The expression log₃4 + log₃y + log₃8x can be written as [tex]log_{3}32xy[/tex] in a single logarithm form.
Given that the expression is log₃4 + log₃y + log₃8 x.
We are told to write the expression as a single logarithm.
Change of base theorem is basically used when we have to find the log values having different bases from 10 as we have tables which tell the log values with base 10. We know that [tex]log_{a}b[/tex]=[tex]log_{x}b/log_{x}a[/tex] and
log mn=log m+log n.
The expression is log₃4 + log₃y + log₃8 x.
log₃4 + log₃y + log₃8x=[tex]log_{3}[/tex] (4*y)+ [tex]log_{3}[/tex] 8x
=[tex]log_{3}[/tex] (4*y*8x)
=[tex]log_{3}[/tex] 32xy
Hence the expression log₃4 + log₃y + log₃8x can be written as [tex]log_{3}32xy[/tex] in a single logarithm form.
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I NEED HELP HURRRYYYY
The rate which the mulch is being applied is 250,000 cm^3/cm^2
How to determine the rate which the mulch is being applied?The statement is given as
Rita is applying 250,000 cm^3 of mulch per m^2 of the garden space
This means that the rate is
Rate = Volume of mulch/Area of garden space
Substitute the known values in the above equation
So, we have
Rate = 250,000 cm^3/cm^2
Hence, the rate which the mulch is being applied is 250,000 cm^3/cm^2
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2 3/4 - 1 1/2
30 points
Answer:
Step-by-step explanation:
it is - 2 3/4 or it would be -2.75
What is the slope and y-intercept of the line y=-3x + 7?
m=
b=
Answer:
slope = -3
y-intercept = (0,7)
All numbers that are divisible by 3, are divisible by 9. What is a gals Statement?
Answer: False, it's the other way around
Step-by-step explanation:hope it helps, brainliest? i could really use it
What is the equation of this line?
Responses
y=2x−3
y=−12x−3
y=−2x−3
y=12x−3
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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Does anyone know how to solve 7 and 8?
The area and perimeter of the figures are 7) area=544 cm² and perimeter = 120 cm (8)area = 90cm² and perimeter = 46 cm .
Area is defined as the total surface occupied by a figure. The SI unit of area is m² .
Area of rectangle is given by the product of its two sides the length and Width
Perimeter is the sum of all sides of a two-dimensional figure.
7) In the first figure we have to separate it into a square and a rectangle.
Area of the square on top = 16 × 16 = 256 cm²
Length of the longest side in the second rectangle = 16 + 8+12=36cm
Area of the second rectangle = 36 × 8 = 288 cm²
Total area of the figure = (288 + 256) cm² = 544 cm²
Perimeter = 16 + 16 + 8 + 8 + 36 + 8 + 12 + 16 = 120 cm (taking all sides anti-clockwise from the top.)
8)Here we separate the two figures into two rectangles .
Length of the rectangle = 12 cm
Area of the first rectangle = 12 × 5 = 60 cm²
Area of the second rectangle = (6 × 5) cm² = 30cm²
Total area = (60 + 30)cm² = 90cm²
Perimeter = (5 + 6 + 7 + 5 + 12 + 11) cm² = 46 cm
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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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in the polynomial $(ax^6 bx^8 cx^3 d)(x^5 ex^4 f)(x^2 gx h)$, letters $a$ through $h$ are all nonzero constants. what is the degree of the polynomial?
I assume you mean the polynomial
[tex](ax^6 + bx^8 + cx^3 + d) (x^5 + ex^4 + f) (x^2 + gx + h)[/tex]
The degree of this polynomial is the exponent of the largest power of [tex]x[/tex] in the expansion of the product.
This term is the product of the largest power terms in each factor. These are
[tex]ax^6 + bx^8 + cx^3 + d \implies bx^8[/tex]
[tex]x^5 + ex^4 + f \implies x^5[/tex]
[tex]x^2 + gx + h \implies x^2[/tex]
So, the largest power term in the polynomial is
[tex]bx^8 \cdot x^5 \cdot x^2 = bx^{15}[/tex]
and the degree is 15.
In one week, a printing center made 1,222 copies of a 46 page article. The printing center also
printed 485 copies of a 16 page essay. How many pages did the printing center print during the
week?
If in one week, a printing center made 1,222 copies of a 46 page article. The printing center also printed 485 copies of a 16 page essay. The number pages that the printing center print during the week is: 63,972 pages.
Number of pageFirst step is to calculate first sets printed
Number of pages=(1222 copies×46 page article)
Number of pages=56,212
Second step is to calculate the second set printed
Number of pages=(485 copies×16 page article)
Number of pages=7,760
Third step is to calculate the total pages
Total pages=56,212+7,760
Total pages=63,972 pages
Therefore If in one week, a printing center made 1,222 copies of a 46 page article. The printing center also printed 485 copies of a 16 page essay. The number pages that the printing center print during the week is: 63,972 pages.
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What is the distance between points V(1,3) and W(6, -1)?
Either leave the answer exact or round to 1 decimal place.
The distance between points is 9.11 .
What is the Distance Between Two Points?
The length of the line segment connecting any two points represents the distance between them. There is just one line that connects the two places. Therefore, by measuring the length of the line segment that connects the two sites, the distance between them may be determined.the distance between points V(1,3) and W(6, -1)
[tex]d = \sqrt{( x_{2}- x_{1})^{2} + ( y_{2} - y_{1})^{2} }[/tex]
so x₁ = 1 , x₂ = 3 and y₁ = 6 , y₂ = -1
[tex]vw = \sqrt{( 3-1 )^{2} + ( -1 - 6 )^{2} }[/tex]
[tex]vw = \sqrt{( 2 )^{2} + ( -7)^{2} }[/tex]
[tex]vw = \sqrt{4 + 79}[/tex]
[tex]vw = \sqrt{83}[/tex]
vw = 9.110433 ≈ 9.11
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42086
14
12
10+
4
2
422
+ 9
2 4 6
8 10 12 14 16 x
The graph of h(x) = |x-10| +6 is shown. On which
interval is this graph increasing?
O (-00, 6)
O(-00, 10)
(6,00)
O (10,00)
Step-by-step explanation:
42086
14
12
10+
4
2
422
+ 9
2 4 6
8 10 12 14 16 x
42595
Divide and simplify. ∛81 x⁵ y³ / ∛3 x²
The simplest form of the expression is 3xy .
Expressions in science are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by academic degree operator in between.Simplifying expressions mean editing an identical math expression with no like terms and through a compact manner.To change expressions, we have a tendency to tend to combine all kind terms and solve all the given brackets, if any, so at intervals the simplified expression, we have a tendency to are planning to be entirely left with not like terms that cannot be reduced any.We have given an expression ∛81 x⁵ y³ / ∛3 x² .
On simplifying , we get
[tex]\frac{(81x^5y^3)^{1/3}}{(3x^2)^{1/3}} = \frac{(3^4x^5y^3)^{1/3}}{(3x^2)^{1/3}}\\\\= \frac{3^{4/3}x^{5/3}y}{3^{1/3}x^{2/3}} \\\\= 3xy[/tex]
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1x+1.5x=3275 What is the answer?
Answer: x=1308.8
Step-by-step explanation:
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
!!! HELP FAST I ONLY GET 30 MINUTES ON THIS QUIZ !!!! 40 POINTS!
Change the following numbers from standard form to their expanded form.
A. 415.65
B. 2.675
C. 54.906
D. 71.04
E. 9.001
F. 10.298
All you need to put is the answers you don't have to explain it, put all the answers for brainiest, full star, and of course a thanks!!!
Step-by-step explanation:
a 4.1565×10²
b 2.675×10°
c 5.4906×10¹
d 7.104×10¹
e 9.001×10°
f 1.0298×10¹
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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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:
Mayerlin wants to ride her bicycle 56 miles this week. She has already ridden 8 miles. If she rides for 6 more days, what is the average number of miles she would have to ride each day to meet her goal?
Answer:
If in the next 6 days she rides an average of 8 miles per day, she will meet her goal.
Step-by-step explanation:
What is the average number of miles she would have to ride each day to meet her goal?
We know that Mayerlin wants to ride her bicycle for 56 miles this week, and she already has ridden 8 miles, so the distance left is:
56mi - 8mi = 48mi
Now, to find the average distance that she needs to ride each day in order to meet her goal, we need to take the quotient between the distance left and the number days that she has left (6 days), then we will get:
D = 48mi/6 = 8mi
This means that if in the next 6 days she rides an average of 8 miles per day, she will meet her goal.
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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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
Sara paid $15.95 to become a member at a gym. She then paid a monthly fee. Her total cost for all 12 months was $735.95
Write an equation that can be used to find the monthly fee at Sara's gym. Remember to define the variable!
The equation used to find the monthly fee is 12y= 735.95 - 15.95
The monthly fee is $60
How to calculate the monthly fee ?Sara paid a one time fee of $15.95
She then paid a monthly fee, let y represent the monthly fee
For the total period of 12 months she paid $735.95
Therefore the amount she paid monthly can be calculated as follows
12y= 735.95-15.95
12y= 720
y= 720/12
y= 60
Hence the amount Sara paid monthly is $60
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Find the inverse of each function. Is the inverse a function? f(x)=4√x
The inverse for the function f (x) = 4√x will be f ⁻¹ (x) = x² / 16
We are given the function:
f (x) = 4√x
we need to find the inverse of the function.
First we will write the function in the form of x.
y = 4√x
y / 4 = √x
x = y² / 4²
x = y² / 16
So, the inverse function will be:
f ⁻¹ (x) = x² / 16
Therefore, the inverse for the function f (x) = 4√x will be f ⁻¹ (x) = x² / 16
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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
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:
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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What is the quotient of 2 5/6
The value of the quotient is 2. 83
What is a fraction?A fraction can be defined as the part of a whole.
The types of fractions are;
Mixed fractionsProper fractionsImproper fractionsComplex fractionsSimple fractionsIt is also important to note that quotient also mean division.
Now, let's convert the mixed fraction to improper fraction.
Multiply the denominator and the whole number = 6 × 2 = 12Add the value to the numerator , 12 + 5 = 17Divide the value by the denominator, 17/6We then have;
= 17/6
Find the quotient
= 2. 83
Thus, the value of the quotient is 2. 83
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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
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
Use the properties of logarithms to evaluate each expression.
log₃27-2 log₃3
The value of expression log₃27-2 log₃3 is equal to 1.
Given that the expression is log₃27-2 log₃3.
We are told to find the value of the expression by finding the logarithmic functions.
Change of base theorem is basically used when we have the base of the number having different base from 10 as logarithm having 10 base is required to find the log value from table.
log₃27-2 log₃3=log₃27-log₃[tex](3)^{2}[/tex]
([tex]log_{b}a[/tex] is equal to log a/log b and m log a=log [tex]a^{m}[/tex])
=log₃27-log₃9
=log₃(27/9)
=log₃3
=log3/log3
=1
Hence the value of expression log₃27-2 log₃3 is equal to 1.
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