!!Please help!! This is algebra and I don't understand

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Lhs = 2cos[5A+3A/2]cos[5A-3A/2]+2cos[15A+7A/2]cos[15A-7A/2]

=2cos4AcosA+2cos11Acos4A

=2cos4A[cosA+cos11A]

=2cos4A[2cos[11A+A/2]Cos[11A-A/2]

=2cos4A2cos5Acos6A

=4cos4Acos5Acos6A=Rhs

Thank you

Answer:

The answer is below

Step-by-step explanation:

a) T=2.25h+1.75d

To rewrite the equation to find d, we have to make d the subject of the formula.

T=2.25h+1.75d

Subtract 2.25h from both sides:

T - 2.25h = 2.25h + 1.75d - 2.25h

1.75d = T - 2.25h

Divide both sides by 1.75

1.75d/1.75 = (T - 2.25h) / 1.75

d = (T - 2.25h) / 1.75

b) Additive property and law of division

c) The money spent (T) = $18.25 and the number of hot dogs (h) = 5. To get the number of drinks, substitute the value of h and T in the equation d = (T - 2.25h) / 1.75. Hence:

d = (T - 2.25h) / 1.75

d = (18.25 - 2.25(5)) / 1.75

d = (18.25 - 11.25) / 1.75 = 7 / 1.75

d = 4

The number of drinks that can be bought is 4

Answer:

1st use distance formula for each side of the triangle

then use PT for checking if they are equal then u will get it as equal

then use area of triangle formula u will get the ans explanation:

Step-by-step explanation:

Volume of a Trapezoidal Prism. If the prism length is L,trapezoid base width B, trapezoid top width A, and trapezoid height H, then the volume of the prism is given by the four-variable formula: V(L, B, A, H) = LH(A + B)/2

Area of a trapezoid is found with the formula, A=(a+b)/2 x h.

Answer:

To find the surface area, the amount of space on the outside of a solid, of a trapezoidal prism, you'll need to find the area of the trapezoid base and multiply it by two. You'll then add the area of the four rectangles to the area of the two bases. Formula for Volume of a Trapezoidal Prism. If the prism length is L,trapezoid base width B, trapezoid top width A, and trapezoid height H, then the volume of the prism is given by the four-variable formula: V(L, B, A, H) = LH(A + B)/2.

Answer:

CT= $950

Step-by-step explanation:

Dado la siguiente información:

Servicio= $300 primeros dos

Servicio adicional= $150

Descuento= $100

Para calculate el costo total, tenemos que usar la siguiente formula:

CT= 300x + 150y - 100

x= costo normal

y= costo promocional

CT= 300*2 + 150*3 - 100

CT= $950

Answer:

Step-by-step explanation:

1. m/-8 = -2.5

*-8 = *-8

m = -2.5*-8

m = 2.5*8

m = 20

2. 7/8a = 42

*8            *8

7a = 336

/7       /7

a = 336/7

a = 48

Hope this helped,

Kavitha

Answer:

yearly salary = $54,708

Step-by-step explanation:

Let monthly salary be x

Let yearly salary be y

Let number of months be n

To estimate your average monthly salary, divide your yearly salary by the number of months in a year. This can be written as

x = y divided by n

[tex]x = \frac{y}{n}[/tex]

Therefore, writing an equation to determine yearly salary is the same as making the yearly salary 'y' the subject of the formula above:

[tex]x = \frac{y}{n}\\cross-multiplying\\n\ \times\ x= y\\y\ =\ nx[/tex]

where y = ???

x = $4,559

n = 12 months

[tex]y = 4,559\ \times\ 12 \\= \$\ 54,708[/tex]

Therefore yearly salary = $54,708

Answer/Step-by-step explanation:

a. From the bar graph, 1 student scored 9, 4 students scored 10.

Therefore, the no. of students who scored above 8 is: [tex] 1 + 4 = 5 [/tex]

b. From the graph, we have the following:

3 students scored 1

5 students scored 2

2 students score 4

6 students scored 5

12 students scored 8

1 student scored 9

4 students scored 10

Total no. of pupils in year 7 class = 3 + 5 + 2 + 6 + 12 + 1 + 4 = 33 students

c. It is assumed that all the students in Mr Hassan's year 7 class took the test.

Answer:

She bought 5 pounds

Step-by-step explanation:

Original worth of gift card = $80

Balance on card after purchase = $39.55

Amount used for purchase = 80 - 39.55 = $40.45

Next let us determine how many pounds of coffee she bought as follows:

Price of coffee = $8.09 per pound

amount spent on coffee = $40.45

Lett the number of pounds of coffee she bought be x

$ 8.09 = 1 pound

$40.45 = x pounds

since $8.09 = 1 pound

[tex]\$\ 1 = \frac{1}{8.09}\ pounds[/tex]

[tex]\$\ 40.45 = 40.45 \times\ \frac{1}{8.09} \\= \frac{40.45}{8.09}\\ = 5\ pounds[/tex]

Answer:

x = -16

Step-by-step explantion:

Solve for  x  by simplifying both sides of the equation, then isolating the variable.

Hope this helps!

