If you take a number, times by 3 then add 5. You get the same as if you took the number, times by 7 then subtract 8. What is the number?

Answer:

HERE IS THE ANSWER 1407.5 hours

Step-by-step explanation:

Answer:

1. [tex]a=b=\dfrac{3}{4}[/tex]

2. [tex]a=-3,\ b=3[/tex]

Step-by-step explanation:

1. Given:

[tex]\dfrac{3x}{(x-2)(3x+2)}=\dfrac{a}{x-2}+\dfrac{b}{3x+2}[/tex]

To find a and b, add two fractions in right side:

[tex]\dfrac{a}{x-2}+\dfrac{b}{3x+2}\\ \\=\dfrac{a(3x+2)+b(x-2)}{(x-2)(3x+2)}\\ \\=\dfrac{3ax+2a+bx-2b}{(x-2)(3x+2)}\\ \\=\dfrac{(3a+b)x+(2a-2b)}{(x-2)(3x+2)}[/tex]

So,

[tex]\dfrac{3x}{(x-2)(3x+2)}=\dfrac{(3a+b)x+(2a-2b)}{(x-2)(3x+2)}[/tex]

Two fractions with same denominators are equal when they have equal numerators, so

[tex]3x=(3a+b)x+(2a-2b)[/tex]

Equate coefficients:

[tex]At\ x:\ \ 3=3a+b\\ \\At \ 1: 0=2a-2b[/tex]

From the second equation:

[tex]a=b[/tex]

Substitute it into the first equation:

[tex]3b+b=3\\ \\4b=3\\ \\b=\dfrac{3}{4}[/tex]

Hence,

[tex]\dfrac{3x}{(x-2)(3x+2)}=\dfrac{\frac{3}{4}}{x-2}+\dfrac{\frac{3}{4}}{3x+2}[/tex]

2. Given:

[tex]\dfrac{3}{x^2-5x+6}=\dfrac{a}{x-2}+\dfrac{b}{x-3}[/tex]

Note that [tex](x-2)(x-3)=x^2-3x-2x+6=x^2-5x+6[/tex]

To find a and b, add two fractions in right side:

[tex]\dfrac{a}{x-2}+\dfrac{b}{x-3}\\ \\=\dfrac{a(x-3)+b(x-2)}{(x-2)(x-3)}\\ \\=\dfrac{ax-3a+bx-2b}{(x-2)(x-3)}\\ \\=\dfrac{(a+b)x+(-3a-2b)}{(x-2)(x-3)}[/tex]

So,

[tex]\dfrac{3}{(x-2)(x-3)}=\dfrac{(a+b)x+(-3a-2b)}{(x-2)(x-3)}[/tex]

Two fractions with same denominators are equal when they have equal numerators, so

[tex]3=(a+b)x+(-3a-2b)[/tex]

Equate coefficients:

[tex]At\ x:\ \ 0=a+b\\ \\At \ 1: 3=-3a-2b[/tex]

From the first equation:

[tex]a=-b[/tex]

Substitute it into the second equation:

[tex]-3(-b)-2b=3\\ \\3b-2b=3\\ \\b=3\\ \\a=-3[/tex]

Hence,

[tex]\dfrac{3}{x^2-5x+6}=\dfrac{-3}{x-2}+\dfrac{3}{x-3}[/tex]

To turn an equality into an identity, you would find values for 'a' and 'b' that work for all values of 'x'. The process involves equating coefficients and solving the resulting equations. Without specific equations, we must rely on general methods, such as using the quadratic formula when 'c' is known.

Finding Values of a and b

To make the equality into an identity, you'll typically want to find values of 'a' and 'b' that satisfy the given equations for all values of 'x'. It seems like part of your question is missing, as we would need the specific equations to give a precise answer. However, the process involves equating coefficients of the same powers of 'x' from both sides of the equation and solving the resulting system of equations.

For example, if you have an equation of the form ax2 + bx + c = 0 and you want to make it an identity, you can find 'a' and 'b' by applying the quadratic formula when 'c' is given.

In the case of a quadratic equation ax2 + bx + c = 0, you can determine 'a' and 'b' by solving:

-b ± √(b2 - 4ac) / (2a)

Which simplifies down when given specific constants, as shown by the example where a = 3, b = 13, and c = -10. This yields two possible solutions for 'x' which can verify the values of 'a' and 'b'.

If an equation already has set constants like a = 1.00, b = 10.0, and c = -200, then the equation is already defined, and the values are given.

Answer: 15

Step-by-step explanation: Linear equations can be written in the form

y = mx + b where the base "b" represents the y-intercept of the line.

So in this case, the y-intercept of the line would positive 15.

The equation can written as y = 4x + 15.

This equation is written in slope-intercept. y = mx + b

m = slope

b = y-intercept

In this equation the y-intercept (b) is 15.

_______

Best Regards,

Wolfyy :)

Answer:

y= -2x+31

Step-by-step explanation:

Y=-2x+B

7=-2(12)+B

7=-24+B

7+24= (-24+24)+B

31=B

Y=-2x+31

Hope it helps!!

There are 8046.75 meters in 5 miles

Step-by-step explanation:

Method 1:

First of all we have to calculate the unit conversion.

Assuming that 3 miles is equal to 4828.05 meters

We have to find that how many meters make one mile

So,

3 miles = 4828.05 meters

[tex]1\ mile=\frac{4828.05}{3}\\=1609.35\ meters[/tex]

Now we know that:

[tex]1\ mile=1609.35\ meters\\5\ miles=1609.35*5 = 8046.74\ meters[/tex]

Method 2:

We can also use ratios to find the number of meters in 5 miles as:

3:4828.05::5:x

where x is the number of meters in 5 miles

[tex]\frac{3}{4828.05}=\frac{5}{x}\\x=\fac{5*4828.05}{3}\\=8046.75\ meters[/tex]

Hence,

There are 8046.75 meters in 5 miles

Keywords: Conversions, Units

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Answer:

Your answer is 15/2 i hoped i helped

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

3×5/2

15/2

The remainder is 1

Answer: X = 4.33

Step-by-step explanation:

cos angle = hypotenuse / opposite side

cos 30° = X/5

0.866 = X/5

X = 4.33

Answer:

3.75

Step-by-step explanation:

You take your 15 feed and divide it by 4 for the four pieces she cuts the rope into giving you with each section of the cut rope being 3.75 in.

The length of each piece is 3.75 feet long.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have Megan who has a rope that is 15 feet in length and she cuts the rope into 4 pieces.

Assume that the length of each piece is x ft. Then -

4x = 15

x = 15/4

x = 3.75 ft

Therefore, the length of each piece is 3.75 feet long.

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To simplify the expression x² + 3x + 2 / X + 1, factor the numerator and denominator expressions separately. The simplified form of the expression is (x + 2) / 1.

To simplify the expression, x² + 3x + 2 / X + 1, we can use the factoring method. First, we factor the numerator expression. The expression x² + 3x + 2 can be factored as (x + 2)(x + 1). Then, we factor the denominator expression X + 1. So, the simplified form of the expression is (x + 2) / 1.

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Answer:

[tex]x=\frac{1}{4}[/tex]

Step-by-step explanation:

We can use some logarithmic rules to solve this easily.

Note: Ln means [tex]Log_e[/tex]

Now, lets start with the equation:

[tex]ln(2x) + ln(2) = 0\\ln(2x) = -ln(2)[/tex]

Writing left side with logarithmic base e, we have:

[tex]Log_{e}(2x) = -ln(2)[/tex]

We can now use the property shown below to make this into exponential form:

[tex]Log_{a}b=x\\means\\a^x=b[/tex]

So, we write:

[tex]Log_{e}(2x) = -ln(2)\\e^{-ln(2)}=2x[/tex]

We recognize another property of exponentials:

[tex]a^{bc}=(a^{b})^{c}[/tex]

So, we write:

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

Also, another property of natural logarithms is:

[tex]e^{(ln(a))}=a[/tex]

Now, we simplify:

[tex](e^{ln(2)})^{-1}=2x\\(2)^{-1}=2x\\\frac{1}{2}=2x\\x=\frac{\frac{1}{2}}{2}\\x=\frac{1}{4}[/tex]

This is the answer.

Answer:

w ≥ 141/2

Step-by-step explanation:

12 − 4/6 w ≤ 2/8 − 3/6 w

First, combine like terms.  Add 4/6 w to both sides, and subtract 2/8 from both sides.

12 − 2/8 ≤ 4/6 w − 3/6 w

12 − 2/8 ≤ 1/6 w

Reduce 2/8 to 1/4:

12 − 1/4 ≤ 1/6 w

To get rid of the fractions, multiply both sides by 12 (the LCM of 4 and 6):

12 (12 − 1/4) ≤ 12 (1/6 w)

144 − 3 ≤ 2w

141 ≤ 2w

Divide by 2:

141/2 ≤ w

If you'd like, flip the equation:

w ≥ 141/2

Answer:

12(x+2)

Step-by-step explanation:

Factor a 12 out of

12x + 24

12 goes into 12 once

12 goes into 24 twice

= 12(x+2)

Answer:

0/36

Step-by-step explanation:

Answer:

0/36

Step-by-step explanation:

It is impossible to roll two dice and get a sum less than 2.

(I'm assuming this is a 6 sided die, but either way if you have more than one die this is impossible.

The lowest you can roll would be 1+1 therefore adding up to a 2.

1) The standard form of the equation is 2x² - 3x = 0, a = 2 , b = -3 ,

c = 0

2) The standard form of the equation is 4x² - 15 = 0, a = 4 , b = 0 ,

c = -15

3) The standard form of the equation is 3x² - 14x - 4 = 0, a = 3 , b = -14 ,

c = -4

4) The standard form of the equation is 9x² - 11 = 0, a = 9 , b = 0 ,

c = -11

5) The standard form of the equation is 4x² - 48x - 4 = 0, a = 4 , b = -48 ,

c = -4

Step-by-step explanation:

The standard form of a quadratic equation is ax² + bx + c = 0, where

1)

∵ 2x² = 3x

- Subtract 3x from both sides

∴ 2x² - 3x = 0

∵ The coefficient of x² = 2

∴ a = 2

∵ The coefficient of x = -3

∴ b = -3

∵ There is no numerical term

∴ c = 0

The standard form of the equation is 2x² - 3x = 0, a = 2 , b = -3 , c = 0

2)

∵ 4x² - 10 = 5

- Subtract 5 from both sides

∴ 4x² - 10 - 5 = 0

- Add like terms

∴ 4x² - 15 = 0

∵ The coefficient of x² = 4

∴ a = 4

∵ There is no x term

∴ b = 0

∵ The numerical term = -15

∴ c = -15

The standard form of the equation is 4x² - 15 = 0, a = 4 , b = 0 , c = -15

3)

∵ 3(x² - 4x) = 2(x + 2)

- Simplify each side

∴ 3x² - 12x = 2x + 4

- Subtract 2x from both sides

∴ 3x² - 12x - 2x = 4

- Subtract 4 from both sides

∴ 3x² - 12x - 2x - 4 = 0

- Add like terms

∴ 3x² - 14x - 4 = 0

∵ The coefficient of x² = 3

∴ a = 3

∵ The coefficient of x = -14

∴ b = -14

∵ The numerical term = -4

∴ c = -4

The standard form of the equation is 3x² - 14x - 4 = 0, a = 3 , b = -14 ,

c = -4

4)

∵ 3x(x + 2x) = 11

- Add the terms in the bracket

∴ 3x(3x) = 11

- Simplify the left hand side

∴ 9x² = 11

- Subtract 11 from both sides

∴ 9x² - 11 = 0

∵ The coefficient of x² = 9

∴ a = 9

∵ There is no x term

∴ b = 0

∵ The numerical term = -11

∴ c = -11

The standard form of the equation is 9x² - 11 = 0, a = 9 , b = 0 ,

c = -11

5)

∵ 6x(x - 8) = 2x² + 4

- Simplify the left hand side

∴ 6x² - 48x = 2x² + 4

- Subtract 2x² from both sides

∴ 4x² - 48x = 4

- Subtract 4 from both sides

∴ 4x² - 48x - 4 = 0

∵ The coefficient of x² = 4

∴ a = 4

∵ The coefficient of x = -48

∴ b = -48

∵ The numerical term = -4

∴ c = -4

The standard form of the equation is 4x² - 48x - 4 = 0, a = 4 , b = -48 ,

c = -4

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Answer:

[tex]y=-30x[/tex]

Step-by-step explanation:

She has been with her book club for 49 months.

Step-by-step explanation:

Books read = 12 books

Time period = 7 months

Therefore,

12 books = 7 months

1 book = [tex]\frac{7}{12}\ months[/tex]    

Books read so far = 84 books

Total time period = x

84 books = x months

1 book = [tex]\frac{x}{84}\ months[/tex]

Using both unit rates;

[tex]\frac{x}{84}=\frac{7}{12}\\x=\frac{7}{12}*84\\x=\frac{588}{12}\\x=49\ months[/tex]

She has been with her book club for 49 months.

Keywords: Unit rates, multiplication

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Answer:

x=

Step-by-step explanation:

Open parenthesis first:

2x-8x+6=6-6x

Combine like terms:

-6x+6=6-6x

Then move all like terms to one side:

6-6=-6x+6x

Simplify:

0=0

0=0 is true, so x can equal any number and the result will be true. (Like the number 4, for example. If x was 4, you would get 4=4.)

~Stay golden~ :)

Answer:

A. $3,150

B. $2,100

Step-by-step explanation:

A. Given,

Trucks cost price = $40,000

Salvage Value = $8,500

Useful life = 10 years

Since there is no requirement, I am using straight-line depreciation method to calculate the depreciation expense.

We Know,

Depreciation Expenses = (Cost price - Salvage Value) / Useful Life

Therefore,

Depreciation expense = ($40,000 - $8,500)/10

Depreciation Expense = $31,500/10

Depreciation Expense = $3,150

Therefore, under the straight-line method, the depreciation expense will be = $3,150.

B. Given, (When the useful year is 15)

Trucks cost price = $40,000

Salvage Value = $8,500

Useful life = 15 years

Since there is no requirement, I am using straight-line depreciation method to calculate the depreciation expense.

We Know,

Depreciation Expenses = (Cost price - Salvage Value) / Useful Life

Therefore,

Depreciation expense = ($40,000 - $8,500)/15

Depreciation Expense = $31,500/15

Depreciation Expense = $2,100

Therefore, under the straight-line method, the depreciation expense will be = $2,100

Answer:

x = 3

y = 2

Step-by-step explanation:

When 2 triangles are congruent, they will have exact same 3 sides length and exact same 3 angles measure.

So we can say:

-2x + 6y = 6

and

-7x + 8y = -5

Let's multiply first equation by 7 and 2nd equation by -2, to get:

7 [-2x + 6y = 6] = -14x +42y = 42

and

-2 [-7x + 8y = -5] = 14x - 16y = 10

Now adding these 2 new equations and solving for y:

-14x +42y = 42

14x - 16y = 10

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

26y = 52

y = 52/26

y = 2

Now we put y = 2 into 1st equation (or any other) and solve for x:

-2x + 6y = 6

-2x + 6(2) = 6

-2x + 12 = 6

6 = 2x

x = 6/2

x = 3

The price of house is $185000.

Step-by-step explanation:

The percentage formula will be used for finding the price of the house

Given

Down payment = $25900

Percentage = 14%

Let x be the price of the home

Then

[tex]Down\ payment=14\%\ of\ x\\\\25900=0.14 * x\\\\x = \frac{25900}{0.14}\\\\x =185000[/tex]

Hence,

The price of house is $185000.

Keywords: Down payment, percentage

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Answer:

[tex]\dfrac{4}{27}[/tex]

Step-by-step explanation:

A bag contains 8 blue marbles 6 red marbles and 4 green marbles, 8 + 6 + 4 = 18 marbles in total.

The probability of selecting a blue marble is

[tex]P(\text{blue marble})=\dfrac{\text{Number of blue marbles}}{\text{Total number of marbles}}=\dfrac{8}{18}=\dfrac{4}{9}[/tex]

Then the blue marble was replaced in the bag.

The probability of selecting a red marble is

[tex]P(\text{red marble})=\dfrac{\text{Number of red marbles}}{\text{Total number of marbles}}=\dfrac{6}{18}=\dfrac{1}{3}[/tex]

The probability of selecting a blue marble replaced it in the bag and then selecting a red marble is

[tex]P=\dfrac{4}{9}\cdot \dfrac{1}{3}=\dfrac{4}{27}[/tex]

Answer:$728

Step-by-step explanation:

Final answer:

To provide Noreen with her new monthly mortgage payment, the cost of 2 mortgage points is added to the original 20% down payment, resulting in a decreased loan amount. A mortgage calculator or formula is then used to determine the monthly payment at a 5.15% interest rate for the new loan amount over 30 years, which would be higher than with the points purchased. Answer : 725$

Explanation:

To calculate Noreen's monthly mortgage payment, we need to first understand the impact of her decision to apply the price of 2 points to her down payment instead of purchasing points. Points are upfront fees paid to the lender at closing in exchange for a reduced interest rate. One point is equal to 1% of the loan amount. However, since Noreen is opting to add the cost of these points to her down payment, we'll calculate her down payment and loan amount without considering a reduction in interest rate.

1. Calculate the down payment:

Noreen's home costs $170,000, and she is required to make a 20% down payment.

Down payment = 20% of $170,000 = 0.20 * $170,000 = $34,000

2. Calculate the cost of 2 points:

Since Noreen is not buying points and instead adding this cost to her down payment, we calculate the initial loan amount to find out how much 2 points would cost.

Initial loan amount without points = $170,000 - $34,000 = $136,000

Cost of 2 points = 2% of $136,000 = 0.02 * $136,000 = $2,720

3. Adjust the down payment:

Noreen decides to add the $2,720 (cost of 2 points) to her down payment.

New down payment = $34,000 + $2,720 = $36,720

4. Calculate the new loan amount:

New loan amount = Home price - New down payment = $170,000 - $36,720 = $133,280

Now, we use the loan amount of $133,280 and the original interest rate of 5.15% to calculate the monthly mortgage payment over a 30-year term.

The formula for monthly mortgage payments is:

[tex]\[M = P\frac{r(1+r)^n}{(1+r)^n - 1}\][/tex]

First, calculate the monthly interest rate:

[tex]\[r = \frac{0.0515}{12} = 0.00429167\][/tex]

Then, plug in the values into the formula:

[tex]\[M = 133,280\frac{0.00429167(1+0.00429167)^{360}}{(1+0.00429167)^{360} - 1}\][/tex]

This calculation can be complex, so it's often easiest to use a mortgage calculator or financial calculator to compute \(M\).

When you perform this calculation, you should get:

[tex]\[M \approx 725\][/tex]

Thus, Noreen's monthly mortgage payment would be approximately $725 when rounded to the nearest dollar. Please note, the exact payment can slightly vary based on the precision of the interest rate conversion and the calculation method.

Answer:

Part 1) The equation in slope intercept form is [tex]y=4x-8[/tex]

Step-by-step explanation:

Part 1) Write an equation in slope-intercept form for a line that passes through (3,4) (and has a y intercept of -8)

we know that

The equation of a line in slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

we have

[tex]b=-8[/tex]

[tex]point\ (3,4)[/tex]

substitute

[tex]4=m(3)-8[/tex]

solve for m

[tex]4+8=3m[/tex]

[tex]3m=12[/tex]

[tex]m=4[/tex]

therefore

[tex]y=4x-8[/tex]

Answer:

If I'm correct it is 10.

Step-by-step explanation:

The distance was 10 ;-;.

Tip: use desmos for this

Answer:

m=-1

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(3-9)/(1-(-5))

m=-6/(1+5)

m=-6/6

m=-1

Answer: 200cm long

Step-by-step explanation:

Let the length of the rod be x

red = 1/4 of the rod , which means 1/4 of x

orange = 2/5 of x

The remainder = x - ([tex]\frac{x}{4}[/tex] +[tex]\frac{2x}{5}[/tex])

= x - ([tex]\frac{13x}{20}[/tex])

= [tex]\frac{7x}{20}[/tex]

yellow = 2/7 of the remainder , that is

yellow = 2/7 of [tex]\frac{7x}{20}[/tex]

yellow = [tex]\frac{x}{10}[/tex]

and it was given that the yellow section was 20cm long , that is

[tex]\frac{x}{10}[/tex] = 20cm

x = 20 x10

x = 200

Therefore the rod was 200cm long

To determine the length of a rod based on fractions of it being painted different colors, with the yellow section known to be 20cm, we set up a proportion based on the fractions of the rod painted and use this to solve for the total length of the rod, which is 200cm.

The subject of this question is Mathematics, and it is typically encountered at the Middle School level. To find the length of the entire rod when 1/4 is painted red, 2/5 is painted orange, and 2/7 of the remainder is painted yellow with the yellow section being 20cm, we need to set up an equation and solve for the total length of the rod.

First, we determine the fraction of the rod that remains after painting 1/4 red and 2/5 orange:

Let's start the calculations:

1. (1/4) + (2/5) = 5/20 + 8/20 = 13/20.

2. The remaining fraction = 1 - 13/20 = 7/20.

3. Let x be the total length of the rod. Since 2/7 of the remainder is 20cm, we can write the equation (2/7) * (7/20) * x = 20cm.

4. Simplify and solve for x:

(2/7) * (7/20) * x = 20cm,

(1/10) * x = 20cm,

x = 20cm * 10,

x = 200cm.

Therefore, the total length of the rod is 200cm.

Answer:

Asha's present age is 27 years and Nisha's present age is 5 years.

Step-by-step explanation:

Let the present age of Nisha be [tex]x[/tex] years.

As per question, Asha's present age is 2 more than the square of Nisha's age.

[tex]\therefore[/tex] Asha's present age = [tex]x^2+2[/tex]

Now, Nisha will reach her mother's age after [tex]x^2+2-x[/tex] years.

Therefore, age of Asha after [tex]x^2+2-x[/tex] years will be = [tex]x^2+2+x^2+2-x=2x^2-x+4[/tex]

Now, as per question,

[tex]2x^2-x+4=10x-1\\2x^2-x-10x+4+1=0\\2x^2-11x+5=0\\2x^2-x-10x+5=0\\x(2x-1)-5(2x-1)=0\\(2x-1)(x-5)=0\\x=\frac{1}{2}\ or\ x=5[/tex]

As age can't be in fraction, we consider the present age of Nisha as 5 years. So, Asha's present age is [tex]x^2+2=5^2+2=25+2=27[/tex] years.

Therefore, Asha's present age is 27 years and Nisha's present age is 5 years.

Answer:

x=0, exactly one solution.

Step-by-step explanation:

y=3x+3

y=-2x+3

-----------

3x+3=-2x+3

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

3x+2x+3=3

5x+3=3

5x=3-3

5x=0

x=0/5

x=0

Answer:

[tex]\displaystyle 3 = m[/tex]

Step-by-step explanation:

2 = −7 + 3m

+ 7 + 7

__________

[tex]\displaystyle \frac{9}{3} = \frac{3m}{3} \\ \\ 3 = m[/tex]

I am joyous to assist you anytime.

The system that will be used to find the numbers

x+y=142

x-y = 14

Step-by-step explanation:

The linear equations are used for representing real life situations

Let x be the first number

and

y be the second number

Then

According to given statement,

"The sum of two numbers, x and y, is 142."

[tex]x+y=142[/tex]

And

"Their difference is 14."

[tex]x-y=14[/tex]

Hence

The system that will be used to find the numbers

x+y=142

x-y = 14

Keywords: Linear Equations

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