Use distributive property and then combine like terms to write an equivalent expression for:

4(y2 + 2) + 6x - 2y3 + 12x

Answer:

Step-by-step explanation:

Given,

Dimensions of the rectangular garden = 2x+11, 3x + 5

Therefore ,

Area of the rectangular garden

= (2x+11) × (3x + 5)

= 3x(2x + 11) + 5(2x + 11)

[tex] = {6x}^{2} + 33x + 10x + 55[/tex]

[tex] = 6 {x}^{2} + 43x + 55(ans)[/tex]

Answer:

x = number of children tickets sold = 500

y = number of adult tickets sold = 100

Step-by-step explanation:

Let

x = number of children tickets sold

y = number of adult tickets sold

x + y = 600 (1)

8x + 15y = 5,500 (2)

From (2)

x = 600 - y

Substitute x = 600 - y into (2)

8x + 15y = 5,500 (2)

8(600 - y) + 15y = 5,500

4,800 - 8y + 15y = 5,500

- 8y + 15y = 5,500 - 4,800

7y = 700

y = 700/7

y = 100

Substitute y = 100 into (1)

x + y = 600 (1)

x + 100 = 600

x = 600 - 100

x = 500

x = number of children tickets sold = 500

y = number of adult tickets sold = 100

Answer:

5 hours, y= how much money it will cost, and x represents how many hours

Step-by-step explanation:

y= 15x+45

120= 15x+45

-45 -45

75= 15x

75/15×= 5 hours

Answer:

d = 14

Step-by-step explanation:

6d = 84

Divide each side by 6 to isolate d

6d/6 = 84/6

d =14

Answer:

8.

Step-by-step explanation:

first week: 2

second week: 2×2=4

third week: 4×2=8

hence, 8 members joined the club on the third week.

Answer:

Dans 3 ans  l’âge du père sera le triple de celui de sa fille

Step-by-step explanation:

X= années qui doivent passer

3(12+X ) = 42 +X

36+ 3X = 42 +X

2X = 6

X = 3

La fille   15 ans

Le  père 45 ans   (15x3=45)

Answer:

Step-by-step explanation:

45=15+x

45-15=x

30=x

Answer:

9 plus 11 plus 12 =

Step-by-step explanation:

x is 22

Answer:

28

Step-by-step explanation:

V = (1/3)Bh

V = (1/3)(7 ft)(2 ft)(6 ft)

V = 28 ft^3

n & n - 1 are two consecutive numbers which means one of is surely even and the other one is odd.

_______________________________

Suppose that n is an even number;

So we can right n like this :

n = 2t

Thus :

n - 1 = 2t - 1

_______________________________

n( n - 1 ) = 2t( 2t - 1 ) = 2 ( 2t^2 - t )

= 2 ( q ) = 2q

The number obtained is a multiple of 2, so it is definitely even because all numbers are even multiples of 2.

Answer:

Option C.

Step-by-step explanation:

We start with the expression:

[tex]\sqrt{y^3} + \sqrt{16*y^3} - 4*y\sqrt{y}[/tex]

where y > 0. (this allow us to have y inside a square root, so we don't mess with complex numbers)

We want to find the equivalent expression to this one.

Here, we can do the next two simplifications:

[tex]\sqrt{16*y^3} = \sqrt{16} \sqrt{y^3} = 4*\sqrt{y^3}[/tex]

And:

[tex]y*\sqrt{y} = \sqrt{y^2} *\sqrt{y} = \sqrt{y^2*y} = \sqrt{y^3}[/tex]

If we apply these two to our initial expression, we can rewrite it as:

[tex]\sqrt{y^3} + \sqrt{16*y^3} - 4*y\sqrt{y}[/tex]

[tex]\sqrt{y^3} + 4*\sqrt{y^3} - 4\sqrt{y^3} = \sqrt{y^3}[/tex]

Here we can use the second simplification again, to rewrite:

[tex]\sqrt{y^3} = y*\sqrt{y}[/tex]

So, concluding, we have:

[tex]\sqrt{y^3} + \sqrt{16*y^3} - 4*y\sqrt{y} = y*\sqrt{y}[/tex]

Then the correct option is C.

Answer:

C:YsqrtY

Step-by-step explanation:

A P E X:L E A R N I N G

Answer:

y = 50x + 150

Step-by-step explanation:

The y-intercept is 150. b = 150

The slope is found using two points such as (2014, 450) and (2010, 250)

m = (450 - 250)/(2014 - 2010) = 200/4 = 50

y = mx + b

y = 50x + 150

Answer:

[tex]Split \ the \ hexagon \ into \ 2 \ trapezoid .\\\\Area \ of \ trapezoid = \frac{a + b}{2} \times h \\\\a = 5 \ , \ b = 9.28, h = 4\\\\Area \ of \ 1\ trapezoid = \frac{5 + 9.28}{2} \times4 = 28.56cm^2\\\\Total \ area = 2 \times 28.56 = 57.12cm^2[/tex]

Answer:

[tex]Area:-[/tex]

[tex](1/x\times~5\times~4)x2[/tex]

[tex]+4x(1/2\times4.64\times4^2)[/tex]

[tex]=20+37.12[/tex]

[tex]=57.12~cm^2[/tex]

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

hope it helps..

have a great day!!

Answer:

x=8

Step-by-step explanation:

so since the whole thing should equal 180, and the right triangle is 90,

(3x+11)+(5x+15)=90 then solve for that

8x+26=90

8x=64

divide both sides by 8

so x=8

then plug in 8 for the xs so c is 3(8)+11 --> 24+11 so m<C=35*

m<D=90*

5(8)+15    40+15 so m<E=55

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

Explanation:

Let x be the angle measure of that dark area. That angle x must add to the other angles 25, 90, and 25 to get a full 360 degree rotation.

So,

x+25+90+25 = 360

x+140 = 360

x = 360-140

x = 220

The dark area angle is 220 degrees

This is known as a reflex angle due to it being larger than 180 degrees, but it's less than 360 degrees. In symbolic terms, any reflex angle is one such that 180 < x < 360.

Step-by-step explanation:

Write what you know

mean is: Sum of all data points / Number of data points

any unknown number we'll call x

so youd write

(x + $3191) / 2 = $4444

Solve for x

let me know if you need further help

Answer:

Quadrant I and quadrant IV

Step-by-step explanation:

Given that cos x< 0

x < arccos 0

x < 90degres

Since cos s positive in the first and 4th quadrant, hence the angle lies in the Quadrant I and quadrant IV

Answer:

21

Step-by-step explanation:

Answer:

The minimum number of hours is 43.

Step-by-step explanation:

Total money required = $ 800

Saved money = $ 290

Per hour income = $ 12

Let the number of hours be n.

According to the question

[tex]290 + 12n \geqslant 800\\\\12 n \geqslant 510\\\\n\geqslant 42.5[/tex]

So, the minimum number of hours is 43.

Answer:

800 - 290 = 510.  510 = 12h

Step-by-step explanation:

$800 is the amount he is trying to save.

$290 is the amount he has so far.

$800 - $290 = $510.

$510 is the amount more he needs to earn.

12h.

12 represents the amount he is paid every 1 hour

H represents the hours he works.

Answer:

x = 1

y =

5x + 2y = 13

x + 2y = 9

Add both equations.

6x + 4y = 22

Solve for x.

6x = 22 - 4y

x = 22/6 - 4/6y

step-by-step explanation:

Put x as 22/6 - 4/6y in the second equation and solve for y.

22/6 - 4/6y + 2y = 9

-4/6y + 2y = 9 - 22/6

4/3y = 16/3

y = 16/3 × 3/4

y = 48/12

y = 4

Put y as 4 in the first equation and solve for x.

5x + 2(4) = 13

5x + 8 = 13

5x = 13 - 8

5x = 5

x = 5/5

x = 1

Answer: I think it’s the first one

Step-by-step explanation:

It says per hour and 15 bucks plus 5 bucks PERhour so you would have to be multiplying I did a question like this long ago hope you get it right

The equation represents this linear relationship for total cost is y= 5x + 15​  thus option (D) is correct.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

As per the given,

She charges a flat fee of $15 plus $5 per hour.

For x number of hours, the total cost will be as,

y = 15 + 5x

Hence "y= 5x + 15 is the equation that depicts this linear relationship for total cost". ​

For more about the linear function,

brainly.com/question/21107621

#SPJ2

Answer:

100 cars

Step-by-step explanation:

Alex: Pete

7:        3

Multiply by x to get the number of cars

Alex  has 7x cars

Pete has 3x cars

Now Alex gives pete 20

Alex has 7x-20

Pete has 3x+20

They have the same number of cars so set the expressions equal

7x-20 = 3x+20

Subtract 3x from each side

7x-20-3x = 3x+20-3x

4x-20 = 20

Add 20 to each side

4x-20+20 = 20+20

4x= 40

Divide by 4

4x/4 = 40/4

x = 10

Alex had 7x = 7*10 = 70 to start

Pete had 3x = 3*10 = 30 to start

Together 70+30 = 100 cars

Answer:

100 cars

Step-by-step explanation:

Alex: Pete

7:        3

Multiply by x to get the number of cars

Alex  has 7x cars

Pete has 3x cars

Now Alex gives pete 20

Alex has 7x-20

Pete has 3x+20

They have the same number of cars so set the expressions equal

7x-20 = 3x+20

Subtract 3x from each side

7x-20-3x = 3x+20-3x

4x-20 = 20

Add 20 to each side

4x-20+20 = 20+20

4x= 40

Divide by 4

4x/4 = 40/4

x = 10

Alex had 7x = 7*10 = 70 to start

Pete had 3x = 3*10 = 30 to start

Together 70+30 = 100 cars

Answer:

Step-by-step explanation:

here,x1=4,y1=3,x2=x and y2=5

slope=2/3

use formula

slope=y2-y1/x2-x1

2/3=5-3/x-4

2/3=2/x-4(do cross multiplication)

2(x-4)=3*2

2x-8=6

2x=6+8

x=14/2

x=7

Answer:

(47,16)

Step-by-step explanation:

System of Equations Problem.

Solve v(7)+b(6)=394;v(3)+b(12)=612

Solve 6b+7v=394 for b

Add -7v to both sides.

6b+7v+−7v=394+−7v

6b=−7v+394

Divide both sides by 6.

[tex]b=\frac{-7}{6} v+\frac{197}{3}[/tex]

Substitute [tex]b=\frac{-7}{6} v+\frac{197}{3}[/tex] for b in 12b+3v=612

12b+3v=612

[tex]12(\frac{-7}{6} v+\frac{197}{3} )+3v=612[/tex]

Simplify both sides of the equation.

−11v+788=612

Add -788 to both sides.

−11v+788+−788=612+−788

−11v=−176

[tex]\frac{-11v}{-11} =\frac{-176}{-11}[/tex]

v=16

Substitute 16 for v in [tex]b=\frac{-7}{6} v+\frac{197}{3}[/tex]

[tex]b=\frac{-7}{6} v+\frac{197}{3}[/tex]

[tex]b=\frac{-7}{6}(16)+\frac{197}{3}[/tex]

Simplify both sides of the equation.

b=47

Answer:

b=47 and v=16

Answer:

25

Step-by-step explanation:

Answer:

sin (π/3)= √3/2

cos (π/6) =√3/2

Answer:

38π cubic units

Step-by-step explanation:

The volume V = ∫₀²πy²dx  

Since y = 3x + 1, dy = 3dx ⇒ dx = dy/3

So, when x = 0, y = 3(0) + 1 = 0 + 1 = 1

when x = 2, y = 3(2) + 1 = 6 + 1 = 7

So, changing the variable to y and the limits of integration from y = 1 to y = 7, we have

V = ∫₀²πy²dx

V = π∫₁⁷y²dy/3

V = π[y³/3]₁⁷/3

V = π[y³]₁⁷/9

V = [7³ - 1³]π/9

V = [343 - 1]π/9

V = 342π/9

V = 38π cubic units

Given:

The figure of a wallpaper border.

To find:

The total required border.

Solution:

The given figure has 8 vertices and 8 edges (sides).

From the given figure it is clear that the length ( in feet) of 8 edges of the figure are 12, 2, 2, 2, 2, 3, 12, 7.

We need to find the total required border. So, we have to find the perimeter of the figure.

Add the lengths of all edges to get the perimeter of the given figure.

[tex]Perimeter=12+2+2+2+2+3+12+7[/tex]

[tex]Perimeter=42[/tex]

So, Chloe should buy 42 feet of border.

Therefore, the correct option is B.

The Answer is 18

Hope this helps! :)

(sorry I am a bit late)

Answer:

18 is correct on edge