Heyy sorry this is 2 questions but if u can answer one that's fine

find D which is the discriminant and with D < 0.

therefore the equation has an imaginary root and not a real root.

The exact values are:

sin(α + β) = (-6√5 - 8)/25

cos(α + β) = (4√5 - 6)/25

sin(α - β) = (-6√5 + 8)/25

tan(α - β) = (-9√5 + 45)/4

We have,

Recall the trigonometric identities:

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

cos(a - b) = cos(a)cos(b) + sin(a)sin(b)

tan(a - b) = (tan(a) - tan(b))/(1 + tan(a)tan(b))

Using these identities, we can find the exact values of the expressions given.

(a) Sin (α + β)

sin(α + β) = sin(α)cos(β) + cos(α)sin(β)

= (√5/5)(-3/5) + (2/5)(-4/5) (using the values given for sin and cos)

= -6√5/25 - 8/25

= (-6√5 - 8)/25

(b) Cos (α + β)

cos(α + β) = cos(α)cos(β) - sin(α)sin(β)

= (2/5)(-3/5) - (√5/5)(-4/5) (using the values given for sin and cos)

= -6/25 + 4√5/25

= (4√5 - 6)/25

(c) Sin (α - β)

sin(α - β) = sin(α)cos(β) - cos(α)sin(β)

= (√5/5)(-3/5) - (2/5)(-4/5) (using the values given for sin and cos)

= -6√5/25 + 8/25

= (-6√5 + 8)/25

(d) tan (α - β)

tan(α - β) = (tan(α) - tan(β))/(1 + tan(α)tan(β))

= ((√5/5) - (-4/5))/(1 + (√5/5)(-4/5)) (using the values given for sin and cos)

= (9√5/5)/(1 - 4/5√5)

= (-9√5 + 45)/4

Therefore,

The exact values are:

sin(α + β) = (-6√5 - 8)/25

cos(α + β) = (4√5 - 6)/25

sin(α - β) = (-6√5 + 8)/25

tan(α - β) = (-9√5 + 45)/4

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Answer:

The mystery number is 1

Step-by-step explanation:

3 is a prime number meaning only 1 and 3 are factors of it.

(besides decimals)

It only makes sense for it to be 1 since the rest also have 1 as a factor

Answer:

Step-by-step explanation:

148 people

9514 1404 393

Answer:

  77 in²

Step-by-step explanation:

The area of a triangle is given by the formula ...

  A = (1/2)bh

For your triangle, with its base of 14 inches and height of 11 inches, the area is ...

  A (1/2)(14 in)(11 in) = 77 in²

_____

Additional comment

The side lengths added to the figure are incorrect. If we take the 11.5 to be correct, then the left side is about 15.3.

Answer:A

Step-by-step explanation:

the correct choice is: B. The numbers in the pattern are odd.

To determine if the numbers in the pattern are even, odd, or alternate between even and odd, let's examine the first few numbers in the pattern:

First number: 41

Second number: 41 - 4 = 37

Third number: 37 - 4 = 33

Fourth number: 33 - 4 = 29

As we can see, the numbers in the pattern are decreasing by 4 in each step. The first number (41) is odd, and subsequently, each number is decreasing by an even value (4). Therefore, all the numbers in the pattern will be odd.

So, the correct choice is:

B. The numbers in the pattern are odd.

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Answer:

Chances of both even number = 30 times

Step-by-step explanation:

Given:

Chances of both even number = 1/4

Total number of tosses = 120

Find:

How many times both dice show even number

Computation:

Chances of both even number = [Chances of both even number][Total number of tosses]

Chances of both even number = 1/4 [120]

Chances of both even number = 30 times

The graph of the given function is attached.

Given is a function for the rainfall in 5 months in inches.

We need to display the data,

So, as we can see that the data is not showing any proportion or pattern,

So, it can be displayed as a line chart.

Hence the chart is attached for the function.

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The amount of money is 4000 was invested at 3%.

Let x be the amount of money invested at 3%.

Then, the amount of money invested at 5% is 6000 - x.

The interest earned on the amount invested at 3% is 0.03x.

The interest earned on the amount invested at 5% is 0.05(6000 - x) = 300 - 0.05x.

The total interest earned is given as $220.

So, we can write the equation:

0.03x + (300 - 0.05x) = 220

Simplifying and solving for x, we get:

0.03x + 300 - 0.05x = 220

-0.02x + 300 = 220

-0.02x = -80

x = 4000

Therefore, $4000 was invested at 3%.

