Answers
Answer:
2. m = b³ (= 216)
3. logp(x) = -4
Step-by-step explanation:
2. The given equation can be written using the change of base formula as ...
... log(m)/log(b) + 9·log(b)/log(m) = 6
If we define x = log(m)/log(b), then this becomes ...
... x + 9/x = 6
Subtracting 6 and multiplying by x gives ...
... x² -6x +9 = 0
... (x -3)² = 0 . . . . . factored
... x = 3 . . . . . . . . . value of x that makes it true
Remembering that x = log(m)/log(b), this means
... 3 = log(m)/log(b)
... 3·log(b) = log(m) . . . . . multiply by the denominator; next, take the antilog
... m = b³ . . . . . . the expression you're looking for
___
3. Substituting the given expression for y, the equation becomes ...
... logp(x^2·(p^5)^3) = 7
... logp(x^2) + logp(p^15) = 7 . . . . . use the rule for log of a product
... 2logp(x) + 15 = 7 . . . . . . . . . . . . . use the definition of a logarithm
... 2logp(x) = -8 . . . . . . . . . . . . . . . . subtract 15
... logp(x) = -4 . . . . . . divide by 2
Answer:
For #3: [tex]\log_px=-4[/tex]
Step-by-step explanation:
I'm a little rusty on my logarithm rules for #2, but here's an explanation of #3.
Logarithms: the Inverse of ExponentsIn a sense, we can think of operations like subtraction and division as different ways of representing addition and multiplication. For instance, the same relationship described by the equation 2 + 3 = 5 is captured in the equation 5 - 3 = 2, and 5 × 2 = 10 can be restated as 10 ÷ 2 = 5 without any loss of meaning.
Logarithms do the same thing for exponents: the expression [tex]2^3=8[/tex] can be expressed in logarithms as [tex]\log_28=3[/tex]. Put another way, logarithms are a sort of way of pulling an exponent out onto its own side of the equals sign.
The ProblemOur problem gives us two facts to start: that [tex]log_p(x^2y^3)=7[/tex] and [tex]p^5=y[/tex]. With that, we're expected to find the value of [tex]\log_px[/tex]. [tex]p^5=y[/tex] stands out as the odd-equation-out here; it's the only one not in terms of logarithms. We can fix that by rewriting it as the equivalent statement [tex]log_py=5[/tex]. Now, let's unpack that first logarithm.
Justifying Some Logarithm RulesFor a refresher, let's talk about some of the rules logarithms follow and why they follow them:
Product Rule: [tex]\log_b(MN)=\log_bM+\log_bN[/tex]
The product rule turns multiplication in the argument (parentheses) of a logarithm into addition. For a proof of this, consider two numbers [tex]M=b^x[/tex] and [tex]N=b^y[/tex]. We could rewrite these two equations with logarithms as [tex]\log_bM=x[/tex] and [tex]\log_bN=y[/tex]. With those in mind, we could say the following:
[tex]\log_b(MN)=\log_b(b^xb^y)[/tex] (Substitution)[tex]\log_b(b^xb^y)=log_b(b^{x+y})[/tex] (Laws of exponents)[tex]\log_b(b^{x+y})=x+y[/tex] ([tex]\log_b(b^n)=n[/tex])[tex]x+y=\log_bM+\log_bN[/tex] (Substitution)And we have our proof.
Exponent Rule: [tex]\log_b(M^n)=n\log_bM[/tex]
Since exponents can be thought of as abbreviations for repeated multiplication, we can rewrite [tex]\log_b(M^n)[/tex] as [tex]\log_b(M\times M\cdots \times M)[/tex], where M is being multiplied by itself n times. From there, we can use the product rule to rewrite our logarithm as the sum [tex]\log_bM+\log_bM+\cdots+\log_bM[/tex], and since we have the term [tex]\log_bM[/tex] added n times, we can rewrite is as [tex]n\log_bM[/tex], proving the rule.
Solving the ProblemWith those rules in hand, we're ready to solve the problem. Looking at the equation [tex]\log_p(x^2y^3)=7[/tex], we can use the product rule to split the logarithm into the sum [tex]\log_p(x^2)+\log_p(y^3)=7[/tex], and then use the product rule to turn the exponents in each logarithm's argument into coefficients, giving the equation [tex]2\log_px+3\log_py=7[/tex].
Remember how earlier we rewrote [tex]p^5=y[/tex] as [tex]log_py=5[/tex]? We can now use that fact to substitute 5 in for [tex]log_py[/tex], giving us
[tex]2\log_px+3(5)=7[/tex]
From here, we can simply solve the equation for [tex]\log_px[/tex]:
[tex]2\log_px+15=7\\2\log_px=-8\\\\\log_px=-4[/tex]
Related Questions
Answer this please, thanks
Answers
Answer:
B
Step-by-step explanation:
under a dilatation about the origin of scale factor 3
since dilatation is about the origin multiply the coordinates of A, B and C by 3
A(8, 15) → A' (24, 45)
B(12, 13) → B'(36, 39)
C(8, 10) → C'(24, 30)
using the distance formula
with (x₁, y₁ ) = C'(24, 30) and (x₂, y₂ ) = B'(36, 39)
BC = [tex]\sqrt{(36-24)^2+(39-30)^2}[/tex]
= [tex]\sqrt{144+81}[/tex] = [tex]\sqrt{225}[/tex] = 15 → B
2.25 ÷ 2.5 (Long division Work)
Answers
Answer:
Its 0.9
Step-by-step explanation:
this is a good enpugh answer
The graph of the equation y = x2 - 3 is shown. Which equation will shift the graph up 6 units?
Answers
Answer:
Here’s the graph
Step-by-step explanation:
Multiply the polynomial
(4d-3)(-2d+1)
Answers
Answer:
-8d^2+10d-3
Hope i helped if i am wrong tell me please :)
Step-by-step explanation:
combine like terms
3.25+0.5x+1 (1)/(3) + (5)/(6) x=5 (11)/(12)
solve for x
Answers
Answer,
X = 3/4
Explanation,
Step 1: Simplify both sides of the equation.
3.25 + 0.5x + (1)(1)/3 + 5/6x = (5)(11)/12
3.25 + 0.5x + 1/3 + 5/6x = 55/12
(0.5x + 5/6x) + (3.25 + 1/3) = 55/12 (Combine Like Terms)
4/3x + 3.583333 = 55/12
4/3x + 3.583333 = 55/12
Step 2: Subtract 3.583333 from both sides.
4/3x + 3.583333 − 3.583333 = 55/12 − 3.583333
4/3x = 1
Step 3: Multiply both sides by 3/4.
(3/4) * (4/3x) = (3/4) * (1)
x = 3/4
Gregg has a coin collection album with 275 pages. Each coin is displayed on 1/6 of a page. How many coins will fit in the page?
Answers
Answer:
1650
Step-by-step explanation:
If there are 275 pages and each page can fits 6 coins then you multiply 6 by 275.
Answer:
6 on each page; 1,650 in total coins for all the pages
Step-by-step explanation:
1. The first step is to multiply 1/6*6 to find out how many coins can fit on one page.
2.The second step is to multiply 6 *275. That equals 1,650
What are the actual dimensions of a television that has a 15:9 aspect ratio and a screen that is 42 inches?
Answers
Answer:
Let x be the number.
It is given that a 15 : 9 aspect ratio and a screen that is 42 inches.
Aspect ratio states that the ratio of the display image’s width to its height.
Then;
Width of the television of(w) = 15x
and
height of the television(h) = 9x.
Since, television is in the form of Rectangle.
and it is also, given that the screen is 42 inches .
⇒Diagonal of the television(D) = 42 inches
Using formula of diagonal of the rectangle :
[tex]D^2 =w^2+h^2[/tex]
Substitute the given values to solve for x;
[tex]42^2 = (15x)^2+(9x)^2[/tex]
[tex]1764 = 225x^2 + 81x^2 = 306x^2[/tex]
or
[tex]x^2 = \frac{1764}{306} = 5.76[/tex]
[tex]x = \sqrt{5.76} = 2.4[/tex]
Then:
width of the television (15x) = 15(2.4) = 36 inches and
Height of the television (9x) = 9(2.4) = 21.6 inches.
Therefore, the actual dimensions of the television are;
width = 36 inches and height = 21.6 inches.
which expression is equivalent to the given expression after using the distributive property 6*13+6*7
Answers
Answer: 6*(13+7) = 60
Step-by-step explanation:
6*13+6*7
6*(13+7) = 6*10 =60
The required equivalent expression is [tex]6(13+7)[/tex].
Given:
The expression is:
[tex]6\times 13+6\times 7[/tex]
To find:
The equivalent expression of the given expression by using the distributive property.
Explanation:
Distributive property: If [tex]a,b,c[/tex] are three real numbers, then
[tex]a(b+c)=ab+ac[/tex]
We have,
[tex]6\times 13+6\times 7[/tex]
Using the distributive property, we get
[tex]6\times 13+6\times 7=6(13+7)[/tex]
Therefore, the required equivalent expression is [tex]6(13+7)[/tex].
Learn more:
https://brainly.com/question/7627111
Which of these tables represents a function
Answers
Table D if you graph them and do the line test ( where you take a vertical line and see if it touches two points on a graph) you will see that everything else EXCPET D will be touched by the vertical line.
which of the following is the equation of a line that passes through the point (1,2) and is parallel to the x-axis?
A. x=2
B. y=2
C. y=1
D. x=1
Answers
Answer:
The equation of line would be y = 2
Step-by-step explanation:
Since the x-axis is horizontal, we would look for another horizontal line to be parallel. All horizontal lines can be written as y = (a number). We can find that number as the y-coordinate in the ordered pair (2)
y = 2
which equation is represented by the table? a) y=|x-4| b) y=|x|-4 c) y=|x|+4 d) y=|x+4|
Answers
Answer:
option (a) y=|x-4| is correct.
Step-by-step explanation:
Solve the question by elimination method i.e. put values of x in the given equations and check if equality holds.
(b) if x=2, then y= |2| - 4 = -2 , which is wrong
(c) if x=2, then y = |2| + 4 = 6, which is wrong
(d) if x= 2, then y = |2 + 4| = 6, which is wrong
The equality holds for (a).
Perry won 122 lollipops playing horseshoes at the county fair. At school he gave four to every student in his math class. He only has 6 remaining. How many students are in his class
Answers
Answer:
29 students
Step-by-step explanation:
First you subtract 6 from 122 so you aren’t counting the remaining 6. You get 116
Then you divide 116 by 4 to find how many students are in his class which is 29
PLEASE ANSWER ASAP
Which table shows a proportional relationship?
b 1 4 5 7 11
c 3 12 15 21 33
p 1 3 5 7 9
q 0 2 4 6 8
r 3 6 10 12 15
s 2 4 6 8 10
x 1 2 3 4 5
y 9 10 11 12 13
Answers
Answer:
b
Step-by-step explanation:
If you look at the table with b and c, if you multiply b by 3, you get your answer for c directly below.
This does not apply for the rest of the tables. For example, p and q, you cannot multiply 1 by any number to achieve 0, or multiply 3 by a number to get 2.
I hope this helped, and if you don’t mind, giving me brainiest!
Michelle Smith bought 30 shares of James Company stock at $34 per share. The company paid annual dividends of $0.42 per share. What is the total annual dividend? Show work
A) 9.78
B) 12.60
C) 1.69
D) 11.97
Answers
Answer:
The right option is B) 12.60
Step-by-step explanation:
We have given,
Number of shares = 30
Cost of each share = $34
Total cost of shares = 30 × 34 = $1020
Since the company paid annual dividends of $0.42 per share.
i.e Total annual dividend company paid = 0.42 × 30
Total annual dividend company paid = $ 12.60
Hence the right option is B) 12.60
in a parking lot, 43% of the cars have GPS. express this percent as a decimal.
Answers
Answer: 0.43
Think of 43% as 43.0%
Move the decimal 2 spots to the left to go from 43.0 to 0.43
Alternatively, use a calculator to find that 43% = 43/100 = 0.43
"percent" means "per 100", so that's why we're dividing over 100.
The elevations of five points below sea level are given here. Which elevation is closest to sea level? A. -50 feet B. -68 feet C. -77 feet D. -86 feet E. -97 feet
Answers
Answer:
A. -50 feet
Step-by-step explanation:
To find the number closest to sea level, take the absolute value of each number and see which is closest to zero.
A. -50 feet abs (-50) = 50
B. -68 feet abs (-68) = 68
C. -77 feet abs (-77) = 77
D. -86 feet abs ( -86) = 86
E. -97 feet abs (-97) = 97
The smallest number is 50. -50 ft is closest to sea level
Answer:
Step-by-step explanation:
A. 50
Mrs. Bea’s Bakery offers a Saturday morning special where your entire meal is 15% off. How much will a $32.00 meal cost after the special?
Answers
Answer:
27.2
Step-by-step explanation:
32*.85=27.2
Answer:
$27.20
Step-by-step explanation:
15 percent of 32 is 4.8
32-4.8= 27.20 so $27.20
How do I graph this?
Answers
In a diagram shown,
PQRS is a rectangle
XY is parallel to PS
RY= 9cm
Area of PQRS = 84cm^2
Area of PXYS = 21cm^2
Work out the values of a and b
You must show all your working.
Answers
=84-21
=63
a*9=63
/9. /9
a=7
b*7=21
/7. /7
b=3
Answer:
a = 7cm
b = 3cm
Step-by-step explanation:
84 - 21 = 63cm²
XYRQ = 63cm²
63 / 9 = 7cm
a = 7cm
21 / 7 = 3cm
b = 3cm
A certain drug is made from only two ingredients: compound A and compound B. There are
milliliters of compound A used for every
milliliters of compound B. If a chemist wants to make
milliliters of the drug, how many milliliters of compound A are needed?
Answers
Answer:
425 milliliters of compound A are needed
Step-by-step explanation:
We were told that [tex]5[/tex] milliliters of compound A and [tex]6[/tex] milliliters of compound B is needed to make the drug.
This means that each drug contains 11 milliliters of both compounds.
[tex]\frac{935}{11}=85[/tex] milliliters is the volume of each drug.
Therefore the chemist needed [tex]5\times 85=425[/tex] millilirteres of compound A.
In order to find out how much of compound A is needed, we would set up a ratio using the amounts provided of compound A and B. Then, we cross multiply and solve for the unknown amount of compound A needed for the specific quantity of the drug.
Explanation:This problem is about ratios. We know that specific quantities of compound A and compound B are combined to make a certain amount of the drug. However, the quantities of compound A and B are not mentioned in the question. If they were provided, we would set up a ratio equal to the total amount of the drug and cross multiply to solve for the amount of compound A needed.
An example might look something like this: if the drug is made of 2 milliliters of compound A for every 3 milliliters of compound B and we wanted to make 5 milliliters of the drug. You would set it up like this:
2 (Compound A) / 3 (Compound B) = x (Amount of compound A needed) / 5 (Total Amount of drug needed)
Cross multiplying gives us: 2 * 5 = 3 * x
This simplifies to: 10 = 3x
Dividing each side by 3 then gives the amount needed of compound A: x = 3.33 milliliters.
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It is suggested that an adult drink 64 fluid ounces of water every day. Josey, has already consumed 700 milliliters of water. How many more liters should he drink today?
Answers
Answer:
1.3 L more.
Step-by-step explanation:
Givens
8 fluid ounces = 1 cup.
240 mL = 1 cup
Solution
4 cups = 1 L
64 fluid ounces = x cups
8/64 = 1 / x Cross multiply
8x = 64 Divide by 8
8x/8 = 64/8
x = 8 cups
So we should be drinking 8 cups a day
1 L = 4 cups
x = 8 cups Cross multiply
4x = 8 cups Divide by 4
x = 8/4
x = 2 Liters.
1 L = 1000 mL
x L = 700 mL
700 * 1 = 1000 * x
Divide by 1000
x = 700 / 1000
x = 0.7 L
He needs to drink 2 L - 0.7L
1.3 more liters.
Answer: 1.3 L
Step-by-step explanation:
EASY TO ANSWER HELPP PLEASE
Answers
Answer:
(17.8 , 1.6)
Write write an exponential growth function for the following situation you are depositing $5,000 into a bank with an interest rate of 9% for x years
Answers
[tex]\bf \qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &5000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=\textit{elapsed time}\dotfill &x\\ \end{cases} \\\\\\ A=5000(1+0.09)^x\implies A=5000(1.09)^x[/tex]
There are 9 computers and 72 students. What is the unit rate of students to computers? pleaase help meee
Answers
PLEASE GIVE BRAINLIEST
Answer:
1:8
Step-by-step explanation:
We know that every 9 computers there are 72 students, so if we divide 72 by 9 it will be 8. Therefore for 1 computer it has 8 students.
There are 12 boys and 15 girls in your class.Four new students, 3 boys and 1 girl , join your class. Compare the ratio of boys and girls before and after the new students enrolled.
Answers
Answer:
4:5 ,15:16
Step-by-step explanation:
divide 12 and 15 by 3 to get 4 and 5
The area of a trapezoid is 60 square inches. The sum of the bases is 20 inches. Find the height of the trapezoid.
Answers
Answer:
The area of a polygon is the number of square units inside that polygon. Area is 2-dimensional like a carpet or an area rug.
trapezoidA trapezoid is a 4-sided figure with one pair of parallel sides. For example, in the diagram to the right, the bases are parallel. To find the area of a trapezoid, take the sum of its bases, multiply the sum by the height of the trapezoid, and then divide the result by 2, The formula for the area of a trapezoid is:
area_trapezoid1.gif or area_trapezoid2.gif
Where b1.gif is base1.gif, b2.gif is base2.gif, h.gif is height and · means multiply.
Each base of a trapezoid must be perpendicular to the height. In the diagram above, both bases are sides of the trapezoid. However, since the lateral sides are not perpendicular to either of the bases, a dotted line is drawn to represent the height.
In Examples 1 and 3 below, the height is a side of the trapezoid since it is perpendicular to the base. In Example 2, the lateral sides are not perpendicular to the base, so a dotted line is drawn to represent the height.
Example 1: Find the area of a trapezoid with bases of 10 inches and 14 inches, and a height of 5 inches.
trapezoidSolution:
area_trapezoid2.gif
a_0.gif = one_half.gif · (10 in + 14 in) · 5 in
a_0.gif = one_half.gif · (24 in) · (5 in)
a_0.gif = one_half.gif · 120 in2
a_0.gif = 60 in2
Example 2: Find the area of a trapezoid with bases of 9 centimeters and 7 centimeters, and a height of 3 centimeters.
Solution:
trapezoidarea_trapezoid2.gif
a_0.gif = one_half.gif · (9 cm + 7 cm) · 3 cm
a_0.gif = one_half.gif · (16 cm) · (3 cm)
a_0.gif = one_half.gif · 48 cm2
a_0.gif = 24 cm2
Example 3: The area of a trapezoid is 52 square inches and the bases are 11 inches and 15 inches. Find the height.
trapezoidSolution:
area_trapezoid2.gif
52 in2 = one_half.gif· (11 in + 15 in) · h.gif
52 in2 = one_half.gif· (26 in) · h.gif
52 in2 = (13 in) · h.gif
52 in2 ÷ (13 in) = h.gif
h.gif = 4 in
trapezoidSummary: To find the area of a trapezoid, take the sum of its bases, multiply the sum by the height of the trapezoid, and then divide the result by 2, The formula for the area of a trapezoid is:
area_trapezoid1.gif or area_trapezoid2.gif
Where b1.gif is base1.gif, b2.gif is base2.gif, h.gif is height.
Step-by-step explanation:
A pancake recipe calls 4 cups of loud and 3 cups milk. Does a recipe calling for 2 cups flour and 1.5 cups milk use the same ratio of flour to milk
Answers
Both ratios would equal the same if the 4:3 was simplified, leading the two recipes to be 2:1.5
Answer:
yes
Step-by-step explanation:
Because 4:3 simplifies to 2:1.5
What is the value of the expression (-8/9) divided by (-2/3) multiplied by (-4 1/2)
Answers
Final answer:
The value of the expression is -12, obtained by first converting mixed numbers to improper fractions, dividing and then multiplying the resulting fractions, and finally simplifying them.
Explanation:
The value of the expression (-8/9) divided by (-2/3) multiplied by (-4 1/2) is computed as follows:
Convert the mixed number (-4 1/2) to an improper fraction. (-4 1/2) = -4 - 1/2 = (-8/2) - (1/2) = (-9/2).Divide the fractions (-8/9) by (-2/3) by multiplying by the reciprocal of the divisor. (-8/9) ÷ (-2/3) = (-8/9) × (-3/2) = 8/3.Multiply the result by the improper fraction (-9/2). (8/3) × (-9/2) = -72/6.Simplify the resulting fraction, which gives -12 as the final answer.The Law of Large Numbers states that as the number of trials of an experiment increases, the experimental probability of an event occurring approaches the theoretical probability of the event occurring. Jake received a "magic" coin from his uncle. He flipped it 100 times, and found that it came up heads 64% of the time. He flipped it another 500 times, and it came up heads 57% of the time. He then flipped it 1000 times, and it came up heads 58% of the time. Then, he flipped it 1500 times, and it came up heads 62% of the time. Based on the Law of Large Numbers, what do you think the theoretical probability of the magic coin coming up heads is? Explain how you could test your hypothesis.
Answers
The law of large number states that , if number of trials increases in an experiment , in a fair trial where each outcome has same chance of occurring or having equal probabilities,when total number of trials goes higher and higher the probabilities of each single outcome becomes approximately equal.→→In case of Experimental Probability
The Coin Possessed by Jake is a Magic coin.
Now Outcomes received by jake when he tosses the coin certain number of times.He flipped it 100 times, and found that it came up heads 64% of the time. He flipped it another 500 times, and it came up heads 57% of the time. He then flipped it 1000 times, and it came up heads 58% of the time. Then, he flipped it 1500 times, and it came up heads 62% of the time.
Based on the information provided , it appears that coin is not fair . It is Unbiased.So , if we apply law of large numbers here after number of trials will go higher and higher , the chances of coming head will be more than tail i.e theoretical probability of the magic coin coming up heads is> 50%.
To test my hypothesis i have used the information provided by Jake, which shows that coin is not fair. The probability of head has more than tail i.e by 14%, 7%,8% and 12%.
HELPPP PLZZ I REALLY NEED HELP
Answers
Answer: A.
The reason is because if you're adding a negative to a number, it's subtraction, which is in the expression.
Answer:
The answer is A.
Step-by-step explanation:
Adding a negative is the same as subtracting