In any artihmetic sequence, consecutive terms differ by a fixed constant c. So given the first term a, the second term is a + c, the third terms is a + 2c, and so on, up to the n-th term a + (n - 1)c.
If the 15th term is 40, then
40 = -12 + (15 - 1) c ==> c = 52/14 = 26/7
We can then write the n-th term as
-12 + (n - 1) 26/7 = (26n - 110)/7
The sum of the first 15 terms is then
[tex]\displaystyle \sum_{n=1}^{15}\frac{26n-110}7 = \frac{26}7\sum_{n=1}^{15}n - \frac{110}7\sum_{n=1}^{15}n = \boxed{210}[/tex]
Another way to compute the sum: let S denote the sum,
S = -12 - 58/7 - 32/7 + … + 228/7 + 254/7 + 40
Reverse the order of terms:
S* = 40 + 254/7 + 228/7 + … - 32/7 - 58/7 - 12
Notice that adding up terms in the same position gives the same result,
-12 + 40 = 28
-58/7 + 254/7 = 28
-32/7 + 228/7 = 28
so that
S + S* = 2S = 28 + 28 + 28 + … + 28 + 28 + 28
There are 15 terms in the sum, so
2S = 15×28 ==> S = 15×28/2 = 210
What is the solution to the inequality x2 < 16 – 6x?
Question 7 options:
A)
x < –8 or x > 2
B)
x < –8 and x > 2
C)
–8 ≤ x ≤ 2
D)
–8 < x < 2
Answer:
D
Step-by-step explanation:
2x < 16 - 6x
Bring the variables to one side
2x < 16 - 6x
+6x +6x
8x < 16
Divide both sides by the coefficient
8x/8 < 16?8
x < 2
The distance AB rounded to the nearest tenth = [?]
Answer:
4.5 units
Step-by-step explanation:
Use the distance formula
[tex]\sqrt{(-1-3)^{2}+(-1-1)^{2} }[/tex]
[tex]\sqrt{16+4}=\sqrt{20}[/tex]
The distance AB on the diagram rounded to the nearest tenth is: 4.5 units
Meaning of DistanceDistance can me defined as a measure that tells us how far apart two objects or individual are to each other.
Distance is very important as it helps us know where exactly things are located and whether they are close or far apart
In conclusion, The distance AB on the diagram rounded to the nearest tenth is: 4.5 units
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Please answer this!!
Answer:
BC = 6.8
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta =opp /adj
tan C = AB / BC
tan 45 = 6.8/ BC
BC = 6.8 / tan 45
BC = 6.8 / 1
BC = 6.8
Answer: Choice D. 6.8
Step-by-step explanation:
45,45,90 triangles, memorize that the short sides are equal to each other in length and are [tex]\frac{1}{\sqrt{2} }[/tex] the length of the long side.
Instructions: Find the missing side. Round your answer to the nearest
tenth.
22
х
50°
X =
Answer:
x = 16.9
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 50 = x/22
22 sin 50 =x
x=16.85297
To the nearest tenth
x = 16.9
Find the value of x.
A. 176
B. 256
C. 74
D. 128
Answer: D
Step-by-step explanation: Using the angle formed by two chords theorem, angle X is equal to 1/2 times the sum of the degree measures of the two arcs.
The angle x will be equal to 128 degrees. The correct answer is option D.
What are the Angles of Intersecting Chords Theorem?When two chords cross inside of a circle, the resulting angle's measure is equal to the product of the lengths of the arcs it intercepts and its vertical angle, divided by two.
The angle x will be calculated as below:-
Angle x = Sum of angles made by two intersecting chords / 2
Angle x = ( 54 + 202 ) / 2
Angle x = ( 256 / 2 )
Angle x = 128 degrees
Therefore, the angle x will be equal to 128 degrees. The correct answer is option D.
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it's emergency pls.
Answer:
see above there is the answer sorry for rough
can someone explain step by step how to get the answer?
Answer: x³+8x²+11x-20
Step-by-step explanation:
To find which polynomial has the roots of -5, -4, and 1, we want to first put them into an equation.
-5 is the same as x+5=0
-4 is the same as x+4=0
1 is the same as x-1=0
Now that we have the factors, we can multiply them together.
