Answer:
Solution is x= 0 , x = \frac{1}{14} , x = \frac{-1}{12}
Step-by-step explanation:
Given, equation is \sqrt[3]{15x-1} + \sqrt[3]{13x+1} = 4\sqrt[3]{x} →→→ (1)
Now, by cubing the equation on both sides, we get
( \sqrt[3]{15x-1} + \sqrt[3]{13x+1} )³ = (4\sqrt[3]{x})³
⇒ (15x-1) + (13x+1) + 3×\sqrt[3]{15x-1}× \sqrt[3]{13x+1} (\sqrt[3]{15x-1} + \sqrt[3]{13x+1}) = 64 x.
(since (a+b)³ = a³ + b³ + 3ab(a+b) ).
⇒ 28x + 3×\sqrt[3]{15x-1}× \sqrt[3]{13x+1} (\sqrt[3]{15x-1} + \sqrt[3]{13x+1}) = 64x.
(since from (1), \sqrt[3]{15x-1} + \sqrt[3]{13x+1} = 4\sqrt[3]{x} )
⇒ 12×\sqrt[3]{15x-1}× \sqrt[3]{13x+1} (\sqrt[3]{15x-1}×\sqrt[3]{x}= 36x.
⇒ 3x = [tex]\sqrt[3]{(15x-1)(13x+1)(x)}[/tex] .
Now, once again cubing on both sides, we get
(3x)³ = ([tex]\sqrt[3]{(15x-1)(13x+1)(x)}[/tex])³.
⇒ 27x³ = (15x-1)(13x+1)(x).
⇒ 27x³ = 195x³ + 2x² - x
⇒ 168x³ + 2x² - x = 0
⇒ x(168x² + 2x -1) = 0
⇒ by, solving the equation we get ,
x = 0 ; x = \frac{1}{14} ; x = \frac{-1}{12}
therefore, solution is x= 0 , x = \frac{1}{14} , x = \frac{-1}{12}
8 4583/5000 simplified
Answer:
it's already simplified :) your welcome
A cell phone plan cost $200 to start. Then there is a $50 charge each month.
1. what is the total cost (start up fee and monthly charge) to use the cell phone plan for 1 month?
2. what is the total cost for x months?
Answer:
1) $250
2) $200 + $50x
Step-by-step explanation:
1)
$200 (start up fee) + $50 * ( 1 month ) = $200 + $50 = $250
2)
$200 (start up fee) + $50 * ( x months ) = $200 + $50x
Hope this helps :)
dr.smith prescribes gentamicin for a patient with a serious bacterial infection . if a 750 ml bag contains 300 mg gentamicin and the patient receives 300 ml how many mg of gentamicin did tge patient receive?
Answer:
120 mg
Step-by-step explanation:
750 ml 300mg
300 ml x mg
750 / 300 = 300 / x
x = (300 x 300) / 750 = 120 mg
Find the length of an arc
made by an 80° central
angle in a circle with a
10 ft. radius.
I'm not an expert at this but the answer should be 13.9 or 14
Final answer:
The length of the arc made by an 80° central angle in a circle with a 10 ft. radius is approximately 13.96 ft.
Explanation:
In order to find the length of an arc made by an 80° central angle in a circle with a 10 ft. radius, we need to use the formula for the circumference of a circle. The formula for the circumference is C = 2πr, where C is the circumference and r is the radius. In this case, the angle is 80°, so we need to find the fraction of a full circle that the angle represents. Since a full circle is 360°, the fraction is 80/360 = 2/9. Therefore, the length of the arc is 2/9 times the circumference of the circle with a 10 ft. radius.
To find the circumference of a circle with radius 10 ft., we can use the formula C = 2πr. Plugging in the value of the radius, we get C = 2π(10) = 20π ft. Since the length of the arc is 2/9 times the circumference, the length of the arc is (2/9)(20π) ft. Simplifying, we get (40/9)π ft. This is approximately 13.96 ft. Therefore, the length of the arc made by an 80° central angle in a circle with a 10 ft. radius is approximately 13.96 ft.
The sum of 3 consecutive even numbers is 408. What is the largest of the numbers
Answer:135,136,137
Step-by-step explanation:
408 divided by 3=136
136-1=135
136+1=137
135,136,137
The largest number of the three consecutive even numbers that sum to 408 is 138.
Explanation:The problem is a classic arithmetic sequence problem in mathematics, where a common difference exists between each number. For consecutive even numbers, this difference is 2. If the sum of three consecutive even numbers is 408, we can form the equation 3n+6=408 (since the first number is 'n', the next is 'n+2', and the following is 'n+4'). Solving this equation gives us n=134, hence the sequence of numbers is 134, 136 and 138. The largest number in this sequence is 138.
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When Julia is writing a first draft, there is 0.7 probability that there will be no spelling mistakes on a page. One day, Julia writes a first draft that is 4 pages long. Assuming that Julia is equally likely to have a spelling mistake on each of the 4 pages, what is the probability that she will have no spelling mistakes on at least one of them?
Answer:
The required probability is given by, 0.9919.
Step-by-step explanation:
Let, X be the random variable denoting the no. of pages among those 4 pages which Julia writes where she makes no spelling mistake.
clearly,
X [tex]\sim[/tex] Binomial (4, 0.7)
So, P(X = x) = [tex]^4C_{x} \times (0.7)^{x} \times (0.3)^{(4 - x)}[/tex]
[when x = 0, 1, 2, 3, 4]
= 0 otherwise
According to the question, we are to find out P(X ≥ 1) .
Now, P(X ≥ 1)
= 1 - P(X = 0)
= [tex] 1 - (^4C_{0} \times (0.7)^{0} \times (0.3)^{4})[/tex]
= [tex] 1 - 0.0081[/tex]
= 0.9919
So, the required probability is given by, 0.9919
The probability that Julia will have no spelling mistakes on at least one of the pages is approximately 99.19%.
To determine the probability that Julia will have no spelling mistakes on at least one of the four pages she writes, we can first find the probability that she will make at least one spelling mistake on all four pages and then subtract this from 1.
The probability that there will be a spelling mistake on a page:
= 1 - 0.7 = 0.3.
Since the probability of a spelling mistake on each page is independent, we can multiply the probabilities for the four pages together.
The probability of at least one mistake on all four pages:
= 0.3 x 0.3 x 0.3 x 0.3 = 0.3⁴= 0.0081.
The probability that there will be no spelling mistakes on at least one page
= 1 - 0.0081 = 0.9919 or about 99.19%.
So, the probability is 99.19%.
please help me I can fail math
Tonya uses the greatest common factor and the distributive property to rewrite this sum: 96 + 36
Which expression does Tonya write?
4(24 + 9)
6(16 + 6)
12(8 + 3)
18(5 + 2)
Answer:
C) 12(8+3)
Step-by-step explanation:
Answer:C) 12(8+3)
Step-by-step explanation: i took the test
please help me with this question.
Answer:
b. Shift left 3 units
Step-by-step explanation:
You're given
y = √(x + 3)
y = √(x - (-3))
y = √(x - amount_shifted)
amount shifted = -3
so shifted 3 units and the negative means it's shifted to the left
what two digit number is a multiple of 5 and has 3 less tens than ones
Answer:
25
Step-by-step explanation:
If a two digit number is a multiple of 5, then it ends with 0 or with 5.
If a two digit number ends with 0, then the number of ones is 0 and the number of tens must be 3 less that is impossible.
Hence, this two digit number must end with 5. If it ends with 5, then the number of ones is 5 and number of tens must be 5 - 3 = 2.
Therefore, the number is 25.
The question is about two-digit numbers that are multiples of 5 and have fewer tens than ones. Numbers such as 15, 25, 35, 45, 50, 65, 75, 85, and 95 satisfy these conditions.
Explanation:The subject of this question is a mathematical problem solving task regarding two-digit numbers and their properties. The most important criteria are that the number is a multiple of 5 and has less tens than ones. First, multiples of 5 are numbers that end in 0 or 5. Secondly, having less tens than ones implies that the digit in the ones place must be greater than the digit in the tens place.
An example of a number that fulfills these conditions would be 15. Here, the digit in the ones place (5) is greater than the digit in the tens place (1). Also, 15 is a multiple of 5 because it can be divided by 5 without leaving a remainder.
However, 15 is just one of many possible answers. Other numbers that satisfy these conditions are: 25, 35, 45, 50, 65, 75, 85, and 95.
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The sum of 4 times a number and 15 is 47. Find the number.
Answer:
The number is 8.
Step-by-step explanation:
Write an equation then solve by isolating the variable.
let x be the number
4x + 15 = 47 Subtract 15 from both sides
4x = 47 - 15
4x = 32 Divide both sides by 4
x = 32/4
x = 8
Therefore the number is 8.
Answer:
8
Step-by-step explanation:
How many square centimeters are in a rectangle that measures 1 meter by 3 meters
Answer:
30,000 cm^2.
Step-by-step explanation:
The area = 3*1 = 3 square meters.
There are 100^2 = 10,000 cm^2 in a square meter
So the area in square centimeters is 3 * 10,000 = 30,000.
Sam & Avery are making small and large birdhouses for a craft show. Small houses sell for $10 and large houses sell for $15. It takes Sam 3 hours to build small houses and 5 hours to build large houses. He only has 24 hours of building time. Avery only has time to decorate 12 houses of either size. How many small & large houses should be made to make the most money?
If Sam had 30 days instead of only 24 hours and Avery had time to decorate 100 birdhouses instead of only 12, discuss solution methods you used and why.
Answer:
8 small houses; 0 large houses80 small houses; 0 large housesStep-by-step explanation:
a) The maximum number of houses Sam can build in 24 hours is 8, so the constraint is in construction, not decoration. For each small house Sam constructs, he makes $10/3 = $3.33 per hour of work. For each large house Sam constructs, he makes $15/5 = $3.00 per hour. The most money is to be made by building only small houses.
Sam should make 8 small houses and 0 large houses in 24 hours.
__
b) If Sam works 8-hour days, then he can complete at most 80 small houses. The constraint remains in construction, so the answer is the same: build only small houses.
_____
If Sam works more than 16 2/3 hours per day, he can build 100 large houses or more, so the constraint moves to decoration. The decorator makes more money by decorating large houses, so all the effort should go to construction of large houses.
If Sam works between 10 and 16 2/3 hours per day, the best revenue will come from some mix. The problem statement is unclear as to how many hours Sam works in 30 days.
4y+3y=21 simplify as much as possible
Answer:
y=3
Step-by-step explanation:
Add the y and divide
7y=21
21/7=3
y=3
Solve the inequality for u
-5u+27 [less than or equal to] 2
Answer:
5≤u
Step-by-step explanation:
Put the words and numbers into an equation:
-5u+27≤2
Put all like terms on one side:
27-2≤5u ---> Do you see what I did there? Now you don't have to work with negatives. :)
Simplify:
25≤5u
Solve:
5≤u
:)
The garden view hotel is seventeen less than twice the height of the plaza hotel. If their combined height is 361 feet, how tall is the gardenview hotel?
The garden view hotel is 235 feet tall
Step-by-step explanation:
The given is:
The garden view hotel is seventeen less than twice the height of the plaza hotelTheir combined height is 361 feetWe need to find the height of the garden view hotel
Assume that the height of garden view hotel is x feet and the height of the plaza hotel is y feet
∵ The height of the garden view hotel = x feet
∵ The height of the plaza hotel = y feet
∵ The height of the garden view hotel is 17 less than twice the
height of the plaza hotel
- That means x is less than 2 × y by 17, equate x by the difference
of 2 × y and 17
∴ x = 2y - 17 ⇒ (1)
∵ Their combined height = 361 feet
∴ x + y = 361
- Find y in terms of x by subtraction x from both sides
∴ y = 361 - x ⇒ (2)
Substitute y in equation (1) by equation (2)
∵ x = 2(361 - x) - 17
- Simplify the right hand side
∴ x = 722 - 2x - 17
- Add like terms
∴ x = 705 - 2x
- Add 2x to both sides
∴ 3x = 705
- Divide both sides by 3
∴ x = 235
The garden view hotel is 235 feet tall
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The height of the Gardenview Hotel is 235 feet, which we found by first creating a system of equations using the information given and then solving by substitution.
To find the height of the Gardenview Hotel, let's create a system of equations based on the information given. Let G be the height of the Gardenview Hotel and P be the height of the Plaza Hotel. We are told that the Gardenview Hotel is seventeen less than twice the height of the Plaza Hotel, which we can express as G = 2P - 17. Additionally, we know their combined height is 361 feet, so G + P = 361.
Now we can solve the system of equations step by step:
Substitute the expression for G from the first equation into the second equation: (2P - 17) + P = 361.
Combine like terms: 3P - 17 = 361.
Add 17 to both sides of the equation: 3P = 378.
Divide both sides of the equation by 3 to find the height of the Plaza Hotel: P = 126.
Now use the value of P to solve for G using the first equation: G = 2(126) - 17.
Simplify to find the height of the Gardenview Hotel: G = 252 - 17.
Thus, the height of the Gardenview Hotel is 235 feet.
Miss Isaac took her family out to eat at Jason’s deli.The meal came to $25.40.Miss Isaac wanted to tip the waitress 18% and sale tax is 5.5%.Find the total price of their meal after tax and tip
Mindy and Troy combined ate 9 pieces of cake. Mindy ate 3 pieces of cake and Troy at 1/4 of the whole cake. Find C, the total pieces of cake. Also include the equation
Answer:
The total pieces of cake are 24
Step-by-step explanation:
Linear equations
It's a relation between one or more variables and or numbers, connected with the equal sign. An example is 4x-5=7, or 2(x+y)=7-(x-y)
This problem can be easily solved without the use of equations, but we are required to.
We know Mindy and Troy combined ate 9 pieces of cake, we also know that Mindy ate 3 pieces of cake. It leaves 6 pieces to Troy. Since Troy ate 1/4 of the whole cake, then
[tex]\displaystyle \frac{1}{4}X=6[/tex]
Where X is the number of pieces of cake
Solving for X
[tex]X=(4)(6)=24\ pieces[/tex]
in 1982, a belt sold for $11.50 ten years later, the price of the belt increased by 80%. How much more did it sell for in 1992? How much would the belt cost in 1992?
Answer:
It sold for $9.20 more in 1992 than in 1982.
It sold for $20.70 in 1992.
Step-by-step explanation:
The price in 1982 was $11.50.
The price increased by 80% of $11.50.
We need to find 80% of $11.50.
To find a percent of a number, multiply the percent by the number.
80% of $11.50 =
= 80% * $11.50
= 0.8 * $11.50
= $9.20
It sold for $9.20 more in 1992.
The price in 1992 is the original price of the belt plus the amount of increase.
$11.50 + $9.20 = $20.70
It sold for $20.70 in 1992 than in 1982.
Which function has a range of vy s 5)?
of(x) = (x - 4)2 + 5
O (x) = -(x - 4)2 + 5
o f(x) = (x - 5)2 + 4
Of(x) = -(x - 5)2 + 4
Answer:
see the explanation
Step-by-step explanation:
Verify the range of each quadratic function
case 1) we have
[tex]f(x)=(x-4)^2+5[/tex]
This is a vertical parabola open upward (the leading coefficient is positive)
The function is written in vertex form
The vertex represent a minimum
The vertex is the point (4,5)
The range is the interval [5,∞)
[tex]y\geq 5[/tex]
case 2) we have
[tex]f(x)=-(x-4)^2+5[/tex]
This is a vertical parabola open downward (the leading coefficient is negative)
The function is written in vertex form
The vertex represent a maximum
The vertex is the point (4,5)
The range is the interval (-∞,5]
[tex]y\leq 5[/tex]
case 3) we have
[tex]f(x)=(x-5)^2+4[/tex]
This is a vertical parabola open upward (the leading coefficient is positive)
The function is written in vertex form
The vertex represent a minimum
The vertex is the point (5,4)
The range is the interval [4,∞)
[tex]y\geq 4[/tex]
case 4) we have
[tex]f(x)=-(x-5)^2+4[/tex]
This is a vertical parabola open downward (the leading coefficient is negative)
The function is written in vertex form
The vertex represent a maximum
The vertex is the point (5,4)
The range is the interval (-∞,4]
[tex]y\leq 4[/tex]
There are 75 balloons in each package how many balloons are in 20 packages
Answer:
1,500
Step-by-step explanation:
75•20
Answer:1500
Step-by-step explanation: 75 times 20 = 1500
16. A farmer plants 0.4 of a field with wheat.
The field is 2.3 acres.
Part A
Shade the grids to model the multiplication. How do i shade the grid
Step-by-step explanation:
the farmer plants 0.4 of the total field which is 2.3 acres
⇒0.4×2.3= 0.92 acres
now draw a grid of area 2.3 acres and in that area shade 0.92 acres.Use a proper scale to draw the grid. It will a be pictorial representation of the proper and its solution.
Can someone plzzz help me with numbers 8 and 9 plzzz show work plzzz
Answer:
For question 9: Angle 1= 20, angle 2= 70, angle 3= 70, angle 4= 20, angle 5= 20, angle 6= 70, and angle 7= 70.
Step-by-step explanation:
10.31988 to the nearest hundredth
Answer:
10.32
Step-by-step explanation:
10.31988
the 9 makes the 1 to a 2 so...
10.32
What is the simplified expression for the expression below?
1/2 (8x+4)+1/3(9-34)
5x + 5
7x + 1
Ox+7
3x + 5
Answer:
4x-19/3
Step-by-step explanation:
1/2(8x+4)+1/3(9-34)
8/2x+4/2+9/3-34/3
4x+2+3-34/3
4x+5-34/3
4x-19/3
Answer:
3x+5
Step-by-step explanation:
You decide to begin selling glow sticks at the local star wars convention. Your cost for each glow stick is $2.02 plus you have to pay a fixed weekly fee of $190 for the booth. Your plan is to sell each glow stick for $3.60.
You would have to sell approximately 52 bracelets per week in order to pay your fee.
190 ÷ 3.60 = 52.7
This is your net profit after covering both the cost of the glow sticks and the booth fee. The actual profit you make will depend on how many glow sticks you manage to sell at the convention.
To determine the profit you make from selling glow sticks at the Star Wars convention, you can calculate the profit per unit and the total profit considering the costs and selling price.
Here are the key values:
Cost per glow stick: $2.02
Fixed weekly fee for the booth: $190
Selling price per glow stick: $3.60
Now, let's calculate the profit per unit:
Profit per unit = Selling price per unit - Cost per unit
Profit per unit = $3.60 - $2.02 = $1.58
This means you make a profit of $1.58 for each glow stick you sell.
To find the total profit, you need to consider how many glow sticks you sell. Let's assume you sell 'x' glow sticks. Your total profit can be calculated as:
Total Profit = Profit per unit × Number of Units Sold
Total Profit = $1.58x
Now, you need to take into account the fixed weekly booth fee of $190. So, your total profit after deducting the booth fee will be:
Total Profit - Booth Fee = $1.58x - $190
This is your net profit after covering both the cost of the glow sticks and the booth fee. The actual profit you make will depend on how many glow sticks you manage to sell at the convention.
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Which shapes have the same volumes as the given rectangular prism ?
search for the best and accurate answers
One side of a rectangle is 3 feet shorter than twice the other side find the sides if the area is 209 ft.²
The one side of rectangle is 11 feet and other side is 19 feet.
Step-by-step explanation:
Given,
Area of rectangle = 209 square feet
Let one side of rectangle = w
other side of rectangle = 2w-3
Area of rectangle = One side * other side
[tex]209=w*(2w-3)\\209=2w^2-3w[/tex]
[tex]0=2w^2-3w-209\\2w^2-3w-209=0[/tex]
[tex]2w^2+19w-22w-209=0\\w(2w+19)-11(2w+19)=0\\(2w+19)(w-11)=0[/tex]
Either;
2w+19=0 =>2w=-19
Or,
w-11=0 => w=11
As length cannot be negative, therefore,
One side of rectangle = 11 feet
Other side of rectangle = 2w-3 = 2(11)-3 = 22-3 = 19 feet
The one side of rectangle is 11 feet and other side is 19 feet.
Keywords: rectangle, area
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Which is true about the degree of the sum and difference of the polynomials 3x5y – 2x3y4 – 7xy3 and –8x5y + 2x3y4 + xy3?
Both the sum and difference have a degree of 6.
Both the sum and difference have a degree of 7.
The sum has a degree of 6, but the difference has a degree of 7.
The sum has a degree of 7, but the difference has a degree of 6.
Answer:
The option " The sum has degree of 6 , but the difference has a degree of 7 " is correct.
Step-by-step explanation:
Given that the sum and difference of the polynomials [tex]3x^5y-2x^3y^4-7xy^3[/tex] and [tex]-8x^5y+2x^3y^4+xy^3[/tex]
Now sum the given polynomials :[tex]3x^5y-2x^3y^4-7xy^3+(-8x^5y+2x^3y^4+xy^3)[/tex]
[tex]=3x^5y-2x^3y^4-7xy^3-8x^5y+2x^3y^4+xy^3[/tex]
[tex]=-5x^5y+0-6xy^3[/tex]
[tex]=-5x^5y-6xy^3[/tex]
Therefore [tex]3x^5y-2x^3y^4-7xy^3+(-8x^5y+2x^3y^4+xy^3)=-5x^5y-6xy^3[/tex]
In the simplified sum of the polynomials [tex]-5x^5y-6xy^3[/tex] we have the degree is 6
Now difference the polynomials[tex]3x^5y-2x^3y^4-7xy^3-(-8x^5y+2x^3y^4+xy^3)[/tex]
[tex]=3x^5y-2x^3y^4-7xy^3+8x^5y-2x^3y^4-xy^3[/tex]
[tex]=11x^5y-4x^3y^4-8xy^3[/tex]
Therefore [tex]3x^5y-2x^3y^4-7xy^3-(-8x^5y+2x^3y^4+xy^3)=11x^5y-4x^3y^4-8xy^3[/tex]
In the simplified difference of polynomials [tex]11x^5y-4x^3y^4-8xy^3[/tex] we have the degree is 7
Therefore the option " The sum has degree of 6 , but the difference has a degree of 7 " is correct
Answer:
The sum has a degree of 6, but the difference has a degree of 7.
Step-by-step explanation:
TIMEDDDDD PLEASE ANSWER 15 POINTS
Jolianne worked half as many hours as Andrew. Jolianne makes $10 per hour and has saved $27. Andrew makes $8 per hour and has no money saved. After getting paid, they have the same amount of money.
Andrew claims that only his table and equation are correct, but Jolianne claims that both tables and equations are valid. Which statement regarding their claims is true?
Andrew is correct because t cannot be used to represent the number of hours Jolianne worked.
Andrew is correct because Jolianne worked half as many hours as he did and he did not work twice as many hours as she did.
Jolianne is correct because if one lets t = hours Andrew worked, then his equation is valid. If one lets t = hours Jolianne worked, then Andrew worked twice as many so her equation is valid, too.
Jolianne is correct because when solving t in her equation, t = hours Jolianne worked, and when solving for t in Andrew’s equation, t = hours Jolianne worked so they are equal.
Answer:
Andrew is correct because Jolianne worked half as many hours as he did and he did not work twice as many hours as she did
Step-by-step explanation:
Let
x ----> number of hours worked by Jolianne
t ----> number of hours worked by Andrew
we know that
The number of hours worked by Jolianne multiplied by $10 per hour plus $27 saved must be equal to the number of hours worked by Andrew multiplied by $8
The linear equation that represent this situation is
[tex]10x+27=8t[/tex] ----> equation A
[tex]x=\frac{t}{2}[/tex] -----> equation B
substitute equation B in equation A
[tex]10(\frac{t}{2})+27=8t[/tex]
so
Andrew's table and equation is correct
Jolianne's table and equation are not correct, because Andrew did not work twice as many hours as she did
Answer:
the answer is B :)
Step-by-step explanation: