all formulars for solving Trigonometry

Answer:

5) El precio del petróleo en los dos últimos días tuvo las siguientes fluctuaciones: aumentó un 3,5% en el primer día y luego bajó un 2% en el último día. Si el valor final es de U$S 68, ¿cuál era el valor inicial?

La solución al problema matemático es la siguiente:

Supongamos que el valor inicial del petróleo es x. En el primer día, el precio aumentó en un 3,5%, por lo que el nuevo precio es x + 0.035x = 1.035x. En el segundo día, el precio disminuyó en un 2%, por lo que el precio final es 1.035x - 0.02(1.035x) = 0.98(1.035x) = 1.0143x.

Dado que sabemos que el precio final es de U$S 68, podemos establecer una ecuación para resolver x: 1.0143x = 68.

Resolviendo para x, obtenemos x = 68/1.0143 ≈ U$S 67.04.

Entonces, el valor inicial del petróleo era aproximadamente U$S 67.04.

MARCA COMO CEREBRO!!!

The intermediate step in completing the square is[tex]$x^2 + 2ax + (a^2) = b - a^2 + (a^2)$[/tex]

To complete the square for the equation [tex]$(x+a)^2=b$[/tex], we can follow these steps:

1. Expand the left side of the equation: [tex]$(x+a)^2 = (x+a)(x+a) = x^2 + 2ax + a^2$[/tex].

2. Rewrite the equation by isolating the squared term and the linear term: [tex]$x^2 + 2ax = b - a^2$[/tex].

3. To complete the square, take half of the coefficient of the linear term, square it, and add it to both sides of the equation:

[tex]$x^2 + 2ax + (a^2) = b - a^2 + (a^2)$[/tex].

4. Simplify the right side of the equation: [tex]$x^2 + 2ax + (a^2) = b$[/tex].

This step can be represented as: [tex]\[x^2 + 2ax + (a^2) = b - a^2 + (a^2)\][/tex]

This intermediate step helps us rewrite the equation in a form that allows us to factor it into a perfect square.

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A bank is eligible to ask for a service fee because it provides various services to its customers that incur costs.

Banks are financial institutions that offer a range of services such as deposit accounts, loans, credit cards, money transfers, and investment options. These services require infrastructure, technology, staff, and administrative costs to operate effectively.

The service fee charged by a bank helps cover these operational expenses and ensures the bank can continue providing quality services to its customers. Additionally, banks may also charge fees to generate revenue and earn profits. Banks are businesses that need to maintain financial sustainability, and service fees contribute to their overall revenue stream.

Banks typically outline their fee structure and disclose the applicable charges in their terms and conditions or fee schedules. Common examples of service fees include monthly maintenance fees for deposit accounts, transaction fees for certain types of transactions, overdraft fees, wire transfer fees, and fees for additional banking services.

It's important for banks to be transparent about their fee structure and provide clear information to customers regarding the charges. Customers can then make informed decisions about which services to use and understand the costs associated with those services.

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In the given diagram, we have a triangle with two angles labeled as (3x + 10)° and (4x - 30)°. We need to solve for the value of x.

To find the value of x, we can use the property that the sum of the interior angles of a triangle is always 180 degrees. Therefore, we can set up the equation:

(3x + 10) + (4x - 30) + 90 = 180

Let's simplify the equation step by step:

Combine like terms:

3x + 4x + 10 - 30 + 90 = 180

7x + 70 = 180

Next, isolate the variable term by subtracting 70 from both sides:

7x + 70 - 70 = 180 - 70

7x = 110

To solve for x, divide both sides of the equation by 7:

(7x)/7 = 110/7

x = 15.71

Therefore, the value of x is approximately 15.71.

Please note that this solution assumes the given diagram accurately represents the angle measurements, and the calculations provided are based on that assumption.

Answer: There is no solution to this problem.

Step-by-step explanation:

The goal test score pints are 150, 103, and 41. Let's check to see if each statement is true

A. The total points for the tests are:

Type A - 156

Type B -  98

Type C -  40

None of these matches the total points.

B. The total points for the tests are:

Type A - 39

Type B - 98

Type C - 160

None of these matches the total points.

C.

Type A - 156

Type B - 2,352

Type C - 40

None of these matches the total points.

Since none of these statements match this data, there is no solution to this chart. Hope this helps!

-From a 5th Grade Honors Student

The length of AC is 28. so none of the given options is correct.

In square ABCD, AC represents the length of one side of the square. The given information states that AC is equal to 32-4.

To calculate AC, we subtract 4 from 32:

AC = 32 - 4

AC = 28

Therefore, the length of AC is 28. None of the provided options match this result, so none of the given options is correct.

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The minimum amount of vinyl needed for the liner is 502.4 sq. feet.

We have,

An open cylinder is a type of cylinder in which one of its circular surfaces has been removed.

Thus its area can be determined as:

area of an open cylinder = πr² + 2πrh

where r is the radius, and h is the height.

The area of the swimming pool that will be covered by vinyl liner resembles an open cylinder. So that;

area of the open swimming pool = πr² + 2πrh

                                                = πr(r + 2h)

we have,

r = diameter/ 2

= 20/ 2

r = 10 feet

area of the open swimming pool = 3.14×10(10 + 2×3)

                                                   = 31.4×16

                                                   = 502.4

The minimum amount of vinyl needed for the liner is 502.4 sq. feet.

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The inequality expression for the sentence in this problem is given as follows:

[tex](5+3z)^8 < \frac{9b}{7}[/tex]

The sentence in the context of this problem is defined as follows:

"quantity 5 plus 3z, to the 8th power less than 9b divided by 7"

The first quantity, 5 plus 3z, to the 8th power, is expressed as follows:

[tex](5 + 3z)^8[/tex]

The second quantity, 9b divided by 7, is given as follows:

9b/7.

The inequality symbol for the word less is given as follows:

<.

Hence the inequality is given as follows:

[tex](5+3z)^8 < \frac{9b}{7}[/tex]

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37.5 seconds is equivalent to 0.625 minutes for the battery to discharge from 15% to 0% with a discharge rate of 0.12% every 30 seconds.

To calculate how long a battery will last when it discharges at a rate of 0.12% per 30 seconds, we can set up a proportion based on the given information.

Let's assume the battery has a total charge of 100%. We want to find out how long it takes for the battery to discharge from 15% to 0%, given a discharge rate of 0.12% every 30 seconds.

First, let's determine the proportion:

(0.12% / 30 seconds) = (15% / x sec

To solve for x (the time it takes for the battery to discharge from 15% to 0%), we can cross-multiply:

0.12% × x = 30 seconds × 15%

Now, let's solve for x:

0.0012 × x = 0.3 × 15%

0.0012 × x = 0.045

Divide both sides by 0.0012:

x = 0.045 / 0.0012

x ≈ 37.5

Therefore, it would take approximately 37.5 seconds for the battery to discharge from 15% to 0% with a discharge rate of 0.12% every 30 seconds.

To convert 37.5 seconds into minutes, we divide the number of seconds by 60 (since there are 60 seconds in a minute).

37.5 seconds / 60 = 0.625 minutes

Therefore, 37.5 seconds is equivalent to 0.625 minutes.

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Answer:

B, line B

Step-by-step explanation:

Line B closest fits the plotted points (dots). That's the best fit.

Answer:

See below for answer and explanation

Step-by-step explanation:

The Intermediate Value Theorem (IVT) states that there is a value [tex]c[/tex] in [tex][a,b][/tex] such that [tex]f(c)=0[/tex]. Because [tex]f(0)=0^2+5(0)-4=-4[/tex] and [tex]f(2)=2^2+5(2)-4=10[/tex], this must mean that 0 is in between -4 and 10, which concludes that there is a zero over the interval [0,2] for the given function by IVT.

The correct graph is A.

The first equation is y = -3/4x + 2. This can be rewritten as y - 2 = -3/4x. Solving for x, we get x = (4/3)(y - 2).

The second equation is y = -1/2x - 1. This can be rewritten as y + 1 = -1/2x. Solving for x, we get x = -2(y + 1).

The two lines intersect at the point (0, 2). Plugging in x = 0 into both equations, we get y = 2 for both equations. Therefore, the two lines must intersect at the point (0, 2).

The slope of the first line is -3/4. The slope of the second line is -1/2. The slopes are negative inverses of each other. Therefore, the two lines are perpendicular.

A coordinate grid with one line that passes through the points 0 comma 2 and 4 comma negative 1 and another line that passes through the points 0 comma negative 1 and 1 comma negative 3 is incorrect because the two lines are not perpendicular.

A coordinate grid with one line that passes through the points 0 comma 2 and 3 comma negative 2 and another line that passes through the points 0 comma negative 1 and negative 1 comma 1 is incorrect because the two lines intersect at the point (0, 2).

A coordinate grid with one line that passes through the points 0 comma 2 and 3 comma negative 2 and another line that passes through the points 0 comma negative 1 and 2 comma negative 2 is incorrect because the two lines are not perpendicular.

