What is each expression in simplest form?
a. (8 x¹⁵)⁻¹/³
Fractions are in their simplest form when they have no common divisors other than one at their top and bottom. The top and bottom cannot be divided further and remain integers.
You may also hear the simplest form called "lowest term."
In preferred, an expression is in only form while it's far easiest to use not unusual methods to help you simplify:
Combine Like termsFactoringincreasing (the opposite of factoring)clean out fractions by multiplyingrecognizing a pattern you have seen earlier than, just like the difference of squaresInput
(8 x^15)^(-1/3)
Value
1/(2 (x^15)^(1/3))
1/(2x^5)
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What is the justification for each step in solving the inequality?
−7(3+8x)+5x≤1−62x
Select from the drop-down menus to correctly justify each step.
The justification of each step in solving the inequality is;
⇒ - 21 - 56x + 5x ≤ 1 − 62x (Distributive property)
⇒ - 21 - 51x ≤ 1 − 62x (Subtraction property of order)
⇒ - 21 + 11x ≤ 1 (Addition property of order)
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
The inequality is given as;
−7 (3 + 8x) + 5x ≤ 1 − 62x
Now, Find the justification of each step in solving the inequality as;
The inequality is solve as,
−7 (3 + 8x) + 5x ≤ 1 − 62x
(Given)
- 21 - 56x + 5x ≤ 1 − 62x
(Distributive property)
- 21 - 51x ≤ 1 − 62x
(Subtraction property of order)
- 21 + 11x ≤ 1
(Addition property of order)
11x ≤ 22
(Addition property of order)
x ≤ 2
( Division property of order )
Hence, The justification of each step in solving the inequality is;
⇒ - 21 - 56x + 5x ≤ 1 − 62x (Distributive property)
⇒ - 21 - 51x ≤ 1 − 62x (Subtraction property of order)
⇒ - 21 + 11x ≤ 1 (Addition property of order)
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P(x) = 4x³ – x² − 6x + 9
What is the value is 1/a+1/b+1/c
When a, b and c are the polynomials roots
Answer:
2/3.
Step-by-step explanation:
α + β + γ = -b/a
αβ + βγ + γ α = c/a
αβγ = -d/a
These are the relation between the roots α, β and γ and the coefficients of the cubic equation:
P(x) = ax^3 + bx^2 + cx + d
Our equation is:
P(x) = 4x³ – x² − 6x + 9
So, for the above equation:
a + b + c = -(-1)/4 = 1/4
ab + ac + bc = -6/4 = -3/2
abc = -9/4.
1/a + 1/b + 1/c
= (bc + ac + ab) / abc
So, plugging in the above values:
this = (-3/2) / (-9/4)
= 3/2 * 4/9
= 12/18
= 2/3.
What is the slope and y-intercept of the line y=-3x + 7?
m=
b=
Answer:
slope = -3
y-intercept = (0,7)
What is the slope of the line passing through the points (0, 4) and (−8, −1)
Answer: Slope (m) Slopem=5/8
Step-by-step explanation:
Simplify each rational expression. State any restrictions on the variables.
2x / 4 x²-2 x}
According to the question, the given rational expression is as follows:
Rational expression = [tex]\frac{2x}{4x^{2} -2x}[/tex]
To simplify the given expression by performing factors on denominator:
[tex]4x^{2}-2x = 2x(2x-1)[/tex]
Substituting these factors in the final expression, we get:
Rational expression = [tex]\frac{2x}{4x^{2} -2x}=\frac{2x}{2x(2x-1)}=\frac{1}{2x-1}[/tex]
Therefore, the final answer for the given expression is [tex]\frac{1}{2x-1}[/tex].
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Write a function for each situation. Then find the value of each function after five years. Round to the nearest dollar. A $ 12,500 car depreciates 9 % each year.
7800 is the value of each function after five years.
With an example, what is compound interest?
