The [tex]nth[/tex] term rule of the quadratic sequence will be [tex]n^2+5n+2[/tex] .
What is quadratic sequence ?Quadratic sequences are sequences that include [tex]nth[/tex] term. They can be identified by the fact that the differences between the terms are not equal, but the second differences between terms are equal.
Quadratic sequence [tex]=an^2+bn+c[/tex]
Here [tex]a,b,c[/tex] are constant and [tex]n[/tex] is the position of term.
First difference [tex]= 3a+b[/tex]
Second difference [tex]=2a[/tex]
We have,
Quadratic sequence [tex]8,16,26,38,52,68,86,....[/tex]
Quadratic sequence [tex]=an^2+bn+c[/tex]
so,
For [tex]n=1[/tex];
[tex]8=an^2+bn+c[/tex]
[tex]8=a+b+c[/tex] [tex]........(i)[/tex]
For [tex]n=2[/tex];
[tex]16=4a+2b+c[/tex] [tex]........(ii)[/tex]
For [tex]n=3[/tex];
[tex]26=9a+3b+c[/tex] [tex]........(iii)[/tex]
Now,
Subtract equation [tex](i)[/tex] from [tex](ii)[/tex]
we get,
[tex]8=3a+b[/tex] [tex]........(iv)[/tex]
Subtract equation [tex](ii)[/tex] from [tex](iii)[/tex] we get,
[tex]10=5a+b[/tex] [tex]........(v)[/tex]
Subtract equation [tex](iv)[/tex] from [tex](v)[/tex] we get,
[tex]2=2a[/tex] (This is second difference mentioned above)
[tex]a=1[/tex]
Putting [tex]a=1[/tex] in [tex](iv)[/tex]
⇒[tex]b=5[/tex]
Now putting values of [tex]a[/tex] and [tex]b[/tex] in equation [tex](i)[/tex]
[tex]8=1+5+c[/tex]
[tex]c=2[/tex]
Now, putting values of [tex]a[/tex] , [tex]b[/tex] and [tex]c[/tex] in,
Quadratic sequence [tex]=an^2+bn+c[/tex]
we get,
[tex]nth[/tex] term rule [tex]=n^2+5n+2[/tex]
Hence, we can say that the [tex]nth[/tex] term rule of the quadratic sequence will be [tex]n^2+5n+2[/tex].
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Plz helpp
23% of the mix was cadmium. The total weight is 3000 grams. What is the weight of the other constituents?
Answer:
690
Step-by-step explanation:
23% of 3000 is 690 (love your username btw; 2️⃣ Set
Use the incomplete reaction to complete the activity. Ba(ClO3)2 → ____ + 3O2 In one or two sentences, identify the type of reaction that is occurring and identify the other product. Based on the subscripts of the elements in the other product and the fact that chlorine has seven valence electrons, determine the number of electrons in barium’s (Ba) outer shell.
The missing product of the reaction is BaCl2 and we can see that barium has two electrons on its outermost shell.
The complete reaction is Ba(ClO3)2 → BaCl2 + 3O2. From the reaction equation, we can see that the missing product is BaCl2. The compound is composed of one barium atom and two chlorine atoms.
Since chlorine has seven valence electrons, it means that it requires two electrons from barium to complete its octet in BaCl2. This now means that barium has two electrons in its outermost shell.
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OXIDATION UNIT TEST
1. Which statement best explains why magnesium and chlorine combine in a 1:2 ratio?
A. Magnesium has two valence electrons, and chlorine can accept one electron in its outer shell
2. Hydrogen and nitrogen combine to form ammonia. When nitrogen and hydrogen bond, nitrogen pulls the electrons from hydrogen toward itself. Which statement about the reactants is correct?
C. Hydrogen is oxidized, and nitrogen is reduced.
3. C3H8 + 5O2 → 3CO2 + 4H2O + energy
Which type of reaction is shown?
C. combustion
4. Which phrase best defines a redox reaction?
D. a reaction in which electrons are transferred between different atoms
5. Which statement describes the process of oxidation?
D. Oxidation results in a loss of electrons, so the oxidation number increases.
6. Which chemical equation represents a redox reaction?
D. Fe2O3(s) + 2Al(s) → Al2O3(s) + 2Fe(l)
7. Which statement correctly describes the oxidation number of the manganese atom (Mn) in MnI2 and MnO2?
A. Manganese has an oxidation number of +2 in MnI2 and +4 in MnO2.
8. Br2(l) + 2NaI(aq) → I2(s) + 2NaBr(aq)
Which elements are oxidized and reduced in the reaction?
D. Iodine (I) is oxidized, and bromine (Br) is reduced.
9. Which action occurs at an electrode of a galvanic cell?
D. electron transfer
10. Which statement best compares a battery and a galvanic cell?
A. A battery’s source of power is a galvanic cell in which a redox reaction produces electrical energy.
11. Zn + 2H+ → Zn2+ + H2
2Al + 3Cu2+ → 2Al3+ + 3Cu
Which elements are oxidized?
A. zinc (Zn) and aluminum (Al)
12. 2Cr(s) + 3Cu2+(aq) → 2Cr3+(aq) + 3Cu(s)
Which half reaction occurs at the cathode?
B. 3Cu2+(aq) + 6e– → 3Cu(s)
13. Written
14. Written
15. Written
I hope this helps!
solve the equation −4(m+6)=−8
.,........................
jamelia paid $8.40 for sliced turkey the amount she bought was 2.40 lb how much did jamelia pay per pound for the sliced turkey
It costs $11 for 15 granola bars.
What is the unit price, in dollars per granola bar, rounded to the nearest hundredth?
Answer:
0.73
Step-by-step explanation:
QUESTION 9 of 10: You enter a bid. Your cost on the product you make is $112 per unit. If you bid at $138 per unit, what percent is the price
you bid over your cost? (Round to the nearest percent)
O a) 19%
Ob) 23%
O c) 81%
I would say B as the answer... 81 is just to high and 19 doesn't seem right.. so I'm just gonna go with B 23%
I am very sorry if this is wrong in anyway!
Answer:
the answer is 23%
Step-by-step explanation:
i used a percent increase calc... was too lazy to do the work haha
HELP ME RN PLEASE!!!!!!!!!!!!!!!!!!!!!!
Answer:
got ub the naswers is 5x+y==6
Step-by-step explanation:
b/a if a=8 and b=24.
Answer:
I wilm clear you
Step-by-step explanation:
Given,
If a=8
b=24
Now according to question,
or, b/a
or, 24/8
or, 3
On the accompanying grid, draw and label quadrilateral ABCD with points A(1,2), B(6,1), C(7,6), and D(3,7). On the same set of axes, plot and label quadrilateral A′B′C ′D′, the reflection of quadrilateral ABCD in the y-axis. Determine the area, in square units, of quadrilateral A′B′C′D′.
Answer: Refer to figure 1 for the diagram needed.
A ' = (-1, 2)
B ' = (-6, 1)
C ' = (-7, 6)
D ' = (-3, 7)
Area = 24 square units
============================================================
Explanation:
Start by drawing an xy axis. Plot the given points A,B,C,D on this grid.
To reflect any given point over the y axis, we apply this rule
[tex](x,y) \to (-x,y)[/tex]
which means we change the sign of the x coordinate, but keep the y coordinate the same. For example, a point like A(1,2) moves to A ' (-1,2). The other points are handled in a similar fashion.
After all of the points have been reflected, you'll get what is shown in figure 1.
------------------
To find the area of quadrilateral ABCD, we can form a bounding box as small as possible around the quadrilateral. Refer to figure 2.
The area of rectangle FEHG is 6*6 = 36 square units
Then we subtract off the areas of these four outer triangles
Triangle AED = 5*2/2 = 5Triangle AFB = 1*5/2 = 2.5Triangle BCG = 1*5/2 = 2.5Triangle CDH = 1*4/2 = 2Meaning we'll end up with 36-5-2.5-2.5-2 = 24 as the area of quadrilateral ABCD. Because a reflection is a mirror copy, quadrilateral A'B'C'D' will have the same area as ABCD.
Becky's medical bill is $1374. She has a $150 deductible, plus 85% medical insurance
How much will Becky pay?
Helpppp
Answer:
$333.60
Let me know if you have any questionsPlease help!! Picture is provided
Quad. ABCD is a trapezoid.
XY is the median
XY = 12; AB=16
Find DC
Answer:
DC = 8
Step-by-step explanation:
The median is half the sum of the parallel bases, that is
[tex]\frac{AB+DC}{2}[/tex] = XY , substitute values
[tex]\frac{16+DC}{2}[/tex] = 12 ( multiply both sides by 2 to clear the fraction )
16 + DC = 24 ( subtract 16 from both sides )
DC = 8
Answer:
DC = 8
Step-by-step explanation:
The median XY of the trapezoid ABCD is half or the sum of AB and DC.
XY = 1/2 ( AB + DC)
We need to find out DC so we can rewrite this equation isolating DC
XY = (1/2)(AB+DC), multiply both sides by 2
2XY = AB + DC, subtract from both sides AB
2XY - AB = DC, now substitute the given AB = 16 and XY = 12
2* 12 - 16 = DC , using the order of operations rules we multiply first
24 -16 = DC, subtract
8 = DC
A line is drawn so that it passes through the points (-3, -1) and (4, 2).
a. What is the slope of the line?
b. Using the point (4, 2) and the slope found above, write the equation of the line in point-slope form.
Answer:
y - 2 3/7 (x-4)
Step-by-step explanation:
A) To find slope, use the equation:where and are the x and y values of one coordinate point , and and are the x and y values of another coordinate point . Since we are given two coordinate points, (-3,-1) and (4,2), that means we can find the slope using the slope equation.
Let's choose (4, 2) as your point and (-3, -1) as your point, but you can switch those if you want! That makes and x^1 = -3, y1 = -1 . Plug these values into the slope equation:
The slope of the line is 3/7.
B) Remember that the general equation for point-slope form is, where m = the slope, = the x value of a coordinate point on the line, and = the y value of the same coordinate point on the line.
You are given (4, 2) as one of the coordinate points. That means = 4 and = 2. We found the slope, m = in part A. Now plug these values into the general equation for point-slope form to find your point-slope form equation:
Your point-slope form equation is y - 2 3/7 (x-4).
Answer:
a. 3/7 b. y=3/7x+2/7
Step-by-step explanation:
(-1-2)/(-3-4)=3/7
slope is 3/7
apply point for answer
2=3/7(4)+n
n=2/7
apply
y=3/7x+2/7
The graph shows which inequality? The vertex is (-4, -3)
Refer to the attachments.
Plzzz help me plzzzzzz
Answer:
Circumference of a circle = pi * diameter
[tex]219.8=3.14*d[/tex]
[tex]d=\frac{219.8}{3.14}[/tex]
[tex]d=70[/tex]
Radius = half of diameter
[tex]r=\frac{1}{2} d[/tex]
[tex]r=\frac{1}{2}*70[/tex]
[tex]r=35[/tex]
Area of circle = [tex]\pi r^2[/tex], where r is the radius:
[tex]a=3.14*35^2[/tex]
[tex]a=3846.5[/tex]
If they ran around the track 3 times, they would cover the circumference three times.
[tex]219.8*3=659.4[/tex]
Convert to centimetres:
[tex]659.4*100=65940[/tex]
8. You have been asked to repaint the lateral surface area of cone-shaped pylons used for soccer drills. If they have a radius of 5" and a height of 12", calculate the slant height and lateral surface area to be painted to the nearest square inch.??
