We are to find the number of terms in the AP that has a sum greater than 250
The number of teams in the AP which has a sum greater than 250 is at least 11 terms
First term, a = 3
second term, a + d = 8
so
common difference, d = 8-3
= 5
let
n = number of terms in the AP
The sum of n terms is 250
Sum = n/2{2a + (n - 1)d}
250 = n/2{2*3 + (n-1)5 }
250 = n/2{6 + 5n - 5}
250 = n/2(1 + 5n)
500 = n + 5n²
5n² + n - 500 = 0
Solve quadratically using formula
n = -b ± √b² - 4ac / 2a
= -1 ± √1² - 4(5)(-500) / 2(5)
= -1 ± √1 - (-10000) / 10
= -1 ± √1 + 10000 / 10
= -1 ± √10001 / 10
= -1 + √10001 / 10 or -1 - √10001 / 10
= -1/10 + √10001/10
or
-1/10 - √10001 / 20
= 9.9005 or -10.1005
The value of n must be positive and a whole value
Therefore,
n = 9.9005
Approximately, n = 10
The number of teams in the AP which has a sum greater than 250 is at least 11 terms
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Geometry WS (Angle Addition Postulate) (20 pts)
Answer:
x = 17°
m∠MKL = 116°
m∠JKL = 159°
Step-by-step explanation:
JKM = 43
MKL = 8x - 20
JKL = 10x - 11
Since JKL is the whole angle, JKM + MKL = JKL
43 + 8x - 20 = 10x - 11
Add 20 to both sides:
43 + 8x = 10x + 9
Subtract 8x from both sides:
43 = 2x + 9
Subtract 9 from both sides:
34 = 2x
x = 17°
MKL = 8(17) - 20
MKL = 116°
JKL = 10(17) - 11
JKL = 159°
And to check 159 - 116 = 43
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
c) Convert 120 into quinary equivalent.
Assuming 120 is a base 10 numeral, then
120 = 100 + 20 = 4×5² + 4×5¹
so you have
120₁₀ = 440₅
Guys help me in this question pls
Answer:
40+x+5 = 3x +15
2x= 30
x=15
Their present ages are 15 and 55
multiply : (5x+3a) (5x-3a)
0.6m=____mm . answer the question
Answer:
600
Step-by-step explanation:
since 1m=1000mm
You are trying to make a hole in one on the miniature golf green
3
3
5
7
9 X
a. Write an absolute value function that represents the path of the golf ball.
3
$ (z) = – 31x/+6
b. Write the function in part (a) as a piecewise function.
f(x) =
if x < 6
if x26
[tex]\frac{\sqrt{a+b} }{\sqrt{a-b} } +\frac{\sqrt{a-b} }{\sqrt{a+b} }[/tex]
Answer:
[tex]\frac{(a+b)}{a^{2} -b^{2} }[/tex] + [tex]\frac{(a-b)}{a^{2} -b^{2} }[/tex] = [tex]\frac{2a}{a^{2} -b^{2} }[/tex]
Step-by-step explanation:
Step-by-step explanation:
[tex] \frac{ \sqrt{a + b} }{ \sqrt{a - b} } + \frac{ \sqrt{a - b} }{ \sqrt{a + b} } \\ squaring \: on \: both \: sides \\ \frac{a + b}{a - b} + \frac{a - b}{a + b} \\ \frac{(a + b) \times (a + b) + (a - b)(a - b)}{(a - b)(a + b)} \\ \frac{ {(a + b)}^{2} + {(a - b)}^{2} }{ {a}^{2} - {b}^{2} } \\ remaining \: in \: attachment[/tex]
[tex]thank \: you[/tex]
PLEASE HELP ME FAST I WILL GIVE 30 POINTS AND BRAINLIEST AND HEART
Questions 10-12
f(x)= 3x-13
g(x)= 2x^2-4x-5
h(x)=4^x-7
10. Find (f - g) (x)
11. Find (f - h) (x)'
12. Find (f + g) (x)
(f–g)(x)= (3x-13) – (2x²–4x–5)= –2x²+7x-8
(f–h)(x)= (3x-13) – ( 4^x –7) = 3x – 4^x–6
(f+g)(x)= (3x-13) + (2x²–4x–5) = 2x²–x – 18
I hope I helped you^_^
Find the value of x.
