6. The sum of 3 consecutive odd integers is 87. Find the equation used to solve this
problem. Find the three integers.
An +n + 2 +n +4-87:
n-27, n + 2 - 29, n + 4- 31
B
n
+n +1 +n + 2 - 87:
n=28, n + 1 = 29, n + 2 = 30
Cn +n +1+n + 2 = 87;
n = 29, n + 1 = 30. n + 2 = 31
Dn+n + 2 +n + 4-87;
n = 29,0 + 2 = 31, n + 4 = 33

Answer:

x=2

Step-by-step explanation:

Vertical lines have the same x value all the time.  It is of the form x=

Their slope is undefined

The line passes through the point (2,4) and the x value is 2

x=2

Answer:

8x - 5y = - 30

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 8x - 5y = 2 into this form

Subtract 8x from both sides

- 5y = - 8x + 2 ( divide all terms by - 5 )

y = [tex]\frac{8}{5}[/tex] x - [tex]\frac{2}{5}[/tex] ← in slope- intercept form

with slope m = [tex]\frac{8}{5}[/tex]

• Parallel lines have equal slopes, hence

y = [tex]\frac{8}{5}[/tex] x + c ← is the partial equation of the parallel line

To find c substitute (- 5, - 2) into the partial equation

- 2 = - 8 + c ⇒ c = - 2 + 8 = 6

y = [tex]\frac{8}{5}[/tex] x + 6 ← in slope- intercept form

Multiply through by 5

5y = 8x + 30 ( subtract 5y from both sides )

0 = 8x - 5y + 30 ( subtract 30 from both sides )

8x - 5y = - 30 ← in standard form

[tex]2(n-5)\geq2n+10\\2n-10\geq2n+10\\-10\geq 10\\n\in\emptyset[/tex]

Answer:

I think it would be 11:1.

Step-by-step explanation:

360,000 / 30,000 = 12

11/12 of the yearly budget was used on other costs

1/12 of the yearly budget was used for leasing office

space.

Answer:

Step-by-step explanation:

Okay so I may be wrong BUT since it's asking for the other costs, I'm assuming we're subtracting the $30,000 from the $360,000 first. Therefore the original ratio would be 30,000: 330,000 which is simplified to 1:11 ($ on office space: $ on other costs)

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{Note}\rightarrow[/tex] [tex]\leq \& \geq \ = \huge\text{closed circle}\\ < \& > = \huge\text{(o)(p)(e)(n)(e)(d) circle}[/tex]

[tex]\huge\text{So, we know that A or C could be our answer}.[/tex]

[tex]\huge\text{Eliminate option B and D}[/tex]

→ [tex]\huge\text{Find the absolute value of the problem}[/tex]

→ [tex]\huge\text{You can now know that  it could be:}[/tex]  

[tex]\huge\text{x}\large\huge{\ >}\huge\text{ 10 or x }< \huge\text{ -10}[/tex]

→ [tex]\huge\text{Possible answer \#1: x }>\huge\text{10}\\\\\huge\text{Possible answer \#2: x}<\huge\text{ -10}[/tex]

→ [tex]\boxed{\boxed{\huge\text{Answer: C}}}[/tex]  

[tex]\huge\text{Option A. would be too small}[/tex] [tex]\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

The volume of the cone is one third of the volume of the cylinder when they have the same radius and height.

The volume of the sphere is two thirds the volume of the cylinder when the sphere and the cylinder have the same radius and the height of the cylinder is twice its radius.

If a cone has the same radius (r) and height (h) as a cylinder, then the volume of the cone is one third the volume of the cylinder.

This can be determined using the formula for the volume of a cone, which is V = (1/3)πr²h, compared to the volume of a cylinder, which is V = πr²h. Since we have the same 'r' and 'h' for both, the cone's volume will be one third of the cylinder's.

Similarly, if a cylinder and a sphere have the same radius and the cylinder’s height is twice its radius, we can say h = 2r. Thus, the volume of the sphere is calculated to be V = (4/3)πr³.

On the other hand, the cylinder's volume with h=2r would be V = πr²(2r) = 2πr³. The sphere's volume is two thirds of the cylinder's volume, because (4/3)πr³ is two thirds of 2πr³.

[tex]x^2=40^2+9^2\\x^2=1600+81\\x^2=1681\\x=\sqrt{1681}=41[/tex]

To solve this you must use Pythagorean theorem:

[tex]a^{2} +b^{2} =c^{2}[/tex]

a and b are the legs (the sides that form a perpendicular/right angle)

c is the hypotenuse (the side opposite the right angle)

In this case...

a = 9

b = 40

c = x

^^^Plug these numbers into the theorem

[tex]9^{2} +40^{2} =x^{2}[/tex]

simplify

81 + 1600 = [tex]x^{2}[/tex]

1681 = [tex]x^{2}[/tex]

To remove the square from x take the square root of both sides to get you...

41 = x  

Hope this helped!

~Just a girl in love with Shawn Mendes

a) 600340

b) 600300

c) 600000

Answer:

See below.

Step-by-step explanation:

Compare our equation with one  standard form of a circle:

x^2 + y^2 = r^2    where r = the radius.

So x^2 + y^2 = 9 is the equation of a circle with it's center at the origin and it's radius is 3 units.

x^2 + y^2 = 0 is not a circle because r = 0  ( a radius of 0). A circle of radius 0 is really a point!!

The value of the radius of a circle  must be positive  so it cannot have a radius of -3.

Answer

[tex]x ^{2} + {y}^{2} = r^{2} [/tex]

since all the terms are squared so there can be a negative number

but in number line

...... -4,-3,-2,-1,0,1,2,3.......

as we know negative sign indicates only the direction so -3 means in which coordinates will it lie.

.

.

.

[tex] {x}^{2} + {y}^{2} = 9[/tex]

it means the origin is (0,0) and radius 3

Answer:

380 cubic feet of air

Step-by-step explanation:

Volume = height * width * length.

So

Volume = 10 * 2 * 19 = 380 cubic feet of air

Answer:

[tex]380\text{ ft}^3[/tex]

Step-by-step explanation:

We have been that a classroom is 19 ft long 2 ft wide and 10 feet high. We are asked to find the number of cubic feet of air in the room​.

To find the number of cubic feet of air in the room​, we will find the volume of the given room by multiplying all of its side as:

[tex]\text{Volume of the room}=\text{19 ft}\times \text{2 ft}\times\text{10 ft}[/tex]

[tex]\text{Volume of the room}=380\text{ ft}^3[/tex]

Therefore, there are 380 cubic feet of air in the room.  

Answer:

17.167 rounded

Step-by-step explanation:

17+(1/6)

17+0,166

17.167

well, firstly convert the mixed fraction to improper fraction, and then simply divide the numerator by the denominator and round as needed.

[tex]\bf \stackrel{mixed}{17\frac{1}{6}}\implies \cfrac{17\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{103}{6}}~\hfill \stackrel{\textit{to a decimal}~\hfill }{103\div 6 = 17.166\overline{6}}\implies \stackrel{\textit{rounded up}}{17.167}[/tex]

f(12)= square root of(12-3)

f(12)=square root of 9

f(12)=3

Answer:

3

Step-by-step explanation:

[tex]f(12) = \sqrt{12-3}=\sqrt{9} = 3[/tex]

Answer:

4

Step-by-step explanation:

-5x/6=-10/3

or..5x/6=10/3

or..X/2=2

so X=4

Answer:

x = 4

Step-by-step explanation:

note that - [tex]\frac{5}{6}[/tex] x = [tex]\frac{-5x}{6}[/tex], hence

[tex]\frac{-5x}{6}[/tex] = [tex]\frac{-10}{3}[/tex] ( cross- multiply )

- 15x = - 60 ( divide both sides by - 15 )

x = [tex]\frac{-60}{-15}[/tex] = 4, that is

x = 4

Answer:

Mary = 24

Chau = 15

David = 48

Step-by-step explanation:

The formula is

Mary + Chau + David = 87

And we know that

Chau = Mary - 9

David = Mary * 2

So when we fill this in

Mary + Mary - 9 + Mary * 2 = 87

4Mary - 9 = 87

4Mary = 96

Mary = 24

Chau = Mary - 9 = 15

David = Mary * 2 = 48

Final answer:

The problem is solved using basic algebra, yielding Chau has $15, Mary has $24, and David has $48, all adding up to the total amount of $87.

Explanation:

The question involves a three-person word problem focusing on algebraic relationships and equation solving. Mary, Chau, and David have a total of $87 in their wallets. Mary has $9 more than Chau, and David has twice what Mary has. To find out how much each person has, we'll let 'c' represent the amount that Chau has.

Accordingly, Mary has c + $9, and David has 2(c + $9). Together, they have a total of c + (c + $9) + 2(c + $9) = $87. Simplifying this, we get 4c + $27 = $87. Subtracting $27 from both sides gives us 4c = $60. Dividing both sides by 4, we find that Chau has $15.

Now, since Mary has $9 more than Chau, Mary has $24 ($15 + $9). David, having twice what Mary has, possesses $48 (2 x $24). These amounts add up to the total of $87.

Answer:

(arranged from top to bottom)

System #3, where x=6

System #1, where x=4

System #7, where x=3

System #5, where x=2

System #2, where x=1

Step-by-step explanation:

System #1: x=4

[tex]2x+y=10\\x-3y=-2[/tex]

To solve, start by isolating your first equation for y.

[tex]2x+y=10\\y=-2x+10[/tex]

Now, plug this value of y into your second equation.

[tex]x-3(-2x+10)=-2\\x+6x-30=-2\\7x=28\\x=4[/tex]

System #2: x=1

[tex]x+2y=5\\2x+y=4[/tex]

Isolate your second equation for y.

[tex]2x+y=4\\y=-2x+4[/tex]

Plug this value of y into your first equation.

[tex]x+2(-2x+4)=5\\x+(-4x)+8=5\\x-4x+8=5\\-3x=-3\\x=1[/tex]

System #3: x=6

[tex]5x+y=33\\x=18-4y[/tex]

Isolate your first equation for y.

[tex]5x+y=33\\y=-5x+33[/tex]

Plug this value of y into your second equation.

[tex]x=18-4(-5x+33)\\x=18+20x-132\\-19x=-114\\x=6[/tex]

System #4: all real numbers (not included in your diagram)

[tex]y=13-2x\\8x+4y=52[/tex]

Plug your value of y into your second equation.

[tex]8x+4(13-2x)=52\\8x+52-8x=52\\0=0[/tex]

all real numbers are solutions

System #5: x=2

[tex]x+3y=5\\6x-y=11[/tex]

Isolate your second equation for y.

[tex]6x-y=11\\-y=-6x+11\\y=6x-11[/tex]

Plug in your value of y to your first equation.

[tex]x+3(6x-11)=5\\x+18x-33=5\\19x=38\\x=2[/tex]

System #6: no solution (not included in your diagram)

[tex]2x+y=10\\-6x-3y=-2[/tex]

Isolate your first equation for y.

[tex]2x+y=10\\y=-2x+10[/tex]

Plug your value of y into your second equation.

[tex]-6x-3(-2x+10)=-2\\-6x+6x-30=-2\\-30=-2[/tex]

no solution

System #7: x=3

[tex]y=10+x\\2x+3y=45[/tex]

Plug your value of y into your second equation.

[tex]2x+3(10+x)=45\\2x+30+3x=45\\5x=15\\x=3[/tex]

Answer:

Step-by-step explanation:

2y + 4 = 0               subtract 4 from both sides

2y = -4       divide both sides by 2

y = -2

The slope-intercept form of an equation of a line:

y = mx + b

m - slope

b - y-intercept → (0, b)

In the equation

y = -2

slope: m = 0

y-intercept: b = -2 → (0, -2)

y = -2 - it's a horizontal line

Answer:

3x -5

Step-by-step explanation:

(4x – 12) + (–x + 7)

= 4x – 12 –x + 7

= 3x -5 (answer)

Answer:

3x-5

Step-by-step explanation:

(4x – 12) + (–x + 7)

Open the parenthesis

=4x-12-x+7

Solve the like terms:

=3x-5

The answer is 3x-5

Answer:

B. (3, 0), (0, -6)

Step-by-step explanation:

Plug 0 in for each variable one at a time, and you will get both intercepts.

Answer:

It is a Right Triangle.

Step-by-step explanation:

30^2 = 900

24^2 =  576

18^2 = 324

576 + 324 = 900

This satisfies the Pythagoras theorem so it is a Right Triangle.

Answer:

Step-by-step explanation:

For a ≤ b ≤ c:

if a² + b² = c², then a triangle is a right triangle

if a² + b² < c², then a triangle is an obtuse triangle

if a² + b² > c², then a triangle is an acute triangle.

We have a = 18, b = 24, c = 30. Substitute:

18² + 24² = 324 + 576 = 900

30² = 900

18² + 24² = 30² → a² + b² = c²

Answer:

A=$538.82

Step-by-step explanation:

We're going to use the compounded interest formula:

A=P(1+r/n)^n*t

Where,

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per unit t

t = t is the amount of time at which you're checking how much it's worth (yrs)

Using this information, we can use:

A=500(1+0.025/4)^3*4

A=500(1+0.00625)^12

A=500(1.00625)^12

A=500(1.07763259886)

A=538.82

A=$538.82....

Answer:

range=u ± 3.09 sd

Step-by-step explanation:

Given:

mean, u= 26.8 mpg

standard deviation, sd=72 mpg

% contained in interval = 99.8%

the interval for 99.8% of the values of a normal distribution is given by

mean ± 3.09 standard deviation= u ± 3.09 sd

                                                      =26.8  ± 3.09(72)

                                                      =26.8 ± 222.48

                                                      = 249.28 , -195.68

range=u ± 3.09 sd = 249.28 , -195.68 !

The key  property of the absolute value parent function is:

        C. It’s vertex is at the origin.

The absolute value parent function is given by:

                  [tex]f(x)=|x|[/tex]

i.e. the graph of the function lie in the first and second quadrant.

Answer: P(red): 1/2

P(red or black):3/4

Step-by-step explanation: Count the total number of marbles. There are 8. Since there are 4 red marbles out of the 8, put this into a fraction. It will be 4/8, but simplify to 1/2. The P(red) is 1/2.

Since there are 4 red marbles and 2 black marbles, add them. There are 6 out of the 8 marbles. The fraction is 6/8 simplify to 3/4. The P(red or black) is 3/4.

The probability of choosing a red marble from the box is 0.5 and the probability for choosing either a red or black marble is 0.75.

The subject of this question refers to calculating probabilities which is a concept in Mathematics, specifically in the scope of Statistics. To calculate the probability of an event, we need to know the total amount of outcomes and the amount of favorable outcomes. In the context of the question, these outcomes are represented by marbles.

First, we need to add the total number of marbles, which is 4 red + 2 black + 2 green = 8 marbles in total.

To find the probability of picking a red marble, we divide the number of red marbles by the total number of marbles. Hence, P(red) = 4/8 or 0.5.

To find the probability of picking a red or black marble, we add the number of red and black marbles and divide by the total number of marbles. Hence, P (red or black) = (4 red + 2 black) / 8 total = 6/8 or 0.75.

https://brainly.com/question/22962752

#SPJ2

Answer:

Step-by-step explanation:

The correct answer would be -18

To solve this, you would substitute x with the x value, which in this case is -2

That would make it so f(x)= 9(-2)

9*-2=-18

Therefore f(x)=-18

Note that f(x) is another way to write y, therefore...

y = 9x

To solve for this plug -2 in for x in this equation like so...

y = 9 * -2

When a positive number is being multiplied with a negative number the answer will be negative.

y = -18

C. is the answer (assuming that you meant to write -18 instead of 1 18)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

[tex]\3.11\ ounces[/tex]

Step-by-step explanation:

we know that

To find the number of ounces of food each turtle will receive, divide the total ounces of food by the total number of turtles

so

[tex]\frac{84}{27}=3.11\ ounces[/tex]

Answer: 3.1

Step-by-step explanation: which is 3.1 with the line on top!

Answer:

7(a + 2b)(a² - 2ab + 4b²)

Step-by-step explanation:

Given

7a³ + 56b³ ← factor out 7 from each term

= 7(a³ + 8b³) ← sum of cubes which factors in general as

a³ + b³ = (a + b)(a² - ab + b²)

8b³ = (2b)³ ⇒ b = 2b

a³ + 8b³ = (a + 2b)(a² - 2ab + (2b)²) = (a + 2b)(a² - 2ab + 4b²)

Hence

7a³ + 56b³ = 7(a + 2b)(a² - 2ab + 4b²) ← in factored form

Answer:

[tex]\sin(x)=\frac{\sqrt{95}}{12}=0.8122[/tex]

[tex]\cos(x)=\frac{7}{12} \approx .5833[/tex]  

[tex]\tan(x)=\frac{\sqrt{95}}{7} \approx 1.3924[/tex]  

[tex]x=\sin^{-1}(\frac{\sqrt{95}}{12}) \approx 54.3147[/tex] degrees.

I don't know what you want to round to but I can tell you are rounding...

Step-by-step explanation:

Soh Cah Toa is the acronym we will use to help us solve this.

This says sine is opposite over hypotenuse.

It also says cosine is adjacent over hypotenuse.

And finally tangent is opposite over adjacent.

Note:  Opposite and adjacent can change depending on how you are looking at the triangle, like which angle you are referring to.

Let's look at x:

The side that is opposite, not touching, the angle whose measurement is x, is the side that has measurement [tex]\sqrt{95} \approx 9.7[/tex].

I see you already found this measurement. This is really good.  I might use the exact value for now and round at the end.

The side that is the hypotenuse no matter the angle you are referencing is always going to be opposite the angle whose measurement is 90 degrees. It is also the longest side (since it is opposite the largest angle).  This side has measurement 12.

The hypotenuse will be one of the sides touching your angle you are referencing.  The other side that is touching your angle is the adjacent side.  This side has measurement 7.

Anyways let's plug into the definitions we had above:

[tex]\sin(x)=\frac{\sqrt{95}}{12}[/tex]  (O/H)

[tex]\cos(x)=\frac{7}{12}[/tex]   (A/H)

[tex]\tan(x)=\frac{\sqrt{95}}{7}[/tex]   (O/A)

Now we can solve anyone of these for x.

Take your pick.

[tex]\sin(x)=\frac{\sqrt{95}}{12}[/tex]

[tex]x=\sin^{-1}(\frac{\sqrt{95}}{12})[/tex]

[tex]x=54.3147[/tex] degrees.  

The Cube Root Of -343 is ( -7)

Answer:

Cube root of -343 is -7

Step-by-step explanation:

If we square a negative value it becomes positive as ² is an even number

eg: -7² = -7 × -7

= +49

But if we cube it is the value becomes negative as ³ is an odd number

eg: -7³ = -7 × -7 × -7

= -343

Hope it helps u ...

Answer:

option B

Step-by-step explanation:

Given:

per day late costs= 1.50

Purchase price= 9.99

A round trip cab ride to the video store will cost = 10

5 day late cost= 5(1.50)

                       = 7.50

Payment after 5 day late= 5 day late cost + Purchase price

                                       = 7.50 + 9.99

                                       = 17.49

If she gets a cab, then total payment= 10 + 7.50

                                                             = 17.50

Hence both costs almost the same, option B is true

b.

It would cost about the same to keep or return the movie. Susan should keep it!