Answer:
$13.80
Step-by-step explanation:
23% of 60 = .23 x 60
Combine into a single logarithm.
3log(x+y)+2log(x-y)-log(x^2 +y^2)
Answer:
[tex]3\log _{10}\left(x+y\right)+2\log _{10}\left(x-y\right)-\log _{10}\left(x^2+y^2\right)=\log _{10}\left(\frac{\left(x+y\right)^3\left(x-y\right)^2}{x^2+y^2}\right)[/tex]
Step-by-step explanation:
Given the expression
[tex]3log\left(x+y\right)+2log\left(x-y\right)-log\left(x^2\:+y^2\right)[/tex]
solving to write into a single logarithm
[tex]3log\left(x+y\right)+2log\left(x-y\right)-log\left(x^2\:+y^2\right)[/tex]
[tex]\mathrm{Apply\:log\:rule}:\quad \:a\log _c\left(b\right)=\log _c\left(b^a\right)[/tex][tex]3\log _{10}\left(x+y\right)=\log _{10}\left(\left(x+y\right)^3\right)[/tex]
so
[tex]=\log _{10}\left(\left(x+y\right)^3\right)+2\log _{10}\left(x-y\right)-\log _{10}\left(x^2+y^2\right)[/tex]
[tex]\mathrm{Apply\:log\:rule}:\quad \:a\log _c\left(b\right)=\log _c\left(b^a\right)[/tex][tex]2\log _{10}\left(x-y\right)=\log _{10}\left(\left(x-y\right)^2\right)[/tex]
so
[tex]=\log _{10}\left(\left(x+y\right)^3\right)+\log _{10}\left(\left(x-y\right)^2\right)-\log _{10}\left(x^2+y^2\right)[/tex]
[tex]\mathrm{Apply\:log\:rule}:\quad \log _c\left(a\right)+\log _c\left(b\right)=\log _c\left(ab\right)[/tex][tex]\log _{10}\left(\left(x+y\right)^3\right)+\log _{10}\left(\left(x-y\right)^2\right)=\log _{10}\left(\left(x+y\right)^3\left(x-y\right)^2\right)[/tex]
so
[tex]=\log _{10}\left(\left(x+y\right)^3\left(x-y\right)^2\right)-\log _{10}\left(x^2+y^2\right)[/tex]
[tex]\mathrm{Apply\:log\:rule}:\quad \log _c\left(a\right)-\log _c\left(b\right)=\log _c\left(\frac{a}{b}\right)[/tex][tex]\log _{10}\left(\left(x+y\right)^3\left(x-y\right)^2\right)-\log _{10}\left(x^2+y^2\right)=\log _{10}\left(\frac{\left(x+y\right)^3\left(x-y\right)^2}{x^2+y^2}\right)[/tex]
[tex]=\log _{10}\left(\frac{\left(x+y\right)^3\left(x-y\right)^2}{x^2+y^2}\right)[/tex]
Thus,
[tex]3\log _{10}\left(x+y\right)+2\log _{10}\left(x-y\right)-\log _{10}\left(x^2+y^2\right)=\log _{10}\left(\frac{\left(x+y\right)^3\left(x-y\right)^2}{x^2+y^2}\right)[/tex]
Mark takes out a $238,000 mortgage for 30 years. Instead of paying his monthly payment of $1,220.09, he decided to pay $1,420.09. This leads to Mark paying off the entire mortgage in 22 years and 5 months. Mark calculates the percent of the total loan he pays back in interest with and without the extra payments. What is the difference between Mark's calculated percentages?
Answer:
24.04%
Step-by-step explanation:
Given that:
Mortgage = $238,000
Number of years = 30
Monthly payment without extra payment= $1220.09
Monthly payment with extra payment = $1420.09
Total amount paid :
Number of months * monthly payment
12 months = 1year
30 years = (30 * 12) = 360 months (without extra payment)
22 years 5 months = (22 * 12) + 5 = 269 months (with extra payment)
Amount paid without extra payment :
$1220.09 * 360 = $439232.4
Percentage of total loan paid as interest :
((439232.4 - 238000) / 238000) * 100%
= 0.8455142 = 84.55%
Amount paid with extra payment :
$1420.09 * 269 = 382004.21
Percentage of total loan paid as interest :
((382004.21 - 238000) / 238000) * 100%
= 0.6050597 = 60.51%
Difference between percentages:
84.55% - 60.51% = 24.04%
Jeyniel wrote the expression x^3/y^2. If x=4 and y=2; how much is the value of the expression? *
Answer:
The answer is 16
Step-by-step explanation:
X^3=64
Y^2=4
so 64 divided by 4 is 16
Answer:
16
Step-by-step explanation:
this might help you
Fred's art project involves a series of parallel stripes. If he starts by drawing the line 8x+2y=7, select all the equations that could represent lines that could also be drawn for his art project.
Options:
A. [tex]y-1 = 4(x + 8)[/tex]
B. [tex]y = -4x + 15[/tex]
C. [tex]16x + 4y = 9[/tex]
D. [tex]y=-4x[/tex]
E. [tex]4x + 2y = 3[/tex]
Answer:
B. [tex]y = -4x + 15[/tex]
C. [tex]16x + 4y = 9[/tex]
D. [tex]y=-4x[/tex]
Step-by-step explanation:
Given
[tex]8x + 2y = 7[/tex]
Required
Select all equations that could be used.
Equation that could be used in place of [tex]8x + 2y = 7[/tex] must have the same slope.
Calculating the slope of [tex]8x + 2y = 7[/tex]
Make y the subject
[tex]2y = 7 - 8x[/tex]
[tex]y = \frac{7}{2} - \frac{8x}{2}[/tex]
[tex]y = \frac{7}{2} - 4x[/tex]
[tex]y = - 4x + \frac{7}{2}[/tex]
Using y = mx + b
Where
[tex]m = slope[/tex]
The slope is -4
Option A.
[tex]y-1 = 4(x + 8)[/tex]
Open bracket
[tex]y - 1=4x + 32[/tex]
Collect Like Terms
[tex]y - 4x = 32 + 1[/tex]
[tex]y - 4x = 33[/tex]
Make y the subject
[tex]y = 4x + 33[/tex]
The slope of this line is 4;
Hence, it can not be used.
Option B.
[tex]y = -4x + 15[/tex]
The slope of this line is -4;
Hence, it can be used.
Option C.
[tex]16x + 4y = 9[/tex]
Solve for4y
[tex]4y=9 - 16x[/tex]
Solve for y
[tex]\frac{4y}{4} =\frac{9}{4} - \frac{16x}{4}[/tex]
[tex]y =\frac{9}{4} - 4x[/tex]
[tex]y = - 4x + \frac{9}{4}[/tex]
The slope of this line is -4;
Hence, it can be used.
D. [tex]y=-4x[/tex]
The slope of this line is -4;
Hence, it can be used.
E. [tex]4x + 2y = 3[/tex]
Solve for 2y
[tex]2y = 3 - 4x[/tex]
Solve for y
[tex]\frac{2y}{2} = \frac{3}{2} - \frac{4x}{2}[/tex]
[tex]y = \frac{3}{2} - 2x[/tex]
The slope of this line is -2;
Hence, it can not be used.
From the calculations above, equations B, C and D are equivalent
help pls im stuck thank u guys
Answer:
The answer is 36.
Step-by-step explanation:
*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^
First, divide 108 by 12.
The result is 9.
Now square root 9.
The result is 3.
Now, multiply 12 by 3.
The result is 36.
To check that this is the pattern, we multiply 36 by 3, and we indeed see that 3 times 36 is equal to 108.
*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^
#teamtrees #WAP (Water And Plant)
Select the points that are solutions to the system of inequalities. Select all
that apply.
A. (1,2)
B. (-10,10)
C. (-2,0)
D. (0,10)
Answer:
B and D
Step-by-step explanation:
Emma is making two different kinds of cookies for a cookie party she will be attending. She needs 2 and 2/3 cups of sugar for the first recipe and 1 and 1/4 cups of sugar for the second recipe. Emma thinks she will have enough sugar but she isn't quite sure. She knows that her full 2 pound bag of sugar says it contains 4 and 1/2 cups of sugar. Determine the exact difference between the amount of sugar Emma has and the amount of sugar she needs for the recipes.) Emma's mom brought home another 2 pound bag of sugar (4 and 1/2 cups) and wants to make fudge to take to work. Her mom will need 2 and 1/6 cups of sugar. Write a numerical expression that could be used to determine exactly how much sugar will be left over from the two bags of sugar after Emma bakes cookies and her mom makes fudge
Answer:
Step-by-step explanation:
Emma is making two different kinds of cookies for a cookie party she will be attending. She needs 2 and 2/3 cups of sugar for the first recipe and 1 and 1/4 cups of sugar for the second recipe. Emma thinks she will have enough sugar but she isn't quite sure. She knows that her full 2 pound bag of sugar says it contains 4 and 1/2 cups of sugar. Determine the exact difference between the amount of sugar Emma has and the amount of sugar she needs for the recipes.) Emma's mom brought home another 2 pound bag of sugar (4 and 1/2 cups) and wants to make fudge to take to work. Her mom will need 2 and 1/6 cups of sugar. Write a numerical expression that could be used to determine exactly how much sugar will be left over from the two bags of sugar after Emma bakes cookies and her mom makes fudge
Hello can you solve 2+2
Thx and bye
Answer:
4
Step-by-step explanation:
please answer!! will give brainliest
Answer:
third option
Step-by-step explanation:
Differentiate using the product rule
Given f(x). g(x) then the derivative is
f(x). g'(x) + g(x). f'(x) ← product rule
Given
[tex]\frac{d}{dx}[/tex](x² secx )
with f(x) = x² and g(x) = secx , then
f'(x) = 2x and g'(x) = secxtanx, thus
[tex]\frac{d}{dx}[/tex](x² secx)
= x². secxtanx + secx. 2x ← factor out xsecx from each term
= xsecx(xtanx + 2) → third option
CAN SOMEONE HELP ME PLSSSS !!!!!!
Answer:B
Step-by-step explanation:
Answer:
[tex]5 {g}^{2} - 11 {g}^{} + 8[/tex]
Step-by-step explanation:
[tex]this \: is \: your \: answer \: ie \: option \: b \\ hope \: it \: helps \\ need \: thanks \: and \: brainliest...[/tex]
1. Marcus needs to bike at least 80 miles this
week for his training. If he has already biked 25
miles this week, then how many miles should he
bike on each of the 5 remaining days this week?
Variable:
Inequality:
Solution:
Please help fast I will give brainliest! :)
He should ride 11 miles on each of the other 5 days. 11 times 5 equals 55 + 25 = 80.
a plane flies 480 miles with a 15 mph tailwind and then back 480 miles with a 15 mph headwind. if the plane completes the trip in 7.2 hours, how fast is the plane traveling against the wind and with the wind
Please help will give Brainliest, 5 stars and Thanks!
helpppppppppppppppppp
The 1st option is correct.
Answer:
m/15=-3
Step-by-step explanation:
When you see quotient it means to divide
is means equal
I hope this helps
Which line shows the graph of y = 4x - 5 reflected over the y-axis?
y = 4x + 5
y = 4x - 5
Y=2x-5
y = -2x + 5
Answer:
The line y = -4x - 5 shows the reflection over the y-axis.
From the attached graph, the blue line i.e. y = -4x-5 represents the reflection over the y-axis.
Step-by-step explanation:
When we reflect a line function over the y-axis, all we need is to negate the x-coordinate or value of 'x', while y-coordinate or y-value remains the same.
Given the function
y = 4x-5
replace x with -x
y = 4(-x) - 5
y = -4x - 5
Thus, the line y = -4x - 5 shows the reflection over the y-axis.
From the attached graph, the blue line i.e. y = -4x-5 represents the reflection over the y-axis.
From the graph, it is clear that that that x-coordinate of y = 4x-5 is negated.
Write an equation of the line that passes through (–2, 8) and (–4, –4).
PLEASE HEEEELP MEEE! PLEASE ACTUALLY PROVIDE AN EXPLANATION! BEST EXPLANATION AND ANSWER GETS BRAINLIEST! THANKS
Answer:
sorry bro
Step-by-step explanation:
Answer:
Y=6x+20
Step-by-step explanation:
Solve the system of equations by substitution. What is the solution for x? (1 point)
2x + y = 1
4x + 2y = −2
Answer:
No Solution
Step-by-step explanation:
2x + y = 1
y = 1 - 2x
4x + 2(1 - 2x) = -2
4x +2 - 4x = -2
2 = -2
The statement is false, therefore there is no solution.
What is the product?
4^3 4^-3
Answer:
Im pretty sure its 1
Step-by-step explanation:
If you meant 4^3*4^-3, then yeah, its 1
what does a decimal look like
Answer:
It could look like 3.2, 0.9, 22.64 it is a number that has a decimal point in it somewhere
Step-by-step explanation:
[tex] \ \sqrt{348} [/tex]
Answer:
explanation:
√348 =
18.6547581062
The radio station in North Pole, AK plays Christmas songs all day and night from Thanksgiving through Christmas. They play 12 per hour for 15 hours a day, and 8 songs per hour for the rest of the day. They like to have a mix of traditional and modern songs with a relationship of 9 traditional songs to every 5 modern songs. How many traditional songs and how many modern songs will they play in one day?
Answer:
Traditional = 162
Modern = 90
Step-by-step explanation:
Given that:
12 songs per hour for 15 hours
8 songs per hour for the rest of the day ; (24 - 15) = 9 hours ;
That is ; 8 songs per hour for 9 hours
Total number of songs played per day :
(12 * 15) + (8 * 9) = 252 songs
If songs are mixed using the ratio 9:5 (traditional : modern)
Traditional songs :
(9 * 252) / (9 + 5) = 162
Modern songs :
(5 * 252) / (9 + 5) = 90
Tom and Jason both collect marbles Tom has collected 510 marbles and Jason has collected 842 marbles. How many marbles do they on together..?Estimate the total number of marbles nearest to hundred
Answer:
They had 1,352 marbles all together, rounded to the nearest hundred, 1,400.
Step-by-step explanation:
All we have to do is add the number of marbles they collected.
510 + 842 = 1,352
1,352 rounded to the nearest hundred is 1,400.
Last weekend, Joshua's parents drove 810 miles in 9 hours when they came to visit him. What was their
constant speed?
Answer:
90mph
Step-by-step explanation:
Answer:
90 miles per hour
Step-by-step explanation:
810 / 9
Use the polygon on the coordinate plane to complete the statements. This polygon is a The length of side RV The length of side ST
Answer:
pentagon
is 14 units
cannot be determined
Step-by-step explanation:
Answer:
Step-by-step explanation:
Use the polygon on the coordinate plane to complete the statements. This polygon is a The length of - Brainly.com
yw thanks for the points have a nice day :}
HELPPPP!!!!!!
1) Consider the sequence:
7,4, 1, -2
A) Arithmetic or Geometric (and why?)
B) What is the common difference or common ratio?
C) Explicit equation:
D) Find the 12th term of the sequence:
Josh kept 75% of the ride tickets he bought at a carnival and gave the rest to his friend Sam. Sam gave 50% of these tickets to Rob. If Rob was given 3 tickets, how many tickets did Josh buy?
Please help me out.
Answer:
i think its the 3rd one or the second one........
Step-by-step explanation:
if im wrong pllzzzzz dont report me....
Write the expression in simpleist form PLZ WILL GIIVE BRAINLIEST
4 + 4x + 6x - 3
1. 29x + 3
2. 75x + 3
3. 22x + 1
4. 10x + 1
Choose the answer that shows exponential decay?*
A) y=1/3•2^x
B) y=4•(1/2)^x
C) y=4•2^x
D) y=1/2•2^x
2. The oil company wants to transport 27L/min of oil through the pipes. Find the maximum
flow of oil that can flow through the pipes (per minute) to show that this demand cannot
be met. Clearly explain how you have found the maximum flow.
D
2
A
10
4
5
8
F
6
с
17
12
B.
12
G
E
Answer:
2. The oil company wants to transport 27L/min of oil through the pipes. Find the maximum
flow of oil that can flow through the pipes (per minute) to show that this demand cannot
be met. Clearly explain how you have found the maximum flow.
D
2
A
10
4
5
8
F
6
с
17
12
B.
12
G
E