A. 5.58
B. 9.14
C. 15.2
D. 10
PLEASE HELP!!! :(
Answer:
D. 10
Step-by-step explanation:
[tex]{ \sf{(12x + 12) \degree = 79\degree + (5x + 3)\degree}} \\ { \sf{ \{outer \: angle \: is \: equal \: to \: sum \: of \: inner \: angles \}}} \\ { \sf{12x - 5x = 79 + 3 - 12}} \\ { \sf{7x = 70}} \\ { \sf{x = 10}}[/tex]
edward has $48 to spend at the grocery store. six cases of soda he has $21 left. how much does one case of soda cost? brainly
Answer: $4.50
Step-by-step explanation:
48-21=27
27 divided by 6= 4.50
Therefore each case costs 4.50
Answer:
$4.50
Step-by-step explanation:
48 - 21
27
divide by 6
4.50
Permudahkan 3/5xy × (-25x²y)
Simplify 3/5xy × (-25x²y)
A) -35x³y²
B) -35x²y²
C) -15x³y²
D) -15x²y²
Answer:
C) -15x³y²Step-by-step explanation:
[tex] \frac{3}{5} xy \: \times ( - 25 {x}^{2} y)[/tex]
[tex] = \frac{3}{5} \times ( - 25) \times x \times {x}^{2} \times y \times y[/tex]
[tex] = - 15 \times {x}^{3} \times {y}^{2} [/tex]
[tex] = - 15 {x}^{3} {y}^{2} (ans)[/tex]
Which of the following represents the relationship
between h and C ?
A) C = 5h
3
B) C = - +5
4
C= +5
C) C = 3h + 5
D) h = 3C
Answer:
I think its c I hope I'm right
The function f(x)=x^2+2 is not one to one. Determine a restricted domain that makes it one to one and find the inverse function
Answer:
Hope it helped
Step-by-step explanation:
The restricted domain that makes the given function one to one is (-∞,0] or [0.∞) and the inverse function would be f⁻¹ (x) = [tex]\sqrt{x-2}[/tex] if we restrict the domain of original function to [0.∞) and the inverse function would be f⁻¹ (x) = -[tex]\sqrt{x-1}[/tex] if we restrict the domain to (-∞,0] .
What is inverse of a function?An inverse function or an anti function is defined as a function, which can reverse into another function.
Now the given quadtratic function is,
f(x) = x² + 2
Now vertex of the given quadratic function is (0,2)
Thus the range of the function is [2,∞)
If we restrict the domain of this function to either (-∞,0} or [0.∞), it will become one to one function.
Now the inverse function is given as,
y = x² + 2
Upon interchanging x and y, we get:
x = y² + 2
⇒ y² = x - 2
or, y = ±[tex]\sqrt{x-2}[/tex]
Hence, the inverse function would be f⁻¹ (x) = [tex]\sqrt{x-2}[/tex] if we restrict the domain of original function to [0.∞) and the inverse function would be f⁻¹ (x) = -[tex]\sqrt{x-1}[/tex] if we restrict the domain to (-∞,0] .
Thus, the restricted domain that makes the given function one to one is (-∞,0] or [0.∞) and the inverse function would be f⁻¹ (x) = [tex]\sqrt{x-2}[/tex] if we restrict the domain of original function to [0.∞) and the inverse function would be f⁻¹ (x) = -[tex]\sqrt{x-1}[/tex] if we restrict the domain to (-∞,0] .
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Complete the set of ordered pairs for the relation.
{(x, y): y = 2 |x + 1| and x {-2, -1, 0, 1, 2}}.
(-2, __)
-2
-3
2
Answer:
Step-by-step explanation:
[tex]U=\{(x,y)\ \zeta\ y=|x+1| \ and\ x \in \{-2,-1,0,1,2\}\ \}\\\\\begin{array}{|c|c|}x&y\\---&---\\-2&2\\-1&0\\0&2\\1 & 4\\2&6\\---&---\\\end{array}\\\\U=\{(-2,2),(-1,0),(0,2),(1,4),(2,6)\}\\[/tex]
Answer:
2 / (-2,2)
Step-by-step explanation:
Please help me
Find this value
Answer:
<CAB =30°
Step-by-step explanation:
<DAB=80°
<DAC=50°
<DAB=<DAC+<CAB
<CAB=<DAB-<DAC
=80°-50°
=30°
Which expression is equivalent to 180?
Answer:
[tex] \sqrt{2.2.3.3.5} [/tex]
[tex]\sqrt{2.2.3.3.5}[/tex] is equivalent to [tex]\sqrt{180}[/tex]. Correct option is 1. First, we look for perfect square factors within 180. We can factor 180 as follows: [tex]\(180 = 2^2 \times 3^2 \times 5\)[/tex]
Next, we can group the perfect square factors together:
[tex]\(180 = (2 \times 3)^2 \times 5\)[/tex]
Since we are taking the square root of 180, we can rewrite it as the square root of its perfect square factors multiplied by the remaining non-perfect square factor:[tex]\(\sqrt{180} = \sqrt{(2 \times 3)^2 \times 5}\)[/tex]
The square root of a perfect square is just the value of the number itself:
[tex]\(\sqrt{180} = 2 \times 3 \times \sqrt{5}\)[/tex]
Finally, we can simplify the expression by multiplying the numbers outside the square root [tex]\(\sqrt{180} = 6\sqrt{5}\)[/tex]
So, the expression [tex]\(6\sqrt{5}\)[/tex] is equivalent to [tex]\(\sqrt{180}\)[/tex], and it represents the positive square root of 180 with any perfect square factors taken outside the square root sign.
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*Plz it due today HELP!!!!!!Justin has been collecting baseball cards for years. He bought 137 cards the first year
and 143 cards the second year. He plans on putting them in a binder that will hold seven
cards per page. How many pages must the binder have to hold Justin's collection? *Plz tell me what the math action word is I need to box it*
Answer:
40
Step-by-step explanation:
137+143=280
280/7= 40
Answer:
Division/dividing/divide
Step-by-step explanation:
If Justin has 280 baseball cards, and if each page will only hold 7 cards per page, then by dividing 280 by 7 (280÷7) would equal to 40 pages.
Help me plz snsnsns sn
Answer:
If the exponent is 0 the answer is 224/y^2
Step-by-step explanation:
6x+6=-5+3x+17
I need help
Answer:
Get all the terms with x on the left. Get all the terms without x on the right. Simplify by adding and subtracting the terms without x and adding and subtracting the terms with x. Finally divide to get the value of x.
Step-by-step explanation:
6x+6 =- 5+3x+17
6x+6 -6 =- 5+3x+17 -6
6x = 5+3x+11
6x = 3x + 16
6x - 3x = 3x + 16 -3x
3x = 16
3x / 3 = 16 / 3
x = 15/3 + 1/3
x = 5 1/3
x = 5.33333...
slope 1/6 , x-intercept at -1
Answer:
[tex]{ \underline{ \sf{6y = x + 1 }}}[/tex]
Step-by-step explanation:
[tex]y = mx + c[/tex]
m is slope
c is y intercept.
at x-intercept, y = 0
[tex]0 =( \frac{1}{6} \times - 1 )+ c \\ \\ c = \frac{1}{6} [/tex]
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of the given line is 6y=x+1.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
Given that the slope of the equation of the line is 1/6, while the x-intercept is at -1. Therefore, if we substitute the coordinate of the intercept and the slope in the equation in the general equation of the line. We will see,
y = mx + c
0 = (1/6)(-1) + c
0 = -1/6 + c
c = 1/6
Now, the equation of the line can be written as,
y = (1/6)x + (1/6)
y = (x/6) + (1/6)
y = (x+1)/6
6y = x + 1
Hence, the equation of the given line is 6y=x+1.
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Find the orthogonal decomposition of vector b = 9, 0, 0 with respect to vector a = 4, −5, 0 . (Your instructors prefer angle bracket notation < > for vectors.)
