What is the value of 2cos2(105⁰) − 1? Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction Negative one-half One-half StartFraction StartRoot 3 EndRoot Over 2 EndFraction

The function given as f(x) = (x² - 16)/(6x - 24) is discontinuous at x = 4

We are given the function as;

f(x) = (x² - 16)/(6x - 24)

We have to find the discontinuities of the function.

Now, the denominator 6x - 24 becomes 0 when x = 4.

This means that when x = 4, the function now becomes undefined.

Therefore, we can say that there is a discontinuity at x=4

However, this discontinuity can be removed due to the fact that we have x = 4 in the numerator.

But despite the above, it is still discontinuous at that value of x.

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3x + 2y = 18

2x + 5y = 14 are both linear equations

The system of linear equations in two variables is an equation with two different variables. Any equation with different variables can be in this system.

The solution for this type of equation by solving and getting two different values for both x and y but the same values are used in both equations.

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Answer:

3 tacos and 3 burritos cost $11.25; 4 tacos and 2 burritos cost $10. The difference is 1 more taco and 1 less burrito, for $1.25 less.

So adjust the order repeatedly the same way, adding one taco and taking away one more burrito, and decreasing the cost by $1.25 each time.

3 tacos, 3 burritos, $11.25

4 tacos, 2 burritos, $10.00

5 tacos, 1 burrito, $8.75

6 tacos, 0 burritos, %7.50

The cost of each taco is $7.50/6 = $1.25.

3 of each cost $11.25, so 1 of each cost $3.75; the taco costs $1.25, so the burrito costs $2.50.

ANSWERS: taco $1.25, burrito $2.50

Answer: 12 Chaperones, 80 Students

Step-by-step explanation:

92 total - 12 chaperones = 80 students

3 Chaperones per 20 students, sizing that up by 4 you get 12 and 80.

The slope of the line in the function is 1

The slope of a line is defined as the change in y-coordinate with respect to the change in x-coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx. So the change in y coordinate with respect to the change in x coordinate can be written as,

m = y₂ - y₁ / x₂ - x₁

Taking two points;

Substituting the values into the formula;

m = -2 - 0 / 3 - 5

m = -2 / - 2

m = 1

The slope is calculated as 1

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Answer: julia dog is 300% bigger than jake's

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

There are 8 total professors and 4 are below the age of 35

32, 28, 34, 29

Answer:

Graph a solid line, then shade the area above the boundary line since y y is greater than −3x+5 - 3 x + 5 . y≥−3x+5 y ≥ - 3 x + 5.

Step-by-step explanation:

Answer:5 days.w<0.5*34x

Step-by-step explanation:

The value of 3M + 7N will be;

⇒ 3M + 7N   = [tex]\left[\begin{array}{ccc}-29&-16\\14&81\\\end{array}\right][/tex]

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The values are;

⇒ M = [tex]\left[\begin{array}{ccc}2&-3\\0&6\\\end{array}\right][/tex]

⇒ N = [tex]\left[\begin{array}{ccc}-5&-1\\2&9\\\end{array}\right][/tex]

Now,

The value of 3M + 7N will be;

⇒ 3M + 7N = [tex]\left[\begin{array}{ccc}6&-9\\0&18\\\end{array}\right] + \left[\begin{array}{ccc}-35&-7\\14&63\\\end{array}\right][/tex]

                 = [tex]\left[\begin{array}{ccc}-29&-16\\14&81\\\end{array}\right][/tex]

Thus, The value of 3M + 7N after simplification is;

⇒ 3M + 7N   = [tex]\left[\begin{array}{ccc}-29&-16\\14&81\\\end{array}\right][/tex]

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Comparing the √17 and 29/7 using <, > or = , we have √17 < 29/7.

Mathematical number comparison is the process or method of comparing two numbers to determine whether one is less, bigger, or equal to the other. The comparison symbols for numbers are "=", which stands for "equal to," "=", which stands for "greater than," and " ", which stands for "less than." Comparing amounts is a technique for figuring out how much to compare units in relation to a different standard or reference unit. A common reference point is necessary for two comparing units to be compared; otherwise, they cannot be compared.

Given,

Comparing the following using <, > or = ,

Numbers:

√17 and 29/7

For √17

Simplifying,

√17 = 4.123

For 29/7

29/7 = 4.14

√17 < 29/7

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Answer: 18/24 and 10/24

Step-by-step explanation:

We can consider that table (A) shows a proportional relationship of 7/1.

Relationships between two variables that are proportional occur when their ratios are equal.

Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value.

The "constant of proportionality" is the name of this constant.

So, consider the tables as follows:

Table A:

7/1

14/2 = 7/1

28/4 = 7/1

35/5 = 7/1

Proportional relationship: 7/1

Now, we don't need to calculate further.

Therefore, we can consider that table (A) shows a proportional relationship of 7/1.

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The value of the secant angle will be equal to 60°.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given that the secant angle secθ is equal to 2. The value of the angle will be calculated as,

secθ = 2

θ = sec⁻¹(2)

θ = 60°

The secant angle will have a value of 60°.

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By using the concept of fraction, it can be calculated that

I will get 64 meals

What is a fraction?

Suppose there is a collection and a part of a collection has to be taken. The part which is taken is called fraction. In other words, part of a whole is called fraction. The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.

This is a word problem on fraction

Weight of 1 meal = [tex]\frac{3}{8}[/tex] pounds

Total weight of meal = 24 pounds

Number of meals I will get = [tex]24 \div \frac{3}{8}[/tex]

                                            = [tex]24 \times \frac{8}{3}[/tex]

                                            = 64

I will get 64 meals

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Answer:

Step-by-step explanation:

You want to know if David's solution of -2x for (5x-4) -(3x) is correct, and what David should have done.

David's solution is correct up to Step 4.

At that point, it appears as though David treated -4 as if it were -4x. The constant cannot be combined with x terms. Step 4 should have been ...

  Step 4: (5 -3)x -4 = 2x -4

David's incorrect solution should have been 2x -4.

Answer:

Each boy earned $88.50.

Step-by-step explanation:

Jordan and Ronald each earned $88.50 since they each earned the same amount after Jordan was reimbursed the $20 he spent for gas. This means that the total earnings they received was $177, and since they each earned the same amount, they each earned $177/2 = $88.50.

Answer:

----------------------------

Total amount is 16000 and its 25% is spent on expenses.

Find the amount of expenses:

The main characteristics of a correct diet are those mentioned below:

A correct diet is a diet that is characterized by having the following elements:

Having a correct diet is important for the care of our health in general.

¡Hope this helped!

Answer:

42

Step-by-step explanation:

Answer:

Linear

Step-by-step explanation:

I'd say this because the line is straight so I think it's linear. (If wrong sorry)

Answer:

4/6 and 1/6

Step-by-step explanation:

6 is the least common denominator found by multiplying 3 by 2

The volume of liters equivalent to a 2/3 serving shown using the proportional relationship displayed on a double number line is 4 liters

A number line consists of numbers spread in equal increments or spacing on an horizontal or vertical line.

The volume equivalent to 1/4 serving = 3/2 liters

A volume of 3/2 liters = 1.5 liters

If 3/2 liters = 1/4 serving, therefore;

1 serving = 4 × (3/2) liters = 6 liters

2/3 serving = (2/3) × 6 liters = 4 liters

Similarly: 0.5 liters = (1/4)/3 = 1/12

Expressing the above information on a double number line, we get;

[tex]{}[/tex]                                1.5      2.0     2.5         3.0           3.5            4.0

Vol. in Liters <--------|----------|----------|-----------|-------------|--------------|------------->

[tex]{}[/tex]                               (1/4)    (1/3)        (5/12)    (1/2)        (7/12)        (2/3)

Serving        <---------|----------|-----------|-----------|-------------|-------------|------------->

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Answer:

x = 19

Step-by-step explanation:

So cos and sin are closely related, but they are not equal. In order for these two to be equal to each other, the angles (in the parenthesis by the cos and by the sin) have to be complementary. That is, they have to add up to 90°

Use this idea to set up an equation.

x + 16 + 3x - 2 = 90

Combine like terms.

4x + 14 = 90

Subtract 14.

4x = 76

Divide by 4.

x = 19

x = 19

If you are kooking for the angles:

x + 16

= 19 + 16

= 35

and

3x - 2

= 3(19) - 2

= 57 - 2

= 55

Check: 35 + 55=90

Also,

cos35 = sin55

To find the number of successes x, we need to first find the total number of defective shoes. To do this, we can multiply the total number of shoes selected for quality assurance by the percentage of defective shoes, expressed as a decimal: 386 shoes * 0.0312 = 12.0736. Since we cannot have a fraction of a shoe, we can round down to the nearest whole number to find the number of successes x: 12.0736 rounded down = 12. Therefore, the number of successes x is 12, and the answer is 12.

Answer:

If Manuel has $20,000 in a savings account that earns 7% interest per year and the interest is not compounded, then after two years he will earn $2,800 in interest. This is because 7% of $20,000 is $1,400, and since the interest is not compounded, this amount will remain constant for each year. Therefore, after two years Manuel will earn a total of $1,400 + $1,400 = $2,800 in interest.

In general, if a savings account earns x% interest per year and the initial amount in the account is y dollars, then after n years the account will earn n * (x/100) * y dollars in interest. For example, if the interest rate is 7% and the initial amount is $20,000, then after two years the account will earn 2 * (7/100) * $20,000 = $2,800 in interest.

Step-by-step explanation:

Answer:

The answer is $2800.

Step-by-step explanation:

Now,

(20000 × 7) ÷ 100 = $1400

Here, we get for 1 year

for two years,

1400 × 2 = $2800

Thus, He will earn $2800 in 2 years.

Answer:

It is not possible to determine the dimensions of a rectangle with only the information that its area is 2/9. The area of a rectangle is calculated by multiplying its length by its width, so a rectangle with an area of 2/9 could have many different combinations of length and width. For example, a rectangle with dimensions of 1/3 by 2/3 would have an area of 2/9, as would a rectangle with dimensions of 2/9 by 1.

2/3 is the probability of selecting silver coin from Urn III.

It is a branch of mathematics that deals with the occurrence of a random event.

Urn I: 5 gold coins

Urn II: 2 gold coins and 2 silver coins

Urn III: 3 silver coins

The probabilities of choosing an urn are calculated as shown below:

P(Urn1)+P(Urn2)+P(Urn3)=1/3

First, calculate the probability of choosing a silver coin from the first urn.

P(S1)=0/5

Now, calculate the probability of choosing a silver coin from the second urn.

P(S2)=2/4=1/2

Now, calculate the probability of choosing a silver coin from the third urn.

P(S3)=3/3=1

Now, calculate the probability that the silver coin is selected from Urn III.

P(Silver coin chosen from urn III)=Favorable outcome/Total outcome

=1/3×1/1/3×0+1/3×1/2+1/3×1

=1/3/(1/6+1/3)

=2/3

Hence, the probability of selecting silver coin from Urn III is 2/3.

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