Equivalent Express SIC
Which expression has an equivalent value to x² + 9x + 8 for all values of x?
a (x + 1)(x + 8)
b (x + 2)(x + 6)
c (x + 4)(x + 4)
d (x + 5)(x + 4)

Answer:

An obtuse triangle can not have more than one angle measured greater than 90.

Step-by-step explanation:

Obtuse triangles have 2 acute angles (less than 90 degrees) and 1 obtuse angle (greater than 90).

The farmer sold approximately 3.905 kilograms of pears at the farmer's market. In fraction form, this is 781/200 kilograms.

Answer:

200 feet

Step-by-step explanation:

In the illustration above, a circle with a few lines intersecting at various locations is shown. So, if we split the circle in half, the resulting semicircle has a vertical angle of 180 degrees. Since ∠ROP = 125°, ∠POS = 55° is obtained by taking 180° away from 125°. ∠POS and ∠QOR are equivalent terms. Also, ∠ROP = ∠QOS.

What is lines intersecting?

In a plane, intersecting lines are any two or more lines that cross one another. The point of intersection, which can be found on all intersecting lines, is where the crossing lines share a common point.

the characteristics of intersecting lines

The intersecting lines (two or more) never cross over at more than one location.

Any angle may be used to intersect the lines in any direction. Always larger than 0° and less than 180°, this angle is generated.

A pair of vertical angles are created by two intersecting lines. The vertical angles have the same vertex and are opposing angles (which is the point of intersection).

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Answer:

20 questions were on the test

Step-by-step explanation:

SOLUTION

We will apply the amount formula

Substituting each into the equation, we have

Hence the answer is $10,333.71 to two decimal places

Answer:

Step-by-step explanation:

\((1.6x + 7.3) + (-0.6x + 2) - (7.8 -3.4x)\\Ope- the- brackets\\1.6x+7.3-0.6x+2-7.8+3.4x\\Collect-like-terms\\1.6x-0.6x+3.4x+7.3+2-7.8\\4.4x+1.5\)

Answer:

4.4

Step-by-step explanation:

The median of a normal distribution with a mean of $\mu$ and standard deviation of $\sigma$ is simply equal to the mean $\mu$. Therefore, for a normal distribution with a mean of 61 and a standard deviation of 14, the median is also 61.

This is because the normal distribution is a symmetric distribution, with the mean, median, and mode all located at the same point on the horizontal axis. The mean represents the center of the distribution and is also the balance point for the distribution, so half of the observations will be less than the mean and half will be greater than the mean.

Therefore, for a normal distribution with a given mean and standard deviation, we can use the mean as an estimate of the median. In this case, the mean is exactly equal to the median, so the median is 61.

It is worth noting that this property of normal distributions only holds for normal distributions, and not necessarily for other types of distributions. For example, in a skewed distribution, the mean and median may be quite different from each other.

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The expected acceleration of an object is based on the acceleration due to gravity, which is a constant value of 9.8 m/s2. To calculate the expected acceleration, we use the equation: Expected acceleration = (5/7)gsin(θ), where θ is the angle at which the object is moving.

This equation takes into account the angle of the object and uses the acceleration due to gravity to calculate the expected acceleration. In this equation, the acceleration due to gravity is multiplied by a fraction, which is determined by the angle at which the object is moving. Therefore, the higher the angle at which the object is moving, the greater the expected acceleration.

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According to Zaller's Receive-Accept-Sample (RAS) model, individuals who are most susceptible to the message of a political action committee launching a new advertisement aimed at expanding health insurance to low-income Americans through increased government funding would be those who both receive and accept the message.

The RAS model suggests that individuals have varying levels of political knowledge and are exposed to different sources of information. Those who are more likely to receive the message are individuals who are politically interested and engaged, while those who are more likely to accept the message are individuals who have limited political knowledge and are less critical of the information presented to them.

Therefore, in the context of the advertisement aiming to expand health insurance to low-income Americans, the most susceptible individuals would be those who are politically interested but have limited political knowledge. These individuals may be more likely to accept the message without critically evaluating its content.