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Answer:

Step-by-step explanation:

\(w=(\frac{1}{7}).V_{1}+(\frac{4}{7}).V_{2}\)

We have the following vectors :

\(w=\left[\begin{array}{c}3&-1&2\end{array}\right]\)

\(V_{1}=\left[\begin{array}{c}-3&1&2\end{array}\right]\)

\(V_{2}=\left[\begin{array}{c}6&-2&3\end{array}\right]\)

In order to express \(w\) as a linear combination of the vectors \(V_{1}\) and \(V_{2}\), we will search for \(a,b\) ∈ IR such that :

\(a.V_{1}+b.V_{2}=w\)      (I)

Now we are going to work matrixically with the equation (I) :

\(a\left[\begin{array}{c}-3&1&2\end{array}\right]+b\left[\begin{array}{c}6&-2&3\end{array}\right]=\left[\begin{array}{c}3&-1&2\end{array}\right]\)

Distributing mathematically and matching ''component to component'' we lead to the following equations :

\(-3a+6b=3\\a-2b=-1\\2a+3b=2\)

Working with the system associated matrix :

\(\left[\begin{array}{ccc}-3&6&3\\1&-2&-1\\2&3&2\end{array}\right]\)

Applying matrix operations we lead to the following equivalent matrix :

\(\left[\begin{array}{ccc}1&0&\frac{1}{7}\\0&1&\frac{4}{7}\\0&0&0\end{array}\right]\)

In this matrix we obtain that :

\(a=\frac{1}{7}\)  and \(b=\frac{4}{7}\)

We can verify this solution by replacing the values of \(a\) and \(b\) in the equation (I) :

\((\frac{1}{7}).V_{1}+(\frac{4}{7}).V_{2}=w\)  ⇒

\((\frac{1}{7}).\left[\begin{array}{c}-3&1&2\end{array}\right]+(\frac{4}{7}).\left[\begin{array}{c}6&-2&3\end{array}\right]=\left[\begin{array}{c}3&-1&2\end{array}\right]\)    ⇒

\(\left[\begin{array}{c}3&-1&2\end{array}\right]=\left[\begin{array}{c}3&-1&2\end{array}\right]\)    

Answer:

All real numbers are solutions for this problem.

Step-by-step explanation:

Answer:

surface area of cube = 37.5 units

Step-by-step explanation:

Find the area of one side of the cube with the formula sidexside:

2.5 x 2.5 = 6.25 units

now multiple the area of one side by the number of sides of the cube which is 6 sides:

6.25 x 6 = 37.5 units

9514 1404 393

Explanation:

Subtraction is the same as adding the opposite. The difference of fractions with the same denominator is the difference of the numerators expressed over their common denominator.

  \(\dfrac{12}{13}+\left(\dfrac{-1}{13}\right)\\\\=\boxed{\dfrac{12}{13}}-\boxed{\dfrac{1}{13}}\\\\=\boxed{\dfrac{11}{13}}\)

The total weight of the liquid in the tank is approximately 12,628 pounds.

To calculate the weight of the liquid, we need to determine the volume of the hemisphere and then multiply it by the density of the liquid. The formula for the volume of a hemisphere is V = (2/3)πr³, where r is the radius of the hemisphere.

In this case, the diameter of the tank is given as 24 feet, so the radius is half of that, which is 12 feet. Plugging this value into the formula, we get V = (2/3)π(12)³ ≈ 904.78 cubic feet.

Finally, we multiply the volume by the density of the liquid: 904.78 cubic feet * 92.5 pounds per cubic foot ≈ 12,628 pounds. Therefore, the total weight of the liquid in the tank is approximately 12,628 pounds.

In summary, to calculate the weight of the liquid in the tank, we first determine the volume of the hemisphere using the formula V = (2/3)πr³. Then, we multiply the volume by the density of the liquid.

By substituting the given diameter of 24 feet and using the appropriate conversions, we find that the total weight of the liquid is approximately 12,628 pounds.

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Answer:

1.3

Step-by-step explanation:

8 divided by 6 = 1.3

BRAINLIEST PLEASE

Answer:

1.3

Step-by-step explanation:

Hope this helped have an amazing day!

The answer to this question is 5775 different ways.

So total number of ways can be calculated

C(12,4)*C(8,4)*C(4,4)

= 495*70*1

= 34650

So 3 groups are formed and the order of the selected group is not important. Therefore:

Total number of ways = 34650 / 3! = 34650 / 6 = 5775

You can take a look the following questions and try to solve it as well.

----

The answer is 1140.

The number of ways that students can be grouped into 3 group is C(20,3) = 1140

The answer is 28.

Groups of 2 can be made from 8 is C(8,2) = 28

The answer to this question is C.

Given that 10 persons divide into three groups having 2,3, and 5 persons.

C(10,2)*C(10,3)*C(10*5) = 45*120*252 = 1360800

The answer is 369 000 combinations.

The answer is 45.

The number of ways 10 students can be grouped into 2 groups is C(10,2) = 45.

The possible values for the discriminant include the following:

A. -1

D. -18

In Mathematics and Geometry, the x-intercept is the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

Since the graph of this quadratic function has no x-intercepts, we can logically deduce that the zeros, roots, or x-intercepts of this quadratic function must be an imaginary number.

Discriminant, D = b² - 4ac

In conclusion, we can reasonably infer and logically deduce that negative numbers such as -1 and -18 are possible values for the discriminant.

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Complete Question:

The graph of a certain quadratic function has no x-intercepts. Which of the following are possible values for the discriminant? Check all that apply.

A. -1

B. 3

C. 0

D. -18

Answer:

Step-by-step explanation:

The translation 5 to the right adds 5 to the x-value.

The translation 1 unit down subtracts 1 from the y-value.

  (x, y) ⇒ (x+5, y-1)

P(0, 0) ⇒ P'(0+5, 0-1) = P'(5, -1)

Q(2, 4) ⇒ Q'(2+5,4-1) = Q'(7, 3)

R( 5, 2) ⇒ R'(5+5, 2-1) = R'(10, 1)

Answer:

P'[5,-1], Q' [7,3], R'[10,1]

Step-by-step explanation:

Since the object translates 5 unit to the right and 1 unit down ;it means the value of X will move 5 units positively and the value of y will decrement by 1 of its original value to create the image.

Answer:

7 songs costs $8.4

Step-by-step explanation:

6/5=  $1.2 for each song

1.2 times 7=  $8.4

7 songs costs $8.4

Answer:

Below

Step-by-step explanation:

From 7 to 10 AM is THREE hours (if the times are all on the same day)

The relative frequency of the pitcher throwing exactly 4 pitches in an at-bat is given as follows:

3/20.

A relative frequency is calculated as the division of the number of desired outcomes by the number of total outcomes.

The total number of at bats in this problem is given as follows:

80.

In 12 of them, the pitcher threw exactly four pitches, hence the relative frequency of the pitcher throwing exactly 4 pitches in an at-bat is given as follows:

12/80 = 3/20.

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Answer:

6  3/5

Step-by-step explanation:

finding the difference?

im guessing you might wanna ask your teacher? ummmmm....

Answer:

$568.75.

Step-by-step explanation:

To find the area of the combined rectangles, we need the dimensions (length and width) of each rectangle. However, the provided text and numbers do not seem to correspond to a clear description of the rectangles or their dimensions. Could you please provide more specific information or clarify the question?

Answer:

Step-by-step explanation:   привет как вы это t6767

To sketch the graph of the function y = 4(4)^x, we can start by plotting a few points to get an idea of the shape of the graph.

Let's choose some x-values and calculate the corresponding y-values:

For x = -2, y = 4(4)^(-2) = 4(1/16) = 1/4

For x = -1, y = 4(4)^(-1) = 4(1/4) = 1

For x = 0, y = 4(4)^0 = 4(1) = 4

For x = 1, y = 4(4)^1 = 4(4) = 16

For x = 2, y = 4(4)^2 = 4(16) = 64

Now we can plot these points on a coordinate plane and connect them to form the graph of the function.

The graph of y = 4(4)^x will start at the point (0, 4) and increase rapidly as x increases. It is an exponential growth function where the base is 4.

The domain of the function is all real numbers since there are no restrictions on the values of x.

The range of the function is the set of positive real numbers greater than zero. As x increases, y grows without bound, approaching positive infinity but never reaching zero or becoming negative.

Answer:

70.48% probability that it was infected with Dummy

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

\(P(B|A) = \frac{P(B)*P(A|B)}{P(A)}\)

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Fixed by Bob

Event B: Infected with Dummy

65% of the customers with virus problems are bothered by Dummy

This means that \(P(B) = 0.65\)

If the computer is infected by Dummy, Bob has a 90% chance of fixing the problem.

This means that \(P(A|B) = 0.9\)

Probability of Bob Fixing

90% of 65%(fixing a Dummy-infected virus)

70% of 35%(fixing a Smarty-infected virus).

So

\(P(A) = 0.9*0.65 + 0.7*0.35 = 0.83\)

What is the probability that it was infected with Dummy

\(P(B|A) = \frac{0.65*0.9}{0.83} = 0.7048\)

70.48% probability that it was infected with Dummy

Using the expression 5x/12 = 20, the amount that A originally had was $48.

We have,

Let x be the amount of money that A originally had.

Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.

The amount received by B is 1/2 of the remaining amount,

which is (x - x/6)/2 = 5x/12.

We know that 5x/12 = 20,

Solving for x.

5x/12 = 20

5x = 240

x = 48

Therefore,

The amount that A originally had was $48.

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