[tex]\bf \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \\\\[-0.35em] \rule{34em}{0.25pt}\\[1em] [\log(3)-\log(4)]-\log(2)\implies \log\left( \cfrac{3}{4} \right)-\log(2)\implies \log\left( \cfrac{\frac{3}{4}}{~~2~~} \right) \\\\\\ \log\left( \cfrac{\frac{3}{4}}{~~\frac{2}{1}~~} \right)\implies \log\left( \cfrac{3}{4}\cdot \cfrac{1}{2} \right)\implies \log\left( \cfrac{3}{8} \right)[/tex]
To write the expression as a single logarithm, we'll use the properties of logarithms to combine them. The given expression is:
(log3 - log4) - log2
We start by combining the first two logarithms inside the parenthesis using the difference of logarithms property:
log(a) - log(b) = log(a/b)
Applying this property to (log3 - log4), we get:
log(3/4)
Now, our expression looks like this:
log(3/4) - log2
We can use the same property to combine this with the remaining logarithm:
log(a) - log(b) = log(a/b)
So we apply it with a = 3/4 and b = 2:
log((3/4)/2)
When dividing by 2, we are effectively multiplying by 1/2, so we have:
log(3/4 * 1/2)
Now we perform the multiplication inside the logarithm:
log(3/8)
And that is the expression written as a single logarithm:
log(3/8)
WILL MARK BRAINLIEST !!!!!! PLEASE HELP ASAP
Answer:
[tex]\large\boxed{Q1.\ \left\{\begin{array}{ccc}y\leq-2x-1\\y\leq x+5\end{array}\right}\\\boxed{Q2.\ 6\leq y-3\leq8}\\\boxed{Q3.\ y\leq x-4}[/tex]
Step-by-step explanation:
<, > - dotted line
≤, ≥ - solid line
<, ≤ - shaded above the line
>, ≥ - shaded below the line
=================================================
The slope intercept form of a line: y = mx + b
m - slope
b - y-intercept (0, b)
If m > 0, then the function is increasing
If m < 0, then the function is decreasing
==================================================
Q1.y = -2x - 1 → m = -2 < 0 and b = -1
decreasing function, y-intercept -1 → (0, -1)
y = x + 5 → m = 1 > 0 and b = 5
increasing function, y-intercept 5 → (0, 5)
y = 2x - 1 → m = 2 > 0, and b = -1
increasing function, y-intercept -1 → (0, -1)
y = -x + 5 → m = -1 < 0 and b = 5
decreasing function, y-intercept 5 → (0, 5)
From the picture we have
(1) increasing function and y-intercept 5 → y = x + 5
shaded below the solid line → y ≤ x + 5
(2) decreasing function and y-intercept -1 → y = -2x - 1
shaded below the solid line → y ≤ -2x - 1
=======================================================
Q2.[tex]9\leq y\leq11[/tex] subtract 3 from both sides
[tex]9-3\leq y-3\leq11-3\\\\6\leq y-3\leq8[/tex]
=======================================================
Q3.solid line (≤ or ≥)
shaded below the line (≤ or <)
y ≤ x - 4
evaluate the polynomial for the given value of x: f(x) =3x^3+5x^2+x-2 when x=2
Answer: [tex]f(2)=44[/tex]
Step-by-step explanation:
Given the polynomial [tex]f(x) =3x^3+5x^2+x-2[/tex], you can evaluate it for the given value of the variable "x" by substituting the value [tex]x=2[/tex] into the polynomial.
Therefore, when [tex]x=2[/tex], you get the following result:
[tex]f(x) =3x^3+5x^2+x-2 \\\\f(2) =3(2)^3+5(2)^2+(2)-2\\\\f(2)=3(8)+5(4)+2-2\\\\f(2)=24+20\\\\f(2)=44[/tex]
-1/2 (4x+2) (is less than) 0
Answer:
x > -1/2
Step-by-step explanation:
Step 1: Use the Distributive Property
-2x - 1 < 0
Step 2: Isolate x
-2x < 1
Step 3: Simplify
x > -1/2
Note that when dividing by a negative in an inequality, reverse the inequality symbol.
Is 7/12 close to 0, 1/2 OR 1
Answer: 1/2, because its 0.583 and 1/2 is 0.5
Step-by-step explanation:
Answer:
Final answer is 1/2.
Step-by-step explanation:
Given numbers are 0, 1/2 and 1.
Now we need to find about which one of those three numbers is close to 7/12.
Since 7/12 has denominator 12 so let's convert each of the given number into their equivalent fractions with denominator 12.
0=0/12
1/2=6/12
1=12/12
Now we can easily compare them with 7/12 and find that 6/12 or 1/2 is closest.
Hence final answer is 1/2.
Need Help PLZ!!!!!!!!!
Answer:
Final answer is [tex]W=\frac{CL}{100}[/tex].
Step-by-step explanation:
Given equation is [tex]C=\frac{100W}{L}[/tex].
Now we need to solve the given equation [tex]C=\frac{100W}{L}[/tex] for indicated variable W.
That means we need to isolate W. In other words move 100 and L to the right side of the equation.
[tex]C=\frac{100W}{L}[/tex]
[tex]CL=100W[/tex]
[tex]\frac{CL}{100}=W[/tex]
[tex]W=\frac{CL}{100}[/tex]
Hence final answer is [tex]W=\frac{CL}{100}[/tex].
what is the standard form of the number shown in this caculator display? 3.82eplus7
3.82 E+7 is just an engineering format, another way to write it will be 3.82 x 10⁷ in scientific format, or just 3.82 x 10000000 <--- notice, seven zeros.
and the product of the above is just 38200000, or standard form.
Ethan and Adien share a reward of $126 in a ratio of 4:3. what fraction of the total reward does Adien get?
Answer:
Step-by-step explanation: 4+3 =7 126/7= 18 (Ethan is 4*18) and (Aiden is 3*18) because 72+54=126 so aiden gets 54
Adíen gets 54 dollars hope this helps
Help me answer this question
Answer:
well this old so like yeah u prob know by now...
Step-by-step explanation:
Makayla has $8 to buy tickets at the school fair. Each ticket costs @1.5. Which inequality best represents how many tickets she can buy?
n=number of tickets
a. n<=5 b. n<8 c. n<=6 d. n<5
Answer:
[tex]n\le 5[/tex]
Step-by-step explanation:
Let n be the number of tickets Makaya has to buy.
If the cost of one ticket is $1.5, then the cost of n tickets is $1.5n.
Makayla has $8 to buy tickets at the school fair, thus
[tex]1.5n\le 8\\ \\n\le \dfrac{8}{1.5}\\ \\n\le \dfrac{80}{15}\\ \\n\le \dfrac{16}{3}\\ \\n\le 5\dfrac{2}{3}[/tex]
The maximum number of tickets Makaya can buy is 5, so
[tex]n\le 5[/tex]
someone solve this question!!!??Thank you
Combing like terms you have 0.25k - k = -0.75k
and 1.5 - 3.5 = -2.0
The answer would be -0.75k - 2.0
0.25k + 1.5 - k - 3.5
You must combine like terms. Like terms are the numbers with the same variable (letter) attached (in this case the numbers with the letter k are like terms)
(0.25k + (-k) )+ 1.5 - 3.5 <<<Remember that a variable with no number in front of it still has and invisible 1
(0.25k + (-1k) ) + 1.5 - 3.5
-0.75k + 1.5 - 3.5
Numbers without any variable are also like terms
-0.75k + 1.5 - 3.5
-0.75k -2
Hope this helped!
~Just a girl in love with Shawn Mendes
How many solutions does the equation 6y - 3y -7 = -2 +3 have?
Answer:
6y - 3y - 7 = -2 +3
Simplify both sides:
3y -7 = 1
Add 7 to both sides:
3y = 8
Divide both sides by 3:
y = 8/3 = 2 2/3
There is only one solution.
Please answer right away
Answer:
The correct answer option is [tex] \frac { 4 } { 4 9 } [/tex].
Step-by-step explanation:
We are to find the probability that both your parents were born on weekend (either Saturday or Sunday).
Total number of days in a week = [tex] 7 [/tex]
Number of days in weekend = [tex] 2 [/tex]
Probability of being born on weekend = [tex] \frac { 2 } { 7 } [/tex]
P (both parents were born on weekend) = [tex]\frac{2}{7} \times \frac{2}{7}[/tex] = 4/49
Please help me thank you
Answer:
[tex]\large\boxed{-\dfrac{8}{\sqrt{63}}}[/tex]
Step-by-step explanation:
[tex]\csc\theta=\dfrac{1}{\sin\theta}\\\\\cos\theta=-\dfrac{1}{8}\qquad\text{use}\ \sin^2\theta+\cos^2\theta=1\\\\\sin^2\theta+\left(-\dfrac{1}{8}\right)^2=1\\\\\sin^2\theta+\dfrac{1}{64}=1\qquad\text{subtract}\ \dfrac{1}{64}\ \text{from both sides}\\\\\sin^2\theta=\dfrac{64}{64}-\dfrac{1}{64}\\\\\sin^2\theta=\dfrac{63}{64}\to\sin\theta=\pm\sqrt{\dfrac{63}{64}}\\\\180^o<\theta<270^o\to III\ quadrant,\ \sin\theta<0.\\\\\text{Therefore}\ \sin\theta=-\sqrt{\dfrac{63}{64}}=-\dfrac{\sqrt{63}}{\sqrt{64}}=-\dfrac{\sqrt{63}}{8}.[/tex]
[tex]\csc\theta=\dfrac{1}{-\frac{\sqrt{63}}{8}}=-\dfrac{8}{\sqrt{63}}[/tex]
If it takes Bianca 30 minutes to bake 2 pans of brownies, how many pans of brownies can she bake in 7 hours?
