9514 1404 393
Answer:
t(n) = -n^2 -n +102
Step-by-step explanation:
We can use the first 3 terms to find a, b, c.
a(1)^2 +b(1) +c = 100
a(2)^2 +b(2) +c = 96
a(3)^2 +b(3) +c = 90
Subtract the first equation from the other two:
3a +b = -4 . . . . . . [eq4]
8a +2b = -10 . . . . [eq5]
[eq5] can be reduced to
4a +b = -5 . . . . . . [eq6]
Subtracting [eq4] from [eq6] gives ...
(4a +b) -(3a +b) = (-5) -(-4)
a = -1 . . . . . . . . simplify
Filling that into [eq4], we get
3(-1) +b = -4
b = -1 . . . . . . . add 3
Putting the values for 'a' and 'b' into the first equation gives ...
-1 +-1 +c = 100
c = 102
Then the n-th term t(n) of the sequence is ...
t(n) = -n^2 -n +102
_____
Additional comment
As you might guess, there is a generic solution for quadratic sequences. In terms of the first term (a1), first first difference (d1), and second difference (d2), the coefficients can be written as ...
a = d2/2b = d1 -3ac = a1 -d1 +d2This sequence has first differences of -4, -6, -8, -10, and second differences of -2. Putting the sequence values into the above formulas, we find ...
a = -2/2 = -1b = -4 -3(-1) = -1c = 100 -(-4) +(-2) = 102 . . . . . as aboveIn December yanni’s chocolate shop received 180 telephone orders. In January they received only 72 telephone orders. By what percent did the number of telephone orders decrease from December to January
Answer:
Step-by-step explanation:
Find two positive numbers whose difference is 30 and whose product is 2584.
Answer:
[tex]38[/tex] and [tex]68[/tex].
Step-by-step explanation:
Let [tex]x[/tex] be the smaller one of the two number.
[tex]x[/tex] must be a positive integer. The other number would be [tex](x + 30)[/tex].
The question states that the product of the two numbers is [tex]2584[/tex]. In other words:
[tex]x\, (x + 30) = 2584[/tex].
Rearrange this equation and solve for [tex]x[/tex]:
[tex]x^{2} + 30\, x - 2584 = 0[/tex].
The first root of this quadratic equation would be:
[tex]\begin{aligned}x_{1} &= \frac{(-30) + \sqrt{30^{2} - 4 \times (-2584)}}{2} \\ &= \frac{(-30) + \sqrt{900 + 10336}}{2} \\ &= \frac{(-30) + \sqrt{11236}}{2} \\ &= \frac{(-30)}{2} + \sqrt{\frac{11236}{2^{2}}} \\ &= (-15) + \sqrt{2809} \\ &= (-15) + 53 \\ &= 38 \end{aligned}[/tex].
Similarly, the second root of this quadratic equation would be:
[tex]\begin{aligned}x_{1} &= \frac{(-30) - \sqrt{30^{2} - 4 \times (-2584)}}{2} \\ &= (-15) - 53 \\ &= -68\end{aligned}[/tex].
Since the question requires that both numbers should be positive, [tex]x > 0[/tex]. Therefore, only [tex]x = 38[/tex] is valid.
Hence, the two numbers would be [tex]38[/tex] and [tex](38 + 30)[/tex], which is [tex]68[/tex].
9514 1404 393
Answer:
38 and 68
Step-by-step explanation:
Let x represent the average of the two numbers. Then their product is ...
(x -15)(x +15) = 2584
x^2 = 2584 +225 = 2809 . . . . . . use relation (x -a)(x +a) = x^2 -a^2; add a^2
x = √2809 = 53
Then the two numbers are ...
53 +15 = 68
and
68 -30 = 38
The two numbers are 38 and 68.
_____
Additional comment
Solving the problem in this way is equivalent to writing the quadratic equation for the smallest (or largest) number and solving that by completing the square. The "solution" x = -53 is not relevant in this problem.
The triangle shown below has an area of 20 units.
Find the missing side.
8.
2
2
units
Her jump rope Ella can make 17 jumps in 15 second.at this rate how make jumps can she make in20 minute?
Answer:
1360
Step-by-step explanation:
there are 1200 seconds in 20 minutes. if Ella can do 17 jumps in 15 seconds, you would divide 1200 by 15 (which equals 80) because that would be the number of 15 seconds in 20 minutes. then you would divide 80 by 17, which gives you your final answer of 1360 jumps in 20 minutes.
Gabriella goes for a power walk every three days, and Mona walks every fivedays. They both walked on Monday this week.a.After how many days will they both walk again on the same day?[3 pts]b.What day of the week will it be when they walk again on the same day?
Power Walking has been at the top of a natural range to walk with such a speed. A walk defines as a walking journey, and the further discussion can be defined as follows:
Given:
Power walking by the Gabriella by every 3 days
Walking by the Mona by every 5 days
Both walk on Monday then They both walked together,
after taking LCM of 5 and 3 that is = 15 days
For question a:
When both walk again after the same day is = 15 days
For question b:
"Tuesday" is the weekday that will it be when they walk again on the same day.
Learn more:
brainly.com/question/4546421
P(x) = x^4+ax^3-x^2+bx-12 has factors of (x-2) and (x+1). Solve the equation P(x)=0
Answer:
because P(x) has factors of (x-2) and (x+1) => x = 2 and x = -1 are the solutions of P(x)
so we have:
[tex]\left \{ {{2^{4}+2^{3}a-2^{2}+2b-12 =0} \atop {1-a-1-b-12=0}} \right.\\=>\left \{ {{8a+2b=0} \atop {a+b=-12}} \right.\\<=>\left \{ {{4a+b=0} \atop {a+b=-12}} \right.\\<=>\left \{ {{a=4} \atop {b=-16}} \right.[/tex]
=> [tex]P(x)=x^{4} + 4x^{3}-x^{2} -16x-12[/tex]
With P(x) = 0
=> [tex]x^{4}+4x^{3}-x^{2} -16x-12 = 0[/tex]
=> ........
Step-by-step explanation:
Question 5
1 pts
Write the equation of a line through (5,1), parallel to y=-*+1
o
Answer:
3rd, y=-1/5x
Step-by-step explanation:
What is the Gcf of 10 and 6?
The GCF of 10 and 6 is 2. May this will help you.
Emily gets paid $40 just for showing up to watch her sister’s dog. Her sister then pays her $25 per everyday she watches the dog.
Answer:
Step-by-step explanation:
Find an ordered pair (x, y) that is a solution to the equation. 4x-y=4 (x, y) = 00 X Х ?
What inequality does this number line show?
What is 8(9h - 6) simplifyed
How to numerically write five and eight then multiply by 4
Answer:
5 + 8 × 4
Assuming "five and eight" means 5 + 8
Look at image for question and answers
Answer:
d
Step-by-step explanation:
i did this last year
Use the map below. Find the distance between the cities Everett and Fairfield to the nearest tenth
I have a question if anybody answers the reward is brainlist
Whats 0÷0
Answer:
0
Step-by-step explanation:
You can't divide anything by zero
0÷0=
=0
Going to sleep goodbye
\lim_(x->0)(cos2x)^((3)/(x^(2)))
Answer:
ffffgggghhhuukufgnjsdhn
Answer:
∞
Step-by-step explanation:
since cos(0) = 1, you have 1/0
if a + 1 by a is equal to 3 find the value of bracket a minus 1 by a bracket square
a+1 = 3
To find:(a - 1)^2
[tex] {a}^{2} - 2.a.b + {b}^{2} \\ \\ a - 2a + 1 \\ \\ 1 + 1 = 2[/tex]
So, the answer is 2Hope it help youWalter car gets 41 miles per gallon. Walter is planning a vacation which is 372 miles away. How many gallons of gas will Walter use for this round trip?
Find the probability that a student earns a grade of A,B, or C
P=
Answer:
Step-by-step explanation:
Answer: 0.86
Step-by-step explanation:
What is the point on the graph of f(x+5)
Answer:
=fx+5f
Step-by-step explanation:
=fx+5f
An unknown polynomial is added to the expression -3x^3+2x-5 and the resulting sum is 4x^3+7x^2-3. what is the unknown polynomial?
Answer:
7x³ + 7x² + 2x - 8
Step-by-step explanation:
Let the unknown polynomial be a
a + -3x³ + 2x - 5 = 4x³ + 7x² - 3
a = 4x³ + 7x² - 3 - (-3x³ + 2x - 5)
a = 4x³ + 7x² - 3 + 3x³ + 2x - 5
a = 7x³ + 7x² + 2x - 8
2x2 − 2z4 + y2 − x2 + z4 if x = −4, y = 3, and z = 2.
answer: 9
Step-by-step explanation:
x = - 4; y = 3; z = 2;2 x² - 2 z^4 + y² - x² + z^4 = = 2 * (-4)² - 2 * 2^4 + 3² - ( -4)² + 2^4 == 2 * 16 - 2 * 16 + 9 - 16 + 16 = = 32 - 32 + 9 - 16 + 16 = 9
20+8
100+75
49+28
32+24
DRAG & DROP THE ANSWER
8(4+3)
25(3+4)
7(7+4)
4(5+2)
Answer:
give brainliest please I need it to level up
Step-by-step explanation:
20 + 8
4(5 + 2)
100 + 75
25(4 + 3)
49 + 28
7(7 + 4)
32 + 24
8(4 + 3)
Answer:
Ans; 8 +20 —> 4(2+5)
Ans; 75+100 —> 25(4+3)
Ans; 28+49 —> 7(4+7)
Ans; 24+32 —> 8(3+4)
I hope I helped you^_^
Can someone please help me please?
9514 1404 393
Answer:
D. G(x) = (x+3)² -2
Step-by-step explanation:
G(x) is translated left 3 and down 2 from F(x). The transformation ...
G(x) = F(x -h) +k
is a translation right h units and up k units. We have h=-3 and k=-2, so the function of interest is ...
G(x) = F(x +3) -2
G(x) = (x +3)² -2
A. Your friend says that the solutions to the inequality 9x-18x ≥ - 18 are x ≥ 2 Solve the inequality correctly. B. What error did your friend make?
Answer:
A. x≤2; B. wrong unequality after dividing by negative number.
Step-by-step explanation:
9x-18x≥ -18;
-9x≥ -18;
0≥ -18+9x;
18≥9x;
9x≤18;
x≤2.
Emergency funds are important because they
Answer:
an emergency fund allows you to live for a few months if you lose your job or if something unexpected comes up that costs a fair chunk of money to cover
Answer:
If there ever was an emergency you will need money to pay/afford the injury
Step-by-step explanation:
What number should go in the empty boxes to complete the calculation for finding the product of 0.53 × 0.67?
(Hint: it is the same number. Input only one number in the blank.)
will give (brainlist)
Answer:
1st box: 1
2nd box: 1
Step-by-step explanation:
1: 3 * 7 = 21, so only put the 1 and carry the 2.
2: 5 * 6 = 30, but we have a 1 from the previous answer given so 31, but only put the 1.
I hope this helps :)
Give the slope of a line perpendicular to AB
Answer:
m = -1
Step-by-step explanation:
Find the equation in slope intercept form [ y = mx + b ] for line AB. Find the slope using the formula [ y2-y1/x2-x1 ].
8-5/7-4
3/3
1
Find the y-intercept.
5 = 1(4) + b
5 = 4 + b
1 = b
So the equation of the line AB is y = x + 1.
The slope of a perpendicular line is the opposite reciprocal of the original line.
1 -> -1/1 -> -1
Best of Luck!
