6m + 2 - 4m =


help with this please ​

Step-by-step explanation:

1. if the number of pages in the 1st day is 'x', then the 2d day - 'x+10', the 3d day - 'x+20', the 4th day - 'x+30', the 5th day - 'x+40' and the last day - 'x+50' pages;

2. if the sum of all the pages is 300, then it is possible to make up the equation:

x+x+10+x+20+x+30+x+40+x+50=300;

3. x=25, it means:

1st day - 25;

2d day - 35;

3d day - 45;

4th day - 55;

5th day - 65;

6th day - 75 pages.

The probability of pulling a blue or yellow card, written as a reduced fraction is 7/50

From the question, we have the following probabilities:

P(Pink) = 1/5

P(Blue) = 1/25

P(Yellow) = 1/10

P(Black) = 1/15

The probability of pulling a blue or yellow card, written as a reduced fraction is the calculated as:

P(Blue or yellow card) = P(Blue card) + P(Yellow card)

Substitute the known values in the above equation

P(Blue or yellow card) = 1/25 + 1/10

Express 1/25 as 2/50 and 1/10 as 5/10

P(Blue or yellow card) = 2/50 + 5/50

Take the LCM

P(Blue or yellow card) = (2+ 5)/50

Evaluate the sum

P(Blue or yellow card) = 7/50

Hence, the probability of pulling a blue or yellow card, written as a reduced fraction is 7/50

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Answer:

10

Step-by-step explanation:

The transformation that occurred after the dilation of the parallelogram is a translation of 9 units to the right.

A unique variety of quadrilateral made up of parallel lines is called a parallelogram. A parallelogram can have any angle between its neighboring sides, but it must have opposite sides that are parallel for it to be a parallelogram. If the opposite sides of a quadrilateral are parallel and congruent, it will be a parallelogram. Consequently, a quadrilateral in which both pairs of opposite sides are parallel and equal is referred to as a parallelogram.

The initial parallelogram was dilated by a scale factor of 2 about point P.

The points of the initial parallelogram are: (-4, 0), (-2, 0), (-3, -3), (-5, -3).

The parallelogram obtained on dilation will have the points: (-6, 0), (-2, 0), (-4, -6), (-8, -6).

The points of the final parallelogram are: (3, 0), (7, 0), (5, -6), (1, -6).  

(-6,0) →(3,0)  ⇒ (x,y)→(x+h , y+k)

x = -6 , x+h = 3 ⇒ h=3-x = 3-(-6) = 9

y = 0 , y+k = 0 ⇒ k = 0

The transformation rule is (x,y)→( x+9 , y )

That is, a translation of 9 units to the right.

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Answer:

A. a translation of 9 units to the right

Step-by-step explanation:

Edge 2023

The measure of arc RT is 156 degree.

Given:

arc TRM=102°

Hence:

arc RST=2×1O2°

arc RST=204°

Measure of arc RT

arc RT= 2(180° - 102°)

arc RT = 2(78°)

arc RT = 156 degrees

Therefore the correct option is B.

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Answer:

A) 39

Step-by-step explanation:

If you calculate the volume of the cube which is the V=a^3 you get 27, then calculating the pyramid, the Length is 3, and the Width is also 3. Then the height is 4. so you put that into the formula to calculate the volume which is V=L*W*H
    --------

        3

you get 12. Now its simple, you just add the 2 volumes, so you do 27+12 and its 39.

39 is the answer by calculating the volume using formula!

Step-by-step explanation:

So generally whenever you have a problem like this, you want to factor out the denominator and numerator, that way when dividing, you can easily see what the domain is by looking at factors.

So let's start by factoring the numerator and denominator of f(x)

[tex]f(x) = \frac{3x-6}{2x+10}\implies \frac{3(x-2)}{2(x+5)}[/tex]

Now let's do this with the g(x)

[tex]g(x) = \frac{-2x+8}{x+2}\implies\frac{-2(x-4)}{x+2}[/tex]

Now when you divide f(x) by g(x), you keep f(x), change division to multiplication, and flip the g(x) so it's the reciprocal. This gives you the expression

[tex]\frac{f(x)}{g(x)}=\frac{3(x-2)}{2(x+5)}*\frac{x+2}{-2(x-4)}[/tex]

Now just multiply the numerator and denominator

[tex]\frac{f(x)}{g(x)}=\frac{3(x-2)(x+2)}{2(x+5)*-2(x-4)}[/tex]

So the main point of factoring was to easily see when the denominator is  zero, (since if one of the factors is zero, the entire thing will be zero, since zero * anything = zero), but it was also to find any removable discontinuities. Which are just when you have factor in the denominator and numerator, so you can simplify the fraction further by canceling it out. To give an example: [tex]f(x)=\frac{(x-2)(x+4)}{(x-2)(x+3)}\implies\frac{x+4}{x+3}[/tex]. But the domain of f(x) is still restricted so that: [tex]x\ne 2, -3[/tex]. But there will not be a vertical asymptote at x=2 like with traditional domain restrictions in a rational function. This is because you can technically define f(2), but only if you use the most simplified form. This will result in a hole being at that point to signify that it's a removable discontinuity.

Anyways a bit off topic, but something that may be necessary in other examples. Anyways, now to find the domain, we just need to find when f(x)/g(x) is not defined. Or more specifically we find when the denominator is going to be zero. So we just need to set both factors equal to zero.

[tex]0 = 2(x+5)\\\text{divide both sides by 2 (a bit redundant)}\\0 = x+5\\\text{subtract 5 from both sides}\\-5 = x[/tex]

[tex]0 = -2(x-4)\\\text{divide both sides by -2 (a bit redundant)}\\0 = x-4\\\text{add 4 to both sides}\\x=4[/tex]

So the domain restrictions would be: [tex]x\ne-5, 4[/tex]

This can be expressed in interval notation: [tex](-\infty, -5) \cup (-5, 4) \cup (4, \infty)[/tex].

You can also express this in terms of set builder notation: [tex]D: \{x|x\ne-5, x\ne4\}[/tex]

308 gallons of 7% and 77 gallons of 2% are needed to obtain the desired 385 gallons.

Since a dairy needs 385 gallons of milk containing 6% butterfat, to determine how many gallons each of milk containing 7% butterfat and milk containing 2% butterfat must be used to obtain the desired 385 gallons, the following calculation must be performed:

Therefore, 308 gallons of 7% and 77 gallons of 2% are needed to obtain the desired 385 gallons.

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Answer: [tex]g(x) \ge f(x)[/tex] for all x such that [tex]x\le-2[/tex] or [tex]x\ge0[/tex]

Step-by-step explanation:

This question is essentially asking at what x values would the graph of g(x) be greater than (higher than) or equal to f(x).

In the graph, we can see that g(x) is greater than (or higher than) f(x) at all x's before (to the left of) point E and after (to the right of) point A. An easy way to find the points E and A is by setting f(x) = g(x).

[tex]f(x)=g(x)\\1-x^2=2x+1\\1=x^2+2x+1\\0=x^2+2x\\0=x(x+2)\\x=0\hspace{0.1cm}or\hspace{0.1cm}x=-2[/tex]

Since any value with x=-2 is left of the y-axis, we know that point E would have its x-coordinate as -2. Similarly, any point on the y-axis would have x=0; therefore, we can tell that point A would have its x-coordinate at 0.

If we remember that g(x) is greater than f(x) to the left of E and to the right of A, we can say that

[tex]g(x) \ge f(x)[/tex] for all x such that [tex]x\le-2[/tex] or [tex]x\ge0[/tex]

The unknown number of the given expression is 8

Let the unknown number be x such that three times the sum of some number plus 3 is equal to 7 times the number minus 23 is expressed as;

3(x + 3) = 7x - 23

Expand

3x + 9= 7x - 23

Collect the like terms

3x-7x = -23 - 9

-4x = -32

x = 8

Hence the unknown number of the given expression is 8

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Answer:

56

Step-by-step explanation:

solution

Here

P=8a=8·7=56

Answer:

56 units

Step-by-step explanation:

the perimeter of a rectangular octagon  with sides of length a

is equal to:  8 × a

Then

the perimeter of a regular octagon with a side length of 7 units

is equal to:  8 × 7 = 56 units

The sum accumulated by 31st December 2018 is Rs 4,163,060.00

What is future value?

Future value is the accumulated amount that investments would yield in future period when the amounts invested are added with the total interest earned.

Note in this case that Rs500,000  would be invested subsequently for 4 years( 2015-2018 , January 1st of each year)

We can determine the future value of each investment using the future value formula shown below:

FV=PV*(1+r)^N

PV=amount invested

r=interest=10%

N=number of years that an amount is invested(for instance, the amount invested on 1st January 2014 will earn interest in 2014,2015,2016, 2017 and 2018 i.e. for 4 years)

Total FV=1,000,000*(1+10%)^5+500,000*(1+10%)^4+500,000*(1+10%)^3+500,000*(1+10%)^2+500,000*(1+10%)^1

Total FV=Rs 4,163,060.00

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Using proportions, it is found that the total percentage increase in the investor's stock account was of 6.2%.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The values of the stocks of Company A and Company B, after the increase are given, respectively, by:

The total values are given as follows:

The percent increase is given by the increase divided by the initial value and multiplied by 100%, hence:

P = (8668 - 8160)/8160 x 100% = 6.2%.

The total percentage increase in the investor's stock account was of 6.2%.

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Answer:

7.5. hours

Step-by-step explanation:

Trust me

12 men will take 3.34 hours to build a similar storeroom if they work at the same rate.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

It is given that it took 8 hours for 5 men to build a storeroom. The time required by 12 men to do the same work will be calculated as below:-

Time taken by one man  = 8 x 5 = 40 hours

Time is taken by 12 men will be = 40 / 12 = 3.34 hours

Therefore, 12 men will take 3.34 hours to build a similar storeroom if they work at the same rate.

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It is possible to arrange the total of mangoes by using 20 piles of 9 mangoes, 18 piles of 10 mangoes, or 15 piles of 12 mangoes.

The conditions for mangoes to be arranged are that the piles should have either 9, 10 or 12 mangoes and reminders are not allowed. This means you need to fit all the mangoes and no mangoes can be left.

Based on the conditions and the total number of mangoes (180 mangoes), here are the possibilities that you can determine using division:

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Using proportions, it is found that:

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The heights are measured in units, hence the ratio is:

[tex]r = \frac{5}{25} = \frac{1}{5}[/tex]

The surface areas are measured in units squared, hence the ratio is:

(1:5)² = 1:25.

The volumes are measured in cubic units, hence the ratio is:

(1:5)³ = 1:125.

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Answer:

C. 16 days

Step-by-step explanation:

Let´s say each worker does 1 ¨work¨, for each day, in order to complete the job in 15 days. That´s a total of 150 work.

If only 6 workers worked for the first 5 days, then we only do 30 by Day 5.

2 more workers join, so they do 8 work each day, 24 work in 3 days, 54 work by Day 8.

4 more workers join to complete the job, so we now do 12 work each day.

150 - 54 = 96

96 work is left to do, which would be done in 8 days by 12 workers.

8 days + 8 days = 16 days

The total cost to laminate the tabletop is $96.

The first step is to determine the area of the trapezoid.

Area of the trapezoid = 0.5 (sum of parallel sides) x height

0.5 x (6 + 10) x 3 = 24 feet²

The total cost of laminating = cost per square feet x area

$4 x 24 = $96

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Answer:

10.6 ft

Step-by-step explanation:

to find the diagonal length of the stairway we can use the pythagorean theorem or a^2 + b^2 = c^2

6'4" is also 6 1/3' or 19/3'

8'6" is also 8 1/2' or 17/2'

now square them both

361/9 + 289/4

make them have the same denominator

1444/36 + 2601/36

add them

4045/36

take the square root

10.6000524 is your answer

10.6 ft

The solution to the system of equation is (0, 1)

Given the following system of equation as shown below

2^(x)+3^(y)=5,

2^(x+2)+3^(y+1)=18

Rewrite

2^(x)+3^(y)=5,

2^x*2^2 + 3^y*3^1 = 18

___________

2^(x)+3^(y)=5,

4(2^x) + + 3(3^y) = 18

Let a = 2^x and b = 3^y

Substitute

a + b = 5

4a + 3b = 18

a = 5 - b

Substitute

4(5-b) + 3b = 18

20 - 4b + 3b = 18

-b = -2

b = 2

since a = 5 - b

a = 5 - 2

a = 3

Recall that a = 2^x and b = 3^y

2^x = 2

x = 0

Similarly

3^y = 3

y =1

Hence the solution to the system of equation is (0, 1)

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The number of bacteria present after 15 hours is 18928

An exponential equation is represented as;

y = ab^x

Where

a = y, when x = 0

From the table, we have:

y = 1796 when x = 0

So, we have:

y = 1796b^x

Also, we have the point (1, 2097)

This gives

2097 = 1796b^1

Divide by 1796

b = 1.17

Substitute b = 1.17 in y = 1796b^x

y = 1796(1.17)^x

This means that the exponential equation is y = 1796(1.17)^x

After 15 hours, we have:

y = 1796(1.17)^15

Evaluate

y = 18928

Hence, the number of bacteria present after 15 hours is 18928

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Answer:

20% increase

Step-by-step explanation:

To find the percent increase, use this formula

New value - original value

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

original value

114-95

-----------

95

19

---- = .2

95

.2 is 20%, so it is a20% increase

The sum of the first five terms is 11/2

The series is given as:

1/2, -1,2,-4…

Calculate the common ratio of the series using

r = -4/2

Evaluate

r = -2

The sum is then calculated as:

[tex]S_n = a\frac{1 - r^n}{1 - r}[/tex]

This gives

[tex]S_n = \frac{1}{2} * \frac{(1 - (-2)^5}{1 + 2}[/tex]

Evaluate

[tex]S_n = \frac{1}{2} * \frac{33)}{3}[/tex]

Evaluate

[tex]S_n =\frac{11}{2}[/tex]

Hence, the sum of the first five terms is 11/2

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Using secant rule, the value of variable x in the diagram is 10.

A secant is a line that intersect a circle in two points.

Therefore, the following rule guides a secant.

(x + 32)32 = (20 + 28)28

Hence,

32x + 1024 = (48)28

32x + 1024 = 1344

32x = 1344 - 1024

32x = 320

divide both sides by 32

32x / 32 = 320 / 32

x = 10

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The value of m∠7, given the data from the question is 80°

Alternate angle theorem states as follow:

When two parallel lines are cut by a line (i.e transversal), then the alternate interior angles or alternate exterior angles are aqual.

From the diagram,

From the above, we can see that m∠3 and m∠7 are alternate angles.

Therefore,

m∠7 = m∠3

m∠7 = 80°

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Complete question

please see attached photo

The return on the investment is 3%

The given parameters are:

Buying rate = 7%

Selling rate = 10%

The return on the investment is

ROI = Selling - Buying

So, we have:

ROI = 10% - 7%

Evaluate

ROI = 3%

Hence, the return on the investment is 3%

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The monthly payments for each add-on interest loan will be $29.71.

Given Information and Formula Used

Principal Amount, P = $1150

Rate of Interest, R = 6%

Duration of loan in years, T = 4

The formula for simple interest is given as,

I = (P × R × T)/100

Calculating the Add-On Interest For Each Month

Interest, I = (P × R × T)/100

Substituting the values of P, R, and T in the above formula, we get,

I = $ (1150 × 6 × 4)/100

I = $ 27600/100

I = $276

Calculating the Total Monthly Payment With Interest

Amount of add-on interest loan, A = P + I

A = $1150 + $276

A = $1,426

Monthly payment with interest = A/(4×12)

= $ 1426/48

= $29.71

Hence, the monthly payments for each add-on interest loan would be $29.71.

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Answer:

12705

Step-by-step explanation:

The problem could be solved in two different methods:

1:

231×(55)=12705

2.

231×40+231×15=9240+3465=12705

By algebra, if one solution for the second order polynomial b² - 9 = 0 is 3, then the other solution to the expression is - 3.

Herein we have a quadratic equation, that is, a second order polynomial, of the form b² - a² = 0. By algebra we know that the polynomial of such form have the following equivalence:

b² - a² = (b - a) · (b + a), which means that the roots of the interval are x₁ = a and x₂ = - a.

If we know that a² = 9, then the roots of the second order polynomial are:

b² - 9 = (b - 3) · (b + 3)

By algebra, if one solution for the second order polynomial b² - 9 = 0 is 3, then the other solution to the expression is - 3.

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The value of n given the form of the function is (b) positive odd number

The form of the graph is given as:

f(x) = a(x + k)^1/n + c

For the given graph, we have the following features:

a > 0 --- a is positive

k > 0 --- k is positive

c < 0 --- c is negative

If n is an even number, the function would be undefined because the even root of a number is undefined

However, the function is defined if n is an odd number,

Hence, the value of n given the form of the function is a positive odd number

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