What’s b = 3x + 9xy ? Solving the equation for x.
Answer:
x= [tex]\frac{b}{3+9y}[/tex] .
Step-by-step explanation:
Given : b = 3x + 9xy.
To find : Solving the equation for x.
Solution : We have given
b = 3x + 9xy.
Taking common 3x from right hand side
b = 3x ( 1 + 3y).
On dividing both sides by 1 + 3y .
[tex]\frac{b}{1+3y}[/tex] = 3x
On dividing both sides by 3
[tex]\frac{b}{(3+9y)}[/tex] = x .
Therefore, x =[tex]\frac{b}{(3+9y)}[/tex] .
x = b/(3 + 9y)
Further explanation[tex]\boxed{ \ b = 3x + 9xy \ }[/tex]
In the equation, there are three variables, namely b, x, and y. The coefficients of x and xy are 3 and 9, respectively.
We need solving for x from the equation.
Let us reposition it by swapping sides. The aim is to prepare x as the subject on the left-hand side.
[tex]\boxed{ \ 3x + 9xy = b \ }[/tex]
On the left-hand side, 3x is pulled out of the brackets because it is the GCF (The Greatest Common Factor) of 3x and 9xy.
[tex]\boxed{ \ 3x(1 + 3y) = b \ }[/tex]
Both sides divided by 3(1 + 3y).
[tex]\boxed{ \ x = \frac{b}{3(1 + 3y)} \ }[/tex]
Hence, the final result is
[tex]\boxed{\boxed{ \ x = \frac{b}{3 + 9y} \ }}[/tex]
That's all the steps to get x as a subject.
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An Apple orchard sells apples in bags of 10. the orchard sold a total of 2,430 apple One day. how many bags of apples was this?
X/3 - x/5 = 2/15 what does x equal
simplify the following expression: 2(6x + 18)
a. -12x + 36
b. 8x + 20
c. 6x + 36
d. 12x + 36
of an item is $480. After 6 months of not selling, it is marked down by 10%. After another 6 months of not selling, it is further marked down by 20%. Find the sale price after both markdowns
Final answer:
The item with an original price of $480 is marked down twice, first by 10%, reducing it to $432, and then by another 20%, making the final sale price $345.60.
Explanation:
The original price of the item is $480. The first markdown of 10% reduces the price by $48 (10% of $480), which makes the new price $432. After six months, the item is marked down again by 20%, which is $86.40 (20% of $432). The final sale price of the item after both markdowns is $432 - $86.40 = $345.60.
the sides in a rectangle are in the ratio 3:2. What is the length of each side if the perimeter of the if the rectangle is 55cm
Answer: 11cm, 11cm, 16.5cm, 16.5cm
Step-by-step explanation:
To find the length of each side of a rectangle in ratio of 3:2, set up the equation for the perimeter and solve for the sides using algebraic manipulation.
Explanation:To find the length of each side of the rectangle, we must solve for the sides using the given ratio. Let's assume the ratio is 3x:2x, where x is a common factor. The perimeter of a rectangle is equal to 2 times the length plus 2 times the width. So, we can set up the equation: 2(3x) + 2(2x) = 55 cm. Simplifying the equation, we get 6x + 4x = 55. Combining like terms, 10x = 55, and dividing both sides by 10, we find x = 5. Therefore, the length of each side is 3x = 3(5) = 15 cm, and the width is 2x = 2(5) = 10 cm.
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2/5 (y-40) = 5 (solve for y)
Evaluate the expression for the given values.
mx−y when m=2, x=7, and y=5
Write an algebraic expression for each verbal expression
Jessica went to the grocery store and purchased a box of cereal for $3.75, milf for $1.50, and bread for $2.25. She paid with a $20.00 bill. How much change did Jessica receive?
Jessica will receive a $12.5 change back.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
For example = 2 + 8 + 9
Subtraction = Minus of any two or more numbers with each other called subtraction.
For example = 4 - 8
Division = divide any two numbers or variable called division.
For example 4/8
Multiplication = to multiply any two or more numbers or variables called multiplication.
For example 5 × 7.
The total cost of all purchased items
cereal for $3.75, milk for $1.50, and bread for $2.25
So,
3.75+1.50+2.25 = $7.5
Jessica paid $20
She will get back = 20 - 7.5 = $12.5
Hence "Jessica will receive a $12.5 change back".
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34=−2t can u help me
567,433 to the nearest hundred thousand
The number 567,433 nearest hundred thousand is 600,000 after rounding off, the answer is 600,000.
What is rounding off the number?Rounding is a technique to reduce a large number to a smaller, more approachable figure which is very similar to the actual. Rounding numbers can be achieved in a variety of ways.
It is given that:
The number is 567,433
600,000
Rounded to the nearest 100,000 or
the Hundred Thousands Place.
Thus, the number 567,433 nearest hundred thousand is 600,000 after rounding off, the answer is 600,000.
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I need help solving these problem 14=8-6r
The solution of expression is, r = 1
We have to give that,
An expression to solve,
14 = 8 - 6r
Now, Simplify the expression by combining the like terms as,
14 = 8 - 6r
Add 6r on both sides,
14 + 6r = 8 - 6r + 6r
14 + 6r = 8
Subtract 14 on both sides,
6r = 8 - 14
6r = 6
Divide into both sides by 6,
r = 6/6
r = 1
Therefore, The solution is, r = 1
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A 16 foot piece of string is cut into two pieces so that the longer piece is 1 foot longer than twice the shorter piece find the length of both pieces
x = long piece
y = short piece
x = 2y+1
2y +1 +y =16
3y +1 = 16
3y =15
y = 15/3 =5
y = 5
x = 2(5) +1 = 11
short piece is 5 feet
long piece is 11 feet
Discussion Explain why 2 < x < 6 can be considered the short method for writing the AND compound inequality x > 2 AND x < 6.
Slope=5,through(3,13)
Answer:
y=5x-2.Step-by-step explanation:
This question wants us to write the given line in a slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept. We already know the slope, which is 5, so just insert 5 in for m. We get y = 5x = b. We're not done, however, we still need to solve for b. (3,13) equals 5(3)+b=13. This gives us our final result of b=-2. insert this into the equation for b, and the equation becomes y = 5x -2.
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What is 39.39 rounded to the nearest 10th
Adam needs both small and large cones to set up for a soccer practice. He knows there are fewer than 30 cones in the storage room. He needs at least a dozen large cones. Let x represent the number of small cones and y represent the number of large cones. Select all inequalities that model this situation.
x>0
y≥12
x+y≤30
y>12
x≥0
x+y<30
Final answer:
The inequalities that accurately model the situation where Adam needs fewer than 30 cones, with at least a dozen large ones, are y≥12, x+y≤30, and x≥0. These inequalities represent the constraints on large cones, total cones, and the feasibility of small cones respectively.
Explanation:
The student asks about modeling a situation with inequalities where Adam needs both small and large cones for soccer practice, with fewer than 30 cones total and at least a dozen large ones. The variables x represent the number of small cones and y represent the number of large cones. To accurately model this scenario, the following inequalities are correct:
y≥12: Adam needs at least a dozen large cones.
x+y≤30: The total number of cones, both small and large, is less than or equal to 30.
x≥0: The number of small cones can be zero but not negative, as you can't have a negative number of cones.
Thus, the inequalities that model this situation are y≥12, x+y≤30, and x≥0. These inequalities account for the constraints on the number of large cones needed, the total limit on cones, and the feasibility of the number of small cones respectively.
Nine cave explorers will carry 120 ft of the rope with them during an expedition next month what’s they total number of yards of rope that the explorers will carry
A town's population increases in one year from 100,000 to 110,000. If the population is growing exponentially at a steady rate, then at the end of a second year it will be
A jet plane costs an airline $69,500,000. What is the place value of the digit 5 in this number
Simon has a bag of marbles. Six are green marbles, four are red, two are blue and ten are black. If he selects one at random, the probability that it will be black is
John has 2,456 pennies in his coin collection. He has the same number of pennies in each of 3 boxes. Estimate to the nearest hundred the number of pennies in each box.
Which integer is less than –4?
A.
–6
B.
–2
C.
0
D.
3
Three equivalent ratio of 36:48
How do you read 12.0045 in standard form
What is the LCm of two numbers if one number is a multiple of the other
Rafael has 118 baseball cards arranged in an album. Each page of the album can hold 9 cards. How many pages are full and how many cards are on the last page? Show your work.
The division is one of the four fundamental arithmetic operations. The number of pages of the album that are completely filled is 13, while the last page of the album has only 1 card.
What is Division?The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
Given that Rafel has 118 baseball cards arranged in an album. Also, Each page of the album can hold 9 cards.
Therefore, the number of pages that will be full can be found by dividing the total number of cards available by the total number of cards that each page can have.
In the division, the quotient represents the number of pages which have 9 photos, therefore are full. And the remainder represents the number of photos that will be left on the last page.
The division can be carried out as shown below.
Hence, the number of pages of the album that are completely filled is 13, while the last page of the album has only 1 card.
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In order to join an online learning community, there is a $20 startup fee and a $5 monthly fee. Write an equation in slope-intercept form that models this situation.
Equation in slope intercept form will be 5x + 20.
It is given that to join a online learning community, startup fee is $ 20 and the monthly fee is $ 5.
We have to write an equation in slope-intercept form.
What is the equation for slope intercept form ?
Equation for slope intercept form is y = mx + c.
Let's assume ;
y = total cost
x = months
c = startup fee
∵ equation in a slope intercept form is y = mx + c.
Putting the values , we get ;
y = 5x + 20
Thus the equation in slope intercept form will be y = 5x + 20.
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find the factors and the greatest common factor 375,66,333
Answer:
the greatest common factor is 3
Step-by-step explanation:
375: 1, 3, 5,11, 15, 25, 75, 125, 375
66: 1, 2, 3, 6, 11, 22, 33, 66
333: 1, 3, 9, 37, 111, 333