Log x + log 6= log(2x+1)

The equation of the line, with slope equal to 0 and passing through the point located at (4 , -2), is y = -2.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Using the point slope form, plug in the values to set up the equation.

(y - y1) = m(x - x1)

where m = 0 and (x1 , y1) = (4 , -2)

(y - -2) = 0(x - 4)

(y + 2) = 0

y = -2

In slope-intercept form, the equation of the line is:

(y + 2) = 0

y = -2

In standard form, the equation of the line is:

y = -2

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Answer:

6

Step-by-step explanation:

Let's call the bands by numbers :

So we have Band 1,2 and 3

The orders can be :

1,2,3

2,3,1

3,1,2

1,3,2

3,2,1

2,1,3

so there must be 6 different orders

Another method of doing this is to called product rule of counting :

3 × 2 × 1 = 6

Hope this helped and have a good day

Answer:

3.24x10^-5,    5.48x10^-2,    1.2x10^1,      4.68x10^6,         8.34x10^6

Step-by-step explanation:

3.24 x 10^-5 = 0.0000324

5.48 x 10^-2 = 0.0548

1.2 x 10^1 = 12

4.68 x 10^6 = 4680000

8.34 x 10^6 = 8340000

Using the distance formula, the distance between the pair of points A(0,0) and B(15,20) is 25 units

Given,

The points = A(0,0) and B(15,20)

We know the distance formula = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]

Substitute the values in the equation

The distance = [tex]\sqrt{(15-0)^{2}-(20-0)^{2} }[/tex]

[tex]=\sqrt{15^{2}+20^{2} } \\=\sqrt{225+400}\\ =\sqrt{625}[/tex]

=25 units

Hence, using the distance formula, the distance between the pair of points A(0,0) and B(15,20) is 25 units.

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The cost of 8 oranges is $7.52

The first step is to find the cost of one orange

6 oranges cost 5.65

1 orange= 5.64/6

= 0.94

Therefore the cost of 8 oranges can be calculated as follows

= 0.94×8

= 7.52

Hence 8 oranges cost $7.52

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Answer: A

Step-by-step explanation: took the quiz got it right

Option c is the correct answer. Sam's total earning for the day is equal to

E(n) = 2.5n + 24

Given data

Sam earning per hour = $6

Sam earning on tips per person = $2.5

Sam's total hour per day =4

Sam's daily earning excluding tips = Sam earning per hour * Sam's total hour per day

= $6 * 4 hours = $24

If n represents the number of people Sam serves that day, then Sam's earnings on tips in a day = $2.5 * n = $2.5n

The function for Sam's total earning is given by  E(n)

E(n) = Sam's daily earning excluding tips +  Sam's earnings on tips in a day

E(n) = $24 + $2.5n

this is re arranged as

E(n) = 2.5n + 24

Therefore we can say that Sam's total earning for the day is equal to

E(n) = 2.5n + 24

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Complete question

Sam is a waiter at a local restaurant where he earns wages of $6 per hour. Sam figures that he also earns about $2.50 in tips for each person he serves. Sam works 4 hours on a particular day. If n represents the number of people Sam serves that day, which of the following functions could Sam use to figure E, his total earnings for the day?

A. E(n) = 2.5n

B. E(n) = 4n + 10

C. E(n) = 2.5n + 24

The midpoint is at ([tex]-\sqrt{3} , 3 ,3\sqrt{2}[/tex])

In the given statement is

To find the midpoint of the line segment joining the pair of points

B(√3, 2,2√2) and C(-2√3, 4,4√2)

Midpoint:

The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.

m = (A +B)/2

If we are given three points and we wish to find the midpoint of those points, we need to use the midpoint formula m =([tex]\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2} , \frac{z_{1}+z_{2} }{2} ,[/tex] )

where:

(x1 , y1 ,z1) are the coordinates of the first point:

(x2 , y2 , z2) are the coordinates of the second point:

