Simplify this expression.
6x + 3 – 4x + 2y + 7

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:

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]

12

3 + 3 + 3 + 3 = 12

3 x 4 = 12

Thanks!! <3

Answer:

first one is SAS

Step-by-step explanation:

Answer:

c(h)=12h+6

because the swimsuit only needs to be paid for once, whereas the surfboard is charged on an hourly basis

Answer:

April 25 150 days

Step-by-step explanation:

Answer:

uh 351,000? im not sure..

Step-by-step explanation:

Answer:

33.25 g

Step-by-step explanation:

Answer:

33.25 g

plz refer to the picture

Answer:

760

Step-by-step explanation:

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

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:

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:

gravitational force or  A the first one

Step-by-step explanation:

Answer:

Step-by-step explanation:

it a

Answer:

Um the North China Plain

Step-by-step explanation:

Is dis math...

Answer:

f(-5) = -74 you have to change the x to -5 and then solve

Answer:

Step-by-step explanation:the answer is 0.8020

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:(5,-9)

Step-by-step explanation:

Answer: let's try 2.2 for the first one (sorry if i make you get it wrong but i tried)

Step-by-step explanation:

Answer:

−a2+17b

Step-by-step explanation:

Answer:

54

Step-by-step explanation:

Answer:

54

Step-by-step explanation:

Adding a negative number is the same thing as subtracting a positive number, so 86 + (-32) is the same thing as 86 - 32, which is 54.

Answer:

15 miles

Step-by-step explanation:

if she runs 5 miles in 40 minutes her average speed is 5÷40 = 0.125 miles per min

2 hours = 60 mins × 2 = 120 mins

if she runs 0.125 miles per minute, then 2 hrs = 120 mins × 0.125 = 15 miles

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:

[tex]S_{10}=280[/tex]

Step-by-step explanation:

Given that,

[tex]t_n=2n+3[/tex] ...(1)

We need to find the value of [tex]S_{10}[/tex].

Put n = 1 to find the first term.

[tex]t_1=2(1)+3=5[/tex]

Put n = 2 to find the second term.

[tex]t_2=2(2)+3=7[/tex]

Put n = 3 to find the third term.

[tex]t_3=2(3)+3=9[/tex]

Put n = 10 to find the tenth term.

[tex]t_{10}=2(10)+3=23[/tex]

It means we need to find the sum of 5,7,9,.....,23.

The formula for the sum of n terms is given by :

[tex]S_=\dfrac{n}{2}(a+a_n)[/tex]

We have, n = 10, a = 5 and [tex]a_n=23[/tex]

So,

[tex]S=\dfrac{10}{2}(5+23)\\\\S_{10}=10\times 28\\\\=280[/tex]

So, the value of [tex]S_{10}[/tex] is equal to 280.

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.

Answer:

10 is ≈8.47% of 118

Step-by-step

(10/118)(100)

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]

Learn more about the volume of the solid here;

https://brainly.com/question/2254156

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.