Solution of log₅x = log₃20 is , x = [tex]5^{log_3(20)}[/tex]
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as .
[tex]log_ax =N[/tex]
where, a is the base of function or equation
x define expression
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms are :
log_c (a) +log_c (b) = log (a b)log a/b = log a - log blog a^x = x log alog a^a = 1What is change of base formula ?Change of base formula generally use to change the logarithm base to another base.
The formula for base change is :
[tex]log_bx = \frac{log_cx}{log_cb}[/tex]
where, c is the new base.
In the given question,
log₅x = log₃20
using base change this can be written as :
[tex]\frac{log_{10}x}{log_{10}5} = \frac{log_{10}20}{log_{10}3} \\\\= > log_{10}(x) = \frac{log_{10}20 . log_{10}5}{log_{10}3}\\ \\= > x = 5^{log_320}[/tex]
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Hamburgers can be purchased from two different popular fast food restaurants. restaurant a sells 11 burgers for $14.19, and restaurant b sells 2 burgers for $2.64. which restaurant offers the best value per hamburger, and what is its amount? restaurant a for $1.29 restaurant b for $1.29 restaurant a for $1.32 restaurant b for $1.32
Restaurant A offers the best value as one hamburger is $1.29
How to calculate the Restaurant with the best value ?The first step is to calculate the price of one burger in restaurant A
11= 14.19
1= x
cross multiply
11x= 14.19
x= 14.19/11
x= 1.29
The next step is to calculate the price on one burger in restaurant B
2= 2.64
1= x
Cross multiply
2x= 2.64
x= 2.64/2
x= 1.32
Hence the price of the hamburger at Restaurant A is $1.29 and the price at Restaurant B is $1.32.
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Answer:
(A) Restaurant A for $1.29
Step-by-step explanation:
Got it right on my quiz.
Use the distance-rate-time formula (d = rt) to solve the following problem.
d = distance
r = rate of speed
t = time
A train carrying cattle left Miami and traveled toward New York. The train took 28 hours to arrive in
New York and traveled the distance of 1092 miles. Find the rate of speed of the cattle.
9) Cell phone company A charges $20 per month plus $0.05 per text
message. Cell phone company B charges $10 per month
per text message. Is there any number of text
plus $0.07
messages that will
result in the exact same charge from both companies?
The number of the text messages where it will result in the exact same charge from both companies is 500 messages
What is number system?Number systems are mathematical systems that allow computers to understand and express numbers in various ways. A number is a mathematical value that is used to count and measure items as well as execute arithmetic calculations.
Natural numbers, whole numbers, rational and irrational numbers, and so on are all types of numbers. Similarly, different number systems with differing properties exist, such as the binary number system, the octal number system, the decimal number system, and the hexadecimal number system.
Let the number calls be x where the messages will result in the exact same charge
So, Cell phone company A charges $20 per month plus $0.05 per text
message is 20 + 0.05x
And, Cell phone company B charges $10 per month plus $0.07 per text message is 10 + 0.07x
As we want the numbers to be equal, following equation is obtained
20 + 0.05x = 10 + 0.07x
Lets find x
20 + 0.05x = 10 + 0.07x
0.07x - 0.05 = 20 -10
0.02x = 10
x = 10/0.02
x = 500
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Add or Subtract.
11/12 - 7/45
Solution=0.76
How to solve 11/12 - 7/45?
[tex]\frac{11}{12} -\frac{7}{45} \\=\frac{(11*45-7*12)}{540} \\=\frac{411}{540} \\=0.76[/tex]
What is a fraction?
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such one-half, eight-fifths, or three-quarters, indicates the number of parts of a particular size.Numerator and denominator are both natural numbers in positive common fractions. The denominator tells us how many of those equal parts there are in the numerator.The numerator tells us how many of those parts there are in the numerator. Zero pieces can never make up a whole, hence the denominator cannot be zero.Ex: 1/2 = 0.5
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what is 3 times 60? because i dont know
Answer: 180
Step-by-step explanation: 3 times 6 is 18 so just add a zero
Answer: 180
Step-by-step explanation:
3x60
60+60+60
PLEASE HELP!! The area of a square is 16 square units. Since 4^2 = 16 and (-4)^2 = 16, both 4 and -4 are square roots for 16. Explain how "both square roots for 16, the area of the square, are the length of each side of the square" is incorrect.
I will mark brainliest!
we can't say that "both square roots for 16, the area of the square, are the length of each side of the square"
Because one of these solutions does not have a meaning in the given contest.
Why is the statement incorrect?So we have a square with an area of 16 square units, then the side length of that square will be given by:
S^2 = 16 square units
Now, there are two solutions for the above equation, these are:
S = 4 units
S = -4 units.
But being a solution of the equation does not mean that the solutions have sense in the context of the problem.
When we talk about dimensions of figures, negative numbers are not really well defined. We can't say that a square has a side length of "negative 4 units"
That does not make sense, remember that math is just a language, and it should be used to communicate things to others.
So the logical solutions (4 and -4) is not the only thing we need to look at when we state the solutions of a problem, but also the problem itself.
That is why we can't say that "both square roots for 16, the area of the square, are the length of each side of the square"
Because one of these solutions does not have a meaning in the given contest.
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HELP ITS URGENT! AND HAVE A GOOD DAY
Answer:
the answer is D
hope this helps!
Marianna went running and had 1/6 of a bottle of water left when she stopped to rest. She went to a water fountain and filled it until it was 2/3 full.
How much water (as a fraction of a bottle) did Marianna put in her bottle at the water fountain?
Mari put 1/2 of a bottle of water at the water fountain .
Expression in maths is outlined because the assortment of numbers variables and functions by mistreatment signs like addition, subtraction, multiplication, and division.Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping will all be pictured by mathematical symbols, which might even be accustomed indicate the logical syntax's order of operations and different options.Let the capacity of the bottle holding water be 100 .
It is given that Marianna went running and had 1/6 of a bottle of water left when she stopped to rest. She went to a water fountain and filled it until it was 2/3 full.
The amount of water is given by :
2/3 of 100 - 1/6 of 100 = 2/3 × 100 - 1/6 × 100
= 100( 2/3 - 1/6)
= 100(1/2)
= 50
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7(x-3)=9x-3
Please help!!
Answer:
x=-9
Step-by-step explanation:
x=-9
Thank you so much!
Find the value of $A$ if the $4$-digit number $3A5A$ is divisible by $15$.
The value of A in the 4-digit number, 3A5A is 5.
What is the value of A?The 4-digit number provided in the question has to be a multiple of 15 given the information in the question. A multiple of a number is divisible by that number. A multiple of 10 is 100 because when 100 is divided by 10 , the value gotten is 10.
A multiple of a number is the product of an integer and that number. For example, a multiple of 2 is 100. This is because 2 multiplied by 50 is equal to 100.
The multiplies of 15 either have a unit value of 5 or 0.
If A is 5, the number becomes 3555.
3555 / 15 = 237
If A is 0, the number becomes 3050
3050 / 15 = 203.33
Thus, the value of A is 5 because 3555 is divisible by 15.
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which number falls between -25/4 and -400% on a number line
The number falls between [tex]-\frac{25}{4}[/tex] and - 400 % is [tex]-\frac{43}{8}[/tex] = 5.375
first we convert fraction into decimal number
[tex]-\frac{25}{4}[/tex] = - 6.25
and for remove percentage we divide by 100
- 400 % = - 4
from choose the option,
[tex]-\frac{43}{8}[/tex] = 5.375
- 720 % = - 7.2
[tex]-\frac{20}{3}[/tex] = - 6.6
then, choose [tex]-\frac{43}{8}[/tex]
therefore, number lies between [tex]-\frac{25}{4}[/tex] and - 400 % is [tex]-\frac{43}{8}[/tex] = 5.375
A fraction is any number of the form a/b where both “a” and “b” are whole numbers and b≠0. On the other hand, a rational number is a number which is in the form of p/q where both “p” and “q” are integers and q≠0.
Thus, a fraction is written in the form of m/n, where n is not 0 and m & n are whole (or natural numbers). For example, 12/23, 10/32, 12/10, 4/21. A rational number can also be written in the form of a/b, where b is not 0 and a & b are integers. For example, 15/7, -18/13, 3/-7, -6/-12.
All fractions can be termed as rational numbers; however, all rational numbers cannot be termed as fractions. Only those rational numbers in which ‘p’ and ‘q’ are positive integers are termed as fractions. Let a/b be any fraction. Now, a and b are natural numbers. Since all natural numbers are also integers, a and b are also integers. Thus, the fraction a/b is the quotient of 2 integers such that b ≠ 0. Hence, a/b is a rational number. One of the examples in which a number is a rational number but not a fraction is:
Consider the fraction 12/-32. It is a rational number but not a fraction because its denominator (n) is not a natural number.
A fraction is expressed in the form of the ratio of whole numbers, a/b and b≠0.
A rational number is also expressed in the form of a ratio, p/q, where numerator and denominator are integers and q≠0.
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What’s the answer please help
Answer:
Step-by-step explanation:
where?
Which expression correctly represents "three less than the product of a number and two, increased by five"? 2 n minus 3 5 3 minus 2 n 5 3 minus (2 n 5) 2 (n minus 3) 5
Answer: 2n+5-3
Step-by-step explanation:
Break this quote down:
"three less than the product of a number and two, increased by five"
To this:
"three less than the product" ==> product-3
Now break this quote down
Product: "product of a number and two, increased by five"
To this:
"product of a number and two" ==> 2*n
"increased by five" ==> +5
"product of a number and two, increased by five" ==> 2*n+5
Product: 2*n+5
Product-3: 2*n+5-3=2n+5-3
Is 12/24 equivalent to 24/72?
Answer:
No
Step-by-step explanation:
12/24 = (1 * 12) / (2 * 12) = 1/2
24/72 = (1 * 24) / (3 * 24) = 1/3
1/2 ≠ 1/3
Determine whether each sequence is arithmetic or geometric. Then identify the common difference or common ratio. 1620,540,180,60,20, . . . .
The sequence 1620,540,180,60,20, . . . .. is a geometric sequence with common ratio 1/3.
To determine whether the sequence is an arithmetic or geometric one, we need to check how the consecutive terms relate to each other.
If it is an arithmetic sequence, then:
a(n) = a(n-1) + d
where d is the common difference.
If it is a geometric sequence, then:
a(n) = a(n-1) . r
where r is the common ratio.
The given sequence is:
1620,540,180,60,20, . . . .
In this sequence:
a(1) = 1620
a(2) = 540
a(3) = 180
First we check the difference between 2 consecutive terms:
a(2) - a(1) = 540 - 1620 = -1080
a(3) - a(2) = 180 - 540 = -360
Since the difference is not constant, then the sequence is not an arithmetic one.
Now we check the ratio,
a(2) : a(1) = 540 : 1620 = 1/3
a(3) : a(2) = 180 : 540 = 1/3
and so on
Since the ratio of consecutive terms are constant, then the given sequence is a geometric sequence. Furthermore, its ratio, r = 1/3
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in chicago, the tenperature dropped from 21 degrees to -7 degreees over the course if 6 hours, identify the rational number that represents the average temperature change per hour
Answer:
4.6667
Step-by-step explanation:
6266226ghsgjshss if she cut
Answer:
Step-by-step explanation:
solve by factoring
you get x=3/2
A cargo van delivers only 50-pound and 80-pound packages. for each delivery trip, the van must carry at least 20 packages, and the total weight of the packages cannot exceed 1,500 pounds. write a system of inequalities to determine the maximum number of 80-pound packages that the van can carry per trip.
If a cargo van delivers only 50-pound and 80-pound packages and the total weight of the packages cannot exceed 1,500 pounds, then a system of inequalities to determine the maximum number of 80-pound packages that the van can carry per trip is x + y ≥ 20; 80x + 50y ≤ 1,500.
A system of inequalities is a term used in mathematics that is a set of two or more than two inequalities in one or more than one variable.
Consider,
the number of 80-pound packages = x
the number of 50-pound packages = y
As the van can carry a minimum of 20 packages, the sum of x and y can be given as,
x + y ≥ 20
The weight of 80-pound boxes can be given as 80x and the weight of 50-pound boxes can be given as 50x. As the total weight of the packages cannot be more than 1500 pounds,
80x + 50y ≤ 1500
If we consider x to be 19,18 or 17 and the remaining to be y, it will exceed the limit of 1500 pounds. If x is considered to be 16,
80(16) + 50 (4) = 1480
Hence, the maximum number of 80-pound packages that the van can carry per trip is 16.
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Here are the ingredients needed to make 8 pancakes.
250 ml milk
1 egg
140 g flour
5 g butter
Simon makes 4 pancakes.
Work out how much milk he needs.
Craig makes 12 pancakes.
Work out how much butter he needs.
Step-by-step explanation:
Simon only used 125ml milk
250÷2=125
Craig used 375ml milk
250x1.5=275
Suppose that f(1) = 4, f(4) = 8, f '(1) = 7, f '(4) = 3, and f '' is continuous. find the value of 4 xf ''(x) dx 1 .
It looks like you want to find
[tex]\displaystyle \int_1^4 x f''(x) \, dx[/tex]
Integrate by parts:
[tex]u = x \implies du = dx[/tex]
[tex]dv = f''(x) \, dx \implies v = f'(x)[/tex]
Then
[tex]\displaystyle \int_1^4 x f''(x) \, dx = x f'(x) \bigg|_{x=1}^{x=4} - \int_1^4 f'(x) \, dx[/tex]
By the fundamental theorem of calculus,
[tex]\displaystyle \int_1^4 f'(x) \, dx = f(4) - f(1)[/tex]
so that
[tex]\displaystyle \int_1^4 x f''(x) \, dx = 4 f'(4) - f'(1) - f(4) + f(1) = 12 - 7 - 8 + 4 = \boxed{1}[/tex]
Simplify the expression: – 8n+– 8n+– 6n
Answer:
The simplified answer would be: -22n
Please correct me if I am wrong, hope this helps! ;)
Answer:
-22n.
Step-by-step explanation:
'+-' = '-' so,
– 8n+– 8n+– 6n
= -8n - 8n -6n
= -22n.
The three sides of a triangle are n. 3n+2, and 4n - 13. If the perimeter of the triangle is 69 inches, what is the length of each side?
Separate multiple entries with a comma.
Answer:
8, 26 and 19
Step-by-step explanation:
Perimeter is the length of all sides of a polygon. It is simply the length of the boundary around a closed shape. Perimeter of a triangle = Sum of all three sides.
Hence,
[tex]\Rightarrow[/tex] n + 3n + 2 + 4n - 13 = 69 (acc. to Q)
[tex]\Rightarrow[/tex] n + 3n + 4n + 2 - 13 = 69
[tex]\Rightarrow[/tex] 8n - 11 = 69
[tex]\Rightarrow[/tex] 8n = 80
[tex]\Rightarrow[/tex] n = 80/10
[tex]\Rightarrow[/tex] n = 8
Length of all three sides:
n = 83n + 2 = 3(8) + 2 = 264n - 13 = 4(8) - 13 = 19
Solve each system by substitution. Check your answers.
3c + 2d=2 , d=4
By substitution, the solution of the system of equations, 3c + 2d = 2 and d = 4, is (c , d) = (-2 , 4).
A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given two linear equations in variables c and d,
3c + 2d = 2 (equation 1)
d = 4 (equation 2)
Since the second equation is already expressed in d in terms of a constant, substitute the second equation to the first equation.
3c + 2d = 2 (equation 1)
3c + 2(4) = 2
3c + 8 = 2
Combining all terms containing the variable c on one side and the constants on the other side of the equality, and solving for c.
3c + 8 = 2
3c = 2 - 8
3c = -6
c = -6/3
c = -2
Hence, the solution of the given system of equations is (c , d) = (-2 , 4).
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SOMEONE PLEASE HELP :’( Solve the equation | 4x + 7| = 9. Graph
Answer:
-4
Step-by-step explanation:
Split the problem into two cases: one positive and one negative
|4x+7| =9
4x+7=9
(4x+7) =9
Subtract 7 from both sides
4x+7 - 7 = 9 - 7
Solution
x = 1/2
x = -4
The turtle population on an island is increasing at a rate of 1.4% per year. The population was 3800 in the year 2009.
What is the predicted population in the year 2014?
Question
The turtle population on an island is increasing at a rate of 1.4% per year. The population was 3800 in the year 2009.
What is the predicted population in the year 2014?
Answer:
3541
There are 5 children and 3 adults going on a trip. What fraction of the people going on the trip are ADULTS
answer=
Children =5
Adults = 3
3/8 are adults
Ann had about $2,135 in savings while her sister had double that amount in savings. what is a reasonable amount that the sisters have saved? a. $4,000 b. $4,200 c. $5,200 d. $6,400
In this problem, you will investigate the relationships among three points of concurrency in a triangle.
b. Draw an obtuse triangle and find the circumcenter, centroid, and orthocenter.
Construct the centroid (medians), circumcenter (perpendicular bisectors), and orthocenter of an obtuse triangle (altitudes). Take note of how these three centers interact with one another.
What is an obtuse triangle?An obtuse-angled triangle or obtuse triangle is one in which one of the angles is an obtuse angle or greater than 90°. The sum of the obtuse triangle's interior angles is only 180°. This means that the angle sum property of any triangle remains unchanged.
An obtuse-angled triangle is one in which one of the interior angles is greater than 90°. If one angle in an obtuse triangle measures more than 90°, the sum of the remaining two angles is less than 90°.
Construct the centroid (medians), circumcenter (perpendicular bisectors), and orthocenter of an obtuse triangle (altitudes). Take note of how these three centers interact with one another.
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Position and label triangle JKLon the coordinate plane so that its base JL is a units long, vertex K is on the y-axis, and the height of the triangle is b units.
ΔJKL has been drawn such that its base JL is a unit long, vertex K is on the y-axis, and the height of the triangle is b units.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.
The right angle triangle JKL with base JL and perpendicular KJ has been drawn.
Height = KJ = a
Since J(0,0) so K(0,a)
Hence "ΔJKL has been drawn such that its base JL is a unit long, vertex K is on the y-axis, and the height of the triangle is b units".
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13. Which of these descriptions could the equation 16x - 17 = 26 represent
Check all that apply.
W 910/1
A The difference between sixteen times a number and seventeen is 26.
B. The difference between seventeen times a number and sixteen is 26.
When sixteen times a number is decreased by seventeen, the result
is 26.
riew
b. When seventeen times a number is decreased by sixteen, the result
is 26.
The sum of sixteen times a number and seventeen is 26.
The sum of seventeen times a number and sixteen is 26.
When seventeen times a number is increased by sixteen, the result
is 26.
H. When sixteen times a number is increased by seventeen, the result
is 26.
Answer:
when sixteen times a number is decreased by seventeen the result is 26
