log(base 6)6+log(base 6)(x-5)=log( base 6)6

Given : Molly bought a pair of Gloves which cost £4

Given : Molly sold the Gloves and Skirt for a Total of £48

Given : Molly made 100% Profit on the Cost of the Gloves

⇒ Molly sold the Gloves at a Cost of £8

Selling Price of Gloves + Selling Price of Skirt = £48

⇒ £8 + Selling Price of Skirt = £48

⇒ Selling Price of Skirt = £40

Given : Molly made 20% Profit on the Total Cost

[tex]\mathsf{\implies (\frac{Selling\;Price\;of\;Skirt\;and\;Gloves - Cost\;Price\;of\;Skirt\;and\;Gloves }{Cost\;Price\;of\;Skirt\;and\;Gloves}) \times 100 = 20}[/tex]

[tex]\mathsf{\implies (\frac{48 - 4 - Cost\;Price\;of\;Skirt}{4 + Cost\;Price\;of\;Skirt}) \times 100 = 20}[/tex]

[tex]\mathsf{\implies (\frac{44 - Cost\;Price\;of\;Skirt}{4 + Cost\;Price\;of\;Skirt}) \times 5 = 1}[/tex]

[tex]\mathsf{\implies 5(44 - Cost\;Price\;of\;Skirt) = 4 + Cost\;Price\;of\;Skirt}[/tex]

[tex]\mathsf{\implies 220 - 5(Cost\;Price\;of\;Skirt) = 4 + Cost\;Price\;of\;Skirt}[/tex]

[tex]\mathsf{\implies 6(Cost\;Price\;of\;Skirt) = 216}[/tex]

[tex]\mathsf{\implies (Cost\;Price\;of\;Skirt) = 36}[/tex]

Profit Percentage on the Cost of the Skirt :

[tex]\mathsf{\implies (\frac{Selling\;Price\;of\;Skirt - Cost\;Price\;of\;Skirt}{Cost\;Price\;of\;Skirt}) \times 100}[/tex]

[tex]\mathsf{\implies (\frac{40 - 36}{36}) \times 100}[/tex]

[tex]\mathsf{\implies (\frac{4}{36}) \times 100}[/tex]

[tex]\mathsf{\implies (\frac{1}{9}) \times 100}[/tex]

[tex]\mathsf{\implies 11.11\%}[/tex]

Answer:

(x - 1)(3x - 5)

Step-by-step explanation:

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x-term.

product = 3 × 5 = 15 and sum = - 8

The factors are - 3 and - 5

use these factors to split the middle term

3x² - 3x - 5x + 5 ( factor the first/second and third/fourth terms )

= 3x(x - 1) - 5(x - 1) ( take out the common factor (x - 1) )

= (x - 1)(3x - 5)

Answer:

(x - 1)(3x - 5)

By definition, BF = 1/2 * CE;

So, BF = 1/2 * 90 = 45.

BF = 45

(Midsegment Length Theorem)

Answer:

BF=45

Step-by-step explanation:

Here the given point B and point [tex]F[/tex] are the midpoint of the sides AC and AE respectively in triangle ACE .

According to converse of Thales theorem -if a line divides any two sides of a triangle in equal parts then that line will be parallel to the third side of the triangle.

Also ,

In the above said condition, that line will be half of the third side

On applying this concept in the given triangle ACE

[tex]BF= \frac{1}{2} *CE\\BF=\frac{1}{2} *90\\BF=45[/tex]

Hence BF=45

Answer:

Option A is correct.

An inequality:  [tex]7+5>6+2[/tex]

Step-by-step explanation:

Given the sentence: Seven plus five is greater than six plus two.

"Seven" means 7

"Plus" means +

"Five" means 5

"Greater than" means >

"six" means 6

"two" means 2

Then, the inequality for the given sentences is;  

[tex]7+5>6+2[/tex]

Answer:

i think your answer is 90

Answer:

[tex]\frac{45y}{56x}[/tex]

Step-by-step explanation:

[tex]\frac{5}{-7x} times \frac{-9y}{8}[/tex]

When we multiply two fractions we multiply numerator with numerator and denominator with denominator

5 times -9y is -45y

Then -7x  times 8 is -56x

So the fraction becomes [tex]\frac{-45y}{-56x}[/tex]

we have negative at the top and bottom so it becomes positive

[tex]\frac{45y}{56x}[/tex]

We cannot simplify further

a. The percentage of students who prefer strawberries is 33.33%.

b. The percentage of students who prefer the least favorite fruit is 8.33%.

c. The percentage of students who prefer apples or pears is 45.83%.

A) To find the percentage of students who prefer strawberries:

Add up the total number of students surveyed: 30 (apples) + 15 (oranges) + 40 (strawberries) + 25 (pears) + 10 (peaches) = 120 students.

Determine the number of students who prefer strawberries: 40.

Calculate the percentage: (Number of students who prefer strawberries / Total number of students surveyed) * 100 = (40 / 120) * 100 = 33.33%.

B) To find the percentage of students who prefer the least favorite fruit:

Identify the least favorite fruit, which is peaches with 10 preferences.

Calculate the percentage: (Number of students who prefer peaches / Total number of students surveyed) * 100 = (10 / 120) * 100 = 8.33%.

C) To find the percentage of students who prefer apples or pears:

Add up the number of students who prefer apples and pears: 30 (apples) + 25 (pears) = 55.

Calculate the percentage: (Number of students who prefer apples or pears / Total number of students surveyed) * 100 = (55 / 120) * 100 = 45.83%.

So, the answers are:

A) 33.33%

B) 8.33%

C) 45.83%

The detailed answer provides percentages for students preferring specific fruits from a survey.

A) What percent of students surveyed prefer strawberries?

B) What percent of students surveyed prefer the least favorite fruit?

C) What percent of students surveyed prefered apples or pears?

Answer:

905.26

Step-by-step explanation:

905.255

We are rounding to the hundredths place, so we need to look at the thousandths place.  That digit is also a 5. 5>= 5 so we need to round the 5 in the hundredths place up to a 6

905.255 rounds to 905.26

Answer:

905.26 is your answer

Step-by-step explanation:

The 5 you are solving for will be underlined and bolded.

905.255

Note the place value to the right of the value you are solving for. It is a 5. Because it is a 5, round up.

905.255 rounded to the nearest hundredth is 905.26

905.26 is your answer

~

Answer:

6 bowls

Step-by-step explanation:

10/1 • 3/5

That would equal 30/5 which simplified, is 6

Answer:

x = 55

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

the sum of the 4 angles in a quadrilateral = 360°

the angles to the left and above 130° angle = 50°

Since 130° and 50° form a straight angle and are supplementary

the third angle in the left triangle = 180° - (50 + 30)° = 100°

thus the angle to the right = 180° - 100° = 80°  ( straight angle )

the third angle in the upper triangle = 180° - (50 + 45)° = 85°

the angle below it = 180° - 85° = 95° ( straight angle )

We now have 3 angles inside the quadrilateral of 130°, 80° and 95°

x = 360° - (130 + 80 + 95)° = 55

Answer:

50

Step-by-step explanation:

12*5=60---------------1 hour

5*2=10

10*5=50

In 2 hours 50 City blocks will be covered.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Five city blocks covered = 12 minutes

So, in one minutes the blocks covered = 5/12

Then, to walk 2 hours the number of block covered

= 120 x 5 /12

= 5 x  10

= 50 blocks

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Answer:

43.25

Step-by-step explanation:

You answer is going to be 43.25.

Thank you

Answer:

x = 2.5

Step-by-step explanation:

Multiply 2.5 to remove the denominator

x/2.5 * 2.5 = 1

Multiply 2.5 on the other side.

2.5 * 1

x = 2.5

Answer:

x = 2.5

Step-by-step explanation:

x/2.5=1

To solve this equation, multiply both sides by 2.5

x/2.5* 2.5=1 * 2.5

x = 2.5

Answer:

the answer is C because the slope of the line is what you need to look for with these kinds of problems. it could be any point on the line, but answer C is the only one of its kind.

Step-by-step explanation:

The ordered pair is the solution to the system is (5,3).

A pair of numbers that are written in a particular order, enclosed in brackets are known as ordered pairs.

Malique solved the system of equations below;

[tex]\rm 2x+4y=22\\\\6x+2y=36[/tex]

Reduce the greatest common factor on both sides of the equation

[tex]\rm x+2y=11\\\\3x+y=18[/tex]

From equation 1

[tex]\rm x+2y=11\\\\x=11-2y[/tex]

Substitute the value of x in the equation 2

[tex]\rm 3x+y=18\\\\3(11-2y)+y=18\\\\33-6y+y=18\\\\-5y=18-33\\\\-5y=-15\\\\5y=15\\\\y=\dfrac{15}{5}\\\\y=3[/tex]

Substitute the value of y in the equation 1

[tex]\rm x+2y=11\\\\x + 2(3)=11\\\\x+6=11\\\\x=11-6\\\\x=5[/tex]

Hence, the ordered pair is the solution to the system is (5,3).

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The formula for the side length of 3 inches is P = 5s; 15 inches. So option (a) is correct.

To find the perimeter of a regular pentagon, we can use the formula:  P = 5s , where  P  is the perimeter and  s  is the length of a side.

Let's evaluate this formula for a side length of 3 inches:

P = 5s

P = 5 x 3

P = 15

So, the perimeter of the pentagon with a side length of 3 inches is 15 inches.

The correct option is (a) ( P = 5s; 15)  inches.

To find the perimeter of a regular pentagon, multiply the number of sides (5) by the length of one side.

To find the formula for the perimeter of a regular pentagon in terms of the length of a side, let's first understand the properties of a regular pentagon. A regular pentagon is a polygon with five equal sides and five equal angles.

The perimeter of any polygon is the sum of the lengths of all its sides. Since a regular pentagon has five equal sides, we can express its perimeter as the product of the number of sides (5) and the length of one side (s). Therefore, the formula for the perimeter [tex](\( P \)) of a regular pentagon in terms of the length of a side (\( s \)) is \( P = 5s \).[/tex]

Now, to evaluate the formula for a side length of 3 inches, we substitute  [tex]\( s = 3 \) into the formula:[/tex]

[tex]\[ P = 5 \times 3 = 15 \text{ inches} \][/tex]

This means that the perimeter of the regular pentagon with a side length of 3 inches is 15 inches.

Therefore, the correct answer is option a: [tex]\( P = 5s; 15 \text{ inches} \).[/tex]

This solution provides a clear explanation of how to derive the formula for the perimeter of a regular pentagon and how to evaluate it for a specific side length.

Answer:

36/25

Step-by-step explanation:

[tex](\frac{5}{6})^{-2}=(\frac{6}{5})^{2}\\(\frac{6}{5})^2=\frac{6}{5}\times\frac{6}{5}\\=\frac{36}{25}[/tex]

Steps:

Flip the fraction (negative exponent)

Square the fraction

Answer:

36/25 or 1 11/25

Step-by-step explanation:

(5/6)^-2

A negative exponent tells us to flip the fraction.  It only eliminates the negative part of the exponent.

(6/5) ^2

We can split it apart (a/b)^x = a^x/b^x

6^2/5^2

36/25

1 11/25

Answer:

the value of the home after 12 years =$275,165.60

Step-by-step explanation:

To find value of appreciation after 12 years

We apply exponential growth formula

[tex]y=a(1+r)^x[/tex]

Where a represents the initial amount (purchased amount)

a= 182,100

r = rate of interest ( appreciation percentage) = 3.5% = 0.035

x  represents the time period= 12 years

Plug in all the values

[tex]y=a(1+r)^x[/tex]

[tex]y=182100(1+0.035)^12[/tex]

y= 275165.6025027724  

y=$275165.60

Answer:

(x + 2)(x² - 2x + 4)

Step-by-step explanation:

x³ + 8 ← is a sum of cubes, which factors in general as

• a³ + b³ = (a + b)(a² - ab + b²)

x³ = (x)³ ⇒ a = x and 8 = 2³ ⇒ b = 2

x³ + 8 = (x + 2)(x² - 2x + 4) ← in factored form

Answer:

[tex]x^{3} +8=(x+2)(x^{2} -2x+4)[/tex]

Step-by-step explanation:

The binomial can be factored by the binomial form by trinomial. This binomial is a sum of cubes, whose general form presents the following result.

[tex](x^{3} +y^{3} )=(x+y)(x^{2} -xy+y^{2} )[/tex]

Substituting the values ​​of x and y we will have

[tex]x^{3} =x^{3} ;     y^{3} =8[/tex]

Obtaining the cubic roots of each variable

[tex]x=x; y=2[/tex]

So

[tex]x^{3} +8=(x+2)(x^{2} -2x+4)[/tex]

Answer:

10mph

Step-by-step explanation:

it's a ratio

6.2 miles divided by .62=10

Answer:

h = 1558.8

Step-by-step explanation:

Let x be the distance from the vertex of the 30 degree angle to the base of Blue mountain.

Tan (30) = h/x                       Multiply both sides by x.

x * Tan(30) = h

Tan(25) = h/(x + 200)           Multiply x + 200 on both sides.

(x + 200) * Tan(25) = h

Now you have 2 equations both equal to h. The two sides can be equated to each other.

x*tan(30)  = (x + h) * Tan(25)         Divide both sides by tan(25)

x*tan(30)/tan(25) = x + 200          Find Tan(30)/Tan(25)

Tan30 / tan(25) = 1.23813 so

1.23813 x = x  + 200                      Subtract x from both sides.

0.23813x = 200                             Divide both sides by 0.23813

x = 200/0.23813

x = 839.99

================

That is not the answer you have been asked for. What you need is h.

Tan(30) = x / h                                Multiply both sides by h

h*tan(30) = x                                   Divide both sides by tan(30)

h = x/tan(30)

h = 839.99/tan(30)                        Tan 30 = 0.57735

h = 839.99/0.57735

h = 1558.8

Answer:

[tex]\sqrt{2}[/tex]

Step-by-step explanation:

We plug in [tex]i[/tex] into [tex]f(x)[/tex] to get:

[tex]f(i)=1-i[/tex]

Here, [tex]i[/tex] is the imaginary number [tex]i=\sqrt{-1}[/tex]

To get absolute value of an imaginary number, we use the following formula:

[tex]a+bi=\sqrt{a^2+b^2}[/tex]

So absolute value of [tex]f(i)[/tex] is:

[tex]|f(i)|=\sqrt{(1)^2+(1)^2} \\=\sqrt{1+1} \\=\sqrt{2}[/tex]

The equation y = 5(6.8)x represents an exponential growth relationship, where an increase in the variable 'x' leads to a proportional increase in the dependent variable 'y'.

The equation y = 5(6.8)x is an expression of exponential growth, not decay. In this type of equation, known as an exponential relationship, a change in the independent variable x produces a proportional change in the dependent variable y. The factor 6.8>1 which means as x increases, y increases at a faster rate, indicating growth.

For example, this form of equation is often used to describe population growth such as bacteria under ideal conditions. Each generation of bacteria reproduces, increasing the growth rate as the bacteria population rises. This growth-based relationship can be visualized using a graph where the growth rate would be represented as a rising curve.

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Answer:

The equation of the line is y=-x

Step-by-step explanation:

To find the equation for a line, we need to know 2 points.

One of the points is (0,0) because it goes through the origin.  Another point is (5,-5).  We can calculate the slope because we have 2 points using the formula.

m = (y2-y1)/(m2-m1)

m = (-5-0)/(5-0)

m = -5/5

m=-1

The slope is -1

We know the y intercept (where it crosses the y axis) is 0.  Using the slope intercept form of a line

y = mx+b

y =-1x+ 0

y = -x

The equation of the line is y=-x

Answer:depending on what type of equation but ussuming in standard form it is Ax+By+c

Step-by-step explanation:

To rearrange an equation, balance operations on both sides to isolate a specific variable, maintain units, use calculators correctly, and always check the solution by substituting back into the original equation.

Rearranging an equation involves moving terms from one side of the equation to the other to isolate a specific variable. This process is guided by the principle of balance, which means whatever operations you do to one side of the equation, you must do to the other side to keep the equation balanced. For instance, if you need to move a constant to the opposite side, you would add or subtract it from both sides.

Steps to Rearrange an Equation

For example, while dealing with chemical equations, you'll often need to rearrange the formulas for reactants and products to balance the equation.

Chemical Equation Rearrangement Steps

The answer is:  " 7:45 a.m. "  .

__________________________________________

Step-by-step explanation:

__________________________________________

Start at:

____________________

6:00 a.m.

____________________

Add 1  1/4 hours ; which is

1 + (1/4) hours:

Note:  " 1 hr = 60 min." .

_____________________

So:

 (1/4 hr) *  ([tex]\frac{60 min }{ 1 h}[/tex]) ;

                                       =  (1/4) * 60 min;

                                       = (60/4) min.

                                       = 15 min.

______________________

So:  1  1/4 hr =  1 hr. 15 min.;

______________________

So:  Start at:  6:00 a.m .

Add  " 1  1/4 hrs."  ;  i.e. add 1 hr 15 min.

_______________________

6:00 a.m + 1 hr = 7:00 a.m.  ;

 7:00 a.m.  +  15 min. =  7: 15 a.m. ;

_______________________

Now, we are at:

_______________________

7:15 a.m.  ;

Now add:  "1/2 hour" to "7:15 a.m." to this time.

Note:  " 1 hr = 60 min.

So;

"1/2 hr = (1/2) * (60 min) = (60 / 2) min. = 30 min.

________________________

So: we have 7:15 a.m. ;

we add "30 min." to this time.

and we have:  7:45 a.m.

___________________________________________________

The answer is:  " 7:45 a.m. "  .

__________________________________________________

Answer:

it's 8:15

Step-by-step explanation:

start at 6:00+1:15 (aka 1 1/4 an hour) =7:45+30 min=8:15

Answer:

1 plain = $0.75; 1 cheese = $0.95; 1 super = $1.25

Step-by-step explanation:

We have three conditions

(1) 5P = 3S

(2)  S = C + 0.30

(3)  P = C – 0.20                           Substitute (3) into (1)

=====

(4)   5(C – 0.20) = 3S                   Substitute (2) into (4)

      5(C – 0.20) = 3(C + 0.30)     Remove parentheses

         5C – 1.00 = 3C + 0.90       Add 1.00 to each side

                    5C = 3C + 1.90        Subtract 3C from each side

                    2C = 1.90                 Divide each side by 2

                      C = $0.95              Substitute C into Equation (2)

=====

                      S = 0.95 + 0.30

                      S = $1.25               Substitute C into Equation (3)

=====

                     P = 0.95 – 0.20

                    P = $0.75

1 plain = $0.75; 1 cheese = $0.95; 1 super = $1.25

f(x) + n - move the graph n units up

f(x) - n - move the graph n units down

f(x + n) - move the graph n units to the left

f(x - n) - move the graph n units to the right

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

[tex]f(x)=-\dfrac{1}{5}x^2\\\\f(x+5)=-\dfrac{1}{5}(x+5)^2\\\\f(x+5)+2=-\dfrac{1}{5}(x+5)^2+2[/tex]

The equation y = -1/5 (x + 5)^2 + 2 is translated from the standard position by moving up and to the left.

In the equation y = -1/5 (x + 5)^2 + 2, the transformation of the graph from its standard position is determined by the constants within the equation. The -5 inside the parentheses causes a shift to the left by 5 units and +2 outside the parentheses represents an upward shift by 2 units. Therefore, the graph of the equation is moved up and to the left from its standard position where the vertex is at the origin.

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