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Which trigonometric expression can be used to find value of x? Replace a and b with the correct values.
(trigonometry)

The component form of the vector that translates the top house figure to the bottom house figure is (6, -4).

The component form of a vector is known to be depicted as < x, y >.

Note that:

x  - tells the distance or how far to the right or left, a vector is known or seen to be going.

y -  tells the distance or how far to  the upper part or downward a vector is known or seen to be going.

From the question and looking at the image attached, we were able to obtain (-4,4) and (2, 0)

So:

⇒  (-4,4)  --------(-4+6)(4-4)-------(2,0)

⇒ (6,-4)

Hence, The component form of the vector that translates the top house figure to the bottom house figure is (6, -4).

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Answer: 8/50 = 16%

Step-by-step explanation:

The spread of the disease will take a time 100 days to reach 2,500 infected people.

In this problem we have a radical equation that represents the number of infected people as a function of time, we are suppose to find the time when that number will be 2,500 by algebra properties: (N = 2,500)

2,500 = 250 · √t

√t = 2,500 / 250

√t = 10

t = 10²

t = 100

The spread of the disease will take a time 100 days to reach 2,500 infected people.

The statement is poorly formatted and presents typing mistakes, correct form is shown below:

The spread of a disease can be modeled as N(t) = 250 · √t, where N is the number of infected people, and t is time (in days). How long will it take until the number of infected people reaches 2,500?

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The number with the given properties is 17

Let the tens be x and the units be y.

So, the number is 10x + y

The relationship between the digits is

[tex]y = x + 6[/tex]

The relationship between the number and the reverse is

[tex]2(10x + y + 10y + x) = 6 + 10 * (10x + y)[/tex]

Simplify the second equation

[tex]2(11x + 11y) = 6 + 100x + 10y[/tex]

Open the brackets

[tex]22x + 22y = 6 + 100x + 10y[/tex]

Substitute y = x + 6

[tex]22x + 22(x + 6) = 6 + 100x + 10(x + 6)[/tex]

Expand

[tex]22x + 22x + 132 = 6 + 100x + 10x + 60[/tex]

Collect like terms

[tex]22x + 22x - 100x - 10x = 6 + 60 - 132[/tex]

Evaluate the like terms

[tex]-66x = -66[/tex]

Divide by -66

x = 1

Substitute x = 1 in y = x + 6

[tex]y = 1 + 6[/tex]

y = 7

Recall that the number is 10x + y

So, we have

Number = 10 * 1 + 7

Evaluate

Number = 17

Hence, the number is 17

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Based on the given current and the given resistance, the voltage of the current is 14 + j8

From the question, we have the following parameters

current of 4+j2 amps and a resistance of 2-j3 ohms.

This can be rewritten as:

Current (I) = 4+j2 amps

Resistance (R) = 2-j3 ohms.

The formula to calculate voltage is given as

Voltage=(current) × (resistance)

Rewrite as:

V = I * R

Substitute the known values in the above equation

V = (4 + j2) * (2 - j3)

Expand the brackets

V = 8 - j4 + j12 + 6

Collect the like ters

V = 8 + 6 - j4 + j12

Evaluate the like term

V = 14 + j8

Based on the given current and the given resistance, the voltage of the current is 14 + j8

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The FOIL method is a method of expanding two given brackets by following the required steps. Thus using the FOIL method, the required answer is: -7

Expansion of brackets may be done using different methods, but these methods would give the same answer. Some methods that can be used are the binomial expansion method, FOIL method, etc.

The FOIL method is a shortened form of the steps required for the process. These required steps are First, Outside, Inside, and last.

Thus to expand the given brackets in the question, we have;

(5+2)(4-5) = 5(4 - 5) + 2(4 - 5)

                = 20 - 25 + 8 - 10

                = 28 - 35

(5+2)(4-5) = -7

Thus using the FOIL method, the answer to the question is -7.

Quick check: (5+2)(4-5) = (7)(-1)

                             = -7

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Give f(x) a dotted boundary and shade it above.

Give g(x) a solid boundary and shade it above.

The solution set is the region that is in the shaded region of both graphs.

Answer:

50/20

Step-by-step explanation:

Rate of money raised raises per jump is  

                          money raised / jumps

                                       $50/ 20 jumps

We can think that if we divide the $50 into 20 equal parts,

each part will represent 1 jump and will have 50/20 = $2.5  per 1 jump.

Answer:

35

Step-by-step explanation:

Since the two sides are equal in a parallelogram angle B = y ,so we have angle to be equal to 145°

We sum both angles and divide from

360° - [145° +145°]

360° - 290° = 70

Since the left sides( X And Z) are equal then we divide what we got into 2

70 ÷ 2 = 35

therefore angle X equals 35

The area of the region enclosed by the curves x + y = 1, x - 3 = y, y = √x and x = 0 is 16.815 square units.

In this question we must determine the area generated by four functions: three linear functions and a radical function. First, we plot the four functions to determine the required combinations of definite integrals need for calculation:

[tex]A = \int\limits^{0.382}_0 {[f(x) - g(x)]} \, dx + \int\limits^2_{0.382} {[h(x) - g(x)]} \, dx[/tex], where f(x) = √x, g(x) = x - 3 and h(x) = - x + 1.

[tex]A = \int\limits^{0.382}_{0} {[\sqrt{x} - x + 3]} \, dx + \int\limits^{2}_{0.382} {[- 2 \cdot x + 4]} \, dx[/tex]

[tex]A = \int\limits^{0.382}_{0} {\sqrt{x}} \, dx - \int\limits^{0.382}_{0} {x} \, dx + 3 \int\limits^{0.382}_{0}\, dx - 2 \int\limits^{2}_{0.382} {x} \, dx + 4 \int\limits^{2}_{0.382}\, dx[/tex]

[tex]A= 2 \cdot x^{\frac{3}{2} }|_{0}^{0.382} - \frac{x^{2}}{2}|_{0}^{0.382} + 3\cdot x |_{0.382}^{2} - x^{2} |_{0.382}^{2}+4\cdot x |_{0.382}^{2}[/tex]

[tex]A = 2 \cdot (0.382^{\frac{3}{2} }-0^{\frac{3}{2} })-\left(\frac{1}{2} \right)\cdot (0.382^{2}-0^{2}) + 3 \cdot (2 - 0.382) - (2^{2}-0.382^{2})+4\cdot (2^{2}-0.382^{2})[/tex]

A = 16.815

The area of the region enclosed by the curves x + y = 1, x - 3 = y, y = √x and x = 0 is 16.815 square units.

The statement reports an inconsistency with at least one function and needs to be modified in order to apply definite integrals in a consistent manner. New form is shown below:

Sketch the region enclosed by the given curves and find its area: (i) x + y = 1, (ii) x - 3 = y, (iii) y = √x, (iv) x = 0.

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Answer:

29.5

Step-by-step explanation:

[tex]UV=\frac{27+32}{2} \\ \\ UV=29.5[/tex]

The probability that a randomly selected member did not volunteer for the recent activity is 19/43.

Probability determines the odds that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

The probability that a randomly selected member did not volunteer for the recent activity = 1 - ratio of randomly selected members that volunteered

1 - 24/43

(43/43) - (24/43) = 19/43

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Answer:

C looks most correct

Step-by-step explanation:

See attachment for the graph of the inequality expression x + 2y > 6

The condition is given as:

{(x, y): x + 2y > 6}

This means that

x + 2y > 6

The above is an inequality expression, where the variables are x and y

So, we simply plot the graph of the inequality expression x + 2y > 6

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Answer:

1&2)

GH = 28

FH = 56

XY = 7

XZ = 14

3-6) Acute, Obtuse, Acute, Right

7) Perimeter: 40 in. Area: 84 in^2

8) Perimeter: 42 m.  Area: 84 m^2

9) Perimeter: 15.2 yd. Area: 14.44 yd^2

10) 1, 8, 27, 64, 125 These are the cubes of 1, 2, 3, 4, 5 so it's just the cube of the next number that was cubed before.

11) 128, 32, 8, 2, 1/2 Divide the previous number by 4.

12) 2, -6, 18, -54, 162 Multiply the previous number by -3

13-15) I'm sorry we didn't do those so I don't really know how that works sorry.

