Translate this sentence into an equation.
The product of Matt's score and
6
is
96
.
Use the variable
m
to represent Matt's score.

The measure of the fourth interior angle of the given quadrilateral is: B. 68°

The sum of all the interior angles of a quadrilateral equals 360 degrees.

The given interior angles of the quadrilateral are: 55°, 117°, and 120°

The measure of the fourth interior angle = 360 - 55 - 117 - 120

The measure of the fourth interior angle = 68 degrees.

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Answer is B, 25, because 300 Divided 12 is 25 & 25x12=300.

Answer:

Hence the values of a and b are given by:

a=240

and b=1.16.

Step-by-step explanation:

It is given that:

A population of 240 birds increases at a rate of 16% annually.

i.e. the initial population of birds is 240.

Also they are increasing at a rate of 16% =0.16.

Hence, it clearly implies that the growth is exponential and the function that represents the population of the birds after x years is given by:

[tex]f(x)=240\times (1+0.16)^x\\\\\\f(x)=240\times (1.16)^x[/tex]

Hence, on comparing our function with the exponential function:

[tex]f(x)=ab^x[/tex]

we have:

a=240

and b=1.16.

Answer:

p ↔ q

Step-by-step explanation:

Given :

Let p: The integer has one digit.

Let q: The integer is less than 10.

To Find:Which represents "The integer has one digit if and only if the integer is less than 10”?

Solution:

1. p ∧ q denotes “p and q”

2.p ∨ q denotes “p or q" (or both)

3.p → q denotes “if p then q”

4. Biconditional p ↔ q denotes “p if and only if q"

Thus Biconditional p ↔ q represents "The integer has one digit if and only if the integer is less than 10”

Hence Option D is correct p ↔ q

Final answer:

Linear angle pairs are always supplementary and formed by intersecting lines, while supplementary angles can be any two angles that add up to 180 degrees.

Explanation:

In mathematics, linear angle pairs are formed by two adjacent angles that add up to 180 degrees. This is known as supplementary angles. Linear angle pairs always occur when two lines intersect, creating opposite angles or a straight angle, such as in the case of a triangle.

On the other hand, supplementary angles do not have to be linear pairs. Supplementary angles are any two angles that add up to 180 degrees, regardless of their position or relation to each other. They can be adjacent angles, non-adjacent angles, or angles across parallel lines.

For example, two angles measuring 60 degrees and 120 degrees are supplementary angles but not a linear pair, since they are not adjacent to each other or formed by intersecting lines.

When there is the no of ways where the president and the vice president should be selected from the grouping of 10 people does not represent the combination.

The following information should be considered:

Therefore we can conclude that when there is the no of ways where the president and the vice president should be selected from the grouping of 10 people does not represent the combination.

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Answer:

The answer is 2 so C

Step-by-step explanation:

The correct answer is D. 4, The value of x is 4.

To find the value of [tex]\( x \)[/tex] in the diagram, we need to apply the properties of similar triangles. Assuming the diagram shows two similar triangles with corresponding sides labeled, we can set up a proportion between the sides of the similar triangles.

Let's denote the sides of the smaller triangle as [tex]\( a \), \( b \), and \( c \)[/tex], and the corresponding sides of the larger triangle as [tex]\( ka \), \( kb \), and \( kc \),[/tex] where [tex]\( k \)[/tex] is the scale factor between the two similar triangles.

Given that one side of the larger triangle is 4 times the corresponding side of the smaller triangle, we have [tex]\( k = 4 \)[/tex].

Now, if we let [tex]\( a = 21 \)[/tex] (as per the options given), then the corresponding side of the larger triangle is [tex]\( ka = 4 \times 21 = 84 \).[/tex]

The problem states that the side labeled [tex]\( x \)[/tex] in the larger triangle corresponds to the side labeled [tex]\( 1 \)[/tex] in the smaller triangle. Therefore, we have the proportion:

[tex]\[ \frac{x}{ka} = \frac{1}{a} \][/tex]

Substituting the known values, we get:

[tex]\[ \frac{x}{84} = \frac{1}{21} \][/tex]

To solve for [tex]\( x \)[/tex], we cross-multiply:

[tex]\[ x \times 21 = 84 \times 1 \][/tex]

[tex]\[ 21x = 84 \][/tex]

Now, we divide both sides by 21 to isolate [tex]\( x \)[/tex]:

[tex]\[ x = \frac{84}{21} \][/tex]

[tex]\[ x = 4 \][/tex]

The required, 60 percent of 22.5 is equal to 13.5, as of the given condition.

The percentage is a way of expressing a fraction or a decimal number as a portion of 100. It is denoted by the symbol '%'. For example, the percentage of 0.75 can be calculated as 0.75 x 100% = 75%. In other words, we are expressing 0.75 as a fraction of 100.

Here,
To find out what number 60% of is equal to 13.5, we can use algebra. Let x be the number we are looking for. Then we can write:

60% of x = 13.5

We can convert 60% to a decimal by dividing by 100:

0.6x = 13.5

Finally, we can solve for x by dividing both sides of the equation by 0.6:

x = 13.5 ÷ 0.6

x = 22.5

Therefore, 60% of 22.5 is equal to 13.5.

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The Laplace transform method is applied to solve the differential equation y' + 6y = e^4t with the initial condition y(0)=2. After transforming, simplifying, and solving for Y(s), we use inverse Laplace transform to find the solution y(t) in the time domain.

Laplace transform is a powerful tool in the field of mathematics used for solving differential equations. To solve the given initial value problem y' + 6y = e^4t ; y(0)=2, we can start by taking the Laplace transform of both sides of the equation.

The Laplace transform of y' is sY(s) - y(0) and the Laplace transform of y is Y(s). Therefore, the Laplace transform of y' + 6y gives sY(s) - y(0) + 6Y(s). Given that y(0)=2, this simplifies to sY(s) + 6Y(s) - 2.

On the right-hand side, the Laplace transform of e^4t is 1/(s-4). Thus, we have the equation sY(s) + 6Y(s) - 2 = 1/(s-4).

By solving for Y(s), we can find the inverse Laplace transform to get the solution y(t) in the time domain.

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Out of the given options, B (y = 4sin(x +ext{ extpi}/2 ) - 2) and D (y = 4cos(-x) - 2) are equivalent to the function y = 4cos x - 2, due to trigonometric identities and properties.

To determine which of the given options are equivalent to the function y = 4cos x - 2, we need to look at trigonometric identities and properties of cosine and sine functions.

B.

He has used the highest recommended percentages to calculate the amounts for the three categories.

After finding the simplest form by dividing 100 the fraction equivalent to 170 percent we get 17/10.

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means.

Here we have to convert:

170 percent into a fraction

Divide it by 100 to condert into fractions,

170/100

Divide both the numerator and denominator by 10

17/10

Since 17 and 10 are co-primes,

Therefore, it is in simplest form.

Hene,

The fraction 17/10 is equivalent to 170%.

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If f(x) = 8, then f(x) when x = 10 is also 8, because the function's value is constant for all x.

If the function f(x) is defined as f(x) = 8 for all values of x, then regardless of the value we substitute for x, the function's output remains constant at 8. So when x = 10, the value of f(x) is still 8. This is an example of a horizontal line on a graph where the y-value does not change regardless of the x-value. In terms of probability, if we're dealing with a continuous probability distribution where f(x) is a constant, then to find P(0 < x < a), we would simply evaluate the integral of f(x) over the interval from 0 to a. However, given that in this case f(x) is not a probability density function and is a constant value, P(x) would not be applicable.