Simplify each given equation and show your work. Tell whether it has one solution, an infinite number of solutions, or no solutions, and identify each equation as an identity, a contradiction, or neither. Explain your answers.
(a)6x + 2(2x – 3) = 24 + 9x
(b)25 – 4x = 3(5 – x) + 10 – x
(c)4(x + 2) = 2x + 7 + 2(x – 10)

Answers

Answer 1

a) The answer is one solution, neither

6x + 2(2x - 3) = 24 + 9x
6x + 2 * 2x + 2 * (-3) = 24 + 9x
6x + 4x - 6 = 24 + 9x
10x - 6 = 24 + 9x
10x - 9x = 24 + 6
x = 30

b) The answer is infinity solutions, identity
25 – 4x = 3(5 – x) + 10 – x
25 - 4x = 3 * 5 - 3 * x + 10 - x
25 - 4x = 15 - 3x + 10 - x
25 - 4x = 25 - 4x
4x - 4x = 25 - 25
0x = 0

x can be any number, so an infinite number of solution

c) The answer is no solution, contradiction

4(x + 2) = 2x + 7 + 2(x – 10)
4 * x + 4 * 2 = 2x + 7 + 2 * x - 2 * 10
4x + 8 = 2x + 7 + 2x - 20
4x + 8 = 4x - 13
4x - 4x = - 8 - 13
0 = -13

this is contradiction

Related Questions

Please help !!
Answer correct for a brainliest and also a thanks ! Don't answer if you don't know it .

Answers

b) between one and two months....
....................................................
look on graph and you see it....

I'd say between 1 and 2 months

The sales tax rate in jans town is 7.5.if she buys 3 lamps for $23.59 each and a sofa for $769.99 , how much sales tax does she own ?

Answers

I believe that tax rate are in percent, so tax rate = 7.5%

Now, lets we total the money that she must pay without tax ( just for 3 lamps and 1 sofa ) :
3 lamps = 3 . $23.59 = $70.77
1 sofa = $ 769.99
Total amount = $769.99 + $70.77 = $840.76

We have to find tax amount, the tax amount of the total amount is about 7.5% of the price. Then we have to adding the tax amount into the total amount. So that we have the Total amount including the tax.

tax amount = 7.5% . 840.76 = $63.057
Total amount (inc. tax amount) =
$840.76 + $63.057 = $903.817

Therefore, she must pay those sofa and lamps about $903.817. So expensive huh? =))

PLEASE HELP
A line has slope -5/3. Through which two points could this line pass?

A. (12,13), (17,10)

B. (16,15), (13,10)

C. (0,7), (3,10)

D. (11,13), (8,18)

Answers

m = -5/3

slope formula:
m = y2 - y1 / x2 - x1

A) m = 10-13 / 17-12 = -3/5
B) m = 10-15 / 13-16 = -5/-3
C) m = 10-7 / 3 -0 = 3/3 = 1
D) m = 18-13/8-11 = 5/-3 or -5/3

D. (11,13); (8,18) are the two points the line could pass

Integrate sin^-1(x) dx

please explain how to do it aswell ...?

Answers

If you're using the app, try seeing this answer through your browser: https://brainly.com/question/2264253

_______________

Evaluate the indefinite integral:

[tex]\mathsf{\displaystyle\int\!sin^{-1}(x)\,dx\qquad\quad\checkmark}[/tex]

Trigonometric substitution:

[tex]\mathsf{\theta=sin^{-1}(x)\qquad\qquad\dfrac{\pi}{2}\le \theta\le \dfrac{\pi}{2}}[/tex]

then,

[tex]\begin{array}{lcl} \mathsf{x=sin\,\theta}&\quad\Rightarrow\quad&\mathsf{dx=cos\,\theta\,d\theta\qquad\checkmark}\\\\\\ &&\mathsf{x^2=sin^2\,\theta}\\\\ &&\mathsf{x^2=1-cos^2\,\theta}\\\\ &&\mathsf{cos^2\,\theta=1-x^2}\\\\ &&\mathsf{cos\,\theta=\sqrt{1-x^2}\qquad\checkmark}\\\\\\ &&\textsf{because }\mathsf{cos\,\theta}\textsf{ is positive for }\mathsf{\theta\in \left[\dfrac{\pi}{2},\,\dfrac{\pi}{2}\right].} \end{array}[/tex]

So the integral [tex]\mathsf{(ii)}[/tex] becomes

[tex]\mathsf{=\displaystyle\int\! \theta\,cos\,\theta\,d\theta\qquad\quad(ii)}[/tex]

Integrate [tex]\mathsf{(ii)}[/tex] by parts:

[tex]\begin{array}{lcl} \mathsf{u=\theta}&\quad\Rightarrow\quad&\mathsf{du=d\theta}\\\\ \mathsf{dv=cos\,\theta\,d\theta}&\quad\Leftarrow\quad&\mathsf{v=sin\,\theta} \end{array}\\\\\\\\ \mathsf{\displaystyle\int\!u\,dv=u\cdot v-\int\!v\,du}\\\\\\ \mathsf{\displaystyle\int\!\theta\,cos\,\theta\,d\theta=\theta\, sin\,\theta-\int\!sin\,\theta\,d\theta}\\\\\\ \mathsf{\displaystyle\int\!\theta\,cos\,\theta\,d\theta=\theta\, sin\,\theta-(-cos\,\theta)+C}[/tex]

[tex]\mathsf{\displaystyle\int\!\theta\,cos\,\theta\,d\theta=\theta\, sin\,\theta+cos\,\theta+C}[/tex]

Substitute back for the variable x, and you get

[tex]\mathsf{\displaystyle\int\!sin^{-1}(x)\,dx=sin^{-1}(x)\cdot x+\sqrt{1-x^2}+C}\\\\\\\\ \therefore~~\mathsf{\displaystyle\int\!sin^{-1}(x)\,dx=x\cdot\,sin^{-1}(x)+\sqrt{1-x^2}+C\qquad\quad\checkmark}[/tex]

I hope this helps. =)

Tags: integral inverse sine function angle arcsin sine sin trigonometric trig substitution differential integral calculus

Which pair of variables has a clear causal link between the two named variables?
the number of hats sold and the number of mittens sold in a city
the amount of butter and the amount of bread consumed by a family
the number of notebooks sold and the number of pens sold in a stationery store
the number of air conditioners sold per day in a city and the daily temperature
the number of hours a person can swim and the depth of the pool
NextReset

Answers

Answer: The number of air conditioners sold per day in a city and the daily temperature

Step-by-step explanation:

We know that if there is a causal relationship between two variables then one variable is responsible for causing the other variable.

the number of hats sold and the number of mittens sold in a city.

there is no causal relationship between the variables since both are independent variables.

the amount of butter and the amount of bread consumed by a family .

there is no causal relationship between the variables since both are independent variables.

the number of notebooks sold and the number of pens sold in a stationery store .

there is no causal relationship between the variables since both are independent variables.

the number of air conditioners sold per day in a city and the daily temperature .

there can be causal relationship between the variables since by increasing or decreasing temperature the the number of air conditioners sold per day in a city can be increased or decreased respectively.

the number of hours a person can swim and the depth of the pool.

there is no causal relationship between the variables since both are independent variables.

If your teacher tells you to do questions 28 through 41 in your math book for homework, how many questions is that?

(Do not include units in your answer.)

Answers

41-28=13 questions, but you also have to do 41 and 28, so 15 questions

Answer:

14 questions.

Step-by-step explanation:

We have been given that your teacher tells you to do questions 28 through 41 in your math book for homework. We are asked to find he total number of questions.

Since we need to solve questions 28 through 41, this means we have to solve question number 28 and 41 as well.

We know that 28-37 would be 10 questions and 38-41 would be 4 questions.

[tex]\text{Total questions}=10+4[/tex]

[tex]\text{Total questions}=14[/tex]

Therefore, you need to solve 14 questions to complete the homework.

Damion found a new game system he wanted to buy. the price of the system was reduced from $250 to $200. by what percentage was the price reduced?

Answers

the price-reduced
250-200=50
50 is the amount reduced.
50/250=1/5 or 20%

What is y=5/6x-3 in standard form

Answers

The answer is negative 2.5 why because...

take out any common factors
so..
5/ 2(3×-1)

The perimeter of dawna's new flat screen television is 70 inches. the ration from length to width is 4:3. write and solve an algebraic equation to determine the dimensions of the television

Answers

I hope this helps you

Find the missing number in this proportion.

7 / 35 = ? / 28

Answers

Final answer:

To find the missing number in the proportion 7 / 35 = ? / 28, we can use the concept of cross-multiplication. The missing number is 5.6.

Explanation:

To find the missing number in the proportion 7 / 35 = ? / 28, we can use the concept of cross-multiplication. Cross-multiplication involves multiplying the numerator of one fraction by the denominator of the other fraction, and then setting the two products equal to each other. In this case, we have 7 * 28 = ? * 35. Solving for the missing number, we get:

7 * 28 = ? * 35
196 = ? * 35
? = 196 / 35
? = 5.6

So, the missing number is 5.6.

find two consecutive odd integers whose sum is -88

Answers

Instead of guessing (guess and check) or me giving you the answer, lets solve this mathematically.

first number is x. Second number is the next (or consecutive) odd number so its x+2 (can also do x-2)

Using (x+2)
x + (x+2) = -88
2x = -90
x = -45
and the other number will be -43

Using (x=2)
x + (x-2) = -88
2x = -86
x = -43
and the other number will be -45

The answer: -45, -43.
______________________
Explanation:
_________________________________
Let "x" = one of the odd integers.

Let "x + 2" = the other odd integer.
_________________________________
x + (x + 2) = - 88 ;

x + x + 2 = - 88;

2x + 2 = - 88 ; Now, subtract "2" from EACH side of the equation:
_______________________
2x + 2 - 2 = - 88 - 2 ; to get:
______________________________
2x = -90 ; Now, divide EACH side of the equation by "2"; to isolate "x" on one side of the question; and solve for "x";
_________________________________
2x/2 = -90/2 ;
______________
x = -45
_________
So one of the integers is -45. It is an odd number? Yes!

The next consecutive integer is: "(x+2)" ; or, (-45 + 2) = -43. Its it an odd number? Yes!

Are "-45", and "-43" consecutive odd integers? Yes!
_______________________________
The two consecutive integers are: -45 and -43.
_________________________
To check our work:
___________________
Do the sum of our two consecutive integers equal -88?
___________
-45 + (-43) =? -88 ? Yes!
___________________________

A, 4, D, H, 16, M, 25, _, _ What are the next two in the sequence?

Answers

I would say that the new two in sequence are S and 36.
There are two numbers between A and D, three between D and H, four between H and M, which means that S is the fifth number after M.
I think you are missing number 9 between D and H, which means that 4 + 5 =9, 9 + 7 = 16, 16 + 9 = 25, and 25 + 11 = 36, 2 is added to each number.

The sequence alternates between letters and squares of integers. The letters seem to follow a particular positional increment pattern, and the numbers are squares of consecutive positive integers. The missing elements in the sequence are R and 36.

The given sequence is: A, 4, D, H, 16, M, 25, _, _. This sequence appears to have two separate patterns interleaved. One pattern is a sequence of letters and the other is a sequence of numbers. For the letters part, A (1st letter), D (4th letter), H (8th letter), M (13th letter), so the next letters might follow an increasing pattern with the position of the letters in the alphabet. For the numbers, we have 4, 16, 25 which are squares of 2, 4, and 5 respectively. To solve for the next elements in the pattern, we would have to decipher the rule that connects the letters with their positions and the next squares of numbers.

The numbers are squares of consecutive positive integers: 2², 4², 5². The next number is 6² which is 36. Following the pattern in letters, after M (the 13th letter), the next letter should be the letter that is five positions ahead because the interval between the previous letters increased by 3 each time (D is 3 letters after A, H is 4 letters after D, M is 5 letters after H), so the next letter should be R (the 18th letter, which is 5 letters after M).

Therefore, the sequence should continue with R, 36.

Arrange the following polynomial into descending order for x, then interpret the degree of the 2nd term.

7x3y3 + 4 − 11x5y2 − 3x2y

Answers

Answer:

Always double check first but I am pretty sure that it is 6

What is the general term for the sequence 1,6,11,16,...?

n + 5
5n - 4
5n + 1

Answers

5n-4
Just plug numbers into it. Make this a table.
n 0 1 2 3
y 1 6 11 16

Answer:

Step-by-step explanation:

The given sequence is:

1,6,11,16,...

Since, the sequence is Arithmetic progression, therefore

The general term for the sequence is:

[tex]A_{n}=a+(n-1)d[/tex]

where a is the first term of the sequence and d is common difference.

Substituting the given values, we get

[tex]A_{n}=1+(n-1)5[/tex]

[tex]A_{n}=1+5n-5[/tex]

[tex]A_{n}=5n-4[/tex]

which is the required general term.

Thus, option B is correct.

Alex has 520 yards of fencing to enclose a rectangular area.

A retangle that maximises the enclosed area has a length of _ yards and a width of _ yards.

The maxium area is _____ yards

Answers

Perimeter =2w+2L= 520.
We can solve this by understanding that the area is maximized by a square
Therefore L=w.

p=2w+2w=520=4w
w=130

Area

A=wL=130(130)= 16900 square yards

The first thing we are going to do for this case is define variables.

We have then:

w: width

l: length

The perimeter is given by:

[tex] 2w + 2l = 520
[/tex]

The area is given by:

[tex] A = w * l
[/tex]

The area as a function of a variable is:

[tex] A (w) = w * (260-w)
[/tex]

Rewriting we have:

[tex] A (w) = -w ^ 2 + 260w
[/tex]

To obtain the maximum area, we derive:

[tex] A '(w) = -2w + 260
[/tex]

We equal zero and clear the value of w:

[tex] -2w + 260 = 0

2w = 260
[/tex]

[tex] w = \frac{260}{2}

w = 130
[/tex]

Then, the length is given by:

[tex] l = 260 - w

l = 260 - 130

l = 130
[/tex]

Finally, the maximum area obtained is:

[tex] A = w * l

A = 130 * 130

A = 16900
[/tex]

Answer:

A retangle that maximizes the enclosed area has a length of 130 yards and a width of 130 yards.

The maxium area is 16900 square yards

What is the range of the function h(x) = -8x?

Answers

Final answer:

The range of the function h(x) = -8x is all real numbers, as there are no restrictions on the output the function can produce. This is typical of a linear function.

Explanation:

The range of a function refers to the possible outputs it can produce. In the case of the function h(x) = -8x, it is a linear function, and there are no restrictions on the values that x can take, meaning x can be any real number between -∞ and +∞. The output, h(x), therefore, can be any real number, also between -∞ and +∞, given that it will be the result of -8 multiplied by x. Therefore, the range of the function h(x) = -8x is all real numbers from -∞ to +∞.

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. SOMEONE PLEASE HELP ME?!?!

5. This is the Reed family budget. How much discretionary income does the family have each month?
Housing $800.00
Groceries $425.00
Utilities $285.00
Miscellaneous $120.00
Transportation $150.00
Insurance $286.00
Savings $200.00
Healthcare $60.00
Clothing $50.00

Total Expenses $2,376.00
Net income $2,850.00
$______

8. Paula created a monthly budget. A pie graph shows a clear picture of where her money is spent. How much of the circle would be shaded for the total of housing, utilities, food, and insurance?
Housing $500.00
Insurance $283.00
Food $225.00
Utilities $174.00
Miscellaneous $75.00
Transportation $64.00
Clothing $50.00
Medical $25.00
Savings $20.00

10. You are making a pie graph of the expenses in the Reed family budget. How much of the pie graph would be used to represent the amount spent on housing?
Housing $800.00
Utilities $285.00
Groceries $425.00
Miscellaneous $120.00
Transportation $150.00
Insurance $286.00
Savings $200.00
Healthcare $60.00
Clothing $50.00

Total Expenses $2,376.00
Net income $2,850.00
A. half of the circle
B. less than half
C. over 75% of the circle
D. 50% to 75%
Total Expenses $1,416.00
A. half of the circle
B. less than half
C. over 75% of the circle
D. 50% to 75%

Answers

Q5. The answer is $474.

Discretionary income = Net income - Total Expenses
Total Expenses = $2,376.00
Net income = $2,850.00

Discretionary income = $2,850.00 - $2,376.00 = $474

Q8. The answer is 83.47% (over 75% of the circle).

Total Expenses = Housing + Insurance + Food + Utilities + Miscellaneous + Transportation + Clothing + Medical + Savings

Total Expenses = $500.00 + $283.00 + $225.00 + $174.00 + $75.00 + $64.00 + $50.00 + $25.00 + $20.00 = $1416

Total of housing, utilities, food, and insurance is: $500.00 + $174.00 + $225.00 + $283.00 = $1182

Calculate the percent of $1182 in $1416:
$1182 : $1416 * 100 = 83.47%

Q10. The answer is 33.67% (less than half).

Total Expenses $2,376.00
Housing = $800.00

Calculate the percent of $800 in $2,376.00:
$800 : $2,376.00 * 100 = 33.67%

What are the least common multiples of 7 and 11

Answers

I think is the least common number is 77 because it multiple of 7 and 11 both

NEED YOUR HELP!! I WILL UPVOTE!
Combining Like Terms:

Solve the equations by combining like terms. Show all the steps.
Then write two of your own problems where you combine like terms. Show all steps, as well as your solution.
1. 16x − 4x = -48

Answers

12x=-48 (divide 12 from both sides)
x=-4

10y-13y=30
-3y=30 (divide -3 from both sides)
-10=y

10x+14x=48
24x=48 (divide 24 from both sides)
x=2

Factor completely: 2x2 + 6x − 80

(2x − 5)(x + 8)

(2x − 10)(x + 8)

2(x − 5)(x + 8)

2(x − 10)(x + 8)

...?

Answers

Correct answer is C.

[tex]2x^2+6x-80 \\2(x^2+3x-40) \\2(x^2+8x-5x-40) \\2(x(x+8)-5(x+8)) \\2(x+8)(x-5)[/tex]

Quadratic functions are functions that has a degree of 2. The factored form of the function is (2x-10)(x+8)

Factorization of functions

Quadratic functions are functions that has a degree of 2. Given the function below;

2x^2 + 6x - 80

Factorize

2x^2+16x - 10x - 80

Group

(2x^2+16x)-(10x+80)

Factor out the GCF

2x(x + 8)-10(x+8)

(2x-10)(x+8)

Hence the factored form of the function is (2x-10)(x+8)

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If 3x-1=11, then 2x=?

Answers

Final answer:

To find 2x, we first need to solve for x in the equation 3x - 1 = 11. We isolate x by adding 1 to both sides and divide by 3 to obtain x = 4. Finally, multiplying x by 2 gives us 2x = 8.

Explanation:

To solve the equation 3x - 1 = 11 for 2x, we need to isolate x first. Adding 1 to both sides, we get 3x = 12. Dividing both sides by 3, we find that x = 4. Now, to find 2x, we simply multiply x by 2, which gives us 2(4) = 8.

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which of the following represents the most accurate estimation if 75-33?

Answers

40 is the most accurate.

You could round 75 to 80 and 33 to 30. Then subract to get 50

you have a full job that pays 2400 per month you decide to take a part time job delivering newspapers that pay 200 per week if 15% is withheld for taxes from both jobs how much would you make in a year after taxes

Answers

ft (full time)= $2,400/ monthpt (part time)= $200/ week15% taken from taxes------------------------- 1 year= 12 months; 1 month= 4 weeks (12*2,400) + (4*12*200)= $38,400 you made in a year I set up the problem this way because you want to know how much you made that whole year, so if there are 12 months in a year, and you get paid $2,400 a month, then from your full time job you ear (12*2,400). From your PT job you make $200 a week, there are 4 weeks in a month and 12 months in a year, so to calculate what you earned from your PT job, you do: 4*12*200 15% of what you made is deducted from taxes:0.15(38,400)= $5,760 After taxes, you made:$38,400-$5760= $32,640

The number 72 is between what two perfect squares? Enter a numerical answer only.

Answers

Well a perfect square looks like this:

6 x 6
2 x 2

So the number 72 is between the PRODUCT of two perfect squares such as those.

One product has to be above 72, and the other below it.

So lets multiply.

8 x 8 = 64
9 x 9 = 81

Oh look at that, 72 is between 64 and 81.

64=8^2
81 = 9^2

72 is between what two perfect squares 64=8^2 and 81 = 9^2

What does the inequality x + 3 ≤ 2 say?

A number and three is at most two.
A number and three is less than two.
A number and three is at least two.
A number and three is no less than two.

Answers

A number and three is at most 3.

Answer:

A number and three is at most 3.

Step-by-step explanation:

Your poor health causes you to miss one work day every two weeks. You do not get paid when you are out sick. You normally work 8 hours a day and get paid $9.29 per hour. How much pay are you losing each year

Answers

Final answer:

The annual loss of income due to missing one work day every two weeks at $9.29 per hour, working 8 hours per missed day, is $1,932.32.

Explanation:

To calculate the amount of pay being lost each year due to missing one work day every two weeks, we need to consider the weekly work schedule and hourly wage.

Step-by-Step Calculation

First, determine the hourly wage and the number of hours missed per day. In this case, the hourly wage is $9.29 and each missed day accounts for 8 hours of work.
Second, calculate the daily loss of income due to illness. Multiply the hourly wage by the number of hours missed: $9.29 x 8 = $74.32.
Third, calculate how many work days are missed per year. Since one work day is missed every two weeks, and there are 52 weeks in a year, there would be a total of 52 / 2 = 26 missed work days per year.
Finally, multiply the daily loss of income by the number of missed work days per year to find the annual loss: $74.32 x 26 = $1,932.32.

The annual loss of income due to missing one day of work every two weeks at an hourly wage of $9.29 is $1,932.32.

Abcd is a rectangle. Find the length of each diagonal. .AC= 3y/5 BD=3y-4

Answers

I hope this helps you

Answer:

AC = BD = 1 unit

Step-by-step explanation:

Given : length of diagonal of rectangle ABCD [tex]AC=\frac{3y}{5}[/tex] and [tex]BD=3y-4[/tex]

We have to find the length of diagonal.

We know In rectangle diagonal are of equal lengths.

Therefore, for rectangle ABCD diagonals AC= BD

Substitute the values, we get,

[tex]\frac{3y}{5}=3y-4[/tex]

Cross multiply , we get

[tex]3y=5(3y-4)[/tex]

On simplyfy , we get

[tex]3y=15y-20[/tex]

Solve for y , we get

[tex]15y-3y=20[/tex]

[tex]12y=20[/tex]

Divide both side by 12, we get,

[tex]y=\frac{20}{12}=\frac{10}{6}[/tex]

Thus, put the values of y in AC and BD to find the length of diagonals , we get,

[tex]AC=\frac{3y}{5}=\frac{3}{5}\times\frac{10}{6}=1[/tex]

Similarly for BC, we get,

[tex]BD=3y-4=3(\frac{10}{6})-4=5-4=1[/tex]

Thus, AC = BD = 1 unit

Antarctica comprises about 10.5% of the total land area on Earth. Antarctica has a surface area of about 5,400,000 square miles. What is the total land area on Earth?

Answers

Solution
(5.4 x 10^6)/10.5 = 514285.71
514285.71 x 100 = 51,428,571 square miles

isabella bought 1.1 kilograms of top quality hamburger meat at $5.00 per kilogram. how much did it cost?

Answers

1.1 kg * $5 / kg = $5.50

The cost of 1.1 kilograms of hamburger meat at $5.00 per kilogram is $5.50

Multiply the weight of the meat (1.1 kg) by the price per kilogram ($5.00):

1.1 kg x $5.00/kg = $5.50.

Therefore, it cost Isabella $5.50 to buy 1.1 kilograms of top-quality hamburger meat.

Round this number 15,680

Answers

nearest ten thousand : 20,000
nearest thousand: 16,000
nearest hundred: 15,700
nearest ten: 15,680

hope this helps you

Other Questions

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