Write the equation in exponential form. Assume that all constants are positive and not equal to 1. logz(w) = p ________
Write the equation in exponential form. Assume that all constants are positive and not equal to 1. log(s) =r ________
Write the equation in logarithmic form. Assume that all constants are positive and not equal to 1. 7m = a ________
Answers
To write the equation in exponential form we must follow certain rules:
1. Logarithm product rule - log b ( x ∙ y) = log b ( x) + log b ( y)
2. Logarithm quotient rule - log b ( x / y) = log b ( x) - log b ( y)
3. Logarithm power rule - log b ( x y) = y ∙ log b ( x)
4. Logarithm base switch rule - log b ( c) = 1 / log c ( b)
1. ㏒z(w) = p
Here all constants are taken to be positive and not equal to 1
z = base of the logarithmic function
z^p = w --------> (1)
This z^p = w is the exponential form of ㏒z(w) = p
2. ㏒(s) = r
Here all constants are taken to be positive and not equal to 1
e = base of the logarithmic function
e^r = s --------> (2)
This e^r = s is the exponential form of ㏒(s) = r
3. 7m = a
Here we have to write the equation in logarithmic form
㏒(7m) = log r
log(7m) - log r = 0
We know quotient rule :-
log b ( x / y) = log b ( x) - log b ( y) --------(A)
Applying that same principle to our question by using this equation we have:
log (7m/r)
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Related Questions
Lin's family has traveled 25 miles which is only 20% of the trip.
How far is the whole trip?
a.
5 miles
c. 100 miles
b.
125 miles
d. 250 miles
Please hurry
Answers
Answer: 125 miles
Step-by-step explanation:
We know that 25 miles is 20% of the trip.
20% is 1/5 of 100, so that means we will multiply the number of miles driven by the denominator of the fraction.
25 × 5 = 125 miles
The answer to the question is 125 miles.
Rectangle ABCD is reflected over the y axis. what rule show input and output of the reflection, and what is the new coordinate?
answers are in pic
Answers
Answer:
C. (x,y) → (-x,y); A' is at (5,1)
Please HELP!!!!!
The domain (input values) of the cosine function is:
A. angle measures less than 2π radians.
B. angle measures between 0 and π radians.
C. angle measures less than 90°.
D. all negative and positive angle measures.
SUBMIT
Answers
Answer: D. all negative and positive angle measures.
solve the triangle for which angle a =30\degree, angle b=45\degree, and a=20
Answers
The triangle for which angle a =30\degree, angle b=45\degree, and a=20, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636
Two angles (a and b) and one side (a) are provided for us to solve the triangle. Let's call the side across from angle a side A, the side across from angle b side B, and the side across from the final angle (angle c) side C.
Here, it is given that,
angle a = 30 degrees
angle b = 45 degrees
side a = 20
angle c = 180 - (angle a + angle b)
angle c = 180 - (30 + 45)
angle c = 180 - 75
angle c = 105 degrees
We know that, a/sin(A) = b/sin(B) = c/sin(C)
a/sin(A) = b/sin(B) = c/sin(C)
20/sin(30) = b/sin(45) = c/sin(105)
b/sin(45) = 20/sin(30)
b = (sin(45) * 20) / sin(30)
b ≈ (0.7071 * 20) / 0.5
b ≈ 14.142 / 0.5
b ≈ 28.284
Now,
c/sin(105) = 20/sin(30)
c = (sin(105) * 20) / sin(30)
c ≈ (0.9659 * 20) / 0.5
c ≈ 19.318 / 0.5
c ≈ 38.636
Thus, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636.
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PLEASE HELP DUE SOON!
I'm so confused, help determine the 100th line segment from question below!
Answers
Answer:
20200
Step-by-step explanation:
As you're in a hurry, I can give it later? xx
Write an equation in slope intercept form for a line with points (3,1)and(7,9)
Answers
First of all, we need to remember that the equation to find the slope m, given 2 points with coordinates:
\(\begin{gathered} (x_1,y_1);\text{ point 1} \\ (x_2,y_2);\text{ point 2} \\ \text{slope = m = }\frac{(y_2-y_1)}{(x_2-x_1)} \end{gathered}\)Now, for given points:
\(\begin{gathered} \text{slope = m = }\frac{(y_2-y_1)}{(x_2-x_1)};(x_1,y_1)\text{ = (3,1); }(x_2,y_2)\text{ = (7,9)} \\ \text{slope = m = }\frac{(y_2-y_1)}{(x_2-x_1)}=\frac{(9-1)}{(7-3)}=\frac{8}{4}=2 \\ \text{slope = m =2} \end{gathered}\)Finally, the answer is that the value of the slope is 2.
What is the equation of the line that passes through the point (-6,8) and has a slope of -5/3? Please show step by step solution,
Answers
Answer:
The equation of the line that passes through the point (-6,8) and has a slope of -5/3 is y = (-5/3)x - 2.
Step-by-step explanation:
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
We have the point (-6,8) and a slope of -5/3.
Step 1: Use the point-slope formula to find the equation of the line in point-slope form.
y - y1 = m(x - x1)
where x1 and y1 are the coordinates of the given point.
y - 8 = (-5/3)(x - (-6))
Simplify this equation:
y - 8 = (-5/3)(x + 6)
Step 2: Convert the equation to slope-intercept form.
Distribute (-5/3) to get:
y - 8 = (-5/3)x - 10
Add 8 to both sides:
y = (-5/3)x - 2
This is the equation of the line in slope-intercept form. Therefore, the equation of the line that passes through the point (-6,8) and has a slope of -5/3 is y = (-5/3)x - 2.
show that d^2y/dx^2=-2x/y^5, if x^3 + y^3=1
Answers
Answer:
y³ + x³ = 1
First, differentiate the first time, term by term:
\({3y^{2}.\frac{dy}{dx} + 3x^{2}} = 0 \\\\{3y^{2}.\frac{dy}{dx} = -3x^{2}} \\\\\frac{dy}{dx} = \frac{-3x^{2}}{3y^{2}} \\\\\frac{dy}{dx} = \frac{-x^{2}}{y^{2}}\)
↑ we'll substitute this later (4th step onwards)
Differentiate the second time:
\(3y^{2}.\frac{dy}{dx} + 3x^{2} = 0 \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + 6y(\frac{dy}{dx})^{2} + 6x = 0 \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + 6y(\frac{dy}{dx})^{2} = - 6x \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + 6y(\frac{-x^{2} }{y^{2} })^{2} = - 6x \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + 6y(\frac{x^{4} }{y^{4} }) = - 6x \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + \frac{6x^{4} }{y^{3} } = - 6x \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} = - 6x - \frac{6x^{4} }{y^{3} } \\\\\)
\(3y^{2}.\frac{d^{2} y}{dx^{2}} = - \frac{- 6xy^{3} - 6x^{4} }{y^{3}} \\\\\frac{d^{2} y}{dx^{2}} = - \frac{- 6xy^{3} - 6x^{4} }{3y^{2}. y^{3}} \\\\\frac{d^{2} y}{dx^{2}} = - \frac{- 2xy^{3} - 2x^{4} }{y^{5}} \\\\\frac{d^{2} y}{dx^{2}} = - \frac{-2x (y^{3} + x^{3})}{y^{5}} \\\\\frac{d^{2} y}{dx^{2}} = - \frac{-2x (1)}{y^{5}} \\\\\frac{d^{2} y}{dx^{2}} = - \frac{-2x}{y^{5}}\)
f is a trigonometric function of the form f(x)=asin(bx+c)+d. The function intersects its midline at (π,−4) and has a minimum point at ( π/4 , − 5.5 ). Find a formula for f(x). Give an exact expression.
Answers
The given point on the midline of (π, -4), and the minimum point of (π/4, -5.5), give the exact expression for f(x) as; f(x) = 1.5•sin((2/3)•(x - π)) - 4.
Which method can be used to find the trigonometric function?The amplitude, a = The difference between the y-values at the minimum point and the midline
Therefore;
a = -4 - (-5.5) = 1.5
d = The difference between the y-values of the midline and the x-axis
Therefore;
d = -4 - 0 = -4
The given function is presented as follows;
f(x) = a•sin(b•x + c) + d
Which gives;
-4 = 1.5•sin(b•π + c) - 4
sin(b•π + c) = 0
(b•π + c) = 0
-c/b = π
c = -b•π
Therefore;
-5.5 = 1.5•sin(b•π/4 + c) - 4
-1.5 = 1.5•sin(b•π/4 + c)
-1 = sin(b•π/4 - b•π) = sin(-3•b•π/4)
-3•b•π/4 = arcsine (-1) = -π/2
-3•b•π/4 = -π/2
3•b/4 = 1/2
b = 2/3
c = -(2/3)•π
Therefore, f(x) = a•sin(b•x + c) + d, gives;
f(x) = 1.5•sin((2/3)•x - (2/3)•π) - 4
By simplification, the exact expression for f(x) is therefore;
f(x) = 1.5•sin((2/3)•(x - π)) - 4Learn more about the the general form of the sine function here:
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Which description could be written as a linear function?
a
eight more than twice a number
b
nine more than one divided by a number
c
ten more than the square of a number
d
three more than the product of two numbers
Answers
Answer:
a
Step-by-step explanation:
because it is more then eight numbers
Determine whether the following symbolized arguments are valid or invalid by identifying the form of each. In some cases the argument must be rewritten using double negation or commutativity before it has a named form. Those arguments without a specific name are invalid. G ⊃ ∼R G ∼R a. DS—invalid. b. DA—valid. c. MT—valid. d. HS—valid. e. MP—valid.
Answers
(a) The argument is invalid.
(b) The argument is valid.
(c) The argument is valid.
(d) The argument is valid.
(e) The argument is invalid.
What are symbolized arguments?
A symbolic argument consists of a set of premises and a conclusion. It is called a symbolic argument because we generally write it in symbolic form to determine its validity. An argument is valid when its conclusion necessarily follows from a given set of premises.
a. The argument is invalid. It has the form of Denial of the Antecedent (DA), which is a fallacious form of argument. The form of an argument is the pattern of the logical structure of the argument, not the content of the argument.
b. The argument is valid. It has the form of Modus Tollens (MT), which is a valid form of argument. In this form, if the consequent of a conditional statement (the part after the "if" or "⊃") is denied, then the antecedent (the part before the "if" or "⊃") must also be denied.
c. The argument is valid. It has the form of Hypothetical Syllogism (HS), which is a valid form of argument. In this form, if two conditional statements are given, and the antecedent of the first is the consequent of the second, then the consequent of the first can be inferred.
d. The argument is valid. It has the form of Modus Ponens (MP), which is a valid form of argument. In this form, if the antecedent of a conditional statement is true and the conditional statement itself is true, then the consequent of the conditional statement must also be true.
e. The argument does not have a specific named form and is therefore invalid.
Hence, We have determined whether the statements are valid or not.
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A hacker is trying to guess someone's password. The hacker knows (somehow) that the password is 9 characters long, and that each character is either a lowercase letter, (a, b, c, etc.), an uppercase letter (A, B, C, etc.) or a numerical digit (0, 1, 2, 3, 4, 5, 6, 7, 8, or 9). Assume that the hacker makes random guesses. What is the probability that the hacker guesses the password on his first try? Enter your answer as a decimal or a fraction, not a percentage.
Answers
The probability that the hacker guesses the password on their first try is extremely low.
What is the probability that the hacker guesses the password on his first try?
There are 26 lowercase letters, 26 uppercase letters, and 10 numerical digits, for a total of 62 possible characters for each position in the password. Since the password is 9 characters long, there are \(62^{9}\) possible passwords.
The probability that the hacker guesses the password on their first try is 1 out of the total number of possible passwords:
Probability = 1 / (\(62^{9}\))
Using a calculator, this can be simplified to approximately 1.2 x \(10^{-16}\)
Therefore, the probability that the hacker guesses the password on their first try is extremely low.
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I need to know the simplified expression for the third side length of the triangle
Answers
Answer:
4n² - 6
Step-by-step explanation:
Perimeter of the triangle is sum of all sides.
Perimeter = -6n² - 2
-8n² +2 -2n² + 2 + third side = -6n² - 2
Combine the like terms in the LHS,
-8n² - 2n² + 2 + 2 +third side = -6n² - 2
-10n² + 4 + third side = -6n² - 2
We can find the third side by subtracting the sum of other two sides from the perimeter.
third side = -6n²- 2 + 10n² - 4
= -6n² + 10n² -2 - 4
= 4n² - 6
PLS HELP ASAP BRAINLIEST IF RIGHT AND 100 POINTS PLSSS
Train A is traveling north at a steady speed of 70 miles per hour. After 2
hours, it is 150 miles north of Hillsboro.
Train B is traveling north on a parallel track. Its distance north of Hillsboro is
represented by the graph.
Answers
Answer:
its d
Step-by-step explanation:
PLEASE IF YOUR A MATH EXPERT ANSWER THIS I'M LOSING MY SANITY
What is the value of 7m−3n when m = 3 and n = 2?
A: 5
B: 15
C: 24
D: 36
Answers
Answer:
B: 15
Step-by-step explanation:
To answer this question, simply plug in the values according to each variable. So, because m = 3, plug the m next to 7 with 3, so then that means that 7 is now multiplied by 3. Then, plug in 2 into n because n = 2, so 3 is being multiplied to n. This is what we get:
7(3) - 3(2)
Now, multiply!
21 - 6
Finally, solve:
21 - 6 = 15
Therefore, the answer is:
B: 15
Hope this helps :)
Explanation: First you plug in the values that are given m=3 and n=2
7(3) - 3(2)=
So then you multiple and it would be
21-6=
Then you subtract
21-6=15
There for the answer is B: 15
The library has 1,880 magazines. Each bin holds 8 magazines. How many bins does the
library need to hold all of its magazines?
bins
Submit
I don't kno
Answers
NO LINKS!!! Complete the tables of ratios for similar polygons
Answers
Here is the table
\(\boxed{\begin{array}{c|c|c|c}{\underline{\bf Scale\:factor}}&{\underline{\bf Ratio\:of\: corresponding\:sides}}&{\underline{\bf Ratio\:of\: perimeters}}&{\underline{\bf Ratio\:of\:areas}}\\ \rm 3:4 &\rm 3:4&\rm 3:4&\rm 9:16\\ \rm 12:5&\rm 12:5&\rm 12:5&\rm 144:25\\ \rm 3:7&\rm 3:7&\rm 3:7&\rm 9:49\\ \rm x:y&\rm x:y&\rm x:y&\rm x^2:y^2\end{array}}\)
4) If g(x) = 13x2 what is the value of g(-3)?
Answers
Answer:
Function :---
\( \boxed{g(x) = 13 {x}^{2}}\\ g( - 3) = 13 \times {( - 3)}^{2} = 13 \times 9 = \boxed{117}✓\)
g(-3)=117 is the right answerthe greatest common factor of 12 and 26 pls explain the steps
Answers
Step-by-step explanation:
12- 2*6
26- 2*13
gcf =2
the least greatest common factor is 2
Please look at the photo. Thank you.
Answers
The output value of (f∘g)(x) is: \((f \circ g)(x) = \frac{4x^2-29x+60}{x +3}\)
The domain of (f∘g)(x) is (-∞, -3) U (-3, ∞).
How to determine the corresponding output value for this function?In this scenario, we would determine the corresponding composite function of f(x) and g(x) under the given mathematical operations (multiplication) in simplified form as follows;
\(f(x) = \frac{x-6}{x +3}\)
g(x) = 4x - 15
Next, we would write the numerators and denominators in factored form as follows;
(x - 6)(4x - 15)
4x² - 15x - 24x + 60
4x² - 29x + 60
Now, we can derive the corresponding composite function of f(x) and g(x);
\((f \circ g)(x) = \frac{4x^2-29x+60}{x +3}\)
For the restrictions on the domain, we would have to equate the denominator of the rational function to zero and then evaluate as follows;
x + 3 ≠ 0
x ≠ -3
Domain = (-∞, -3) U (-3, ∞).
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which congruency statement is correct
Answers
show the answers i cant tell u the answer without the choices
Find the y-intercept and the x-intercept of the line below. Click on "None" if applicable.
Answers
The required y-intercept for the given line on the graph is -1.
What is the intercept in the equation?In the equation intercept is the value of the linear function where either of the variables is zero.
here,
From the graph, the line intersects the y-axis at (0, -1).
Since y-intercept is defined as the point of the y-axis over the coordinate plane where any line or curve intersects the y-axis.
So y - intercept = -1
Thus, the required y-intercept for the given line on the graph is -1.
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which value of x makes this inequality true? x+9<4x
Answers
Answer:
Step-by-step explanation:
x+9
Let x, be 4
4+9=13
given condition,
x+9<4x
4+9<4(4)
13<16
The answer is:
x > 3Work/explanation:
Our inequality is:
\(\sf{x+9 < 4x}\)
Flip it
\(\sf{4x > x+9}\)
Solve
\(\sf{4x-x > 9}\)
Combine like terms
\(\sf{3x > 9}\)
Divide each side by 3
\(\sf{x > 3}\)
Hence, x > 3K > 18 Which value for K would make the inequality false? a) 33 b) 7 C) 21 d) 19
Answers
Answer:
b. 7
If the value of the K is 7 then the inequality K> 18 would be false.
Hope it will help :)❤
Answer:
B
Step-by-step explanation:
7 is not greater than 18
Can this expression be simplified? If not, explain why. WILL MARK BRAINLIEST.
Answers
Answer:
yes
Step-by-step explanation:
see attached graph - there are two real roots for y=2x^4-6x^2+10x-7
so 2x^4-6x^2+10x-7 can be expressed as:
(x - root1)(x - root2)(2x^2+Bx+C)
Answer:
Yes, it can be.
Step-by-step explanation:
Using solver program, the expression 2x^4-6x^2+10x-7 has:
two real roots at x≈-2.3888 and x≈1.1424
and
two complex roots at x≈0.62321 - 0.94559 i and x≈0.62321 + 0.94559 i
Because it has two real roots, the expression can be simplified.
6thousandths times 8
Answers
Answer:
.048
Step-by-step explanation:
6 thousandths = 0.006
So, 0.006 times 8 would be...
.006
x 8
.048
Hope this helps you out! I'm not exactly sure how to explain how to multiply, but if you're confused, you can always ask someone for help...have a great day :)
Please help with any you can, i will give brainliest.
Answers
Answer:
11.4
Step-by-step explanation:
7b))60+40+x=180
x=180-100
x=80
sin60÷10=sin80÷x
xsin60=10sin80
x=10sin60÷sin60
=11.371
=11.4
Determine whether the sampling method described below appears to be sound or is flawed. In a survey of 511 human resource​ professionals, each was asked about the importance of the age of a job applicant. The survey subjects were randomly selected by pollsters from a reputable market research firm.
a) it is flawed because it is a census.
b) it is flawed because it is not statistically significant.
c) it appears to be sound because the data are not biased in anyway.
d) it is flawed because it is a voluntary response sample.
Answers
Answer:
c) it appears to be sound because the data are not biased in anyway.
Step-by-step explanation:
From the information given regarding the sample selection method , the size, the larger sample from which the survey subject were selected, we can conclude that the data is sound and not in anyway biased. The subject were selected from a reputable market research firm, which means the subjects were chosen from a larger sample which is reliable and not just a voluntary pool of subjects. Also, the selection process is randomized. Based on these, there are no flaws which are likely to cause the introduction of bias into the sample selected. Hence, the data is sound and not in any way biased.
Can someone help me I’m really bad in geometry
Answers
He travelled 52.6 feet which is the hypotenuse. Then use sin ratio to solve for h.
A bag contains 10 green,8 blue, and 2 white balls. Naomi seclets 2 balls from the bag at random, one at a time, without replacing them. What is the probability that she selects all two white balls?
E.) 2/95
F.) 1/95
G.) 1/190
H.) 1/380
Answers
To find the probability that Naomi selects both white balls, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes:
Naomi selects 2 balls without replacement, so the total number of outcomes is the number of ways she can choose 2 balls out of the total number of balls in the bag. This can be calculated using combinations:
Total outcomes = C(20, 2) = (20!)/(2!(20-2)!) = (20 * 19)/(2 * 1) = 190
Number of favorable outcomes:
Naomi needs to select 2 white balls. There are 2 white balls in the bag, so the number of favorable outcomes is the number of ways she can choose 2 white balls out of the 2 white balls in the bag:
Favorable outcomes = C(2, 2) = 1
Probability = Favorable outcomes / Total outcomes = 1/190
Therefore, the correct answer is (G) 1/190.