Step-by-step explanation:
the rules of logarithm.
log(a×b) = log(a) + log(b)
log(a^b) = b×log(a)
2×log(x) = log(16) + log(4)
now, using the above knowledge :
log(x²) = log(16×4)
=>
x² = 16×4 = 64
x = ±8
and since a logarithm of a negative number is undefined the only plausible solution is
x = 8
Does each pair of expressions form an equation when joined with an equals sign?
Select Yes or No for each pair of expressions.
Expressions
(1/3) ² +1 and 2 - 8/9
(1+ 1/5)^2 and 2
16/25
Equations are expressions with equal values
(1/3) ² +1 and 2 - 8/9 form an equation when joined together with an equals sign(1+ 1/5)^2 and 2 16/25 do not form an equation when joined together with an equals sign(a) (1/3) ² +1 and 2 - 8/9
Rewrite as:
[tex]\mathbf{(1/3)\² +1 = 2 - 8/9}[/tex]
Evaluate the exponent
[tex]\mathbf{1/9 +1 = 2 - 8/9}[/tex]
Take LCM
[tex]\mathbf{1\frac 19 = \frac{18- 8}{9}}[/tex]
[tex]\mathbf{1\frac 19 = \frac{10}{9}}[/tex]
Simplify
[tex]\mathbf{1\frac 19 = 1\frac{1}{9}}[/tex]
Hence, (1/3) ² +1 and 2 - 8/9 form an equation when joined together with an equals sign
(b) (1+ 1/5)^2 and 2 16/25
Rewrite as:
[tex]\mathbf{(1+ 1/5)^2 =2\frac{ 16}{25}}[/tex]
Take LCM
[tex]\mathbf{(\frac{5 + 1}{5})^2 =2\frac{ 16}{25}}[/tex]
[tex]\mathbf{(\frac{6}{5})^2 =2\frac{ 16}{25}}[/tex]
[tex]\mathbf{\frac{36}{25} =2\frac{ 16}{25}}[/tex]
Rewrite as:
[tex]\mathbf{1\frac{9}{25} =2\frac{ 16}{25}}[/tex]
Hence, (1+ 1/5)^2 and 2 16/25 do not form an equation when joined together with an equals sign
Read more about equations at:
https://brainly.com/question/13636476
Answer:
(1/3)^2 + 1 and 2 - 8/9 : Yes
(1 + 1/5)^2 and 2 - 16/25 : No
Need help with this geometry question
Answer:
The first option:yellow shirt, white trouseryellow shirt, black trousergreen shirt, white trousergreen shirt, black trouserStep-by-step explanation:
To find the possibilities, you would see that you would have two yellow shirts and two green shirts with different trousers, so you can eliminate the bottom two. And because there will be two of each shirt with defferent trousers, it will be the same for trousers: two of each trouser will be in the possibilities. The only one that fits this description, is the first one.
yellow shirt, white trouser
yellow shirt, black trouser
green shirt, white trouser
green shirt, black trouser
Evaluate 4c - 3
When c = -2
Answer:
-11
Step-by-step explanation:
Answer: -5
Step-by-step explanation:
4*-2=-8
-8 -3=-5
Quiz
2² =
4² =
use the method, no calculation
Step-by-step explanation:
2²
= 2 × 2
= 4
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4²
= 4 × 4
= 16
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I Hope This HelpSegments KN and LM are transversals. What is true about the measure of angle N?
Answer:
It is congruent to M
Step-by-step explanation:
39. The area of a triangle A varies jointly as b and h. If A = 225 in- when b = 18 in. and h = 25
in., find A when b = 35 in. and h = 40 in.
37
Answer: B
Step-by-step explanation:
Answer:
700 in^2
Step-by-step explanation:
If A = 225 in- when b = 18 in. and h = 25
225 = 18 * 25 / 2
a = 35 * 40 / 2
a = 700
y varies directly as x and x=20 when y=15. Find y when x=68
Name x1, x2, y1, and y2. Then, find the distance between the points.
Answer:
wwwwwwwwwwwwwwwwwwwwwwhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaatttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt what
Solve the given equations. PLEASE show your work. Choose if the equation has infinite many solutions or no solution. It can have a solution
-2(x + 4) + 9x = 4 - 7x
We are flying at 30 000 feet.
Our speed is 500 miles per hour.
Our total flight time will be 10 hours and 20 minutes.
Mark knows the distance from London to Cancun is 4944 miles. He asks his daughter to check the information given by the pilot. She knows this formula for speed.
s = dt
s = speed (miles per hour) d = distance (miles)
t = time (hours)
Evaluate the information given by the pilot.
Show calculations to support your answer.
Answer:
Step-by-step explanation:
500 mph with a flight time of 10 hours and 20 minutes [(20 min)*(1 h/60 min) = 0.333 hr]
Distance = Speed * Time
Time = 10.333 hours
Distance = (500 miles/hr)*(10.333 hrs) = 5166.5 miles
The pilot's numbers indicate a distance of 5167 miles, compared to Mark's number of 4944 miles. That is a 4.3% reduction from the pilot's numbers. Not too bad, so we might question 1) Mark's knowledge, or 2) the impact that the approach and landing speeds have of the total miles flow.
My preference would be to trust the pilot's data. I don't know where Mark got his math education.
The table gives the temperature (in °F) in five citiesſat 6 a.m. on the same day. Use the table to answer the questions.
City
Temperature
(°F)
Toronto
-16
Fairbanks
:-24
Dayton
43
San Antonio
74
Buffalo
-3
5
?
(a) By noon, the temperature in Buffalo had risen by 10 °F.
What was the temperature there
at noon
How much higher was the 6 am temperature in Toronto than in Fairbanks
Answer:
a) buffalo will be at 7
b) it will be -8
Step-by-step explanation:
a) because if u add - 3 + 10 it will equal 7
b) reason why is because if u substract -24 from - 16 it will be - 8
I took a test on the same thing thats why i kno it
√12 - 1 √3=?
is correct the answer is 1/√3
THANK YOU
Answer:
[tex]\huge\boxed{\text{Is inorrect. Correct answer is:}}\\\boxed{\dfrac{6-\sqrt3}{3}\neq\dfrac{1}{\sqrt3}}[/tex]
Step-by-step explanation:
[tex]\dfrac{\sqrt{12}-1}{\sqrt3}=\dfrac{\sqrt{12}}{\sqrt3}-\dfrac{1}{\sqrt3}=\sqrt{\dfrac{12}{3}}-\dfrac{1}{\sqrt3}=\sqrt4-\dfrac{1}{\sqrt3}\cdot\dfrac{\sqrt3}{\sqrt3}=2-\dfrac{\sqrt3}{3}\\\\=\dfrac{6}{3}-\dfrac{\sqrt3}{3}=\dfrac{6-\sqrt3}{3}\neq\dfrac{1}{\sqrt3}\\\\\dfrac{1}{\sqrt3}\cdot\dfrac{\sqrt3}{\sqrt3}=\dfrac{\sqrt3}{3}[/tex]
Which of these situations can be represented by this graph?
Answer:
Step-by-step explanation:
Pls Help! Worth 8 Points Will Give Brainlest
Answer:
D. x - 5
Step-by-step explanation:
The text said that Sienna's hight is LESS than her brothers hight and less = minus
Answer:D
Step-by-step explanation:hope i helped i love helping people like you. :)
Find one value of x for F(x)=-4
F(x) = -4 means y = -4. That means whatever the x is, the answer is going to be -4.
Kaylee needed to fold 586 paper notices for a fundraiser. The notices would be mailed in 22 days. Which expression gives the best estimate of the number of notices she must fold each day to meet her goal?
A.
500
÷
20
B.
500
÷
30
C.
600
÷
20
D.
600
÷
30
Answer: C
Step-by-step explanation: Round to the nearest 100
The temperature of a substance in an experiment changes by −8.7°F from 10 a.m. to 1 p.m. At 5 p.m., the temperature is 33.5°F. It is 2/3 of what the temperature was at 1 p.m. What was the temperature at 10 a.m. of the substance? Enter your answer as a decimal in the box.
PLS HELP
The temperature of the substance at 10am = 63.95°F
Let the temperature at 10 am be x
The temperature changes by −8.7°F from 10 a.m. to 1 p.m
The temperature at 1 pm = x - 8.7
At 5 p.m., the temperature is 33.5°F
The temperature at 5 pm = 33.5°F
The temperature at 5 pm is 2/3 of what the temperature was at 1 p.m
[tex]33.5 = \frac{2}{3} ( x-8.7 )[/tex]
Solve for x
3(33.5) = 2(x - 8.7)
110.5 = 2x - 17.4
2x = 110.5 + 17.4
2x = 127.9
x = 127.9/2
x = 63.95°F
The temperature of the substance at 10am = 63.95°F
Learn more here: https://brainly.com/question/25522357
Three business partners, Ren, Jaffary and Abel put money into a business in the ratio 2:3:4. From the profits they shared, Abel got 3400 dollars. How much did ren and Jaffary receive?
HELP GUYS PLS I HAVE 3 MIN TO GO
Answer:
Ren has 755.4
Jaffray has 1,133.1
Abel has 1,510.8
pls help its an image scroll down
Answer:
D. y = 3x + 9
Step-by-step explanation:
Use the point-slope formula to find the equation in slope-intercept form.
[tex]y-y_1=m(x-x_1)\\\\y-33=3(x-8)\\\\y-33=3x-24\\\\y=3x+9[/tex]
Which relation has a domain of (2, 4) and a rang of (2, 8)
A (2, 4) (2,8)
B (2, 2) (2,8) (4,2)
C{(2,4)(8,2)(8,4)}
D{(2,2)(2,4)(4,2)(8,8)}
How many Solutions does 6 + x/5 = x/5 - 5 - 3x/10 have?
9514 1404 393
Answer:
1 solution (x = -36 2/3)
Step-by-step explanation:
6 + x/5 = x/5 - 5 - 3x/10 . . . . . . . given
60 +2x = 2x -50 -3x . . . . . . . . . multiply by 10
3x = -110 . . . . . . . . . . . . . . . . add x-60 to both sides
x = -110/3 = -36 2/3 . . . . . .divide by the coefficient of x
There is one solution to the equation.
_____
Additional comment
The coefficient of x on the left side of the equation is not equal to the coefficient of x on the right side. When that is the case, the equation will have one solution.
When the coefficients are equal, there will be no solutions if the constants are different, and there will be infinite solutions if the constants are the same.
share £650 in the ratio of 4:9
Answer:
200:450 that would be the answer i believe
Henry steps onto an elevator at the first floor. He goes up to the 9th floor and then comes down 2 floors. He then goes up 4 floors and down 6 floors. What floor is Henry on?
Answer:
He is on the 5th floor
Step-by-step explanation:
9 - 2 = 7
7 + 4 = 11
11 - 6 = 5
Answer:
he goes 1 +9=10
10-2=8
8+4=12
12-6=6
so he is ont the sixth floor
A driver travels 120 miles, stops, and then travels ¼ of the distance she has already driven. After stopping again, the driver travels ⅔ of the distance she has already traveled. Now, the entire distance she has driven is 55 miles more than 1 ⅔ of the remaining trip. How many miles does the driver still have to travel?
Answer:
75 miles
Step-by-step explanation:
We know that she has driven 120 miles before the first stop.
Then she drives for 1/4 of the the distance she has already driven (120 miles). One fourth of 120 is 30.
So now, she's driven for 120 + 30 miles, or 150 miles.
She drives for another 2/3 of the distance she's traveled (150 miles). Two thirds of 150 is 100.
So now, she's driven for 150 + 100 miles, or 250 miles.
What we need to find out now is how much of the trip has she traveled.
We know that the entire distance she has driven is 55 miles more than 1 ⅔ of the remaining trip. So, in other words, the distance she has traveled minus 55 is equal to 1 2/3 of the trip.
To put this in an equation:
250 - 55 = 1 2/3t
t = the whole trip
Now, we solve for t.
250 - 55 = 195
1 2/3 = 5/3
so, 195 = 5/3t
t = 325
We subtract what she has already driven to the total to get the remaining distance.
325 - 250 = 75
Solve each equation for the specified variable.
a. a-q=a+sx for x
b. kx-bf=fy/m for y
c. a-q=a+sx for q
d. kx-bf=fy/m for m
PLEASE HELP I WILL GIVE GREATEST ANSWER TO WHOEVER SOLVES ALL OF THEM THE BEST. THANK YOU SO MUCH
Answer:
a.
a - q = a + sx
a - a - q = a - a + sx
-q = sx
[tex]\frac{-q}{s} = \frac{sx}{s}[/tex]
x = [tex]\frac{-q}{s}[/tex]
b.
kx - bf = [tex]\frac{fy}{m}[/tex]
m(kx - bf) = m([tex]\frac{fy}{m}[/tex])
mkx - mbf = fy
[tex]\frac{mkx - mbf}{f}[/tex] = [tex]\frac{fy}{f}[/tex]
y = [tex]\frac{mkx - mbf}{f}[/tex]
y = [tex]\frac{mkx}{f}[/tex] - [tex]\frac{mbf}{f}[/tex]
y = [tex]\frac{mkx}{f}[/tex] - mb
c.
a - q = a + sx
a - a - q = a - a + sx
-q = sx
-q × (-1) = sx × (-1)
q = -sx
d.
kx - bf = [tex]\frac{fy}{m}[/tex]
m(kx - bf) = m([tex]\frac{fy}{m}[/tex])
m(kx - bf) = fy
[tex]\frac{m(kx - bf)}{kx - bf}[/tex] = [tex]\frac{fy}{kx - bf}[/tex]
m = [tex]\frac{fy}{kx - bf}[/tex]
change the following numbers to decimals and round to the nearest hundredth 3÷4 and ✔10
Answer:
0.75 and 10.00
Step-by-step explanation:
Explain what a graph for Jed’s test scores {61%, 65%, 73%, and 79%} would look like if it was not misleading. Make sure it is different than Jed’s graph – that some may say is misleading.
Answer:
61
^
^
^ 65 73
^ 79 ^ ^
^ ^ ^ ^
-----------------------------------------------------------------------------------------------------------------
Test 1 Test 2 Test 3 Test 4
Answer: the test doesn't explain the order it was taken or dates. So it can be misleading
Step-by-step explanation:
It takes 40 cents worth of meat to make 2 sandwiches. What is the cost of the meat for 20 sandwiches?
Make a Selection:
A. $2.00
B. $3.20
C. $1.60
D. $4.00
Answer:
D. 4.00
$4.00 will be your cost for meat for 20 sandwiches.
. Bobignment In what year was the LAWMA Established-
Evaluate. 2 (14–32 +1) 1:3.-
Answer:
432
Step-by-step explanation:
Answer:
27
Step-by-step explanation: