Answer: The length of the other diagonal is 10 cm...
So the diagonal formula is - 1/2* (d1*d2) d1 is the first diagonal and d2 is the second diagonal.
So,
1/2 * (8*d2) = 40
8d2= 40*2
d2= 80/8
d2= 10
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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Can i get some help :
The store owner is adding cost, so we will use addition. The answers should be as follows:
[] c + $3.49 = $9.84
[] c = $6.35 <- subtract $3.49 from both sides of the equation
[] Solution of answer represents the old cost of the toy.
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Which values of k would cause this system of equations to have no solution? Check all that apply. 6x 4y = 14, 3x 2y = k â€"2 5 7 10 21.
The values of k that will cause the system of equations to have no solution is; k = 7 and 21
We are given the simultaneous equations;
6x - 4y = 14
3x - 2y = k
Now, for both equations not to have a solution it means that x and y can't be made to be subjects.
Now, by inspection see see that the left hand side of the second equation when multiplied by 2 gives the left hand side of the first equation.
By implication, for both equations not to have a solution, k must also be multiplied by 2 to give 14.
Thus;
2k = 14
k = 14/2
k = 7
Also, since 21 is 1.5 multiplied by 14, it means that when we make 21 to be k, there will also be no solution.
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Answer:
-2, 5, 10, 21
A, B, D, E
Let a and b be real numbers where ab+0. Which of the following functions could represent the graph below?
O f(x) = x(x – a)3(x – b) 3
O f(x) = (x – a)2(x – 614
O f(x) = x(x – a) (x – 5)2
O f(x) = (x – a)5(x – b)
The following functions could represent the graph below then the correct option is B; y = (x - a)^2 (x - b)^4.
What is graph ?A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
we have given that a and b are real numbers different than zero.
From the graph, we can see that the line touches the x-axis in two values.
Now, if we would have an equation such as:
y = x(x - a)^3 (x - b)^3
then when x = 0
y = 0(0-a)^3 (0-b)^3
y = 0
But in the graph, we can see that when x = 0, the value of y is different than zero,
(For example, if x > a and x < b we would have a negative value for y)
Then the correct option is B ;y = (x - a)^2 (x - b)^4
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how do I do this question?
Answer:
x = (y +2)/3
Step-by-step explanation:
y= 3x-2
y+2=3x
x=(y +2)/3
The function f is given by f(x) = (x + 3)^2 - 1.
1) Write the coordinates of the vertex of the graph of f.
2) Does the graph open up or down? How do you know?
Answer:
the coordinate of the vertex is going to be (-3,-1) and it's concave up
Step-by-step explanation:
1.notice this function is in graphing form (x-h)^2+k, where (h,k) is your coordinate of the vertex, hence in this problem it's going to be (-3,-1)
2. notice that this function have a parent function of x^2, where it's a parabola that is concave up which in this case is basiclly the same shape it's also concave up
In calculus, we can proof it by finding the first derivatives and find the critical points, then take the second derivative at that critical points to see if that's negative or positive in this case it's positive
The perimeter of a rectangle is 80 feet.
Find the dimensions if the length is 5 feet longer than four times the width.
Then find the area of the rectangle.
Answer:
l=33 feet
w=7 feet
Area= 231 feet
Step-by-step explanation:
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
14. The number of customers that a small
restaurant serves increases by 25% each
week. The restaurant served 400 customers
the first week it was open.
How many customers did the restaurant
serve during the third week?
Answer:
625
Step-by-step explanation:
ok so, 25% of 400 is 100 since 25 is 1/4 of 100 just like 100/400. Now, we do 100+ 400 for the second week which is 500. Now, 500 divided by 25 is next and if we had 4 boxes wed be able to fit 100 in each and the last 100 is split so 100 divided by 4 is 25. so we add 25 to each box. Now we have 125 in each box. so thats it divided by 25% or 1/4. 125 + 500 is 625 and thats your awnser. Have a good day!
Tell whether the ordered pair is a solution to the system.
(-1, -2) 3x + 5y = 3
-9x - 8y = -9
no
yes
Answer:
no
Step-by-step explanation:
no. substitute -1 for x and -2 for y.
the first one is -1 - 10
this equals -11 not 3
I think of a number, increase it by four and double the answer. The
result is 20 more than the number. Find this number.
Answer:
(x+4)2=x+20
2x+8=x+20
2x-x=20-8
x=12
The number I thought of is 12.
How to convert statements into numerical expressions ?To convert statements into numerical expression break the statement into chunks write the terms with mathematical operations.Interpret twice, thrice, half of this etc logically.Practice a lot.
According to the given question I think of a number,Let the number be x.
I increase it by four and double (x+4)×2 = 2(x+4).
The result is 20 more than the number which is (x+20).
∴ 2(x+4) = (x+20)
2x + 8 = x + 20.
2x - x = 20 - 8.
x = 12.
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HELP ASAPPPPPPP!!!!!
Select all the intervals where f is increasing.
A. −3 < x < −2
B. -1.5 < x < 0
C. 3.5 < x < 4.5
D. None of the above
Step-by-step explanation:
since f(x) is overall increasing for the interval -3 < x < 0,
A and B both fit in there and are correct answers.
Answer:
C. 3.5 < x < 4.5
Step-by-step explanation:
Anything that is above 1 (4, 9, etc) is increasing and anything that is below 1 (0.4, -3, etc) is decreasing. A and B are wrong because they are negative or below 1 and it isn't D because C is increasing.
Jenna has 38 coins. She uses 19 coins to buy a notebook. How many coins does she have left?
Explain how you can solve and check this problem.
Answer: 19 coins
Step-by-step explanation:
38-19=19
To check, take any one of the nubers and replace it with x, and when you solve for x. you'll get that number back. For example:
Let x represent the amount used to buy a notebook
19+x=38
x=38-19
x=19
What is the solution set for x^2 - 2x - 15 = 0
A. {-5, -3}
B. {5, -3}
C. {3, 5}
D. {-3, 5}
Answer:
B
Step-by-step explanation:
I have done this before
I need help on this question. please help me.. I don't have idea on this.
Answer:
D.
Step-by-step explanation:
5(-4 +10) × 4.8 ÷ [tex]\frac{3}{4}[/tex]
5(6) × 4.8 ÷ [tex]\frac{3}{4}[/tex]
30 × 4.8 ÷ [tex]\frac{3}{4}[/tex]
30 × 4.8 × [tex]\frac{4}{3}[/tex]
_________________________________
Hope this helps!!
If I have made a mistake, please let me know; I enjoy leaning from them:)
Answer:
Step-by-step explanation:
468 divided by 3 step by step solution
Answer:
156Step-by-step explanation:
468 ÷ 3
= 156
hope u liked the answer :)
#keep learning4 1/2 x 5 Multiply and answer with a mixed number in the simplest form.
Answer:
[tex]22\frac{1}{2}[/tex]
Step-by-step explanation:
(4.5)(5) = 22.5
[tex]22.5 = 22\frac{1}{2}[/tex]
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.
PLEASE SHOW ALL WORK AND DO CORRECTLY
For #8 , fill in the missing information for the following trapezoids. SHOW YOUR WORK to solve for the missing value.
8.
height = 19.8 cm
b1 = ________
b2 = 14.4 cm
area = 401.94 cm2
Answer:
26.2 cm
Step-by-step explanation:
Area = (b1 + b2)/2 * h
401.92 = (x + 14.4)/2 * 19.8
Divide each side by 19.8
20.2989 = (x + 14.4)/2
Multiply each side by 2
40.6 = x + 14.4
Subtract 14.4 from each side
x = 26.2
Answer:
116.82
Step-by-step explanation:
Since your trying to find a missing base
19.8 x 14.4= 285.12
401.94-285.12=116.82
Hopes This Helps
How do u Keep change change this number???
1.3 - -300=????
I don’t know what to do
When the swimming pool is 25% full, it takes 2250 cubic meters (m3) to fill it up from that point. When it is full, it can be emptied at a rate of 120 m3/h. How many hours does it take to empty an 80% full pool?
Answer:
20 hours
Step-by-step explanation:
The volume of water when the pool is 80% full can be found using the proportion ...
2250/75% = v/80%
v = (80/75)(2250) = 2400 . . . cubic meters
Emptying at the rate of 120 m³/h will take ...
time = volume/rate
time = (2400 m³)/(120 m³/h) = 20 h
It will take 20 hours to empty the pool from 80% full.
if 240 slices of cake are shared into the same ration 3:5 among the boys and girls how many slices will each students recieve
Statins are used to keep cholesterol in check and are a top-selling drug in the U.S. The equation: S = 5.1 + 1.5 x estimates the amount of sales ( S ) of statin in billions of dollars x years after 1998.
Please help me with this math problem!! NO LINKS PLEASE!! IT'S DUE TONGIHT AT 11:59PM!! :)
Answer:
∆L = 51°
∆Y = 28°
∆B = 101°
∆U = 51°
UG = 10.66666
BG = 4x
A racing track is shaped like an oval. Each time around
the track is 1.2 miles. The total distance for the
race is 480 miles.
What percentage is one lap around the track of
the total race?
(b) How many laps will it take to complete 75% of the
race?
Answer:
Percentage of one lap around the track of
the total race = 0.25%
It will take 300 laps to complete 75% of the race.
Step-by-step explanation:
1.2/480=0.0025
0.0025*100=0.25
480/100*75= 360
360/1.2=300
Given g(r) = 3 – 8r, find g (–3).
Answer: R = 3/5
Step-by-step explanation:
i think
Write the gcf of:
200x^2y^5 and 1000x^3y^2
Answer:
Step-by-step explanation:
200 divides into 1000 so that is part of the HCF.
x^2 and x^3 are present so the HCF contains x^2
y^2 and y^5 are present so the HCF contains y^2
HCF = 200*x^2 * y^2
Smallest Positive fraction
Answer: 1/5?
Step-by-step explanation:
what is the modulus of the complex number -4+3i
The modulus of the complex number -4+3i is 5.
Complex number is an element of a number system that contains the real numbers and a specific element denoted i, called the imaginary unit,
A complex number is a number of the form a + bi, where a and b are real numbers.
The modulus (z) of a complex number x + iy is given by:
z = √(x² + y²)
The modulus of the complex number -4+3i is:
[tex]z=\sqrt{(-4)^2+3^2} =\sqrt{25}=5[/tex]
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