Three consecutive odd integers whose sum is 243

Answers

Answer 1

Final answer:

The three consecutive odd integers whose sum is 243 are 79, 81, and 83. The integers were found using the algebraic expression for consecutive odd numbers and solving for the sum equal to 243.

Explanation:

To find three consecutive odd integers whose sum is 243, we can represent the first of these integers as 'n', the second as 'n + 2', and the third as 'n + 4', since each consecutive odd integer is 2 more than the previous one. The equation we would use to portray their sum is:

n + (n + 2) + (n + 4) = 243

Simplifying the equation, we combine like terms:

3n + 6 = 243

Next, we subtract 6 from both sides to isolate the 3n term:

3n = 243 - 6

3n = 237

Now we divide by 3 to solve for n:

n = 237 / 3

n = 79

The first odd integer is 79, the second odd integer is 79 + 2 = 81, and the third odd integer is 79 + 4 = 83.

Therefore, the three consecutive odd integers are 79, 81, and 83.

Related Questions

Assume that the weights of all packages of a certain brand of cookies are normally distributed with a mean of 32 ounces and a standard deviation of 0.3 ounce. find the probability that the mean weight, x¯, of a random sample of 20 packages of this brand of cookies will be between 31.8 and 31.9 ounces.

Answers

That probability is about 6.7%.

guy finds how car his house is several locations and makes the table shown how much farther away from guy's house is the library than the cafe?

Answers

5/10's of a mile is the answer

what term has to be added to x^2-3x to be a trinomial 3/2 9/4 6 9

Answers

Your question is probably what should be added to the given expression to make it a perfect square.

The given expression is:

[tex] x^{2} -3x[/tex]

The formula of [tex] (a-b)^{2} [/tex] is [tex] a^{2} -2ab+ b^{2} [/tex]

Re-writing the given expression:

[tex] x^{2} - 2(x)( \frac{3}{2}) [/tex]

So, we have the square of first term and twice the product of first and second term. What is missing is the square of second term.

So, the complete expression for perfect square will be:

[tex] x^{2} -2(x)( \frac{3}{2})+ ( \frac{3}{2} )^{2} \\ \\ x^{2} -2(x)( \frac{3}{2})+ \frac{9}{4} [/tex]

Therefore, 9/4 should be added to the given expression to make it a perfect square.

Answer: The correct option is (B) [tex]\dfrac{9}{4}.[/tex]

Step-by-step explanation: We are given to find the term that has to be added to [tex]x^2-3x[/tex] to be a perfect trinomial.

Let, c denote the term to be added.

Then,

[tex]x^2-3x+c\\\\=x^2-2\times x\times \dfrac{3}{2}+c\\\\\\=x^2-2\times x\times \dfrac{3}{2}+\dfrac{9}{4}+c-\dfrac{9}{4}\\\\\\=\left(x-\dfrac{3}{2}\right)+c-\dfrac{9}{4}.[/tex]

Therefore, the given expression will be a perfect trinomial if

[tex]c-\dfrac{9}{4}=0\\\\\\\Rightarrow c=\dfrac{9}{4}.[/tex]

Thus, the required term to be added is [tex]\dfrac{9}{4}.[/tex]

Option (B) is CORRECT,

which quadrant is (8, -1) in (A) | (B) || (C) ||| (D) ||||

Answers

because X is positive the point would be to the right of the Y axis and because the Y value is negative, the point would be below the X axis
this would be the 4th quadrant.

the answer is D
see picture:

Leo multiplied all numbers from 1 to 11 and wrote the answer on the board. During the break three digits were erased 39,9...6,8... ... . What are the erased digits?

Answers

11! = 39,916,800

The erased digits are 1, 0, 0.

Use the following diagram to complete the required information. m∠ROS = 20 deg 15' 40", m∠SOT = 10 ° 12' 30" m∠ROT = 30 ° 27' 10" 31 ° 28' 10" 30 ° 28' 10"

Answers

Answer:

Third option 30° 28' 10"

Brainlist?

Step-by-step explanation:

m∠ROT, formed by adjacent angles m∠ROS (20° 15' 40") and m∠SOT (10° 12' 30"), measures 30° 28' 10" according to the Angle Addition Postulate.

Attached diagram.

To find the measure of angle ROT (m∠ROT), you can use the Angle Addition Postulate.

The Angle Addition Postulate states that the measure of an angle formed by two adjacent angles is equal to the sum of the measures of those two angles.

Here m∠ROS and m∠SOT as adjacent angles forming m∠ROT.

m∠ROS = 20 degrees 15 minutes 40 seconds

m∠SOT = 10 degrees 12 minutes 30 seconds

To find m∠ROT, add the measures of m∠ROS and m∠SOT:

m∠ROT = m∠ROS + m∠SOT

First, add the degrees, then the minutes, and finally the seconds separately:

Degrees: 20 degrees + 10 degrees = 30 degrees

Minutes: 15 minutes + 12 minutes = 27 minutes

Seconds: 40 seconds + 30 seconds = 70 seconds

Now, simplify the seconds by converting any excess seconds into minutes:

70 seconds = 1 minute and 10 seconds

Now, add the minutes to the total:

27 minutes + 1 minute = 28 minutes

So, m∠ROT is:

30 degrees 28 minutes 10 seconds

Therefore, the measure of the angle m∠ROT = 30 degrees 28 minutes 10 seconds.

learn more about angles here

brainly.com/question/30147425

#SPJ3

The above question is incomplete, the complete question is:

Use the following diagram to complete the required information. m∠ROS = 20 deg 15' 40", m∠SOT = 10 ° 12' 30"

m∠ROT =

30 ° 27' 10"

31 ° 28' 10"

30 ° 28' 10"

Attached diagram.

Let u = (1,0,2) , v = (0,-1,2) and w = (2,1,0). Compute

(i) the area of the parallelogram bounded by u and v (5)

(ii) the equation of the plane parallel to v and w pass through the tip of u

Answers

Answers:

(i) 3
(ii) [tex]-2x + 4y + 2z = 2[/tex]

Explanation:

(i) The area of the parallelogram bounded by vectors u and v is given by:

[tex]\text{Area} = \left \| u \times v \right \|[/tex]

Note that if [tex]u = (u_1, u_2, u_3) = (1, 0, 2), v = (v_1, v_2, v_3) = (0, -1, 2) [/tex],

[tex]u \times v \\ = \left(u_2v_3-u_3v_2, u_3v_1-u_1v_3, u_1v_2-u_2v_1\right) \\ = \left((0)(2)-(2)(-1), (2)(0)-(1)(2), (1)(-1)-(0)(0)\right) \\ \boxed{u \times v = \left(2, -2, -1 \right)}[/tex]

Thus, the area of the parallelogram formed by vectors u and v is calculated as

[tex]\text{Area} = \left \| u \times v \right \| \\ = \left \| \left(2, -2, -1 \right) \right \| \\ = \sqrt{(2)^2 + (-2)^2 + (1)^2} \\ \boxed{\text{Area} = 3}[/tex]

Hence, the area of the parallelogram is 3.

(ii) To obtain the equation of the plane, we must get its normal vector and a point in the plane.

As calculated in (i), the normal vector to the plane is [tex]v \times w[/tex] because the plane is parallel to vectors v and w. Note that if [tex]v = (v_1, v_2, v_3) = (0, -1, 2), w = (w_1, w_2, w_3) = (2, 1, 0)[/tex],

[tex]v \times w \\ = \left(v_2w_3-v_3w_2, v_3w_1-v_1w_3, v_1w_2-v_2w_1\right) \\ = \left((-2)(0)-(2)(1), (2)(2)-(0)(0), (0)(1)-(-1)(2)\right) \\ \boxed{v \times w = \left(-2, 4, 2 \right)}[/tex]

Thus, a normal vector to the plane is [tex]\left(-2, 4, 2 \right)[/tex].

To get a point in the plane, note that vector u can be represented by any pairs of points. So, we can take (0, 0, 0) to be the starting point of vector u. Since [tex]u = (1, 0, 2)[/tex], the tip of vector u is [tex](0 + 1, 0, 0 + 2) = (1, 0, 2)[/tex]. Because the plane passes thru the tip of vector u, a point in the plane has coordinates [tex] (1, 0, 2)[/tex].

So for any point [tex](x, y, z)[/tex] in the plane, the equation is given by

[tex]n \cdot (x - 1, y - 0, z - 2) = 0[/tex]

Where n is the normal vector to the plane.

Since [tex]n = \left(-2, 4, 2 \right)[/tex], the equation becomes

[tex]\left(-2, 4, 2 \right) \cdot (x - 1, y - 0, z - 2) = 0 \\ \left(-2, 4, 2 \right) \cdot (x - 1, y, z - 2) = 0 \\ -2(x - 1) + 4y + 2(z - 2) = 0 \\ -2x + 2 + 4y + 2z - 4 = 0 \\ -2x + 4y + 2z - 2 = 0 \\ \boxed{-2x + 4y + 2z = 2 }[/tex]

If the sum of four consecutive odd integers is 208, what is the smallest of the four integers?

Answers

The least of these numbers is 20.

How many times bigger is 7 billion than 700 million

Answers

7 billion is 10 times greater than 700 million.

7,000,000,000/700,000,000=10

is possible to have a shape with different dimensions while having the same volume?

Answers

Yes, they could be different and still have the same volume

yes,

a cuboid with dimensions 2, 4, 8 has volume = 64 unit^3

a cube with side 4 has volume = 64 unit^3

so, they have different shapes but same volume

2x+5y=-6 , wht is the x intercept, what is the y intercept

Answers

Final answer:

The x-intercept is (-3,0) and the y-intercept is (0,-6/5).

Explanation:

The x-intercept is the point where the line crosses the x-axis. To find the x-intercept, we set y=0 and solve for x. In the equation 2x+5y=-6, we substitute 0 for y and solve for x:

2x + 5(0) = -6

2x = -6

x = -3

So, the x-intercept is the point (-3,0).

The y-intercept is the point where the line crosses the y-axis. To find the y-intercept, we set x=0 and solve for y. In the equation 2x+5y=-6, we substitute 0 for x and solve for y:

2(0) + 5y = -6

5y = -6

y = -6/5

So, the y-intercept is the point (0,-6/5).

if tyrone works 40 hours per week and has no other sources of income what is his total monthly cash inflow

Answers

[tex]18 \times 40 = 720[/tex]

[tex]720 \times 4 = 2880[/tex]

[tex]2880 - 1800 = 1080[/tex]

~~

Answer : B

~~

I hope that helps you out!!

Any more questions, please feel free to ask me and I will gladly help you out!!

~Zoey

Peyton has two pizzas each Pizza is cut into 10 equal slices she and her friends eat 14 slices what part of the pizzas did they eat write your answer as a decimal please help

Answers

10 × 2 = 20 <---Total amount of slices.
14/20 <---Fraction eaten over total
7/10 <---Fraction reduced to tenths
0.7 <---is a decimal equal to 7/10

What is the constant term in the expression 4x3y + 8x2 + 6x + 5?

Answers

Answer:

Step-by-step explanation:

The constant term is the one with no variables in it: +5.

Answer:

i took the test and its 5.

Push technology is also known as _____.

simulcast
Webcasting
connectivity
data-driven decision-making

Answers

Push technology is also know as Webcasting

WEBCASTING

According to wikipedia ,

push technology is is a style of Internet-based communication where the request for a given transaction is initiated by the publisher or central server.

A webcast is a media presentation distributed over the Internet using streaming media technology to distribute a single content source to many simultaneous listeners/viewers.

A cylinder has a radius of 4x+2 and a height of 5x+4. Which polynomial in standard form best describes the total volume of the cylinder. Use the formula V=pir^2h for the volume of a cylinder.

Answers

[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ -----\\ r=4x+2\\ h=5x+4 \end{cases}\implies V=\pi (4x+2)^2(5x+4) \\\\\\ V=\pi [(4x+2)(4x+2)](5x+4)\\\\\\ V=\pi \stackrel{FOIL}{(16x^2+16x+4)}(5x+4) \\\\\\ V=\pi[ (80x^3+80x^2+20x)+(64x^2+64x+16)] \\\\\\ V=80\pi x^3+144\pi x^2+84\pi x+16\pi [/tex]

The sum of two numbers is 44. One number is 3 times as large as the other. What are the numbers?

Answers

let one of the number be x

one number = x
the other number = 3x

Given that the sum of these two number is 44.
x + 3x = 44
4x = 44
x = 44 ÷ 4
x = 11

x = 11
3x = 11 x 3 = 33

The two numbers are 11 and 33

Set up 2 variables:
x = larger number
y = smaller number

Set up equations:
[tex]x + y = 44[/tex]
[tex]3y = x[/tex]

Solve by substituting. I will use the x already given to us (in second equation) to substitute in 1st equation (x = 3y):
[tex]3y + y = 44[/tex]
[tex]4y = 44[/tex]
[tex]y = 11[/tex]

Plug it back into 2nd equation to solve for x:
[tex]3y = x[/tex]
[tex]3(11) = x = 33[/tex]

So, our two values are: x = 33 and y = 11.

We can check, x + y = 33 + 11 does equal 44 and 33 times is 3 times larger than 11. So, the initial criteria work out and we are right.

What is the equation for 5n+7=21

Answers

21 - 7 = 14

5n = 14

14 / 5 = 2.8

N = 2.8

Hope I helped!

Let me know if you need anything else!

~ Zoe (Rank:'Genius')

Hey there!

To start, you must first isolate the 5n term so that you can solve for the variable of n.

To do this, subtract 7 from both sides:
5n+7=21
-7 -7
5n=14

Now, divide both sides by 5 to isolate the n term:
5n/5=14/5

You should get a result of n=14/5

Therefore, your final answer should be n=14/5.

To check if the answer is correct, simply plug 14/5 for the variable n in the original equation. If you get a correct mathematical statement when you simplify, the value is correct:
n=14/5
5(14/5)+7=21
14+7=21
21=21

Therefore, n=14/5 is correct.

Hope this helps and have a marvelous day! :)

Charlie reads quickly. He reads 1 and 3 seventh pages every 2 third minutes. Charlie reads at a constant rate. How many pages does charlie read per minute?

Answers

The unit rate would be 1 3/7 ÷ 2/3 10/7 ÷ 2/3 10/7 · 3/2 separate by division, rearrange and multiply 15/7

Charlies reads 15/7, or 2 1/7, page per minute.

Hope this helps a bit.

When searching for a lost animal, the search party often creates a circular area with a search radius. Two points of interest in the search are the last known locations the animal was sighted. The two points of interest in this case are the pet’s home, which is located at (-4,5), and the neighbor’s yard, located at (-9,10). If the pet’s home is the center of the circle and the neighbor's yard is on the circle, find the radius of the circle.

Answers

Let
C----------> the center of a circle
C (-4,5)
A-----------> a point on the circle
A (-9,10)

we know that
the distance between point A and point C is the radius of the circle
A (-9,10) C (-4,5)

d=√[(y2-y1)²+(x2-x1)²]--------> √[(5-10)²+(-4+9)²]
=√[(-5)²+(5)²]------> √[(25)+(25)]---------> √50
d=7.07 units
r=d--------> r=7.07 units

the equation of a circle is
(x+4)²+(y-5)²=50
see the attached figure

the answer is
the radius of a circle is 7.07 units

Find the percentages. 15m is what percent of 60m; 3m; 30m; 1.5 km?

Answers

15m is:
25% of 60m
500% of 3m
50% of 30m
1000% of 1.5m

Here are the calculations to find the percentages:

1. [tex]15\text{m}$ is what percent of $60\text{m}?[/tex]

[tex]\frac{15\text{m}}{60\text{m}} \times 100\% = \frac{1}{4} \times 100\% = 25\%[/tex]

2. [tex]15\text{m}$ is what percent of $3\text{m}?[/tex]

[tex]\frac{15\text{m}}{3\text{m}} \times 100\% = 5 \times 100\% = 500\%[/tex]

3. [tex]15\text{m}$ is what percent of $30\text{m}?[/tex]

[tex]\frac{15\text{m}}{30\text{m}} \times 100\% = \frac{1}{2} \times 100\% = 50\%[/tex]

4. [tex]15\text{m}$ is what percent of $1.5\text{km}?[/tex]

[tex]1.5\text{km} = 1500\text{m}[/tex]

[tex]\frac{15\text{m}}{1500\text{m}} \times 100\% = \frac{1}{100} \times 100\% = 1\%[/tex]

Therefore, the percentages are:

1. [tex]15\text{m}$ is $25\%$ of $60\text{m}[/tex]

2.[tex]15\text{m}$ is $500\%$ of $3\text{m}[/tex]

3. [tex]15\text{m}$ is $50\%$ of $30\text{m}[/tex]

4. [tex]15\text{m}$ is $1\%$ of $1.5\text{km}[/tex]

solve x=4+(4x-4)^(1/2)

Answers

x = 4 + (4x-4) ^ (1/2)
First, we rewrite the expression:
x = 4 + (4x-4) ^ (1/2)
x = 2 (2+ (x-1) ^ (1/2))
x = 4 + 2 (x-1) ^ (1/2)
From here we get a solution for x = 10
To check it we substitute x = 10 in the expression:
10 = 4 + 2 (10-1) ^ (1/2)
10 = 4 + 2 (9) ^ (1/2)
10 = 4 + 2 (3)
10 = 4 + 6
10 = 10
Answer:
The solution is:
x = 10

Answer: Option B

x = 10

Step-by-step explanation:

just did it on edge

10 + 1 = a. dieciuno c. veintiuno b. once d. nueve

Answers

The answer is B. once. Which is eleven in Spanish.

the correct answer would be B.) once

martin paid $120 towards his $2400 credit card bill. what percentage did he pay

Answers

5%
120/2400*100/1 =120/24 =5%

116=0.0625. Which calculation is NOT a way to find 1516?

Answers

we have that
1/16=0.0625

we know that
Multiply (0.0625) by 15 is a way to find (15/16)--------> 0.0625*15=0.9375
so
any operation that results in any other value is not a way to find (15/16)

Answer: 16 divided by 15

Step-by-step explanation:

I got it right.

15% of the toddlers in a preschool class drink water with their lunch. How many toddlers
are in the class if 3 toddlers drink water with their lunch?
(a) Draw a model for the situation (if you prefer to use a 100-grid model or ratio table
model, that’s fine too!) and label the “part,” “whole,” and “percent.”

Answers

15/100 = 3/x

15x = 300
x = 300/15
x = 20 kids

Answer and how you get then answer

Answers

Percent Change = ((new value)/(old value) -1) * 100%
= (480/540 -1)*100%
≈ -11.11%

The number of calories in a child's meal was reduced about 11%.

5 plus 500% of 10 is the same as 110% of what number?

Answers

5+10×500%=5+50=55
55÷110%=50
so 5 plus 500% of 10 is the same as 110% of 50

Find the values of a b and c for which the quadratic equation ax^2+bx+c=0 has the solutions -3 and 1

Answers

It may be easier to start from

.. a(x +3)(x -1) = 0
.. a(x^2 +2x -3) = 0

The quadratic
.. ax^2 +bx +c = 0 will have solutions -3 and 1 for ...

.. a ≠ 0
.. b = 2a
.. c = -3a

how do you write 6 less than the product of 3 and a number X?

Answers

3x - 6 is your answer.

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