log base 3 of the quantity x to the seventh z to the fourth end quantity divided by y to the sixth end log
Sure hope this helps you :D
The simplified form of the logarithmic expression, 6 log₃x - 7 log₃y + 4 log₃z, is log₃{(x⁶z⁴)/y⁷}. Hence, the third option is the right choice.
What are the laws involved in the simplification of logarithmic expressions?The laws involved in the simplification of logarithmic expressions are:
Power law: [tex]a log_x b= log _xb^a[/tex]Product law: [tex]log_xa + log_xb = log_xab[/tex]Quotient law: [tex]log_xa - log_xb = log_x\frac{a}{b}[/tex]Base changing law: [tex]log_ab = \frac{log_xb}{log_xa}[/tex]How to solve the question?In the question, we are asked to simplify the logarithmic expression,
6 log₃x - 7 log₃y + 4 log₃z.
The simplification of the provided logarithmic expression can be done as follows:-
6 log₃x - 7 log₃y + 4 log₃z,
= log₃x⁶ - log₃y⁷ + log₃z⁴ {Using the Power law: [tex]a log_x b= log _xb^a[/tex]}
= log₃x⁶ + log₃z⁴ - log₃y⁷
= log₃x⁶z⁴ - log₃y⁷ {Using the Product law: [tex]log_xa + log_xb = log_xab[/tex]}
= log₃{(x⁶z⁴)/y⁷} {Using the Quotient law: [tex]log_xa - log_xb = log_x\frac{a}{b}[/tex]}.
Thus, the simplified form of the logarithmic expression, 6 log₃x - 7 log₃y + 4 log₃z, is log₃{(x⁶z⁴)/y⁷}. Hence, the third option is the right choice.
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You pick a card at random.
2
3
4
5
What is P(prime)?
Write your answer as a fraction or whole number.
Answer:
[tex]\displaystyle P(\text{Prime})=\frac{3}{4}=0.75[/tex]
Step-by-step explanation:
[tex]\displaystyle P(\text{Prime})=\frac{\text{Number of Primes}}{\text{Total}}=\frac{3}{4}=0.75[/tex]
The region outside the circle r = 2 and inside the circle r = -4sin
The area of the region which is inside the curve r = -4 sinθ but outside r = 2 will be 4.21 square units
What is an area bounded by the curve?When the two curves intersect then they bound the region is known as the area bounded by the curve.
The region outside the circle r = 2 and inside the circle r = - 4 sinθ.
Then the intersection point will be given as
[tex]\rm 2 = -4 \sin \theta\\\\\theta = 3.66519 ,5.7595[/tex]
Then by the integration, we have
[tex]\rightarrow \dfrac{1}{2} \int _{3.6652}^{5.7595} [(-4\sin \theta)^2 - (2)^2] dx\\\\\\\rightarrow \dfrac{1}{2} \int _{3.6652}^{5.7595} [16 \sin ^2 \theta - 4]dx\\\\\\\rightarrow \dfrac{1}{2} \int _{3.6652}^{5.7595} [ 8(1- \cos 2\theta -) - 4]dx\\\\\\\rightarrow \dfrac{1}{2} \int _{3.6652}^{5.7595} [4 - \cos 2\theta] dx\\\\\\[/tex]
[tex]\rightarrow \dfrac{1}{2} \left [ 4\theta + \dfrac{1}{2} \sin 2\theta \right ]_{3.6652}^{5.7595} \\\\\\\rightarrow \dfrac{1}{2} \left [ 4(5.7595 - 3.6652) + 0.5 (0.19969-0.12759) \right ][/tex]
[tex]\rightarrow \dfrac{1}{2} \left [ 4(2.0943) + 0.5 (0.0721) \right ]\\\\\rightarrow \dfrac{1}{2} \left [ 8.41325 \right ]\\\\\rightarrow 4.2066 \approx 4.21[/tex]
Thus, the area of the region is 3.75 square units.
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HELP ME!!!! 50 POINTS!!!!!
Answer:
1. Height of the prism= h
2. area of the base= B
3. Perimeter of the base= P
Step-by-step explanation:
Here are what the letters mean:
P = perimeter of the base
h = height of the prism
B = area of the base
write a real-world problem that can be represented by the equation x+500=4732
Answer:
7858
Step-by-step explanation:
hope it helps you bye
(7z+1) + (-4z-5) simplify
Step-by-step explanation:
[tex] = (7z + 1) + ( - 4z - 5)[/tex]
[tex] = 7z + 1 - 4z - 5[/tex]
[tex] = 7z - 4z + 1 - 5[/tex]
= 3z - 4
hence 3z - 4 is the answer...
hope it helped !!!
HELP!!!!!!!!!!!!!!!!!
Answer:
To do this I am pretty sure your going to have to do some hard calculations.
Lets go deeper
so because it is a rectangle every angle is a right angle according to the property of a rectangle.
A right angle is 90 degress
So 8x+18=90
90-18=72
8x=72
72/8=9
x=9
Feel free to do brainlest if correct
Valerie is wrapping a box with wrapping paper the volume of the box is 476.16 cubic inches, and the length and width of the box are 4.8 inches and 8 inches respectively. How much wrapping paper is needed to cover the box?
The surface area of the rectangular box = the amount of wrapping paper needed to cover the rectangular box = 394.24 in.²
What is the Surface Area of a Rectangular Box?Surface area = 2(wl + hl + hw).
Volume = lwh.
Given the following:
Volume = 476.16 in.³
Length = 4.8 in.
Width = 8 in.
Find the height (h) using the volume formula:
476.16 = 4.8 × 8 × h
476.16 = 38.4 × h
476.16/38.4 = h
h = 12.4 in.
Surface area = 2(wl + hl + hw) = 2(8 × 4.8 + 12.4 × 4.8 + 12.4 × 8) = 394.24 in.²
The amount of wrapping paper needed to cover the rectangular box = Surface area = 394.24 in.²
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Please help me on this!
Answer:
C
Step-by-step explanation:
Linear functions will be greater than exponential functions at first- however, exponential equations will gradually surpass the linear equation.
Bruce is going to call one person from his contacts at random. He has 252525 total contacts. 202020 of those contacts are from his neighborhood.
What is \text{P(call a person not from his neighborhood})P(call a person not from his neighborhood)start text, P, left parenthesis, c, a, l, l, space, a, space, p, e, r, s, o, n, space, n, o, t, space, f, r, o, m, space, h, i, s, space, n, e, i, g, h, b, o, r, h, o, o, d, end text, right parenthesis?
If necessary, round your answer to 222 decimal places.
The probability of calling a person, not from his neighborhood, is 1/5 or 0.2 if the total number of contacts is 25
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
Total number of contacts = 25
Total number of contacts of neighbors = 20
Total number of contacts which is not of the neighbors = 25 - 20 = 5
The probability of call a person not from his neighborhood:
P = 5/25 = 1/5
P = 0.2
Thus, the probability of calling a person, not from his neighborhood is 1/5 or 0.2 if the total number of contacts is 25
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Answer: 1/5 or 0.2
Step-by-step explanation:
In the diagram, A||B and B||C . Find the values of X
keeping in mind that an absolute value expression is really a duet in disguise, namely there's positive and negative version of it, Check the picture below.
[tex]\pm (3x+12)~~ = ~~105 \\\\[-0.35em] ~\dotfill\\\\ +(3x+12)~~ = ~~105\implies 3x=93\implies x=\cfrac{93}{3}\implies \boxed{x=31} \\\\[-0.35em] ~\dotfill\\\\ -(3x+12)~~ = ~~105\implies 3x+12=-105\implies 3x=-117 \\\\\\ x=\cfrac{-117}{3}\implies \boxed{x=-39}[/tex]
helpp asap 59 points
Answer:
A=7
B=10
C=2
D=2
Surface area= 208
Pretty sure this is correct.
Area of perimeter of composite figures puzzle question B.
Area and perimeter of figure be: 562.08 m² and 123.68 m
What is Area and perimeter?Perimeter is the distance around the outside of a shape. Area measures the space inside a shape.
The figure comprises of a parallelogram and semicircle.
1. For Area
Area of parallelogram = base x height
= 24 x 14
= 336 m²
Area of semicircle = (π x r²)/2
= (3.14 * 12 * 12)/2
= 226.08 m²
Total Area of the figure = 336+ 226.08 =562.08 m²
2. Perimeter
Perimeter of parallelogram= 2 (a+b)
= 2 (19 +24)
= 86 m
Perimeter of semicircle= π * r
= 3.14 * 12
= 37.68 m
Total Perimeter of the figure= 86 + 37.68 = 123.68 m
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What is the arc length of ab?
Answer:
Step-by-step explanation:
[tex]\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=13\\ \theta =115 \end{cases}\implies \begin{array}{llll} s=\cfrac{(115)\pi (13)}{180}\implies s=\cfrac{299\pi }{36} \\\\\\ s\approx 26.09~in \end{array}[/tex]
Which of the following represents the solution set to the equation: x2 + 2x + 26 = 0?
(1) 1 + 10i
(3) -2 + 2iV5
(2) 2 + iv5
(4) -1 ‡ 5i
Answer:
i think the answer is 4
Step-by-step explanation:
hope it's correct
Find the area and perimeter of this shape.
Answer:
55
Step-by-step explanation:
since, it is a parallelogram we can find the area easily just by multiplying the base and height
A=bh
A=55m2
Check whether (2,-3) and (-1, 5) are solutions of the equation
4x+ y =1
Answer:
So the first one the false the second one it true
Step-by-step explanation:
4(2)+(-3)=1 FALSE
4(-1)+5 = 1 TRUE
Solve the inequalities -150x ≥ − 2,400 and -336 ≥ − 21y.
x<
y >
Answer:
x ≤ 16y ≥ 16Step-by-step explanation:
-150x ≥ − 2,400
[tex]\Longrightarrow -\frac{1}{150} \times \left( -150\right) x \leq -\frac{1}{150} \times \left( -2400\right)[/tex]
[tex]\Longrightarrow x\ \leq \frac{-2400}{-150}[/tex]
[tex]\Longrightarrow x\ \leq 16[/tex]
===============
-336 ≥ − 21y
[tex]\Longrightarrow -\frac{1}{21} \times \left( -336\right) \leq -\frac{1}{21} \times \left( -21\right)y[/tex]
[tex]\Longrightarrow 16\geq y[/tex]
[tex]\Longrightarrow y\geq 16[/tex]
A square picture is mounted on a larger rectangular sheet of poster paper leaving a border around the picture of 2 inches on the bottom and 1 inch on each remaining sides. The sheet of poster apper has an area of 42 square inches. If x represents the length of a side of the square picture, then an equation that can be used to determine the value of x is
An equation that can be used to determine the value of x is x² + 5x - 36 = 0.
To answer the question, we need to know what equations are
What is an equation?An equation is an expression which shows the relationship between two variables.
Given that the x represents the length of side of the square picture and the rectangular sheet poster leaving a border around the picture of 2 inches on the bottom and 1 inch on each remaining sides.
Then,
The width of the rectangular poster is W = x + 2 + 1 = x + 3. The length of the rectangular poster is L = x + 1 + 1 = x + 2So, the area of the rectangular sheet poster is A = LW
= (x + 2)(x + 3)
Since the rectangular sheet poster has an area of 42 square inches, A = 42 in².
So, (x + 2)(x + 3) = 42
x² + 3x + 2x + 6 = 42
x² + 5x + 6 - 42 = 0
x² + 5x - 36 = 0
So, an equation that can be used to determine the value of x is x² + 5x - 36 = 0.
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The weights of 5 girls are 70 pounds, 68 pounds, 85 pounds, 62 pounds, and 70 pounds. Nina finds measures of center and measures of variation of this data. Match the descriptions to the type of measure.
Answer:
360 I'm sure that's is answer thank you po………………………………………………..
Answer:
option c, 20
Step-by-step explanation:
Interquartile range is Q3 - Q1
Q3 is the upper end of the box: 35
Q1 is the lower end of the box: 15
35 - 15 = 20
Answer this please Answer
Answer:
A. 6/10
Step-by-step explanation:
Answer:
the answer is a 6
_
10
Step-by-step explanation:
What is the solution to:
2x - 8 < 12
a. x < 2
b. x < 8
c. x < 10
d. x < 40
- -- - - -- - - - -- - - - - -- - - - - -- - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - -- - -
[tex]\blue\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]
What is the solution to 2x-8<12
[tex]\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}[/tex]
First, add 8 on both sides:-
2x<12+8
2x<20
Divide by 2 on both sides:-
x<10 (Option C)
So the numbers less than 10 will make this inequality true.
Good luck.- -- - - - - - - - - - - -- - - - - - - - - - - - -- - - - - - - - - - - - - - -- - - - - -
Rule 1: Add 6 starting from 0. Rule 2: Add 3 starting from 0. Complete the first 5 terms using the rules. How are the corresponding terms related? Each term in the second sequence is double the corresponding term in the first sequence. Each term in the second sequence is half the corresponding term in the first sequence. Each term in the first sequence is four times the corresponding term in the second sequence. Each term in the first sequence is half the corresponding term in the second sequence.
Solve the 3D figure Rectangle is A=BH
Triangle is A=1/2BH
Answer:
The area of the 3d figure
Step-by-step explanation:
the area of the one of triangle is 8.7
and the reactangle is 5 x 7 = 35
and the big one is 10 x 7 = 70
so 8.7 + 8.7 + 35 + 35 + 70 = 157.4
What are the square roots of 36100?
−9/25 and 9/25
−6/25 and 6/25
−6/10 and 6/10
−18/50 and 18/50
Answer: Heyaa!!
its 3/5 :)
Step-by-step explanation:
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
Hopefully this helps you
- Matthew <333
Answer:
The square root of 36/100 is c. -6/10 and 6/10
Step-by-step explanation:
as of right now im not sure how to confirm this other then a calculator, but it is mathmatically correct
also with mathews answer, 3/5 = 6/10 so be sure to look at his explanation as well
((if you happen to know, please let me know in the comment below!!))
Please Help ! Its a math problem !!! Given the tables below, what is the difference between the average rates of change over the interval [1, 4]?
Answer:
-4
Step-by-step explanation:
Average rate of change (Table 1) :
A(x) = h(4) - h(1) / 4 - 1A(x) = 9 - 3 / 4 - 1A(x) = 6/3 = 2Average rate of change (Table 2) :
A(x) = j(4) - j(1) / 4 - 1A(x) = 0 - 6 / 4 - 1A(x) = -6/3 = -2Difference : -2 - 2 = -4
An ice cube tray holds 12 ice cubes. If the total volume of the ice in the
tray is 12 in3, what is the total surface area of the ice cubes?
Answer:
36
Step-by-step explanation:
12 multiplied by 3 is 36
From the set of the first ten natural numbers,if you pick a number at a time what is the probability of the number you pick to be:an even number
Answer:
0.5
Step-by-step explanation:
Half the natural numbers picked are going to be even numbers:
{2, 4, 6, 8, 10}. Thus the probability of the picked number being even is 5/10, or 0.5.
How many centimeters are equal to 12 meters?
Hi!1200 centimetres are equal to 12 meters.
Answer:
1200cm
Step-by-step explanation:
1m = 100cm
12m = 1200cm
Alpha particles are accelerated in a cyclotron to a final orbit radius of 0. 50 m. The magnetic field in the cyclotron is 0. 90 t. The period of circular motion of the alpha particles is closest to
Alpha particles are accelerated in a cyclotron to a final orbit radius of 0. 50 m. The magnetic field in the cyclotron is 0. 90 t. The period of the circular motion of the alpha particles is closest to 0.11μs.
How do find the time period in a cyclotron?The period of the circular motion of the alpha particles moving along an in the presence of the magnetic field is given by;
[tex]T = \dfrac{2\pi m}{qB}[/tex]
Alpha particles are accelerated in a cyclotron to a final orbit radius of 0. 50 m. The magnetic field in the cyclotron is 0. 90 t.
We are given;
Mass; m = 6.68 × 10^(-27) kg
Magnetic field;B = 0.90 T
Charge;q = 2e
Now, e is the charge on an electron and it has a value of 1.6 × 10^(-19) C
So, q = 2 × 1.6 × 10^(-19)
q = 3.2 × 10^(-19) C
we know that,
[tex]T = \dfrac{2\pi m}{qB}[/tex]
we have;
[tex]T =\dfrac{ (2\pi \times 6.68 \times 10^{-27})}{(3.2 \times 10^{-19}\times 0.9)}\\T =11.798 \times 10^{-8} s[/tex]
This can also be written as;
T ≈ 0.11 μs
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