[tex]\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{\log(2)}{2}+\cfrac{\log(4)}{3}\implies \cfrac{1}{2}\log(2)+\cfrac{1}{3}\log(4)\implies \log(2^{\frac{1}{2}})+\log(4^{\frac{1}{3}}) \\\\\\ \log(2^{\frac{1}{2}})+\log( ~~ (2^2)^{\frac{1}{3}} ~~ )\implies \log(2^{\frac{1}{2}})+\log(2^{\frac{2}{3}})\implies \log( ~~ 2^{\frac{1}{2}}\cdot 2^{\frac{2}{3}}~~) \\\\\\ \log( ~~ 2^{\frac{1}{2}+\frac{2}{3}} ~~ )\implies \log( ~~ 2^{\frac{3+4}{6}} ~~ )\implies \log (~~ 2^{\frac{7}{6}} ~~ )\implies {\LARGE \begin{array}{llll} \log(\sqrt[6]{128}) \end{array}}[/tex]
Fill in the blanks
The inverse of an exponential function with a base e is the ________.
The inverse of an exponential function with a base e is the logarithm.
A logarithm is defined simply?
The power to which a number must be increased in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents). For instance, since ten raised to the power of two equals 100, the base ten logarithm of 100 is 2: log 100 = 2.How does exponential growth utilise e?
e is the constant growth rate that all processes that are growing continuously share. With e, you may compare a simple growth rate—where all change occurs at the end of the year—with a compound, continuous growth rate, where growth occurs once per nanosecond or quicker.Learn more about logarithm
brainly.com/question/28346542
#SPJ4
1. A $6,000 investment grows to $7,351.81 in 5.5 years. If the investment has compounded monthly,
determine the interest rate..
Answer:
3.7%
Step-by-step explanation:
You want the annual interest rate that results in an investment of $6000 growing to a value of $7351.81 in 5.5 years, when the interest is compounded monthly.
Account valueThe value of an account in which principal P is invested for t years at annual rate r compounded n times per year is ...
a = P(1 +r/n)^(nt)
ApplicationFor this problem, we have ...
a = 7351.81P = 6000n = 12t = 5.5These values make the equation be ...
7351.81 = 6000(1 +r/12)^(12 ·5.5) . . . . . . equation with given values
(7351.81/6000) = (1 +r/12)^66 . . . . . . . . divide by 6000
(7.35181/6)^(1/66) = 1 +r/12 . . . . . . . . . . rewrite fraction, take 66th root
(7.35181/6)^(1/66) - 1 = r/12 . . . . . . . . . subtract 1
(12)((735181/6)^(1/66) -1) = r ≈ 0.03700003
The interest rate is about 3.7%.
m∠ABC=(6x+8)° and m∠DEF=(12x−8)°. If ∠ABC and ∠DEF are supplementary, what is the measure of each angle?
A) m∠ABC = 68°; m∠DEF = 122°
B) m∠ABC = 47°; m∠DEF = 122°
C) m∠ABC = 47°; m∠DEF = 112°
D) m∠ABC = 68°; m∠DEF = 112°
Answer:
d is the correct answer
Step-by-step explanation:
m∠ABC = 68°; m∠DEF = 112°
Answer:
D is correct
Step-by-step explanation:
Supplemental angles add to 180
6x + 8 + 12x -8 = 180 Combine line terms
18x = 180 Divide both sides by 18
x = 10
Substitute 10 in for x
ABC
6x + 8
6(10) + 8
60 + 8
68
DEF
12x - 8
12(10) - 8
120 - 8
112
Evaluate v(x)=12-2x-5 when x=-2,0, and 5.
v(-2)=
v(0)=
v(5)=
v(x) = 12 - 2x - 5
v(-2) = 12 - 2×(-2) - 5 = 12 + 4 - 5 = 11v(0) = 12 - 2×(0) - 5 = 12 - 5 = 7v(5) = 12 - 2×(5) - 5 = 12 - 10 - 5 = -35. A bird is at 20 feet above sea level. A fish is 14 feet below sea level. What is the difference?
Answer:
it's either 6 or -6 because if uts Like negative and positive then it should be either one of those
Answer:
Step-by-step explanation:
34
Tank B, which initially contained 80 liters of water, is being drained at a rate of 2.5 liters per minute. How many liters of water remain in the tank after the following amounts of time?
a. 30 seconds
b. 7 minutes
c. t minutes
In a radio station contest, 20 people are eligible for a prize drawing. There will be 2
winners, and each winner gets two tickets to an upcoming concert. How many
different sets of 2 winners can be chosen?
Answer:
i think its 10 sets of 2 winners
Step-by-step explanation:
Solve each equation. Check for extraneous solutions. √2 x+9 - √x=3
the extraneous solution for the equation √(2 x +9) - √x = 3 is x = 0 or x = 6.
We are given an equation:
√(2 x +9) - √x = 3
√(2 x +9) = 3 + √x
Raise both sides to the power 2, we get that:
2 x + 9 = 9 + x + 6√x
x = 6√x
Squaring both sides again, we get that:
x² = 6 x
x² - 6 x = 0
x ( x - 6) = 0
x = 0 or x = 6.
Therefore, we get that, the extraneous solution for the equation √(2 x +9) - √x = 3 is x = 0 or x = 6.
Learn more about equation here:
https://brainly.com/question/1214333
#SPJ4
Please help with problem 24, Algebra 1 question, question in the attachments
Let [tex]x[/tex] be the "given angle" mentioned here. Then its complement indeed has measure [tex]90-x[/tex], and its supplement [tex]180-x[/tex].
Now translate the following sentence into an equation:
"The supplement of a given angle is 10° more than twice its complement."
[tex]\implies 180 - x = 10 + 2 (90 - x)[/tex]
Solve for [tex]x[/tex].
[tex]180 - x = 10 + (180 - 2x)[/tex]
[tex]180 - x = 190 - 2x[/tex]
[tex]2x - x = 190 - 180[/tex]
[tex]\boxed{x = 10}[/tex]
Point F is between points T and K.
The points are collinear.
Answer:
the answer isssssssssssssß
Complete the table given the following function:
y = 3x + 1
x y Ordered Pair
1
(1, 4)
2
(2,__)
3
(___,___),(____,____)
-1
(-1,___)
Considering the numeric values of the function, the points and ordered pairs are given as follows:
x = 2, y = 7, ordered pair (2,7).x = 3, y = 10, ordered pair (3,10).x = -1, y = -2, ordered pair (-1,-2).How to find the numeric value of a function/expression?To find the numeric value of a function, we replace each instance of the variable by the desired value.
An ordered pair is given by:
(x, f(x)).
In which f(x) is the numeric value.
For this problem, the function is given by the following rule:
y = 3x + 1.
When x = 2, the numeric value is given by:
y = 3 x 2 + 1 = 6 + 1 = 7.
Hence the ordered pair is (2,7).
When x = 3, the numeric value is given by:
y = 3 x 3 + 1 = 9 + 1 = 10.
Hence the ordered pair is (3,10).
When x = -1, the numeric value is given by:
y = 3 x -1 + 1 = -3 + 1 = -2.
Hence the ordered pair is (-1,2).
More can be learned about the numeric values of a function at brainly.com/question/28367050
#SPJ1
In the diagram of circle P, mXYZ is 72. What is the value of x
Answer:
108°
Step-by-step explanation:
PLEASE HELP ME ASAP!
graph f(x)= -2|x+4|
use the khan academy graph
Answer:[tex]f\left(x\right)\le \:0[/tex]
Step-by-step explanation:
[tex]\begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\le \:0\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:0]\end{bmatrix}[/tex]
Should I take Pre-Calculus 12 or Foundation of Math 12? PLEASE HELP ME Tell me the difference which one Is better when I graduate please help me
Answer:
honestly i say foundation of math12 ithink it will come more in handy in life
If there's anyone who can actually like tell me th answer, please do. I don't understand this homework.
Answer:
domain is horizontal and range is vertical
Step-by-step explanation:
domain is left to right so you look for farthest point on the left side and range you look for the highest point
how do i solve -4x+10>5x+55
Answer:
x<-5
Step-by-step explanation:
Which system is equivalent to StartLayout Enlarged left-brace 1st row y = negative 2 x squared 2nd row y = x minus 2 EndLayout? StartLayout Enlarged left-brace 1st row y = negative 2 y squared minus 2 2nd row x = y minus 2 EndLayout StartLayout Enlarged left-brace 1st row y = negative 2 y squared + 2 2nd row x = y + 2 EndLayout StartLayout Enlarged left-brace 1st row y = negative 2 y squared minus 8 y minus 8 2nd row x = y + 2 EndLayout StartLayout Enlarged left-brace 1st row y = negative 2 y squared + 8 y minus 8 2nd row x = y minus 2 EndLayout
The system of equations that's corresponding to the given function are y = 5 - x and 5 - x = 9x².
According to the statement
We have to find that the linear equation.
So, For this purpose, we know that the
The systems of equations, sometimes called simultaneous equations, are a group of relationships between various unknown variables that can be expressed in terms of algebraic expressions.
From the given information:
Given the systems of equations;
y = 9x²
and
x + y = 5
From equation 2:
y = 5 - x
Substitute into equation 1 to have;
5 - x = 9x²
From the resulting equation, we are able to see that the system of equations that's corresponding to the given function are y = 5 - x and 5 - x = 9x².
So, The system of equations that's corresponding to the given function are y = 5 - x and 5 - x = 9x².
Learn more about systems of equations here
https://brainly.com/question/14323743
#SPJ9
Maria made a bunch of muffins for a bake sale. She made 5 corn, 6 banana, 2 blueberry, and 10 chocolate chip. What is the ratio of bananas to total?
If your skateboarding on top of a small hill and take a break. You have 100 J of potential energy. If your mass is 80 kg, how high is the hill your skating on?
The height of the hill is 12.8 cm.
What is Gravitational potential energy?
The gravitational potential energy of an object is given by:
U = mgh
where,
m is the mass of the object.
g is the acceleration of gravity.
h is the height of the object.
Given that;
The potential energy = 100 J,
In this problem, we have;
The potential energy of the person is = U = 100 J
The mass of the person = m = 80 kg
Now, Solving for h, we find at what height the person is:
h = U /mg
h = 100 / 80*9.8
h = 12.8 cm
Hence, The height of the hill is 12.8 cm.
Learn more about the Gravitational potential energy visit:
brainly.com/question/15896499
#SPJ1
Are they similar? Yes or no
Answer: Yes
Step-by-step explanation:
one is just bigger than the other if you blow the little one up than you can see they are the same!
each side of a square is lengthened by 2 inches. the area of this new, larger square is 49 square inches. find the length of a side of the original square.
Length of a side of original square = 5 inches
Let's take the value of the length of the original square be to x.
As it is known that the area of the larger square has = 49 square inches, and the side are lengthened by 2 inches from the original square side.
So we have the expression:
[tex](x + 2)^{2}[/tex] = 49
x + 2 = 7
x= 5
Therefore the original side of the square is 5 inches.
To know more about the square refer to the link given below:
https://brainly.com/question/24487155
What is an equation for the translation of y=2/x that has asymptotes at x=3 and y=-5 ?
(A) y=2/x-3 -5 (B) y=2/x+3+5 (C) y=2/x+5-3 (D) y=2/x-5+3
Correct option is A. Equation for the translation of y=2/x that has asymptotes at x=3 and y=-5 is y=2/x-3 -5.
Why do we use asymptotes?A curve's asymptote is the point at which the curve converges. In other words, despite being endlessly near, the curve and its asymptote never collide. Asymptotes are utilized in big O notation, are straightforward approximations to complicated equations, and are helpful for charting rational equations, among other uses.
Typically, the limit of a value when the function is not specified can be used to determine the asymptote(s) of a curve. Examples of such points include and as well as the location where the numerator of a rational function equals zero.
Given,
y = 2/x
asymptotes at x=3 and y=-5
⇒ denominator is (x-3)
⇒ y = -5 is highest degree of the equation.
⇒ The equation will be y=2/x-3 -5.
To learn more about Asymptotes from given link
https://brainly.com/question/4138300
#SPJ4
A sofa is on sale for 66% off. The sale price is $231.20.
The regular price of the sofa if 66% is given off, is $680.00
What is regular price?
The regular price of the sofa is the price at which it is sold without considering the coupon of 66%, in essence, it is 100% of the original price of the sofa, in short, if 66% is given off, then the sale price is 34% of the original price
34% of regular price=$231.20
1% of regular price=231.20/34
1% of regular price=$6.80
100% of regular price=$6.80*100
100% of regular price=$680
Find out more about regular price on:brainly.com/question/4817441
#SPJ1
Full question
A sofa is on sale for 66% off. the sale price is $231.20 . what is the regular price?
:
What Is 30332 Times 98663
Answer:
2,992,646,116
Step-by-step explanation:
I am big brain
Answer:
2992646116
Step-by-step explanation:
multiply starting with 98663
8p + 4 = −9 + 7p help
The given equation is 8p + 4 = −9 + 7p.The value of p is -13.
The required solution for the given equation is p = -13
A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1.There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.
Now the given equation is,
8p + 4 = −9 + 7p
Solving them,
Taking variables to one side and constant to another, we get
8p-7p=-9-4
p=-13
To learn more about equation visit https://brainly.com/question/11908287
#SPJ9
Circle Theorum!
We haven’t gone through it much, but have homework.
Answer:
38°
Step-by-step explanation:
1. Angles subtended at the circumference is half at the centre. Therefore angle at the centre is 61x2=122
2. Isosceles triangle have equal base angle. 19°
3. Tangent subtends 90° with the radius.
4. 90-19=71
5. 71x2=142°
6. Angles in a triangle add up to 180°
180-142=38°
ASAP PLEASE HELP IF RIGHT ANSWER WILL GIVE BRAINLIEST, 15 POINTS, AND 5 STAR OVERALL!!!! IF WRONG ANSWER OR INVALID WILL REPORT, PLEASE, PLEASE, PLEASE!!
Answer:
D
Step-by-step explanation:
Answer:
D [tex]y = - 5 - 17[/tex]
Step-by-step explanation:
To make y the subject of formula in:
[tex]5x + y = - 17[/tex]
Mover 5x to the other side of the equation which makes it -5x due to the equality sign
Therefore:
[tex]y = - 5 - 17[/tex]
George has two routes that he likes to use for walking. He can walk 672 yards in 6 minutes on Path A, and he can walk 984 yards in 8 minutes on Path B. How many more yards per minute can George walk on Path B?
Answer:
11 more yards per minute on Path B.
Step-by-step explanation:
Path A: 672 yards in 6 minutes = 112 yards per minute.
Path B: 984 yards in 8 minutes = 123 yards per minute.
123 - 112 = 11 yards per minute longer on Path B.
Answer:
156 yards per minute
Step-by-step explanation:
first off remember to have a label
it is change in Y over change in X so
984-672/ 8-6
you could get 312/2
which equal 156
I attached a photo to make it clear
linda is riding her bike to the restaurant. she rides at a constant speed of 32 feet per second. the restaurant is 6271 feet from her house. let t represent the number of seconds since linda left her house and let d represent linda’s distance from the restaurant.
Solving the distance-time problem here, the taken time to reach the restaurant is 196 seconds (approx.)
This is a distance-time problem.
To solve this problem the required formula is, d/t = v or, d/v = t,
where d is the represented distance and t denotes the required time, and v is denoted as the velocity or speed.
Here v, velocity is 32 feet/second, and d, distance is 6271 feet.
So, the taken time to reach the restaurant is 6271/32 = 196 seconds (approx.)
To know more about distance-time problems, refer to the following link:
https://brainly.com/question/26608770
#SPJ4
express the terms of the following geometric sequence recursively 3,6,12,24,4&
Answer:
aₙ = 2aₙ₋₁ for n ≥ 2
a₁ = 3
Step-by-step explanation:
A geometric sequence can be expressed recursively using the following general equation
aₙ = r . (aₙ₋₁), n ≥ 2
where
aₙ is the nth term
a₁ is the first term of the geometric sequence
r is the common ratio = aₙ/aₙ₋₁
Here we have the terms 3, 6, 12, 24, 48
The common ratio r = 6/3 = 12/6 = ....... = 48/24 = 2
The first term a₁ = 3
So the recursive relation is
aₙ = 2aₙ₋₁ for n ≥ 2
a₁ = 3