Verify the trig identity and show all expanded steps

Answer:The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.

Step-by-step explanation:

The solution of the system of equations is y = 5 and x = 3, and the difference x - y gives:

x - y = -2

Here we have the system of equations:

5x + 3y = 30

-5x - 2y = -25

If we add the two equations we will get:

(5x + 3y) + (-5x - 2y) = 30 + (-25)

y = 5

So just by doing that we found the value of the variable y.

To find the value of x, we can replace the known value of y on one of the equations, doing that we will get:

5x + 3y = 30

5x + 3*5 = 30

5x + 15 = 30

5x = 30 - 15 = 15

x = 15/5 = 3

x = 3

Then the difference x - y gives:

x - y = 3 - 5 = -2

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From the given graphs the values of 'c' and 'd' are c = -0.84,

d = 0.84.

What is sinusoidal wave?

A mathematical curve defined in terms of the sine trigonometric function, of which it is the graph, is known as a sine wave, sinusoidal wave, or simply sinusoid. It is a smooth periodic function and a particular kind of continuous wave.

Let the graphs of y = cos(x) and y = cos(x/2) are given.

From this graphs we have to find the value of c and d.

First from y = cos(x) to find the value of 'a'.

Consider, the point  [tex](a, \frac{1}{8})[/tex]

⇒

[tex]cos(a) = \frac{1}{8} \\a = cos^-^1(\frac{1}{8})\\ a = 82.82[/tex]

Now to find the value of 'c'.

Plug a = 82.82 in y = cos(x/2).

[tex]cos(\frac{82.82}{2}) = c \\c = -0.84[/tex]

Hence, the value of 'c' is 'c = -0.84'.

Now to find the value of 'd'.

Consider, the point [tex](b, \frac{1}{8})[/tex]

⇒

[tex]cosb = \frac{1}{8} \\b = cos^-^1(\frac{1}{8})\\b = 82.82[/tex]

Now, plug b = 82.82 in y = cos(x/2)

[tex]cos(\frac{82.82}{2}) = d\\ d = 0.84[/tex]

Hence, from the given graphs the values of 'c' and 'd' are c = -0.84,

d = 0.84.

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43 Beacuse mee smart Beacuse mee smart

Answer: x=5

Step-by-step explanation:

5

x

+

10

=

35

Subtract

10

from both sides.

5

x

=

35

−

10

Simplify.

5

x

=

25

Divide both sides by

5

.

x

=

25

5

Simplify.

x

=

5

Answer:

X=5

Step-by-step explanation:

Answer:

y = 4x – 23

Step-by-step explanation:

(7,5) and m= 4

x1 = 7, y1 = 5

using the one point form formula

y – y1 = m(x – x1)

y – 5 = 4(x – 7)

y – 5 = 4x – 28

y = 4x – 28 + 5

y = 4x – 23

i hope this helps

pls rate as brainliest answer

The population 2 hours before that is 2691 if the population of a colony of bacteria increases by 4% of what the population was at the beginning of the hour.

A population is a distinct group of individuals that can be distinguished for the purposes of data collection and analysis by at least one feature. Populations are used in statistics and other branches of mathematics. Data is typically collected from a sample while learning about a large population.

Between sample size and population, the population will always be larger in number. The entire group of individuals under study is referred to as the population. 250 persons make up the population in the illustration, which is the same size as the high school under consideration.

We have P₀=2488

Rate of increase=R=4%

Time=2 hours

Bacteria count =P

P=P₀[tex](1+(R/100)^{T}[/tex]

=2488×(1+(4/100))²

=2488×1.0816

=2691.0208≈2691

Therefore, the population 2 hours before that is 2691.

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Answer: -9/y

Step-by-step explanation: quotient is a fancy word for divide

-9/y

Answer:

Below

Step-by-step explanation:

Value = 33000 ( .88)^t        each year, t , the value is only 88% ( or in decimal:  .88) of the prior year  ( 12 % decrease leaves 88% )

Answer:

  3³

Step-by-step explanation:

You want an expression using an exponent to represent the number 3·3·3.

As you know, a coefficient is used to represent repeated addition:

  a + a + a = 3a

The coefficient 3 in the above expression signifies that 'a' appears in the sum 3 times.

Likewise, repeated multiplication can be represented using a specific notation. An exponent signifies the number of times a factor appears in a product:

  a · a · a = a³ . . . . . 'a' is a factor 3 times

You have a sequence of numbers of telephone calls:

  3 the first day

  3·3 the second day

  3·3·3 the third day

The calls on the third day can be represented using an exponent:

  3³

__

Additional comment

When superscript formatting is not available for the exponent, it is signified by a caret (^). The same number is 3^3 when written in plain text.

As you might expect, a plain text exponent must be enclosed in parentheses if it is other than a single letter or number.

Answer:

x1 =1.317

x2=-5.317

Step-by-step explanation:

Answer: [tex]y+5=\frac{3}{2}(x-2)[/tex]

Step-by-step explanation:

[tex]2y=3x+10 \implies y=\frac{3}{2}x+5[/tex]

Parallel lines have the same slope, so the slope of the line we need to find is 3/2.

Substituting into point-slope form, the equation is [tex]y+5=\frac{3}{2}(x-2)[/tex].

Answer:

Step-by-step explanation:

Step-by-step explanation:

Steps for Solving Linear Equation

3x+14y=x

Subtract x from both sides.

3x+14y−x=0

Combine 3x and −x to get 2x.

2x+14y=0

Subtract 14y from both sides. Anything subtracted from zero gives its negation.

2x=−14y

Divide both sides by 2.

2x/2=-14y/2

Dividing by 2 undoes the multiplication by 2.

x=-14y/2

​Divide −14y by 2.

x=−7y

The angles BAX and CDX are equal and the length of CX is 8.2 cm.

What are angles?

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

Given that, the points A, B, C, D lie on a circle and AC and BD intersect at X.

The angles BAX and CDX, they are subtended by the same arc AD, hence, according to the property of angles subtended by the same arc, they are equal.

Thus ∠BAX = ∠CDX

Since, corresponding sides opposite to the equal angles are proportional.

CX/BX = CD/AB

⇒ CX/3.84 = 9.40/4.40

⇒ CX = (9.40*3.84)/4.40

⇒ CX = 8.2

Thus, length of CX is 8.2cm

The angles BAX and CDX are equal and the length of CX is 8.2 cm

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From the calculations triangle DEF ≠ triangle PQR

The side lengths of each triangle are

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

Triangle DEF

D(-7,-3), E(- 4, - 1)

D(-7,-3), F(- 2, - 5)

E(- 4, - 1)), F(- 2, - 5)

Triangle PQR

P(2,- 2) Q(5, - 4)

P(2,- 2) R(0, - 5)

Q(5, - 4) R(0, - 5)

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The classifications of the densities of these objects are given as follows:

The density of an object is calculated as the division of the object's mass by the object's volume, according to the equation presented as follows:

Density = mass/volume.

The standard unit of the mass of an object is in grams per cubic centimeters, that is, g/cm³.

Most of the known substances on earth also have known densities, and two examples are cooking oil and water, for which the densities are given as follows:

1 > 0.6, hence we have that:

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The number of classes per month that had same total amount paid was 21

The total amount is $115

let the number of group class be represented by x

first membership plan, Jen can pay $52 per month, plus $3 for each group class she attends

= $52 + $3x

second membership plan, Jen can pay $31 per month plus $4 per class

= $31 + $4x

when the total amount are equal

$52 + $3x = $31 + $4x

52 - 31 = 4x - 3x

21 = x

The total amount

= $52 + $3 * 21

= $115

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The percent of the increase in Paulina’s earnings is 15.55%.

The percentage is defined as a ratio expressed as a fraction of 100.

Last month, she earned $520.60. This month, she works overtime and earns $601.30.

The percent of increase = ($601.30 - $520.60)/520.60 x 100%

The percent of increase = (80.7)/520.60 x 100%

The percent of increase = 0.15501 x 100%

Apply the multiplication operation,

The percent of increase = 15.55 %

Thus, the percentage of the increase in Paulina’s earnings is 15.55%.

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Answer: they must have used up around 40% of the money if I’m wrong I’m so sorry

Step-by-step explanation: Good luck!

Answer:

[tex]18x+27y-45z[/tex]

Step-by-step explanation:

[tex]9(2x+3y-5z)[/tex]

[tex]= 9(2x)+9(3y)+9(-5z)[/tex]

[tex]=18x+27y-45z[/tex]

I would appreciate it if you mark my answer as brainliest.

Answer:  18x + 27y -45z

Step-by-step explanation:

9(2x + 3y - 5z)

= 18x + 27y -45z

Answer:

The value of the car at the end of 3 years will be £5,062.50.

Answer:

1) y=-2/3x+5

Step-by-step explanation:

Now I know that I didn't actually do the math for this one. I did see though that it needs to have the point (3,3) on the graph. So then I went to desmos graphing calculator, and I put all of them on the graph. The only one with a (3,3) point was number 1. I put it in the image below so you could see. I know that the rest aren't on there, that's because I removed them because they were in the way.

I hope this helps!!!

The Rileys will pay a total of $37500 in $250000 cost for the closing costs and down payment on their mortgage.

Given that,

The Rileys are spending $250,000 on a house. They are making a down payment of 12% and paying 3% in closing expenses.

We have to fill the blanks.

We know that,

$250000 Rileys are spending on a house.

The down payment for 12% and closing cost for 3%

So,

$250000×(12+3)%

$250000×15%

$37500

Therefore, The Rileys will pay a total of $37500 in $250000 cost for the closing costs and down payment on their mortgage.

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Answer:

6 (3x + 1)(x - 2) = 3x^2 - 2x + x - 2 = 3x^2 - x - 2

7 (x − 3)(2x - 1) = 2x^2 - x - 3x + 3 = 2x^2 - 4x + 3

8 (x-3y) (2x - y) = 2x^2 - yx - 3xy + 3y^2 = 2x^2 - 4xy + 3y^2

9 (2x - y)(x-2y) = x^2 - 3xy + 2y^2 = x^2 - 3xy + 2y^2

Each pound of fish and chicken will cost $3.75 and $2.25 respectively

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation

Given that:

1. A customer pays a total of $11.10 for 1.6 pounds of chicken

and 2 pounds of fish.

2. Another customer pays a total of $12.15 for 2.4 pounds of

chicken and 1.8 pounds of fish

Let C and F represent the cost of one pound of chicken and fish respectively

Statement 1:

1.6C + 2F = 11.10  ---- (1)

Statement 2:

2.4C + 1.8F = 12.15  ---- (2)

we have simultaneous equations now, let's solve using the elimination method:

1.6C + 2F = 11.10      ---- (1)

2.4C + 1.8F = 12.15  ---- (2)

2.4 × (1.6C + 2F = 11.10) =     3.84C + 4.8F = 26.64

1.6 × (2.4C + 1.8F = 12.15) =  3.84C + 2.88F = 19.44

                                            ..........................................

                                                           1.92F  = 7.2

Thus, 1.92F  = 7.2

F = 7.2/1.92 = $3.75

Put F = $3.75 into (1):

1.6C + 2F = 11.10

1.6C + 2(3.75) = 11.10

1.6C + 7.5 = 11.10

1.6C = 11.10 - 7.5

1.6C = 3.6

C = 3.6/1.6 = $2.25

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Answer:

  n = -104

Step-by-step explanation:

You want to identify a solution to the inequality -5 +n/13 < -12.

Adding 5 we get ...

  n/13 < -7

Multiplying by 13 gives ...

  n < -91

Of the choices available, only -104 is less than -91.

  n = -104

<95141404393>

Answer:

(1,2) - function

(3, -4) - function

(-3, -2) - function

(0, 0) - function

(-4,5) - function

(0, 4) - not a function

The 25 teams can there be at most.

What is the LCM?

Least Common Multiple(LCM) is a method to find the smallest common multiple between any two or more numbers. A common multiple is a number which is a multiple of two or more numbers.

We have,

75 fifth graders

125 fourth graders.

They are going to be grouped in teams for a field day with the same number of students on each team.

the same number of teams if there must also be the same number of fifth graders on each team.

take the LCM of the 75  & 125 Which is the 25.

3 fifth graders each

5 fourth graders each

Hence, the 25 teams can there be at most.

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Answer:

90 units²

Step-by-step explanation:

The scale factor of the lengths of the sides of a solid must be squared to to find the ratio of the areas and cubed to find the ratio of the volumes.

For example, if you are given two solids with a scale factor of the lengths of the sides of 2, meaning that the sides of the second solid are twice the length of the sides of the first solid, then the surface area of the second solid is 2² (= 4) times the surface area of the original solid, and the volume of the second solid is 2² (= 8) times the volume of the original solid.

Let's say you have a cube with edge of 1 cm. The volume is (1 cm)³ = 1 cm³.

The surface area is the sum of the areas of the 6 faces which are squares 1 cm by 1 cm. 6 × (1 cm)² = 6 × 1 cm² = 6 cm².

The original cube with edge of 1 cm has a volume of 1 cm³ and total surface  area of 6 cm².

Now double the size of the edge of the cube. The new cube has an edge of 2 cm. The volume is (2 cm)³ = 8 cm³. Each face of the cube is a square 2 cm by 2 cm. The total surface area of the new cube is 6 × (2 cm)² = 24 cm².

The new cube has volume 8 cm³ and total surface area 26 cm².

Compare the edges, surface areas and volumes of the two cubes:

                             Original Cube     Dilated Cube    Ratio new/dilated

Edge                              1 cm                    2 cm                    1:2

Surface area                 6 cm²                 24 cm²                 1:4

Volume                          1 cm³                  8 cm³                   1:8

Now here is your problem.

We start with the ratio of the volumes.

Original solid: 128 u³

Dilated solid: 54 u³

ratio of volumes: 54/128 = 27/64 = 3³/4³

The ratio of volumes is the cube of the ratio of the lengths.

ratio of lengths: 3/4

ratio of area: 3²/4² = 9/16

Surface area of original solid: 160 u² × 9/16 = 90 u²

Answer: 90 units²