Now, We are given the three points B(√3, 2,2√2) and C(-2√3, 4,4√2)

Solving for the midpoint , we have,

m = ([tex]\frac{\sqrt{3}+(-2\sqrt{3} ) }{2}, \ \frac{2+4}{2}, \frac{2\sqrt{2} +4\sqrt{2} }{2}[/tex])

m = [tex]\frac{-2\sqrt{3} }{2} ,\frac{6}{2},\frac{6\sqrt{2} }{2}[/tex]

m = ([tex]-\sqrt{3} , 3 ,3\sqrt{2}[/tex])

Therefore, the midpoint is at( [tex]-\sqrt{3} , 3 ,3\sqrt{2}[/tex])

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The two consecutive odd integers are less than 76 is the numbers are 37 and 39.

Any integer's reverse and sum are both equal to zero.

A positive sum results from adding two positive numbers, whereas a negative sum results from adding two negative integers.

Take the absolute value of each integer, then subtraction, to obtain the total of a positive and a negative integer.

Let two consecutive odd numbers be x and x+2

According to question

⇒ x........... equation (1)

⇒ x+2........equation (2)

by adding equation 1 and 2

⇒ x+x+2=76

⇒ 2x+2=76

⇒ 2x=76-2

⇒ 2x=74    

⇒  x=74/2

⇒ x=37

We apply the value of x=37 in equation (2)

⇒ x+2

⇒ 37+2

⇒ 39

so, the numbers are 37 and 39.

Therefore, the two consecutive odd integers are less than 76 is the numbers are 37 and 39

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The transformation rule for the triangle P by translating the vector (2, -7) is ( x , y ) <=> ( x + 2 , y - 7 )

Transformation rule says that, if a translation occurs then each point of the shape will be shifted in the same direction with the same distance.

According to the rule , the translation for the triangle P using the vector (2,-7) is ( x + 2 , y - 7 ).

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The measures of the sides of ΔXYZ are XY = 9.1, YZ = 11.4, XZ =  8. and the triangle XYZ must be an acute triangle

In this questions we have been given the the coordinates of the triangle XYZ.

X(-4, -2), Y(-3, 7), Z(4, -2)

We need to find  the measures of the sides of ΔXYZ .

We find the the measures of the sides using distance formula.

XY = √[(7 + 2)² + (-3 + 4)²]

XY = √[9² + 1²]

XY = √(81 + 1)

XY = √(82)

XY = 9.1

Now side YZ

YZ = √[(-2 - 7)² + (4 + 3)²]

YZ = √[(-9)² + (7)²]

YZ = √81 + 49

YZ = √130

YZ = 11.4

And the length of side XZ would be,

XZ = √[(-2 + 2)² + (4 + 4)²]

XZ = √0 + 8²

XZ = 8

We find the sum of the squares of the two smaller sides, and compare the sum to the square of the largest side.

the sum of the squares of the two smaller sides is,

= 8² + 9.1²

= 64 + 82.81

= 146.81

= 12.12²

And 11.4² = 129.96

Since the sum of the squares of the two smaller sides is greater than the square of the largest side, the triangle must be an acute triangle.

Therefore, the measures of the sides of ΔXYZ are XY = 9.1, YZ = 11.4, XZ =  8. and the triangle XYZ must be an acute triangle

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Kittens without black markings to kittens with black markings: 2:5

Kittens without black markings to total kittens: 2:7

Kittens with black markings to total kittens: 5:7

Using system of three equations, the equation of the circle that contains the points (0 , 0), (6 , 8), and (7 , 7) is (x - 3)^2 + (y - 4)^2 = 25.

