How can we check the binomial factors to verify that they are truly factors? Are the factors (x + 5)(x – 8) truly factors of x2 – 2x – 30. Show your work.

The exponential function gotten from the table is given by y = 4(1/2)ˣ

An exponential function is in the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multipliers.

From the table, at point (0, 4):

At point (3, 1/2):

The exponential function gotten from the table is given by y = 4(1/2)ˣ

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The fraction of students who take Composition at the college is 2/3.

To find the fraction of students who take the Composition class, we need to multiply the fraction of students who take an English class (4/5) by the fraction of English students who take the Composition class (5/6).

Multiplying these fractions, we get (4/5) * (5/6) = 20/30 = 2/3.

Therefore, 2/3 of the students at the college take Composition.

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Answer:

-23/36 pi

Step-by-step explanation:

(-115 x pi) / 180

The question uses proportional reasoning to determine the quantity of coffee beans Diana would need to make a different volume of coffee. By setting up a ratio based on the original 30 grams for 48 fluid ounces, we can calculate the necessary amount of coffee beans for any new volume of coffee required which is 60 grams.

The question relates to proportion and unit conversion, both key concepts in mathematics, specifically in dealing with ratios and measurements. Diana uses 30 grams of coffee beans to make 48 fluid ounces of coffee. If 'company comes' and she needs to make more or less coffee, the same ratio of coffee beans to water would apply. To determine the amount of coffee beans Diana would need for a different volume of coffee, you would set up a proportion based on the given ratio and solve for the unknown quantity.

To calculate the amount of coffee beans for a new volume, you can use the following steps:

Determine the new volume of coffee in fluid ounces.

Set up a ratio comparing 30 grams of coffee beans to 48 fluid ounces.

Use the new volume in the ratio to solve for the amount of coffee beans required.

For example, if Diana wants to make 96 fluid ounces of coffee for her company, the proportion would be:

30 grams / 48 fluid ounces = X grams / 96 fluid ounces

Solving this gives us X = (30 grams * 96 fluid ounces) / 48 fluid ounces = 60 grams. Hence, Diana would need 60 grams of coffee beans for 96 fluid ounces of coffee.

This is a problem of system of linear equations. We form two equations from the conditions given in the problem, and solve the system of equations to find the number of text messages and pictures sent.

This is a problem of system of linear equations. Here are two conditions mentioned: The total cost and difference of number of text messages and pictures.

Let's denote the number of text messages as x and pictures as y as per your question.

From the cost, we have the equation: $0.05x + $0.10y = $4.

From the difference of the number of sent messages and pictures, we have: x = y + 5.

Now we can substitute x from the second equation into the first one, get the value for y, and calculate the value for x after. Here you have step-by-step solution for your problem.

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16 = 4²

So, by the definition of logarithms

[tex]\log_4{16}=2[/tex]

The value of [tex]\( \tan(A + B) \)[/tex] in quadrant 2, where [tex]\( \tan A = \frac{1}{3} \)[/tex] and [tex]\( \sin B = \frac{20}{29} \)[/tex], is [tex]\( \frac{11}{57} \)[/tex].

To find [tex]\( \tan(A + B) \)[/tex], we can use the formula [tex]\( \tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} \)[/tex]. Given that \[tex]( \tan A = \frac{1}{3} \)[/tex] and [tex]\( \sin B = \frac{20}{29} \)[/tex], we can determine [tex]\( \cos B \)[/tex] using the fact that [tex]\( \sin^2 B + \cos^2 B = 1 \)[/tex]. Therefore, [tex]\( \cos B = \sqrt{1 - \sin^2 B} = \frac{21}{29} \)[/tex].

Now, substitute the values into the formula for [tex]\( \tan(A + B) \)[/tex]:

[tex]\[ \tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} \][/tex]

[tex]\[ = \frac{\frac{1}{3} + \frac{20}{29}}{1 - \frac{1}{3} \cdot \frac{20}{29}} \][/tex]

[tex]\[ = \frac{\frac{29 + 60}{87}}{\frac{87 - 20}{87}} \][/tex]

[tex]\[ = \frac{\frac{89}{87}}{\frac{67}{87}} \][/tex]

[tex]\[ = \frac{89}{67} \][/tex]

Therefore, [tex]\( \tan(A + B) = \frac{11}{57} \)[/tex] in quadrant 2.

To find (tan A+B) when A and B are in quadrant 2, find the components of A and B along the x- and y-axes using A = 34.0 m, θA = 63.0°. Calculate Ax = A cos θA and Ay = A sin θA. Then use the formula tan(A + B) = (tan A + tan B) / (1 - tan A tan B) to find the sum of the tangents.

First, we find the components of A and B along the x- and y-axes. From the problem, we know that A = B = 34.0 m, and θB = 63.0°. We find the x-components by using Ax = A cos θ, which gives Ax = 34.0 cos 63.0° = -15.23 m.

Similarly, we find the y-components by using Ay = A sin θ, which gives Ay = 34.0 sin 63.0° = 29.88 m.

Now, we can find the sum of the tangents of A and B using the formula tan(A + B) = (tan A + tan B) / (1 - tan A tan B). Substituting the given values, we have tan(A + B) = (1/3 + Ay/Ax) / (1 - (1/3)(Ay/Ax)).

Answer:

B on edge 190

Step-by-step explanation:

For a 6-digit zip code with no restrictions, there would be 1,000,000 possible zip codes. If the first digit could not be a '0', the number of possible zip codes would decrease to 900,000.

We're dealing with a counting problem here. This problem involves basic principles of combinatorics.

Firstly, if there are no restrictions on the digits used, each of the six positions in the zip code can hold any digit from 0 to 9. There are 10 choices (from 0 to 9) for each of the 6 digits in the zip code which leads to 10^6 = 1,000,000 possible zip codes.

However, if the first number could not be 0, there are 9 possible choices for the first digit and 10 choices for each of the remaining 5 digits. Therefore, the number of possible zip codes would be 9 * 10^5 = 900,000.

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The measure of angle ABC and BDC is 80° and 90° respectively.

In geometry, a triangle is a closed, two-dimensional shape with three straight sides. A triangle is also a polygon.

Given the ΔABC in which AB ≅ BC, m∠ABD = 40° and BD is the median of ΔABC.

We have to find the measure of angle ∠ABC and ∠BDC.

As the median of the isosceles triangle split the angle at the vertex into two equal parts i.e ∠ABC is twice the angle ∠ABD.

[tex]\rm \angle ABC=2\angle ABD\\\\\angle ABC=2 \times 40\\\\\angle ABC=80[/tex]

Also, the median of an isosceles triangle is perpendicular to the opposite side i.e to the base. Here, BD is perpendicular to AC.

∠BDC=90°

Therefore, the measure of angle ABC and BDC is 80° and 90° respectively.

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Answer: Line Plot

Step-by-step explanation: A line plot is a display that shows how the values in a data set are distributed.

Answer: histogram

Step-by-step explanation:

Answer: A

Step-by-step explanation: