A is the area, L is the length, and W is the width or girth, where

A = L * W.

The corresponding sides of the rectangular rug and the rectangular floor must be proportional if they are alike.

Let's use "x" to represent the rug's width. The floor measures 32 feet in length and 26 feet in width, and the length of the rug is 16 feet according to the details provided. Since the rug and the surface are comparable, we can establish the following ratio:

Rug width/floor width = rug length/floor length

x / 26 = rug's length / 32

We can cross-multiply and then solve for "x" to find the answer:

32x = 26 * Rug's length

x =  (26 * Rug Length) / 32

\(= \frac{26 * 16}{32} \\= \frac{26}{2} \\= 13\)

Therefore x ( the width of the rug) is = 13 feet.

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Complete question:

The rectangular rug is similar to the rectangular floor. If the floor of the room measures 32 feet in length and 26 feet in width, and the length of the rug is 16 feet, what is the width of the rug?

The three degree polynomial with the real coefficients which have zeroes of 5 and 2i with the lead coefficients of 1 is found as:

P(x) = x³  -  5x² - 4x + 20

Given roots are :

5 and 2i and conjugate of 2i that is -2i.

Let the three degree polynomial be P(x).

So,

P(x) = 1(x - 5)(x -2i)(x + 2i)

P(x) = (x - 5)(x² - 4i²)

Since, i² = 1

P(x) = (x - 5)(x² - 4)

On simplification:

P(x) = x³  -  5x² - 4x + 20

Thus, the three degree polynomial with the real coefficients which have zeroes of 5 and 2i with the lead coefficients of 1 is found as:

P(x) = x³  -  5x² - 4x + 20

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Answer:

no solutions

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

equation of blue line is y = x + 2 , in slope- intercept form

with slope m = 1

equation of red line is y = x - 3 , in slope- intercept form

with slope m = 1

• Parallel lines have equal slopes

then the blue and red lines are parallel.

the solution to the system is at the point of intersection of the 2 lines

since the lines are parallel then they do not intersect each other.

thus the system shown has no solution.

The correct answer is that the data set {3, 7, 4} is represented in the given histogram.(option-a)

The given histogram represents the number of children in each age group who need to travel to school. Since the histogram has only three bars, we can conclude that there are only three age groups.

The first bar represents children aged 5-10, of which there are 3. The second bar represents children aged 11-13, of which there are 7. The third bar represents children aged 14-18, of which there are 4.

Therefore, the data set that is represented in the histogram is:

{3, 7, 4}

None of the other data sets given match the values in the histogram. The first data set has duplicate values and is not sorted by age group. The second data set includes ages that are not represented in the histogram. The third data set has values for ages 6, 11, 12, 13, 14, 15, 17, and 18, but the histogram does not have bars for all those ages. (option-a)

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Answer: 7.8

Explanation: 8.9 - 2.9 = 6.0 + 1.8 = 7.8