Answer:
When x = 3
f(3) = 3 + 7 = 10
When x = -5
f(-5) = -5 + 7 = 2
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the Following table shows alexandra's investment options over the course of three years. Her initial investment was $1,000 . write one function for each option to describe the value of the investment f(n), in dollars, after n years.
The pattern in the given series of amount in the account are in the form of
arithmetic and geometric progression.
The function for Option 1 is; [tex]\underline{ f(n) = 1,100 + (n - 1) \cdot 100}[/tex]The function for Option 2 is; [tex]\underline{f(n) = 1,100 \times 1.1^{(n - 1)}}[/tex]Reasons:
The given table of values is presented as follows;
[tex]\begin{tabular}{c|c|c|c|}Number of years&1&2&3\\Option 1 (Amount in dollars)&1,100&1,200&1,300\\Option 2 (Amount in dollars)&1,100&1,210&1,331\end{array}\right][/tex]
In Option 1, the amount in dollars for each year has a common difference of d = 100
The first term, a = 1,100
Therefore;
The Option 1 can be represented as an arithmetic progression , A.P. in the
form, tₙ = a + (n - 1)·d as follows;
For the Option 1, we have;
The amount in dollars after n years, [tex]\underline{ f(n) = 1,100 + (n - 1) \cdot 100}[/tex]For Option 2, it is possible to find;
1,331 ÷ 1,210 = 1,210 ÷ 1,100 = 1.1
Therefore;
The terms in the Option 2 have a common ratio of r = 1.1
The Option 2 is a geometric progression, G.P.
The first term in Option 2 is a = 1,100
Which gives, the nth term, tₙ = a·r⁽ⁿ ⁻ ¹⁾
Therefor;
The function for the Option 2 is; [tex]\underline{f(n) = 1,100 \times 1.1^{(n - 1)}}[/tex]Learn more about arithmetic and geometric progression here:
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2) A right isosceles triangle has legs that are each 10 mm. What is the length of its hypotenuse?
round to the nearest whole number
[tex](b) ^{2} + {(h)}^{2} = {(x)}^{2} \: \: \: ( by \: \: \: pythagoras \: \: \: theorem)\\ = > {(10)}^{2} + {(10)}^{2} = {(x)}^{2} \\ = > 100 + 100 = {x}^{2} \\ = > 200 = {x}^{2} \\ = > x = \sqrt{200} mm \\ = > x = \sqrt{2 \times 2 \times 2 \times 5 \times 5}mm \\ = > x = 2 \times 5 \sqrt{2} mm \\ = > x = 10 \sqrt{2} mm[/tex]
So, the length of the hypotenuse is 10√2 mm.Answer:
10√2 mm.
Hope you could get an idea from here.
Doubt clarification - use comment section.
How I can answer this question, NO LINKS, if you answer correctly I will give u brainliest!
Answer: 54 words does Rachel type per minute
Step-by-step explanation:
Rachel types 162 words in 3 minutes Rachel types at a constant rate.
We have to find how many words does Rachel type per minute.
By definition of unit rate: all we do is divide 162 by 3 which gives us 54
Answer:
54 words per minute
Step-by-step explanation:
In 3 minutes Rachel types 162 words
Then
In 1 minutes,Rachel types 162÷3 words
In 1 minutes Rachel types 54 words
.
. . Rachel types 54 words per minute
ASAP HELP *Can a triangle have sides with the given lengths? Explain, showing all the work
9 cm, 11 cm, 15 cm
please Explain
Answer:
yes
Step-by-step explanation:
For the sides to form a triangle , then the sum of any 2 sides must be greater than the third side
9 + 11 = 20 > 15
9 + 15 = 24 > 11
11 + 15 = 24 > 9
The 3 sides given will form a triangle
Note that
The length of any two sides must be greater than the third side
So
9+11=16>1511+15=26>99+15=24>11Yes it's a triangle
Simplify the expression:
10v + -5 + 7
Answer:
10v + 2
Step-by-step explanation:
Answer:
10v + 2
Step-by-step explanation:
Ok, so when were adding varibles, whenever theres the same varible, we add them. In this case we have v and numbers. -5+7 is 2 because -5 and positive 5 cancel eachother out so were left with 2 from the 7. now the equation is 10v+2!
Meg visited her Aunt Clare for lunch. After they ate, Aunt Clare made tea. She put the same amount of black tea and milk in both their cups, but Meg decided to add some extra milk to hers. Which cup of tea was darker after they had finished adding milk?
Answer:
Aunt Clare
Step-by-step explanation:
Milk makes tea weaker, therefore the one with less milk (Aunt Clare's) is darker.
Answer:Aunt clares is darker
Given that(16 watermelons cost $48) which of these are equivalent ratios of number of watermelons to cost in dollars? Choose all that apply. (A) 16:48 B) 3:1 C 1:3 D 48:16 E) 3:9 le 5
Answer:
A, C, and E
Step-by-step explanation:
if 16 watermelons cost 48, then 1 watermelon costs 3$ meaning A C and E apply to that.
At Simba Travel Agency, the price of a climbing trip to Mount Kilimanjaro includes an initial fee plus a constant fee per meter.
The variable f models the fee (in dollars) for climbing d meters.
f=110+0.12d
What is the initial fee?
110 is the initial fee.
intial fee is the y-intercept.
A 15 foot slide casts a shadow that is 25 feet long. A tree is standing next to the slide and casts a shadow that is 40 feet long. How tall is the tree?
Answer:
30 feet
Step-by-step explanation:
The height of the tree is 24 feet casting a shadow of 40 feet long.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Assuming the height of the tree to be x feet.
15 : 25 : : x : 40.
15/25 = x/40.
25x = 600.
x = 24
learn more about proportion here :
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The two parallel sides of a trapezium are 19.8 and 7.2 and its area is 135 cm²..find its height
Answer:
10cm
Step-by-step explanation:
the formula for an area of a trapezium:
[tex] \frac{(a + b) \times h}{2} = area[/tex]
where a and b are the parallel sides and h is the height. equating what we have:
[tex] \frac{(19.8 + 7.2) \times h}{2} = 135[/tex]
simplify the numerator by adding 19.8 and 7.2=27
[tex] \frac{27h}{2} = 135[/tex]
multiply both sides by 2
[tex]27h = 270[/tex]
divide both sides by 27
[tex]h = \frac{270}{27} = 10[/tex]
the height is 10cm
A biologist wonders if the life span of bats will be affected by two new food sources from invasive species moving into an area. To conduct the experiment, the biologist needs three treatment groups: a group where the diet will not include invasive species (control), a group where the diet will include one invasive species (treatment group 1), and another group where the diet will include the other invasive species (treatment group 2). The biologist chooses the first cloud-free night and catches the first 18 bats that fly out of a cave, placing them into three equal groups of six bats. To decide the treatment for each group, the biologist places three slips of paper labeled control, treatment group 1, and treatment group 2 in a hat and randomly selects 2 slips of paper. The first piece of paper gives the treatment for the first group, the second piece of paper gives the treatment for the second group, and the remaining treatment is given to the third group.
Which component is missing from the biologist’s process?
The biologist did not use proper labeling on the pieces of paper.
The biologist did not use the appropriate number of treatment groups.
The biologist did not randomly assign the individual bats to the treatment groups.
The biologist did not randomly choose the weather on the night for bat capture.
Answer:
The biologist did not use proper labeling on the pieces of paper.
Hit Brainliest if this was helpful :)
The height and age of
a child.
Student Recording Sheet
Is it positive correlation, No correlation , or negative correlation ?
Answer: positive correlation
Step-by-step explanation:
sorry if im wrong
If 3 is added to three quarter of a certain number, the result is 30.find the original number.
Answer:
Original number is 36
Step-by-step explanation:
Let,
Number be x
3x/4 + 3 = 30
3x + 12/4 = 30
3x + 12 = 30 × 4
3x + 12 = 120
3x = 120 - 12
3x = 108
x = 108/3
x = 36
Find the inverse function. f(x) = x - 5
Answer:
f^-1 (x) = x^2 + 5
Step-by-step explanation:
f(x) = √x - 5
replace x with y
x= √y - 5
solve for y,
x =√y-5
x^2 + 5
Answer -
f^-1(x) = x^2 + 5
HOPES THIS HELPS :)
An item is regularly priced at $55. Miguel bought it on sale for 40% off the regular price. How much did miguel pay?
Answer: so Miguel payed $33
steps:
1. first find what 40% of $55 which gives us $22
2. Final Price = Original Price - Discount
Final Price = 55 - 22
Final Price = $33.00
I cannot figure this out. Any help would be appreciated.
omg guys pls help me, its due at 5pm
Answer:
1) 3:4
Step-by-step explanation:
Answer:
1. 3 ratio 5
2. 4 ratio 4
3. 2 ratio 5
4. 2 ratio 4
HHHHHHHHHHHHHHHH 100 POINTS PLEASE HELP ASAP!!!!!!!!!1!1!11!1!1!1!1!1!11!!
*Average Speed
v=d/t
Distance
d=yt
Time
t = d/v
* remember v = average speed
Solve the following problems for average speed, distance or time. Round to tenths
place:
.
. Find the distance traveled by a car that travels with an average
speed of 110 km/h for 3.5 h.
• How long does it take a baseball moving with an average
speed of 35 m/s to travel 18 m?
• What is the average speed of a car that travels 870 km in 14.5
h?
Answer:
110x3.5=385
Step-by-step explanation:
I HOPE THIS HELPS!!!!
a pair of shoes is 80 dollars they are %25 off. how much money is %25 of 80 dollars
Answer
55$
Step-by-step explanation:
Does anybody know how to does this pleaseee helppppp. The first 2 my teacher did them for me but I’m still confused pleaseee helpppp
Answer:
below
Step-by-step explanation:
A triangle can only be a triangle if the two shortest sides add up to be greater than the longest side.
For example on the first one, the segments 1 2 and 3 will not make a triangle as 1 + 2 = 3 and if the two smallest sides of a triangle are equal to the longest side it will not be a triangle at all.
So to make this easy, out of the three numbers given: add the two smallest numbers. This number has to be greater than the third number given, and it cannot be equal.
For question three: 3+9 = 12
And 12 is greater than 11, therefore this can make a triangle.
how do i write 125 as a repeated multiplication of 5s
Step-by-step explanation:
Multiply 5 by itself until you get 125.
Four people can paint a fence in 6 hours how long would three people take to paint it?
Answer:
8 hours
Step-by-step explanation:
4 people = 6 hours
→ Work out how long 1 person takes
1 person = 24 hours
→ Work out how long 3 people takes
3 people = 8 hours
EASY 25 POINTS
IF YOU GET IT WRONG I WILL NOT MARK BRAINLYEST
Answer: minimum: free
maximum: infinite
what are some expressions that are equivalent to 3(7x–6).
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{3(7x - 6)}\\\large\rightarrow\textsf{3(7x) + 3(-6)}\\\large\rightarrow\textsf{21x - 18}\\\\\\\huge\text{Therefore, your answer is: \boxed{\textsf{21x - 18}}}\huge\checkmark[/tex]
[tex]\large\textbf{Note: All you had to do is DISTRIBUTE 3 the}\\\large\textbf{WITHIN PARENTHESES. }\large\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
What is the value of the expression below when z=
5?
5z - 4
Answer:
Well we’ll just substitute
So 5z-4
And z is 5
5*5-4
25-4=21
The value is 21
From 7x^2+5xy-3y^2 subtract the sum of 2x^2+3xy-5y^2 and x^2-7xy-4y^2
Answer:
4x^2 +9xy +6y^2
Step-by-step explanation:
Combine like terms. I find it useful to factor out the variable part of the expression so I can see what coefficients are being combined.
7x^2+5xy-3y^2 - (2x^2+3xy-5y^2 + x^2-7xy-4y^2)
= (7 -2 -1)x^2 +(5 -3+7)xy +(-3 +5 +4)y^2
= 4x^2 +9xy +6y^2
(10²)²
(EXPONENT FORM ONLY)
(i think it's 10⁴ but im not sure)
Answer: 10^4
Step-by-step explanation:
You can multiply the exponents to get 10^4.
You guys are awesome with these questions I'm really struggling with this one p[lease help me out.
Try 12.
Hope it helps?
Answer:
12
Step-by-step explanation:
12 x 4 = 48
48 + 9 = 57
Need NOW help FAST PLS . hs geometry
Hope you could get an idea from here.
Doubt clarification - use comment section.
True or False. If true, give a convincing argument. If false, explain why it is false. Be sure to use mathematical language in your explanation.
As an airplane flies toward you, its angle of elevation increases.
Answer:
True.
Step-by-step explanation:
We assume that the plane is flying at a constant height above the ground.
The angle of elevation is the angle made between the plane, you and the point on the ground directly below the plane. As the plane approaches you the distance between you and the point on the ground decreases and therefore the angle of elevation increases.