4x² + 6x = 12
Solve by completing square​

Answer:

  yes

Step-by-step explanation:

The commutative property of addition applies to let you swap the order of the summands.

__

Here is how the commutative property can be applied.

  5x = 3 -x . . . . . given

  5x = (3) +(-x) . . . . shown as a sum

  5x = (-x) +(3) . . . . order swapped using commutative property of addition

  5x = -x +3 . . . . . . equivalent equation

Answer:

8 units

Step-by-step explanation:

ratios  

(x-3) /( x+1)  = (x-2)/(x+3)     cross multiply

x^2 -x -2 = x^2 - 9

  -x - 2 + 9 = 0

    x = 7          

           so TS = x + 1 = 8 units

Answer:

2ab(a2b−2)

Step-by-step explanation:

Here's your answer down here↓:

Step-by-step explanation:

x^3 - y^3 = (x - y)(x^2 + xy + y^2)

(x^4 - y^4) = (x^2 - y^2)(x^2 + y^2) = (x - y)(x + y)(x^2 + y^2)

Ok. So the factor (x-y) appears once in the top line and once in the second line. So we are going to take it the least amount of times.

So, the factor (x + y) appears in the top line zero times and in the second line one time so we will take it where it appears the least which is zero times so we are still at (x - y)

And it Same goes for the factors of (x^2 + y^2) and (x^2 + xy + y^2)

Answer:

A five units right and three units up

Step-by-step explanation:

take coordinate C for example and count how many spaces you need to go either right or left and then up and down for the two triangles to be in the same place

The theoretical probability of at least one 4 on the spinners is 0.4375

The sections on the spinners are:

Spinner 1 = 4

Spinner 2 = 4

So, the number of different outcomes is:

Outcomes = 4 * 4

Outcomes = 16

Hence, the number of different outcomes is 16

The spin results that have at least one 4 are:

Results = {(4,1), (4,2), (4,3), (4,4), (1,4), (2,4), (3,4)}

The count of these results is 7.

So, the theoretical probability of at least one 4 on the spinners is:

P = 7/16

P = 0.4375

Hence, the theoretical probability of at least one 4 on the spinners is 0.4375

The theoretical probability and the experimental probability are different because:

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Answer:

20 can be the answer of it

ANSWER :

The pH level of a swimming pool indicates the level of acidity or alkalinity

of the swimming pool.

Correct Responses;

First Part:  Please find attached the required graph of the pH function created with MS Excel.

The pH value is 0 when x = 1

The pH value is 1 when x = 0.1

The pH level if the hydronium ions is raised to 0.50 is approximately 0.301029996.

Second Part: The transformation that results in a y-intercept is f(x + 1), because f(0 + 1) exists and is equal to 0.

STEPS

Method by which the above responses are obtained

First part

The given pH function is f(x) = -㏒₁₀x

Where;

x = The amount of hydronium ions

A substance with a pH < 7 is acidic

A substance with a pH > 7 is alkaline

A neutral solution has pH = 7

Water is a neutral solution

The graph of the pH function created with MS Excel is attached

The table of values of the graph is as follows;

From the graph, we have;

When the pH value is 0, the hydronium ion concentration is 1

The pH value is 1 when x = 1 × 10⁻¹ = 0.1

The pH level if the hydronium ions, x = 0.5 is given from the graph as follows;

pH = f(0.5) = -㏒₁₀(0.5) ≈ 0.301029996

The pH value when the hydronium ions is 0.5 is pH ≈ 0.301029996

Second Part

Using f(x) = -㏒₁₀x as the parent function, the graph of f(x) + 1, and f(x + 1) are plotted

From the graph, we have;

The graph of f(x) + 1 = -㏒₁₀x + 1

The graph of f(x + 1) = The graph of -㏒₁₀(x + 1)

At the y-intercept, x = 0, therefore;

f(x) + 1 = f(0) + 1 = -㏒₁₀0 + 1 = Undefined

f(x + 1) = f(0 + 1) = -㏒₁₀(0 + 1) = 0

Therefore;

The transformation that results in a y-intercept is f(x + 1) because f(0 + 1) is 0, which is defined.

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Answer:

13x = 39

x=3

y=10

Answer:

this is step by step explenation

see more...

Answer:

Given sequence in the table is a Geometric sequence and The sum for term 5 through term 11 in sigma notation is given by:

[tex]$\sum_{n=5} ^{\111} 2(-5)^n^-^1$[/tex]

Step-by-step explanation:

Geometric sequence - it is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio

here the given terms :

a1 = 2, a2 = -10, a3 = 50

you can see it is a geometric sequence as the ratio is constant  [tex]\frac{a2}{a1}{=}\frac{a3}{a2}{=}{-5}[/tex]

now the nth term for geometric sequence :

[tex]a_{n} {=}{a}{r}^{n-1}[/tex]

here,

now substituting the given values in the expression,

[tex]a_{n} {=}{2}{{(}-5}{)}^{n-1}[/tex]

we have to find the sum from term 5 to term 11,

therefore using sigma notation and putting n= 5 and n=11 at the below and above the sigma respectively,

[tex]$\sum_{n=5} ^{\111} 2(-5)^n^-^1$[/tex]    

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The complete question is

"Given that the expression “p dollars for every q items” describes a unit price, which statement must be true?

p = 1

p = q

q = 1

pq = 1"

The statement that must be true would be from option D; pq = 1.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given that the expression “p dollars for every q item” describes a unit price,

So, the equation will be formed as

p x q = 1

pq = 1

Hence, the statement that must be true would be from option D; pq = 1.

