Given:
The value of home in 2011 is $95,000.
The value of home in 2018 is $105,000.
To find:
The exponential model for the value of the home.
Solution:
The general exponential model is
[tex]y=ab^x[/tex] ...(i)
where, a is initial value and b is growth factor.
Let 2011 is initial year and x be the number of years after 2011.
So, initial value of home is 95,000, i.e., a=95,000.
Put a=95000 in (i).
[tex]y=95000b^x[/tex] ...(ii)
The value of home in 2018 is $105,000. It means the value of y is 105000 at x=7.
[tex]105000=95000b^7[/tex]
[tex]\dfrac{105000}{95000}=b^7[/tex]
[tex]\dfrac{21}{19}=b^7[/tex]
Taking 7th root on both sides, we get
[tex]\left(\dfrac{21}{19}\right)^{\frac{1}{7}}=b[/tex]
Put [tex]b=\left(\dfrac{21}{19}\right)^{\frac{1}{7}}[/tex] in (ii).
[tex]y=95000\left(\left(\dfrac{21}{19}\right)^{\frac{1}{7}}\right)^x[/tex]
[tex]y=95000\left(\dfrac{21}{19}\right)^{\frac{x}{7}}[/tex]
Therefore, the required exponential model for the value of home is [tex]y=95000\left(\dfrac{21}{19}\right)^{\frac{x}{7}}[/tex], where x is the number of years after 2011.
Solve |x| < 12
I’m so lost with this stuff.
Answer: (-12,12)
Step-by-step explanation: hope it helps!
( 2 − k ) + 3 ( − 4 k + 2 )
Find the Sum of the Linear Expressions:
Answer:
inear equations Dear Dr Math: I hope you ... 10-(k+5) = 3(k+2) I would also appreciate any explanation. ... So we have to try to get all the "k's" on one side of the equation, and all the ... Let's look at the right side: 3(k+2) Okay, we could say this as 3 times the sum of k and 2.
Step-by-step explanation:
Answer:
5k-7
Step-by-step explanation:
I just combined like terms
a reflection across the y-axis maps the point (4,-5) to the point
Answer:
(-5, 4)
Step-by-step explanation:
Pls mark brainliest, I need 4 more to lvl-up.
PLEASE ANSWER THIS ASAP !!!!
Answer:
C
Step-by-step explanation:
Answer:
answer is B
Step-by-step explanation:
7. Consider the equation x/3+ 7 = 13.
Part A: Write an equivalent equation using the multiplication property of
equality.
Part B: What properties will you use next to solve the equations?
Answer:
9
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
i know it
Can anyone help me please?
1. 40,60,80
2.48,35,23.7
Convert 15°C to Fahrenheit. Use the formula F = C + 32
A. 33°F
B. 27°F
C. 85°F
D. 59°F
Using the equation given, F = 15 + 32 which equals 47, so I don't see how any of the choices are accurate, but if I had used the proper equation, I would get 59 Farenheit or answer D!
Hope this helps, if not, comment below please!!!
okay so i got (1,1) but it's not on here ;-;
an equation of the line that passes through (2, −4) and (0, −4).
Answer:
what
Step-by-step explanation:
Answer:
y = 0x - 4
Step-by-step explanation:
The slope is 0
josh earned $30,000 last year if the tax rate was 15%,how much money can he keep after taxes
Answer:
25500
Step-by-step explanation:
15% of 30000 is (multiply 30000 by .15 to get this) 4500
Subtract 4500 from 30000 and you got the answer
Using the information given, select the statement that can deduce the line segments to be parallel. If there are none, then select none.
When m2 = m6
1. AD BC
2. DC AB
3. none
Answer:
Its DC and AB
divide 25/1658 To find the quotient, start by dividing _
into _.
Answer:
To find the quotient, you must start by dividing 25 into 1,658.
Step-by-step explanation:
A recipe for Potato Soup is listed below:
3 1/2 cups of peeled and diced potatoes
1/3 cup finely chopped onion
3 1/4 cup water
2 cups of milk
1/2 teaspoon salt
5 tablespoons of butter
1/3 cup diced celery
3/4 cup of diced ham
2 tablespoons of chicken bouillon granules
1 tablespoon ground black pepper
5 tablespoons of all purpose flour.
You accidently use 5 cups of potatoes. Approximately how many cups of water will you need for 5 cups of potatoes?
5x + 5 - 2x - 1 which of the following is an equivalent expression
Answer:
3x + 4
Step-by-step explanation:
5x + 5 - 2x - 1
3x + 5 - 1
3x + 4
2 of 8
© What single decimal multiplier would you use to decrease by 2% followed by a
3% decrease?
Help me find D please
Answer:
21 deg
Step-by-step explanation:
3x + 5x - 2 + 18x = 180 deg (sum angles of triangle)
26x = 182 deg
x = 7 deg
angle D = 3x = 3 x 7 = 21 deg
easy question just need to be sure
Answer: 46
Step-by-step explanation:
Answer:
72m²
Step-by-step explanation:
yeh that's pretty easy actually
Pls help me on 21 , 22 , and 23
9514 1404 393
Answer:
21. perpendicular
22. neither
23. parallel
Step-by-step explanation:
It can help to plot the points on a graph and draw lines through them. This can also let you count grid squares, which can make it easier to find the slope.
21. See attachment 1. The lines are perpendicular.
QR has a slope of -3/2. ST has a slope of 2/3, the opposite reciprocal.
__
22. See attachment 2. The lines are neither parallel nor perpendicular.
__
23. The x-coordinates of Q and R are the same, so this is a vertical line at x=-1. The x-coordinates of S and T are also the same, so it is a vertical line at x=11. The two vertical lines are parallel to each other.
_____
Additional comment
When you have a number of problems that all require similar arithmetic, it can be useful to embed that arithmetic in a spreadsheet. You have to enter the numbers somewhere to "show work" or perform a calculation, so you may as well enter them into a spreadsheet that does the calculation for you.
Of course, the slope formula is ...
m = (y2 -y1)/(x2 -x1)
If you simply show the values of m for each pair of points, you can see if they are equal (lines are parallel). You can also have the spreadsheet compute their product to see if it is -1 (lines are perpendicular). If you get a #DIV/0! error, it means the line is vertical (and the product will also give an error). You can avoid error messages by making the spreadsheet more sophisticated, but that isn't necessary for the purpose here.
How many quarters are there in $2?
A. 2
B. 4
C. 6
D. 8
I NEED HELP NOW!!! I ONLY HAVE 5 MIN TO TURN THIS IN
Answer:
a)
28000 + 3000·x = 36000 + 2000·x --> x = 8 years
b)
28000 + 3000·8 = $52000
Answer:
a. x = 8 yearsb. 52,000Step-by-step explanation:
company A = 28,000 + 3,000 (x)
company B = 36,000 + 2,000 (x)
where x = no. of years.
company A = company B28,000 + 3,000 (x) = 36,000 + 2000 (x)
3,000 (x) - 2,000 (x) = 36,000 - 28,000
1,000 (x) = 8,000
x = 8,000
1,000
x = 8 yearsplugin value of x = 8 into company A and Bcompany A = 28,000 + 3,000 (8)
company A = 52,000company B = 36,000 + 2,000 (8)
company B = 52,000Pls help i will mark brainliest シ♡︎
Answer:
D:95 mm Hg
Step-by-step explanation:
Using the linear model, y=x+95, x represents the age and y represents the blood pressure.
For a newborn, x=0 this gives us
> y=0+95 = 95<
Answer: 1mm hg per year
Step-by-step explanation:
Kyle missed 3 questions on the math exam. If he missed 15% of the questions, how many questions were on the exam all together?
Answer:
There were 20 questions on the test.
Hope this helps!
11. Samuel's current salary is $30,000. He has been
promised a raise to $31,500 next year. His raise
will be what percent increase over his current
salary?
A. 3%
B. 3.5%
C. 4%
D. 5%
Find the midpoint of the line segment joining the points (9,2) and (-3,-2)
Answer:
(3,0)
Step-by-step explanation:
The midpoint formula is as follows:
[tex]( (x1+x2) /2, (y1 + y2) /2 )[/tex]
x1 would be 9, x2 would be -3, y1 would be 2, y2 would be -2. When plugged in, you should get 6/2, and 0/2 for y. When simplified, x would be 3 and y would be 0. This means that the midpoint of the line segment is (3,0)
Mr. G drove a total of 252 miles and used 12 gallons of gas last weekend. What is the unit rate of miles to 1 gallon?
Answer:
21 miles per gallon
Step-by-step explanation:
252 miles to 12 gallons
= 252/12
= 21
The unit rate of miles to 1 gallon is 21 miles to 1 gallon.
What is the length of side A in centimeters?
Answer:
6
Step-by-step explanation:
Answer:
10 cm
Step-by-step explanation:
Michael spends a half hour adding water to his pool part of the time at a rate of 15 gallons per minute and the rest of the time at a rate of 9 gallons per minute. Let t be the time in minutes that he adds water at the faster rate write an algebraic expression to represent the total number of water added to the pool
Answer:
24t + 270 gallons
Step-by-step explanation:
Given that :
Addition rate 1 = 15 gallons per minute
Addition rate 2 = 9 gallons per minute
Total time spent adding water = half an hour = 30 minutes = 0.5 hour
Time spent adding water at faster rate = t
Time spent addition water at slower rate = (30 - t)
Total number of water added to the pool :
Amount of water added = addition rate * time
Hence,
Amount of water added at faster rate :
(15 gal / min) * t = 15t gallons
Amount added at slower rate :
(9 gal / min) * (30 - t) = (270 - 9t) gallons
Total amount of water added to the pool:
15t gallons + (270 - 9t)gallons
15t + 270 + 9t
24t + 270 gallons
im doing an escape do you think you can help me with the riddle? Who Am I?
I am a member of the Patuxet tribe. I taught the English settlers how to survive the harsh American wilderness. It helped that I spoke the English language. So, I could act as an interpreter between the pilgrims and the native americans. My people taught them how to find medicinal plants, build wigwams, and use fish for fertilizer. Most people know me by ______, but I am also known as Tisquantum.
Answer:
Squanto
Step-by-step explanation:
They were known as Tisquantum, and knew how to speak English. They were essentially the translator between the native americans and the English
A man 2 m high observes the angles of elevation of the rops of house and a window on its sode are 45 and 60 respectively. If the top is at height of 12m above the ground , find the height.
Answer:
The height of the window = x + 2 = 4.23 + 2= 6.23m
Step-by-step explanation:
The angle of elevation of the top of the house and the window is 60 and 45 degree.
We can proceed as drawing a diagram as a man of height 2m and a building of total height 12m.
draw a horizontal line along the height of a man so that it touches building at height 2mtill the window height we assume its height as 'x' from the man's height.distance till the top from the window will be 'y'we don't know the distance between man and the building let it be 'b'
[tex]\frac{x}{b}=tan 45[/tex] =1
x=b .............(1)
total height of the building is given as 12m
x + y + 2=12
x + y = 10 .....................(2)
[tex]\frac{x+y}{b} =\frac{x+y}{x }[/tex] = tan 60
[tex]\frac{10}{x} = \sqrt{3}[/tex]
x = [tex]\frac{10}{\sqrt{3} }[/tex] ≈ 5.77m
y = 10 - [tex]\frac{10}{\sqrt{3} }[/tex]
y= 10(1-[tex]\frac{1}{\sqrt{3} }[/tex] ) ≈ 4.23m
The height of the window = x + 2 = 4.23 + 2= 6.23m
Please help asap (math)!!
Answer: 3
Step-by-step explanation: