Solve for x
8x + 3=19
x + 4 = 11

The answer of the given question based on the trigonometry is ,  the value of tan(2x) is - (16√10) / 9.Option (f) is correct. None of these.

Given: cos(x) = -7/3

Here, we have to find the value of tan(2x) Formula used:

tan(2x) = 2tan(x) / (1 - tan²(x))

Now, we have to find the value of tan(x).

For that, we will use the Pythagorean identity, i.e.,

sin²(x) + cos²(x) =

1cos(x) = -7/3sin²(x) + (-7/3)²

= 1sin²(x) = 1 - (-7/3)²

= 1 - 49/9= (9 - 49) / 9

= -40/9    [We took negative square root because 270° < x < 360°, in which sin(x) is negative]

sin(x) = - √(40/9)

= - (2√10)/3tan(x)

= sin(x) / cos(x)

= - √40 / 7

Now, putting the value of tan(x) in the formula,

tan(2x) = 2tan(x) / (1 - tan²(x))

= 2(-√40/7) / [1 - (-40/49)]

= - (16√10) / 9

So, the value of tan(2x) is - (16√10) / 9.Option (f) is correct. None of these.

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Step-by-step explanation:

First digit :  6 choices

Second digit:  6 choices

Third digit:   3 choices   ( 2, 4 or 6 to be an even number)

6 x 6 x 3 = 108 possibles

Answer:

Step-by-step explanation:

Down payment = $150

Monthly Payment = $48.5

Buyer price = $1250

Number of months = 30  (2 1/2 years)

The total amount of monthly payments = Monthly payments × Number of months

                                                                  = 48.5 × 30

                                                                  = 1447.50

The total cost = Total amount of monthly payments + Down payments

                       = 1447.50 + 150

                       = 1597.50

Finance charge =  Total cost  - Buyer price

                          = 1597.50 - 1250

                          = 347.50

The area of the real object represented by the scale drawing is 128 square cm. Thus, the correct answer is option A: 128 square cm.

A scale factor of 1:8 means that every measurement on the scale drawing is 1/8th of the corresponding measurement on the real object. Since the scale drawing has an area of 2 square cm, we need to determine the area of the real object.

To find the area of the real object, we can use the relationship between the scale factors of length and area. Since the scale factor is 1:8, the length ratio between the scale drawing and the real object is 1:8. However, the area ratio is squared, so the area ratio between the scale drawing and the real object is (1:8)^2, which simplifies to 1:64.

Since the area of the scale drawing is 2 square cm, we can multiply it by the area ratio (1:64) to find the area of the real object.

2 square cm * 64 = 128 square cm.

Therefore, the area of the real object represented by the scale drawing is 128 square cm. Thus, the correct answer is option A: 128 square cm.

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Answer:

Step-by-step explanation:

remember that the surface area is

S=2lw+2lh+2hw

S=2(15*20)+2(15*8)+2(8*20)=600+240+320=1160 cm^2

The surface area of the cuboid is 1160 square cm whose dimensions are

l= 20cm, w= 8 cm and h = 15 cm.

Given:

Length = 20 cm

width = 8 cm

Height = 15 cm

So, the formula for Surface area of Cuboid is

= 2(lw+ wh + lh)

Substituting the values l= 20cm, w= 8 cm and h = 15 cm into the formula as

= 2(lw+ wh + lh)

= 2 (20 x 15 + 8 x 15 + 8 x 20)

= 2 (300 + 120 + 160)

= 2 (580)

= 1160 square cm

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Answer:

24 pots 2 plates

Step-by-step explanation:

Answer:

24 pots and 2 plates

Step-by-step explanation:

The rule of the simple interest is

I = Prt, where

P is the money invested

r is the rate

t is the time

In the question

P = $7500

r = 3% = 3/100 = 0.03

t = 5

Substitute these values in the equation above

I = 1125

The interest is $1125

Answer:

0,3

Step-by-step explanation:

   6x + 3y = 9

+  -6x + 4y = 12

=

7y = 21

y = 3

Replace 3 into one of the equations and solve for x

6x + 3(3) = 9

6x + 9 = 9

6x = 0

x = 0

Answer:

There are 640 pigs after 5 years.

