[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\\\ \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]12^3~~ = ~~x^4 y^3 z^6\implies \log_{12}(x^4 y^3 z^6)=3 \\\\\\ \log_{12}(x^4)~~ + ~~\log_{12}(y^3)~~ + ~~\log_{12}(z^6)~~ = ~~3 \\\\\\ 4\log_{12}(x)~~ + ~~3\log_{12}(y)~~ + ~~6\log_{12}(z)~~ = ~~3[/tex]
Solve the equation on the
interval [0,21).
2 csc x + 17 = 15 + CSC X
Answer:
7π/6, 11π/6
Step-by-step explanation:
2cscx + 17 = 15 + cscx
1. Subtract cscx and 17 from both sides ⇒ cscx = -2
2. cscx = 1/sinx ⇒ 1/sinx = -2
3. Multiply by sinx and divide by -2 ⇒ sinx = -1/2
When is sinx equal to -1/2? ⇒ 7π/6, 11π/6
The solution of the equation 2cosec x+17 = 15+cosec x is 7π/6 and 11π/6.
What is the solution of the given equation in the interval [0, 2π)?Given:
The equation which is given is 2Cosec x + 17 = 15 + Cosec x.The interval is [0,2π).Find:
The solution of the given equation.Solution:
2Cosec x + 17 = 15 + Cosec x
⇒ 2Cosec x - Cosec x = 15 - 17
⇒ Cosec x = -2
Now, 1/sinx = -2
⇒ sinx = -1/2
we know, sin 30° = 1/2
Since, sinx is negative,
x will be in 3rd and 4th quadrant.
value in 3rd quadrant = 180° + 30° = 210°
value in 4th quadrant = 360° - 30° = 330°
So, x = 210° = 210 * π/180 = 7π/6
Also, x = 330° = 330 * π/180 = 11π/6
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Write 19% as a fraction.
Answer:
19/100
Step-by-step explanation:
Answer:
19/100
Step-by-step explanation:
The answer is 19/100 because the percentage should be out of 100. Therefore, the fraction is 19/100.
Evaluate a=81 and b=3.
a/9 -b=
Answer:
6
Step-by-step explanation:
once you replace the letters with numbers you get, 81/9-3 and 81/9 is equal to 9 and 9-3=6
O parte din traseul Bușteni-Babele a fost parcurs de mai multi turiști astfel: in prima ora 1/3 din distanta, a doua ora 1/4 din distanta. Dupa cele doua ore le-au mai ramas de parcurs 5km. Care este distanta parcursa de turiști?
Answer:
7km
Step-by-step explanation:
[tex] \frac{1}{3} x + \frac{1}{4} x = \frac{4}{12} x + \frac{3}{12} x = \frac{7}{12} x \\ \\ \\ x - \frac{7}{12} x = \frac{12}{12} x - \frac{7}{12} x = \frac{5}{12} x \\ \\ \frac{5}{12} x = 5 - - - > x = 12[/tex]
[tex]12 \times \frac{7}{12} = 7[/tex]
Let x represent the paper 1 score (out of 40) and y
represent the predicted paper 2 score (out of 100).
Which correctly states the equation for the least-
squares regression line and the interpretation of its
slope?
Answer:
A
Step-by-step explanation:
What is the estimate for 54×31
Answer:
50 * 30 = 1500
Answer:
Actual Product =54*31= 1,674
Estimated Product = 50*30=1,500
Step-by-step explanation:
The endpoints of AB are A(4,3) and B(1,1). What are the coordinates of A’’ after the image has been translated (x,y)—> (x-5,y-1) and rotated 180 degrees about the origin?
Answer:
A"(1, -2)
Step-by-step explanation:
In addition to the translation transformation given, you are asked to transform the figure further by rotating it 180° about the origin. The translation for that is ...
(x, y) ⇒ (-x, -y)
Then the composition of the two transformations is ...
(x, y) ⇒ (-(x -5), -(y -1)) = (-x +5, -y +1)
__
Applied to the given point(s), we have ...
(x, y) ⇒ (-x +5, -y +1)
A(4, 3) ⇒ (-4 +5, -3 +1) = A"(1, -2)
B(1, 1) ⇒ (-1 +5, -1 +1) = B"(4, 0)
The coordinates of A" after translation and rotation are (1, -2).
NO LINKS!! Please help me with this problem
#1
[tex]\\ \rm\Rrightarrow \dfrac{WX}{GH}=\dfrac{UY}{JI}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{8}{14}=\dfrac{UY}{28}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{8(28)}{14}=UY[/tex]
[tex]\\ \rm\Rrightarrow UY=8(2)=16[/tex]
#2
[tex]\\ \rm\Rrightarrow \dfrac{UV}{UY}=\dfrac{FJ}{JI}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{UV}{16}=\dfrac{21}{28}[/tex]
[tex]\\ \rm\Rrightarrow UV=\dfrac{3}{4}\times 16[/tex]
[tex]\\ \rm\Rrightarrow UV=3(4)=12[/tex]
#3
[tex]\\ \rm\Rrightarrow \dfrac{WX}{XY}=\dfrac{GH}{HI}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{8}{XY}=\dfrac{14}{35}=\dfrac{2}{5}[/tex]
[tex]\\ \rm\Rrightarrow 2XY=40[/tex]
[tex]\\ \rm\Rrightarrow XY=20[/tex]
Answer:
UY = 16
UV = 12
XY = 20
Step-by-step explanation:
If UVWXY ~ JFGHI
then:
UV~JF
VW~FG
WX~GH
XY~HI
UY~JI
The only pair of sides that both have measures is WX and GH:
WX = 8
GH = 14
⇒ GH/WX = 14/8 = 1.75
Therefore, JFGHI is and enlargement of UVWXY by scale factor 1.75
As IJ = 28
⇒ UY = 28 ÷ 1.75 = 16
As JF = 21
⇒ UV = 21 ÷ 1.75 = 12
As HI = 35
⇒ XY = 35 ÷ 1.75 = 20
One root of the equation "[tex]x^{2} -m^{2}x -m + 1 = 0[/tex]" (with unknown x) is the number "x1 = 1". Determine the other root "x2".
Answer:
0; 3.
Step-by-step explanation:
1) if to substitute x=1 into the given equation, it is possible to calculate the value of 'm':
1-m²-m+1=0; ⇔ m²+m-2=0; ⇒ m₁=-2; m₂=1;
2) if m=-2 and m=1, then the initial equation is:
x²-4x+3=0 or x²-x=0;
3) according to the item 3), the 2d root is:
x₂=3 or x₂=0.
Find the slope of the line if it exists
Answer:
m = 7/6
Step-by-step explanation:
Find coordinates of two points:
(-2,3)
(-8,-4)
Slope formula =
y1 - y2 / x1 - x2
So...
-4-3 / -8 -- 2
-7 / -6
7/6
remember brainliest and have a great day!
Polly is a server at a
restaurant. A table spends $34
and leaves Polly an 18% tip.
What is Polly's tip?
Answer:
They gave her a $6.12 tip
Step-by-step explanation:
You have to multiply the total ($34) by the Percent (18% = 0.18), and then you will have your final answer.
Suppose that you are a member of the typical American household and your family carries a credit card debt of
$7942. Use the TVM (Time-Value-of-Money) Solver to model a few credit card scenarios. (Note: Use months
rounded to the nearest hundredths on all calculations.)
1. If the average annual interest rate is 17.11%, how many months will it take the average American family
to pay off their debt of $7,942 if they make a minimum payment of $175 each month and no additional
purchases are made?
2. How much interest did you pay during this time?
1. At an annual interest rate of 17.11%, an average family needs 74 months to settle $7,942 at a $175 monthly payment.
2. The total interest is $4,932.10.
What is a monthly payment?The monthly payment is the amount paid each month to settle the loan within its maturity period.
The monthly payment can be computed using an online finance calculator.
We can also determine the period of payment using the same online finance calculator as below.
Data and Calculations:I/Y (Interest per year) = 17.11%
PV (Present Value) = $7,942
PMT (Periodic Payment) = $-175
FV (Future Value) = $0
Results:
N = 73.566
Sum of all periodic payments = $12,874.10
Total Interest = $4,932.10
Thus, while it will take 74 months for the average American family to pay off the loan of $7,942 with a monthly payment of $175 at 17.11% interest, the total interest paid is $4,932.10.
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PLEASE PLESE HELP ME WITH THIS!!!!
The new center is 5 units away from the original, hence we added 5 to the x-value.
If you notice the sides of the new triangle are twice the size of the original one, meaning that it was dilated by a scale factor of 2.
Thomas works 12 days out of every month.
1. Does Thomas work the same percent of days each month? Explain.
Answer:
no (see below)
Step-by-step explanation:
Not all of the months have the same amount of days therefore Thomas does not work the same percentage of days each month.
fx) = X. What is g(x)?
f(x) = x
g(x)?
PLEASE HELP ASAP!!!!
Answer:
C
Step-by-step explanation:
vertex form:
[tex]y = {a(x - h)}^{2} + k[/tex]
the negative sign in front of x^2 is also -1, which is the "a". A controls if the parabola will opek up or down, and the width of the function. In this problem, the parabola opens down. the -3 corresponds to "k" in vertex form. K is the vertical shift or the y coordinate of the vertex. If k is positive it moves up, and if it is negative it moves down. Because of the -3, the vertex of the parabola will move down 3 units on the y-axis.
What’s the inverse of the function?
f(x)=3^x+1
[tex]y= f(x) = 3^x+1\\\\\text{Replace x with y and solve for y}\\ \\~~~~~~x=3^y+1\\\\\implies 3^y = x-1\\ \\\implies \ln(3^y) = \ln(x-1)\\\\\implies y \ln 3= \ln(x-1)\\\\\implies y= \dfrac{\ln(x-1)}{\ln 3}\\\\\implies f^{-1}(x) = \dfrac{\ln(x-1)}{\ln 3}[/tex]
xy=10
4x+2y=30
I need help asap
Answer:
x = 25/3; y = -5/3
Step-by-step explanation:
You did well so far by multiplying both sides of the first equation by 2.
Now notice that you have -2y in the new first equation and 2y in the second equation. -2y and 2y add to 0.
Now add the equations to eliminate y.
2x - 2y = 20
(+) 4x + 2y = 30
-------------------------
6x = 50
6x/6 = 50/6
x = 50/6 = 25/3
2x - 2y = 20
2(25/3) - 2y = 20
50/3 - 2y = 60/3
-2y = 60/3 - 50/3
-2y = 10/3
-2y/2 = (10/3)/(-2)
y = -5/3
Solution: x = 25/3; y = -5/3
giving brainliest :D
show steps in a simple way (not to long of an example ty :))
Answer:
[tex]\boxed{8x+6 \: units= base}[/tex]
Step-by-step explanation:
Altitude = 3x
Area = 12x² + 9x
We know that
Area of right triangle = ½ × base × altitude
Then,
12x² + 9x = ½ × 3x × base
[tex]12x ^ { 2 } +9x= \frac{ 3x }{ 2 } \times \: base[/tex]
[tex]\frac{6x\left(4x+3\right)}{3x} = \frac{3x\times \: base}{3x}[/tex]
[tex]\frac{6x\left(4x+3\right)}{3x} = base[/tex]
[tex]\underline{\underline{8x+6 \: units= base}}[/tex]
________
Hope it helps ⚜
PLS HELP ASAP DUE TODAY
Solve the following equation algebraically:
x^2 = 192
A. 13.86
B. -13.86, 13.86
C. -14.36, 14.36
Emergency!!
Mrs. Reynolds has $153. She buys a bicycle for $105.
Then, she finds $20 at the bottom of her purse.
How much money does she have now? Use the bar diagrams to help you.
Step 1:
Step 1: a bar diagram shows 105 and m, the money left after buying a bike. Together 105 and m is equal to 153.
Step 2:
Step 2: a bar diagram shows that 20 and m is equal to s, the money now.
Enter your answer in the box.
Mrs. Reynolds has $
now.
Answer:
$68
Step-by-step explanation:
Mrs. reynolds now has 68 dollars. 153-105=48. 48+20=68
Answer:
She has $68 dollars remaining
Step-by-step explanation:
(no bar diagram needed, lol jk.)
anyways she started off with 153, right?
She then buys a bike worth $105; thats -$105 which leaves here with $48 dollars
Then ooo its her lucky day, she finds a $20 dollar bill, you add it to $48 (+$20) , now she has $68 dollars in total.
<3
A researcher is studying the growth of bacteria. He starts eith 280 of the bacteria. It grows continuously at a rate of 6% per hour. How many bacteria will there be in 16 hours?
18/2x-6
step by step please
Answer:
[tex]\frac{9}{x-3}[/tex]
Convert the problem into split up expressions.
[tex]\frac{18}{2}(x - 6)[/tex]
Take both 6 and 18's most common factor here, 2, and divide by 2 to simplify.
[tex]\frac{18}{2} = 9\\\\\frac{6}{2} = 3[/tex]
Cancel.
18 becomes 9
6 becomes 3
The equation turns into:
[tex]\frac{9}{x - 3}[/tex]
note that because we, "canceled" 2, that also means it does not appear in the simplified form since it was a factor.
What is the area of the shaded sector of Point B below?
Answer:
A) 175π / 9 squared inches,
Step-by-step explanation:
Radius = 10 inches
AB = BD = 10 = radius
Triangle ABD is isosceles
Angle DAB = Angle BDA = 35 degrees,
Base angles theroem
35 + 35 + x = 180, angles in triangle
x = 180 - 70
x = 110 degrees
Angle DBC is supplementary with ABD
110 + x = 180
x = 70
70 degrees is angle for the sector
70 is 70/360, 7/36 of the circle
The area will also be 7/36 of the circle area
Area of circle = πr^2
Area = 100π
Area of sector = (100π * 7) / 36
Area of sector = 700π / 36
Simplified area = 175π / 9 squared inches
solve:
-7=12x-16
If you help me with this I will be your best friend!!!
Answer:
x = 0.75
Step-by-step explanation:
first make the x term the subject
-7 = 12x - 16
-7 + 16 = 12x
add the like terms
9 = 12x
solve for x
9÷ 12 = 12x ÷ 12
0.75 = x
The reference angle for (5pi)/4 is pi/4 , which has a terminal point of (sqrt2/2), (sqrt2/2). What is the terminal point of 5pi/4?
Using the unit circle, it is found that the terminal point of the angle 5pi/4 is given by:
A. [tex]\left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)[/tex]
What is the unit circle?For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].
The angle 5pi/4 is in the third quadrant, as it is greater than pi and less than 1.5pi, in which both the sine and the cosine are negative. Hence, considering the reference angle, we have that:
[tex](\cos{(\left(\frac{5\pi}{4}\right)}, \sin{(\left(\frac{5\pi}{4}\right)}) = (-\cos{(\left(\frac{\pi}{4}\right)}, -\sin{(\left(\frac{\pi}{4}\right)}) = \left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)[/tex]
Hence option A is correct.
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what is 3/4 of 1/3
Reduce your answer to simplest form.
Answer:
1/4.
Step-by-step explanation:
3/4 of 1/3
= 1/3 * 3/4
= 3/12
= 1/4
help an someone help
HELP PLEASEE ITS EASY!!!!!!!!!
Answer:
4 inches
Step-by-step explanation:
The scale is 1:3 based on that info, x:12
There is a 4-factor increase, meaning x=4
The Zoo is 16 Inches from the school
rudy has punch cards for his favorite tea house abs his favorite coffee shop. he currently has 1 punch on the tea punch card and 2 punches on the coffee punch card. given his regular routine he consistently earns 7 new punch cards per week on the tea punch card and 6 on the coffee punch card. before too long rudy will have the same number of punches on each card. how long will it take? how many punches will rudy have on each card?
The time it would take for Rudy to have the same number of each punch card is 1 week.
The number of punches on each card Rudy would have is 8 punches.
How long will it take to have the same number of punches on each card?The equation that represents the number of punches on the tea punch card is: 1 + 7t
The equation that represents the number of punches on the coffee punch card is: 2 + 6t
Where t represents the number of weeks
When both cards would have the same amount of punches, the two above equations would be equal:
1 + 7t = 2 + 6t
To find the value of t, take the following steps:
Combine similar terms
7t - 6t = 2 - 1
t = 1 week
What will be the number of punches on each card?
Number of punches on each card = 1 + 7(1) = 8 punches
To learn more about when the two different variables would have the same amount, please check: https://brainly.com/question/25711114