Find the length of the third side. If necessary, round to the nearest tenth.

Answer:

This sum is the sum of an arithmetic sequence.  There is a formula for the sum of an arithmetic sequence which can be looked up or derived by a variety of means.

A nice approach for this sequence is the following.  Notice  that the sum of first and last number in the sequence is the same as the sum of the second and second last, and also the same as the sum of the third and third last, and so on.

There are n of these pairs.  So the desired sum is n x (first number + last number).   But the first number is 1 and the last on is 2n.   Thus the desired sum is n(1 + 2n).

Hope this helps!!

Mark Brainleast!!!!!!!!!!!

Consider the set {1, 2, 3, 4, ..., m} where m is some natural number, i.e. a positive whole number.

Now let's say we wanted to add everything in that set.

What we can do is write out the terms

1, 2, 3, 4, ..., m

then just underneath, we write the reverse of that set

m, ..., 4, 3, 2, 1

Here's an example of what I mean. I'll use m = 7

[tex]\begin{array}{|c|c|c|c|c|c|c|} \cline{1-7}1 & 2 & 3 & 4 & 5 & 6 & 7\\\cline{1-7}7 & 6 & 5 & 4 & 3 & 2 & 1\\\cline{1-7}\end{array}[/tex]

For each column, add straight down

The third row will be nothing but 8's

[tex]\begin{array}{|c|c|c|c|c|c|c|} \cline{1-7}1 & 2 & 3 & 4 & 5 & 6 & 7\\\cline{1-7}7 & 6 & 5 & 4 & 3 & 2 & 1\\\cline{1-7}8 & 8 & 8 & 8 & 8 & 8 & 8\\\cline{1-7}\end{array}[/tex]

We can see there are seven copies of '8' being added here, so the sum of all the numbers in the set {1,2,3,4,5,6,7} is 8*7 = 56. But wait, we double-counted each item when we formed the second row. So we must divide by 2 to fix the double-counting error.

Therefore, 1+2+3+4+5+6+7 = 56/2 = 28 instead.

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

That previous example showed that adding from 1 to 7 means we have 7 copies of (1+7). In other words, 7 copies of 8 being added.

We could write that as 7(1+7)

Then divide that by 2 to fix the double-counting error.

We have 7(1+7)/2

Now imagine that we applied all of what was mentioned to the set {1,2,3,4,5,6,7,8}. Instead of 7's, we use 8's this time to get 8(1+8)/2

Then we can extend it out to the set {1,2,3,4,..., m} and we get the formula m(1+m)/2

We have m copies of (1+m) being added; hence the m(1+m). Don't forget to divide by 2 to fix the double-counting error.

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

The key takeaway here is that summing 1+2+3+4+...+m gets us m(1+m)/2

In this case, m = 2n because we want the first 2n natural numbers.

Therefore,

m(1+m)/2

2n(1+2n)/2

n(1+2n)

n(2n+1)

represents the sum 1+2+3+...+n+...+2n

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

Try out a value like n = 5 to find that 2n = 2*5 = 10, and,

1+2+3+4+5+6+7+8+9+10 = 55

also

n(2n+1) = 5(2*5+1) = 5*(11) = 55

Showing that the formula works for n = 5. I'll let you try other values of n.

Answer:

92%

Step-by-step explanation:

To convert a fraction to a percent, you can divide the numerator by the denominator to end up with a decimal, in this case 0.92. Then, to convert to a percent, move the decimal two places to the left. As a result, we have 92%.

hope this helps!

Answer:

Negative

Step-by-step explanation:

This is the same as saying -12,365 + 110

This equals -12,265

Hope that helps!

Answer:

Same sign - Positive

Different sign - Negative

only for some maths

#1

Put it

[tex]\\ \rm\Rrightarrow p=100000(0.25)^{3}[/tex]

[tex]\\ \rm\Rrightarrow p=100000(0.015625)[/tex]

[tex]\\ \rm\Rrightarrow p=1562.5[/tex]

Now

#2

Let's see

[tex]\\ \rm\Rrightarrow 100000(0.25)^d=1000000[/tex]

[tex]\\ \rm\Rrightarrow 0.25^d=10[/tex]

[tex]\\ \rm\Rrightarrow ln0.25^d=ln10[/tex]

[tex]\\ \rm\Rrightarrow dln0.25=2.3[/tex]

[tex]\\ \rm\Rrightarrow d(-1.39)=2.3[/tex]

[tex]\\ \rm\Rrightarrow d=-1.654[/tex]

Answer:

D

Step-by-step explanation:

3s = 8s - 5s

8s = 8s

s = 0, 1, 2, 3.......

so infinite solutions

D)

Given equation:

To simplify this equation, we need to isolate the variables on one side of the equation and the constants on the other side of the equation. To do this, we can simplify the R.H.S as like terms can subtract.

⇒ [tex]3s = 8s - 5s[/tex]

⇒ [tex]3s = s(8 - 5)[/tex]

⇒ [tex]3s = s(3) = 3s[/tex]

⇒ [tex]3s= 3s[/tex]

Since both sides of the equation are the same, this system of equations has infinite solutions.