Step-by-step explanation:

if it doubles each year the first year it doubles it is 40 then the second 80 third 160 fourth 320 and fifth 640.

graph it by having the X axis the years and the Y axis do it by 40s

The area of the triangle is 25 square units.

we can use the formula for the magnitude of the cross product of two vectors. Let's consider two vectors formed by the given points: vector A = (1, 1, 1) - (0, 0, 0) = (1, 1, 1) and vector B = (0, -6, 7) - (0, 0, 0) = (0, -6, 7). The cross product of A and B can be calculated as follows:

A × B = |i j k |

|1 1 1 |

|0 -6 7 |

The cross product A × B yields the vector (-13, -7, -6). The magnitude of this vector can be calculated using the formula: √((-13)^2 + (-7)^2 + (-6)^2) = √(169 + 49 + 36) = √254 = 2√(63) ≈ 15.94. Since the area of a triangle is half the magnitude of the cross product of two of its sides, the area of the given triangle is 0.5 * 15.94 = 7.97 square units.

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\(\\ \rm\Rrightarrow \sqrt{3tan(2x-10)}+1=0\)

\(\\ \rm\Rrightarrow \sqrt{3tan(2x-10)}=-1\)

\(\\ \rm\Rrightarrow 3tan(2x+10)=1\)

\(\\ \rm\Rrightarrow tan(2x+10)=1/3\)

\(\\ \rm\Rrightarrow 2x+10=18\)

\(\\ \rm\Rrightarrow 2x=8\)

\(\\ \rm\Rrightarrow x=4\)

Answer:

\(\frac{1}{7^6}\)

Step-by-step explanation:

When we have a negative exponent in the form a^-x, this is equal to 1/a^x.

We can apply this here, where a = 7, and x = 6.

Hence, 7^-6 = 1/(7^6)

Answer:

x = 0; x = \(\frac{-276}{5}\)

Step-by-step explanation:

45x = 25x(57 + x)

45x = 1425x + 25x²

25x² + 1425x - 45x = 0

25x² + 1380x = 0

5x(5x + 276) = 0

\(\left \{ {{5x=0} \atop {5x + 276=0}} \right.\)

\(\left \{ {{x=0} \atop {x=\frac{-276}{5} }} \right.\)

\(\frac{11}{13}\) % of a quantity is equal to 0.00846 of the quantity.

A percentage is a figure or ratio that can be stated as a fraction of 100 in mathematics. If we need to determine a percentage of a number, multiply it by 100 and divide it by the total. So, a part per hundred is what the percentage refers to. Percent signifies for every 100. The sign "%" is used to denote it.

When a fraction of a whole is expressed as a number between 0 and 100, it is called a percentage. All of something is 100 percent, half of it is 50 percent, and none of it is 0%.

11/ 13 % of a quantity or 0.846 % of a quantity means

0.846 / 100 = 0.00846

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The inequality that describes the problem is x - 30 ≤ 15

Let x represent how much money Michael expects to spend on sports wear

If Michael just started middle school this year, and his grandmother will give him some money to buy new spirit wear and buys hoodie for $30, the balance remaining will be x - 30

If Michael figures he'll need at most $15 more to buy a T-shirt, hence the resulting inequality will be:

x - 30 ≤ 15

Add 30 to both sides

x - 30 + 30  ≤ 15 + 30

x  ≤ 45

Hence the inequality that describes the problem is x - 30 ≤ 15 and Michael expects to spend at most $45 on sports wear.

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The type of triangle is a Right isosceles triangle.

An isosceles triangle is a type of triangle with two angles equal and corresponding sides equal. A right angle triangle is a type of triangle in which one if it's sides is exactly 90°.

Therefore an Isosceles Right Triangle is a right triangle that consists of two equal length legs.

This means one side must be 90° and the other two angles must be equal.

Therefore the value of the other two angles =

2x +90 = 180

2x = 180-90

2x = 90

x = 90/2

x = 45°

therefore each side will be 45°

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The statement "The height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is 1/(a-b)" is False.

In a uniform distribution, the probability density function (PDF) is constant within the interval [a, b]. The height of the PDF represents the density of the probability distribution at any given point within the interval. Since the PDF is constant, the height remains the same throughout the interval.

To determine the height of the PDF, we need to consider the interval length. In a uniform distribution defined on the interval [a, b], the height of the PDF is 1/(b - a) for the PDF to integrate to 1 over the entire interval. This means that the total area under the PDF curve is equal to 1, representing the total probability within the interval [a, b].

Therefore, the correct statement is that the height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is not 1/(a - b), but rather it is a constant value necessary for the PDF to integrate to 1 over the interval, i.e., 1/(b - a).

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Answer:

x = 8

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion , that is

\(\frac{RT}{WU}\) = \(\frac{RS}{WV}\) ( substitute values )

\(\frac{6x+15}{28}\) = \(\frac{108}{48}\) ( cross- multiply )

48(6x + 15) = 28 × 108 = 3024 ( divide both sides by 48 )

6x + 15 = 63 ( subtract 15 from both sides )

6x = 48 ( divide both sides by 6 )

x = 8

Using the formula for the equivalent resistance that we have known from the question; x = -9 ± √91/5

The equivalent resistance is a measure of the total resistance of a circuit that is made up of multiple resistors. When resistors are connected in a circuit, they can be arranged in series or parallel configurations, which affects the overall resistance of the circuit.

Using;

1/Rn = 1/R1 + 1/R2

1/2 = 1/x + 4 + 1/5x

1/2 = 5x + x + 4/5x (x + 4)

1/2 = 6x + 4/5x^2 + 20x

6x + 4 = 10x^2 + 40x

10x^2 - 6x + 40x - 4 = 0

10x^2 + 36x - 4 = 0

x = -9 ± √91/5

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Answer:

the answer is y=3x+3

Step-by-step explanation:

Answer: 3x+3

Step-by-step explanation:

Find the mx+b

B= 3, starting point on y-axis

M = 3, find rise over run.

Answer:

x = 20

Step-by-step explanation:

X = 20 Because the values are Corresponding Angles This means that they are congruent

well, you'd have the 2000 plus the 7% :|

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7\% of 2000}}{\left( \cfrac{7}{100} \right)2000}\implies 140~\hfill \underset{ new~balance }{\stackrel{ 2000~~ + ~~140 }{\text{\LARGE 2140}}}\)

Answer:

3.5% means that their is 3.5 grams of salt in 100 grams of water

so 3.5 grams

Hope This Helps!!!

Answer:

3.5 grams

Step-by-step explanation:

Given the following question:

100 grams of sea water

3.5% of salinity

In order to find the answer, we have to find 3.5% of 100.

\(\frac{3.5\times100}{100} =3.5\times100=350\div100=3.5\)

\(=3.5g\)

Hope this helps.

The inequality to determine the number of sets of glasses is

166 + 18x ≥ 643

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Number of glasses available = 166

Number of glasses needed at the least = 643

Number of glasses in a set = 18

Now,

The number of sets of glasses to have enough glasses.

166 + 18x ≥ 643

18x ≥ 643 - 166

18x ≥ 477

x ≥ 26.5

Thus,

The number of sets of glasses required is 27.

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Answer:

C (a, b) is the cordinates of point c.

Given:

\(ABDF\sim VXZT\)

To find:

The pairs of congruent angles and the extended proportion that relates the corresponding sides for the similar polygons.

Solution:

We have,

\(ABDF\sim VXZT\)

The corresponding angles of similar polygons are congruent. So,

\(\angle A\cong \angle V\)

\(\angle B\cong \angle X\)

\(\angle D\cong \angle Z\)

\(\angle F\cong \angle T\)

The corresponding sides of similar polygons are proportional. So,

\(\dfrac{AB}{VX}=\dfrac{BD}{XZ}=\dfrac{DF}{ZT}=\dfrac{A F}{VT}\)

Therefore, the required solutions are \(\angle A\cong \angle V,\angle B\cong \angle X,\angle D\cong \angle Z,\angle F\cong \angle T\) and \(\dfrac{AB}{VX}=\dfrac{BD}{XZ}=\dfrac{DF}{ZT}=\dfrac{A F}{VT}\).

Answer:

107.76

Step-by-step explanation:

We are told in the above question that:

He flew 3,610 miles in 33.5 hours. If he flew about the same number of miles each hour, how many miles did he fly each hour?

We solve the above question by:

33.5 hours = 3610 miles

1 hour = x miles

Cross Multiply

33.5 hours × x miles = 3610 miles × 1 hour

x miles = 3610 miles × 1 hour/33.5 hours

x miles = 107.76119403 miles

Approximately = 107.76 miles per hour

Therefore, he flew 107.76 miles each hour

Answer:

8 x 12 = 96    10 x 8 = 80   96 + 80 = 176 so the answer is 8 helmets and 10 pumps

Step-by-step explanation:

Answer:

C. x > 15

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

This can be calculated by taking 10 (the number of digits available) to the power of 6 (the number of digits that must be different) and multiplying that by 10 (the number of digits available to be repeating number). 10^6 * 10 = 3,628,800.

The number of different 9-digit pins where exactly three of the digits are the same and none of the remaining digits may be repeated can be calculated using the formula 10^6 * 10. The first part is 10^6, which is taking 10 (the number of digits available) to the power of 6 (the number of digits that must be different). This means that each of the 6 digits that must be different can be any of the 10 digits available. The second part is the multiplication of 10 (the number of digits available). This is to represent the fact that the remaining three digits can be any of the 10 digits available, and none of them can be repeated. Finally, the result of 10^6 * 10 is 3,628,800, which is the number of different 9-digit pins where exactly three of the digits are the same and none of the remaining digits may be repeated.

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