Need help asap!!

Find the value of X

We can use the trigonometric identities to find the exact values of the expressions.

First, we can find cos(alpha) and cos(beta) using the Pythagorean identity:

cos(alpha) = sqrt(1 - sin^2(alpha)) = sqrt(1 - (24/25)^2) = 7/25

cos(beta) = -sqrt(1 - sin^2(beta)) = -sqrt(1 - (15/17)^2) = -8/17 (since beta is in quadrant II, where cosine is negative)

Next, we can use the sum formulas for sine and cosine to find sin(alpha + beta) and cos(alpha + beta):

sin(alpha + beta) = sin(alpha)cos(beta) + cos(alpha)sin(beta) = (24/25)(-8/17) + (7/25)(15/17) = -117/425

cos(alpha + beta) = cos(alpha)cos(beta) - sin(alpha)sin(beta) = (7/25)(-8/17) - (24/25)(15/17) = -24/85

Finally, we can use the quotient identity for tangent to find tan(alpha + beta):

tan(alpha + beta) = sin(alpha + beta) / cos(alpha + beta) = (-117/425) / (-24/85) = 39/85

Therefore, cos(alpha + beta) sin(alpha + beta) = (-24/85)(-117/425) = 936/7225, and tan(alpha + beta) = 39/85.

Answer: there all divided by 2

so it's 2

The matrix that represents the system of equations shown below

4x + 5y = 12

6x-2y = 15 is option B which is Matrix C.

The matrix that represents the system of equations shown below is:

C

[4 5 | 12]

[6 -2 | 15]

Here, we have two equations with two variables x and y. We can represent this system in matrix form by taking the coefficients of x and y and placing them in the left matrix, and the constants on the right-hand side in the right matrix. This gives us:

[4 5 | 12]

[6 -2 | 15]

Therefore, the correct answer is option C

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Since magnesium has a larger volume than nickel, it will displace more water from an overflow can.

We need to compare their volumes.

We can use the formula:

Density = mass / volume

To solve for volume, we rearrange the formula:

Volume = mass / density

For nickel:

Volume = 130g / 8.90 g/cm³ = 14.61 cm³

For magnesium:

Volume = 60g / 1.78 g/cm³ = 33.71 cm³

Therefore, Since magnesium has a larger volume than nickel, it will displace more water from an overflow can.

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The approximate distance from the origin to the point (-2, -7, -4) is 8.3 units.

In three-dimensional space, the distance formula is used to calculate the distance between two points (x₁, y₁, z₁) and (x₂, y₂, z₂) in a three-dimensional coordinate system.

The formula is given by:

d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

Here we have

The point (-2, -7, -4)

We need to find the distance between the origin to the point

Let (x₁, y₁, z₁) = (-2, -7, -4) and (x₂, y₂, z₂) = (0, 0, 0)

Using the distance formula,

d = √ [(x₂ - x₁)² + (y₂ - y₁)²+ (z₂ - z₁)² ]

d = √ [(0 - (-2))² + (0 - (-7))²+ (0 - (-4))² ]

d = √ [(2)² + (7)²+ (4)² ]

d = √ [4 + 49 + 16 ]

d = √69 = 8.3066

d = 8.3

Therefore,

The approximate distance from the origin to the point (-2, -7, -4) is 8.3 units.

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The interpretation of the Chicago white sox data is shown below

The record 53-28 for the Chicago White Sox in the 2021 season means that they won 53 games and lost 28 games in the home games they played during the season.

This record indicates that the White Sox were a strong team at home, winning more games than they lost.

It also suggests that they had a good advantage playing in their home stadium, as winning a high percentage of home games is generally seen as a positive factor in sports.

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Answer:

data given

interest rate 12%

amount to be received 15ooo

time9years

Step-by-step explanation:

from

A=p[1+r/100]^n

where

A is amount

p is principal

r is rate interest

n number of interist period

now,

15000=p[1+12/100]^8

15000/1.12^8 =p×1.12^8/1.12^8

p=6058.24

p=6058)

: .you should invest 6,058

The amount to be invested initially if you want to have fifteen thousand dollars after nine years is $3947.18.

If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:

[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]

We are given that:

A=15000

r=0.12

t=9

We need to find P. You can do this by rearranging the formula:

P=ertA​

Then plug in the given values and use a calculator:

P=e0.12×915000​

P≈3947.18

Therefore, by the given interest rate the answer will be $3947.18.

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Answer: To find two complex numbers that add up to c = -11 + 3i, we can set up the following system of equations:

a + b = -11

ai + bi = 3i

Solving for a and b, we can multiply the first equation by i and subtract it from the second equation multiplied by -1 to eliminate b:

ai + bi = 3i

-ai - bi = 11i

0 + 10bi = 14i

Simplifying, we get b = 1.4. Substituting this into the first equation gives:

a + 1.4 = -11

a = -12.4

So the two complex numbers that add up to c are -12.4 + 1.4i and 1.4i.

To find the value of iº, we need to evaluate i raised to the power of 90 degrees (or pi/2 radians) using Euler's formula:

e^(iθ) = cos(θ) + i sin(θ)

So we have:

iº = i^(90°) = e^(iπ/2) = cos(π/2) + i sin(π/2) = 0 + i(1) = i

Therefore, iº = i.

Step-by-step explanation:

The required graph of the function given; h (x) has been attached.

In mathematics, graph theory is the study of graphs, which are mathematical structures used to represent pairwise interactions between objects. In this definition, a network is made up of nodes or points called vertices that are connected by edges, also called links or lines. In contrast to directed graphs, which have edges that connect two vertices asymmetrically, undirected graphs have edges that connect two vertices symmetrically. Graphs are one of the primary areas of study in discrete mathematics.

Here as per the question the graph of the function, h (x) has been attached.

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Answer:

D

Step-by-step explanation:

Answer:

D. [tex]8a^{9} -4a^{3} +1[/tex]

Step-by-step explanation:

Given [tex]r(x)=x^{3} -2x+1[/tex] and find [tex]r(2a^{3} )[/tex] :

Solve for [tex]r(2a^{3} )[/tex] :

1. [tex]r(2a^{3} )=(2a^{3})^{3} -2(2a^{3})+1[/tex]

2. [tex]r(2a^{3} )=8a^{9} -2(2a^{3})+1[/tex]

3. [tex]r(2a^{3} )=8a^{9} -4a^{3}+1[/tex]

Answer:

So, if [tex]r(x)=x^{3} -2x+1[/tex], then [tex]r(2a^{3} )=(2a^{3})^{3} -2(2a^{3})+1=8a^{9} -4a^{3}+1[/tex].

Then the answer is D. [tex]r(2a^{3} )=8a^{9} -4a^{3}+1[/tex]

Therefore, the maximum height the ball will attain is 221.875 feet.

We are given the equation for the height of a projectile as a function of time:

[tex]h(t) = -16t^2 + v0t + h0[/tex]

where v0 is the initial velocity, h0 is the initial height, and t is the time. We are also given that a tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 120 feet per second. Therefore, we can plug in the values of v0 and h0 into the equation:

[tex]h(t) = -16t^2 + 120t + 2[/tex]

To find the maximum height, we need to find the vertex of this parabola. The x-coordinate of the vertex is given by:

[tex]t = -b/2a[/tex]

where a = -16 and b = 120. Substituting these values, we get:

[tex]t = -120/(2(-16)) = 3.75 seconds[/tex]

To find the corresponding maximum height, we can plug this value of t back into the equation:

[tex]h(3.75) = -16(3.75)^2 + 120(3.75) + 2 = 221.875 feet[/tex]

Therefore, the maximum height the ball will attain is 221.875 feet.

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Answer: A residual value of –0.8 means that the given point is 0.8 units above the line of best fit.

The equation that represents the approximate line of best fit for data, where x represents font size and y represents the number of words on one page is:

y = –38x + 922.

Therefore, the answer is y = –38x + 922.

Step-by-step explanation:

Answer:

f(x) = 4(1.095)^x.

Step-by-step explanation:

The function f(x) = 4(1+0.1/0.5)^0.5x can be simplified using the order of operations, which is PEMDAS (parentheses, exponents, multiplication and division, and addition and subtraction).

First, we can simplify 0.1/0.5 to get 0.2.

Next, we can simplify (1 + 0.2) to get 1.2.

Then, we can simplify (1.2)^0.5 to get approximately 1.095.

Finally, we can multiply 4 by 1.095^x to get the simplified function:

The option that is true about the equations for these two lines iis that they represent the same lines.

The trick to questions like this is to get both equations into the slope-intercept form.  That is done for our first equation (y = 3x + 5).  However, for the second, some rearranging must be done:

5y – 25 = 15x; 5y = 15x + 25; y = 3x + 5

Note: Not only do these equations have the same slope (3), they are totally the same; therefore, they represent the same equation.

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Two lines are described by the equations:

y = 3x + 5 and 5y – 25 = 15x

Which of the following is true about the equations for these two lines?They represent perpendicular lines.

None of the other answers

They represent non-perpendicular, intersecting lines.

They represent the same lines.

They represent parallel lines.

Answer:

To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction.

So, 7/10 divided by 1/3 can be written as:

(7/10) ÷ (1/3) = (7/10) x (3/1)

Multiplying the numerators and denominators, we get:

(7 x 3) / (10 x 1) = 21/10

Therefore, the answer is 21/10, which is an improper fraction. We can simplify it to a mixed number by dividing the denominator into the numerator.

21 ÷ 10 = 2 with a remainder of 1, so the mixed number is:

= 1 1/10

Hence, the answer is 1 1/10 or 11/10.

Step-by-step explanation:

7/10  /  (1/3)   is equal to   7/10  *  3/1   =  (7*3) / (10*1) = 21/10 = 2  1/10

The area and perimeter of the parallelogram are: 56 square units and 30 units respectively

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The parameters that will help us do the math are

base = 7

height = 8

Area = 8*7 = 56 square units

perimeter 2b + 2h

perimeter = 2*7 + 2*8

= 14 +16

P = 30 units

Therefore, the perimeter of the parallelogram and area are 30 units and 56 square units

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Answer:

380 weight

Step-by-step explanation:

please brilliant answer me

the population of the U.S consumes approximately [tex]4.62 * 10^{12}[/tex] grams of rice each year.

What is marginal utility?

The additional pleasure a consumer has from owning one extra unit of an item or service is known as marginal utility.

We can calculate the total amount of rice consumed in the U.S per year by multiplying the population by the amount of rice consumed per person per year:

Total amount of rice consumed = (Population of the U.S) x (Amount of rice consumed per person per year)

Total amount of rice consumed = [tex](3.3* 10^8) * (14,000)[/tex]

Total amount of rice consumed = [tex]4.62* 10^{12} grams[/tex]

Therefore, the population of the U.S consumes approximately [tex]4.62 * 10^{12}[/tex] grams of rice each year.

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Answer:

Step-by-step explanation:

2.1 so a

The control group for the experiment would be option C: some plants will receive no sunlight.

The control group in an experiment is the group that does not receive the treatment or intervention being tested, so that the effects of the treatment can be compared to a baseline or reference point. In this experiment, the treatment being tested is the provision of sunlight as an energy source for plant growth.

Therefore, the control group should not receive sunlight, so that the effects of sunlight can be compared to the baseline of plant growth without sunlight.

Therefore, the control group for the experiment would be option C: some plants will receive no sunlight.

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Answer:

[tex]y = \frac{5}{2} x[/tex]

[tex] \frac{y}{x} = \frac{5}{2} [/tex]

The constant of proportionality is the ratio of y to x. Here, the ratio of y to x is 5 to 2. We see that y is directly proportional to x.

Answer:

To find the slope of the line tangent to the graph of the function at x = -3, we need to find the derivative of the function and evaluate it at x = -3.

First, let's find the derivative of the function y = x^4 + 2x^3 + 2x + 2:

y' = 4x^3 + 6x^2 + 2

Now, let's evaluate y' at x = -3:

y'(-3) = 4(-3)^3 + 6(-3)^2 + 2

= -108 + 54 + 2

= -52

Therefore, the slope of the line tangent to the graph of the function y = x^4 + 2x^3 + 2x + 2 at x = -3 is -52.

Answer:

$357

Step-by-step explanation:

Hours = h

Oil changes = o

Money = m

m = 8.5h + 3o

Now we can substitute:

m = 8.5(36) + 3(17)

m = 306 + 51

m = 357

The requried quantity of drug that remains in the body, in the long run, is 220 mg.

Let's denote the amount of drug in the body just before taking the nth tablet by [tex]D_n[/tex]. We know that [tex]D_0 = 0[/tex](since the patient hasn't taken any tablets yet) and that 5% of the drug is present in the body just before taking a tablet remains in the body. Therefore, we can write:

[tex]D_1 = 110\\D_2 = 0.95 * D_1 + 110 = 203.5\\D_3 = 0.95 * D_2 + 110 = 292.225\\D_4 = 0.95 * D_3 + 110 = 376.81375[/tex]

We can see that the formula for [tex]D_n[/tex] is:

[tex]D_n = 110 * (1 - 0.05)^n + 110 * (1 - (1 - 0.05)^n) / 0.05[/tex]

Simplifying this formula, we get:

[tex]D_n = 220 * (1 - 0.95^n)[/tex]

Now, we want to find the amount of drug that remains in the body in the long run. This means we want to find the limit of [tex]D_n[/tex]  as n goes to infinity. Using the formula above, we can see that:

[tex]lim_ {n- > oo} D_n = lim_ {n- > oo} 220 * (1 - 0.95^n) = 220[/tex]

Therefore, the quantity of drug that remains in the body, in the long run, is 220 mg.

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Answer:

40 units

Step-by-step explanation:

a = 8

b = 15

To find c, we can use the formula: [tex]a^{2} +b^{2} =c^{2}[/tex]

[tex]8^{2} +15^{2} =x^{2}[/tex]

64 + 225 = c^2

289 = c^2

c = 17

a + b + c = perimeter

8 + 15 + 17 = 40

Answer:

  40 units

Step-by-step explanation:

You want the perimeter of the triangle shown in the graph.

You can count the grid squares to find the horizontal and vertical dimensions of the triangle. You find they are 8 units and 15 units, respectively.

The length of the slant side is the hypotenuse of a right triangle with sides 8 and 15. If you don't recognize this {8, 15, 17} Pythagorean triple, you can find the hypotenuse using the Pythagorean theorem:

  c² = a² +b²

  c² = 8² +15² = 64 +225 = 289

  c = √289 = 17

The long side of the triangle is 17 units.

The perimeter of the triangle is the sum of the lengths of its sides:

  P = 8 + 15 + 17 = 40

The perimeter is 40 units.

__

Additional comment

A "Pythagorean triple" is a set of three integer side lengths that form a right triangle. The triple is "primitive" if the numbers have no common factor. There are a few Pythagorean triples that regularly show up in algebra, trig, and geometry problems. Some of them are ...

  {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}

You will also see multiples of these, for example, 2·{3, 4, 5} = {6, 8, 10}.

The smallest is {3, 4, 5}, and it is the only set that is an arithmetic sequence (has constant differences between lengths). In every case, the sum of the numbers is even. (A right triangle cannot have integer side lengths and an odd perimeter value.)

The rational inequality f(x) > 0 has the solution x > - 7

A rational inequality is an inequality in the form of a fraction

Given the function f(x) = (x + 7)/(x² - 4x + 3)

To find the value of x for which the function f(x) > 0, we proceed as follows

Given that f(x) > 0

So, this means that

(x + 7)/(x² - 4x + 3) > 0

This implies that

x + 7 > 0

Subtracting 7 from both sides, we have that

x + 7 - 7 > 0 - 7

x + 0 > - 7

x > - 7

So, f(x) > 0 has the solution x > - 7

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Answer:

Step-by-step explanation:

If P = 3x² - x + 2 and Q = x² + 5x - 6, then P+ Q =  3x² - x + 2 + x² + 5x - 6 =

4x^2 +4x - 4

D = 16 + 64 = 80

x12 = [tex]\frac{-4+-\sqrt{80} }{8}[/tex]

Answer: 1809.6

Step-by-step explanation: I got to be honest is looked up the cone calculator and I tried 3 three and they all go me 1809.6 (rounded)

The calculated value of the percent of decrease from 8 to 6 is 25%.

To find the percent of decrease from 8 to 6, we need to find the difference between the two numbers and express it as a percentage of the original number (8).

The difference between 8 and 6 is 8 - 6 = 2.

To express this difference as a percentage of 8, we can use the formula:

percent decrease = (difference / original number) x 100%

Substituting the values we get:

percent decrease = (2 / 8) x 100% = 0.25 x 100% = 25%

Therefore, the percent of decrease from 8 to 6 is 25%.

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