What is the sum of the first six terms of the geometric series?

2 – 6 + 18 – 54 +

The number of students in the 9th grade is 250.

Based on the information, the percentage of those who brought their good from home will be:

= 100 - 24%

= 76%

Therefore, 76% of x = 190

0.76x = 190

x = 190/0.76

x = 250

Therefore, the number of students in the 9th grade is 250.

Learn more about percentages on:

brainly.com/question/24304697

#SPJ1

[tex]

\cot(a-b)=\frac{\frac{1}{(x+1)(x-1)}+1}{\frac{1}{x-1}+\frac{1}{x+1}} \\ \\ =\frac{1-1+x^2}{2} \\ \\ =\frac{x^2}{2} \\ \\ \therefore 2\cot(A-B)=x^2[/tex]

Answer:

See below for proof.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5 cm}\underline{Trigonometric Identities}\\\\$\cot \theta=\dfrac{1}{\tan \theta}$\\\\$\tan (A \pm B)=\dfrac{\tan A \pm \tan B}{1 \mp \tan A \tan B}$\\\end{minipage}}[/tex]

[tex]\begin{aligned}\implies 2\cot (\alpha - \beta) & =\dfrac{2}{\tan (\alpha - \beta)}\\\\ & =\dfrac{2}{\dfrac{ \tan \alpha - \tan \beta}{1+\tan \alpha \tan \beta}}\\\\ & =\dfrac{2(1+\tan \alpha \tan \beta)}{ \tan \alpha - \tan \beta}\\\\ & =\dfrac{2(1+(x+1)(x-1))}{ (x+1) - (x-1)}\\\\& = \dfrac{2(1+(x^2-x+x-1))}{x+1-x+1}\\\\& = \dfrac{2(1+(x^2-1))}{2}\\\\& = \dfrac{2x^2}{2}\\\\& = x^2\end{aligned}[/tex]

Hence verifying that 2cot(α - β) = x².

The ratio of the height to the perimeter of this mural 57 : 152.

We are given that:

Length = 135 feet

height = 285 feet

Mural is of a rectangular shape

We will first find the perimeter.

Perimeter = 2(l + w)

Perimeter = 2(95 + 285)

Perimeter = 2(380)

Perimeter = 760 feet

We will now find the ratio of the height to the perimeter of this mural.

Height : perimeter = 285 : 760

Reduce to lowest terms

Height : perimeter = 57 : 152

Therefore, we get that, the ratio of the height to the perimeter of this mural 57 : 152.

Learn more about ratio here:

https://brainly.com/question/2328454

#SPJ9

The expression acquired is h(x) = 3.5 sin(1/3x ₊ 4π/3)₊2.5

Given h(x) = a sin(bx ₊ c) ₊ d

The h(x) function intersects its mid line at (₋4π , 2.5)

and has its maximum points at (₋5π/2 , 6)

therefore, x₂ ₋ x₁  = ₋5π/2 ₋ (₋4π)

= ₋5π/2 ₊ 4π

= 3π/2

⇒ 2π/b = 3π/2  4

⇒ 2π/b = 6π

⇒b = 1/3

hence, a = b ₋ 2.5

a = 3.5

now h(x) = 3.5 sin(1/3x ₊ c) ₊ 2.5

x = ₋4π

h(₋4π) = 3.5 sin( ₋4π/3 ₊ c) ₊ 2.5

₋4π/3 ₊ c = 0

c = 4π/3

therefore, h(x) = 3.5 sin(1/3x ₊ 4π/3)₊2.5

hence after solving the equation we get the expression for h(x) as

h(x) = 3.5 sin(1/3x ₊ 4π/3)₊2.5

Learn more about Trigonometric functions here:

brainly.com/question/24349828

#SPJ9

< TSU = 4y + 11 = 23 degrees

What does angle relationship mean?

We talk of angle relationships because we are comparing position, measurement, and congruence between two or more angles. For example, when two lines or line segments intersect, they form two pairs of vertical angles

we have to find m < TSU if SU bisects < TSV, m < TSU = 4y + 11, m < USV = 6y + 5

SU bisects < TSV

=>    < TSU = < USV

4y + 11 = 6y + 5

-2y = -6

y = 3

< TSU = 4y + 11 = 23 degrees   ( put the value of y=3)

∠USV = 6y + 5 = 23 degrees      ( put the value of y=3)

Hence ,< TSU = 4y + 11 = 23 degrees

learn more about of angle relationship here

https://brainly.com/question/12654098

#SPJ9

By using subtraction method we get 55.157.8987

What is subtraction method?

In mathematics, subtraction refers to the act of removing something from a set of related objects or numbers. What is left in the group decreases as a result of subtraction.

Let cost of each cow=x

cost of each goat =y

Given 2x+9y=98200------------(equation 1)

9y=98200-2×Y=98200-2x/9-----------(equation 2)

Also 3x+4y= 9800+2200

          3x+4y=1004004y=100,

400-3xY=100400-3x/4---------(equation 3)

From equation 2 and 3 we get

Y=Y98200-2x/9

 =100400-3x/4

 =196,400-8x

 =301200-27x

 =19x

 =104,800

 =x=55.157.8987

To learn more about subtraction method click

https://brainly.com/question/17301989

#SPJ9

The interest rate 2% per year

The time period is 7 years

The initial investment is $600

The current investment is $84

The interest rate can be calculated as follows

84/600 × 7

= 84/4200

= 0.02

The interest rate is

= 0.02 × 100

= 2%

Hence the interest rate is 2%

Read more on interest rate here

https://brainly.com/question/17204408

#SPJ1

Answer:

(1,10) is not a solution to the inequality.

Step-by-step explanation:

First, you want to insert the values of x and y in the inequality.

So, [tex]10\leq 4(1) +1[/tex]

[tex]10\leq 5[/tex]

That inequality is not true, so we know that (1,10) is not a valid solution.

Answer:

2 associate property

Step-by-step explanation:

(3 + 4) + 5 3 + (4 + 5)  On the left side, the 4 is "associating" with the 3", but on the left side the 4 is "associating;" with the 5.

Answer:

It's the first one: 7 to the fourth over 3 to the tenth.

Step-by-step explanation:

Answer:

I think it is the first one

Step-by-step explanation:

The profit per bag for the bags sold at 3$ each is $1.5 per bag.

The total cost will be:

= $300000 + (1 × $600000)

= $900,000

The revenue will be:

= $3 × 600000

= $1,800,000

Therefore, the profit per bag will be:

= ($1800000 - $900000) / 600000

= $900000/600000

= $1.5

The profit is $1.5.

Learn more about profit on:

brainly.com/question/1078746

#SPJ1

When you subtract two numbers, if you reduce the first number in the subtraction by one, the result is one less. This is true.

It should be noted that in subtraction when you reduce the first number, you will get a value that's lesser by 1.

In this case, if we have 20 - 5 = 15, then 19 - 5 = 14. We can see that 14 and 15 is a difference of 1.

Therefore, when you subtract two numbers, if you reduce the first number in the subtraction by one, the result is one less. This is true.

Learn more about expressions on:

https://brainly.com/question/25968875

#SPJ1

Answer: width of the garden is 42

Step-by-step explanation:

let's say "x" = the garden's length

and "y" = the garden's width

the length of the garden is 10 feet longer than its width

x-10=y

the garden's perimeter is 188 feet

we can set up a new equation like this:

2x+2y=188

now we have two equations and we can solve using the system of equations.

x-10=y

add 10 on both sides to isolate "x"

x=y+10

2x+2y=188

substitue x for y+10 in the second equation

2(y+10)+2y=188

expand

2y+20+2y=188

combine like terms

4y+20=188

subtract 20 from both sides

4y=168

divide by four on both sides

y=42

the width of the garden is 42 feet

Answer:

3x^2

Step-by-step explanation:

Explained in image.

the number that makes it correct is 10

let's write it like this

23+5=x+18

28=x+18

you would subtract 18 from each side to get x

28-18=10

18-18=0

x=10

The expression -4x² + 2x - 5(1 + x) is equivalent to the expression - (4x² + 3x + 5).

The equivalent is the expression that is in different forms but is equal to the same value.

The quadratic expression is given below.

⇒ -4x² + 2x - 5(1 + x)

Simplify the expression, then the expression will be given as,

⇒ -4x² + 2x - 5(1 + x)

⇒ -4x² + 2x - 5 - 5x

⇒ -4x² - 3x - 5

⇒ - (4x² + 3x + 5)

The expression -4x² + 2x - 5(1 + x) is equivalent to the expression - (4x² + 3x + 5).

More about the equivalent link is given below.

https://brainly.com/question/889935

#SPJ1

Answer: 3.69

Step-by-step explanation:

Answer:

3.69

Step-by-step explanation:

If the last digit in the fractional part of 3.691 is less than 5, then simply remove the last the digit of the fractional part.

The two consecutive whole numbers that it lies between are 28 and 29.

The consecutive numbers are those number which follow each other continuously in the order from smallest to largest numbers.

Let the two consecutive numbers be x and x + 1

x + x + 1 = 57

Combine like terms;

2x + 1 = 57

Now Subtract 1 from both sides;

2x = 57- 1

2x = 56

Divide both sides by 2

x = 56/2

x = 28

Thus, x + 1 = 28 + 1 = 29

The two consecutive whole numbers that it lies between are 28 and 29.

Learn more about the consecutive whole numbers;

https://brainly.com/question/24912446

#SPJ1

Using proportions, it is found that the total job cost for Randi is of $6,674.24.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

The total amount of square yards that she needs is given by:

111.02 + 31.82 + 161.92 = 304.76.

The cost per square yard is given by:

15.01 + 3.12 + 3.77 = $21.9.

Hence the total cost is given by:

304.76 x 21.9 = $6,674.24.

The total job cost for Randi is of $6,674.24.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

The number of squirrels that the biologists predict there will be 2 years after they started counting will be 43 squirrels.

It should be noted that a function is used to show the relationship between the variables.

It should be noted that the function that's given is illustrated as:

n = 40 + 1.5t

In this case, it should be noted that t = 2 years.

Therefore, the number of squirrels that the biologists predict there will be 3 years after they started counting will be:

n = 40 + 1.5t

n = 40 + 1.5(2)

n = 40 + 4

n = 43

Therefore, the number of squirrels that the biologists predict there will be 2 years after they started counting will be 43 squirrels.

Learn more about functions in:

brainly.com/question/25638609

#SPJ1

For the given figures, both Priya and Tyler's opinions are incorrect.

Scaling is the process of measuring as well as assigning numbers to objects according to predefined rules.

Scaling is the process of locating the measured items on the continuum, an ongoing sequence of numbers with which the objects are assigned.

As, for the given question;

As a result, both Priya as well as Tyler are incorrect. None of them are acceptable to us.

To know more about the scale factor, here

https://brainly.com/question/25722260

#SPJ9

The complete question is-

Priya and Tyler are discussing the figures shown below. Priya thinks that B, C, and D are scaled copies of A. Tyler says B and D are scaled copies of A. Do you agree with Priya, or do you agree with Tyler? Explain your reasoning.

Step-by-step explanation:

X=48 becase 42+90=132

180-132= 48

Applying addition of integers, the final results of the expressions are given as follows:

a) -6.

b) -6.

c) 35.

d) -1.

To add two integers, we have to keep in mind their signals, if they are the same or different, as follows:

Hence, for item a, we have that:

For item b, the solution is found as follows:

For item c, the solution is found as follows:

For item d, the solution is found as follows:

More can be learned about addition of integers at https://brainly.com/question/17695139

#SPJ1

The volume of D10W solution required to be diluted to make 850 mL of D8W solution is 680 mL.

The dilution formula can be presented as follows;

[tex]C_1 \cdot V_1 = C_2 \cdot V_2[/tex]

Where;

[tex]C_1 = Initial \: concentration = D10W [/tex]

[tex]V_1 = Initial \: volume [/tex]

[tex]C_2 = Final \: concentration = D8W[/tex]

[tex]V_2= Final \: volume = 850 \: mL [/tex]

Which gives;

[tex]V_1 = C_2 \cdot V_2/C_1[/tex]

V1 = 8×850/10 = 680

Learn more about dilution in chemistry here:

https://brainly.com/question/14669363

#SPJ1

Answer: The answer is C

Step-by-step explanation:

Employee’s total annual contribution is $1513.75

And, Employee’s monthly deduction is $126.15

Here,

Dorsey Williams has a single plan.

And, His PPO annual premium is $4,325.

His employer pays 65%.

We have to find the Employee’s total annual contribution.

And, Employee’s monthly deduction.

What is Annual contribution?

The amount credited to Account balance after the end of each Plan Year for which the Performance Goals are achieved is called Annual contribution.

Now,

His PPO annual premium is $4,325.

And, His employer pays 65%

Hence,

Employee’s total annual contribution = 4,325 (1 - 65%)

                                                        = 4,325 (35%)

                                                        = 4,325 x 35/100

                                                        = 1513.75

And, Employee’s monthly deduction = 1513.75 ÷ 12 = 126.15

Therefore, Employee’s total annual contribution is $1513.75

And, Employee’s monthly deduction is $126.15

Learn more about the Annual contribution visit:

https://brainly.com/question/18063635

#SPJ1

Answer:

270cm2

Step-by-step explanation:

you have to split the figure into 2.

the triangle above is = 1/2 x20cmx13cm=130cm2

the rectangle is = 20cmx7cm=140cm2

total area=140cm2+130cm2

               =270cm2