Answer:

  x = -0.25

Step-by-step explanation:

You want to solve for x when corresponding sides of the similar triangles have lengths 6 and 15, and (2x -3) and (3x -8).

Corresponding sides are proportional in similar triangles, so we have ...

  (2x -3)/6 = (3x -8)/15

  5(2x -3) = 2(3x -8) . . . . . . multiply by 30

  10x -15 = 6x -16 . . . . . . simplify

  4x = -1 . . . . . . . . . . . . add 15-6x

  x = -0.25

The value of x is -0.25.

__

Additional comment

This negative value of x gives side length ratios in the two triangles of -7/12. Negative side lengths of -3.50 and -8.75 make no sense geometrically. The proportion is satisfied, but the figure cannot be drawn with a negative side length.

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Answer:

789.40 square feet (to nearest hundredth)

Step-by-step explanation:

surface area = area of circular base + curved surface area

= πr² +  πrL, where L is length of sloped edge.

using Pythagoras' Theorem, L² = 22² + 8² = 548.

L = 2√137 (do not round the answer yet, keep it in this form).

surface area =  πr² +  πrL

= π(8)² +  π(8)(2√137)

= 789.40 square feet (to nearest hundredth)

Answer:

know side: 3

Unknown side: 5

Answer: The trigonometric ratio that I would use to find the distance from the base of the tower to the keys is the tangent; tan (86°) = height / distance.

Explanation and calculation:

You can draw a right triangle with angle 86°, opposite leg equal to the height (50 meter) and adjacent leg equal to the distance from the base of the tower to the keys: tan (86°) = 50 m / x

=> x = 50 m / tan(86°)

x = 50 m / 14.30 = 0.98 m

Answer: 0.98 m

Step-by-step explanation:

The answer is 5/6 ÷ 1/3 = 5/18

because

5/6 × 1/3 = 5/18 and it's true

Answer:

[tex]\huge\boxed{\sf S= 7.85 \ cm}[/tex]

Step-by-step explanation:

arc AB = θ = 45 degrees

Radius = r = 10 cm

π = 3.14

Length = S = ?

[tex]\displaystyle S= \frac{\theta}{360} \times 2 \pi r[/tex]

Put the given data in the formula.

Finding arc length.

[tex]\displaystyle S = \frac{45}{360} \times 2(3.14)(10)\\\\S = 0.125 \times 62.8\\\\S= 7.85 \ cm\\\\\rule[225]{225}{2}[/tex]

Using the parentheses to rewrite the equation 8×9-2-3​ gives 67.

In mathematics, the order of operations are the rules that tell the sequence in which the multiple operations in an expression should be solved.

A way to remember the order of the operations is PEMDAS, where each letter stands for a mathematical operation. There is also another version called BODMAS but the principles are the same

Parenthesis            (  )

Exponent                a⁷

Multiplication          ×

Division                   ÷

Addition                  +

Subtraction             -

Given: 8×9-2-3​

We can rewrite the equation using parenthesis using PEMDAS:

Multiplication first, then followed by addition/subtraction:

8×9-2-3​ = (8 × 9) - 2 - 3

             = 72 - 2 - 3​

             = 67

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Issa invested $2600 at a 4 percent interest rate and $3300 at a 10 percent interest rate.

Let's assume Issa invests x dollars at a 4 percent interest rate and y dollars at a 10 percent interest rate.

The equation that describes the total investment is:

x + y = 5900

The equation that describes the interest earned is:

0.04x + 0.1y = 434

To solve this system of equations, we can use substitution or elimination method. Here, we'll use the substitution method.

From the first equation, we can express x in terms of y:

x = 5900 - y

Substituting this value of x into the second equation, we have:

0.04(5900 - y) + 0.1y = 434

Now, let's solve this equation to find the value of y:

0.04(5900 - y) + 0.1y = 434

236 - 0.04y + 0.1y = 434

0.06y = 198

y = 198 / 0.06

y = 3300

Now that we have the value of y, we can substitute it back into the first equation to find x:

x + 3300 = 5900

x = 5900 - 3300

x = 2600

Therefore, Issa invested $2600 at a 4 percent interest rate and $3300 at a 10 percent interest rate.

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Okay!

In the given diagram, we have two intersecting lines. To determine the relationship between the angles and solve for x, we can use the properties of angles formed by intersecting lines.

From the diagram, we can see that angle K is vertically opposite to the angle (4x-10)°. In a case of intersecting lines, vertically opposite angles are equal.

So, we can write:

K = (4x-10)°

To solve for x, we need more information or another equation involving x. Without any additional equations or information, we cannot determine the value of x.

If you have any additional equations or information related to the problem, please provide them, and I'll be happy to assist you further in solving for x.

Answer:

∠ 3 = 35° , ∠ 7 = 145° , ∠ 8 = 35° , ∠ 5 = 145°

Step-by-step explanation:

∠ 3 and ∠ 1 are vertically opposite angles and are congruent , then

∠ 3 = 35°

-----------------

∠ 3 and ∠ 5 are same- side interior angles and sum to 180°, that is

∠ 5 + ∠ 3 = 180°

∠ 5 + 35° = 180° ( subtract 35° from both sides )

∠ 5 = 145°

------------------

∠ 5 and ∠ 7 are vertically opposite angles and are congruent , then

∠ 7 = 145°

--------------

∠ 1 and ∠ 8 are corresponding angles and are congruent , then

∠ 8 = 35°

---------------

The length of the rectangle is about 12.37 feet.

We are given that;

Width= 4 feet

Diagonal length= 13feet

Now,

The width and length of the rectangle are the legs and the diagonal is the hypotenuse. We can label them as:

w = 4 (width) l = ? (length) d = 13 (diagonal)

Plugging these values into the Pythagorean theorem, we get:

w^2 + l^2 = d^2 4^2 + l^2

= 13^2 16 + l^2 = 169

l^2 = 169 - 16

l^2 = 153

l = √(153)

l ≈ 12.37

Therefore, by Pythagoras theorem the answer will be 12.37 feet.

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Answer:

-------------------

Use the formula for z-score

Substituting the given values, we get:

Solve it for mean μ:

Therefore, the mean of the normal distribution is 8.79.

Step-by-step explanation:

Formula for sphere volume = 4/3 pi r^3

V = 4/3 pi r^3    solve for 'r'

r = cubrt ( 3/4 v / pi ) = cubrt ( 3/4 * 123 / 3.14) = 3 cm

The account balance will be approximately $11,390 after 19 years.

In this case, Mark invests $7,938 with an annual interest rate of 2% compounded semiannually. Therefore:

P = $7,938

r = 2% = 0.02 (as a decimal)

n = 2 (compounded semiannually)

t = 19 years

Plugging these values into the formula, we have:

[tex]A = \$7,938(1 + 0.02/2)^{(2*19)[/tex]

Calculating the expression inside the parentheses:

(1 + 0.02/2) = 1.01

Raising this to the power of (2*19):

[tex](1.01)^{(2*19)} = 1.43[/tex]

Multiplying this by the principal amount:

A ≈ $7,938 * 1.43

A ≈ $11,390

Therefore, the account balance will be approximately $11,390 after 19 years.

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you will have put approximately $1,014,706.40 into the account over the 35 years. The interest will you have earned is -$714,706.40.

To calculate the amount you need to deposit each quarter, we can use the formula for the future value of a series of regular deposits:

FV = P * ((1 + r)^n - 1) / r

Where:

FV is the future value (target amount) you want to achieve ($300,000.00)

P is the deposit amount per quarter (what we need to find)

r is the interest rate per quarter (8% or 0.08)

n is the number of quarters (35 years * 4 quarters per year = 140 quarters)

Now, let's substitute the values into the formula and solve for P:

$300,000.00 = P * ((1 + 0.08)^140 - 1) / 0.08

$300,000.00 * 0.08 = P * ((1.08)^140 - 1)

$24,000.00 = P * (4.31793257 - 1)

$24,000.00 = P * 3.31793257

P = $24,000.00 / 3.31793257

P ≈ $7,243.21

Therefore, you would need to deposit approximately $7,243.21 into the account each quarter to accumulate $300,000.00 for retirement in 35 years.

To calculate the total amount of money you will have put into the account over the 35 years, you can multiply the deposit amount per quarter by the number of quarters:

Total deposit = P * n = $7,243.21 * 140 = $1,014,706.40

Therefore, you will have put approximately $1,014,706.40 into the account over the 35 years.

To calculate the interest earned, you can subtract the total deposit amount from the target amount:

Interest earned = Future value - Total deposit = $300,000.00 - $1,014,706.40 = -$714,706.40

The negative value indicates that the interest earned is negative, meaning that you will have fallen short of your target amount by $714,706.40 due to the interest earned being less than the total deposit made.

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Answer:  b, 20°

Step-by-step explanation: Since triangles MNO and JKL are congruent, we know that all of their corresponding angles are congruent. This means that m<L = m<O = 20°

Answer:

Area is 140

Step-by-step explanation:

This might be hard at first, but if you can figure out that the triangle on the left can be moved to the right, it forms a rectangle!

So, 10 x 14 = 140 Square units