The standard form of the equation of  circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Substituting the values of the x and y coordinates of each point to the standard form of the equation of a circle, the three system of equations are:

(x - h)^2 + (y - k)^2 = r^2

(0 , 0) : (0 - h)^2 + (0 - k)^2 = r^2

(6 , 8) : (6 - h)^2 + (8 - k)^2 = r^2

(7 , 7) : (7 - h)^2 + (7 - k)^2 = r^2

Expanding these equations,

(0 , 0) : h^2 + k^2 = r^2     (equation 1)

(6 , 8) : 36 - 12h + h^2 + 64 - 16k + k^2 = r^2     (equation 2)

(7 , 7) : 49 - 14h + h^2 + 49 - 14k + k^2 = r^2     (equation 3)

Subtracting equation 1 from equation 2 and 3.

36 - 12h + h^2 + 64 - 16k + k^2 = r^2

-                (h^2 +                 k^2 = r^2)

36 - 12h           + 64 - 16k           = 0

100 - 12h - 16k = 0

12h + 16k = 100

Dividing both sides by 4,

3h + 4k = 25     (equation 4)

49 - 14h + h^2 + 49 - 14k + k^2 = r^2

-                (h^2 +                 k^2 = r^2)

49 - 14h            + 49 - 14k          = 0

98 - 14h - 14k = 0

14h - 14k = 98

h + k = 4     (equation 5)

h = 7 - k

Substitute h = 7 - k to equation 4 and solve for k.

3h + 4k = 25     (equation 4)

3(7 - k) + 4k = 25

21 - 3k + 4k = 25

k = 25 - 21

k = 4

Substitute the value of k to equation 5 and solve for h.

h = 7 - k     (equation 5)

h = 7 - 4

h = 3

Substitute the value of h and k to equation 1 and solve for r.

h^2 + k^2 = r^2     (equation 1)

3^2 + 4^2 = r^2

9 + 16 = r^2

r^2 = 25

r = 5

Hence, the equation of the circle that contains the points (0 , 0), (6 , 8), and (7 , 7) is (x - 3)^2 + (y - 4)^2 = 25.

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Answer:

[tex]4x^2+2x+1[/tex]

Step-by-step explanation:

[tex]f(x)=4x^2+5\\g(x)=2x-4\\\\f(x)+g(x)=(4x^2+5)+(2x-4)\\\\4x^2+5+2x-4\\\\4x^2+2x+1[/tex]

According to the question, determine whether the given sequence converges or diverges.

The given sequence is: [tex]a(n) = \frac{9+3n^{2} }{n+8n^{2} }[/tex]

Taking limits tends to infinity on both sides. And dividing numerator and denominator by [tex]n^{2}[/tex]

Therefore, the final term can be re-written as: [tex]a(n) = \frac{9+3n^{2} }{n+8n^{2} } = \frac{3}{8}[/tex].

Hence, the given sequence converges and the limit is [tex]\frac{3}{8}[/tex].

What converges and diverges in limits?

When the limits of the sequence exist and have finite value that means the sequence is a convergent sequence. The calculated value is a real number. And the tem divergence means limits do not exist.

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The solution of the above equation y/5 + y/2 = 7 for y is 10.

According to the given question.

We have an equation y/5 + y/2 = 7.

Since, we have to solve the above equation y/5 + y/2 = 7 for y.

Therefore, the solution of the above equation for the above equation y/5 + y/2 = 7 is given by

y/5 + y/2 = 7

⇒ (2y + 5y)/10  = 7

⇒ 7y /10 = 7

⇒ 7y = 70

⇒ y = 70/7

⇒ y = 10

Hence, the solution of the above equation y/5 + y/2 = 7 for y is 10.

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The value of the function  (f + g)(−8) (f + g)(−8) for f (x) = x + 3 and g (x) = x² - 2 is 3249.

We are given the functions:

f(x) = x + 3

g(x) = x² − 2

Now,

(f + g) (−8) × (f + g)(−8)

= [ (f + g) (−8) ]²

Substituting the values of the functions, we get that:

=(x + 3 + x² - 2)² ,   where x = -8

= ( -8 + 3 + 64 - 2 )²

= ( -5 + 62)²

= (57) ²

= 3249

So, the value of the function  (f + g)(−8) (f + g)(−8) for f (x) = x + 3 and g (x) = x² - 2 is 3249.

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Using a system of equations, it is found that there were a total of 825,000 Arabic speakers, and the diagram is completed as follows:

A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.

For this problem, the variables are given as follows, considering the situation described:

There were 639,000 French Creole speakers, hence:

f = 639,000.

There were 186,000 more Arabic speakers than French Creole speakers, hence:

a = 186,000 + f = 186,000 + 639,000 = 825,000.

There were a total of 825,000 Arabic speakers, and the diagram is completed as follows:

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The solution using the square root property for given complex numbers would be x = 10i where i is an imaginary number.

A complex number is a combination of real values and imaginary values. It is denoted by z = a + ib,

where a, and b are real numbers and i is an imaginary number.

We have been given the equation of complex numbers x² = -100

Using the square roots property to solve the above equation

⇒ x² = -100

⇒ x = √-100

⇒ x = √(-1×10×10)

∵ i² = - 1 or i = √-1

Here i is an imaginary number.

⇒ x = 10(√-1)

⇒ x = 10i

Therefore, the solution of given complex numbers would be x = 10i where i is an imaginary number.

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Answer:

1.76.

Step-by-step explanation:

1.32 ÷ 12 = 0.11

16 x 0.11 = 1.76.

Hope this helped! ..・ヾ(。＞＜)シ xx

Answer:

It's B

Step-by-step explanation:

Step-by-step explanation:

[tex]\displaystyle\\12-15x > 22\\12-15x+15x > 22+15x\\12 > 22+15x\\12-22 > 22+15x-22\\-10 > 15x\\Divide\ both\ parts\ of \ the \ equation\ by\ 15:\\-\frac{10}{15} > x\\\\-\frac{5*2}{5*3} > x\\\\-\frac{2}{3} > x \\\\Thus,\\\\x < \frac{-2}{3}[/tex]

Answer: A

[tex]\displaystyle\\4\leq 3x+10 < 19\\\\4-10\leq 3x+10-10 < 19-10\\\\-6\leq 3x < 9\\\\Divide\ the\ inequality\ by \ 3:\\\\-2\leq x < 3\\\\Answer:\ -2\leq x < 3[/tex]

Answer:Your answer would be x=1/10

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

i ink

The number of packs of markers Mr. Sowers can purchase is 6.4 packs.

According to the task content, it is required that an inequality should be written and solved for the number of packs of markers Mr. Sowers can purchase.

5.49x ≤ 35

x ≤ 35 / 5.49

x ≤ 6.375227686703096

Approximately

x ≤ 6.4

Therefore, the number of packs of markers Mr. Sowers can purchase is 6.4 packs

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If Max is building a set of shelves and he buys a board that is 4 yards long and he wants to cut as many pieces of board that are 3/4 yards long as he can, then the no of pieces he can cut is 5 and he will have 0.25 yards of board left over.

3/4 is a fraction which can be represented as,

3/4 = 0.75

The number of pieces of board that Max can cut that is 4 yards long can be determined by the division of the length of the board by the length of the cut pieces. Therefore,

number of pieces cut = length of the board ÷ length of a cut piece

number of pieces cut = 4 ÷ 0.75

number of pieces cut = 5.33, that is round off to 5

Thus he can cut 5 pieces of 3/4 yards.

As 5 × 3/4 = 3.75 yards

The remaining yards of the board can be calculated by subtraction.

Board leftover = 4 - 3.75 = 0.25 yards

Hence, Max can cut 5 pieces of 3/4 yards and will have 0.25 yards of the board left over.

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Answer:

Step-by-step explanation:

B) is correct

Answer:-5/4

Step-by-step explanation:

Domain - { 3, 11, 121, 34 , 23 , } is domain of  each relation is a function.

What is domain and range ?

How are the domain and range determined?

  Domain - { 3, 11, 121, 34 , 23 , }

 Range  -  { 9, 21 , 34 , 1 , 45 }

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