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Answer: 9

Step-by-step explanation:

Formula : Mean = \(\dfrac{\text{Sum of observations}}{\text{Number of observaions}}\)

Given: 5 students participated in a push-up competition.

The amount of push-ups each student completed is listed: 12, 7, 10, 11,5.

Mean = \(\dfrac{12+7+10+77+5}{5}\)

\(=\dfrac{45}{5}=9\)

Hence, the mean number of push-ups = 9

Answer:

it is 32units

Step-by-step explanation:

There are 450 ways a person can order a two-course meal consisting of an appetizer and a main course according to the counting principle.

The fundamental of counting principle defines that if we have to choose one item from a group of M items and a second item from another group of N items, then the total number of two item choices is

                              M*N

Here we have been given that there are 15 appetizers and 30 main courses that is according to the fundamental of counting principle we have been given

M = 15     and N = 30

Thus the total number of two-course meal is = M*N

                                                                                = 15*30

                                                                                = 450

Hence there are 450 ways a person can order a two-course meal consisting of an appetizer and a main course.

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Answer:

90=square

72=nonagon

60=hexagon

45=pentagon

40=octagon

I am not entirely sure tho

The equation model of the given statement in question is 6 + 7× x.

The model of equation is defined as the model of the given situation in the form of an equation using constants and variables.

In math, it deals with numbers of operations given according to the statements. The four major arithmetic operators are, addition, subtraction, multiplication, and division.

Given that;

6 is added to product of a number and 7

Now,

Let, the number multiplied by 7 be x,

=7*x

6 is added to the product;

= 6 + 7 × x

Therefore, the equation of model will be given as 6 + 7 × x;

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An increase in the cost of a variable input shifts the​ average total cost curve upward. The correct answer is B. Only i is correct.

An increase in the cost of a variable input, such as labor or raw materials, will cause an increase in the marginal cost (MC) of producing each additional unit of output, because more money is needed to purchase the inputs required to produce each unit.

This increase in marginal cost will not, by itself, shift the marginal cost curve upward, since it only represents a movement along the curve.

However, this increase in marginal cost will cause the average total cost (ATC) curve to shift upward. The reason for this is that average total cost is calculated as total cost divided by the quantity produced.

As the marginal cost of each unit increases, the total cost of producing each unit also increases. This causes a higher total cost to be divided among the same quantity produced, leading to a higher average total cost.

Thus, an increase in the cost of a variable input shifts the average total cost curve upward, but does not shift the marginal cost curve.

The correct answer is B. Only i is correct.

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The rate of change of a circle diameter with respect to radius is 0.

The rate of change of a circle diameter with respect to radius (D2(r)) can be calculated by using the formula dD2/dr. This formula states that the rate of change of a function at a given point is equal to the derivative of the function at that point.

To calculate the rate of change of a circle diameter with respect to radius, we must first calculate the derivative of the circle diameter with respect to radius. The formula for diameter of a circle is D = 2r, where r is the radius of the circle. Taking the derivative of the equation with respect to r gives us dD/dr = 2. This means that the rate of change of a circle diameter with respect to radius is 2.

We can also calculate the rate of change of a circle diameter with respect to radius using the formula dD2/dr. This formula states that the rate of change of a function at a given point is equal to the second derivative of the function at that point. Taking the second derivative of the equation for the diameter of a circle with respect to radius gives us d2D/dr2 = 0. This means that the rate of change of a circle diameter with respect to radius is 0.

Therefore, the rate of change of a circle diameter with respect to radius is 0.

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Answer:

z>-4

Step-by-step explanation:

Answer:

z>4

Step-by-step explanation:

-2z-3<5

add 3 to 5: -2z < 8

divide by -2: z < -4

but since you divided by a negative number, you have to change the way the inequality is facing so the answer is z>-4

Calculating this expression, we find that the length of the image of the rectangle is 36 in.

To find the length of the image of the rectangle after dilation, we can use the property of similar triangles. Since the width of the image is known to be 21 in., we can set up a proportion:

(image width) / (original width) = (image length) / (original length)

Substituting the known values, we have:

21 in. / 14 in. = (image length) / 24 in.