We can check our answer by substituting the value of "s" into the equation. As a result, you will see that many values of "s" are satisfying the equation. Thus, Option D is correct.

Answer: 4. A 5. C 6. D

Step-by-step explanation: that’s it!!!!!!!!!!

Answer:

Step-by-step explanation:

3.993,

3.99

Answer:

y = -2 -3x

x = -2/3 -y/3

y =-3x -2

Slope=-6.000/2.000=-3.000

2*y+6*x-(-4)=0

2y + 6x + 4  =   2 • (y + 3x + 2)

Step-by-step explanation:

The bold letters are the important and answer :)

hoped this helped

if the answer is wrong tell me pls

Answer:

Parallel lines 1

perpendicular lines -1

Step-by-step explanation:

2x-2y = -6

Solve for y to get it in slope intercept form

-2y = -2x-6

Divide by -2

y = x+3

This is slope intercept form y = mx+b  where m is the slope

Parallel lines have the same slope

A parallel line would have a slope of 1

Perpendicular lines would have a slope that is a negative reciprocal

-1/1

Perpendicular lines would have a slope of -1

Let us first put it into slope-intercept form ⇒ [tex]y = mx + b[/tex]

To put it into that format, we need to simply put y on one side of the equation and the rest on the other side

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

What do we want to find first ⇒ a line parallel to the original line

          [tex]y = x +5[/tex]

What do we also want to find ⇒ a line perpendicular to the original line

         ⇒ original slope is 1 ⇒ negative reciprocal is - 1/1 = -1

            ⇒ so an example is

                     [tex]y = -x + 3[/tex]

Answer:

Hope that helps!

Answer:

6 rides

Step-by-step explanation:

Total balance = $13.50 = ($2.25/ride)x, where x is the remaining number of rides.  Dividing both sides by $2.25/ride yields 6.

Justin has enough on his bus card for 6 more rides.

Step-by-step explanation:

Doesn't the line show where the median is? Then it would be class 1

Step-by-step explanation:

Check out the attached photo.

A cube that has a height of 1 unit, will also have length and width that are both 1 unit in length.

A cube is a three-dimensional shape that has equal length, width, and height.

We are given that the height of a cube is 1 unit. Since the length, width, and height of a cube are always equal, therefore:

Length of the cube =1 unit

Width of the cube = 1 unit.

In summary, a cube that has a height of 1 unit, will also have length and width that are both 1 unit in length.

Learn more about cube on:

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Answer:

Low

Step-by-step explanation:

Low because it only overlaps twice.

this is what would make sence for me

the frist one was confusing

Answer:

written out in the explanation.

Step-by-step explanation:

Area of a circle = [tex]\pi r^{2}[/tex]

Circumference of a circle = [tex]2\pi r[/tex]

The radius is the center point of a circle to the edge of a circle. The diameter is a line from one edge of a circle to the opposite edge.

So, the radius is simply half of the diameter.

For circle A, the radius is 12. Therefore, the diameter is 24.

The circumference is 2·[tex]\pi[/tex]·12 ≈ 75.39822 inches. rounded, the circumference is 75.4 inches.

The area is [tex]\pi 12^{2}[/tex] ≈ 452.38934. rounded, the area is 452.39.

For B,

you have already solved the diameter and radius correctly, good job :). The steps for finding the circumference are the same as for circle A.

the circumference is 2·[tex]\pi[/tex]·6 ≈ 37.69911. rounded, the circumference is 37.7 inches.

the area is [tex]\pi 6^{2}[/tex] ≈ 113.09734. rounded, the area is 113.1.

For C,

the circumference is 12. We can use the circumference equation to solve for the radius.

12 = [tex]2\pi r^{2}[/tex]

divide both by 2[tex]\pi[/tex]

7.63943726841 = [tex]r^{2}[/tex]

square root of 7.63943726841 = 2.76395319577

radius = 2.76395 inches. rounded, the radius is 2.8 inches.

so, radius ·2 = 5.52790639154.

meaning diameter = 5.52791. rounded, the diameter is 5.5 inches.

the area is [tex]\pi 2.76395^{2}[/tex] ≈23.99994. rounded, the area is 24.

[tex] \huge\rightarrow\sin( θ ) = \frac{ - 2 \sqrt{5} }{5} [/tex]

[tex] \huge\rightarrow\cos( θ ) = \frac{ \sqrt{5} }{5} [/tex]

We know that,

sine is the ratio of adjacent side over the hypotenuse.

[tex] \rightarrow\sin( θ ) = \frac{ - 2 \sqrt{5} }{5} = \frac{adjacent \: side}{hypotenuse} \\ [/tex]

also,

cosine is the ratio of base over the hypotenuse.

[tex]\rightarrow\cos( θ ) = \frac{?}{5} \\ [/tex]

[tex]\rightarrow\cos( θ ) = \frac{ \sqrt{ {5}^{2} - ( - 2\sqrt{ 5} {}^{} ) {}^{2} } }{5} \\ [/tex]

[tex]\rightarrow\cos( θ ) = \frac{ \sqrt{ {5}^{2} - {(2\sqrt{ 5})}^{2} } }{5} \\ [/tex]

[tex]\rightarrow\cos( θ ) = \frac{ \sqrt{25 - 20} }{5} \\ [/tex]

[tex]\rightarrow\cos( θ ) = \frac{ \sqrt{5} }{5} \\ [/tex]

since ,cosine is always positive in the quadrant IV, option 3rd =√5/5 is correct ✓

Note:-

★theta to be used as A

[tex]\\ \rm\Rrightarrow sinA=\dfrac{-2\sqrt{5}}{5}[/tex]

Now

[tex]\\ \rm\Rrightarrow cosA=\sqrt{1-(dfrac{-2\sqrt{5}}{5})^2}[/tex]

[tex]\\ \rm\Rrightarrow cosA=\sqrt{1-\dfrac{20}{25}}[/tex]

[tex]\\ \rm\Rrightarrow cosA=\sqrt{\dfrac{25-20}{25}}[/tex]

[tex]\\ \rm\Rrightarrow cosA=\dfrac{\sqrt{5}}{5}[/tex]

Option C

Answer:

4 1/4 cups were served

Step-by-step explanation:

Just multiply 5 2/3 cups by 3/4:  

17      3

---- * ---- = 4 1/4 cups were served.

 3      4

An equation shows the amount of juice that Jose served is x= 3/4 × 17/3.

The product of two fractions is the product of the numerators and the product of the denominators.

Product of two fractions = Product of their numerators / Product of their denominators.

Given that, Jose made [tex]5\frac{2}{3}[/tex] cups of juice. He served 3/4 of it at dinner.

Here, [tex]5\frac{2}{3}[/tex] cups can be written as 17/3

Let the amount of juice that Jose served be x

Now, x= 3/4 × 17/3

x= 17/4

x= [tex]4\frac{1}{4}[/tex] cups

Therefore, an equation shows the amount of juice that Jose served is x= 3/4 × 17/3.

To learn more about the product of two fractions visit:

https://brainly.com/question/7335118.

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Answer:

[tex]2n=\dfrac{15}{2}[/tex]

Multiply both sides by 2:

[tex]\implies 2 \cdot 2n=2 \cdot \dfrac{15}{2}[/tex]

[tex]\implies 4n=15[/tex]

Divide both sides by 4:

[tex]\implies \dfrac{4n}{4}=\dfrac{15}{4}[/tex]

[tex]\implies n=\dfrac{15}{4}[/tex]

[tex]\dfrac14=\dfrac{n}{5}[/tex]

Multiply both sides by 5:

[tex]\implies 5 \cdot \dfrac14=5 \cdot \dfrac{n}{5}[/tex]

[tex]\implies \dfrac54=n[/tex]

[tex]\implies n=\dfrac54[/tex]

Answer:

Step-by-step explanation:

2n = 15/2

Divide both sides b y 2:

n = 15/2 / 2

   = 15/2 * 1/2

    = 15/4.

1/4 = n / 5

Multiply both sides by the LCM (20):

20/4 = 20n/5

5 = 4n

n = 5/4.

Answer:

x<2

Step-by-step explanation:

5<-5(3x-7)

divide by 5

1<-3x+7

3x<7-1

3x<6

x<2

Transforming the points involves changing their coordinates

The image of the points are:  (3, 6), (-11, 12) and  (-3, -12)

The coordinates of the points are given as:

X(2, 4)

Y(5,-3)

Z(-7, 1)

The rule of this transformation is:

(x, y) to (y, -x)

So, we have:

X' = (4, -2)

Y' = (-3, -5)

Z' = (1, 7)

The rule of this transformation is:

(x, y) to (2x, 2y)

So, we have:

X'' = (8, -4)

Y'' = (-6, -10)

Z'' = (2, 14)

The rule of this transformation is:

(x, y) to (x, -y)

So, we have:

X''' = (8, 4)

Y''' = (-6, 10)

Z''' = (2, -14)

The rule of this transformation is:

(x, y) to (x -5, y + 2)

So, we have:

X'''' = (3, 6)

Y'''' = (-11, 12)

Z'''' = (-3, -12)

Hence, the image of the points are:  (3, 6), (-11, 12) and  (-3, -12)

Read more about transformation at:

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Answer:

78000000

Step-by-step explanation:

(7.8 x 10^3) (1.0 x 10^4) =?

Answer:

False

Step-by-step explanation:

Check if there is a right angle using the Pythagorean Theorem:

7.2^2 + 9.1^2 ≟ 12^2

134.65 ≠ 144,

so since there isn't a right angle, this is not a rectangle.

Answer: 1,950,000

Step-by-step explanation: Divide by 2 beginning with the first digit which is 3 up to the last zero

Let that be x

Use the general formula used for calculating half-life

[tex]\\ \rm\Rrightarrow A=A_o(0.5)^{\frac{t}{h}}[/tex]

put values

The equation is

[tex]\\ \rm\Rrightarrow A=90(0.5)^{x/17.5}[/tex]