Answer:
[tex]log_{2\sqrt 2} X = \frac{1}{3}k[/tex]
Step-by-step explanation:
Given
Let the number be X
From the first statement, we have:
[tex]log_{\sqrt 2} X = k[/tex]
Required
Find [tex]log_{2\sqrt 2} X[/tex]
[tex]log_{\sqrt 2} X = k[/tex]
using the following law of logarithm
[tex]log_ab = n, b=a^n[/tex]
So:
[tex]log_{\sqrt 2} X = k[/tex]
[tex]X = \sqrt{2}^k[/tex]
Substitute: [tex]X = \sqrt{2}^k[/tex] in [tex]log_{2\sqrt 2} X[/tex]
[tex]log_{2\sqrt 2} X = log_{2\sqrt 2} ( \sqrt{2}^k)[/tex]
[tex]log_{2\sqrt 2} X = klog_{2\sqrt 2} \sqrt{2}[/tex]
Apply the following law:
[tex]log_ab = \frac{log\ b}{log\ a}[/tex]
[tex]log_{2\sqrt 2} X = k\frac{log\ \sqrt 2}{log\ {2\sqrt 2}}[/tex]
Express the square roots as power
[tex]log_{2\sqrt 2} X = k\frac{log\ 2^\frac{1}{2}}{log\ {2 * 2^\frac{1}{2}}}[/tex]
[tex]log_{2\sqrt 2} X = k\frac{log\ 2^\frac{1}{2}}{log\ {2^\frac{3}{2}}}[/tex]
using the following law of logarithm
[tex]log_ab = n, b=a^n[/tex]
[tex]log_{2\sqrt 2} X = k\frac{\frac{1}{2}log\ 2}{\frac{3}{2}log\ 2}}[/tex]
[tex]log_{2\sqrt 2} X = k\frac{\frac{1}{2}}{\frac{3}{2}}}[/tex]
Rewrite as:
[tex]log_{2\sqrt 2} X = k * \frac{1}{2} \div\frac{3}{2}[/tex]
[tex]log_{2\sqrt 2} X = k * \frac{1}{2} *\frac{2}{3}[/tex]
[tex]log_{2\sqrt 2} X = k * \frac{1}{1} *\frac{1}{3}[/tex]
[tex]log_{2\sqrt 2} X = \frac{1}{3}k[/tex]
Which type of graph uses images to represent data?
line graph
bar graph
pictograph
pie chart
Answer:
pictograph is a type of graph that use images to represent data or a given information and it is also called picture graph
a recipe calls for 3/4 of a cup of flour to make 5/8 of a pond of bread dough . how many cups of flour are needed to make 1 pound of douugh
A cell phone plan charges $19.90 a month, plus $0.05 per text message
Create & solve an inequality that represents the number of texts, t, that can be
sent while still keeping the monthly bill under $25?
Answer:
[tex]19.9+0.05t<25[/tex]
Less than 102 text messages.
Step-by-step explanation:
Monthly charge of cell phone = $19.90
Cost of one text message = $0.05
Let number of text messages be [tex]t[/tex]
The monthly bill should be less than $25. So,
[tex]19.9+0.05t<25[/tex]
The required inequality is [tex]19.9+0.05t<25[/tex]
[tex]19.9+0.05t<25\\\Rightarrow 0.05t<25-19.9\\\Rightarrow t<\dfrac{5.1}{0.05}\\\Rightarrow t<102[/tex]
So, the number of text messages that can be sent while keeping the bill under $25 is less than 102.
Write each percentage as a fraction in simplest form.
1. 50% 2. 99% 3. 15%
4. 200%
Answer:
1. 1/2
2. 99/100
3. 3/20
4. 2
A lab currently has 70 mg of radioactive material that decays at 3.5% per year. Federal regulation for the substance says that the material must be safely stored until it reaches its half-life, at which time the material can be disposed.
How many years will the lab have to safely
store the material before disposal?
Answer:
The lab will have to wait 19.45 yers to safely store the material before disposal.
Step-by-step explanation:
Exponential equation for substance decay:
A exponential equation for the amount of a substance after t years is given by:
[tex]A(t) = A(0)(1-r)^{t}[/tex]
In which A(0) is the initial amount and r is the decay rate, as a decimal.
Decays at 3.5% per year.
This means that [tex]r = 0.035[/tex]
So
[tex]A(t) = A(0)(1-r)^{t}[/tex]
[tex]A(t) = A(0)(0.965)^{t}[/tex]
How many years will the lab have to safely store the material before disposal?
It needs to reach half-life, that is, t for which A(t) = 0.5A(0). So
[tex]A(t) = A(0)(0.965)^{t}[/tex]
[tex]0.5A(0) = A(0)(0.965)^{t}[/tex]
[tex](0.965)^t = 0.5[/tex]
[tex]\log{(0.965)^t} = \log{0.5}[/tex]
[tex]t\log{0.965} = \log{0.5}[/tex]
[tex]t = \frac{\log{0.5}}{\log{0.965}}[/tex]
[tex]t = 19.45[/tex]
The lab will have to wait 19.45 yers to safely store the material before disposal.
Write an equation in slope-intercept form for the line with slope -3/2 and y -intercept 2 .
Answer:
Y= -3/2x + 2
If the y-intercept was negative it would be y= -3/2-2
PLEASE I NEED HELP I GOT A PUPPY AND IM EXHAUSTED HE DOESNT SLEEP AT NIGHT
Answer:
False
Step-by-step explanation:
Plug 16 into the function as x
16+12=28
4≠28
Select the correct answer. The hiking club is getting new T-shirts and will vote to choose the design. Marianna and Chloe are each designing a T-shirt using a computer program. Marianna’s design features an image of the mountains, with the peaks and valleys modeled by function m, where x is the horizontal distance, in inches, from the left edge of the design. Chloe’s design also features an image of the mountains, with the peaks and valleys modeled by function c, where x is the horizontal distance, in inches, from the left edge of the design. Which T-shirt design has the lowest valley floor over the first 6 inches of the design? Both designs have valley floors at the same height over the first 6 inches of the design. Marianna’s design doesn’t have a valley floor over the first 6 inches of the design. Chloe’s design has the lowest valley floor over the first 6 inches of the design. Marianna’s design has the lowest valley floor over the first 6 inches of the design.
Answer:
Step-by-step explanation:
What are the choices
Answer:
mariannas design has the lowest valley floor over the first 6 inches of the design
Step-by-step explanation:
correct.
ann and bill share an amount of money in ratio 7:n. Ann gets 28%of the money. workout value of n
Lila collected the honey from 3 of her beehives. From the first hive she collected 2/3 gallon of honey. The last two hives yielded 1/4 gallon each.
How many GALLONS of honey did Lila collect in all?
Answer: 1 1/6
Step-by-step explanation: i dont know if this is right, but hope it helps
Answer:
1 1/6
Step-by-step explanation:
Given function:
find the three beehives honey Lila total collected2/3,1/4,1/4Combine the terms:
[tex]\frac{2}{3}+\frac{1}{4}+\frac{1}{4}=\frac{2}{3}+\frac{2}{4}[/tex]Simplfly the fraction terms:
[tex]\frac{2}{3}[/tex]·[tex]4=\frac{8}{12}[/tex] [tex]\frac{2}{4}[/tex]·[tex]3=\frac{6}{12}[/tex]Combine the terms:
[tex]\frac{8}{12}+\frac{6}{12}=\frac{14}{12}[/tex]Simplifly the final value:
[tex]\frac{14}{12}=1\frac{2}{12}[/tex] [tex]1\frac{2}{12}=1\frac{1}{6}[/tex]Therefore, the three beehives gives a total of 1 1/6 honey..
PLEASE HELP I WILL MARK BRAINLIST!!
14: [tex]\frac{1}{2} = \frac{8}{1}[/tex] [tex]\frac{x}{y} = \frac{56}{1}[/tex]
56/8 = 7 so multiply 1/2 by 7/1 to get the unidentified fraction "x/y"
1/2 · 7/1 = 7/2 or 3 1/2
15. [tex]\frac{2}{5} = \frac{x}{100}[/tex]
to get from 100 to 5, you would divide by 20, so to solve for x, multiply 2 by 20, to get a product of 40.
40/100 = 40% or D
16. [tex]\frac{3}{5} = \frac{12}{x}[/tex]
A
Please help 30 points pls
Answer:
4.75b; 8
Step-by-step explanation:
Area of triangle: height ÷ 2 × base
38 = 9.5 ÷ 2 × b
= 4.75 × b
38 = 4.75b
b = 38 ÷ 4.75
b = 8
Answer:
4.75 & 8
Step-by-step explanation:
Hope this helps
Convert 5.5 feet to inches. There are 12 inches in 1 feet.
Answer:
GIVE BRAINLIEST PLZ
Answer:66
Step-by-step explanation:
5.5* 12=66
There you go
find the distance between the two points
(1, 2), (-3, 5)
Answer:
13
Step-by-step explanation:
if you cannot find the awnser next time try mathaway it gives you the awnser and tells you an explanation.
Subtract the polynomials:
(1 Point)
f(x) = 10x4 + 2x² +1; 8 (x) = 3x4 + 3x + 11
O f (x) – 8(x) = 7x4 + 2x2 – 3x – 10
O f(x) – 8 (x) = 7x4 + 2x2 – 3x + 12
O f (x) – 8(x) = 7x4 + 2x2 + 3x + 12
O f(x) – 8(x) = 7x4 + 2x2 + 3x - 10
Answer: thats the answer
Step-by-step explanation:
Your boss has given you two options for salary increase. Your current salary is $45,000 per year.
Option 1: A raise of $2000 per year (linear growth).
Option 2: A yearly 4% raise (exponential growth).
a) Write an explicit equation for both options.
b) Fill in the table below,
Answer:
Step-by-step explanation:
There is no table but I will do the equations
Option 145000+2000t
let "t" represent the number of years
Option 245000*1.04t
let "t" represent the number of years
Find the surface area
Will give brainliest to first answer!!!!
how many roots does y= x^5- 4x^2+ 3x
A.3
B.4
C.5
D.6
(x^2 is the power to)
Answer: 4
Step-by-step explanation:
We can write the equation as
[tex]x(x-1)^{2}(x^{2}+2x+3)=0\\\\x=0, 1, -1 \pm i\sqrt{2}[/tex]
Therefore, there are 4 distinct roots.
What is the area of this face? 12ft 6ft 6ft 6ft
Answer:
I don't know. I think I need the picture that is associated with it.
Step-by-step explanation:
If you are looking for an i-Ready answer, It is 180 ft squared
What is 0.5 (0.1)(1/2)
Answer:
0.025
Step-by-step explanation:
a patients dose of medication increased from 100mg to 150mg. What is the percent increase in medication?
Answer:
The answer is 50% increase. Hope this helped!
Step-by-step explanation:
Consider the following graph.
The x y coordinate plane is given. The curve begins at (0, 5) goes down and right becoming less steep, changes direction at (1, 2) goes up and right becoming more steep, goes through the approximate point (2, 3.1), goes up and right becoming less steep, changes directions at (3, 4), goes down and right becoming more steep, sharply changes direction at (4, 1), goes up and right becoming less steep passing through the approximate point (5, 4.2) and ends at (6, 6).
(a) Find the interval(s) on which f is increasing. (Enter your answer using interval notation.)
(b) Find the interval(s) on which f is decreasing. (Enter your answer using interval notation.)
(c) Find the open interval(s) on which f is concave upward. (Enter your answer using interval notation.)
(d) Find the interval(s) on which f is concave downward. (Enter your answer using interval notation.)
(e) Find the coordinates of the point(s) of inflection.
(x, y) = ( )
a)Function is increasing in intervals (1,3) and (4,6).
b)Function is decreasing in intervals (0,1) and (3,4).
c)Graph is concave upward in the interval (0,2) and (3,5).
d)Graph is concave downward in the interval (3,4).
e)Points of inflection are x=3 and x=5.
Let us make the graph of the given function. In the graph, We have connected points linearly, please consider it as a curve.
What is the point of inflection?The point of inflection or inflection point is a point in which the concavity of the function changes.
Therefore, From the attached graph, we can see that:
a)Function is increasing in intervals (1,3) and (4,6).
b)Function is decreasing in intervals (0,1) and (3,4).
c)Graph is concave upward in the interval (0,2) and (3,5).
d)Graph is concave downward in the interval (3,4).
e)Points of inflection are x=3 and x=5.
To get more about graphs visit:
https://brainly.com/question/1869945
Answer:
a.(1,3)U(4,6)
b.(0,1)U(3,4)
c.(0,2)
d.2,6
e. 2,3
Step-by-step explanation:
Looking at graph and finding intervals.
!!!!please helppppppp
9514 1404 393
Answer:
13/18
Step-by-step explanation:
5 of the 18 students have a cat, so 13 of them do not.
The probability that a student in the group does not have a cat is 13/18.
Real answer not a scam
Answer:
Area = 240 cm²
Step-by-step explanation:
Area of the shape = area of rectangle + area of triangle
= L*W + ½*bh
L = 18 m
W = 10 m
b = 10 m
h = 30 - 18 = 12 m
Plug in the values
Area of the shape = 18*10 + ½*10*12
= 180 + 60
= 240 cm²
How can postulates and theorems relating to similar
and congruent triangles be used to write a proof?
A child gets 1 egg on their
1st birthday. They get 2 on
their 2nd, 3 on their 3rd etc.
How many years will it be
before they have received 91
eggs in total?
Answer:91 years
Step-by-step explanation:
what is the answer of
reciprocal of 1/7
Answer:
7/1
Step-by-step explanation:
A reciprocal means you flip the numerator and the denominator (the top number and the bottom number) so In this case the reciprocal for 1/7 s 7/1.
Hope I could help!
How do you graph x+6y=0
Answer:
We need to put this equation into either form of a line, pererably, slope intercept form!
Step-by-step explanation:
To do this, out goal is to get y alone.
1. We subtract x on both sides.
2 We divide 6 on both sides.
3. Our answer is y= -x/6 ( negative x divided by 6)
4. The y-intecept value is when x is equal to zero, so plug in 0 for x and solve for y.
5. The y intercept is (0,0)
6. From (0,0) point, you go down -1 and move 1 to the right each time!
The graph will be a line with a slope of -1/6 that passes through the points (0,0), (6,-1), and (-6,1).
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
To graph this equation, start by rearranging it to solve for y.
y = -x/6
Next, plot a few points to fill in the graph.
when x is 0,
y is 0.
When x is 6,
y is -1, and
when x is -6, y is 1.
Finally, connect the plotted points with a straight line.
The final graph will be a line with a slope of -1/6 that passes through the points (0,0), (6,-1), and (-6,1).
Hence, graph will be a line with a slope of -1/6 that passes through the points (0,0), (6,-1), and (-6,1).
To learn more on Graph click:
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In the diagram below, O is circumscribed about quadrilateral ABCD. What is
the value of ?
Answer:
21
Step-by-step explanation:
Trust
The value of x is 21 because, in a quadrilateral, the sum of the opposite angles is equal to 180 degrees. option (A) is correct.
What is quadrilateral?
It is defined as the four-sided polygon in geometry having four edges and four corners and two pairs of congruent sides.
We have:
In the diagram below, O is circumscribed about quadrilateral ABCD.
In a quadrilateral, the sum of the opposite angles is equal to 180 degree
5x + 75 = 180
5x = 105
x = 21
Thus, the value of x is 21 because, in a quadrilateral, the sum of the opposite angles is equal to 180 degrees. option (A) is correct.
Learn more about the quadrilateral here:
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what is -1/8 - 6 7/8
Answer:
-7
Step-by-step explanation:
I am sorry if I got it wrong.