(・∀・(・∀・(・∀・*)

Answer:

Step-by-step explanation:

+ si

Answer:

2.2%

Step-by-step explanation:

Given the following :

Population in year 2000 (A) = 4.2 million

Expected population every 32 years = 2 *A

The growth rate per year =?

The population figure after 32 years = (2 * 4.2 million) = 8.4 million

Using the exponential growth formula :

P(t) = A × (1 + r)^t

(1 + r) = g = Total growth percent

A = Initial population

t = time

P(t) = 8.4 million

8,400,000 = 4,200,000 × g^32

g^32 = (8400000/4200000)

g^32 = 2

Taking the root of 32 on both sides

g = 1.02189714865

g = (1 + r)

1.02189714865 = 1 + r

r = 1.02189714865 - 1

r = 0.02189714865

.rate = 0.02189714865 * 100

= 2.18971486541%

= 2.2% ( nearest tenth)

==============================================

Explanation:

The left endpoint is -2. The right endpoint is 10. Both endpoints are open holes, meaning we do not include them as part of the green shaded solution region. If x is a solution, then the solution can be described as [tex]-2 < x < 10[/tex] which converts to the interval notation [tex](-2, 10)[/tex]. The curved parenthesis says "do not include the endpoint".

Note: this is not ordered pair notation (x,y). Unfortunately math tends to reuse symbols so it might be a bit confusing at first.

Answer:

sqrt 46

Step-by-step explanation:

irrational numbers are numbers cannot be define in a fraction. sqrt of 46 will give you infinite decimal which could not be express in a fraction form.

Answer:

Step-by-step explanation:

We apply the properties of the power.

[tex]\left(r^3 \right)^{-2}=r^{3*(-2)}=r^{-6}=\dfrac{1}{r^6}[/tex]

Answer:

r^-6  OR  1 / (r^6)

Step-by-step explanation:

For this expression, we can use exponential power rules to simplify.

Power to a power, you multiply the exponents.

So, (r^3)^-2 == r^-6

We can use the fact that negative exponents will be the base to the power in the denominator.

r^-6 == 1/(r^6)

Cheers.

Answer:

Domain: All Real numbers

CoDomain : All Real numbers

Range: [tex]\left\{y|y\geq 0 \right\}[/tex]; that is: Real numbers larger than or equal to zero

Step-by-step explanation:

Notice that the graphed function can use any Real number x (from - infinity to + infinity) and produce an output.  Therefore, the Domain of the function plotted in graph 3 is : All Real numbers.

The set of possible outputs (CoDomain) is also the set of all Real numbers (notice that the y-axis extends form - infinity to + infinity

But the Range (the actual set of the collection of outputs of the function) is just a subset of the CoDomain consisting of the Real numbers larger than or equal to zero (notice that the drawing of the function touches the x axis and lies completely on the upper half of the plane.

Step-by-step explanation:

Constructions are useful in life. From learning it, you are able to use the required tools, and get familiarized with different shapes and angles. This would help you prepare for the task of proving theorems that involved those shapes and angles. It is not the end, ultimately, it prepares you for real life. Constructions are applied in building houses, estates, etc, and constructions of roads, bridges, etc.

Answer: 0.137.

Step-by-step explanation:

Let p be the population proportion of musicians that are left-handed.

Given: Sample size : n= 2690   [subset of population]

Number of musicians that are left-handed: x= 368

Then the sample proportion: [tex]\hat{p}=\dfrac{368}{2690}\approx0.137[/tex]

Since sample proportion is the best point estimate of the population proportion.

Hence, a point estimate for p, the population proportion of musicians that are left-handed is 0.137.

Answer:

x = -3

Step-by-step explanation:

See steps of solution:

Answer is -3

Answer:

x = -3

Step-by-step explanation:

5(5x+3) - 4(2x-9) = 0     Multiply out.

5*5x + 5*3 - 4*2x + 36 = 0

25x + 15 - 8x + 36 = 0 Combine like terms.

25x - 8x + 15 + 36 = 0

17x + 51 = 0 Subtract 51 from both sides.

17x = - 51   Divide each side by 17.

17x/17 = -51/17

x = - 3

Answer:

a. True.

Step-by-step explanation:

32k + 24 = 8(4k + 3)

32k + 24 = 32k + 24

32k - 32k = 24 - 24

0 = 0

Since 0 does equal 0, the statement is a. True.

Hope this helps!

Answer:

[tex]\Large \boxed{\mathrm{a. \ True}}[/tex]

Step-by-step explanation:

[tex]32k+24[/tex]

[tex]\sf Factor \ out \ 8 \ from \ the \ expression.[/tex]

[tex]8(4k)+8(3)[/tex]

[tex]8(4k+3)[/tex]

[tex]32k+24=8(4k+3)[/tex]

[tex]\sf The \ equation \ is \ true.[/tex]

The values of n which the company break even are option (c) n = 20 and n = 250

From the question, the parameters are given as

Cost function, C(n) = 8n + 500

Revenue function, R(n) = 35n - 0.1n²

At the break even point, the functions C(n) and R(n) have the same value

This is represented as

C(n) = R(n)

Substitute the known values in the above equation

So, we have the following equation

8n+ 500 = 35n - 0.1n²

Collect the like terms

-0.1n² + 35n - 8n = 500

So, we have

-0.1n² + 27n - 500 = 0

Divide both sides by -0.1

n² - 270n + 5000 = 0

Factorize

(n -20)(n - 250) = 0

Solve for n

n - 20 = 0 and n - 250 = 0

This gives

n = 20 and n = 250

Hence, the company breaks even at n = 20 and n = 250

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Answer:

145 feet

Step-by-step explanation:

The computation of the elevation of the bottom of the canyon is shown below;

Given that

A = sea level

B = The point at which the canyon starts

C = Canyon bottom

AB = 40 feet

BC = 105 feet

Based on the above information

The AC or elevation of the canyon bottom is

AC = AB + BC

= 40 feet + 105 feet

= 145 feet

Answer:

167°

Step-by-step explanation:

<LMN = <LMT + <TMN

23° + 144° = 167°

<LMN = 167°

Answer:

m= 4/5

Step-by-step explanation:

The equation of the line is in slope-intercept form.

y=mx+b

where m is the slope and b is the y-intercept.

Basically, the number that is being multiplied by x is the slope, and the number added or subtracted from that is the y-intercept.

We are given the equation:

y= 4/5x -3

4/5 is the coefficient of x. 3 is being subtracted from 4/5x.

Therefore, the slope of the line is 4/5 and the y-intercept is -3.

The question asks us to find the slope of the line, so the answer is 4/5.

The slope of the line represented by the equation y = 4x/5 - 3 is 4/5.

Given that an equation y = 4x/5 - 3 we need to find the slope of the equation.

In the slope-intercept form of a linear equation (y = mx + b), "m" represents the slope of the line.

The slope determines how steep or shallow the line is. It also tells us the rate at which the line is rising or falling as we move along the x-axis.

In the given equation, the coefficient of "x" is 4/5. This is the slope of the line.

To understand this better, compare the equation with the slope-intercept form: y = mx + b.

In the given equation, m (the slope) is 4/5. It means that for every 1 unit increase in the x-coordinate, the y-coordinate increases by 4/5 (or decreases by 4/5 if the slope were negative).

So, the line rises (or falls) at a rate of 4/5 for every unit increase along the x-axis.

In this case, since the slope is positive, the line will rise as we move from left to right on the coordinate plane.

Graphically, the line with a slope of 4/5 would look like a rising line, making an angle with the positive x-axis, and moving upwards from left to right.

So, the slope of the line represented by the equation y = (4/5)x - 3 is 4/5.

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Answer:

x = 0

Step-by-step explanation:

because the x coords are still 0 and y is changing.

Answer:

7

Step-by-step explanation:

This is so because (+) × (-) is (-).

Just like (+) × (+) is (+) and (-) × (-) is (-).

So 10 + (-3) = 10 - 3 = 7.

Answer:

[tex]7[/tex]

Step-by-step explanation:

[tex]10 + ( - 3) \\ \\ (+) \: \times \: (- )= (- ) \\ so \: 10 - 3 \\ = 7[/tex]

Answer:

Given that the triangle with point C is the blue triangle and the triangle with the point C' is the red triangle, then to shift from the blue triangle to the red triangle, you must shift each point two units to the left and five units down, which is also T₍₋₃, ₋₅₎, by transformation notation

Step-by-step explanation:

The coordinates of the point C is (1, -1)

The coordinates of the point C' is (-2, -6)

Therefore, the translation required to shift the point C from to point C' is found as follows;

The difference between the x, and y-coordinates of the points C and C' are given as follows;

Δx, C to C' = (-2 - 1) = -3

Δy, C to C' = (-6 - (-1)) = (-6 + 1) = -5

Therefore, the the transformation from C to C' it T₍₋₃, ₋₅₎

Which can be presented as, given that the triangle with point C is the blue triangle and the triangle with the point C' is the red triangle, then to shift from the blue triangle to the red triangle, you must shift each point two units to the left and five units down.

Answer:

.3

Step-by-step explanation:

P( defective) = number defective/ total

                     = 3/10

                      .3

Answer:

[tex]\huge\boxed{0.3}[/tex]

Step-by-step explanation:

Total CDs = 10

Defective CDs = 3

P(Defective) = 3/10

P(Defective) = 0.3

Answer:

2/5x³ + 1/5x² + 1/5x

Step-by-step explanation:

You have to divide each term in the polynomial by the monomial.

(4x⁴ + 2x³ + 2x²)/10x

2/5x³ + 1/5x² + 1/5x

The solution is, 2/5x³ + 1/5x² + 1/5x is the answer of the division.

Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

given that,

(4x^4+2x^3+2x^2)÷10x

now,

we have to divide each term in the polynomial by the monomial.

so, we get,

(4x⁴ + 2x³ + 2x²)/10x

=(4x⁴/ 10x + 2x³/ 10x  + 2x²/ 10x )

=2/5x³ + 1/5x² + 1/5x

Hence, The solution is, 2/5x³ + 1/5x² + 1/5x is the answer of the division.

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