The lengths of the four sides of a quadrilateral (in feet) are consecutive even integers. If the perimeter is 9292 feet, find the value of the longest of the four side lengths.

The value of the given function [tex]log_6x+log_6(x-1)=1[/tex] is x = 3 or x =-2

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x. In the simplest case, the logarithm counts the number of occurrences of the same factor in repeated multiplication; e.g. since 1000 = 10 × 10 × 10 = 10^3, the "logarithm base 10" of 1000 is 3, or [tex]log_1_01000=3[/tex].

We know that

Log (a) + log (b) = log (ab)

So, [tex]log_6x+log_6(x-1)=1[/tex]

[tex]log_6(x(x-1))=1\\log_6(x^2-x)=1\\x^2-x=6^1\\x^2-x-6=0\\[/tex]

(x-3)(x+2)=0

So, x = 3 or x = -2

Therefore the value of the given Logarithmic function is x = 3 or x = -2

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Answer:

Step-by-step explanation:

57m

Tate and Nathan will leave $ 19.48 to the server to cover up the bill and the tip when they go out to dinner at Red Robin.

As given in the question,

Since Tate and Nathan both order burgers for $12.49 each,

Total amount payable is

$12.49 + $12.49= $24.98.

Now 18% tip is equal to

18% of $24.98

(18/100) × 24.98

= $4.4964

= $4.50 (rounded to nearest cent).

Total gross amount payable (including 18% tip) is

24.98 + 4.50 = $29.48.

Now subtracting the birthday coupon for $10.00 off,

the net amount payable in the bill is

29.48 - 10.00

= $ 19.48

= 19.48 cents

Therefore, after using the coupon, they will leave the server $19.48 to cover the bill and the tip.

The complete question is:

Tate and Nathan go out to dinner at Red Robin They both order burgers for $12.49 each. Tate has a birthday coupon for $10.00 off, but the boys want to leave an 18% tip before subtracting the cour

After using the coupon, how much money will they leave the server to cover the bill and the tip? Round to the nearest cent.

a. $14.49

b. $2768

c. $4.79

d.$19.48

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The angle AOB has a measure of 72 degrees

The formation of angles is as a result of the intersection of multiple lines intersect.

The given parameters are:

The above means that

AOB = BOC

So, we have

6x - 12 = 3x + 30

Evaluate the like terms

3x = 42

Divide by 3

x = 14

Substitute x = 14 in AOB= 6x -12°

So, we have

AOB= 6 x 14  -12°

Evaluate

AOB= 72°

Hence, the measure of the angle is 72 degrees

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[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{5})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies {\Large \begin{array}{llll} y-\stackrel{y_1}{5}=\stackrel{m}{ 2}(x-\stackrel{x_1}{7}) \end{array}}[/tex]

Answer:

  Multiplying both sides of the equation by 35 eliminates the fractions

Step-by-step explanation:

You want to know how to eliminate the fractions from the equation n/5+3/7=2.

The multiplication property of equality allows you to multiply both sides of an equation by the same number without changing the value of the variable. To eliminate fractions, the number we choose can be the least common denominator of the fractions.

Fractions with denominators 5 and 7 will have a least common denominator of 5·7 = 35. Multiplying the equation by 35 gives ...

  35(n/5 +3/7) = 35(2)

  7n +15 = 70

Multiplying both sides of the equation by 35 eliminates the fractions.

__

Additional comment

The solution to this 2-step equation is ...

  n = (70 -15)/7 = 55/7 = 7 6/7

The distance that is between the ball and the goal line after these five plays is D. 36 yards.

From the information, the Eagles gain 31 yards on a pass toward the goal line and on the next four plays, the Eagles lose 3, 5, 7, and 4 yards, respectively.

After the first day, the yards remaining will be:

= 48 - 31

= 17

Now, the total distance between the goal line and the ball will be:

= 17 + 3 + 5 + 7 + 4

= 36

Therefore, the total distance is 36 yards.