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Answer:

0.7855 square feet

Step-by-step explanation:

90/360×3.142×1 squared

=0.7855

The amount paid by sam will be 11526.75k for the meal.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that:-

Sam pays 512 .75k less than the amount rob pays for his meal .ridwan pays three times the amount rob pays for his meal. if the total amount paid by them is 47,645.25k.

We will form an expression from the data given above in the question.

Amount paid by Sam  = ( r - 512.75 )

Amount paid by rob = r

( r - 512.75 ) + 3r = 47645.25

( r + 3r ) = 47645.25 + 512.75

4r = 48158

r = 12039.5

The amount paid by sam will be calculated as:-

S = r - 512.75

S = 12039.5 - 512.75

S = 11526.75

Therefore the amount paid by sam will be 11526.75k for the meal.

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Answer:

the first one listed (y = -[tex]2^{x}[/tex] + 4)

Step-by-step explanation:

a 0 at an x-intercept means that when plugging in that number, you get a 0 as a y-value.

So, the easiest method to use is to plug x=2 into each equation listed, because we can see that (2,0) is a point on this graph

if y= -[tex]2^x\\[/tex] + 4

y = -2² + 4

y = -4 + 4

y = 0

This means that this graph has corresponding real zero(s) to the function    y= [tex]-2^x[/tex] + 4

(I chose which graph to test by looking to see which option seemed right)

Answer: I know two methods of solving both of the sums. One is the method of elimination, the other is method of substitution. You can do any of the given methods which is easier for you. Both methods will be shown below:

1) 5x + y = 9       - - - - (i)
  10x - 7y = - 18 - - - - (ii)

eq. (i) multiplied by 2
   10x + 2y = 18  - - - - (i)
   10x - 7y = - 18 - - - - (ii)       {subtraction of eq. (ii) from eq. (i)}
    0   + 9y = 36
              y = 36/9
              y = 4

From eq. (i),
   5x + y = 9
-> 5x + 4 = 9
-> 5x = 9 - 4
->  x = 5/5
-> x = 1

So, x = 1 and y = 4

2) - 4x + 9y = 9 - - - - (i)
      x - 3y = - 6 - - - - (ii)

eq. (ii) multiplied by 3
    - 4x + 9y = 9 - - - - (i)
     3x - 9y  = - 18 - - (ii)        {addition of eq. (ii) and eq. (i)}
      - x + 0 = - 9
              x  =  9

From eq. (ii),
    x - 3y = - 6
->  9 - 3y = - 6
->  - 3y = -6-9
->  y = -15/-3
->  y = 5

So, x = 9 and y = 5

1) 5x + y = 9       - - - - (i)
  10x - 7y = - 18 - - - - (ii)

eq. (i)

  5x + y = 9
-> y = 9 - 5x

Value of eq. (i) in eq. (ii)
   10x - 7y = - 18
-> 10x - 7(9 - 5x) = - 18
-> 10x - 63 + 35x = - 18
-> 45x = - 18 + 63
-> x = 45/45
-> x =  1

From eq. (i),
   5x + y = 9
-> 5 + y = 9
-> y = 9 - 5
-> y = 4

So, x = 1 and y = 4

2) - 4x + 9y = 9 - - - - (i)
      x - 3y = - 6 - - - - (ii)

eq. (i)
   - 4x + 9y = 9
-> - 4x = 9 - 9y
-> x = (9 - 9y) / -4

Value of eq. (i) in eq. (ii)
      x - 3y = - 6
-> (9 - 9y) / -4  -3y = - 6
-> (9 - 9y + 12y) = - 6 * - 4
-> 3y = 24 - 9
-> y = 15/3
-> y =  5

From eq. (ii)
   x - 3y = - 6
-> x - 3(5) = - 6
-> x - 15 = - 6
-> x = - 6 + 15
-> x = 9

So, x = 9 and y = 5

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┗━━━━━━━┛

Answer:Shake hands when you meet someone.Make direct eye contact with the person you are speaking with.Unless the movie theater is crowded, do not sit right next to someone.Do not stand close enough to a stranger to touch arms or hips.Cover your coughs.

Step-by-step explanation:trust me

$2.50

Step-by-step explanation:

10 dimes are 100 aka 1 dollar, and 30 nickels make 250

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: x² + y² = 64[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Standard equation of circle is :

[tex]\qquad \tt \rightarrow \: (x - h) {}^{2} + (y - k) {}^{2} = {r}^{2} [/tex]

Since the circle is centered at origin, h = k = 0

[tex]\qquad \tt \rightarrow \: (x - 0) {}^{2} + (y - 0) {}^{2} = {8}^{2} [/tex]

[tex]\qquad \tt \rightarrow \: {x}^{2} + {y}^{2} = 64 [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The area of a regular octagon with an apothem of 2 cm is 3cm ^2.

The area of a regular octagon with an apothem of 2 cm.

Given the apothem length,

the area of a regular polygon becomes,

[tex]A=\frac{1}{2}\times P\times A[/tex]

P=  the perimeter of the regular polygon

A is the apothem of the regular polygon

Here, we get

p=2=2cm, a=3cm.

So, plugging in the given values, we get

[tex]A=\frac{1}{2} \times 2cm\times 3cm[/tex]

A=1cm⋅3cm

A=3cm^2

Therefore the area of a regular octagon with an apothem of 2 cm is 3cm ^2.

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[tex]14-a=19-12\\14-a=7\\a=14-7\\a=7[/tex]

Answer:

7

Step-by-step explanation:

14-a=19-12

14-a=7

14-7=a

7=a

Combine like terms

The measure of the other side of a quadrilateral is [tex]3\sqrt{13}[/tex] cm.

In the given quadrilateral one side is unknown we need to find the unknown side.

By dividing the given quadrilateral into a rectangle and a triangle we can find the other side.

The Pythagoras theorem states that if a triangle is right-angled, then the square of the hypotenuse is equal to the sum of the squares of the other two sides. That is, [tex]c^{2}=a^{2}+b^{2}[/tex].

Now, [tex]x^{2} =9^{2}+6^{2}=81+36=17[/tex]

⇒[tex]x=\sqrt{13 \times 9} =3\sqrt{13}[/tex]

Therefore, the measure of the other side of a quadrilateral is [tex]3\sqrt{13}[/tex] cm.

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The LinReg line of best fit for this data set is ŷ = -1.24X + 0.66

A linear regression line has an equation of the form Y = a + bX, where X is the explanatory variable and Y is the dependent variable.

Given:

(−5, 6.3),

(−4, 5.6),

(−3, 4.8),

(−2, 3.1),

(−1, 2.5),

(0, 1.0),

(1, −1.4)

Sum of X = -14

Sum of Y = 21.9

Mean X = -2

Mean Y = 3.1286

Sum of squares (SSX) = 28

Sum of products (SP) = -34.6

Regression Equation,

ŷ = bX + a

b = SP/SSX = -34.6/28 = -1.23571

a = MY - bMX = 3.13 - (-1.24*-2) = 0.65714

ŷ = -1.23571X + 0.65714

ŷ = -1.24X + 0.66

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:Domain : \fbox{-3}\leqslant x \leqslant \fbox{-1}[/tex]

[tex]\qquad \tt \rightarrow \:Range :\:\:\fbox{-4}\leqslant x \leqslant \fbox{-3}[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Domain = All possible values of x for which f(x) is defined

[ generally the extension of function in x - direction ]

Range = All possible values of f(x)

[ generally the extension of function in y - direction ]

[tex] \large\textsf{For the given graph : } [/tex]

[tex]\qquad \tt \rightarrow \: domain : \fbox{-3}\leqslant x \leqslant \fbox{-1}[/tex]

[tex]\qquad \tt \rightarrow \: range : \:\:\fbox{-4}\leqslant x \leqslant \fbox{-3}[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

Yes

Step-by-step explanation:

Yes, 8.6 is a rational number because it can be expressed in the form of p/q

[tex]8.6 = \frac{86}{10} = \frac{43}{5} [/tex]

53) Vertical angles are congruent, so [tex]m\angle IDA=121^{\circ}[/tex]

54) [tex]\angle YDA[/tex] and [tex]\angle YDF[/tex] are supplementary, so [tex]m\angle YDA=180^{\circ}-121^{\circ}=59^{\circ}[/tex]

55) Because vertical angles are congruent, [tex]m\angle FDI=59^{\circ}[/tex]. Now, because DR bisects [tex]\angle FDI[/tex], this means [tex]m\angle RDI=\frac{59}{2}=29.5^{\circ}[/tex]

56) This is a geometric sequence where the next term is obtained by multiplying the previous term by -2, so the next two numbers are 16, -32

For a system of equations to have no real solution, the lines of the equations must be parallel to each other. The correct option is A.

Inconsistent System

For a system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

For a system of the equation to be a Dependent Consistent System, the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

For a system of the equation to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.

If the two of the given system of equations are plotted on the graph, then it can be observed that the two lines have different slopes. Therefore, the correct option is A.

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Answer:

The smallest number all three numbers can be divided by is 4.

Step-by-step explanation:

12/4=3

16/4=4

24/4=6

Hope this helps!

If not, I am sorry.