An arithmetic series is represented by the equation (picture). Which of the following is true?


A. The value of the series is greater than the value of the 24th number in the series.

B. The value of the series is between the values of the 1st and 24th numbers in the series.

C. The value of the series is equal to the value of the 1st or 24th numbers in the series.

D. The value of the series is less than the value of the 1st number in the series.

the measure of those two angles equals 180 since it forms a line

so you add up both angles and set that equal to 180.

(I'll use x as the variable but it's still the same answer)

5x-3+9+x=180

combine like terms

6x+6=180

subtract 6

6x=174

then divide by 6

x=29

To find the value of angle H in a triangle, you subtract the sum of the other two angles from 180. This is based on the triangle angle theorems which state that the sum of the angles in a triangle always equals 180 degrees.

In triangle angle theorems, the sum of the angles of a triangle always add up to 180 degrees. If you need to find the value of angle H in your triangle, you'll need to know the measures of the other two angles. For example, if one angle measures 60 degrees and the other measures 50 degrees, you would subtract the sum of these two angles from 180 to find the value of angle H.

Sum of angles in triangle = 180 degrees

So, Angle H = 180 - (60 + 50) = 70 degrees

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The cotangent function has a period of π, and we don't bother with the amplitude.

The period for the cotangent function is equal to π.

Hence, The period for the cotangent function is equal to π.

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Answer:

Step-by-step explanation:

The value of the function f(x) at x=a can be determined by substituting a instead of x into the function expression.

1. When x=-1, then

f(-1)=2\cdot (-1)^3-3\cdot (-1)^2+7=-2-3+7=2.

2. When x=1, then

f(1)=2\cdot 1^3-3\cdot 1^2+7=2-3+7=6.

3. When x=2, then

f(-1)=2\cdot 2^3-3\cdot 2^2+7=16-12+7=11.

Answer:

f(-1)=2

f(1)=6

f(2)=11

Step-by-step explanation:

The given function is [tex]f(x)=2x^3-3x^2+7[/tex]

Substitute x = -1 to find the value of f(-1)

[tex]f(-1)=2(-1)^3-3(-1)^2+7\\\\=-2-3+7\\\\=2[/tex]

Thus, f(-1)=2

Substitute x = 1 to find the value of f(1)

[tex]f(1)=2(1)^3-3(1)^2+7\\\\=2-3+7\\\\=6[/tex]

Thus, f(1)=6

Substitute x = 2 to find the value of f(2)

[tex]f(2)=2(2)^3-3(2)^2+7\\\\=16-12+7\\\\=11[/tex]

Thus, f(2)=11

Answer:  a quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression

Step-by-step explanation:

for example

10  x 10 = 100

to simplify this you put a small 2 on the top right corner of the number 10

Final answer:

An exponent, or a power, is mathematical shorthand for repeated multiplications. It is used to multiply a number by itself a certain number of times.

Explanation:

An exponent, or a power, is mathematical shorthand for repeated multiplications. For example, the exponent "2" means to multiply the base for that exponent by itself (in the example here, the base is "5").

5² = 5 x 5 = 25

The exponent is "2" and the base is the number "5." This expression (multiplying a number by itself) is also called a square. Any number raised to the power of 2 is being squared. Any number raised to the power of 3 is being cubed.

[tex]\bf \textit{surface area of a cone}\\\\ SA=\pi r\sqrt{r^2+h^2}+\pi r^2~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=9\\ h=13 \end{cases}\implies SA=\pi (9)\sqrt{9^2+13^2}+\pi (9)^2 \\\\\\ SA=9\pi \sqrt{250}+81\pi \implies SA=9\pi (\sqrt{250}+9)\implies SA\approx 701.53[/tex]

3,301927249 = ³√36

As discussed in one of my videos on my channel [USERNAME: MATHEMATICS WIZARD] on the Six Rational Exponential Rules, this one states that with a numerator of 1 in the exponent, you take the multiplicative inverse [reciprocal] of the fraction, and set the whole number equal to the root, bringing your a inside the radical, which is 36.

ⁿ√aᵐ = aᵐ\ⁿ → works for both: numerator ≥ 1

I am joyous to assist you anytime.

Answer:

6x - 24y

Explanation:

Expand -3(10x + 4y): -30x - 12y

= [tex]\bold{-30x-12y+6\left(6x-2y\right)}[/tex]

Simplify [tex]\bold{-30x-12y+6\left(6x-2y\right): \ 6x-24y}[/tex]

= 6x - 24y

Mordancy.

For this case we must simplify the following expression:

[tex]-3 (10x + 4y) +6 (6x-2y)[/tex]

We apply distributive property to the terms of the parenthesis, taking into account that:

[tex]- * - = \\- * + = -[/tex]

So, we have:

[tex]-30x-12y + 36x-12y =[/tex]

We add similar terms:

[tex]-30x-12y + 36x-12y =[/tex]

Equal signs are added and the same sign is placed, while different signs are subtracted and the sign of the major is placed:

[tex]6x-24y[/tex]

ANswer:

[tex]6x-24y[/tex]

So you have:

25v² + 5v² + 30v + 6

First you combine the like terms (all of the v²)

25v² + 5v² + 30v + 6

= 30v² + 30v + 6                                  (25v² + 5v² = 30v²)

Now notice that the largest common factor of all those numbers is 6. So you can take out a factor of 6:

30v² + 30v + 6  

= 6 (5v² + 5v + 1)  

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

Answer:

25v² + 5v² + 30v + 6

= 30v² + 30v + 6

= 6 (5v² + 5v + 1)

Answer:

The cost of a pen is $0.60 and the cost of a pencil is $0.35

Step-by-step explanation:

Let

x-----> the cost of a pen

y----> the cost of a pencil

we know that

24x+12y=20-1.40

24x+12y=18.60 -----> equation A

12x+24y=20-4.40

12x+24y=15.60 -----> equation B  

Solve the system of equations by graphing

Remember that the solution is the intersection point both graphs

The solution is the point (0.60,0.35)

see the attached figure

therefore

The cost of a pen is $0.60

The cost of a pencil is $0.35

Answer:

71

Step-by-step explanation:

This is an arithmetic sequence with n th term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here d = 2 - (- 1) = 5 - 2 = 8 - 5 = 3 and a₁ = - 1, so

[tex]a_{25}[/tex] = - 1 + (24 × 3) = - 1 + 72 = 71

It looks like the practice ones are all that matter so I'm only going to answer those. If you need the others answered let me know.

1. 5k-9=-3k+7

Add 9 to both sides: 5k-9+9=-3k+7+9

5k=-3k+16

Add 3k to both sides: 5k+3k=-3k+16+3k

(You are adding 3 and 9 instead of subtracting them because in the equation, they are negative numbers and you have to do the opposite operation to get rid of them.)

8k=16

Divide both sides by 8: 8k/8=16/8

k=2

2. 2(w-3)+5=3w-2

Use the distributive property: 2*w-2*3+5=3w-2

2w-6+5=3w-2

Combine like terms: 2w-1=3w-2

Add 1 to both sides: 2w-1+1=3w-2+1

2w=3w-1

Subtract 3w from both sides: 2w-3w=3w-1-3w

-w=-1

Divide both sides by -1: -w/-1=-1/-1

w=1

3. 8t+9=7t+6

Subtract 9 from both sides: 8t+9-9=7t+6-9

8t=7t-3

Subtract 7t from both sides: 8t-7t=7t-3-7t

t=-3

Answer:

The 3rd sequence could not be described by the following recursive definition tn+1 = tn + 6

Step-by-step explanation:

* Lets revise the recursive formula

1. Determine if the sequence is arithmetic (Do you add, or subtract, the

  same amount from one term to the next?)

2. Find the common difference. (The number you add or subtract.)

3. Create a recursive formula by stating the first term, and then stating

   the formula to be the previous term plus the common difference.

   a1 = first term;

   an+1= an + d

- Where:

# a1 = the first term in the sequence

# an = the nth term in the sequence  

# an+1 = the term after the nth term  

# n = the term number

# d = the common difference.

* Now lets solve the problem

∵ tn+1 = tn + 6

∴ d = 6 ⇒ common difference

- The 1st sequence 5 , 11 , 17 , 23 , 29 , .... has common difference 6

- The 2nd sequence 0 , 6 , 12 , 18 , 24 , .... has common difference 6

- The 3rd sequence 6 , 9 , 12 , 15 , 18 , .... has common difference 3

∴ This sequence could not be described by the following recursive

  definition tn+1 = tn + 6

* The 3rd sequence could not be described by the following recursive

  definition tn+1 = tn + 6

Answer: 375 calories

Form a proportion. Let x be the number of calories burned on a 5 km run.

[tex]\frac{120}{1.6} = \frac{x}{5}[/tex]

Solve for x by cross-multiplying.

[tex]1.6x = (120)(5)\\1.6x = 600\\x = 375[/tex]

Answer:

375 calories

Step-by-step explanation:

[tex] \frac{120}{1.6} = \frac{x}{5} [/tex]

next you would cross multiply

[tex]1.6x = 600[/tex]

then you would divide by 1.6 on both sides

[tex]x = 375[/tex]

and 375 calories should be ur answe

To find the infinite geometric sum of the series 80 + 10 + 1.25 + ..., use the formula S = a / (1 - r), with 'a' as the first term and 'r' as the common ratio. Apply the significant figures principle for accurate rounding when approximating to a certain number of decimal places.

The student's question involves finding the infinite geometric sum of the series 80 + 10 + 1.25 + .... To determine this sum, we use the formula for the sum of an infinite geometric series, S = a / (1 - r), where 'S' is the sum of the series, 'a' is the first term, and 'r' is the common ratio between terms. In this series, 'a' is 80, and the common ratio 'r' can be found by dividing the second term by the first term, which is 10/80 or 1/8.

Plugging the values into the formula gives us S = 80 / (1 - (1/8)) which simplifies to S = 80 / (7/8) = 80 * (8/7) = 640/7. Calculating this yields an infinite sum which can be approximated to decimal places as needed.

For precise calculations, especially when rounding to a certain number of decimal places or significant figures, the rules of significant figures must be followed. As the sample information shows, if a number in the tenths place is to be dropped and it's greater than 5, we round up to ensure the final value adheres to the significant figures principle, consistently providing a more accurate and professional result.

Answer:

Step-by-step explanation:

The sum of the angles in a triangle is 180.  So for the triangle on the right:

36 + 84 + x = 180

x = 60

The two angles in the corner add up to 90.  So:

60 + y = 90

y = 30

Finally, for the triangle on the left:

30 + 86 + z = 180

z = 64

Answer:

if it has two real repeated solutions then t=-9/8

if it has two real distinct solutions then t>-9/28

Step-by-step explanation:

Given:

tx^2+3x-7=0

Also above equation has two real solutions

Now what can deduced about the value of t?

For any quadratic equation "ax^2 +bx +c=0" the solution is given by the quadratic formula

x= [tex]\frac{-b+/-\sqrt{b^{2}-4ac } }{2a}[/tex]

The part under the square root i.e b^2 - 4ac is called the discriminant and it decides whether the equation will have 1 solution, 2 solution or no solution.

if discriminant is negative, i.e. <0 then equation will have no real solution

if discriminant is zero, i.e. =0 then equation will have two repeated real solution

if discriminant is positive, i.e >0 then equation will have two real distinct solution

As given equation has two real solutions:

if they are distinct then

b^2-4ac>0

Putting values of a=t, b=3, c=-7 in above we get,

9+28t>0

28t>-9

t>-9/28

if they are repeated then

b^2-4ac=0

Putting values of a=t, b=3, c=-7 in above we get,

9+28t=0

28t=-9

t=-9/28!

Answer : 19.23 round if you have to

Step-by-step explanation:

Divide 150 by 24 which is 6.15

Then divide 120 by 6.15

Which is 19.23

And thats your answer :)

Answer:

19.2 grams of medicine should be received by 120 pound woman

Step-by-step explanation:

150 pound woman receive medicine = 24 grams, we need to find how many grams of medicine should 120 pound women receive?

Solution:

150 pound woman receive medicine = 24 grams

1 pound woman receive medicine = 24 /150

120 pound woman receive medicine = (24 /150) * 120 = 19.2 grams.

So, 19.2 grams of medicine should be received by 120 pound woman.

Answer:

4 pretzels and 9 popcorn

Step-by-step explanation:

x=popcorn and y=pretzels

x+y=13 solve for x

x=13-y

6.5x+4.75y=77.5 plug 13-y in for x

6.5(13-y)+4.75y=77.5 distribute

84.5-6.5y+4.75=77.5 combine like terms

84.5-1.75y=77.5

-84.5          -84.5

-1.75y=-7 divide both sides by -1.75

*y=4* plug into x+y=13

x+4=13 subtract 4 from each side

*x=9*

The percentage of the discount given on television is 17.72%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that a $79 television is on sale for $65. The percentage of the discount will be calculated as:-

Discount% = ( Original price - Discounted price ) / Original price

Discount% = ( 79 - 65 ) / 79

Discount% = 17.72%

Therefore, the discount per cent on television is 17.72%.

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Answer:

1/3

Step-by-step explanation:

Find two corresponding sides that have lengths.

24 in Figure 1 corresponds to 8 in Figure 2.

Divide the length in Figure 2 by the corresponding length in Figure 1.

scale factor = (length in Figure 2)/(corresponding length in Figure 1)

scale factor = 8/24

scale factor = 1/3

Answer:

$97.75

Step-by-step explanation:

since its 15% off, the price would be 85% of its original price.

85/100 x $115 = $97.75

Jeanine paid $97.75 for the hiking boots after receiving a 15% discount on the regular price of $115.00. The discount was calculated by converting the percentage to a decimal and multiplying it by the regular price, then subtracting it from the regular price.

Jeanine bought hiking boots with a 15% discount off the regular price of $115.00. To calculate how much Jeanine paid for the hiking boots, we first need to find the amount of the discount. The discount amount is calculated as 15% of the regular price.

The calculation for the discount is as follows:

Convert the percentage to a decimal by dividing by 100: 15% / 100 = 0.15.

Multiply the regular price by the decimal: $115.00  imes 0.15 = $17.25.

Subtract the discount from the regular price: $115.00 - $17.25 = $97.75.

Thus, Jeanine paid $97.75 for the hiking boots.

For this case we have that by definition, the circumference of a circle is given by:

[tex]C = \pi * d[/tex]

Where:

d: It is the diameter of the circle

We have as data that:

[tex]C = 6 \pi[/tex]

So:

[tex]6 \pi = \pi * d[/tex]

Thus, the diameter of the circle is 6, therefore the radius is 3.

The area of a circle is given by:

[tex]A = \pi * r ^ 2[/tex]

Where:

r: It is the radius of the circle

[tex]A = \pi * 3 ^ 2\\A = 9 \pi[/tex]

Answer:

Option B

Answer:

9π in. ²

Step-by-step explanation:

The circumference of a circle is diameter times pi.

To find the area of a circle, you multiply the radius by itself, and the product by pi.

Diameter (6 in.) divided by two equals the radius (3 in.).

3 x 3 = 9 in.²

Then multiply by pi to get, 9π in.²

Hope this helps! :)

Answer:

193.8

Step-by-step explanation:

Add each value together, we get 969.

Divide by the number of values in the set, we get (969)/5, or 193.8

I'm only a few Brainliests away from ranking up, so one would be much appreciated. Thank you!

Answer:

193.8

Step-by-step explanation:

Answer:

- 4

Step-by-step explanation:

Using the rule of exponents

• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex]

• [tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]

[tex](\frac{1}{9}) ^{a+1}[/tex] = [tex]9^{-(a+1)}[/tex] = [tex]3^{-2(a+1)}[/tex]

and right side

= [tex]3^{4(a+1)}[/tex] × [tex]3^{3(2-a)}[/tex]

Hence

[tex]3^{-2a-2}[/tex] = [tex]3^{4a+4}[/tex] × [tex]3^{6-3a}[/tex]

[tex]3^{-2a-2}[/tex] = [tex]3^{a+10}[/tex]

Equating exponents on both sides gives

a + 10 = - 2a - 2 ( add 2a to both sides )

3a + 10 = - 2 (subtract 10 from both sides )

3a = - 12 ( divide both sides by 3 )

a = - 4

Answer:

the answer to the question you is A on edg

Step-by-step explanation:

6,000 - 1,800 = 4,200

4,200 / 1/4 (or 25)

she donated 168.0% of her money.

Answer:

Step-by-step explanation:

6000-1800 = 4200 divided by 1/4 = 1050

Answer:

Required probability is 0.3025.

Step-by-step explanation:

Given that probability of landing heads up in a toss of bent coin = 0.55

Then probability of getting head in 1st toss = 0.55

2nd toss is independent of the first toss.

Then probability of getting head in 2nd toss = 0.55

Hence probability of getting head in two tosses of the coin = (0.55)(0.55) =0.3025

Hence required probability is 0.3025.

Answer:

0.3025

Step-by-step explanation:

Given:

The probability of landing heads P(h) = 0.55  

The probability of landing heads when the coin is tossed again is 0.55 as both the events are independent and we are given the probability of heads P(h) = 0.55

So,

The probability of getting 2 heads in a row=0.55*0.55

                                                                   =0.3025  

Answer:

2

Step-by-step explanation:

9999 = 4, so each 9 has a value of 1.

8888 = 8, so each 8 has a value of 2.

1212 = 0, so each 1 and 2 has a value of 0.

1816 = 6, so 6 has a value of 4.

Therefore, 1919 = 0 + 1 + 0 + 1 = 2.

bearing in mind that the sum of all interior angles in a polygon is

180(n - 2)    n = number of sides in the polygon

a DECAgon, DECA=10, has 10 sides, and thus the sum of all its interior angles is 180(10 - 8) = 1440.

[tex]\bf 156+135+147+160+116+150+150.2+119.2+146.6+z=1440 \\\\\\ 1280+z=1440\implies z=1440-1280\implies z=160[/tex]

Final answer:

The angle z in the decagon is calculated by subtracting the sum of the given angles from the total interior angle sum of a decagon, which is 1440°. The measure of angle z is 159.8°.

Explanation:

In geometry, the sum of the interior angles of an n-sided polygon is given by the formula (n - 2) × 180°. For a decagon, which is a 10-sided polygon, this sum is (10 - 2) × 180° = 8 × 180° = 1440°. To find the measure of the unknown angle z in the decagon with the given angle measurements, we can subtract the sum of the known angles from this total.

First, let's add up the given angles: 156° + 135° + 147° + 160° + 116° + 150° + 150.2° + 119.2° + 146.6° = 1280.2°. Now, subtract that sum from the total sum of the angles for a decagon: 1440° - 1280.2° = 159.8°. Therefore, the measure of angle z is 159.8°.

he should round to the hundredths place so 17.32

Answer:

Karen should round to hundredth place.

Step-by-step explanation:

We are given that Kalen is trying to find the average of three measurements.

The measurements are 13.8, 15.64, and 22.51.

Now we are given that He adds the  numbers and divides by three. The result on the calculator shows 17.3167

Now we are asked Where should Kalen round the final answer.

Since the values in the given data is upto hundredth place

So, we are supposed to round the final answer to hundredth place.

So, final answer after round off = 17.32

Hence Karen should round to hundredth place.

It will cost $440 to carpet the room.

To find the cost of carpeting the room, we need to calculate the area of the room in square yards.

First, let's convert the dimensions of the room from feet to yards:

15 ft = 5 yd (since 1 yd = 3 ft, 15 ft = 5 yd)

12 ft = 4 yd

Next, calculate the area of the room in square yards:

Area = Length x Width = 5 yd x 4 yd = 20 square yards

Finally, multiply the area by the cost per square yard:

Cost = Area x Price

= 20 x $22/square yard

= $440

Complete question

A bedroom is 15 ft long and 12 ft wide. How much will it cost to carpet the room if carpeting costs $22 per square yard?