9514 1404 393
Answer:
3. yes: a[1] = -8, a[n] = a[n-1] +7; an = -8 +7(n -1)
4. no (no common difference)
Step-by-step explanation:
An arithmetic sequence is one in which each term has the same difference from the term before it.
__
3. -1 -(-8) = 7; 6 -(-1) = 7; 13 -6 - 7. The differences are all 7, so the terms have a common difference. This sequence is arithmetic.
The general form of the recursive rule for an arithmetic sequence with first term a1 and common difference d is ...
a[1] = a1; a[n] = a[n-1] +d . . . . . recursive rule
a[1] = -8; a[n] = a[n-1] +7
The general form of the explicit rule for an arithmetic sequence is ...
an = a1 +d(n -1)
an = -8 +7(n -1)
__
4. The differences are ...
8 -1 = 7; 27 -8 = 19; 81 -27 = 54 . . . the differences are not common
This sequences is not arithmetic.
A vertical parabola goes through (-2,-18), (3, -13), and (5, -39). Use matrices to solve for D, E, and F,
given the general form x2 + y2 + Dx + Ey + F = 0 (since it is a vertical parabola there is not a
yż term).
The general formula for the parabola is [tex]x^{2}+y^{2}-21\cdot x +51\cdot y +548 = 0[/tex].
We need the knowledge of three distinct points to determine all coefficients of the vertical parabola based on the following general formula:
[tex]x^{2} + y^{2} + D\cdot x + E\cdot y + F = 0[/tex] (1)
If we know that [tex](x_{1}, y_{1}) = (-2, -18)[/tex], [tex](x_{2}, y_{2}) = (3,-13)[/tex] and [tex](x_{3}, y_{3}) = (5,-39)[/tex], then we have the following system of linear equations:
[tex]-2\cdot D -18\cdot E + F = -328[/tex] (2)
[tex]3\cdot D -13\cdot y + F = -178[/tex] (3)
[tex]5\cdot D -39\cdot E + F = -1546[/tex] (4)
The solution of the system of equations is: [tex]D = -21[/tex], [tex]E = 51[/tex], [tex]F = 548[/tex].
The general formula for the parabola is [tex]x^{2}+y^{2}-21\cdot x +51\cdot y +548 = 0[/tex].
We kindly invite to check this question on parabolae: https://brainly.com/question/4074088
You just paid $435,000 for a policy that will pay you and your heirs $17,300 per year forever with the first payment in one year. What rate of return are you earning on this policy?
Answer:
3.98%
Step-by-step explanation:
R = $17,300/$435,000 = .0398, or 3.98%
Select the action you would use to solve 3x = 12. Then select the property
that justifies that action.
Select all that apply.
O A. Action: Add 3 to both sides.
B. Action: Multiply both sides by 3.
O C. Action: Divide both sides by 3.
D. Property: Addition property of equality
O E. Property: Multiplication property of equality
F. Property: Division property of equality
Answer:
C. Action: Divide both sides by 3.
F. Property: Division property of equality
Step-by-step explanation:
you are trying to get x by itself so if you divide by 3 you are taking the 3 from x, and what you do to one side you do to the other.
Answer:
C. Action: Divide both sides by 3.
F. Property: Division property of equality.
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other.
First, divide 3 from both sides of the equation:
(3x)/3 = (12)/3
x = 12/3
x = 4
C. Action: Divide both sides by 3.
F. Property: Division property of equality.
~
Help me please:) ✨✨✨✨✨✨✨✨✨✨
Hello there I think the measure of EBC is 58 degrees.
That's because angles EBC and DBE are complementary. it means that they add up to 90 degrees.
We are given that
DBE=32 degrees.
And we know that angles EBC and DBE add up to 90 degrees.
So we take 90 and subtract the measure of angle DBE (32 degrees)
90-32=58
Hope this helps!
[tex]GraceRosalia[/tex]What is the area of a circle with a radius of 6 inches?
9 pi in^2
12 pi in^2
36 pi in^2
81 pi in^ 2
Answer:
Area of circle = πr² ( Putting π = 22/7) Area = 3.14×6×6Area = 113.04Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
The lines 5x+2y=14 and y=-5x+9 are?
A: Parallel
B: Perpendicular
C: Neither
An insurer knows that the proportion of smokers in a population is 0.3. Furthermore, it is known that: 40% of applicants who are smokers say they do not smoke on their applications. None of the non-smoking applicants are lying on their application.
Calculate what is the probability that one of the applicants says that he does not smoke, and that in fact do not smoke.
===================================================
Explanation:
Let's say this population had 1000 people. You can pick any number you want, but I'm going for some nice big round number to work with.
The proportion of smokers is 0.3, which means 0.3*1000 = 300 people in this population are smokers and 1000-300 = 700 are nonsmokers.
Of the 300 people who do smoke, 40% of them lie on the application. This means 0.40*300 = 120 people lied. These 120 people say they don't smoke, but in fact they do smoke.
So if we were to survey this population, then 700+120 = 820 people would say they don't smoke
Only considering the people who write "don't smoke" on the survey, which is that 820 figure, 700 of them are true nonsmokers. Therefore, the probability we want is 700/820 = 0.8537 approximately
Plz help me thank you
Answer:
159.29-159.29(5/100)=151. 3255
what is 13.6 - x = -64.2
Answer:
13.6 - x = -64.2
Step-by-step explanation:
x = 77.8
13.6 - 77.8 = -64.2 True!
Answer:
x=77.8
Step-by-step explanation:
13.6-x=-64.2
-13.6. -13.6
---------------------
since there is already -x it wouldn't be -77.8 bc that would cancel it out
A bird flies at an altitude of 520 feet. A diver dives to a depth of 50 feet below sea level. What is the difference in their elevations? Show how you arrived at your answer.
Answer:
The answer is 570 feet.
Step-by-step explanation:
First, the bird is 520 feet HIGH.
The diver is 50 feet BELOW sea level, which is also -50.
To find the difference, you would SUBTRACT right?
So 520 - -50 OR 520 + 50 (This is because two negatives make a positive, and you are also subtracting negatives, which in turn means adding).
520 + 50 = 570 - HOPE THIS HELPED!
Solve the attached question.
No spam!
Step by step explanation needed!
[tex]▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ { \huge \mathfrak{Answer}}▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ [/tex]
The value of given expression is 2
Solution is in attachment ~
Wxy is a right triangle.
Answer:
B. False
Step-by-step explanation:
To check if its a right angle triangle, you need to check if pythagoras' theorem works:
a² + b² = c²
(√17)² × (√17)² = 289 which is not equal to (√34)²
What is the slope of this graph?
Find the derivative of f(x) =4cot(x) + 10 sin(x)
d/dx cot(x) = -csc²(x)
d/dx sin(x) = cos(x)
So, if f(x) = 4 cot(x) + 10 sin(x), then
f '(x) = -4 csc²(x) + 10 cos(x)
PLEASE HELP ITS MATH THANK YOUUUU
Answer:
2inch=1 foot
Step-by-step explanation:
so 2 to 1 2:1
5. In (triangle) ABC, what is the expression for the length of BC? A sin 38/15 b.15sin 87/sin 38 c.15sin 55/sin 38. D, sin 87/15 sin 38
e. Sin 38/15 sin 87.
A
15 (55 triangle 38)
C
B
If f(x)=4x2−2x+8, then calculate f(2 )
What is the answer?
Answer:
f(x)=4x2−2x+8,
or, f(2)=4*2*2-2*2+8
or,f(2)=16-4+8
or,f(2)=20....
f(2)=20
Find the area of right triangle def,round to nearest tenth if necessary D(-6,-1),E(1,-3),F(3,4)
HELP
Answer:
Step-by-step explanation:
Two of the legs will be at right angles to each other and have negative reciprocal slopes. Area will be half of the product of these two legs.
slope of DE (-3 - (-1)) / (1 - (-6)) = -2/7
slope of EF (4 - (-3)) / (3 - 1) = 7/2
so these two are perpendicular
check the DF line to be certain
slope of DF (4 - (-1)) / (3 - (-6)) = 5/9
Length of DE = √(-2² + 7²) = √53
Length of EF = √(7² + 2²) = √53
Area of triangle
A = ½√53√53 = 26.5 units²
Find the sum of the following fractions. Your answer needs to be a mixed number in simplest form: 4/5 + 2/9
Answer:
1 1/45
Step-by-step explanation:
What is the answer for this question?
Answer:
I don't know sorry.....
I’m so lost i have no idea how to get the function please see pic
You should first recognize the shape of the curve - it's an exponential function, so its equation takes the form [tex]y(x)=a\cdot b^{cx}[/tex] for some constants a, b, and c.
The curve lies above the x-axis, so a must be positive.
The curve is defined everywhere (there are no discontinuities), so b must be positive.
As you move left to right, the function is increasing, so c must also be positive. But to make things simpler, let's assume c = 1.
When x = 0, the curve passes through the point (0, 1). In our equation, we have
[tex]y(0) = a\cdot b^0 = a[/tex]
so it follows that a = 1.
When x = 1, the curve approximately passes through the point (1, 4); so
[tex]y(1) = b^1 = 4[/tex]
so b = 4.
Then the equation of the curve might be [tex]\boxed{y = 4^x}[/tex].
Evaluate the expression when x=-6
Answer:
Step-by-step explanation:
x² + 5x - 5 = (-6)² + 5*(-6) - 5
= 36 - 30 - 5
= 36 - 35
= 1
Answer:
1
Step-by-step explanation:
-6^(2)+5(-6)-5
36 + 5(-6) -5
36- 30- 5
6 - 5
1
What is the inverse of f(x) = 1/3x + 2 ?
A. h(x) = 1/3x + 2
B. h(x) = 1/3x - 2
C. h(x) = 3x - 2
D. h(x) = 3x - 6
Pls provide an explanation. I need help, and I will mark the person who helps me understand this Brainliest.
Answer:
D
Step-by-step explanation:
We are given the function:
[tex]\displaystyle f(x) = \frac{1}{3} x + 2[/tex]
And we want to find its inverse h.
To find the inverse of a function, we can switch the y and x variables and solve for the new y. This will be our inverse.
We begin with:
[tex]\displaystyle f(x) = y = \frac{1}{3} x+ 2[/tex]
Switching the variables yield:
[tex]\displaystyle x = \frac{1}{3}y + 2[/tex]
And solving for y yields that:
[tex]\displaystyle y = h(x) = 3x - 6[/tex]
In conclusion, the inverse function to f is 3x - 6. Our answer is D.
To understand why we switch the variables, recall that by the definition of inverse functions, if f(a) = b, then f⁻¹(b) = a. So, by switching the variables, we are essentially solving for f⁻¹(x).
FI h(x) = 3x + 8 , h(a) = 29 then what is the value of a?
Answer:
the value of a = 7..............
Answer:
[tex]h(x) = 3x + 8 \\ h(a) =3 a + 8 [/tex]
But, it is given that
[tex]h(a) = 29[/tex]
Therefore,
[tex]3a + 8 =29 \\ 3a = 29 - 8 \\ 3a = 21 \\ a = \frac{21}{3} \\ \boxed{ a = 7}[/tex]
Hence, the value of a is 7
a = 7 is the right answer.HELP ME ASAPPPP I HAVE 12 MIN LEFT
Answer:
The sum is about 22
Step-by-step explanation:
When you round the values at the ones place, you get:
7 + 6 + 9 = 22
Answer:22
Step-by-step explanation:
Please help! I have 10 mins to do this! (-4.5 x 8.61 x (-2/9)
Or look at the picture! I will mark BRAINLIEST as well
Answer:
8.61
Step-by-step explanation:
Answer:
8.61 I think try that okay
Please help with this question asap
8. What angle do the hour and minute hands of a clock form when it is exactly 9.00p.m.?
Answer:
90 degrees
Step-by-step explanation:
please say thanks
the first discount on a certain laptop was 15% the second was 28% after two discounts the price become $306. What was the original price?
Answer:
$437.58
Step-by-step explanation:
15% + 28%
= 43%
43/100 × 306
= $131.58
$131.58 + $306
= $437.58
HELP!
Ruben, Shelly, and Malcolm have recorded a hit song. Ruben gets 2/5 of the income, Shelly gets 1/3, and Malcolm gets the rest. If they earn $300,000, how much does Malcolm earn?
Answer:
$ 80,000
Step-by-step explanation:
2/5 + 1/3 = (6 + 5)/15 = 11/15
15/15 - 11/15 = 4/15
4/15 of 300,000
4/15 x 300,000 = 1,200,000/15 = 80,000