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]
x^4 − 3x^2 − 90 x= -3
Answer:
-36
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
x⁴ - 3x² - 90
x = -3
Step 2: Evaluate
Substitute in x: (-3)⁴ - 3(-3)² - 90Exponents: 81 - 3(9) - 90Multiply: 81 - 27 - 90Subtract: 54 - 90Subtract: -36The Spanish Club has 78 members, 42 girls and 36 boys. What is the ratio of
girls to boys in the Spanish Club?
A. 6:7
B. 8:7
O C. 7:6
Answer:
C. 7:6
Step-by-step explanation:
Take your ratio 42 (G): 36 (B) and divide both numbers by six. This comes out to 7 (G): 6 (B) which is the simplest form of this ratio.
Kara’s bedroom is in the shape of a rectangle. The perimeter of her room is 50 feet. The width of her room is 12 feet. What is the length of Kara’s room?
A. 13 feet
B. 25 feet
C. 26 feet
D. 38 feet
Answer:
13 ft
Step-by-step explanation:
To find the perimeter of a rectangle you have to add the four sides of the rectangle, you have two sides and know the perimeter, this will help you find the length of her room. 12 ft is the width, add 12+12 and you have 24. The perimeter is 50 so subtract 24 from 50 and you have 26 that is the length times two, so divide 26 by 2. Now you have 13, so the length of her room is 13 feet.
Hope you understand now! :)
A factory worker finds 26 products are defective out of a random sample of 400
products. Based on the results, about how many of the 56,000 products produced this
month can be expected to be defective?
Answer: 36,400
Step-by-step explanation:
Answer:
Step-by-step explanation:
36,400
Solve 2x²-x-6=0 by factorisation
Answer:
x = 2, x = -3/2
Step-by-step explanation:
Factors to be (x-2)(2x+3) = 0
x =2, x = -3/2
Answer:
Step-by-step explanation:
2x²-x-6=0
2x²-(4-3)x-6=0
2x²-4x+3x-6=0
2x(x-2)+3(x-2)=0
(x-2)(2x+3)=0
Of 75is90 =120 true or false
Answer:
False
Step-by-step explanation:
kiaras monthly rent increased from $425 to $480 whats the percent increase in her rent rounded to the nearest tenth of a percent
Answer:
1.1
Step-by-step explanation:
480/425=1.129
There was a 1.129 rent increase but you round to the nearest tenth so 1.1
in the graph above, what's the distance between (-1, -4) and (-1, 5)
Answer:
9
Step-by-step explanation:
5-(-4) =
5 + 4 = 9
Hope that helps!9
Help please. It’s base times height.
Answer:
Pretty sure it's 99.
Answer:
11×9=99
99in³ is the area of the parallelogram
can you help me? I am stuck
Answer:
27
Step-by-step explanation:
what is 111/4?
27.75
But they asked exact, or no remainders. So the whole number is 27
The greatest number of stalls he needs is 28.
Since it says "the greatest, I rounded 27.75 up, getting 28.
1. Albert Einstein is driving down a country road at the speed of light. Just kidding. He's
actually going an average of 70 miles an hour. He started driving at 3 PM exactly and
arrived at his destination at 5:27 PM. If we need to calculate the distance from his starting
point to his destination, our answer will be in which units?
A. Miles
B. Hours
C. Miles per hour
D. Kilometers
Answer:
C. Miles per hour
Step-by-step explanation:
Answer:
c. miles per hour
Step-by-step explanation:
because he was driving in miles an hour
Harry is reviewing his finances. He compiled a list of expenses and income. Which bar chart that accurately represents Harry's situation.
Expenses
Income
rent
$1,150.00 paycheck March 2 $1,068.16
insurance payment $187.00 paycheck March 16 $1,068.16
groceries
$423.62 paycheck March 30 $1,068.15
utilities
$124.18
cell phone
$84.33
car loan payment
$365.36
Harry's Finances
Harry's Finances
5,000
3,000
2,500
4,000
2,000
3,000
1,500
2,000
1,000
1,000
500
0
0
Expenses Income
Harry's Finances
Expenses Income
Harry's Finances
O
Answer:
The answer is the (Expenses is between 2,000-2,500) and the (Income is over 3,000)
Step-by-step explanation:
I just took the test i got it right
The bar chart that accurately represents Harry's situation is the one that shows his (Expenses that is between 2,000-2,500) and his (Income that is over 3,000).
What is a A bar chart?This is also known as a bar graph. It is seen as a chart or graph that depicts a kind of categorical data via the use of rectangular bars that has heights or lengths which are known to be proportional to the values that they stand for.
Note that the bars are often plotted vertically or horizontally and as such, The bar chart that accurately represents Harry's situation is the one that shows his (Expenses that is between 2,000-2,500) and his (Income that is over 3,000).
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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 ME DUE IN 10 MIN
Answer:
108
Step-by-step explanation:
9=height
12=wideness
9times12=108
PLEASE HURRY⚠️⚠️
How do you find the length of an unknown leg in a right triangle?
Answer:
by measuring in feet
Step-by-step explanation:
its the easiest way to find what your looking for
Answer:
You can find the length of an unknown leg using the Pythagorean theorem
Step-by-step explanation:
[tex]a^2+b^2=c^2[/tex]
or
[tex]c^2-a^2=b^2[/tex]
or
[tex]c^2-b^2=a^2[/tex]
note c = hypotenuse and b and a = legs
Find the sum:(12x-14)+(2x+3)
Answer:
x= -0.785
Step-by-step explanation:
12x plus 2x equals 14x
negative 14 plus 3 equals negative 11
negative 11 divided by 14 equals x
an airplane cruises 1 kilometer in 1/12 of a minute. what is its cruising speed?
Answer:
An airplane cruises 1 kilometer in 1/12 of a minute. What is its cruising speed?200
A party rental company has chairs and tables for rent. the total cost to rent 5 chairs and 3 tables is $ 27. The total cost to rent 2 chairs and 12 tables is $81.
cost to rent each chair=
cost to rent each table=
Answer:
14 and 16
Step-by-step explanation:
nryjettutwi523iwtietiitqy25
calculate the number of terms in the following arithmetic sequence. 6;1;-4;-9....... -239
Answer:
50
Step-by-step explanation:
Given
first term (a) = 6
Common Difference (d) = 1 - 6 = - 5
Last term (tn )= - 239
Number of terms (n) = ?
We know
Tn = a + ( n - 1 ) d
- 239 = 6 + (n - 1) (-5)
- 239 = 6 - 5n + 5
- 239 = 11 - 5n
5n = 11 + 239
5n = 250
n = 250 / 5
n = 50
The number of terms is 50.
y o u s h a l l g e t 50 p o i n t s
i f y o u a n s w e r t h i s
Answer: 1.) 10
Step-by-step explanation:
-4 + 4 = 0
0 + 6 = 6
6 + 4 = 10
Answer:
3. Z=10 4. B=60
Step-by-step explanation:
For number 3 we work backwards. So, 6 - (-4) would equal 10. To check this -4 + 10 = 6. For number 4, we also work backwards, so 12 x 5 = 60. To check this 60/5 = 12. So z = 10 B = 60.
Which condition would prove ΔDEF ∼ ΔJKL?
Step-by-step explanation:
DE : JK
= 21 : 7
= 1 : 3
#CMIIWThe condition that proves congruent of two given triangles ΔDEF ∼ ΔJKL would be option A; DE : JK.
What is the congruent triangle?Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.
we have given proof two triangles congruent by the postulate of SSS.
Since two corresponding sides of these triangles are congruent so additional third side should also be congruent to prove both the triangles congruent.
AC ≅ DF will complete the SSS property to prove both the triangles are congruent.
DE : JK
= 21 : 7
= 3 : 1
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Is it a function yes or no
Answer:
no
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
2+262+77+8+9+9+8+6+5+5+4+5+56+6+6+6+8+8+65+6+6+8+8
Answer:
583
Step-by-step explanation:
HELPPP I MAKE BRAINLIESTT
A seamstress charges a $5 fee per garment, plus $15 for each hour of work that the garment requires. The graph below shows the cost of having a single garment fixed by the seamstress, according to the number of hours of work that are needed.
Which linear function models the data?
A. c(t) = 5t
B. c(t) = 15t
C. c(t) = 5 + 15t
D. c(t) = 15 + 5t
Answer:
C. c(t) = 5 + 15t
Step-by-step explanation:
Well because the initial fee is $5, the answer must have the value of 5 without a variable next to it because this is the y-intercept.
(Only the slope will have the t next to it.)
Because $15 is charged EACH HOUR this would be the slope because there is a constant increase
Therefore c(t) = 5 + 15t
Answer:
C. c(t) = 5 + 15t
Step-by-step explanation:
She charges $15 per hour, so each hour (represented by "t") she earns 15 dollars. She also charges a $5 fee per germent. So she would get $5 plus 15 times however many hours she worked. So your answer would be c(t) = 5 + 15t.
I need help for that^^
Answer:
1<x<3
x < -4
Hopefully that helps :)
PLS HELP ASAP AAA TYSMM
The coordinates of the vertices of a triangle are A(1,2), B(4,5), and C(4,2). Find triangle A’B’C’ by translating triangle ABC 2 units to the right and 3 units down. Write: (1) the algebraic rule that describes the transformations and (2) the coordinates of A’B’C’.
Answer:
Parallelogram ABCD was translated to parallelogram A'B'C'D'. ... When ΔRST is translated 4 units down, what is the coordinate of T'? ... C. 7 units left and 5 units down. B. 7 units right and 5 units up. D. ... If the triangle DOG with coordinates (2, 2), (2, 10), (8, 6) is translated six units left and three units.
Step-by-step explanation:
Father shared $90 among his three children. Liam, Darreon and Jessie. Jessie gets $10
more than Darreon who gets $10 more than Liam. How much did Jessie and Liam
get
altogether
3. 15 is what percent of 75?.
Show your work
Please hurry this is 100% of my grade and I have an F in math please
Answer:
20%
Step-by-step explanation:
75 divided by 5 equals 15
Simple form:
15+15+15+15+15=75 There are 5 15's.
I hope this helps and your grade gets better. :)
in what category does sugar, brown sugar, butter, eggs, vanilla, flour , unsweetened coca power , baking soda , salt & chocolate chips ? help please i’ll give extra points
Write and solve a system of equations to determine how many tickets were sold before and at the music festival. PLEASE HELPPP
b = number of tickets sold before
a = number of tickets sold after
cost of a ticket = number of tickets times cost per ticket
before cost = 39.95b
after cost = 54.95a
total cost = 925000
39.95b + 54.95a = 925000
total number tickets = 20000
b + a = 20000
we have
39.95b + 54.95a = 925000
b + a = 20000
multiply second equation by -39.95 and add to first equation
39.95b + 54.95a = 925000
-39.95b-39.95a = -799000 +
0b+15a = 126000
15a = 126000
divide bot sides by 15
a = 8400
sub back
b + a = 20000
b+8400 = 20000
minus 8400 both sides
b = 11600
11,600 tickets sold before
8400 tickets sold after