11 Amelia has a rectangular table that measures 4 feet wide and 5 feet long. She rotates the table 90° clockwise so that it fits better in the room. What is the length in feet of the table after the rotation?
​

Answer:

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

Step-by-step explanation:

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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[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]

(a) -5

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

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

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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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 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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Answer:

Step-by-step explanation:

57m

Answer:

The y-intercept is -6.

Step-by-step explanation:

The number after the variable in an equation that is in slope intercept form(y=mx+b) is the y-intercept.

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 is y=-7x. yeah

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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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°

[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]

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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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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Answer:

1/12

Step-by-step explanation:

yellow=1/4

red=5/12

green=1/3

1/4 x 1/3= 1/12

Answer:

k=2

Step-by-step explanation:

[tex]-3k+4=-2-6k \\ \\ 3k+4=-2 \\ \\ 3k=6 \\ \\ k=2[/tex]

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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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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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 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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Answer:

the answer to the question is B thank me later

Step-by-step explanation:

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.

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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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]

With the help of the ratio method, we conclude that 72 grams of sugar should be added.

So, 'n=5' will be the number of rings.

Let 's' be silver. Then,

Now, use the ratio method as follows:

Therefore, with the help of the ratio method, we conclude that 72 grams of sugar should be added.

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The correct question is given below:
A jeweler has five rings, each weighing 18 grams, made of alloys of 10% silver and 90% gold. He decides to melt down the rings and add enough silver to reduce the gold content to 50%. How much silver should he add?

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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