When you add the interest you have already earned back into your principal balance, you are earning compound interest, which increases your profits. Consider that you have $1,000 in a savings account earning 5% interest annually. If you made $50 in the first year, your new balance would be $1,050.The formula is: A = P( 1 + r )ⁿ
r = 0.09
As here the value of the car depreciates every year, so we need to plug the value of as negative. So, - 0.09
Now plugging the above values into the formula, we will get
A = 12500 ( 1 - 0.09)⁵
A = 12500 * ( 0.91)⁵
A = 12500 * 0.6240321451
A = 7800.40181375 ≈ 7800
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please solve this with steps
Answer:
-13/18
Step-by-step explanation:
You have here a multiplication and a division in your expression. You need to multiply and divide in the order that they appear from left to right, according to the order of operations. So multiply first.
To multiply two fractions, you just multiply the top×top and bottom×bottom.
You could simplify it at this point but I waited to the end to simplify. See image.
Next, divide. If you have one or two fractions in a division problem, rewrite the division as a multiplication using Keep-Change-Flip! Keep the first term. Change divide to multiply. And Flip the second term (use the reciprocal is the math word for it.) See image.
Last, simplify.
Find an expression which represents the different
Answer:
(10x-5)-(-4x-5)=
10x-5+4x+5=
14x
i think i did it right?
Step-by-step explanation:
Simplify each expression. Rationalize all denominators. √7 x³ . √14 x
The simplify of the expression is [tex]7\sqrt{2} x^{4}[/tex].
The word simplifies manner to make something less complicated to do or understand. So, by lowering or simplifying the fractions method we make the fraction as simple as viable. We try this by dividing the numerator and the denominator by using the most important number which could divide into both numbers precisely.
to assess an algebraic expression manner to discover the fee of the expression while the variable is changed by way of a given variety. to evaluate an expression, we replace the given wide variety for the variable within the expression and then simplify the expression with the usage of the order of operations.
Whilst you simplify an expression, you are essentially seeking to write it in the handiest manner possible. at the give-up, there should not be any extra including, subtracting, multiplying, or dividing left to do.
⇒ [tex]\sqrt{14} = \sqrt{7} \sqrt{2}[/tex]
= [tex]\sqrt{7} x^{3} \sqrt{x7} \sqrt{2}[/tex]
= [tex]7x^{4} \sqrt{2}[/tex]
= [tex]7\sqrt{2} x^{4}[/tex]
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If a function is defined by an equation in x and y, then the set of points (x,y) in the xy-plane that satisfies the equation is called
A kitten has 5 claws on its paw, a chicken has 4. there are 57 kittens and chickens in the yard and they all have 768 claws. how many kittens and chickens are in the yard?
Using algebraic expressions and equation, there are 26 kittens and 31 chickens in the yard.
An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".
Given that there are 57 kittens and chickens in the yard, we can express this as:
x + y = 57 ⇒ x = 57 - y (equation 1)
where x = number of kittens
y = number of chickens
If a kitten has 5 claws on each of its 4 paws, and a chicken has 4 claws in each of its 2 feet, and they all have 768 claws, then
5(4)x + 4(2)y = 768 ⇒ 20x + 8y = 768 (equation 2)
Substitute equation 1 to equation 2 and solve for y.
20(57 - y) + 8y = 768
1140 - 20y + 8y = 768
-12y = -372
y = 31
number of chickens = 31
Substitute the value of y in either of the two equations and solve for x.
x = 57 - y
x = 57 - 31
x = 26
number of kittens = 26
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2 *(x-0.75)=1/3
a) 11/12
b)5/6
c)2/3
d)7/12
Answer:
а)11/12 I believe the answer is correct
Step-by-step explanation:
your solution is written
Given f(x)=22x+10, find f(4).
Answer:
f(4) = 98
Step-by-step explanation:
Substitute any x values for 4, and then solve.
f(4) = 22(4) + 10
f(4) = 88 + 10
f(4) = 98
Simplify the expression -2x²(4x - 3).
O A. -8x³-6x²
O B. -8x³+ 6x²
O C. 8x³-6x²
O D. 8x³+ 6x²
Simplifying (4x)3 gives 64x3
Answer:
option B
Step-by-step explanation:
-2x^2(4x) -2x^2(-3)
= -8x^3+6x^2
Morganton Company makes one product and it provided the following information to help prepare the master budget:
The budgeted selling price per unit is $65. Budgeted unit sales for June, July, August, and September are 8,400, 15,000, 17,000, and 18,000 units, respectively. All sales are on credit.
Thirty percent of credit sales are collected in the month of the sale and 70% in the following month.
The ending finished goods inventory equals 30% of the following month’s unit sales.
The ending raw materials inventory equals 20% of the following month’s raw materials production needs. Each unit of finished goods requires 5 pounds of raw materials. The raw materials cost $2.50 per pound.
Thirty percent of raw materials purchases are paid for in the month of purchase and 70% in the following month.
The direct labor wage rate is $12 per hour. Each unit of finished goods requires two direct labor-hours.
The variable selling and administrative expense per unit sold is $1.60. The fixed selling and administrative expense per month is $65,000.
According to the production budget, how many units should be produced in July?
In July, 231 units are expected to be produced, according to the production budget.
What exactly is a master budget and how are they created?A master budget is a comprehensive budget that is built from a collection of smaller, more specialized business budgets. The master budget process is divided into two parts: an operating budget and a financial budget, each of which is made up of a succession of smaller budgets.
What is sales budget?A sales budget is a budget that forecasts a company's total revenue for a given time period. It forecasts the company's performance based on two factors: the number of products sold and indeed the price under which they are sold.
What is production budget?The word "production budget" is used specifically within film production sometimes, more broadly, in business. The term "film production budget" refers to the amount of money that will be spent on the complete film project. It entails identifying and estimating cost items for each stage of filmmaking.
According to the given data:The budgeted price per unit is = $65
Budgeted unit sales for July = 15000.
Units should be manufactured in July = ?
The sales budget basically reflects the anticipated sales revenue for the next accounting quarter. It is simply prepared merely displaying the predicted sales quantity multiplied by that of the unit selling price.
sales budget for July = Units selling price × expected units to be sold.
15000 = 65 x expected units to be sold
expected units to be sold = 15000/65
= 231 (approx.)
Units should be manufactured in July = 231 (approx.)
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Make Closing statement on why crocs should be allowed in school
Reasons
1.stability
2.breathable
3.Waterpfroof
A collection contains 98 fiction and 56 nonfiction books. The books are put into stacks so that each stack contains one type of book. If all stacks have the same number of books, what is the largest number of books that could be in each stack?
Answer:
56
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
The GCF of 98 and 56 is 14
A Scale drawing of a school bus has a scale of 1/2 inch to 5 feet. If the length of the school buss is 4 1/2 inches on the scale drawing, what is the actual length of the bus?
Explain or show your reasoning.
45 feet
Im writing this extra because the app said the answer was to short :)
A coach writes the batting order of his starting 9 out of the team of 20 on a piece of paper. How many different ways could the list be written?
There are ______ ways the list could be written.
Answer:
I think there are 2 more ways the list could be written
Write the first four terms of a sequence given the recursive rule below:
f(n)=2\cdot f(n-1)+3\;for\;all\;n\geq2\;and\;f(1)=7f(n)=2⋅f(n−1)+3foralln≥2andf(1)=7
The first four terms of the sequence are 7, 17, 37 and 77, respectively.
How to determine the first four terms of a sequence by a recursive formula
Sequences can be generated by using recursive formulas, that is, formulas that are in terms of the previous elements of a sequence. Herein we find a case of sequences by using recurrence formulas, whose procedure is shown below:
n = 1
f(1) = 7
n = 2
f(2) = 2 · f(1) + 3
f(2) = 17
n = 3
f(3) = 2 · f(2) + 3
f(3) = 37
n = 4
f(4) = 2 · f(3) + 3
f(4) = 77
The first four terms of the sequence are 7, 17, 37 and 77, respectively.
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Dan sees the following number pattern on the chalkboard.
5, 10, 20, 40, ...
What is the rule for this pattern?
Answer:
multiply by 2
Step-by-step explanation:
5x2=10
10x2=20
Answer:
the rule is that each time you go up you add the number by itself to get another for example 5, 10 we now know that 5+5 = 10 continuing 5, 10, 20
10+10 = 20
Each pair of values is from a direct variation. Find the missing value. (4,6),(x, 3)
x = 2 is your missing value.
How to find the missing value from direct variation?The equation below encapsulates the idea of direct variation.
If y is expressed as the product of a constant integer k and x, we say that y varies directly with x.
It becomes clear that k is the constant ratio between y and x if we isolate it on one side. In other words, there is always a constant result when you divide y by x.
K is also referred to as the proportionality constant, constant of variation, or just k.
CALCULATIONYou are finding the direct variation's solution. This indicates that both x and y have the same amount of change:
Observe: (x, y) & (x1, y1)
(x , y) = (4 , 6)
(x₁ , y₁) = (x , 3)
Set the two on an equal footing:
(4 , 6) = (x , 3)
Find common denominators (y). Remember that what you multiply to one you multiply to the other:
(4 , 6) = (x * 2, 3 * 2) = (2x , 6)
Simplify. Isolate the variable x.
Divide:
(4) = (2x)
(4)/2 = (2x)/2
x = 4/2
x = 2
x = 2 is your answer.
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33) Create a word problem that can be represented by the quotient -45÷5.
Answer:
molly is baking cookies. she baked 45 cookies and she needs to put a certain amount in 5 different boxes so that way everyone has an equal amount. how much cookies need to be in each box
Step-by-step explanation:
Answer:Joe is feeding cows and he has 45lbs of grass and there are 5 cows how much does each cow get fed?
Step-by-step explanation:
Find each product.
[1 -2] [2 -5]
You can multiply two matrices only if their dimensions are compatible. That means the number of columns in the first matrix is equal to the number of rows in the second matrix.
The resulting matrix, called the matrix product, has the number of rows of the first and the range of columns of the second matrix. The result of matrices A and B is denoted as AB.
The definition of matrix multiplication means row-by-column multiplication, where the entry in the ith row of A is multiplied by the corresponding entry in the jth column of B, and the results are added. Matrix multiplication is not commutative. If neither A nor B is identity matrices, then AB≠BA.
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Write each expression as a single logarithm. Identify any properties used. 4log₃x+log₃7
According to the given statement the expand form of the logarithm 4log₃x+log₃7 is 11log₃.
What is the Logarithms?Logarithms are another way to write exponents. A number's logarithm with only a base equals another number. Modular multiplication is the inverse function of the logarithm. For instance, if 102 = 100, log10 100 = 2.
According to the given information:4log₃x+log₃7
4log₃x this expression can not be further expand:
log₃7 applying the log property of (log ₐᵇ = b log a)
log₃7 this can be written as 7 log 3
the complete expiration is:
4log₃x+7log3
or
4log₃x+7log₃
So,
11log₃
the expand form of the logarithm 4log₃x+log₃7 is 11log₃.
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HELP PLS 100 POINTS!
Please someone help me!
Answer and Step-by-step explanation:
Considering the definition of an disparity, the imbalance that can be utilized to decide x is 20x + 10≤ 80 Definition of inequality An imbalance is the existing disparity between two arithmetical expressions, associated through the signs: greater than >. less than <. less than or rise to to ≤. greater than or break even with to ≥. An disparity contains one or more obscure values called questions, in expansion to certain known data. Solving an disparity comprises of finding all the values of the obscure for which the disparity connection holds. This case A rental car company charges $20 per day to lease a car and $0.10 for each mile driven. Addison needs to lease a car, knowing that: She plans to drive 100 miles. She has at most $80 to spend. On the other hand, x speaks to the most extreme number of days Alyssa can manage to lease for whereas remaining inside her budget. Then, the disparity that can be utilized to decide x is: 20x + 0.1×100≤ 80 So: 20x + 10≤ 80 In rundown, the disparity that can
SAP PLEASE HELP IF RIGHT ANSWER WILL GIVE BRAINLIEST, 15 POINTS, AND 5 STAR OVERALL!!!! IF WRONG ANSWER OR INVALID WILL REPORT, PLEASE, PLEASE, PLEASE!!
Answer:
D is the correct answer!!
there are 30 people in student council that are running for the offices of president and vice president. in how many different ways can those offices be assigned?
Answer: Assuming that it matters which one is president and which is vice president, and the same person cannot be assigned both posts, the answer is 30*29, or 870.
Step-by-step explanation:
Select all of the true comparisons.
Answer: A, D, B
Step-by-step explanation:
Answer:A,B,D
yw :):):)