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functions has a graph with the largest positive x-intercept is c. f(x) = 2(x-8) +1

The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

A)

0= 2x + 10 - 1

-9 = 2x

-4.5 = x

B)

0= 8x + 64

-64 = 8x

-8 = x

C)

0 = 2x - 16 +1

0 = 2x -15

7.5 = x

D)

0 = 13x - 39

39 = 13x

3 = x

functions has a graph with the largest positive x-intercept is c. f(x) = 2(x-8) +1

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Answer:

[tex]\frac{9x^{2}}{y^{2}}[/tex]

Step-by-step explanation:

First you need to do what is inside the parenthesis

Dividing by a variable with the same base means the powers subtract so if we do this for x we get.

[tex]\frac{x^{\frac{1}{2}}}{x^{-\frac{1}{2}}}=x^{\frac{1}{2}-(-\frac{1}{2})}=x^{1}=x[/tex]

That brings us to

[tex](\frac{3xy^{-\frac{1}{2}}}{y^{-\frac{1}{2}}})^2[/tex]

Then we need to do a similar process for the y variable.

[tex]\frac{y^{-\frac{1}{2}}}{y^{\frac{1}{2}}}=y^{-\frac{1}{2}-(\frac{1}{2})}=y^{-1}=\frac{1}{y}[/tex]

Which brings us to

[tex](\frac{3x}{y})^2[/tex]

From here we just need to square the top and the bottom of the fraction which brings us back to our final answer with

[tex]\frac{9x^2}{y^2}[/tex]

Answer:

[tex]\dfrac{9x^2}{y^2}[/tex]

Step-by-step explanation:

Given expression:

[tex]\left(\dfrac{3x^{\frac{1}{2}}y^{-\frac{1}{2}}}{x^{-\frac{1}{2}}y^{\frac{1}{2}}} \right)^2[/tex]

Separate the variables inside the parentheses:

[tex]\implies \left( 3 \cdot \dfrac{x^{\frac{1}{2}}}{x^{-\frac{1}{2}}} \cdot \dfrac{y^{-\frac{1}{2}}}{y^{\frac{1}{2}}}\right)^2[/tex]

[tex]\textsf{Apply the exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies \left( 3 \cdot x^{(\frac{1}{2}-(-\frac{1}{2}))} \cdot y^{(-\frac{1}{2}-\frac{1}{2})}\right)^2[/tex]

[tex]\implies \left( 3 \cdot x^{1} \cdot y^{-1}\right)^2[/tex]

[tex]\textsf{Apply the exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 3^2 \cdot x^{(1 \cdot 2)} \cdot y^{(-1 \cdot 2)}[/tex]

[tex]\implies 9x^2y^{-2}[/tex]

[tex]\textsf{Apply the exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]

[tex]\implies \dfrac{9x^2}{y^2}[/tex]

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Answer:

the answer to the question is B thank me later

Step-by-step explanation:

The equation of the line that passes through the point (8, 5) and perpendicular to y = −12x +7 is y = (1/12)x + 13/3.

We know that,

The product of the slopes of two perpendicular lines is -1.

The slope intercept form of a line is given by :-

y = mx + c

Comparing it with y = -12x + 7

We get,

m = -12 (slope of the line)

c = 7 (y-intercept of the line)

Let the slope of the line perpendicular to the given line be n.

Hence, we can write,

(-12)*n = -1

n = 1/12

Also, the line passes through (8,5).

Hence, we can write,

5 = (1/12)(8) + c

5 = 2/3 + c

c = 5 - 2/3 = 13/3

Hence, the equation of the line is given by :-

y = (1/12)x + 13/3

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The value of the given expression g = h+9/5 is 127.

So, g = h+9/5:

Insert the values in the expression as follows:

Therefore, the value of the given expression g = h+9/5 is 127.

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The correct question is given below:

Evaluate the expression when g = 30 and h = 14.

g = h+9/5

The result of the factorization of   8y^3-6y is 2y(4y^2-3) .

Factorization  can be described as the mathematical term, that is been used in expressing a particular number  as well as mathematical object to be writing inform of a  product of several factors.

From the question we were given the expression 8y^3-6y  to be factorized,

Then, this can be done as  2y(4y^2-3)

Therefore, the factorization of the given expression is 2y(4y^2-3) .

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1. Noah reads 9 pages.

2. The price of one pizza is $9.

3. Lin shares her stickers is 9.

1.Given,

Elena read three times as many pages as Noah.

and, She read 27 pages.

Now, According to the question:

3x = 27

x = 27/3

x = 9

Hence, Noah reads 9 pages.

2. Given,

Diego paid $27 to have 3 pizzas delivered

and, $35 to have 4 pizzas delivered

In the question, In place of $ 35 should be $36

So, we take the $36

Now, Diego paid $27 to have 3 pizzas delivered

$36 to have 4 pizzas delivered

Let x be the price of 1 pizza

then, 4x = 36

x = 36/4

x = $9

Hence, The price of one pizza is $9.

3. Given,

Lin has 27 stickers.

and, She gives 3 stickers to each of her friends.

Now, 27 is divided by 3  = 9

Hence, Lin shares her stickers is 9.

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Answer:

y = 3x + 1

Step-by-step explanation:

(2, 7); 3x - y = 5

(x₁, y₁)

3x - y = 5

-3x           -3x

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

-y = -3x + 5

÷-1    ÷-1   ÷-1

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

y = 3x - 5

y - y₁ = m(x - x₁)

y - 7 = 3(x - 2)

y - 7 = 3x - 6

  +7          +7

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

y = 3x + 1

I hope this helps!

Answer: y=3x+1

Step-by-step explanation:

[tex]3x-y=5\\3x-y+y=5+y\\3x=5+y\\3x-5=y+5-5\\3x-5=y\\So, \ y=3x-5\\[/tex]

A line parallel to line y=3x-5 will look like this: y=3x+b

The line passes throught the point (2,7), hence:

[tex]7=3(2)+b\\7=6+b\\7-6=6+b-6\\1=b\\Thus,\ b=1\\y=3x+1[/tex]

Answer:

MK= 12.5

AngleJNK=117°

AngleJNM=63°

Step-by-step explanation:

Part A:

MN = 3x + 1

JL = 2x + 9

JL and MK are the diagonals

MN = 1/2 of MK

MK =2(3x +1)

MK = 6x + 2

Therefore, JL = MK

2x + 9 = 6x +2

Collect like terms

2x-6x = 2 - 9

-4x = - 7

x = 1.75

Substituting the value of x,

MK = 6(1.75) + 2

MK = 10.5 + 2

MK = 12.5

Part B

AngleJNK = (5x +2)°

AngleJNM = (3x-6)°

Sum of interior angles of a quadrilateral = 360

Therefore, 2(5x +2)° + 2(3x-6)° = 360

(10x + 4) + (6x - 12) = 360

Collect like terms

10x + 6x - 12 + 4=360

16x = 360 + 8

16x = 368

x = 368/16

x = 23

Substituting the value of x

For angleJNK = 5(23) +2 = 115+2 = 117°

For angleJNM = 3(23) - 6 = 69 - 6 = 63°

The given equation x² + 6x - 5 can be written in the form of (x + a)² + b as

 (x + 3)² - 14.

In math, we can state that the process of "completing the square" is taking a quadratic equation of the form ax² + bx + c = 0 and changing it to write it in the form a(x + p)² + q = 0. Find the roots of a quadratic equation often using this method.

Given quadratic equation is x² + 6x - 5.

To convert it in the form (x + a)² + b, where a and b are numbers.

x² + 6x - 5

x² + 2 × 3x + 3² - 3² - 5 (convert the equation into a perfect square)

(x + 3)² - 9 - 5

(x + 3)² - 14

Hence, the required equation is (x + 3)² - 14.

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Solution:

If

The general form of the coordinates of an ordered pair is

From the given expression;

The x-coordinate is -7

The y-coordiates is -2

Hence, the corresponding ordered pair is

(a) -5

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

(c) [tex]a_{11}=2(-5)^{11-1}=19531250[/tex]

Answer:

1/12

Step-by-step explanation:

yellow=1/4

red=5/12

green=1/3

1/4 x 1/3= 1/12

Answer:

  Part A: no. The bikes/skateboards labels are reversed

  Part B: 8/25 = 0.32; Fraction of students with both bikes, skateboards

Step-by-step explanation:

Given a segmented bar chart, you want to know if it was drawn correctly, and you want to know the value and meaning of the greatest joint relative frequency.

You want to know if the given segmented bar chart is an appropriate representation of the data in the 2-way table.