Solving for the image length, we get:

(image length) = (21 in. / 14 in.) * 24 in.

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A beverage company has decided to manufacture a new juice with mixed flavors, which is prepared from orange and pineapple. The vitamin contents are 5% of vitamin A and 2% of vitamin C in the orange flavor, while pineapple flavor contains 8% of vitamin C.

The company's policies are to add at least 20 L of orange flavor to the new juice and limit the vitamin C content to no more than 5%. The cost of orange flavor is $1000 per liter, while the cost of pineapple flavor is $400 per liter.To satisfy a minimum demand of 100 L of juice, we must determine the optimal amount of each flavor to use.A) A linear programming model is needed for the company to solve this problem (Minimize production cost of the new juice)B) Use a graphic solution for this problem.The objective function of the optimization problem can be given as:min C = 1000x + 400yThe constraints that the company has are,20x + 0y ≥ 100x + y ≤ 5x ≥ 0 and y ≥ 0The feasible region can be identified by graphing the inequality constraints on a graph paper. Using a graphical method, we can find the feasible region, and by finding the intersection points, we can determine the optimal solution.The graph is shown below; The optimal solution is achieved by 20L of orange flavor and 80L of pineapple flavor, as indicated by the intersection point of the lines. The optimal cost of producing 100 L of juice would be; C = 1000(20) + 400(80) = $36,000.C) If the company decides that the juice should have a vitamin C content of no more than 7%, it would alter the problem's constraints. The new constraint would be:x + y ≤ 7Dividing the equation by 100, we obtain;x/100 + y/100 ≤ 0.07The objective function and the additional constraint are combined to create a new linear programming model, which is solved graphically as follows: The feasible region changes as a result of the addition of the new constraint, and the optimal solution is now achieved by 20L of orange flavor and 60L of pineapple flavor. The optimal cost of producing 100 L of juice is $28,000.

In conclusion, the optimal amount of each flavor that should be used to satisfy a minimum demand of 100 L of juice is 20L of orange flavor and 80L of pineapple flavor with a cost of $36,000. If the company decides that the juice should have a vitamin C content of no more than 7%, the optimal amount of each flavor is 20L of orange flavor and 60L of pineapple flavor, with a cost of $28,000.

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Answer:

Step-by-step explanation:

\(\frac{x+6}{x+7}-\frac{x+1}{x+2}=\frac{(x+6)*(x+2)}{(x+7)*(x+2)}-\frac{(x+1)(x+7)}{(x+2)(x+7)}\\\\\)

USE FOIL method

(x +6)(x + 2) = x*x + x*2 +6*x +2*6

                  =x² + 2x + 6x + 12    {Combine like terms}

                  = x² + 8x + 12

(x+ 7)(x + 2) = x*x+ x*2 +7*x + 7*2

                  = x² +2x+ 7x + 14

                 = x² + 9x + 14

(x+1)*(x +7) = x*x + x *7 + 1*x + 1*7

                =x² + 7x +x + 7

                =x² + 8x + 7

\(\frac{x+6}{x+7}-\frac{x+1}{x+2}=\frac{(x+6)*(x+2)}{(x+7)*(x+2)}-\frac{(x+1)(x+7)}{(x+2)(x+7)}\\\\\\ =\frac{(x+6)*(x+2) - [(x+1)(x+7)]}{(x+2)(x+7)}\\\\\\= \frac{x^{2}+8x+12 -[x^{2}+8x+7]}{x^{2}+9x+14}\\\\\\=\frac{x^{2}+8x+12-x^{2}-8x-7}{x^{2}+9x+14}\\\\=\frac{5}{x^{2}+9x+14}\\\\\\\\\frac{x+6}{x+7}-\frac{x+1}{x+2}=\frac{1}{3x+1}\\\\\frac{5}{x^{2}+9x+14}=\frac{1}{3x+1}\\\\\)