Answer:
Bianca can make 28 pans of brownies in 7 hours
Step-by-step explanation:
As we know, 1 hour = 60 minutes
so, 1/2 hour = 30 minutes
Bianca takes 1/2 hour to make pans of brownies = 2 pans
Bianca takes 1 hour to make pans of brownies = 2 / (1/2) pans
Bianca takes 7 hour to make pans of brownies = 4 * 7 pans
= 28 pans
So, Bianca can make 28 pans of brownies in 7 hours.
The function f(x) = 9.75x + 62 models the amount
of money that Hector earned working x hours in a
week. The function g(x) = 7.5x + 84 models the
amount of money that Cart earned working x
hours in the same week Which function, h(x).
models the difference in Hector's and Cari's
earnings?
a. h(x) = 17.25x - 22
b. h(x) = 17.25x + 146
c. h(x) = 2.25x - 22
d. h(x) = 2.25x + 146
The answer is:
The third option,
c) [tex]h(x)=2.25x-22[/tex]
Why?We are given the functions E(x) and K(x), since they both are function of the same variable, we need to calculate the difference between them.
From the statement we know the functions:
[tex]f(x)=9.75x+62[/tex]
and
[tex]g(x)=7.5x+84[/tex]
So, calculating the difference the functions we have:
[tex]h(x)=f(x)-g(x)[/tex]
[tex]h(x)=(9.75x+62)-(7.5x+84)[/tex]
[tex]h(x)=(9.75x+62)-(7.5x+84)[/tex]
[tex]h(x)=9.75x-7.5x+62-84[/tex]
[tex]h(x)=2.25x-22[/tex]
Hence, the answer is the third option,
c) [tex]h(x)=2.25x-22[/tex]
Have a nice day!
Answer: Option C
[tex]h(x)=2.25x-22[/tex]
Step-by-step explanation:
To find the function h(x) that models the difference between Hector's and Cari's gains, subtract the functions f(x) with g(x)
That is to say:
[tex]h (x) = f (x) -g (x)[/tex]
We know that
[tex]f (x) = 9.75x + 62\\\\g (x) = 7.5x + 84[/tex]
Then we can find the function h(x)
[tex]h(x) = 9.75x + 62 - (7.5x + 84)\\\\h(x) = 9.75x + 62 -7.5x -84[/tex]
[tex]h(x)=2.25x-22[/tex]
How many 1/4 foot pieces can you cut from a 12 foot board
Answer:
48
Step-by-step explanation:
Here are two methods for finding the answer.
Method A.
In 1 foot, there are 4 1/4-foot pieces.
In 12 feet, there are 12 times as many as in 1 foot.
12 * 4 = 48
Method B.
Divide 12 ft by 1/4 ft.
12/(1/4) = 12 * 4/1 = 12 * 4 = 48
Answer: 48
48 cut from a 12 foot board.
What is the purpose of foot board?Bed cradles and foot boards are devices that attach to your bed. They keep sheets and blankets from touching and rubbing your legs or feet. Foot boards will also keep your feet in proper position while you are in bed.
In 1 foot, there are 4 1/4-foot pieces.
In 12 feet, there are 12 times as many as in 1 foot.
12 ×4 = 48
Divide 12 ft by 1/4 ft.
12/(1/4) = 12 ×4/1
= 12 × 4 = 48
1/4 foot pieces can you cut from a 12 foot board = 48
To learn more about foot pieces, refer
https://brainly.com/question/1236214
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The number of people playing a new phone app game triples every month. When the app first launched, 800 people started playing the game right away. There are currently 194,400 people playing the game. Write an equation to represent this situation, and determine the number of months, t, that have passed since the app launched.
Answer:
[tex]a_t=ar^{t-1}[/tex]
t=6 months
Step-by-step explanation:
We are given that the number of people playing a new phone app game triples every month
When the app first launch , the number of people started playing the game right away=800
According to question
The number of peoples are currently playing the game=194,400
We solve by using the formula of geometric series because we get a geometric series pattern
The number of people playing the game when app game launch=800
The number of people playing game after one month=2400
800,2400,7200,........,194,400
[tex]a_1=800,a_2=2400,a_3=7200,a_t=194,400[/tex]
We are finding common ratio
[tex]\frac{a_2}{a_1}=\frac{2400}{800}=3[/tex]
[tex]\frac{a_3}{a_2}=\frac{7200}{2400}=3[/tex]
Hence, the common ratio is 3 therefor nth term of G.P
[tex]a_t=ar^{t-1}[/tex]
a=800,r=3,[tex]a_t=194,400[/tex]
Substitute the values then we get
[tex]194,400=800(3)^{t-1}[/tex]
[tex]\frac[194400}{800}=(3)^{t-1}[/tex]
[tex]243=3^{t-1}[/tex]
[tex]3^5=3^{t-1}[/tex]
When base are same on both side then the power are equals
Therefore, t-1=5
t=5+1=6
Hence, when there are 194,400 people currently playing the game then
the number of months ,t=6 that have passed since the app launched.
Answer:
800(3)^t = 194,400; t = 5 months
Step-by-step explanation:
If f(x) = –2x+8 and g(x) = Square root of X+7,
what is (fºg)(2)
Answer:
(fog)(2)=2
Step-by-step explanation:
Given
f(x)= -2x+8
and
g(x)= √(x+7)
For finding (fog)(2), we have to find (fog)(x) first
In order to find (fog)(x) we will put the value of g(x) in f(x) in place of x.
(fog)(x)= -2g(x)+8
Putting the value of g(x)
(fog)(x)= -2√(x+7)+8
We have to find (fog)(2), so we have to put at the place of x in the composition
(fog)(x)= -2√(2+7)+8
(fog)(x)= -2√9+8
= -2(3)+8
= -6+8
=2
So,
(fog)(2)=2 ..
Which pairs of angles in the figure below are vertical angles?
Check all that apply.
ANSWER
A. <AKC and <TKI
D. <IKR and <AKP
EXPLANATION
Vertical angles are also called X-angles.
They are angles in the opposite corners of a figure that looks like X.
From the diagram, the options that are vertical angles are:
A. <AKC and <TKI
D. <IKR and <AKP
The correct answers are A and D.
Answer:
A and D.
Step-by-step explanation:
A pair of angles are vertical if both measure the same and both are opposite by a vertex. Then, in the figure we have that
∠AKC and ∠TKI are vertical angles
∠AKP and ∠PKI are not vertical angles (∠PKI measures more than ∠AKP and these angles are not opposite by a vertex).
∠AKT and ∠PKC are not vertical angles (same reason as the second option).
∠IKR and ∠AKP are vertical angles.
(30 points)
Solve for x:
-4x+8=42
Answer:
-8.5
Step-by-step explanation:
-4x+8=42
42-8=34
34/-4=8.5
Answer:
x = -8.5
Step-by-step explanation:
minus 8 on both sides and the eight should cancle on the left side
42 minus 8 is 34
then you divide negative 4 on both sides
Carlos is sorting apples for a large orchard.He sorts them into 75 baskets of 30 and 50 baskets of 45.
Which of the following expressions could you use to figure out how many apples Carlos sorted?
A) 75 +30 +30 (50+45)
B) 75x45) x (30x50)
C) 75x30) +(50x45)
D) 45x50X30x75
Answer:
C
Step-by-step explanation:
Because if you have 75 baskets of 30 then you have to multiply 75x30 it is the same thing with 50x45. Hope this helps
Answer:C) 75x30) +(50x45)
Step-by-step explanation: 75 * 30 for the 30 apples in each basket and 50 * 45 for the 45 in each and put them into their own equation with parenthesees. Then add to find the total
which angle is conterminal with -pi/6
Answer:
Subtract 360° to find a negative coterminal angle. Angles that measure 240° and –480° are coterminal with a –120° angle. For an angle θ in standard position, the reference angle is the positive acute angle formed by the terminal side of θ and the x-axis.
Step-by-step explanation:
An 18ft ladder leans against a house, reaching a point 14ft above the ground. How far is the foot of the ladder from the bottom of the house
Answer: a^2+b^2=c^2
Step-by-step explanation: (18^2=14^2+c^2)=324=196+c^2
324-196=128 and the square root of 128 is 8 radical 2 or in decimal form 11.31
Answer:
11.3137085 ft
Step-by-step explanation:
The length (l) of the ladder is 18ft
The height (h) of the ladder from the ground is 14 ft
The distance (x) of the foot of the ladder to the bottom of the house is:
Applying the Pythagorean theorem:
x² = l² - h²
x = [tex]\sqrt{l^2 - h^2}[/tex]
x = [tex]\sqrt{18^2 - 14^2}[/tex] = 11.3137085 ft
Ann needs 3/4 of a book in 2 days. At this rate how many books can she read in 4 1/3 days.
[tex]\bf \begin{array}{ccll} book&days\\ \cline{1-2}\\ \frac{3}{4}&2\\\\ x&4\frac{1}{3} \end{array}\implies \cfrac{~~\frac{3}{4}~~}{x}=\cfrac{~~2~~}{4\frac{1}{3}}\implies \cfrac{~~\frac{3}{4}~~}{x}=\cfrac{~~2~~}{\frac{13}{3}} \implies \cfrac{~~\frac{3}{4}~~}{\frac{x}{1}}=\cfrac{~~\frac{2}{1}~~}{\frac{13}{3}}[/tex]
[tex]\bf \cfrac{3}{4}\cdot \cfrac{1}{x}=\cfrac{2}{1}\cdot \cfrac{3}{13}\implies \cfrac{3}{4x}=\cfrac{6}{13}\implies 39=24x\implies \cfrac{39}{24}=x\implies \cfrac{13}{8}=x \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 1\frac{5}{8}=x~\hfill[/tex]
9:6 and 4:3 are they equivalent?
No because 9:6 is 1.5 and 4:3 is 1.333...
Answer:
NOStep-by-step explanation:
[tex]9:6=\dfrac{9}{6}=\dfrac{9:3}{6:3}=\dfrac{3}{2}\neq\dfrac{4}{3}=4:3\\\\\text{Other method:}\\\\9:6=\dfrac{9}{6}\\\\4:3=\dfrac{4}{3}\\\\\dfrac{9}{6}=\dfrac{4}{3}\qquad\text{cross multiply}\\\\(9)(3)=(6)(4)\\\\27=24\qquad\bold{FALSE}[/tex]
A car travels at 40 miles per hour. Deb wrote the equation ys 40x, Deb then graphed the
equation and noticed that the point (3,120) was on the line, What does this point represent?
A.The car traveled 43 miles
B.120 hours,
C.The car traveled 120 miles In 3 hours,
D. The car traveled 3 miles In 120 hours,
E. The car traveled 120 miles In 40 hours,
Answer:
C
Step-by-step explanation:
The equation represents speed as a function of time. The point (3,120) implies that the car with a speed of 40 miles per hour, travelled a total of 120 miles in a time span of 3 hours.
Explanation:In this scenario, the equation ys = 40x relates the speed of the car (40 miles per hour) to the time travelled (x in hours). The 'y' in the equation represents the distance travelled by the car. So, when interpreting the point (3,120) on the graph for this equation, '3' refers to time (hours) and '120' refers to distance travelled (miles).
Thus, the point (3,120) on the graph signifies that the car travelled 120 miles in 3 hours, so the correct answer is C. The car traveled 120 miles In 3 hours.
Learn more about Interpreting Graphs here:
https://brainly.com/question/1638242
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Anyone understand this if so plz respond with answer
Answer:
I dont know the answer
Step-by-step explanation:
But you can find the answer by figuring out what a domain and a range iss and chose which one is a domain and a range you can find what a domain and a range is on google
-The domain has all possible values of S so is the amount of sugar transported.
-The range has all possible values of C so is the cost to transport sugar
Martin runs 100 meters in 15 seconds. What is the equation for d, the distance in meters that Martin covers per second?
A.
15 + d = 100
B.
100 + d = 15
C.
d × 15 = 100
D.
d × 100 = 15
GUYS I GOT BANNED FOR 25 HOURS LOL
Answer:
C. d × 15 = 100
Step-by-step explanation:
The distance d in meters that Martin covers per second is 100 m/15 sec.
We write this as: d= 100/15. It is the same as:
d × 15 = 100
Thus, the correct answer would be C.
Answer:
The answer is C for sure . Hope everyone has a good day .
Step-by-step explanation:
Answer plzzzz I need it ok
Answer:
There are 26 different possible outcomes. the probability of the computer choosing the first letter of your name is 1 out of 26.
Help plzzz, you could just tell me to go left or right
I ussually think of them as arrows telling me where to go.
if it is > you go ----->
if it is < you go <------