Answer:
See answer below.
Step-by-step explanation:
LA = π rl
1st find l
The radius is 5" and the height is 12" l = ?
h and the r is the two legs in the right triangle when drawn in a cone.
Use a² + b² = c² ⇔ h² + r² = l²
12² + 5² = l²
144 + 25 = l²
169 = l²
[tex]\sqrt{169} = l[/tex]
13 = l
Formula for LA = π r l
LA = 3.14 × 5 ×13 or with a calculator LA = π × 5 × 13
LA = 204.1 sq.in LA = 204.2035225 sq. in
I use 3.14 = for π but you know what the teacher uses in class.
help me please
A
B
C
D
E
F
Answer:
F because you cannot prove that any of the angles are the same with only one set of parallel lines
David was thinking of a number. David doubles it, then adds 3 to get an answer of 81. 6. What was the original number?.
Answer:
The answer is 39.3
Step-by-step explanation:
81.6 - 3 = 78.6
78.6 ÷ 2 = 39.3
Solve for the unknown side of each right triangle
x is 9.1 accordingly to the phytagores therom
How many inches is the box's side?
And please explain how you found the answer
Thank you :)
Answer:
[tex]x\approx 13.27 in[/tex]
Step-by-step explanation:
I'm assuming 24' is the diagonal of the box (red dashed line) and not of the bottom face (black dotted line).
Option 1: easiest if you know/remember the formula for the distance of two points in space (or for the diagonal of a parallelepiped): [tex]d= \sqrt{\Delta x^2+\Delta y^2+\Delta z^2}[/tex] where replacing (and squaring both sides to get rid of the square root) we get
[tex]24^2 = x^2 + 16^2+12^2 \rightarrow 576= x^2+256+144 \rightarrow x^2=176\\x\approx13.27 in[/tex]
Option 2: look at the triangle that has sides the forward left edge of the box, the dotted diagonal and the dashed diagonal. It's a right triangle of hypotenuse 24 and side length 12. Pythagorean theorem to find the missing side lenght
[tex]24^2 = l^2+12^2 \rightarrow l^2 = 432 \rightarrow l\approx 20.78 in[/tex]
At this point we're back at the right triangle of the bottom face of the box, of hypotenuse 20.78' and side lenght 16'. Phythagorean theorem again:
[tex](20.78)^2= 16^2 +x^2 \rightarrow 432 = 256+x^2\\x^2 = 176 x \approx 13.27[/tex]
The prices of items in a shop were reduced by 10% during reduction sales. if a costumer buys an electric fan at $810.00. What was the original price?
Answer:
See below:
Step-by-step explanation:
Hello! I hope you are having a nice day.
We can solve the problem in 2 steps, one being Solving, and the second being Comprehending. I'll start with comprehending.
Comprehending
We can start by analyzing the problem and creating an equation to then begin solving.
So, we know that a number, which we will call [tex]x[/tex] has a discount of 10% to get the current price of $810. We know that when there is a discount, we need to find what the 10 percent is then add it to the current price;$810.
We can create a formula and steps by doing the following:
[tex]x*0.9=810[/tex]
We have 0.9 as there is a 10% discount (0.1) and we subtract 1.00 by 0.1 to get 0.9. (Which is 90%).
This states that 90% of a number is equal to 810.
Now that we have an equation, we can begin solving.
Solving
We can solve the problem by using basic algebra.
[tex]x*0.9=810\\x*\frac{9}{10}=810\\x=(810*10)\div 9\\x=8100 \div 9\\x=900[/tex]
On step 1, we convert the decimal to a fraction for easy simplification/solving.
On step 2, we split the fraction into two and since we're dividing, we can flip the fraction and multiply by 10 and divide by 9.
On step 3, we use basic algebra and after step 4 we get our answer.
We can double check out answer by doing the following:
[tex]900-(900*0.10)=810?\\900-90=810?\\810=810[/tex]
We have checked our answer and gotten our answer of $900.
Cheers!
PLZZZ HELP ASAP I NEED IT FAST!
Answer:
5.4
Step-by-step explanation:
Step 1: Take any two side lengths from the quadrilaterals (one from ABCD and one from PQRS)
For this case, I'm going to take 4 and 7.2Step 2: Divide the length you took from PQRS by the length you took from ABCD.
[tex]\frac{7.2}{4}[/tex] [tex]1.8[/tex] (1.8 is the scale factor (SF))Step 3: Since CD and RS and corresponding sides, multiply 3 by 1.8
[tex]3 * 1.8[/tex] [tex]5.4[/tex]Therefore, x = 5.4.
Answer:
5.4
Step-by-step explanation:
Look at photo for explanation
math question please help meeee
Answer: what the math question is
Step-by-step explanation:
Answer:
3/4
Step-by-step explanation:
7 plus 5 (painters plus photographers) equals 12. The remaining (4) adds to 16. 12/16 can be simplified to 3/4
Hope it helps
Would appreciate a brainliest
3x4y=-2
9x-10y=38
elimnation method
Answer:
x = 2
y = -2
Step-by-step explanation:
N.B. Assuming the first equation is actually 3x + 4y = -2
The elimination method is an incredibly useful tool used to save large amounts of time when working with small systems of equations.
First, set one variable in the top equation to have an equal coefficient as that same variable in the bottom equation.
3(3x + 4y) = 3(-2)
Then, you are left with this. Simply subtract the equations.
9x + 12y = -6
9x - 10y = 38
0 + 22y = -44
Then, simply solve
y = -2
9x + 20 = 38
9x = 18
x = 2
Hope it helps :) and let me know if you want me to elaborate.
Prove algebraically that the straight line with equation x = 2y + 5 is a tangent to the circle with equation x² + y² = 5.
Answer:
15
Step-by-step explanation:
How to write in simplified slope intercept form
Answer:
y = 4x - 3
Step-by-step explanation:
1. Pick tow points that is on the line; (1, 1) and (2, 5).
2. Find the Slope: Slope = (change in the y-values)/(change in the x-values)
Slope = (5 - 1)/(2 - 1) = 4/1 = 4
3. Use the slope and one point on the graph and substitute into y = mx + b
and solve for "b"
y = mx + b Slope = 4 point (1, 1)
1 = 4(1) + b
1 = 4 + b
1 - 4 = b
-3 = b
4. Write the equation of the line: m = 4 and b = -3
y = 4x - 3
10 points, please fast !!!!!
Answer:
2/1 a improper fracrion 1/2 is a proper fraction
Step-by-step explanation: i just know those two sorry
Answer:
slope = 2
Step-by-step explanation:
slope is defined as change in y over change in x. for every +1 in the x direction, y receives +2. 2/1 = 2
How would you best describe the angle pair
Drag the expressions to order them top to bottom from least to greatest.
Answer:
|-5[tex]\frac{3}{7}[/tex]|
|5[tex]\frac{1}{7}[/tex]|
|-4[tex]\frac{6}{7}[/tex]|
|-4[tex]\frac{3}{7}[/tex]|
|4[tex]\frac{2}{7}[/tex]|
Step-by-step explanation:
absolute value is how far the the number is away from zero, it does not matter if it is negative or positive
What is dehydrogenation ?
Answer:
Dehydrogenation is the a chemical reaction that involves the removal of hydrogen, usually from an organic molecule. It is the reverse of hydrogenation. Dehydrogenation is important, both as a useful reaction and a serious problem.
16. Colton has a $6 credit balance on his credit card. He uses the credit card to
pay $9 for lunch. Use the number line to subtract $9 from Colton's credit
balance, and complete the equation.
ucation
6
8
10
12
14
text: Oppo...
16
Answer:
He uses the credit card to pay $9 for lunch. Use the number line to subtract $9 from Colton's credit balance, and complete the equation. ucation
Step-by-step explanation: