The solved logarithmic function is 2x - y = e and x + y = 8 for log (2x - y) = 1 and log (x + y) = 3 log 2 respectively.
What is a logarithmic and exponential function?
Logarithmic functions and exponential functions are inverses of each other. The logarithmic function is denoted by using the word log while exponential by using the alphabet, e. For example log 10 = 1 and e^2.
Solving the given expressions: log (2x - y) = 1 and log (x + y) = 3 log 2
Applying given properties of logarithmic and exponential function;
log a + log b = log (ab)
4 log x = log x⁴
e^(log x) = 1
e^(x + y) = (e^x) × (e^y)
Take expression, log (2x - y) = 1
Applying exponential on both sides, we get,
e^(log 2x - y) = e^1
2x - y = e
To Check Results,
Taking logarithm both sides,
log (2x - y) = log e
log (2x - y) = 1
Thus, the answer is verified.
Take expression, log (x + y) = 3 log 2
Applying exponential on both sides, we get,
e^(log (x + y) = e^(3 log 2)
x + y = e^(log 8)
x + y = 8
To Check Results,
Taking logarithm both sides,
log (x + y) = log 8
log (x + y) = 3 log 2
Thus, the answer is verified.
Hence, the solved expression is 2x - y = e and x + y = 8 for log (2x - y) = 1 and log (x + y) = 3 log 2 respectively.
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If x and y vary directly and y is 40 when x is 5, find y when x is 6.
The area of the rectangular arena can be represented as A = (8y2 - 18y) square feet.
Here, we are given the dimensions of a rectangular arena, which are as follows-
Length = 4y - 9 feet
width = 2y feet
The area of a rectangle is given by the formula-
Area of a rectangle = length x breadth
Thus, in this case, area (A) can be calculated as follows
A = (4y - 9) * 2y
Now, we simplify the equation-
A = (4y)(2y) - 9(2y)
A = 8[tex]y^{2}[/tex] - 18y
Thus, the area of the rectangular arena can be represented by the following equation- A = (8[tex]y^{2}[/tex] - 18y) square feet.
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help me my son wont leave me alone!
Answer:
190 square feet
Step-by-step explanation:
25×4 + (25-5×2) × (10-4) = 25×4 + 15×6 = 100+90 = 190
Write An expression that represents the phrase "one third the difference of 15 and a number."
answer:
(15-x)/3
"one third the difference of 15 and a number."
a bull weighs 1,700 pounds. Is it more appropriate to express the bull's weight as 1,700 pounds or 2.72 x 10 to the 4th power onces? explain your reasoning
It is better to express the bull's weight as 1,700 pounds.
How to calculate the value?It should be noted that from the information given, the bull weighs 1,700 pounds.
It should be noted scientific notation isn't required in all situation.
In this case, it's better to express the bull's weight as 1,700 pounds. This aligns better with the weight.
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I’m slow asl bro istg help
Answer:
Area = 1725 ft²
Step-by-step explanation:
In this question, we have to calculate the area of the trapezoid. As mentioned in the hint, the formula for the area of a trapezoid is:
[tex]\boxed{\mathrm{Area = \frac{b_1 + b_2}{2} \times h}}[/tex],
where [tex]\mathrm {b_1}[/tex] and [tex]\mathrm {b_2}[/tex] are the two parallel bases of the trapezoid, and h is the height of the trapezoid.
As we can see in the diagram the two bases are 50 ft and 65 ft respectively, and the height is 30 ft. Using this information and the formula above, we can calculate the formula of the trapezoid:
[tex]\mathrm{Area = \frac{(50 + 65)\: \mathrm{ft}}{2} \times 30 \: \mathrm{ft}}[/tex]
[tex]= \frac{115 \: \mathrm {ft}}{2} \times 30 \: \mathrm{ft}[/tex]
[tex]= \bf 1725 \: ft^2[/tex]
Therefore, the area of the lawn is 1725 ft².
Math on the Spot The Hungarian club needs to earn at least from a bake sale to fund their Goulash Festival. They are selling croissants for each and loaves of French bread for each. Write a linear inequality to describe the situation and graph the solutions.
Answer:
2x +5y ≥ 175 is required inequality
Step-by-step explanation:
round up 1.237 to the nearest hundredths
Answer:
1.24
Step-by-step explanation:
To round 1.237 to the nearest 100th ( you have to know the thousandth one. which the value is 1.237, ) which is 7 and equal to or more than 5. Therefore, the hundredths value of 1.237
Can anyone explain how to simplify the square root of 20, in a simple and detailed way?
Accoreding to the given statement,
The simple method to find the value of √20 is to factorise the number under the root.
What is Factorisation?The process of breaking or decomposing an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorisation or factoring.
According to the given value;
The prime factorisation of 20 = 2 x 2 x 5 = 2 2 x 5
Thus, here we can see, 20 is not a perfect square, because we cannot pair digit 5 after factoring 20.
Only 2 2 can be taken out of the root.
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Help! I know its simple but who is X in X-11=79
Answer:
x = 90
Step-by-step explanation:
x - 11 = 79 ( isolate x by adding 11 to both sides )
x = 79 + 11 = 90
Let f(x)=2x-3. Write a function g whose graph is a reflection in the y axis of the graph of f
The scale drawing is a map of the campus of Central Middle School. The school board needs to know
the distance from the art room to the gym in order to build a walkway.
What is the scale factor from the map to the
actual school?
scale factor =?
Answer:Scale factor is 10 , the second part is 50
Step-by-step explanation:
When is a Fraction and ratio the same
it is actually 1:1 that is 1 all over one
I've tried to solve this but I am still puzzled on what to do.
You are solving a measurement problem where the numbers 5.2187 x 10^−3, 2.05 x 10^7, and 3.40 x 10^3 are multiplied. How many significant digits should the product have?
A. 5
B. 3
C. 2
D. 1
Using scientific notation, the number of significant digits of the product is given as follows:
B. 3.
What is scientific notation?A number in scientific notation is given by:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex].
When two numbers in scientific notation are multiplied, we have that:
The bases are multiplied.The power of 10 is kept.The exponents are added.For this problem, the product is given by:
[tex]5.2187 \times 10^{-3} \times 2.05 \times 10^7 \times 3.4 \times 10^3[/tex]
Multiplying the bases and adding the exponents, we have that:
[tex]5.2187 \times 10^{-3} \times 2.05 \times 10^7 \times 3.4 \times 10^3 = 5.2187 \times 2.05 \times 3.4 \times 10^{-3 + 7 + 3} = 42.8 \times 10^7[/tex]
42.8 has to be divided by 10 to assume for the base have only one digit, thus, to compensate, we have to add one to the exponent(equivalent to multiply by 10), hence:
[tex]42.8 \times 10^7 = 4.28 \times 10^8[/tex]
Hence, considering the rounding, the number has 3 significant digits(4, 2 and 8), and option B is correct.
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mixing alcohol solutions a pharmacist needs to obtain a 70% alcohol solution. how many ounces of a 30% alcohol solution must be mixed with 40 ounces of an 80% alcohol solution to obtain a 70% alcohol solution? hint add x ounces of 30% solution to 40 ounces of 80% solution to get x 40 ounces of 70% solution.
10 Ounces of 30% alcohol solution must be mixed.
Let the amount of 30% solution to be added = x ounces
So , total solution is (40+x) ounces.
we know that 30%=0.30 , 80%=0.80 , 70%=0.70
According to the question
x ounces of 30% alcohol solution + 40 ounces of 80% alcohol solution = (40+x)ounces of 70% alcohol solution.
x*(0.30)+40(0.80)=(40+x)*0.70
0.30x+32=40*0.70+0.70x
0.30x+32=28+0.70x
Rearranging the terms we get
0.70x-0.30x=32-28
0.40x=4
x=4/0.40
x=10
Therefore , 10 ounces of 30% alcohol solution must be mixed with 40 ounces of an 80% alcohol solution to obtain a 70% alcohol solution.
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Rewrite 50,800,000 in scientific notation.
Question:
Rewrite 50,800,000 in scientific notation.
Answer:
5.08 x 10 to the power 7
Step-by-step explanation:
To get the answer you would first need to change the number into a decimal which would be 50800000.0 then you count the number of zeros in this case there is 7 but then number is not 1-10 so you could use the bumps to make it a decimal which is 5.08
I hope it helps you!
~XxBells is a cute girlxX~
#Learn with Brainly
Answer:
5.08 times 10, to the power of 7
Step-by-step explanation:
Have a great rest of your day
The one and only
Mr. Universe
2x-20 and x+20 that makes ab parallel
If the two angles corresponds, hence the value of x that makes them to be equal is 40
Lines and angles
An angle is a point where two lines meet or intersect
Using the diagram below such that if the line a and b are parallel to each other hence the given angles are corresponding angles.
Equate both angles
2x - 20 = x +20
Collect the like terms
2x - x = 20 + 20
x = 20 + 20
x = 40
Hence the value of x that will make both angles correspond is 40
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EXTRA POINTS FOR A CORRECT AND SURE ANSWER
Answer: The equivalent decimal is 0.5
Step-by-step explanation: Ok, so 4/8 is a equivalent fraction to 1/2.
0.5 is the decimal form for one half.
I am also 100% sure I am right, so you have no worries :D
Answer: the answer is 0.5
Step-by-step explanation:
m∠PQS=(3x−3)° and m∠RQS=(x+19)°. Find the value of x.
The figure shows straight angle P Q R that consists of two smaller angles, P Q S and R Q S.
34
41
21
56
The value of x is 41 . Option B
How to determine the angleIt is important to note that angles on a straight line are known to be supplementary.
Supplementary angles are defined as angles that sum up to 180 degrees.
From the information given, we have that;
m∠PQS=(3x−3)° m∠RQS=(x+19)Since angles on a straight line sum up to 180 degrees, we have that;
m∠PQS + m∠RQS = 180°
Substitute the values into the equation
3x - 3 + x + 19 = 180°
collect like terms
4x = 180 - 16
4x = 164
Make 'x' the subject of formula
x = 164/4
x = 41
Thus, the value of x is 41 . Option B
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Reasoning At a butcher shop, Hilda
bought beef and pork. She left with
18 8/25 pounds of meat. Express the
number of pounds of pork she bought
using a decimal.
Reasoning At a butcher shop, Hilda bought beef and pork. She left with 18 8/25 pounds of meat. Express the number of pounds of pork she bought using a decimal.
Hilda bought 18.32 pounds of pork.
Hilda purchased 18.32 pounds of pork, which is a terminating decimal, according to the conversion of an improper fraction to a decimal.
She left behind, in pounds, the following amount of meat:
[tex]18 \frac{8}{25}[/tex]
Now we have to convert the improper fraction to decimal, which is made adding the decimal fraction to the integer part, that is:
[tex]18 \frac{8}{25} =18+\frac{8}{25} = 18+0.32 = 18.32[/tex]
Therefore, the number of pounds of pork Hilda bought using a decimal number is 18.32.
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Brandon has a jar of quarters and dimes with a total value of $5.95. The number of quarters is 5 less than twice the number of dimes. How many quarters and how many dimes does Brandon have?
The quarters and dimes that Brandon have will be 13 quarters and 9 dimes.
How to illustrate the information?Based on the information given, the appropriate equation will be:
0.25q + 0.10d = 5.95 .... i
q = 2d - 5 .....
q = quarter
d = dime
From equation i, multiply through by 100
25q + 10 = 595
Put equation ii into i
25q + 10d = 595
25(2d - 5) + 10d = 595
50d - 125 + 10d = 595
Collect like terms
60d = 595 + 125
60d = 720
Divide
d = 720/60
d = 9
q = 2d - 5
q = 2(9) - 5
q = 18 - 5 = 13
Therefore, the quarters and dimes that Brandon have will be 13 quarters and 9 dimes.
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Evaluate a2b2c2 for a = 2, b = 3, and c = 4.
Hey there!
a^2 * b^2 * c^2
= 2^2 * 3^2 * 4^2
= 2 * 2 * 3 * 3 * 4 * 4
= 4 * 9 * 16
= 36 * 16
= 576
Therefore, your answer should be:
576
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Are the ones with answers correct? I just want to make sure I’m right
Answer:
yes just make sure to pay close attention
f(x)=x^2+8x+6 what is the value of f (4)
Answer: the answer would be 54
Step-by-step explanation:
4 x 4 = 16
8 x 4 = 32
16 + 32 + 6 = 54
Dylan prepared 49 kilograms of dough after working 7 hours. How many hours did Dylan work if he prepared 70 kilograms of dough? Solve using unit rates.
Answer:
10 hours
Step-by-step explanation:
49kilograms/7hours = 7 kilograms per hour
70 kilograms ÷ 7 kilograms per hour = 10 hours
I need help, please help!
Answer:
d because every number power of zero is one ande the negative exponent defines to 1/that number
I need help with c and 3. I’ll give brainliest.
Answer:
This might help
Step-by-step explanation:
for C-The number of lines of symmetry in a regular polygon is equal to the number of sides.
for 3 I’m not as sure but all I know is that Y is greater than 90 degrees and x is also greater than 90 degrees
if the mass is 12g and the volume is 13cm3 what is the density
[tex] \rho = \frac{mass}{volume} = \frac{12}{13} \approx0.923 \: g.cm {}^{ - 3} [/tex]
check if each of the following equalities is true for all value of the variables (1-2b)(1-5b+b^2)+(2b-1)(1-6b+b^2)=b(1-2b)
The check done confirmed that the equality is true since the value arrived at while solving the expression is same as the given value
How to check if the equalities is true for all value of the variablesGiven data
[tex](1-2b)(1-5b+b^{2} )+(2b-1)(1-6b+b^{2} )=b(1-2b)[/tex]
breaking the expansion into 2 we have
[tex]=(1-2b)(1-5b+b^{2} )[/tex]
[tex]=(1)(1)+(1)(-5b)+(1)(b^2)+(-2b)(1)+(-2b)(-5b)+(-2b)(b^2)[/tex]
[tex]=1-5b+b^2-2b+10b^2-2b^3[/tex]
[tex]=-2b^3+11b^2-7b+1[/tex]
expanding this [tex](2b-1)(1-6b+b^2)[/tex] gives:
[tex]=2b^3-13b^2+8b-1[/tex]
adding both equation gives
[tex]= -2b^3+11b^2-7b+1 + 2b^3-13b^2+8b-1[/tex]
[tex]= -2b^2 + b[/tex]
[tex]= b - 2b^2[/tex]
[tex]= b (1 - 2b)[/tex]
Since the expansion gave same value we can say that the equality is true
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first to answer gets +10 points and brainliest need help please
The dimensions of the shape allow us to find the length of PR to be 19.8 units.
What is the length of PR?The shape that is given is an equilateral triangle. This allows us to know that all the sides of the shape are equal.
This means that PR and QR are the same:
PR = QR
Equate both formulas as:
2n + 9 = 7n - 18
You can then solve for the value of n:
7n - 2n = 18 + 9
5n = 27
n = 5.4
The length of PR is therefore:
= 2n + 9
= 2 (5.4) + 9
= 19.8 units
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The sum of 15 and the prodcut of 5 and z
the expression for the statement that is given will be 15 + 5 z.
We are given the statement that the sum of 15 and the product of 5 and z
We need to make the expression that represents the statement.
First we will find out that the product of 5 and z
So, we will multiply 5 with z.
We get that:
= 5 × z = 5 z
Now we have to find the sum of 15 and 5 z
For this, we will add both the numbers.
We get that:
= 15 + 5 z
Therefore. we get that, the expression for the statement that is given will be 15 + 5 z.
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