The bar chart is created incorrectly.

There are at least a couple of problems with the chart.

The largest number in the table is 80. The fraction that is of the whole is ...

  80/(70+30+80+70)

  = 80/250 = 8/25 = 0.32

The greatest relative frequency is 0.32. It represents the fraction of students who have both bikes and skateboards.

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The solution of the given system of equation is 136

Fractions are expressed as ratio of two integers. Given the expression below;

20/3.4 = 800/y

Cross multiply to have:

3.4. * 800 = 20 *y

3.4 * 800 =20y

2720 = 20y

Swap

20y = 2720

Divide both sides by 20

20y/20 = 2720/20

y = 136

Hence the solution to the given equation on cross multiplying is 136

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Answer:

? = 4.492385

About 4.5 pounds

Step-by-step explanation:

m = money spent

80 - 44.6 = m

m = 35.4

m / 7.88 = ?

? = 35.4 / 7.88

? = 4.492385

About 4.5 pounds

Answer:

She bought 5 pounds of coffee

Step-by-step explanation:

If you subtract 80-40.60 you would get 39.4/39.40 and since each pound was 7.88 you divided 39.40 and 7.88 and you would get 5

Answer:

The answer would be 92.8 but since we're rounding it'll be 90

Step-by-step explanation:

The coordinates of the midpoint between point E(2, -8) and point F(-12, -6) on segment EF is ( -5, -7 ).

A midpoint is simply a point that divides a line segment into two equal halves.

The midpoint formula is expressed as;

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

Given the data in the question;

Point E(2, -8)

F(-12, -6)

Coordinates of midpoint = ?

To determine the midpoint, plug the given points into the midpoint formula above and simplify.

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

M = ( ( 2 + (-12) )/2, ( (-8) + (-6) )/2 )

M = ( 2 - 12 )/2, ( -8 - 6 )/2 )

M = ( -10 )/2, ( -14 )/2 )

M = ( -5 ), ( -7 )

M = ( -5, -7 )

Therefore, the midpoint of line segment EF is ( -5, -7 ).

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On subtracting "3a – 7b + 12c" from "-5a – 21b + 3c" we get -

- 8a - 14b - 9c

Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Subtraction is signified by the minus sign −.

Given is to subtract "3a – 7b + 12c" from "-5a – 21b + 3c".

Assume that -

A = 3a – 7b + 12c

B = -5a – 21b + 3c

B - A = (-5a – 21b + 3c) - (3a – 7b + 12c)

B - A = -5a - 21b + 3c - 3a + 7b - 12c

B - A = -5a - 3a - 21b + 7b + 3c - 12c

B - A = - 8a - 14b - 9c

Therefore, on subtracting "3a – 7b + 12c" from "-5a – 21b + 3c" we get -

- 8a - 14b - 9c

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Name : Trinomial.

Degree : 4

EXPLANATION

Monomial : A polynomial with just one term.

Binomial : A polynomial with two terms.

Trinomial : A polynomial with three terms.

From the question given;

(12x⁴ + 3x - 1) comprises of 3 terms, hence it is a trinomial.

The degree of a polynomial is the highest exponent in a term of a polynomial.

Hence, the highest exponent in the given expression is 4, this implies that the polynomial is of degree 4.

[tex]f(x) = 3 {x}^{2} - x + 5[/tex]

thus ;

[tex]f( - 3) = 3 \times ({ - 3})^{2} - ( - 3) + 5[/tex]

[tex]f( - 3) = 3 \times 9 + 3 + 5[/tex]

[tex]f( - 3) = 27 + 8[/tex]

[tex]f( - 3) = 35[/tex]

_____________________________________________

[tex]f(4) = 3 \times ({4})^{2} - (4) + 5[/tex]

[tex]f(4) = 3 \times 16 - 4 + 5[/tex]

[tex]f(4) = 48 + 1[/tex]

[tex]f(4) = 49[/tex]

_____________________________________________

So :

[tex]2f( - 3) = 2 \times 35 = 70[/tex]

And ,

[tex] - f(4) = - 49[/tex]

so :

[tex]2f( - 3) - f(4) = [/tex]

[tex]70 - 49 = [/tex]

[tex]21[/tex]