The value of logarithm expression 2log₅(5x³) + (1/3)log₅(x² + 6) is simplified as log₅[{25x⁶}{∛(x² + 6)}].
What is a logarithm?Exponents can also be written as logarithms. The other number is equal to a logarithm with a number base. It's the exact inverse of the exponent function.
The logarithmic expression is given as
[tex]2\log _55x^3 + \dfrac{1}{3} \log _5(x^2 +6)[/tex]
We know that formulas
[tex]a \log b = \log b^a\\\\\log a + \log b = \log ab[/tex]
Then we have
[tex]\rightarrow \log _5(5x^3)^2 + \log _5(x^2 +6)^{1/3}\\\\\rightarrow \log _525x^6 + \log _5\sqrt[3]{(x^2 +6)}\\\\\rightarrow \log _5 25x^6 (\sqrt[3]{(x^2 +6)})[/tex]
More about the logarithm link is given below.
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73 in.
55 in.
b
What is the length of the missing leg? If necessary, round to the nearest tenth.
b =
inches
Answer:
48 (rounded to 10).....
The figure shows a person estimating the height of a tree by looking at the top of the tree with a mirrow. Assuming that both the person and the tree form right angles with the ground, which of the following proportions can be use to estimate the height of the tree
A student usually saves $20 a month. He would like to reach a goal of saving $350 in 12 months. The student writes the equation 350 = 12(x+20) to represent this situation. Solve the equation for x.
Write your answer as a sentence that describes what the variable x represents.
Enter your answers and your work or explanation in the box provided.
Answer:
The student would need to save $9.17 more per month
Step-by-step explanation:
350 = 12(x+20)
350 = 12x + 240
12x = 110
x = 110/12
x = $9.17
Look at this set of 9 numbers:
30
59
44
58
30
69
89
30
44
By how much would the mode increase if the number 80 were added to the set?
Answer:
The mode would not increase or decrease.
Step-by-step explanation:
I say this because the mode is the value(s) in the data set that occur most frequently. 30 is the mode before adding 80 because 30 is in the set 3 times, more than the other values. Because 80 would be the only 80 in the set it would not become the mode once added. I hope this explained my reasoning and helped!
The anwser is down below
Answer:
B) 2/9
Step-by-step explanation:
2 + 3 + 5 = 10 marbles altogether
One blue is taken out, so it's now 2 and 9 (10-1).
Consider f(x) = bx. which statement(s) are true for 0 < b < 1? check all that apply. the domain is all real numbers. the domain is x > 0. the range is all real numbers. the range is y > 0. the graph has x-intercept 1. the graph has a y-intercept of 1. the function is always increasing. the function is always decreasing.
The true statement for f(x)=b^x is the function is always decreasing function.
We have given,
f(x)=b^x where 0<b<1
What is the domain?Domain is all possible values of x for which any function is defined
We can select any values of x for which function
It will be defined for all real x
So, the domain is [tex](-\infty,\infty)[/tex]
The range is all possible values of y for which x is defined
we are given that b is positive
The value of the function will always be positive
So, the range is [tex](0,\infty)[/tex]
y>0
The x-intercept:
Set f(x)=0 and then we can solve for x
f(x)=b^x=0
x is undefined
The x-intercept does not exist
Increasing or decreasing:
Since, 0<b<1
The b is a positive value less than 1
As we increase the value of, [tex]b^x[/tex] will keep decreasing
This is decreasing function
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Use the triangle to answer the question.
ul
diagram not drawn to scale
4
What is the length of the side labeled x?
Ο Α. V11
OB. V21
Oc 11. D.21
The length of the side labeled x is Option B. [tex]\sqrt{21}[/tex].
Pythagorean theorem.Pythagorean theorem is a basic principle to be applied when determining the unknown side of a given right triangle when the values of two sides are given. The theorem states that;
/Hyp/^2 = /Adj/^2 + /Opp/^2
From the triangle given, we have;
/Hyp/^2 = /Adj/^2 + /Opp/^2
x^2 = 4^2 + ((5)^1/2)^2
= 16 + 5
= 21
x = 21^1/2
= [tex]\sqrt{21}[/tex]
The length of the side labeled x is [tex]\sqrt{21}[/tex]. Option B.
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What is the domain of the function graphed below?
A. {x | x = -1,2,4}
B. {x | x=-2,-1,2,4}
C. {x | x=2}
D. {x | x=-2,4}
= is not equal to sign
Answer:
{x | x ≠ -1, 2, 4}
Step-by-step explanation:
Domain: input values (x-values)
Asymptote: a line which the curve gets infinitely close to, but never touches.
Hole: a point on the graph where the function is not defined.
From inspection of the graph:
Vertical asymptotes at x = -1 and x = 4Hole at x = 2As vertical asymptotes and holes restrict the domain of a rational function, the domain is {x | x ≠ -1, 2, 4}
Lamont designs a survey of town residents in an attempt to predict who will be elected mayor. he chooses his sample of 500 people from the town’s 40,000 residents by asking his question to every person leaving the public library on a saturday. which suggestion would most improve lamont’s random sample? lamont should sample only adults. lamont should sample only registered voters. lamont should decrease the sample size. lamont should ask every fifth person.
Lamont should sample only registered voters to predict who will be elected mayor
What is a survey?A survey is a research method used for collecting data from a predefined group of respondents to gain information and insights into various topics
Since Lamont is trying to predict who will be elected, surveying people that are not registered to vote will not give him an accurate prediction. If someone is not registered to vote, they cannot vote for any candidate.
To get more accurate results, Lamont should only sample people that are registered voters.
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Answer:
b
Step-by-step explanation:
edge test
5. 4. Ms. Le has a bag of marbles. The table below shows the amount she drew of each marble. Color Amount Blue 8 Red 10 Yellow 9 Green 6 Purple 7 Based on these results, what is the probability that Ms. Le will choose a yellow or purple marble? A 2/5 B 1/16 C 1/8 D 4/5
Answer:
A, 2/5
Step-by-step explanation:
8 + 10 + 9 + 6 + 7 = 40
9 + 7 = 16
16/40
divide both sides by 8 (common factor)
2/5
Show how to find m<1 using the inverse cos of <1.
[tex]\text{We know that,}\\\\\cos \theta = \dfrac{\text{Base}}{\text{Hypotenuse}}\\\\\\\text{For}~ \angle1,\\\\~~~~~~\cos \angle 1 = \dfrac bc\\\\\\\implies \cos \angle 1 = \dfrac 35\\\\\\\implies \angle 1 = \cos^{-1} \left( \dfrac 35 \right)\\\\\\\implies \angle 1 = 53.13^{\circ}\\\\\\\text{For} ~ \angle 2,\\\\~~~~~~~\cos \angle 2 = \dfrac ac\\\\\\[/tex]
[tex]\implies \cos \angle 2 = \dfrac 45\\\\\\\implies \angle 2 =\cos^{-1} \left( \dfrac 45 \right)\\ \\\\\implies \angle 2 = 36.86^{\circ}[/tex]
[tex]\text{Hence,}~~ m\angle 1 = 53.13^{\circ}~~ \text{and}~~ m\angle 2 =36.86^{\circ}.[/tex]
Write your answer as a fraction or as a whole or mixed number.
Answer:
9 days
Step-by-step explanation:
because if you turn 7 ⅞ into 63/8 then do 63÷7 you get 9
Answer:
9 days.
write 7/8x9, and put a 1 under it.
7x9=63
8x1=8
63/8 simplified is 7 7/8
Step-by-step explanation:
Select the graph that represents h = -16t^2+ 80.
Answer:
Attach the graph options so i can help...
Step-by-step explanation:
who ever gets right 100 points.... HELP ASAP
Answer:
3rd Table
Explanation:
1st and 2nd option does not relate time taken or speed together while jogging and walking. They are irrelevant thus they cancels out.3rd option relates time taken and speed together in a arranged way. It is easy to understand and find the distance covered.4th option seems confusing as there is no numerical digit in the table. We cannot find miles covered from this given information.(WILL MARK BRAINLIST)
Use the function f(x) = x2 – 2x + 8 and the graph of g(x) to determine the difference between the maximum value of g(x) and the minimum value of f(
2.
Answer:
3 or 4, I am confused
Step-by-step explanation:
I'll assume that f(x) = x2 – 2x + 8 is meant to be f(x) = x^2 – 2x + 8
Find the value of f(x) for x = 2:
f(x) = x^2 – 2x + 8
f(2) = (2)^2 – 2*(2) + 8
f(2) = 4 - 4 + 8
f(2) = 8
=============
From the graph, we can find that g(2) = 11
The differece between g(2) and f(2) is thus:
11 - 8 = 3
3 is not an option, so I wonder if the question is asking for the difference between the absolute maximum of g(x) and f(2). If so, the maximum for g(x) is 12, at x = 3.
This would lead to a difference of 12 - 8, or 4. This is still not an option, so I'm confused. Perhaps you can find my error and find the ciorrect answer, or at least one that appears in the options.
The height of a cuboid is 5 cm and its length is 2cm more than the breadth. If its volume is 240cm, find its length and breadth.
Answer:
Final answer -
[tex]length = 6 \: cm \\ breadth = 6 + 2 = 8 \: cm[/tex]
hope helpful :D
A group of friends were working on a student film. They spent all their budget on
equipment and props. They spent $369 on equipment, and 55% of the total budget on
props. What was the total budget for their student film?
Answer:
$820
Step-by-step explanation:
Total = Equipment + Props
T = 369 + 0.55T
0.45T = 369
T = 820
I hope this helps!
Can anyone help me with this one to
Find the perimeter of this semi-circle with radius, r = 42cm. Give your answer as an expression in terms of π .
Answer:
C≈263.89 cm
Step-by-step explanation:
Which of the following reveals the minimum value for the equation 3x2 + 18x + 15 = 0?
can u give me a step by step
Answer:
Step-by-step explanation:
I have no idea
Answer:
3(x+3)^2=12
Step-by-step explanation:
3x^2-18x+15
(3x^2+18x)+15
3(x^2+6x)+15
3(x^2+6x+9)+15-27
3(x+3)^2-12
3(x+3)^2=12
Hope this helps!
Please mark as brainliest! Thanks!
What is the western most state in the United States?
°Hawaii
°Florida
°Wisconsin
°Texas
Hawaii
hope it helps...!!!
EASY! PLEASE HELP, I AM STUCK
Answer:
A. 16 seconds.
Step-by-step explanation:
Well, it would take him 4 seconds to get 4/16 of the way, or 1/4. So just multply that by 4 and boom, 16 seconds. (yes ik my technique is weird)
there are 20 students in mr.clarks fourth grade class there are 5 times as as many students in the entire fourth grade class as there are in mr.clacks. which equation can be used to determine the number of students,n, in the entire fourth grade?
Answer:
there are 20 students in mr.clarks fourth grade class there are 5 times as as many students in the entire fourth grade class as there are in mr.clacks. which equation can be used to determine the number of students,n, in the entire fourth grade?
n= 20(5)
100 kids in the fourth grade
or
there are 140 kids in the 4 th grade
Step-by-step explanation:
the equation is n=20(5)
because 20(5) is the same as 20×5 so that 8s the equation
Find the slant height?
35
43
45
47
Answer:
45
Step-by-step explanation:
Slant height = √(altitude)² - (1/2 base)²
Sh = √53² - 28²Sh = √2809 - 784Sh = √2025Sh = 45Apologies as my previous response was incorrect.
if angle 6 is 25 degrees how much is 7
Given:
Angle 6 = 25 degrees
To Find:
The value of Angle 7
Solution:
We know that,
the value of Angle 6 is equal to 25 Degrees
Since Angle 6 and Angle 7 together comprise of a Straight Line, this means that they are Supplementary Angles.
Therefore,
Angle 6 + Angle 7 = 180 degrees
This implies that,
25 degrees + Angle 7 = 180 degrees. (since Angle 6 = 25 Degrees)
Angle 7 = (180-25) degrees
Thus ,
Angle 7 = 155 degrees
Hence, Angle 7 is 155 degrees (Option 1)
What is the product? startfraction 2 y over y minus 3 endfraction divided by startfraction 4 y minus 12 over 2 y 6 endfraction two-thirds ten-ninths startfraction 4 y over y minus 3 endfraction startfraction 4 y over y 3 endfraction
The product of the expression [tex]\rm \dfrac{\dfrac{2y}{y-3} }{\dfrac{4y-12}{2y+6}}\\\\\\[/tex] is [tex]\rm \dfrac{(y^2+3y)}{(y^2-6y+9)}\\[/tex].
What is the product?In mathematics, the term 'product' refers to the answer to a multiplication problem.
The product of the given expression is determined in the following steps given below.
[tex]\rm =\dfrac{\dfrac{2y}{y-3} }{\dfrac{4y-12}{2y+6}}\\\\\\=\dfrac{2y}{y-3}\times \dfrac{2y+6}{4y-12}\\\\= \dfrac{2y \times 2y + 2y \times 6}{y(4y-12)-3(4y-12)}\\\\=\dfrac{4y^2+12y}{4y^2-12y-12y+36}\\\\=\dfrac{4y^2+12y}{4y^2-24y+36}\\\\=\dfrac{4(y^2+3y)}{4(y^2-6y+9)}\\\\ =\dfrac{(y^2+3y)}{(y^2-6y+9)}\\[/tex]
Hence, the product of the expression [tex]\rm \dfrac{\dfrac{2y}{y-3} }{\dfrac{4y-12}{2y+6}}\\\\\\[/tex] is [tex]\rm \dfrac{(y^2+3y)}{(y^2-6y+9)}\\[/tex].
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Answer:
3
Step-by-step explanation:
D on edge 2022
The figure shows a line graph and two shaded triangles that are similar: A line is shown on a coordinate grid. The x axis values are from negative 15 to positive 15 in increments of 3 for each grid line. The y axis values are from negative 5 to positive 5 in increments of 1 for each grid line. The line passes through the ordered pairs negative 12, negative 4, and 0, 0, and 12, 4. A shaded right triangle is formed so that its hypotenuse is from ordered pair 0, 0 labeled O to negative 6, negative 2 labeled A, one leg is from 0, 0 to 0, negative 2, and the second leg is from 0, negative 2 to negative 6, negative 2. Another shaded right triangle is formed with the hypotenuse from negative 6, negative 2 to negative 9, negative 3 labeled B, one leg is from negative 6, negative 2 to negative 6, negative 3, and the second leg is from negative 9, negative 3 to negative 6, negative 3. Which statement about the slope of the line is true? It is 3 throughout the line. It is fraction 1 over 3 throughout the line. The slope from point O to point A is fraction 1 over 3 time the slope of the line from point A to point B. The slope from point O to point A is three times the slope of the line from point A to point B.
hope this helps
The figure below shows a line graph and two shaded triangles that are similar:
A line is shown on a coordinate grid. The x axis values are from negative 20 to positive 20 in increments of 4 for each grid line. The y axis values are from negative 5 to positive 5 in increments of 1 for each grid line. The line passes through the ordered pairs negative 16, 4, and 0, 0, and 16, negative 4. A shaded right triangle is formed so that its hypotenuse is from ordered pair 0, 0 labeled as O to negative 8, 2 labeled as A, one leg is from 0, 0 to negative 8, 0, and the second leg is from negative 8, 0 to negative 8, 2. Another shaded right triangle is formed with the hypotenuse from negative 8, 2 to negative 12, 3 labeled as B, one leg is from negative 8, 2 to negative 12, 2, and the second leg is from negative 12, 2 to negative 12, 3.
Which statement about the slope of the line is true?
The slope from point O to point A is fraction 1 over 4 times the slope of the line from point A to point B.
The slope from point O to point A is 4 times the slope of the line from point A to point B.
It is fraction negative 1 over 4 throughout the line.
It is −4 throughout the line
Step-by-step explanation:
not my answer found it on a different page but it should help.
if x cubed = -8, what does x equal
Let's start the sum as follows:
x³ = 8
X × X × X = 8
This means there are 3 number which after Multiplication gives answer 8.
If 2 is multtiplied 3 times it will give you 8
Thus the answer of x is 2
x = 2.
x^3 = -8
The cube root of 8 is 2 = 2 x 2 x 2 is 8.
But, the answer is negative, which means that the cube root of -8 must be -2.
-2 x -2 x -2 = -8
x = -2
Hope this helps!
please help me !!!!!!!!!!
[tex]y = - x - 1[/tex]
[tex]y = - 5x - 13[/tex]
Multiply the lower equation by -1:[tex]y = - x - 1[/tex]
[tex] - y = 5x + 13[/tex]
Add the systems:[tex]0 = 4x + 12[/tex]
[tex]4x = - 12[/tex]
[tex]x = \frac{ - 12}{4} = - 3[/tex]
Substitute x=3 in any equation:
[tex]y = - x - 1[/tex]
[tex]y = - ( - 3) - 1[/tex]
[tex]y = 3 - 1 = 2[/tex]
SoLuTiOn PaiR:( -3 , 2 )Find the missing angle using the diagram below. The figure is a parallelogram.
(5x + 5)°
135
28
180
90
145
Answer:
145°
Step-by-step explanation:
35+(5x+5)° = 180° (opposite angles sum up to 180°)
35+5x+5 = 180
40+5x = 180
5x= 180- 40
5x = 140
x = 28
therefore, the missing angle = (5x+5)°
= (5×28+5)= 140+5= 145°