Cross multiply,

5*(3x+1) = x² + 9x + 14

5*3x + 5*1 = x² + 9x + 14

15x + 5 = x² + 9x + 14

x² + 9x + 14 - 5x - 5 = 0

x² + 9x - 5x + 14 - 5 = 0

Combine like terms

x² + 4x  + 9 = 0

a = 1 ; b = 4 ; c = 9

D = b² - 4ac

  = 4² - 4*1*9

  = 16 - 36

  = -20

  = 20i²    {i² = -1}

√D = √20i² = \(\sqrt{2*2*5*i*i}=2i\sqrt{5}\)

\(x = \frac{-b+\sqrt{D}}{2a} \ or \frac{-b-\sqrt{D}}{2a}\\\\\\x= \frac{-4+2i\sqrt{5}}{2} \ or \frac{-4-2i\sqrt{5}}{2}\\\\x = \frac{2*(-2+i\sqrt{5})}{2} \ or \frac{2*(-2-i\sqrt{5}}{2}\\\\x = -2 +i\sqrt{5} \ or -2-i\sqrt{5}\)

Answer:

1/8

Step-by-step explanation:

3/4 x 1/6 = 3/24 or 1/8

10+ 10 = 20j

20j- 9= 11

The answer is 11 or if in the quiz it is 11j

Hope this helps

Answer:

Step-by-step explanation:

C-10,20,-40,80,...\( u_{n+1}=(-2)*u_{n}\). is geometric1

Answer:

5

Step-by-step explanation:

The response is 5. The slope is always the coefficient of x in a slope-intercept equation.

Answer:

The correct answer for this equation is -5 I know this because when I went to my previous middle school my old teacher had me grade this exact question.

Step-by-step explanation:

The 95% confidence interval for the difference between the two population means is (-1,9).

The 95% confidence interval is a range of values that you can be 95% certain contains the true mean of the population. As the sample size increases, the range of interval values will narrow, meaning that you know that mean with much more accuracy compared with a smaller sample.

We have given that,

the point estimate of the difference between the means = 4,

the standard error = 5

and we need to find 95% confidence level for the difference between the two population means.

We know the formula of confidence interval, that is

CI = difference in mean ± error

⇒ CI = 4 ± 5

CI = 4 + 5 = 9

CI = 4 - 5 = -1

Therefore confidence interval for the difference between the two population means is (-1 , 9).  

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Answer: 47.28 miles

Step-by-step explanation: 5.91 times 8= 47.28

Answer:

  45

Step-by-step explanation:

You want the number described by, "twice the sum of a number and 9 is equal to three times the difference of the number and 9."

Let x represent the number. Then "twice the sum of the number and 9" is ...

  2(x +9)

and "three times the difference of the number and 9" is ...

  3(x -9)

These are equal, so we have ...

  2(x +9) = 3(x -9)

Eliminating parentheses gives ...

  2x +18 = 3x -27

  45 = x . . . . . . . . . . . add 27-2x

The number is 45.

Gradients are an important concept in many fields of science and engineering, providing a quantitative measure of how a particular variable changes over space or time.

A gradient is a term used in mathematics and physics to describe the change in a variable over a certain distance. It refers to the rate at which a variable changes as you move from one point to another. In the context of temperature, for example, a temperature gradient would describe how the temperature changes as you move from one location to another. This can help in understanding the spatial distribution of temperature and other variables in various contexts, such as weather forecasting, climate studies, or even engineering applications.

A gradient is a measure of change in a variable, like temperature or pressure, over a specified distance, providing valuable information about the spatial distribution and variations in these variables.

A gradient can be positive, indicating an increase in the variable as you move in a particular direction, or negative, indicating a decrease. In the case of temperature, a positive gradient would mean that the temperature is increasing as you move in a particular direction, while a negative gradient would mean that the temperature is decreasing.

One important application of gradients is in the study of heat transfer. The rate at which heat flows from one location to another is proportional to the temperature gradient between the two locations. In other words, the greater the difference in temperature between two points, the faster heat will flow between them.

Overall, gradients are an important concept in many fields of science and engineering, providing a quantitative measure of how a particular variable changes over space or time.

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Answer: the area is 80

Step-by-step explanation: