The value of the logarithm log₃ (x⁻¹)[tex]^{1/b}[/tex] where x and b positive real numbers is - 5 · b⁻¹ · log₃ b.
How to analyze and solve logarithmic expressionsLogarithms are trascendental functions, that is, functions that cannot be described algebraically.
In this question we must apply logarithm and algebraic properties to determine firstly the value of [tex]x[/tex] and later to find value of the latter logarithm. Now we proceed to find the value of [tex]x[/tex]:
[tex]\log_{b} x^{2} = 10[/tex]
[tex]2\cdot \log_{b} x = 10[/tex]
[tex]\log_{b} x = 5[/tex]
x = b⁵
Then, the value of the latter logarithm is:
log₃ (x⁻¹)[tex]^{1/b}[/tex]
- b⁻¹ · log₃ x
- b⁻¹ · log₃ b⁵
- 5 · b⁻¹ · log₃ b
The value of the logarithm log₃ (x⁻¹)[tex]^{1/b}[/tex] where x and b positive real numbers is - 5 · b⁻¹ · log₃ b. [tex]\blacksquare[/tex]
RemarkThe statement is poorly formated, correct form is described below:
Let [tex]x[/tex] and [tex]b[/tex] be positive real numbers so that [tex]\log_{b} x^{2} = 10[/tex]. Find [tex]\log_{3} \sqrt [b]{\frac{1}{x} }[/tex].
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I need help with this question
Step-by-step explanation:
a/-3=18 what does a equal?
Answer:
I believe a is equal to -54
PLEASE HELP PLEASE I WILL GIVE BRAINLIEST
Answer:
Step-by-step explanation:
This is a quadrilateral.
Sum of all angles of a quadrilateral = 360
x + 100 + 60 + 95 = 360
x + 255 = 360
x = 360 - 255
x = 105°
Answer:
Angle X= 105 Degrees
Step-by-step explanation:
1. Create Equation
100+60+95+x=360
2. Solve
100+60+95+x=360
160+95+x=360
255+x=360
255-255+x=360-255
x=105
3. Check
100+60+95+105=360
160+95+105=360
255+105=360
360=360
Correct!
4. Answer
x=105
Farah has been saving money for years. Pearl's money is 3 times as much as
3
5
of Farah's money. They have $672 altogether. How much does Farah have now?
Answer:
$168
Step-by-step explanation:
x + 3x = 672
4x = 672
x = 672 / 4
x = 168
Farah has $168
Christy bought a 9- foot piece of lumber trim bookshelf. Altogether, she needs 100 inches of lumber. Did Christy buy enough lumber? Show your work and explain.
Answer:
Yes.
Step-by-step explanation:
because 9 feet converted to inches equals 108 inches, we know this because we can convert feet to inches via multiplication. To do this, simply multiply the given number (9) by 12 to get your answer.
a railroad crossing sign has a diameter of 30 inches. what is the area of the sign?
Answer:
706.5m^2
Step-by-step explanation:
The sign is a circle
Area of a circle is (pi)r^2
d = 30 in -> r = d/2 = 30/2 = 15
Area = 3.14 x (15)^2 = 706.5m^2
Answer:
about 706.5 or 706.86
Step-by-step explanation:
to find this answer we need to use the area formula of a circle which is A = πr ^2
we know the diameter is 30, and the radius is half the of diameter, so we take 30 and divide it by 2, which should give us 15 for the radius. ( 30/2 = 15, so r = 15)
depending on how your teacher wants u to answer this you can use π on a calculator or use 3.14
now just plug in your numbers to formula
A = 3.14 * 15^2 or A = π * 15^2
and should equal about 706.5 or 706.86 (depending on if you use 3.14 or π)
How are genetic engineering and artificial selection different? (in your own words)
Artificial selection picks previously existing qualities by breeding individuals with favourable traits, whereas genetic engineering affects the genetic composition of plants or animals by adding new genes or silencing genes.
If measure of angle T= (2x + 85), measure of angle V= (5x + 29), and
the sum of the measures of the angles is
93°, find the measure of each angle.
Answers:
Angle T = 79 degrees
Angle V = 14 degrees
=========================================================
Work Shown:
T + V = 93
(2x+85) + (5x+29) = 93
7x+114 = 93
7x = 93-114
7x = -21
x = -21/7
x = -3
This x value is used to find each angle mentioned.
Angle T = 2x+85 = 2(-3)+85 = -6+85 = 79 degreesAngle V = 5x+29 = 5(-3)+29 = -15+29 = 14 degreesAs a check, T+V = 79+14 = 93 which confirms our answers.
Answer:
An alternate interior angle, c, 180 degrees
Step-by-step explanation:
did it
Mary and Jane went on a tour together. Mary brought twice as much money as Jane. After Mary had spent $800 and Jane had spent $240, they had equal amount of money left. How much money did Mary have at first?
Answer:
Mary has $1120
Step-by-step explanation:
money mary has at first : x
money jane has at first : y
Mary brought twice as much money as Jane : x=2y
Mary had spent $800 and Jane had spent $240, they had equal amount of money left : x-800=y-240
=> [tex]\left \{ {{x=2y} \atop {x-800=y-240}} \right.[/tex]
=> x=1120
y=560
Answer:
Mary had $1,120Step-by-step explanation:
Let the amount mary and jane had be 2x and x respectively.
Let the equal amount be y:
[tex]mary \: (y = 2x - 800) \\ jane \: (y = x - 240)[/tex]
Using the simultaneous equation method, multiply the first equation by the coefficient of x(1) of the second equation and the second equation by the coefficient of x(2) of the first equation:
[tex]y = 2x - 800 \\ 2y = 2x - 480[/tex]
Subtract the second equation from the first equation:
[tex] - y = - 320 \\ y = 320[/tex]
$320 was their equal amount.
Substitute 320 for y in any equation:
[tex]y = x - 240 \\ 320 = x - 240 \\ x = 320 + 240 \\ x = 560 \\ \\ 2x = 1120[/tex]
Therefore, Jane had $560 at first and Mary had $1120 at first.
please help me it's ,due, by 30 minutes please help me.
Step-by-step explanation:
I hope its helped ! studied well.
Answer:
a: The tape diagram represents the story because there’s 5 boxes representing the 5 weeks and x-2 in each box since x represents the amount Andre’s neighbor will pay him weekly to mow the lawn. This all equals 40 because that’s how much money he has to save.
B: Andre’s neighbor pays him 10 dollars each week to mow the lawn.
Step-by-step explanation:
b: For this part you have to make an equation combining all the five weeks which would be 5x-10. Then you would make it equal 40 because that’s how much he needs to save 5x-10=40. The you solve to find x by adding 10 to both sides of the equation and get 5x = 50. Then if you divide 5 on both sides you get 10!
You can check you work by plugging in 10 as x into the diagram.
Find the volume of a box that has a length of 8.9 cm, a
width of 4 cm, and a height of 10.6 cm.
Answer: 377.36cm^2
Step-by-step explanation:
1. find proper equation. to find the volume of any three dimensional cube or box, use: length * width * height
2. plug in given numbers into the equation: 8.9cm * 4cm * 10.6* which gives us our answer, 377.36cm^2
hoped this helped! ♡
round to the nearest hundredth
Answer:
the answer without rounding is 147 but with its 100
Step-by-step explanation:
firsts you add up both sides of the triangle and then you subtract by 180 and now that you your answer but you had to round AN anyting above 150 you would have to run to 200 but you had one 47 so it's 100
What is the probability of picking an orange marble and flipping tails?
Answer:
1/7 and 1/2
Step-by-step explanation:
The probability of orange marble is 1/7
Probability of tails is 1/2
If you need to add this, then it'll be 1/14
7 x 2 = 14
1 x 1 = 1
A department store has 950 customers one day, and 82% of customers made a purchase. Of the customers who made a purchase, 528 bought just one item, 186 bought two items, and the remainder bought three or more items. How many customers bought three or more items?
Answer:
65 bought 3 or more items.
Step-by-step explanation:
See attached summary. The total purchasing customers was 779 (0.82*950). Use the percentages to calculate calculate the numbers of customers who purchased one and two items (528 and 186). Add those and subtract from the total number of customers who purchased anything (779) , to arrive at the number who bought three or more items. 65 bought three or more items.
Leon and Omar went to grab ice cream after track practice. They each chose a container shaped like a cone or a cylinder. The dimensions of each container are shown in the drawing.
The volume of the cone and cylinder with a radius of 7 cm and height of 10 cm is 513.33 cm³ and 1540 cm³ respectively.
What is volume?Volume is the amount of space occupied by a three dimensional shape or object.
Let us assume the cone and cylinder has a radius of 7 cm and height of 10 cm, hence:
Volume of the cone = (1/3) * π * radius² * height = (1/3) * π * 7² * 10 = 513.33 cm³
Volume of the cylinder = π * radius² * height = π * 7² * 10 = 1540 cm³
The volume of the cone and cylinder with a radius of 7 cm and height of 10 cm is 513.33 cm³ and 1540 cm³ respectively.
Find out more on volume at: https://brainly.com/question/12410983
find x and y. use proper postulates or theorems to justify your answer
Answer:
x = 110
y = 23
Step-by-step explanation:
For X :
100 = x -10
110 = x
Corresponding angles are equal
For Y :
180 - 110 = 70
(2y + 24) = 70
2y = 46
y = 23
Adjacent Angles on a straight line add up to 180 Degrees
Calculate the IQR given the box plot
Answer:
10
Step-by-step explanation:
The Interquartile Range (IQR) is the difference between Q3 and Q1.
From the diagram we see that Q1 = 40, and Q3 = 50
IQR = Q3-Q1 = 50 - 40 = 10
What is the area of the parallelogram shown? A) 60in B) 120in C) 140in D) 180in. + What is the area of a parallelogram that has a base 5 inches longer and the height 5 inches taller than a parallelogram shown? A) 230in B) 260in C) 290in D) 310in.
120 in sq. , 260 in sq.Step-by-step explanation:question 1.area of a parralelogram = perperndicular height x basetherefore area = 8in x 15 inarea is 120in sq.question 2.the second parallelogram dimensions are as followsheight = 8 in +5 in = 13 inbase = 15in + 5in = 20therefore area = 13x20area = 260 in sq.
The ingredients for your skillet brownie cost $1.89. You want your food cost percentage for this item to be 30% or lower. What's the lowest price you can charge? Round to the nearest cent.
choices:
a.
$5.98
b.
$6.00
c.
$5.67
d.
$6.30
Answer:
Your want your food cost forthis item to be 30% or lower. What's the lowest price you can charge? Round to the nearest cent.
1 answer
·
1 vote:
$2 / 0.3 = $6.67Check:$6.67 * 0.3 = $2 :)
Missing: choices: $5.98 $6.00 c. $5.67 d. $6.30
Step-by-step explanation:
The lowest price you can charge is $6.30
How to determine the cost?We have:
Skillet brownie = $1.89Percentage of food cost = 30% or lowerThe lowest price you can charge is calculated as:
Lowest = Skillet brownie/Percentage
This gives
Lowest = $1.89/30%
Evaluate
Lowest = $6.30
Hence, the lowest price you can charge is $6.30
Read more about percentages at:
https://brainly.com/question/843074
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I need help with this question really badly please help.
Can someone help me solve this please, I'm stuck.
The expression (3a + 2b)^7 is a binomial expression;
The coefficient of the fourth term is 15120
How to determine the coefficient fourth term?The equation is given as:
(3a + 2b)^7
The above expression is a binomial expression;
Assume the expression is:
(x + y)^n
The equation of the expansion is:
[tex](x + y)^n = ^nC_r * x^{n-k} * y^k[/tex]
When the expression is expanded, the parameters of the fourth term are
n = 7
r = 4
x = 3a
y = 2b
So, we have:
(3a + 2b)^7 = 7C4 * (3a)^(7-4) * (2b)^4
Evaluate each factor
(3a + 2b)^7 = 35 * (3a)^3 * (2b)^4
Evaluate the powers
(3a + 2b)^7 = 35 * 27a^3 * 16b^4
Evaluate the product
(3a + 2b)^7 = 15120a^3b^4
The coefficient of the above expression is 15120
Hence, the coefficient of the fourth term is 15120
Read more about binomial expressions at:
https://brainly.com/question/13602562
PLEASE HELP ME
( I WILL MARK BRAINLIEST )
Explain how you would add 38+45
Answer:
83
Step-by-step explanation:
first add whatever is in the 1's place so for 38, 8 is in the 1's place and for 45, 5 is in the 1's place
so first it will be 8+5 which is 13 so you are going to carry the 1 over to the tens place so now it will be 30 + 40 + 10 and that equals 80 so you add 80 and 3 which looks like 80+3 and that equals 83
How to illistrate 1/3×1/2
Answer:
=1/6
Step-by-step explanation:
thats the answer
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pleassseee
what is the area of the figure?
Answer:
182 m
Step-by-step explanation:
The shape is a trapezoid. The area of the trapezoid formula is [tex]\frac{a + b}{2}h[/tex].
The two bases (AKA a and b) are 8 + 18.
The height is 14.
[tex]\frac{18+8}{2} 14[/tex], Add 18 + 8
[tex]\frac{26}{2}14[/tex], Divide 26 by 2
[tex]13 *14[/tex], 182
Help help help ASAP sap
Answer:
132
Step-by-step explanation:
since they are 180 degrees subtract
Answer:
132
Step-by-step explanation:
since this is a 180 degree angle ABC will be
180-48
132
What does 5/x = 7/x+2 equal?
Solve by cross multiplying.
(5 over x and 7 over x+2)
Answer:
I have no idea ask 567 9922 mathe teacher
Hey there!
[tex] \rm{\frac{5}{x} = \frac{7}{x + 2} }[/tex]
Solve:--
[tex] \sf\rightarrow \: (7)(x) = (5)(x + 2)[/tex]
[tex] \sf\rightarrow \: 7x = 5(x + 2)[/tex]
[tex] \sf\rightarrow \: 7x = 5x + 10[/tex]
[tex] \sf\rightarrow \: 7x - 5x= 5x + 10 - 5x[/tex]
[tex] \sf\rightarrow \: 2x= 10 [/tex]
[tex] \sf\rightarrow \: \frac{ 2x}{2}= \frac{10 }{2}[/tex]
[tex] \sf\rightarrow \: x= 5[/tex]
~Done~
Hey ! Can anyone help me solve these problems please. Thank you !
Please help me understand the problem
Answer:
y = 60 :)
Step-by-step explanation:
Triangle angle total measure: 180
We need to add upp the angles we know and subtract from the total 180, so we can figure out y.
60 + 60 + y = 180
120 + y = 180
180 - 120 = 60
y = 60
Now you know how to solve this type of problem!
Have a great day!!
Please rate and mark brainliest!!
Answer:
The value of y should be 60
Step-by-step explanation:
Tell me if its not right
solve for x ~
[tex]x {}^{2} - 5x + 6 = 0[/tex]
thankyou ~
[tex]\boxed{\bold{x = 2, 3}}[/tex]
Stepwise Solving:
[tex]\rightarrow \sf x^2-5x + 6 = 0[/tex]
[tex]\sf use \ the \ formula : x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ \ when \ ax^2 + bx + c = 0[/tex]
Identify the coefficients:
a = 1b = -5c = 6Solve for x:
[tex]\dashrightarrow \ \sf x=\dfrac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4 \ x \ 1 \ x \ 6}}{2 \ x \ 1}[/tex]
[tex]\dashrightarrow \ \sf x=\dfrac{\left5\right\pm \sqrt{\left25-24}}{2}[/tex]
[tex]\dashrightarrow \ \sf x=\dfrac{\left5\right\pm \sqrt{1}}{2}[/tex]
[tex]\dashrightarrow \ \sf x=\dfrac{\left5\right\pm1}{2}[/tex]
[tex]\dashrightarrow \ \sf x=\dfrac{\left5\right+ 1}{2} \ , \dfrac{\left5\right- 1}{2}[/tex]
[tex]\dashrightarrow \ \sf x=\dfrac{6}{2} \ , \ \dfrac{4}{2}[/tex]
[tex]\dashrightarrow \ \sf x= 3, \ 2[/tex]