-8x = 140

Solve for x

Answer:

[tex]\mathrm{The\:three\: integers\: are\: 11, 12, \: and\:13.}[/tex]

Step-by-step explanation:

We can set up the following equation with the information given:

[tex](x-1)+x+(x+1)=4x-12[/tex], where [tex]x[/tex] is the middle integer.

Solving, we get:

[tex]3x=4x-12, \\-x=-12,\\x=\fbox{12}[/tex].

The three consecutive integers which are 12 less than 4 times the middle integer are 11, 12, and 13.

Integers consist of whole numbers and negative numbers on a number line. For e.g -17, 2, 0, etc. are integers.

Consecutive integers mean integers that come one after another in the number line like 1, 2, 3 or 10, 11, 12, etc.

So if we have to form an equation for three consecutive numbers, it will,

(x-1), x, (x+1),

Now, according to the question,

(x-1) + x + (x+1) =  4x -12

Solve the equation,

3x = 4x -12

x = 12

Hence, first integer = 12 -1 = 11,

Second integer = 12,

Third integer = 12+1 = 13.

Therefore, the three consecutive integers which are 12 less than 4 times the middle integer are 11, 12, and 13.

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Answer:

[tex]AB = 6[/tex]  [tex]BC = 8[/tex]   [tex]AC = 10[/tex]

Step-by-step explanation:

The picture of the triangle is missing.

Given

[tex]AC = x + 4[/tex]

[tex]BC = x + 2[/tex]

[tex]AB = x[/tex]

Required

Find x

When Pythagoras theorem is applied, we have:

[tex](AC)^2 = (BC)^2 + (AB)^2[/tex]

This is so, because AC is the hypotenuse

So, we have:

[tex](x+4)^2 = (x+2)^2 + x^2[/tex]

Open brackets

[tex]x^2 + 4x + 4x + 16 = x^2+2x + 2x + 4 + x^2[/tex]

[tex]x^2 + 8x + 16 = x^2+4x + 4 + x^2[/tex]

Collect Like Terms

[tex]x^2 -x^2 - x^2 + 8x -4x + 16 - 4 = 0[/tex]

[tex]- x^2 + 4x + 12 = 0[/tex]

Expand:

[tex]- x^2 + 6x -2x+ 12 = 0[/tex]

Factorize:

[tex]-x(x -6) -2(x- 6) = 0[/tex]

[tex](-x -2)(x- 6) = 0[/tex]

Split

[tex]-x - 2 = 0[/tex] or [tex]x - 6 = 0[/tex]

[tex]-x = 2[/tex] or [tex]x = 6[/tex]

[tex]x =-2[/tex] or [tex]x = 6[/tex]

Because [tex]BC = x + 2[/tex] and [tex]AB = x[/tex]

[tex]x =-2[/tex] can not be considered.

Hence:

[tex]x = 6[/tex]

Substitute 6 for x in

[tex]AC = x + 4[/tex]

[tex]BC = x + 2[/tex]

[tex]AB = x[/tex]

[tex]AC = 6 + 4[/tex]

[tex]AC = 10[/tex]

[tex]BC = 6 + 2[/tex]

[tex]BC = 8[/tex]

[tex]AB = 6[/tex]

Answer:

x=2;DE,EF=9,DF=5

Step-by-step explanation:

Since DEF is isoceles, you can set the equations

x+7 and 2x+5 equal to each other

x+7=2x+5, now solve for x

-x=-2,

x=2, now plug in for each side

DE,EF=9

DF=3(2)-1=5

Answer:

Answer is true.

Hope this helps.

Step-by-step explanation:

25*x+100=30×x+75

25=5x

x=5

Step-by-step explanation:

Because he always do that non sense thing by this true method and always shout it when they will go from their house

Answer:

760

Step-by-step explanation:

this is the answer you just add zeros and move the decimal

9514 1404 393

Answer:

  recursive: 5, 3, 2

  explicit: 5, 3

Step-by-step explanation:

First of all, you can identify the first term as a1 = 5.

Then you can see that the ratio of consecutive terms is ...

  15/5 = 45/15 = 135/45 = 405/135 = 3 . . . the common ratio

In the recursive formula, a1 is the first term (5), and the multiplier getting you to the next term is the common ratio (3). The recursion relation is good for values of n such that n-1 is at least 1. That is, n ≥ 2.

  [tex]\text{The recursive rule is }a_1=\boxed{5}\text{ and }a_n=\boxed{3}a_{n-1}\text{ for }n\ge\boxed{2}[/tex]

__

The explicit rule is formed the way the problem statement tells you: the first term times a power of the common ratio.

  [tex]\text{The explicit rule is }a_n=\boxed{5}(\boxed{3})^{n-1}[/tex]

Answer:

Um the North China Plain

Step-by-step explanation:

Is dis math...

Answer:

9/10, .90, 90%

Step-by-step explanation:

Answer:(5,-9)

Step-by-step explanation:

Answer:

Step-by-step explanation:

5 * 1/3=5/3

5/3=1 2/3 water for 5 vases

Answer:

B [tex](x,y) \rightarrow \left(\frac{5}{2}x,\frac{5}{2}y\right)[/tex]

Step-by-step explanation:

Dilations

Given a point A(x,y) and a scale factor k the dilated image of A, called A' is calculated as A'=(kx,ky), assuming the same scale factor is applied in both axes.

The pentagon ABCDE was dilated to create pentagon A'B'C'D'E'. To find the dilaton rule used, we must find two clear points where the coordinates of both axes can be easily read from the graph.

Point C(-2,0) maps to C'(-5,0). This gives us the scale factor for the x-axis of -5/(-2)= 5/2.

The y-coordinate of E is 2 and the y-coordinate of E' is 5. This gives us the same scale factor for the y-axis of 5/2.

Thus, the rule to dilate the pentagon is:

B [tex]\mathbf{(x,y) \rightarrow \left(\frac{5}{2}x,\frac{5}{2}y\right)}[/tex]

Answer: Choice D

[tex](-\infty, -2) \cup [4, \infty)[/tex]

=====================================================

Explanation:

The left portion is the interval (-∞, -2)

This is a shorthand way of saying [tex]-\infty < x < -2[/tex]

The curved parenthesis says "do not include this endpoint as part of the solution set". Note the open hole at x = -2 in the diagram.

In contrast, the value x = 4 is included (due to the filled in circle), so we use a square bracket for this endpoint. Therefore, the right-hand portion is represented by [4, ∞) which translates to [tex]4 \le x < \infty[/tex]

Negative and positive infinity will always use a parenthesis, and never a square bracket. This is because we can only approach infinity but never reach it, so we cannot include it as an endpoint.

All of this builds up to the full interval notation to be [tex](-\infty, -2) \cup [4, \infty)[/tex]

The only square bracket is near the 4; everything else is a curved parenthesis. This is why choice D is the final answer.

Step-by-step explanation:

Given that the ratio of zebras are 5 and giraffes are 2

We add them giving is 7

So: giraffe=2/7 × 21 = 6

Zebra 5/7 × 21 = 15

the answer is 22x + 10y

Step-by-step explanation:

7x+7x+x+x+x+x+5y+5y+x+x+x+x = 22x + 10y

Answer:

VW=31

WX=19

YW=36.4 or [tex]\sqrt{1322}[/tex]

ZX= 18.2 or [tex]\frac{\sqrt{1322} }{2}[/tex]

VX= 36.4 or [tex]\sqrt{1322}[/tex]

Step-by-step explanation:

Since the figure is a rectangle certain rules about the lengths of its sides and diagonals apply. One such rule is that opposite sides are equal, so YX=VW and VY=WX. Then you need to find the length of the diagonals by using the Pythagorean theorem since the diagonals cut the rectangle into two right triangles. By using the theorem you can find that the length of the diagonal YW is 36.4 or [tex]\sqrt{1322}[/tex], and since all diagonals are congruent VX is the same. Finally, in rectangle diagonals bisect each other, therefore part of one must be half of the total, so ZX must be half of VX.

Answer:

4/3=1 1/3

Step-by-step explanation:

Answer:

3 1/3 FT 3

Step-by-step explanation:

im not sure if this right but i tried lol

Answer:

There is not enough info you need to add a picture of the box to measure it.

Answer:

slope =1

Step-by-step explanation:

hope it help you

Answer:

Undefined.

Step-by-step explanation:

The x-coordinates of the points along the straight line are always 1.

slope = change in y-coordinate/change in x-coordinate.

Since the change in x-coordinate is 0 (1-1=0), the denominator in the above will be 0 and the fraction (i.e. the slope) would be undefined.

Answer:

The last lines are the final answers, if you need a deeper explanation let me know but I wanted to make sure you understood and got it in time.

Step-by-step explanation:

2(x+4)-3(y+2x)

2x+8-3y-6x

-4x-3y+8

2d+3(4d+2k)-3k

2d+12d+6k-3k

14d+3k

5(4m-2r+7)+4m+3r

20m-10r+35+4m+3r

24m-7r+35

I hope I didn't get anything wrong in a hurry!

Answer:

D. y=-1/2x+5

Step-by-step explanation:

Slope-Intercept Form: y=mx+b

Line passes through y-axis at (0,5) so the "b" part of the equation is positive 5 on the y-axis. Slope is -1/2 so "m" is -1/2.

Answer:

64

Step-by-step explanation:

n/4-3=13

n/4=16

n=64

Answer:

−a2+17b

Step-by-step explanation:

Answer:

723,600 = 7.236 × [tex]10^{5}[/tex]

Step-by-step explanation:

Scientific notation is a way to express numbers in a form that makes numbers that are too small or too large more convenient to write. It is commonly used in mathematics, engineering, and science, as it can help simplify arithmetic operations.

Answer:

I got F but im not 100% sure.

Step-by-step explanation:

Answer:

33.25 g

Step-by-step explanation:

Answer:

33.25 g

plz refer to the picture

Answer:

volume of the solid = [tex]\frac{\pi }{3}[/tex]

Step-by-step explanation:

As given , the region : |x| + |y| [tex]\leq[/tex] 1

when y [tex]\geq[/tex] 0 ,

|x| + y = 1

⇒|x| = 1 - y

when y ≤ 0 ,

|x| - y = 1

⇒|x| = 1 + y

The given region is the rectangle with sides (0, 5) , (0, -5), (5, 0), (-5, 0)

As given , the vertical cross section are semicircle

As we know that the area of semi circle  = [tex]\frac{1}{2}[/tex][tex]\pi x^{2}[/tex]

Now,

Volume = [tex]\int\limits^0_-1 {\frac{\pi }{2} (1+y)^{2} } \, dy[/tex] + [tex]\int\limits^1_0 {\frac{\pi }{2} (1-y)^{2} } \, dy[/tex]

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

           = [tex]\frac{\pi }{6}[/tex][1-0] - [tex]\frac{\pi }{6}[/tex][0-1]

           = [tex]\frac{\pi }{6} + \frac{\pi }{6} = 2\frac{\pi }{6} = \frac{\pi }{3}[/tex]

⇒volume of the solid = [tex]\frac{\pi }{3}[/tex]

Volume of the solid is the value of the capacity of the object that can be hold by it. Thus the value of the volume of the given solid is,

[tex]V=\dfrac{\pi}{3} [/tex]

The vertical cross sections of the solid is perpendicular to the y-axis.

The region of the base is,

[tex]|x|+ |y|\leq 1[/tex]

Volume of the solid is the value of the capacity of the object that can be hold by it.

When the value of the variable y is greater than or equal to zero than the value of the x is,

[tex]|x|=1-y[/tex]

When the value of the variable y is less than or equal to zero than the value of the x is,

[tex]|x|=1+y[/tex].

Given inequality makes a square with the corners (1,0), (0,1),(-1,0),(0,-1).

Now the limit for the given solid is between 0 to 1 and area is equal to the semicircle which is,

[tex]A=\dfrac{\pi x^2}{2} [/tex]

Thus the volume of the solid whose area bounded by the region 1 to -1 and vertical cross section is semicircle can be given as,

[tex]V=\int\limits^1_0 {\dfrac{\pi x^2}{2} } \, dx [/tex]

[tex]V=\dfrac{\pi}{2} [\;\;\int\limits^1_0 {(1+y)^2} \, dy +\int\limits^1_0 {(1-y)^2} \, dy ][/tex]

[tex]V=\dfrac{\pi}{2} [\;\;\dfrac{\int\limits^1_0 {(1+y)^3}}{3} \, +\dfrac{\int\limits^1_0 {(1-y)^3} \, }{3} ][/tex]

[tex]V=\dfrac{\pi}{6} [\;\;\ {(1-0)^3} \, +{(0-1)^3} \, ][/tex]

[tex]V=\dfrac{\pi}{3} [/tex]

Thus the value of the volume of the given solid is,

[tex]V=\dfrac{\pi}{3} [/tex]

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Answer:

Al igual que los cuadrados y los triángulos equiláteros, los hexágonos regulares encajan sin ningún espacio para enlosar el plano (tres hexágonos se encuentran en cada vértice), por lo que son útiles para construir mosaicos.

Step-by-step explanation:

25x² + 100 = 0

25(x² + 4) = 0

x² + 4 = 0

x² = -4

Since x² >= 0 for all real values of x, there is no real solution for x. However there are complex solutions.

=> x = ±√-4

=> x = 2i or x = -2i.