Use r = 2 and r = 5 to determine if the two expressions are equivalent. r + 4(2 + r) – 12 8 + 2r – 6

Answer:

9x² - 12x + 4

Division Property

Step-by-step explanation:

(3x-2)² = (3x-2)(3x-2)

using the foil method we get:

9x² - 6x - 6x + 4

combine 'like' terms to get:

9x² - 12x + 4

2x = 10  To get 'x' by itself, since it's being multiplied by 2 we must do the inverse operation which is division

If we divide one side of an equation by 2 we must do the same to the other side, giving us:

x = 10/2 which is x = 5

Answer:

[tex]9x^{2} - 12x + 4[/tex]

Division property: divide both sides by 2

Step-by-step explanation:

[tex](3x - 2) ^{2} [/tex]

[tex](3x - 2)(3x - 2)[/tex]

[tex]3x(3x−2)−2(3x−2)[/tex]

[tex]3x(3x)+3x(−2)−2(3x−2)[/tex]

[tex] {9x}^{2} - 6x - 6x + 4[/tex]

[tex]9x^{2} - 12x + 4[/tex]

[tex]2x = 10[/tex]

[tex]x = 5[/tex]

Answer:

Both are equal

Step-by-step explanation:

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Answer:1/7

Step-by-step explanation:

Answer:

✺ [tex] \large \tt \: E \: X\: P\: L\: A \: N \: A \: T \: I \: O\: N : [/tex]

☃ [tex] \large{ \tt{GIVEN \: EQUATION}} : [/tex]

[tex] \large{ \bf{↬y = 3x + 5}}[/tex] [ Move 3x from left hand side to right hand side and change it's sign to addition since the opposite of subtraction is addition ]

[tex] \boxed{ \large \:⟿ \tt \:Slope \: (m) = \boxed{ \tt{3} }}[/tex]

[tex] \boxed{ \large { \tt{⟿ \: Y - intercept \: (c \: ) = \boxed {\tt{ 5}}}}}[/tex]

☏ And we're done! Yay , We found our answer !

♕ [tex] \large{ \tt{STUDY \: TIP}}[/tex]

♡ Hope I helped! ✎

☄ Have a wonderful day / night ! ☂

#StayInAndExplore ! ♨

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

Answer:

Todos son números racionales.

Step-by-step explanation:

Un número racional tiene la forma de p / q donde pyq son números enteros y q ≠ 0.

Por ejemplo, un número 1/3 es un número irracional porque es un número decimal recurrente, es decir, puede continuar después del decimal (0.13333333)

Pero los números como 1/5 o 1/2 que no son recurrentes son números racionales.

Todos los números dados 1 / 2,0, 3.8 y 7.2 son números racionales ya que cada uno puede expresarse en forma de p / q

Números p q p / q

1/2 1 2 1/2 = 0,5

0 0 cualquier entero 0

3,8 19 5 19/5 = 3,8

0,72 72100 0,72

Por tanto, todos son números racionales.

English

A rational number is in the form of p/q where p and q are integers and q ≠ 0.

For example a number 1/3 is an irrational number because it is a recurring decimal number i.e it can continue after the decimal ( 0.13333333)

But numbers such as 1/5 or 1/2 which are non recurring are rational numbers.

All the numbers given 1/2,0 ,3.8 and 7.2 are rational numbers as each can be expressed in the form of p/q

Numbers                   p                q                   p/q

1/2                            1                  2                     1/2=0.5

0                              0       any integer                 0

3.8                         19                 5                       19/5=3.8

0.72                       72               100                    0.72

Hence all ae rational numbers.

Answer:

28.9 m

Step-by-step explanation:

30²-8²=900-64= 836

√836 = 28.9 m

The Ladder reach 28.91 ft. up the house which is 8 ft. away from the base.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

Here, Given, length of ladder ( Hypotenuse ) = 30 ft.

Distance from base = 8 ft.

By Pythagoras theorem,

Hypo.² = perp.² + base²

30² = x² + 8²

900 = x² + 64

x² = 900 - 64

x² = 836

x = √836

x = 28.91 ft.

Thus, the Ladder reach 28.91 ft. up the house which is 8 ft. away from the base.

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Answer:

5/4

Step-by-step explanation:

i show the explanation in picture

Answer:

The total number of child ticket sold  = 87

The total number of adult ticket sold = 128

Step-by-step explanation:

Given -  The local theatre performed a Saturday matinee to a crowd of 215 people. Tickets cost $11 child and $15 per adult, bringing in a total of $2877.

To find - Use an inverse matrix to determine the number of each type of ticket sold .

Proof -

Let the total number of child ticket sold = x

Let the total number of adult ticket sold = y

Given that, The local theatre performed a Saturday matinee to a crowd of 215 people.

⇒x + y = 215

Also,

Given that,  Tickets cost $11 child and $15 per adult, bringing in a total of $2877

⇒11x + 15y = 2877

So,

The equations becomes

x + y = 215

11x + 15y = 2877

So,

The matrix form becomes

[tex]\left[\begin{array}{ccc}1&1\\11&15\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}215\\2877\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}1&1\\11&15\end{array}\right| \left\begin{array}{ccc}215\\2877\end{array}\right ] \\\left[\begin{array}{ccc}1&1\\0&4\end{array}\right| \left\begin{array}{ccc}215\\512\end{array}\right ] \\\left[\begin{array}{ccc}1&1\\0&1\end{array}\right| \left\begin{array}{ccc}215\\128\end{array}\right ]\\\left[\begin{array}{ccc}1&0\\0&1\end{array}\right| \left\begin{array}{ccc}87\\128\end{array}\right ][/tex]

By comparing, we get

x = 87

y = 128

So, we get

The total number of child ticket sold = x = 87

The total number of adult ticket sold = y = 128

Answer:

if you solve the question please i request you please read the question carefully after solve the question

Answer:

10 guests

Step-by-step explanation:

Devin wants to play lazer tag for his birthday. He is comparing the cost of two companies.

Let us represent additional guests = g

Lazer Zone charges $50 for parties, and an additional $10 per guest.

=$50 + $10 × g

50 + 10g

For fun place

Fun Palace charges $90 for parties, and an additional $6 per guest.

= $90 + $6 × g

90 + 6g

For how many ?

We equate both Equations together

= 50 + 10g = 90 + 6g

Collect like terms

10g - 6g = 90 - 50

4g = 40

g = 40/4

g = 10

Hence, g = 10 guests

Therefore, the number of guests for which the cost of both companies is the same is 10 guests

Answer:

Step-by-step explanation:

There are no pics

Answer:

a. a = 3, b = 2

b. The coordinate of the center is (2, -1)

c. The eccentricity of the ellipse is √5/3

d. Please see attached graph of the ellipse created with MS Excel

Step-by-step explanation:

7. a. The given equation of the ellipse is presented as follows;

4·x² + 9·y² - 16·x + 18·y - 11

The general equation of an ellipse

[tex]\dfrac{(x - h)^2}{a^2} + \dfrac{(y - k)^2}{b^2} = 1[/tex]

We can write;

4·x² - 16·x + 9·y² + 18·y - 11

4·(x² - 4·x + 4) + 9·(y² + 2·y + 1) - 25 - 11

4·(x² - 4·x + 4) + 9·(y² + 2·y + 1) =  25 + 11 = 36

4·(x - 2)² + 9·(y + 1)² = 36

[tex]\dfrac{4\cdot (x - 2)^2}{36} + \dfrac{9 \cdot (y + 1)^2}{36} = \dfrac{36}{36}[/tex]

[tex]\therefore \dfrac{ (x - 2)^2}{9} + \dfrac{ (y + 1)^2}{4} = \dfrac{ (x - 2)^2}{3^2} + \dfrac{ (y + 1)^2}{2^2} = 1[/tex]

By comparison, a = 3, b = 2, h = 2, k = -1

b. The coordinate of the center, (h, k) = (2, -1)

c. The eccentricity of the ellipse = c/a

c² = a² - b²

∴ c² = 3² - 2² = 5

c = √5

Eccentricity = √5/3

d. Please find attached the graph of the ellipse created with MS Excel

Answer:

1st option is correct

Step-by-step explanation:

Answer:I think its Shannon

Step-by-step explanation:

Answer:

6 hours * 3 kilometers = 18 hours

Answer:

the value of X is 122

Step-by-step explanation:

First, all triangle angles add up to 180 so to find the missing angle we subtract  51 and 71 from 180 and get 58

Now we know straight lines always equal 180 as well so we subtract 58 from 180 and get 122 and that is the value of x

Answer:

4 ft

Step-by-step explanation:

Height  = √[5^2 - 3^2]

= √[25 - 9]

= √16  

= 4 ft

Answer:

4ft

Step-by-step explanation:

Answer:

B) 24

Step-by-step explanation:

The area of the rectangle is 48 units (8 x 6).

The base of the is 6 units and the height is 8 units. The formula for the are of a triangle is A = [tex]\frac{1}{2}[/tex]bh.

b = base

h = height

A = [tex]\frac{1}{2}[/tex](6)(8)

A = 24

Answer:

[tex]24[/tex]

Step-by-step explanation:

If the area of a rectangle is bh, and the area of a triangle is bh/2, then a triangle's area is half a rectangle's area. Hence, if the area of the rectangle is 48, the area of the triangle is half of 48, or 24.

Answer:

F

Step-by-step explanation:

F is the answer because in order to have a right triangle you have to have two of the same lengths and one length that is longer than the two that are the same.

Hope this helps!

Have a good day!

Answer:

A. 25 feet

Step-by-step explanation:

Answer:

Sum of angles of a triangle is 180, so x + y + w = 180

Straight angle is 180 , so y + z = 180

From the first 2 conditions :

=>x + y +w = y + z

=> x + w = z  

Option 1, 2, 5

The equations which are true are given by,

Equation is a mathematical relation between more than one variable, number or mathematical quantities involving mathematical operations using equal sign in between them.

From angle sum property of triangle says that the sum of all interrior angles of a triangle is 180.

Here all interrior angles of triangle are x,y,w

So, x+y+w = 180

Hence first option is correct.

Again the exterrior angle of a triangle is equal to the sum of the opposite two interrior angles.

here exterrior angle is z and opposite two interrior of z are x,w

So, w+x = z

Hence last option is correct.

Again y+z = y+w+x

so second option is also true.

Hence correct options or equations are given by:

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Answer:

0.0952

Step-by-step explanation:

Answer:

7/8

Step-by-step explanation:

Andrea recipe for cranberry relish is

1 3/4

= 7/4

He wants to use 1/2 of that amount

Therefore the amount of sugar he should use can be calculated as follows

= 7/4×1/2

= 7/8

Answer:

1 - 330

Blue one  - 424

Yellow one- 181.6

Step-by-step explanation:

Answer:

The focus of the parabola is (10, 10.0[tex]\overline 5[/tex])

The directrix of the parabola is, y = 1.0[tex]\overline 5[/tex]

The maximum height reached by the ball = 5.[tex]\overline 5[/tex] meters

The vertex of the parabola is (10, 5.[tex]\overline 5[/tex])

Step-by-step explanation:

The general equation of a parabola is y = a·(x - h)² + k

The vertex of the parabola = (h, k)

At 2 meters (horizontal) before landing, the height, h = 2 meters

∴ We have;

2 = a·(2 - h)² + k

2 = a·(18 - h)² + k

(2 - h)² = (18 - h)²

h² - 4·h + 4 = h² - 36·h + 324

36·h - 4·h = 324 - 4

h = 320/32 = 10

h = 10

2 = ut -0.5×9.81×t²

The

The time it takes the ball to fall 2 meters =

y = a·x² + b·x + c

h = -b/(2·a)

At y = 0, x = 0, therefore, c = 0

2 = a·2² + b·2 + c = 4·a + 2·b

2 = 324·a + 18·b

k = a·10² + b·10

20·a = -b

k = 100·a - 200·a = -100·a

2 = a·(2 - 10)² + k = 64·a + k

2 = 64·a + k = 64·a - 100·a = -36·a

a = 2/(-36) = -1/18

a = -1/18

a = 1/(4·p)

∴ 4·p = -18

p = 18/4 = 4.5

The focus of the parabola = (h, k + p) = (10, 10.0[tex]\overline 5[/tex])

The directrix, y = k - p = 1.0[tex]\overline 5[/tex]

k = 100× -1/18 = 5.[tex]\overline 5[/tex]

The maximum height reached by the ball = 5.[tex]\overline 5[/tex] meters

The vertex of the parabola = (10, 5.[tex]\overline 5[/tex])

Answer: the first one

Step-by-step explanation:

-7 and - 9

Step-by-step explanation:

Area of rectangule is length * width

Answer:

[tex]:\implies \boxed{\red{\sf m \in (-1,-\infty)}}[/tex]

Step-by-step explanation:

Given :-

We need to find the solution set for the given inequality . So , on solving it , we have ,

[tex]:\implies[/tex] 4m + 6 < 2

[tex]:\implies[/tex] 4m < 2 - 6

[tex]:\implies[/tex] 4m < -4

[tex]:\implies[/tex] m < -4/4

[tex]:\implies[/tex] m < -1

Hence m can have all values less than -1. Therefore the final answer is ,

[tex]:\implies \boxed{\red{\sf m \in (-1,-\infty)}}[/tex]

Hence m can have all values less than-1.

Answer:

it is eightyseven money