Use logarithms to solve for a.
[tex]3^a = 2 \implies \log_3(3^a) = a\log_3(3) = \log_3(2) \implies a = \log_3(2)[/tex]
Similarly, for b and x.
[tex]3^b = 5 \implies b = \log_3(5)[/tex]
[tex]3^x = 150 \implies x = \log_3(150)[/tex]
Factorize 150:
150 = 2 • 3 • 5²
Then we can expand log₃(150) using the product-to-sum and exponent property,
[tex]\log_3(150) = \log_3(2\times3\times5^2) = \log_3(2) + \log_3(3) + \log_3(5^2)[/tex]
[tex]\implies \log_3(15) = \log_3(2) + 1 + 2 \log_3(5) \iff \boxed{x = 1 + a + 2b}[/tex]
15. Higher Order Thinking Nancy made a
table runner that has an area of 80 square
inches. The length and width of the table
runner are whole numbers. The length is
5 times greater than the width. What are
the dimensions of the table runner?
0
What are the dimensions of the table runner
The length of the rectangle is 20 inches, and the width of the rectangle is 4 inches if the table runner has an area of 80 square inches. The length and width of the table runner are whole numbers. The length is 5 times greater than the width.
What is the area of the rectangle?It is defined as the space occupied by the rectangle which is planner 2-dimensional geometry.
The formula for finding the area of a rectangle is given by:
Area of rectangle = length × width
The area of the table runner = 80 square inches
Let's assume the length of the rectangle is L and the width is W
Then L = 5×W ...(1)
L×W = 80 ...(2)
Put the value of L in the equation (2)
5W(W) = 80
5W² = 80
W² = 16
W = ±4
Width cannot be negative.
W = 4 inches putting this value in the equation (1)
L = 5(4) = 20 inches
Thus, the length of the rectangle is 20 inches, and the width of the rectangle is 4 inches if the table runner has an area of 80 square inches. The length and width of the table runner are whole numbers. The length is 5 times greater than the width.
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Given the functions:
f(x) = 7x + 2
g(x) = -18x + 2
h (x) = –19x – 11
-
Find g (-8)
Find (x+4) (x²+x-2). Write your answer in standard form.
The product is
Answer:
x³ + 5x² + 2x - 8
Step-by-step explanation:
1) Distribute
(x + 4) (x² + x - 2)
x(x² + x - 2) + 4 ( x² + x - 2)
2) Distribute
x(x² + x - 2) + 4 (x² + x - 2)
x³ + x² - 2x + 4 (x² + x - 2)
3) Distribute
x³ + x² - 2x + 4 (x² + x - 2)
x³ + x² - 2x + 4x² + 4x - 8
4) Combine like terms
x³ + x² - 2x + 4x² + 4x - 8
x³ + 5x² - 2x + 4x - 8
5) Combine like terms
x³ + 5x² - 2x + 4x - 8
x³ + 5x² + 2x - 8
50 points each question. Please help. How do I solve?
Answer:
Here's your solution mate..
21-25 Use the form of the definition of the integral given in Theorem 4 to evaluate the integral.
23. [tex]\int_{-2}^{0}\left(x^{2}+x\right) d x[/tex]
[tex]\displaystyle \int^0_{-2} (x^2 +x )~dx\\\\\\=\displaystyle \int^0_{-2} x^2~ dx +\displaystyle \int^0_{-2}x ~ dx\\\\\\=\dfrac 13 \left[x^3 \right]^{0}_{-2}+ \dfrac 12 \left[ x^2\right]^{0}_{-2}\\\\\\=\dfrac 13 (0+8) + \dfrac 12 (0-4)\\ \\\\=\dfrac 83 - \dfrac 42\\\\\\=\dfrac 83 - 2\\\\\\=\dfrac 23[/tex]
What feature might Samantha have used to sort these shapes into the same group
Answer:
picture?
Step-by-step explanation:
How is this answer correct?
Circumference is diameter x pi so the diameter of the circle is 11.
Radius is half the diameter so the radius is 11/2 = 5.5
area of a circle is r^2 x pi
Area = 5.5^2 x pi
5.5^2 = 30.25
Area = 30.25pi
Determine the solution to each of the following single variable equations. A. x-4=1/2(x+3) B -4x=1/2(-8+2) C. 3-2(-3x+1)=6x+1 D. 0.5(x+3)=-3(x-0.5)
Answer:
A. x = 11
B. x = 3/4 (or 0.75)
C. any value
D. x = 0
Step-by-step explanation:
hope this helps:)
How much is Pete's 12%
commission
on $50,000 in sales
I NEED THIS IM FAILING MATH PLSSSS
Given z1 = 5 – 2i and z2 = 3 + 2i, which letter represents z1 – z2?
[tex]z_1 - z_2 \\\\=(5-2i) -(3+2i)\\\\=5-2i-3-2i\\\\=2-4i[/tex]
Answer:
z1 - 2z = 2
Step-by-step explanation:
make 2i stand alone in both equations
therefore, in equation one, we have;
z1-5=-2i
5-z1=2i
we do same in equation 2
z2-3=2i
therefore, comparing the two equations, we can equate them!
2z-3=z1-5
-3+5=z1-2z
2 = z1 - 2z
therefore, z1 - 2z = 2
ABC and ACD are both right angled triangles. a) explain why the length of AC is 13cm.
Answer:
In the picture attached, the question is shown.
a) Applying Pythagorean theorem to triangle ABC, and solving for AC:
CB² + BA² = AC²
5² + 12² = AC²
√169 = AC
13 cm = AC
b) Applying Pythagorean theorem to triangle ACD, and solving for AD:
CD² + AC² = AD²
5² + 13² = AD²
√194 = AD
13.9 cm = AD
Step-by-step explanation:
Giselle works as a carpenter and as a blacksmith.
She earns $20per hour as a carpenter and $25dollar sign per hour as a blacksmith. Last week, Giselle worked both jobs for a total of 30 hours, and earned a total of $690
How long did Giselle work as a carpenter last week, and how long did she work as a blacksmith?
Answer:
she worked 12 hours as a carpenter and 18 hours as a blacksmith
Step-by-step explanation:
Let x = the number of hours for which she worked as a carpenter
Let y = be the number of hours for which she worked as a blacksmith
Total numbers of hours she worked = 30
x + y = 30 (1)
she earned a total $690. She earned $20 dollar per hour as a carpenter and $25 per hour as a blacksmith.
20 x + 25 y = 690 (2)
Equation (2) - 20 × Equation (1),
We get,
5 y = 90 ⇒ y = 18
After substituting this value in equation (1),
We get, x = 12,
Hence, She worked as a carpenter = x hours = 12 hours
And, as a blacksmith = y hours = 18 hours
Money is borrowed at %18 simple interest. After one year, $981.76 pays off the loan. How much was originally borrowed?
Answer:
$805.0432
Step-by-step explanation:
118% was paid, so the original would be 82% of 981.76 (100-18), which is $805.0432 (rounds to $805.04)
26,30,45,43,26,14,28,33,56,29,what is the mean absolute deviation of the data set
Answer: 9.
Step-by-step explanation: To find the MAD (mean absolute deviation) we need to do the following steps below:
1. Find the mean.
2. Subtract the mean from the numbers of the data.
3. Add the results and divide to find the MAD.
The steps are done below:
1. Find the mean: In order to find the mean of a data set, you need to add all the numbers and then divide the result by how many numbers there are in the data set. In this problem, there are 10 numbers in the data set, so whatever we get for adding the data numbers together needs to be divided by 10.
26 + 30 + 45 + 43 + 26 + 14 + 28 + 33 + 56 + 29 = 330.330 / 10 = 33.2. Subtract the mean from the numbers of the data: To do this, we need to subtract 33 from all the numbers on the data. The following is done below. (*Note: You may notice that most equations like 26 - 33 would be in the negatives, but for data, it has to be positive. If you ever run into a situation like that, you simply just make it positive).
26 - 33 = 7.30 - 33 = 3.45 - 33 = 12.43 - 33 = 10.26 - 33 = 7.14 - 33 = 19.28 - 33 = 5.33 - 33 = 0.56 - 33 = 23.29 - 33 = 4.3. Add the results and divide to find the MAD: Now that we have the results, we add those numbers and then divide to find the MAD. Make sure that when you divide that it is 10 that you're dividing because once again, there are 10 numbers for the results.
7 + 3 + 12 + 10 + 7 + 19 + 5 + 0 + 23 + 4 = 90.90 / 10 = 9.Therefore, 9 is the MAD.
Let me know if this is right! :)
Can Someone Explain? The Question Is In The Picture!
[tex](256)^{\tfrac 14}\\\\=(4^4)^{\tfrac 14}\\\\=4^{\tfrac 44}\\\\=4^1 \\\\= 4\\\\\\27^{\tfrac 13}\\\\=(3^3)^{\tfrac 13}\\\\=3^{\tfrac 33} \\\\=3^1\\\\=3[/tex]
There are 25 women in a class of 35 students. Find the percent of men in the class to the nearest tenth of a percent.
Answer:
28.57
Explanation:
35 is the total amount of students.
25 is the amount of women in the class, we can assume the rest are men.
35 Total students - 25 women = 10 men
10 men, 35 Total students
(10/35) × 100 = 28.57%
Please help me on this
to get the equation of any straight line, we simply need two points off of it, so hmm let's use the two points you see in the picture below from the provided table.
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{1}}}\implies \cfrac{5+1}{3}\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{2}(x-\stackrel{x_1}{1}) \\\\\\ y+1=2x-2\implies y=2x-3[/tex]
Consider the following information regarding the performance of a money manager in a recent month. The table
represents the actual return of each sector of the manager's portfolio in column 1, the fraction of the portfolio
allocated to each sector in column 2, the benchmark or neutral sector allocations in column 3, and the returns of
sector indices in column 4.
Index Re
Actual Return
2.28
Actual Weight
0.4
Benchmark Weight
0.5
Equity
Bonds
Cash
2.78 (S&P 500)
1.5 (Barclay's Age
1.1
0.2
0.2
0.7
0.4
0.3
0.8
Required:
a-1. What was the manager's return in the month? (Do not round intermediate calculations. Input all amounts as
positive values. Round your answer to 2 decimal places.)
ces
The manager's return in the month is
%
a-2. What was her overperformance or underperformance? (Do not round intermediate calculations. Input all
amounts as positive values. Round your answer to 2 decimal places.)
a-1. The manager's return in the month, based on the performance table information, is 1.38%.
a-2. The manager's underperformance is 0.51% (1.89 - 1.38).
What is a manager's underperformance?A manager's underperformance occurs when the manager delivers results below expectation.
For instance, the weighted benchmark return was expected to be 1.89%, but the manager achieved an actual weighted return of 1.38%.
Data and Calculations:(1) Actual (2) Actual (3) Benchmark (4) Index
Return Weight Weight Return
Equity 2.2% 0.4 0.5 2.7% (S&P 500)
Bonds 1.1 0.2 0.2 1.5 (Barclays Aggregate Bond index)
Cash 0.7 0.4 0.3 0.8
(1) Actual (2) Actual Weighted
Return Weight Returns
Equity 2.2% 0.4 0.88%
Bonds 1.1 0.2 0.22
Cash 0.7 0.4 0.28
Weighted Returns = 1.38%
Benchmark (4) Index Weighted
Weight Return Benchmark
Equity 0.5 2.7% (S&P 500) 1.35% (0.5 x 2.7)
Bonds 0.2 1.5 (Barclays 0.30 (0.2 x 1.5)
Aggregate Bond index)
Cash 0.3 0.8 0.24 (0.3 x 0.8)
Weighted Benchmark Return = 1.89%
Thus, there was a comparative underperformance of 0.51%.
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A triangle has sides with lengths of 15 meters, 36 meters, and 39 meters. Is it a right triangle?
if x² = 64, then 1/3 + x⁰
Answer:
4/3 or 1 1/3
Step-by-step explanation:
Finding x
x² = 64x = ±8Substitute in the equation
1/3 + (±8)⁰1/3 + 14/3 or 1 1/3Answer:
[tex]\huge\boxed{\bf\:\frac{4}{3} }[/tex]
Step-by-step explanation:
If, [tex]x^{2} = 64[/tex], then,
[tex]x^{2} = 64\\x = \sqrt{64}\\x = (+/-)8[/tex]
Now, remember that any number when folllowed by exponent 0 will always have its value as 1.
Then,
[tex]\frac{1}{3} + x^{0} \\ =\frac{1}{3} + (+/-8)^{0} \\= \frac{1}{3} + 1\\=\frac{1}{3} +\frac{3}{3} \:\:\:\: (LCM = 3)\\ \boxed{\bf\:\frac{4}{3} }[/tex]
[tex]\rule{150pt}{2pt}[/tex]
Determine whether each relation is a function and give a reason?
1. {(24, 1) , (21 , 4 ) , (3 , 22) , (24 ,5)}
2. y= x + 3
Answer:1.1.this relation is function because domains are not repeated
Step-by-step explanation:
In a group of 30 students, the probability that at most 25 of them lime to swim is 45% what is the probability that at least 26 of them like to swim
Its 62%
I took the test
I need help with conversation rates. So it says
Approximately 30,300 citizens of a country died in an automobile accidents in 2015. Express this toll in deaths per day.
Answer:
144 deaths
Step-by-step explanation:
So, assuming it's not a leap year 30,300 must be divided by the number of days in the year to get the daily amount.
30,300/365 = 114.339....
since 3 is not greater than 5, the 144 does not round up but stays the same.
(Since you cannot have a fraction of a death)
114 is your answer
hope this helps :)
Which two expressions are equivalent?
F. 13 + (16 - x) and (16 + x) + 13
G. x + (4 • 5) and (x + 4) • 5
H. 7(10 + x) and (7 • 10)+ x
J. (8 + x) + 9 and 8 + (x + 9)
Graph 4x^2-16 divided by 2x-4
Answer:
2x+4
Step-by-step explanation:
factor 4x²-16
=(2x+4)(2x-4)
=(2x+4)(2x-4)/ 2x-4
cancel out the common factors of 2x-4
Answer= 2x+4
Chaz kept a record of how many gallons of gas he purchased each day last week. Drag and drop the days into the correct boxes to order the days from the least amount of gas Chaz purchased to the greatest amount of gas Chaz purchased.
Day Gas (in gallons)
Monday 4.5
Tuesday 3.6
Wednesday 4.258
Thursday 3.77
Friday 4.252
HELP MEEE!!!
I'm in 5th grade btw
The circumference of a circle is 10π ft. What is the area, in square feet? Express your answer in terms of \piπ.
Answer:
A = 25π square feet
Step-by-step explanation:
C = 2πr
10π = 2πr
10π = 2πx
10π / 2π = 2πx / 2π
5 = x
This means 5 is the radius of the circle. We now need to find the area:
A = πr[tex]r^{2}[/tex]
A = π(5)²
A = π(25)
A = 25π
IF CORRECT ILL MARK BRAINLIEST
FIND THE SURFACE AREA OF THE CYLINDER
Answer: A≈1015.4
Step-by-step explanation:
A=2πrh+2πr2=2·π·8·12.2+2·π·82≈1015.36275
Answer:
407 mm²
Step-by-step explanation:
The formula for the surface area of a clyinder is: A = 2[tex]\pi[/tex]r · (r + h)
Plugging in the given values, we have: A = 2[tex]\pi[/tex]4 · (4 + 12.2)
A = 2[tex]\pi[/tex]4 · (4 + 12.2)
A = 2[tex]\pi[/tex]4 · 16.2
A = 2(3.14)4 · 16.2
A = 406.944
A = 407 (rounded)
hope this helps!
9j/5-6j simplify your answer. Type a interger or a fraction. Type your answer in the form a+bj
Translate the following:
"twice the sum of a number and three is eighteen"
Answer:
7.5
Step-by-step explanation:
how i figured it is 18-3 is 15
2*7 is 14 so in turn 7.5 *2 is 15 so
z=7.5
This can be represented in the form of an equation as: 2(x + 3) = 18.So, the correct Answer is A. 2(x+3)=18.
The correct translation of the given sentence is:" twice the sum of a number and three is eighteen".
The equation "2(x + 3) = 18" correctly represents the statement "twice the sum of a number and three is eighteen."
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