(x+5)(x+4)(x-1) [FOIL]
(x²+4x+5x+20)(x-1) [combine like terms]
(x²+9x+20)(x-1) [FOIL]
x³-x²+9x²-9x+20x-20 [combine like terms]
x³+8x²+11x-20
Therefore, x³+8x²+11x-20 is the correct polynomial with those roots.
Davina uses a diagram to demonstrate the Pythagorean Theorem.
3
hypotenuse
How are the squares related to the sides of the triangle?
The area of each square is equal to the square of the length of the side to which it is adjacent.
The area of each square is equal to the length of the side to which it is adjacent.
The sum of the areas of the squares is equal to the square of the perimeter of the triangle.
The perimeter of each square is twice the length of the side of the triangle squared.
Answer:
the first option : The area of each square is equal to the square of the length of the side to which it is adjacent.
Use the grouping method to factor this polynomial.
x2 + 2x2 + 12x + 24
O A. (x2 +12)(x+2)
O B. (x2 +6)(x+2)
C. (x² + 2)(x+6)
O D. (x2 + 2)(x+12)
Answer:
A. (x² + 12)·(x + 2)
Step-by-step explanation:
Question; Factor x³ + 2·x² + 12·x + 24, using the grouping method
The given polynomial is presented as follows;
x³ + 2·x² + 12·x + 24
Using the grouping method, we have;
(x³ + 2·x²)( + 12·x + 24)
Which gives;
x²·(x + 2) + 12·(x + 2)
Therefore, we get;
(x² + 12)·(x + 2)
The correct option is A. (x² + 12)·(x + 2).
please tell me the angle of elevation
Answer:
32°
Step-by-step explanation:
The model forms a triangle. The sum of the angles of a triangle is 180°. Solve with the following equation:
? + 90 + 58 = 180
? + 148 = 180
? = 32
Therefore, the angle of elevation is 32°.
Write an equation in slope-intercept form for the line with slope -4 and y-intercept - 1. Then graph the line.
Answer:
I posted the steps in my photos for an answer.
Kay left her computer running for 2~ days. How many hours did she leave her computer running for?
she left her computer open for 48 hours
HELPPPP
You invest $2700 in an account at 1.5% per year simple interest. The equation
that represents this scenario is:
A(n) = 2700 + (n - 1)(0.015. 2700)
How much will you have in the account in year 5? Round your answer to the
nearest dollar.
[tex]\sqrt{\frac{x-4\sqrt{x}+4 }{x+4\sqrt{x} +4} }[/tex]
Answer:
\begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}
\begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)=1\:\\ \:\mathrm{Interval\:Notation:}&\:f\left(x\right)=1\end{bmatrix}
Step-by-step explanation:
TIME REMAINING
43:02
Which ordered pair makes both inequalities true?
y < –x + 1
y > x
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, 0). Everything below and to the left of the line is shaded. The second dashed line has a positive slope and goes through (negative 1, negative 1) and (1, 1). Everything above and to the left of the line is shaded.
(–3, 5)
(–2, 2)
(–1, –3)
(0, –1)
Mark this an
the answer of this question is (-2,2)
Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.
Answer:
[tex]6+2\sqrt{21}\:\mathrm{cm^2}\approx 15.17\:\mathrm{cm^2}[/tex]
Step-by-step explanation:
The quadrilateral ABCD consists of two triangles. By adding the area of the two triangles, we get the area of the entire quadrilateral.
Vertices A, B, and C form a right triangle with legs [tex]AB=3[/tex], [tex]BC=4[/tex], and [tex]AC=5[/tex]. The two legs, 3 and 4, represent the triangle's height and base, respectively.
The area of a triangle with base [tex]b[/tex] and height [tex]h[/tex] is given by [tex]A=\frac{1}{2}bh[/tex]. Therefore, the area of this right triangle is:
[tex]A=\frac{1}{2}\cdot 3\cdot 4=\frac{1}{2}\cdot 12=6\:\mathrm{cm^2}[/tex]
The other triangle is a bit trickier. Triangle [tex]\triangle ADC[/tex] is an isosceles triangles with sides 5, 5, and 4. To find its area, we can use Heron's Formula, given by:
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex], where [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are three sides of the triangle and [tex]s[/tex] is the semi-perimeter ([tex]s=\frac{a+b+c}{2}[/tex]).
The semi-perimeter, [tex]s[/tex], is:
[tex]s=\frac{5+5+4}{2}=\frac{14}{2}=7[/tex]
Therefore, the area of the isosceles triangle is:
[tex]A=\sqrt{7(7-5)(7-5)(7-4)},\\A=\sqrt{7\cdot 2\cdot 2\cdot 3},\\A=\sqrt{84}, \\A=2\sqrt{21}\:\mathrm{cm^2}[/tex]
Thus, the area of the quadrilateral is:
[tex]6\:\mathrm{cm^2}+2\sqrt{21}\:\mathrm{cm^2}=\boxed{6+2\sqrt{21}\:\mathrm{cm^2}}[/tex]
Solve 2x−10y=18 for x.
Answer:
x = 5y + 9
Step-by-step explanation:
2x - 10y = 18
(2x - 10y) + 10y = 18 + 10y
2x - 10y + 10y = 10y + 18
2x = 10y + 18
x = 5y + 9
In the SuperLottery, three balls are drawn (at random) from ten white balls numbered from $1$ to $10$, and one SuperBall is drawn (at random) from ten red balls numbered from $11$ to $20$. When you buy a ticket, you choose three numbers from $1$ to $10,$ and one number from $11$ to $20$.
If the numbers on your ticket match the three white balls and the red SuperBall, then you win the jackpot. (You don't need to match the white balls in order). What is the probability that you win the jackpot?
This question is solved using probability concepts.
A probability is given by the number of desired outcomes divided by the number of total outcomes.The order in which the balls are chosen don't matter, which means that the combinations formula is used to find the number of outcomes.Doing this, we get that:
[tex]\frac{1}{1200}[/tex] probability that you win the jackpot.
------------------------------------------
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
----------------------------------------------------
Total outcomes:
3 white from a set of 10(numbered from $1 to $10).1 red from a set of 10(numbered from $11 to $20).Thus:
[tex]T = C_{10,3}C_{10,1} = \frac{10!}{7!3!} \times \frac{10!}{1!9!} = 120 \times 10 = 1200[/tex]
Desired outcomes:
The correct balls, order does not matter, so only one outcome, that is, [tex]D = 1[/tex]
What is the probability that you win the jackpot?
[tex]p = \frac{D}{T} = \frac{1}{1200}[/tex]
[tex]\frac{1}{1200}[/tex] probability that you win the jackpot.
A similar question is given at https://brainly.com/question/23966554
Answer:
6/7200=1/1200
Step-by-step explanation:
[3! ways to arrange the three white balls] over [10x9x8 ways to pick three white balls and 10 ways to pick a red] =3x2x1/10x9x8x10=6/72x100=6/7200=1/1200
<(-_-)>__ConNelL__>(-_-)<
Show that (x+1)(x+3)(x+5) can be written in the form ax3+bx2+cx+d where a b c and d are all positive intergers
Answer:
Step-by-step explanation:
(x+1)(x+3)(x+5), multiply first two parenthesis
(x² +3x +x +3)(x+5), combine like terms
(x² +4x +3) (x+5), multiply the parenthesis
(x³ +5x² +4x² +20x +3x +15), combine like terms
x³ +9x² +23x +15 is in the form ax³ +bx² +cx +d
a=1, b=9, c=23, d=15 are all positive integers
convert f(x) = 5x(x – 6) to standard form
Answer:
[tex]5x^{2} - 30x[/tex]
Step-by-step explanation:
A father is 51 years old and his son is 19. How many years ago was the father 5 times his son's age?
Answer:
x=11
Step-by-step explanation:
51-x-5*19= -5x
51-5*19= -4x
4x=5*19-51
4x=95-51
4x=44
x=11
Step-by-step explanation:
let x year ago son age was 5 time his father age.
age of son before x year = 19-x
age of father before x year = 51-x
NOW
according to the question
5(19-x) =51-x
95-5x =51-x
95-51 = -X-5x
44 = 4x
x=11
so your ans is 11years ago
A Triangle with an area of 24 square feet has a side of length 10 feet. If all 3 sides are even integers, what is the perimeter of the triangle?
Answer:
24 ft
Step-by-step explanation:
so, we don't know anything else about the triangle ?
ok, let's see.
the area of a triangle is (a side length) × (the height from that side to the opposite corner) / 2
At = 24 = side × height / 2
48 = side × height = 10 × height
height = 48/10 = 4.8 = 24/5
let's say that the height on our known side splits this side into 2 parts, p and q (p+q = 10).
we can calculate the triangle side on the right hand side of our know side by calling it a and using Pythagoras :
a² = height² + q² = (4.8)² + q² = 23.04 + q²
as all sides have to be even integers, a² has to be an even square number larger than 23.04.
and because p+q = 10, we know q must be smaller than 10, and therefore q² smaller than 100.
the only candidates for a² are therefore 36 and 64 (6² and 8²).
in a similar way this applies to the left hand triangle side b tool.
b² = height² + p² = 23.04 + p²
with the same restrictions and possible solutions as a².
we have the possibilities that a = b = 6 or 8, or a = 6 and b = 8 (or vice versa).
let's rule out a=b :
a=b wound also mean p=q=5
then
a² = 23.04 + 5² = 23.04 + 25 = 48.04, which is not an even square integer. therefore, this assumption is wrong.
so, the only possible solution is a = 6 and b = 8 (or vice versa, but it did not matter which is which, as we only need the perimeter, which would be the same either way).
proof :
36 = 23.04 + 12.96 = 23.04 + q²
=> q = 3.6 ft
64 = 23.04 + 40.96 = 23.04 + p²
=> p = 6.4 ft
p+q = 3.6 + 6.4 = 10 ft
perfect, it fits, this is the correct solution
so, the perimeter of the triangle is
10 + 6 + 8 = 24 ft
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2.__
3.__
4.__
5.__
6.__
Answer:
eegwhwiwveejekjeevwhejecs
NEEDED ASAP will MARK THE CORRECT ONE
Answer:
→ m∠ABE + m∠EBC =180°
→ m∠ABF + m∠FED + ∠DBC =180°
→ ∠ABF ≅ ∠EBC
→ ∠ABE ≅ FBC
~OAmalOHopeO
What is the y-intercept of the line whose equation is y=−3x ?
Answer:
y=mx+b
b is the y intercept
b=0, so 0 is the y intercept
Step-by-step explanation:
The diagram above shows the quadrant OPQ centred at O.
ORST is a square.
Given OP = 10 cm and OR = 7 cm.
Calculate the area of the shaded region, in cm². State the answer in pi.
Answer:
the square is 49cm^2
A=pi(r)^2/4
A=pi(10)^2/4
A=100pi/4
A=25pi
25pi -49
29.5398
Step-by-step explanation:
SOMEBODY GET IT RIGHT FOR ME PLS I NEED HELP ITS PYTHAGOREAN THEOREM
Answer:
a^2+b^2=c^2
a^2=c^2-b^2
a^2=10^2-5^2
a^2=100-25
a^2=75
a=7.7cm
Step-by-step explanation:
Which expression is equivalent to….
Answer:
the answer is {2^5}
hope it helps :)
(2^1/2×2^3/4)^2
(2^(2/4+3/4))^2
(2^5/4)^2
2^(5/4×2)
2^(5/2)
√2^5
Answered by Gauthmath must click thanks and mark brainliest
Alex owns 80 orange trees. He has estimated that there are between 35 and 40 oranges on each tree. Which is the closest estimate to the total number of oranges?
Hi~! can someone help me with this~?
It costs 3 bowls and a jug 13.70, the jug costs $4.10 more that the bowl, how much does the jug cost-?
Thank u~!
Answer:
$6.50
Step-by-step explanation:
Let the cost of a bowl and a jug be $b and $j respectively.
3b +j= 13.70 -----(1)
j= b +4.10 -----(2)
Substitute (2) into (1):
3b +b +4.10= 13.70
4b +4.10= 13.70 (simplify)
4b= 13.70 -4.10 (-4.10 on both sides)
4b= 9.60
b= 9.60 ÷4 (÷4 on both sides)
b= 2.40
Substitute b= 2.40 into (2):
j= 2.40 +4.10
j= 6.50
Thus, the jug costs $6.50.
