Answer:
The sum of the first 650 terms of the given arithmetic sequence is 2,322,775
Step-by-step explanation:
The first term here is 4
while the nth term would be ai = a(i-1) + 11
Kindly note that i and 1 are subscript of a
Mathematically, the sum of n terms of an arithmetic sequence can be calculated using the formula
Sn = n/2[2a + (n-1)d)
Here, our n is 650, a is 4, d is the difference between two successive terms which is 11.
Plugging these values, we have
Sn = (650/2) (2(4) + (650-1)11)
Sn = 325(8 + 7,139)
Sn = 325(7,147)
Sn = 2,322,775
GUYS, PLEASE HELP!!! THIS IS REALLY NEEDED! (20 POINTS!)
The area of a square is (16x2 − 8x + 1) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work.
Thea has a key on her calculator marked $\textcolor{blue}{\bf\circledast}$. If an integer is displayed, pressing the $\textcolor{blue}{\bf\circledast}$ key chops off the first digit and moves it to the end. For example, if $6138$ is on the screen, then pressing the $\textcolor{blue}{\bf\circledast}$ key changes the display to $1386$. Thea enters a positive integer into her calculator, then squares it, then presses the $\textcolor{blue}{\bf\circledast}$ key, then squares the result, then presses the $\textcolor{blue}{\bf\circledast}$ key again. After all these steps, the calculator displays $243$. What number did Thea originally enter?
Answer:
$9$
Step-by-step explanation:
Given: Thea enters a positive integer into her calculator, then squares it, then presses the $\textcolor{blue}{\bf\circledast}$ key, then squares the result, then presses the $\textcolor{blue}{\bf\circledast}$ key again such that the calculator displays final number as $243$.
To find: number that Thea originally entered
Solution:
The final number is $243$.
As previously the $\textcolor{blue}{\bf\circledast}$ key was pressed,
the number before $243$ must be $324$.
As previously the number was squared, so the number before $324$ must be $18$.
As previously the $\textcolor{blue}{\bf\circledast}$ key was pressed,
the number before $18$ must be $81$
As previously the number was squared, so the number before $81$ must be $9$.
The berry-picking boxes at Bingo Berry Farm have square bottoms that are 8 centimeters on each side. Kendrick fills his box with raspberries to a height of 6 centimeters. What is the volume of raspberries in Kendrick's box? cubic centimeters
Answer:
384 cm³
Step-by-step explanation:
To find the volume of raspberries in Kendrick's box you have to use the formula to calculate the volume of a box:
V= l*w*h, where
l=Length: 8 cm
w=width: 8 cm
h= height: 6 cm
Then, you can replace the values in the formula:
V= 8cm*8cm*6cm
V=384 cm³
According to this, the answer is that the volume of raspberries in Kendrick's box is 384 cm³.
root 3 minus root 2 divided by root 3 + root 2
Answer:
[tex] 5 - 2 \sqrt{6} [/tex]
Step-by-step explanation:
Perhaps you are interested in rationalising the denominator of the given problem. Let's do it.
[tex] \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \\ \\ multiplying \: numerator \: and \: denominator \: \\ by \: (\sqrt{3} - \sqrt{2}) \\ \\ \frac{( \sqrt{3} - \sqrt{2} ) }{ (\sqrt{3} + \sqrt{2} )} \times \frac{ (\sqrt{3} - \sqrt{2} )}{ (\sqrt{3} - \sqrt{2} )} \\ \\ = \frac{{( \sqrt{3} - \sqrt{2} )}^{2} }{ { (\sqrt{3} })^{2} - {( \sqrt{2} })^{2} } \\ \\ = \frac{ { (\sqrt{3} )}^{2} + { (\sqrt{2} )}^{2} - 2 \sqrt{3 \times 2} }{3 - 2} \\ \\ = \frac{3 + 2 - 2 \sqrt{6} }{1} \\ \\ = 5 - 2 \sqrt{6} [/tex]
A bicycle manufacturing company knows that the equation R=-2.5p?+ 500 p models
the relationship between the price (p) and the revenue (R) for one of its product lines.
What is the maximum revenue possible?
$
Answer:
The maximum revenue is $25,000
Step-by-step explanation:
The model equation is;
R = -2.5p^2 + 500p
To find the maximum value, we differentiate this and set result = 0
The first differential of this model equation is -5p + 500
we set this to zero to get the maximum price
5p = 500
p= 500/5
p = 100
Now to get the maximum revenue, we simply substitute the value of the maximum price
That would be -2.5(100)^2 + 500(100)
= -2.5(10,000) + 50,000
= 25,000 + 50,000
= 25,000
what is product of 3 1/3 * 2 1/6 in its simplest form
Answer:
65/9
Step-by-step explanation:
3 1/3=(3*3+1)/3=10/3
2 1/6=(2*6+1)/6=13/6
10/3*13/6=130/18=65/9
Answer:
[tex]7\frac{2}{9}[/tex]
Step-by-step explanation:
[tex]3 \frac{1}{3} = \frac{10}{3}[/tex]
[tex]2\frac{1}{6} = \frac{13}{6}[/tex]
10 × 13 = 130
3 × 6 = 18
[tex]\frac{130}{18} = 7\frac{2}{9}[/tex]
10
12:22
Which statement can be supported by the information in
the table?
The table shows the height of the tree that Margo planted
over an 11-month period.
Growth of Margo's Tree
Month Height of Tree (ft)
1.4
3
1.5
5
2.1
7
2.7
9
3.0
11
1.8
1
The tree increased in height each month during the
entire 11-month period.
The tree decreased in height each month during the
entire 11-month period.
The tree increased in height each month until the time
period between month 9 and month 11.
The tree decreased in height each month until the time
period between month 9 and month 11.
Mark this and return
Save and Exit
Next
Submit
Answer:
on edge
Step-by-step explanation:
The tree increased in height each month until the time period between month 9 and month 11
The statement that can be supported by the given information is, "The height of the tree increased in height each month until the time period between month 9 and month 11".
Given a table that shows the height of the tree that Margo planted over an 11-month period.
When the months are 1, 3, 5, 7, 9, and 11, the height of the tree is 1.4, 1.5, 2.1, 2.7, 3, and 1.8 respectively.
It is clear that the height of the tree increases during the months from 1 to 9.
During the time period between 9 and 11, the height of the tree decreases to 1.8 from 3.
So, the height of the tree increased in height each month until the time period between month 9 and month 11.
Hence the correct option is c.
Learn more about Table Interpretation here :
https://brainly.com/question/32499877
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What’s the value of x in centimeters
Answer:22.5
Step-by-step explanation:
multiply by 1.5
Answer:
22.5 cm
Step-by-step explanation:
Since the triangles are similar, we can use ratios to solve
AC BC
-------- = ---------
FH GH
12 15
-------- = ---------
18 x
Using cross products
12x = 15*18
Divide each side by 12
12x/12 = 15*18/12
x =22.5
The expression f(x) = x^2 + 18x + c and g(x) = x^2 - x + d are perfect - square trinomials. What is the value of g(0) - f(0)?
Answer:
0
Step-by-step explanation:
This is because any number that is plugged in is going to be multiplied by 0. Anything multiplied by 0 is 0. Lastly, 0-0=0, which brings you to your final answer.
Please answer correctly !!!!!! Will mark brainliest !!!!!!!!!
Answer:
11 + x m
Step-by-step explanation:
[tex]width = \frac{area \: of \: rectangle}{length} \\ \\ = \frac{121 - {x}^{2} }{11 - x} \\ \\ = \frac{ {11}^{2} - {x}^{2} }{11 - x} \\ \\ = \frac{(11 + x)(11 - x)}{11 - x} \\ \\ = (11 + x) \: m[/tex]
x^2+1/x^2=18 find x-1/x
Notice that
[tex]\left(x-\dfrac1x\right)^2=x^2-2+\dfrac1{x^2}=18-2=16[/tex]
which tells us
[tex]x-\dfrac1x=\pm4[/tex]
how do I find the x
Answer:
1/2(6)(2 + x) = 27
3(2 + x) = 27
6 + 3x = 27
6 - 6 + 3x = 27 - 6
3x = 21
3x / 3 = 21 / 3
x = 7
Step-by-step explanation:
Answer:
7 m.Step-by-step explanation:
Use the formula A = a + b/2 · h
b = 2·A/h - a
b = 2 · 27/6 - 2
b = 7
2 Points
A bag has 4 balls: 1 red (R), 1 green (G), 1 yellow (Y), and 1 orange (O).
You randomly choose a ball. What is the sample space?
A. {R, B}
B. {R, G, Y, O}
Ο Ο Ο Ο
C. {G, O}
D. {R, G, Y, B}
Answer:
B
Step-by-step explanation:
The sample space is a set of any and all possible outcomes.
How long the altitude of an equilateral triangle with side length 10cm
Equilateral triangles have 3 sides of the same length, so if you split it down the middle, you will end up with one side length of 10cm and another with 5cm. Pythagorus can be used to find the missing side length, because the line of symmetry creates a right angle.
a^2 + b^2 = c^2
5^2 + b^2 = 10^2 (substitute given values in, remember the longest side, or the side opposite the right angle is c)
25 + b^2 = 100 (simplify)
b^2 = 75
b = 8.6603
Check answer
5^2 + 8.6603^2 = 10^2
25 + 75 = 100
PQR is an isosceles triangle in which pc=pr m and n are points on PQ and PR such that angle MQR =angle NQR Prove that triangle QNR and RMQ are congruent
Answer:
We are given that triangle PQR is an isosceles triangle in which PQ = PR .
Since the base angles of an isosceles triangle are equal,
angle PQR = angle PRQ
Also, And we are given that
angle MRQ = angle NQR
In ΔQNR and ΔRMQ
∠NQR=∠MRQ (given)
QR = QR (common)
-triangles QNR is congruent to triangles RMQ - ASA - angle side angle
You have an envelope full of coupons that you received 253 days ago. If
the coupons expire 9 months from the day they are given to you, will you
be able to use your coupons at the store or will they have already expired?
Answer:
you should be able to use them
Step-by-step explanation:
At the end of the day, I choose you.
Answer:
For real
Step-by-step explanation:
HEELPPP how do I solve this equation please do it step by step
Answer:
x = -24/7 or x = -3 3/7
Step-by-step explanation:
In this equation, the first thing we will do is to get rid of the denominators -- they complicate everything. So, we can multiply the entire equation by 10, since 10 is the lowest common multiple of 5 and 2, which are the denominators.
Then, the equation will look like this:
2(4x-2) + 5(1) = 5(3x+7) - 10(1)
Notice that the denominators will no longer exist.
Now, distribute on both sides of the equation.
The equation will look like this now:
8x - 4 + 5 = 15x + 35 - 10
Then, we must combine like terms. We want to isolate the variable x on one side of the equation. Let's isolate it on the right side. So, subtract 8x from both sides. The equation will look like this now: - 4 + 5 = 7x + 35 - 10
Now that x is on one side, let's move all the other terms to the left side. Subtract 25 from both sides (35 - 10 = 25 on the right side, get rid of it by subtracting 25). The equation now looks like this: - 4 + 5 - 25 = 7x
Finally, combine all on the left side.
Final equation: -24 = 7x
Now, we know 7x = -24. We want to solve for the value of x. So, divide both sides by 7.
x = -24/7 or x = -3 3/7
The maximum grain for corn is achieved by planting at a density of 40,000 plants per acre. A farmer wants to maximize the yield for the field represented on the coordinate grid. Each unit on the coordinate grid represents one foot. How many corn plants, to the nearest thousand, does the farmer need? ( hint 1 acre =43,560 square) The farmer needs approximately about how many corn plant
Answer:
514,400 plants.
Step-by-step Explanation:
From the attached diagram given below which shows the coordinate grid, we can say the shape of the farm is that of a trapezium.
Number of plants to be planted by the farmer at 40,000 plants per acre = area of land in acres * 40,000.
Let's find the area of the land(trapezium):
Area of trapezium = ½(a+b)*h
From the coordinate grid, from point E to H on the y-axis, we have 900 units = 900 ft (Given that 1 unit = 1 foot).
Also, from F to G, we have 500 units = 500ft; and the height of the trapezium is represented by the number of units the trapezium covers on the x-axis = 800units = 800ft.
a = 900ft, b = 500ft, c= 800ft
==> Area of Land/trapezium = ½(a+b)*h
= ½(900+500)*800
= ½(1400)*800
= 700*800 = 560,000ft²
Given that 1acre = 43,560ft²
x acre = 560,000ft²
x = 560,000*1 /43,560
x = 12.86 acres
Therefore, number of plants to be planted = 12.86 acres * 40,000 plants = 514,400 plants.
Find the measure of arc EB. Circle A is intersected by line CD at points D and E and line CB at point B, forming angle ECB outside of the circle, the measure of angle ECB is 25 degrees, arc EB is 4x plus 16 degrees, and arc DB 7x plus 6 degrees.
Answer:
[tex]m\widehat {EB}[/tex] = 96°
Step-by-step explanation:
From the figure attached,
m∠ECB = 25°
[tex]m\widehat {EB}={(4x+16)}[/tex] degrees
[tex]m\widehat{DB}=(7x+6)[/tex] degrees
From the theorem of secants intersecting outside the circle,
m∠ECB = [tex]\frac{1}{2}[m\widehat {DB}-m\widehat{EB}][/tex]
25° = [tex]\frac{1}{2}[(7x + 6) - (4x + 16)][/tex]
25° = [tex]\frac{1}{2}(3x-10)[/tex]
50 = 3x - 10
3x = 60
x = [tex]\frac{60}{3}[/tex]
x = 20
[tex]m\widehat {EB}[/tex] = (4 × 20 + 16)°
= (80 + 16)°
= 96°
Therefore, measure of arc EB is 96°.
Answer:
96°
Step-by-step explanation:
Got it right on the test
I do not know how to go at this question Halp!!!!
Answer:
I think
all the rectangle in the shape u have to find the area of the rectangle
55×55 for each rectangel \ l ×W
now do the squares
25×25 for each rectangle
now when u got all the sides add them up
Please answer correctly !!!!!!!! Will mark brainliest !!!!!!!!!!! No explanation needed !!
Answer:
c
Step-by-step explanation:
An ice cream store has two new flavors: Fantasy and Ecstasy. Each barrel of Fantasy requires 4
pounds of nuts, 3 pounds of chocolate, and brings in a profit of $50. Each barrel of Ecstasy
Answer:
Fantasy: 3 barrelsEcstasy: 1 barrelStep-by-step explanation:
Given
Fantasy uses 4 lb of nuts, 3 lb of chocolate, for a profit of $50
Ecstasy uses 4 lb of nuts, 1 lb of chocolate, for a profit of $40
In stock are 16 lb of nuts, 10 lb of chocolate
Find
amount of each to maximize profit
Solution
Let x and y represent barrels of Fantasy and Ecstasy, respectively. Then the limitations on production are ...
4x +4y ≤ 16 . . . lb of nuts
3x +y ≤ 10 . . . . lb of chocolate
We want to maximize
50x +40y
The graph shows the feasible region. Its vertices are ...
(0, 4), (3, 1), (3.33, 0)
Profit is maximized at $190 when production is 3 barrels of Fantasy and 1 barrel of Ecstasy.
The sum of two numbers is 49 and the difference is 25 . What are the numbers?
Answer:
x = 37 y = 12
Step-by-step explanation:
Let x be one number
Let y = other number
x+y = 49
x-y = 25
Add the equations together
x+y = 49
x-y = 25
---------------
2x = 74
Divide by 2
2x/2 = 74/2
x =37
x+y = 49
37+y = 49
Subtract 37 from each side
37+y-37 = 49-37
y = 12
Sarah burned 280 calories running 20 minutes. The next day, Sarah burned 490 calories running for 35 minutes. Let c represent the number of calories. Let t represent time, in minutes, spent running. Which equation represents this relationship?
Answer:
c = 14 * t
Step-by-step explanation:
we have to calculate the average to make the equation, the first thing is to calculate the calories burned per minute in the two days:
the first day:
280/20 = 14
second day:
490/35 = 14
that is, how it does not change from day to day, the average is 14 calories per minute, therefore, the equation would be:
c = 14 * t
The equation represents this relationship is [tex]c = 14 \times t[/tex]
Calculation of an equation:Since Sarah burned 280 calories running 20 minutes. The next day, Sarah burned 490 calories running for 35 minutes. Let c represent the number of calories. Let t represent time, in minutes, spent running.
So, here we need to determine the burned per minute for 2 days
So,
the first day
[tex]= 280\div 20[/tex]
= 14
And, the second day:
[tex]= 490\div 35[/tex]
= 14
Therefore, The equation represents this relationship is [tex]c = 14 \times t[/tex]
Learn more about an equation here: https://brainly.com/question/14006221
What is the area of the square adjacent to the third side of the triangle?
If known could u answer the other as well ?
Answer:
85 units^2 = Area of Blue Square
and
x = 5 units
Step-by-step explanation:
To do this we use the Pythagorean theorem (a^2 + b^2 = c^2). a and b represent the legs of the triangle whereas c represents the longest side of the triangle, or the hypotenuse.
Since we know the area of a square is the side length multiplied by itself (or the side length squared), [tex]\sqrt{35}[/tex] is the side length of the pink square and [tex]\sqrt{50}[/tex] is the side length of the green square.
That means a = [tex]\sqrt{35}[/tex] and b = [tex]\sqrt{50}[/tex] , so...
[tex](\sqrt{35} )^{2} + (\sqrt{50})^{2} = c^{2}[/tex]
35 + 50 = c^2
85 = c^2
[tex]\sqrt{85} = c[/tex]
Now we need to square the square root of 85 to find the area of the blue square.
[tex](\sqrt{85})^{2} = Area of blue square[/tex]
85 units^2 = Area of Blue Square
To solve the other question we use the same formula again.
[tex]x^2 + 12^2 = 13^2\\x^2 +144 = 169\\-144\\x^2 = 25\\x=\sqrt{25} \\x=5[/tex]
x = 5 units
Rewrite the function by completing the square
F(x)=x^2+6x-78
F(x)=(x+?)^2+?
Answer:
F(x) = (x + 3)^2 -87
Step-by-step explanation:
Here, we want to rewrite the function by completing the square.
Firstly, we move the c term(-78) to the right hand side of the equation and that becomes
x^2 + 6x = 78
Then, we can complete the square on the right hand side here, to be
Let’s add 9 to both sides
That would be;
x^2 + 6x + 9 = 78 + 9
x^2 + 6x + 9 = 87
(x+3)^2 = 87
or simply
(x+3)^2 -87 = 0
So our F(x) becomes
F(x) = (x + 3)^2 -87
Answer:
The expression after completing the square is:
[tex]f(x) = (x+3)^{2} -87[/tex]
Step-by-step explanation:
The function is rewritten after making algebraic manipulation:
[tex]f(x) = x^{2} + 6\cdot x +9 - 9 - 78[/tex]
The expression after completing the square is:
[tex]f(x) = (x+3)^{2} -87[/tex]
Select the values that make the statement true. n/100=1/d=p% PLZ HELP ME
Answer:
it will be: n = 5 d = 20 p = 5
Hope it helped!
The sum of 3 consecutive odd integers is 411. State the values of the integers.
Answer:
135, 137, 139
Step-by-step explanation: My bad, I did not see that it said consecutive odd integers
x+x+2+x+4=411
3x+6=411
3x=405
x=135
x+2+137
x+4=139
Represent 3 consecutive odd integers as follows.
X ⇒ first odd integer
X + 2 ⇒ second odd integer
X + 4 ⇒ third odd integer
Since their sum in this problem is 411, x + (x + 2) + (x + 4) = 411.
Now combine like terms to get 3x + 6 = 411.
No subtract 6 from both sides to get 3x = 405.
Now divide both sides by 3 and x = 135.
So x + 2 would be 137 and x + 4 would be 139.
So our consecutive odd integers are 135, 137, and 139.
What’s the polynomial for this?
Answer:
it might be trinomial if not maybe its monomial hope it helps ;/
Step-by-step explanation:
