Answer:
(a).
[tex]S_{n} = \frac{n}{2} (4n + 20) \\ \\S _{n - 1} = \frac{(n - 1)}{2} (4n - 4 + 20) \\ \\ S _{n - 1} = \frac{(n - 1)}{2} (4n + 16) \\ \\S _{n - 1} = \frac{(n - 1)(4n + 16)}{2} \\ \\ { \boxed{S _{n - 1} = {2 {n}^{2} + 6n - 8}}} \\ [/tex]
(b).
from general equation:
[tex]S _{n - 1} = \frac{(n - 1)}{2} (4n + 16)[/tex]
first term is 4n
common difference:
[tex]16 = \{(n - 1) - 1 \}d \\ 16 = (n - 2)d \\ d = \frac{16}{n - 2} [/tex]
Which of the following is equivalent to the radical expression below when
x20?
VAX 1X+7
A. x 47
B. VAXA + 20%
C. VAMAX
D. X* 20%
Answer:
B in the photo
Step-by-step explanation:
another way to write the problem:
square root is also taking the 1/2 power:
[tex](4x)^{1/2} * (x+7)^{1/2} \\[/tex]
since they are raised to the same power:
[tex](4x * (x+7))^{1/2}\\(4x^2 + 28x)^{1/2}\\\\=\sqrt{4x^2 + 28x}[/tex]
Can anyone help me to solve this question ??
find the zeroes for P(x)=6x³-13x²+x+2 given 0.5 is one of the zeroes
The answers :
-1/3 , 0.5 , 2
Step-by-step explanation:
that means the expression is the result of a multiplication with (x-0.5) being one factor.
so, we divide the whole expression by this and then deal with the remaining quadratic equation.
6x³ - 13x² + x + 2 / x - 0.5 = 6x² - 10x - 4
- 6x³ - 3x²
----------------------------
- 10x² + x + 2
- - 10x² + 5x
----------------------------
- 4x + 2
- - 4x + 2
----------------------------
finished. 0
so, the whole expression is also
P(x) = (x-0.5)×(6x² - 10x - 4)
now we need to find the 2 zero points of the quadratic part.
the general solution to a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
a = 6
b = -10
c = -4
x = (10 ± sqrt(100 - 4×6×-4))/12 =
= (10 ± sqrt(100 + 96))/12 = (10 ± sqrt(196))/12 =
= (10 ± 14)/12
x1 = (10+14)/12 = 24/12 = 2
x2 = (10-14)/12 = -4/12 = -1/3
WHY DOES NO ONE ANSWER MY QUESTIONS?? Its kinda annoying that i answer others' questions but no one answers mine. Well if anyone feels like helping me heres my question:
A mathematician reported the results from a particular experiment to the researcher who conducted it. The report states that on one specific part of the experiment, a statistical test result yielded a p-value of 0.21. Based on this p-value, what should the researcher conclude?
The test was not statistically significant because 2 × 0.21 = 0.42, which is less than 0.5.
The test was statistically significant because a p-value of 0.21 is greater than a significance level of 0.05.
The test was not statistically significant because if the null hypothesis is true, one could expect to get a test statistic at least as extreme as that observed 79% of the time.
The test was not statistically significant because if the null hypothesis is true, one could expect to get a test statistic at least as extreme as that observed 21% of the time.
The test was statistically significant because p = 1 − 0.21 = 0.79, which is greater than a significance level of 0.05.
Answer:
The test was not statistically significant because if the null hypothesis is true, one could expect to get a test statistic at least as extreme as that observed 21% of the time.
Step-by-step explanation:
This is the right answer,since this result is only observed 21% of the time, so in general it's not significant, so the first 2 are eliminated. The 2 x 0.21 doesn't matter since, the percent is 21% not 42%, so it doesn't even matter. The last question we eliminate is:"The test was not statistically significant because if the null hypothesis is true, one could expect to get a test statistic at least as extreme as that observed 79% of the time" 79% of the time is a pretty good amount to say it's significant, but it only says 21% of the time.So, it leaves us with:The test was not statistically significant because if the null hypothesis is true, one could expect to get a test statistic at least as extreme as that observed 21% of the time.
Hope this helps lol (: is this a psat or somethin?
In the proof of the Law of Cosines, the equation [tex]c^2=h^2+(b-x)^2[/tex] was created using the Pythagorean theorem. Which equation is a result of expanding [tex](b-x)^2[/tex]?
A [tex]c^2=h^2+b^2-x^2[/tex]
B [tex]c^2=h^2+b^2-2bx+x^2[/tex]
C [tex]c^2=h^2+b^2+x^2[/tex]
D [tex]c^2=h^2+b^2-2bx-x^2[/tex]
9514 1404 393
Answer:
B c² = h² + b² -2bx +x²
Step-by-step explanation:
The square of the binomial can be expanded using the distributive property:
c² = h² +(b -x)²
c² = h² +(b -x)(b -x)
c² = h² +b(b -x) -x(b -x)
c² = h² +b² -xb -bx +x²
c² = h² +b² -2bx +x² . . . . . matches choice B
is a graph with asymptotes discontinious?
Answer:
In order for the function to be discontinuous at an asymptote, the curve needs to exist on both sides of the asymptote. If the curve only exists on one side of the asymptote, then there's no discontinuity at that point.
Step-by-step explanation:
What is the measure of angle 1?
Answer:
Angle 1 is 129
Step-by-step explanation:
You do not need to solve the (3x+3) because you can see that these lines are parallel, so you can simply do 180-51 to get angle 1.
What’s the answer ASAP
Answer:
none
Step-by-step explanation:
38×2=76
43×2=86
45×2=90
x + 3 and x + 2.....
Answer:
x+x+5=10
Step-by-step explanation:
ya
Answer:
x+3+x+2
X+x+3+2
2x+5
Step-by-step explanation:
mark me as brainliest
what is the scale factor from the original copy?
Answer:
Step-by-step explanation:
Oi boa tarde tudo bem
the numeral 16 is a _____ of 4 because it is the product of a given number sbd any whole number
Answer:
perfect square
Step-by-step explanation:
A perfect square is a number multiplied by itself:
16 = 4^2 = 4 * 4
Evaluate: 24 - ( 5 - 3)^ 4
______________
4
24 - (5 - 3)⁴ = 24 - 2⁴ = 24 - 16 = 8
8 : 4 = 2 ← the end solution
Jazmine is on a trịp to San Antonio, a distance of 330 km. She only has 3.5 hours to get to a job interview there. She gets stuck in traffic for the first 1.5 hours out of Houston and averages a speed of 60 km/hr. In order to not be late, what speed does she need to travel for the rest of the trip? (Organize your information carefully - total, first part, second part)
Answer:
Jazmine must travel for the rest of the trip at 120km/hr.
Step-by-step explanation:
To find the speed for the latter half of the trip necessary to arrive on time, we can divide the remaining distance by the remaining time.
The remaining distance, in km, is found by subtracting the distance already covered, which is the product of the speed during the first part of the trip and the elapsed time during this part, from the total distance:
[tex]330-1.5\times60=330-90=240[/tex]
The remaining time, in hr, is found by subtracting the elapsed time during the first part from the total time limit:
[tex]3.5-1.5=2[/tex]
Therefore, the necessary speed in km/hr is:
[tex]\frac{240}2=120[/tex]
18- 3 (2) = ?
show your work
help pls lol thanks
Answer:
12 is the answer
Step-by-step explanation:
18- 3×2= 18- 6 = 12
Gavin and Jim win some money and share it in the ratio 5:2. Gavin gets £39 more than Jim. How much did they get altogether?
Answer:
They got $91 in total
Step-by-step explanation:
I did some trial and error and when I reached 65 dollars for Gavin I realized that Jim would be $29. So 65 - 29 = $39. Btw substitute $ for £
Answer: £91
Step-by-step explanation:
Let x be the amount of money Jim gets
Let x + 39 be the amount of money Gavin gets
Given information
Ratio = 5 : 2 (Gavin to Jim)
Jim = x
Gavin = x + 39
Set up proportion
5 / 2 = (x + 39) / x
Cross multiply to reduce fraction form
5x = 2 (x + 39)
Expand parentheses and apply the distributive property
5x = 2 · x + 2 · 39
5x = 2x + 78
Subtract 2x on both sides
5x - 2x = 2x + 78 - 2x
3x = 78
Divide 3 on both sides
3x / 3 = 78 / 3
x = 26
Find the amount of money they get altogether
Gavin + Jim
=x + 39 + x
=(26) + 39 + (26)
=65 + 26
=[tex]\boxed{91}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
the sum of 3 and a number
Answer:
the number will vary the answer
Step-by-step explanation:
3×1=3
3×2=6
An elevator at a construction site has a maximum capacity of 3325 pounds. If the elevator operator weighs 225 pounds and each cement bag weighs 75 pounds, how many bags of cement can be safely lifted on the elevator in one trip?
$8,375.79 to the nearest thousand
Answer:
$8,000
Step-by-step explanation:
8,375.79 < 8,500 so it will round to 8,000
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
test the validity of the following whenever he participates in a race, he is the winner. either he participates in the race or he is sick he is not the winner. therefore he is sick
To test the validity of a given argument, we need to see if we can find a counter-example that makes one of the statements non-valid. If after analyzing the statements we can't find a counterargument, then we can conclude that the argument is valid.
Here we will find that the argument is valid.
We can write this as:
If he participates in a race then he is the winner.
Either he participates in the race, or he is sick.
He is not the winner, then, he is sick.
Now, from the first statement, we know that always that this person participates in a race, he wins.
From the second statement we know that he only participates if he is not sick, we can rewrite that one as:
"If he is sick, then he does not participate in the race".
Finally, from the third one, if he does not win, then he is sick.
This makes sense, he only does not participate when he is sick, then the only races where he is not the winner, are these races where he does not participate, and he does not participate only if he is sick, then this is a valid argument.
Concluding, the 3 statements are valid, as we can't find any counterargument to any of these 3.
If you want to learn more, you can read:
https://brainly.com/question/7747645
5. Tristan wants to build a square garden in his backyard that will cover an area of 75 ft². If Tristan has 32 feet of material for the perimeter of the garden, does he have enough? Explain.
Lets find side
Area=75ft^2[tex]\\ \sf\longmapsto Area=(side)^2[/tex]
[tex]\\ \sf\longmapsto (side)^2=75[/tex]
[tex]\\ \sf\longmapsto side=8.3ft[/tex]
Perimeter
[tex]\\ \sf\longmapsto 4(side)[/tex]
[tex]\\ \sf\longmapsto 4(8.3)[/tex]
[tex]\\ \sf\longmapsto 33.2[/tex]
He has 1.2ft short materialBenchmark of 6/10, how do I get this worked out
Answer:
0.60 or 60% is the answer!
Step-by-step explanation:
Hope I helped
Can I have some help, please?
Answer:
[tex]-3(t+1)(8t-3)[/tex]
Step-by-step explanation:
First, factor both the denominators completely:
[tex]9-24t\\= 3(3-8t)\\= 3(-8t+3)\\= -3(8t-3)[/tex]
[tex]8t^2+5t-3\\= 8t^2+8t-3t-3\\= 8t(t+1)-3(t+1)\\= (8t-3)(t+1)[/tex]
Now, we can see that the factors of the first denominator are -3 and 8t-3.
The factors of the second denominator are t+1 and 8t-3.
To find the LCD, multiply all of these factors together:
[tex]-3(t+1)(8t-3)[/tex]
Notice how we only multiply 8t-3 in the equation once. This is because it was present in both denominators, unlike the other factors.
I hope this helps!
A store advertises a sale on t-shirts. The advertised price is four t-shirts for $48. Write and solve an equation to find the cost of one t-shirt.
a.) $8
b.) $12
c.) $16
d.) $48
g(x) = sqr root of x+3
What is the domain of g?
Answer:
[tex]all \: real \: numbers \: except \: \\ x + 3 < 0 \\ \: \: \: \: x < - 3[/tex]
Answer:
X is the domain and sqr root of X+3 is the range.
Which of the following is not a polynomial?
O A. 3x4
O B. x8+2x3 +7
O C. 5x10 - 4x8 + 2
O D. 5- x2 + 7x0
Answer:
C
Step-by-step explanation:
is not a polynomial because it has a negative exponent.
Which of the following is equal to 4 and 1 over 2 divided by 2 and 2 over 3?
Answer:
4.91666666667
Step-by-step explanation:
this is what i got
either 9/2 x 8/3 or 9/2 x 3/8
3/8 of a scholarship fund was 1500 find the full amount of the scholarship fund
Answer:
The full scholarship fund will be 4000
Step-by-step explanation:
When doing these types of problems I like to do this.
1500 ÷ 3 = 500 (We do this because you want to find out what 1/8 is)
Since 500 is 1/8 of the part, all you have to do is multiply 500 by 8
500 × 8 = 4000
HELP PLS IM BEGGING YOU PLS HELP, its due todayyy pls. Angle CBD is the only one i got right and the rest is wrong. I dont know how to answer it anymore.
Answer:
try It would be number 81
Step-by-step explanation:
Abc= 110
ceo=70
dbe=110 or 120
and abe= 60 70 or 81
Answer:
ABC=112 degrees
DBE=112 degrees
ABE=68 degrees
Step-by-step explanation:
CBD=ABE
ABE=68 degrees
First let's take these as X,
ABC=DBE=X(Vertically opposite angles)
ABC+DBE+CBD+ABE=360(angles around a point)
x + x +68 +68 =360
2x +136 =360
2x =360-136
2x = 224
x =112 degrees
therefore;
ABC=112 degrees
DBE=112 degrees
S...
Find the length of UT.
12
T
14
W
2x+2
2x + 5
V
A. 32
B. 43
O o
C. 21
D. 39
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Answer:
A. 32
Step-by-step explanation:
The relationship between segment lengths is ...
WT·WU = WC·WV
14(2x +2) = 12(2x +5)
28x +28 = 24x +60
4x = 32
2x = 16
Then the measure we're after is ...
UT = WT +WU = 14 +(16 +2)
UT = 32
solve this equation 2(y + 2) = 3(y - 7)
Answer:
[tex]2(y + 2) = 3(y - 7) \\ 2y + 2 \times 2 = 3y - 3 \times 7 \\ 2y + 4 = 3y - 21 \\ y \: terms \: togther \\ 3y - 2y = 4 + 21 \\ y = 25[/tex]
[tex]thank \: you[/tex]
Maggie studied for 2/5 of an
hour. Julie studied for 1/4 of an
hour. How much longer did
Maggie study?
Answer: 3/20
Concept:
When encountering questions that ask for [how much longer A comparing to B], the basic operation would be the value of A subtracted by the value of B.
Solve:
Given information
Maggie study time = 2/5 hours
Julie study time = 1/4 hours
Given expression deducted from the concept
Maggie (study time) - Julie (study time)
Substitute values into the expression
2/5 - 1/4
Find the denominators' Least Common Multiple (LCM)
First five multiples of 5: 5, 10, 15, 20, 25
First five multiples of 4: 4, 8, 12, 16, 20
Since [20] is the first term that appears in both multiples, it would be the LCM of 4 and 5
Convert the fractions to common denominator
2/5 = (2 × 4) / (5 × 4) = 8 / 20
1/4 = (1 × 5) / (4 × 5) = 5 / 20
Simplify by subtraction
=8/20 - 5/20
=(8 - 5) / 20
=[tex]\boxed{\frac{3}{20} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