16) 3x - 14 = 34

3x = 48 Add 14 to each side (to isolate 3x)

x = 16 Divide by 3 both sides (to get x)

17) -4(x+3) = -28

x+3 = 7 divide by -4 on both sides (to get a step closer to solving for x and isolating x+3)

x = 4 subtract 3 from both sides (to get x (isolating x))

18) 43 - 9(x-7) = -x - 6

43 - 9x + 63 = -x - 6 distribute 9 to x and 7 (to expand)

106 - 9x = -x - 6 combine like terms (easier to deal with)

106 - 8x = -6 add x to both sides (so there's only x on one side)

112 - 8x = 0 add 6 to both sides (only one number left)

112 = 8x move -8x to the right side

x = 14 divide by 8 (to isolate x)

19) x = 29 degrees

20) x = 13 degrees

21) x = 9 degrees, y = 31 degrees

Step-by-step explanation:

4x = 5x-7

x = 7

GH = 5(7) - 7 = 35 - 7 = 28

FH = 4x + 5x - 7 = 4(7) + 28 = 28*2 = 56

3x - 5 = x + 3

x = 4

XY = 3(4) - 5 = 12 - 5 = 7

XZ = 7*2 = 14

Acute is < 90

Obtuse is > 90

Right is = 90

Straight is = 180

7) 2(6+14) = 2(20) = 40 in

6*14 = 84 in^2

8) 13+14+15 = 42 m

(12*14)/2 = 6*14 = 84 m^2

9) 3.8*4 = 15.2 yd

3.8^2 = 14.44 yd^2

19) 34 + 4x + 30 = 180

64 + 4x = 180

4x = 116

x = 29

20) 4x + 7x + 37 = 180

11x = 143

x = 13

21) 3y + 42 = 9x + 54

y + 14 = 3x + 18

y = 3x + 4

3y + 42 + 5x + 9x + 54 + 5x = 360

3y + 19x = 264

substitute y with 3x + 4

3(3x + 4) + 19x = 264

9x + 12 + 19x = 264

28x = 252

x = 9

so y = 3(9) + 4 = 27 + 4 = 31

Answer:

x = 6

Step-by-step explanation:

The missing length of the right triangle is 13.41 inches.

A right angle triangle has one of its angles as 90 degrees.

The side length of a right triangle can be found using Pythagoras theorem.

Therefore,

c² = a² + b²

where

Therefore,

x² = 18² - 12²

x² = 324 - 144

x² = 180

x = √180

x = 13.416407865

x = 13.41 inches

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The probability that a truck drives between 150 and 156 miles in a day is 0.0247. Using the standard normal distribution table, the required probability is calculated.

The formula for calculating the probability distribution for a random variable X, Z-score is calculated. I.e.,

Z = (X - μ)/σ

Where X - random variable; μ - mean; σ - standard deviation;

Then the probability is calculated by P(Z < x), using the values from the distribution table.

The given data has the mean μ = 120 and the standard deviation σ = 18

Z- score for X =150:

Z = (150 - 120)/18

   = 1.67

Z - score for X = 156:

Z = (156 - 120)/18

  = 2

So, the probability distribution over these scores is

P(150 < X < 156) = P(1.67 < Z < 2)

⇒ P(Z < 2) - P(Z < 1.67)

From the standard distribution table,

P(Z < 2) = 0.97725 and P(Z < 1.67) = 0.95254

On substituting,

P(150 < X < 156) = 0.97725 - 0.95254 = 0.02471

Rounding off to four decimal places,

P(150 < X < 156) = 0.0247

Thus, the required probability is 0.0247.

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The vector in component form is given by:

V = i - j.

A vector is given by the terminal point subtracted by the initial point, hence:

(3,-4) - (2, -3) = (3 - 2, -4 - (-3)) = (1, -1)

A vector (a,b) in component form is:

V = a i + bj.

Hence, for vector (1,-1), we have that:

V = i - j.

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Answer: 22.5 inches

Step-by-step explanation:

[tex]p=s+s+s+s+s[/tex]

[tex]5(4.5 in)=p[/tex]

∴ 22.5 inches = perimeter of the pentagon

(i) The exponential growth model to predict the number of rabbits after 'x' years is [tex]A = 2e^{6.21460809842x}[/tex].

(ii) The number of rabbits at the end of 3 years will be 250000000.

A continuous exponential growth function is of the form [tex]A = Pe^{rt}[/tex], where A is the final amount, which was initially P, growing continuously at the rate of r, after a time of t years.

In the question, we are asked to construct an exponential model to predict the number of rabbits after 'x' years.

We assume the exponential growth model to be a continuous model, of the form [tex]A = Pe^{rt}[/tex], where A is the final amount of rabbits, which was initially P, growing continuously at the rate of r, after a time of t years.

The initial quantity of rabbits, P = 2.

Time, t = x years.

Substituting the values, we get:

[tex]A = 2e^{rx}[/tex] ... (i)

We have been told that after 1 year, the number of rabbits was 1000.

Thus, substituting A = 1000, and x = 1, we get:

[tex]1000 = 2e^{r*1}\\\Rightarrow 1000 = 2e^r\\\Rightarrow e^r = 1000/2 = 500[/tex]

Taking log on both sides, we get:

[tex]log_ee^r = log_e500\\\Rightarrow rlog_ee = log_e500\\\Rightarrow r = 6.21460809842[/tex]

Thus, the rate of growth, r = 6.21460809842.

Substituting r = 6.21460809842 in (i), we get:

[tex]A = 2e^{6.21460809842x}[/tex], which is the required model.

To find the number of rabbits at the end of 3 years, we put x = 3, in the above equation to get:

[tex]A = 2e^{6.21460809842*3}\\\Rightarrow A = 2e^{18.6438242953}\\\Rightarrow A = 2*125000000\\\Rightarrow A =250000000[/tex]

Thus, there would be 250000000 rabbits at the end of 3 years.

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The Two sets, A and B, are said to be disjoint sets if A n B=ϕ

The Two sets, A and B, are said to be disjoint sets if A n B=ϕ

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Answer:

Step-by-step explanation:

If they all exist in proportion to one another (READ: ratio) then multiplying each of the angles by the same number (here, some unknown "x" value) will maintain the proportionality. Since all the angles of a quadrilateral have to add up to equal 360, then

2x + 4x + 5x + 7x = 360 and

18x = 360. Divide both sides by 18 to get that

x = 20. That means that

2x = 2(20) = 40 and

4x = 4(20) = 80 and

5x = 5(20) = 100 and

7x = 7(20) = 140. Adding all of those up:

40 + 80 + 100 + 140 = 360

Answer:

40,80,100,140

Step-by-step explanation:

Let the ratio 2:4:5:7 angles be 2x, 4x, 5x, 7x

Now

2x + 4x + 5x + 7x=360 degrees

18x = 360 degrees

x =360/18

x=20

2x=2 *20=40

4x=4 *20=80

5x=5 *20=100

7x=7* 20=140

Triangle MNL and triangle QNL are congruent to each other based on by either ASA or AAS.

A triangle is a polygon with three sides and three angles. Types of triangles are isosceles, equilateral, scalene and right angle triangle. Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent to each other.

From triangle MNL and triangle QNL, in triangle MNL:

∠M + ∠N + ∠L = 180° (sum of angles in a triangle)

90 + 58 + ∠L = 180

∠L = 32°

Hence Triangle MNL and triangle QNL are congruent to each other based on by either ASA or AAS.

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The ratio of cos Z is cos Z = 3 / 5

A right triangle has one angle of the triangle as 90 degrees.

The sides of the right triangle can be found using trigonometric ratios.

Therefore,

sin ∅ = opposite / hypotenuse

sin Z = 3 / 5

Using Pythagoras theorem,

c² = a² + b²

5² - 3² = b²

b² = 25  - 9

b² = 16

b = √16

b = 4

Hence,

P + A = 90 degrees (complementary angles)

Therefore,

sin P = cos Z

cos Z = 3 / 5

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The number shown on the calculator display can be written in standard form as 6 x 10¹⁰.

The product of 200,000 and 300,000 is calculated as follows;

200,000 × 300,000 = 6E+10

Standard form is a mathematical way or a standard way of presenting numbers as a mathematical expression.

It presents numbers in the simplest form.

200,000 × 300,000 = 6 x 10¹⁰

Thus, the number shown on the calculator display can be written in standard form as 6 x 10¹⁰.

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The number of kilometres travelled by the satellite in discuss in which case, the satellite makes 8 revolutions around the earth is; C = 177,271.8 km.

Given from the task content, the earth's diameter is; 6371 km and since, the height at which the satellite orbits the earth is; 343km, it follows that the diameter of orbit if the satellite in discuss is;

D = 6371 + (343)×2

Hence, we have; diameter, D = 7057 km.

Hence, the distance travelled after 8 revolutions is;

C = 8 × πd

C = 8 × 3.14 × 7057

C = 177,271.8 km.

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The amount of George's income that is subject to withholding is $75,000, which excludes the alimony income.

Alimony income represents the amount received from a spouse or a former spouse under a divorce or separation instrument.

The incomes subject to withholding include the following:

Wages income = $50,000

Gambling winning = $20,000

Alimony income = $10,000

Dividend income = $5,000

Income subject to withholding = $75,000 ($20,000 + $20,000 + $5,000)

Thus, George's income that is subject to withholding is $75,000, excluding the alimony income.

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