The orthogonal decomposition of vector [tex]\vec b = <9, 0, 0>[/tex] with respect to vector [tex]\vec a = <4, -5, 0>[/tex] is
[tex]b'=<\frac{16}{5},\frac{8}{5},0>[/tex]
From the Question we are told that
Vector [tex]\vec b = <9, 0, 0>[/tex]
Vector [tex]\vec a = <4, -5, 0>[/tex]
Generally in the orthogonal decomposition of b to a we have
[tex]\vec b=\vec b"+\vec b'[/tex]
Where
[tex]\vec b"=(\frac{\vec b*\vec a}{\vec *\vec a})*\vec a[/tex]
[tex]\vec b"=(\frac{ <9, 0, 0>*<4, -5, 0>}{<4, -5, 0>*<4, -5, 0>})*<4, -5, 0>[/tex]
[tex]\vec b"=<\frac{4}{5},\frac{-8}{5},0>[/tex]
Therefore
[tex]b'= \vec b- \vec b"\\\\b'=<4,0,0>-<\frac{4}{5},\frac{-8}{5},0>[/tex]
[tex]b'=<\frac{16}{5},\frac{8}{5},0>[/tex]
in Conclusion
The orthogonal decomposition of vector [tex]\vec b = <9, 0, 0>[/tex] with respect to vector [tex]\vec a = <4, -5, 0>[/tex] is
[tex]b'=<\frac{16}{5},\frac{8}{5},0>[/tex]
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the area of a children’s square playground is 50m squared, what is the exact length of the playground
Area=50m^2
Let side be a
[tex]\\ \rm\Rrightarrow Area=a^2[/tex]
[tex]\\ \rm\Rrightarrow a^2=50[/tex]
[tex]\\ \rm\Rrightarrow a=\sqrt{50}[/tex]
[tex]\\ \rm\Rrightarrow a=7.1m[/tex]
Answer:
[tex]\displaystyle 5\sqrt{2}\:m.[/tex]
Step-by-step explanation:
Sinse squares are equal in length all around, this formula applies:
[tex]\displaystyle s^2 = A → \sqrt{50} = \sqrt{s^2} \\ \\ 5\sqrt{2} = s[/tex]
Therefore, the length of the playground is [tex]\displaystyle 5\sqrt{2}[/tex] metres.
* Just in case you could not figure out how to find the square root of fifty, here is how using perfect squares:
[tex]\displaystyle \sqrt{50} → \sqrt{2 \times 25} \\ \\ 5\sqrt{2}[/tex]
Sinse we are dealing with measurements, we only want the NON-NEGATIVE root.
I am joyous to assist you at any time.
can someone please give me an example of a position and motion of objects in space
Answer:
position of objects in space
for example: up, down, in front, behind, between, left, right.
motion of objects in space
for example: Stars, planets, moons.
a shea cd player costs $80 last year and $112 this year. what was the percent of increase in its price
Answer:
40% increase
Step-by-step explanation:
c = final value - initial value
------------------------------------
initial value
112 - 80 = 32
32 / 80 = 0.4
0.4 = 40%
In x² , what is the 2 called?
a radical
a subscript
an exponent
an imaginary number
none of these
Answer:
an exponentStep-by-step explanation:
In x², here the 2 is exponent while x is base.
Answer:
an exponent
Step-by-step explanation:
hope it helps:)
What is the period of the function y=tan (n/4(x-n/3)? 3 units 4 units 6 units 8 units
Answer:
8
Step-by-step explanation:
The function u given me is
[tex] \tan( \frac{\pi}{4} (x - \frac{\pi}{3} ) )[/tex]
The period of a function is represented by
[tex] \frac{2\pi}{ |b| } [/tex]
where b is the coefficient of the x variable.
The coefficient is pi/4 so
[tex] \frac{2\pi}{ \frac{\pi}{4} } = 8[/tex]
8 is the answer.
Answer: 4 units
Step-by-step explanation:
y - 4 = 3. what is y = ???
Hi ;-)
[tex]y-4=3\\\\y=3+4\\\\\boxed{y=7}[/tex]
Answer: 7
.....7-4=3
to complete a continuing pattern,identify pattern rule.true or false?
Answer:
true
Step-by-step explanation:
Subtract.
5/23 - 4/23
(Type an integer or fraction.)
Answer:
1/23
Step-by-step explanation:
5/23 - 4/23 would be 1/23. When the denominators of the fractions are the same, you can just subtract the numerators.
c. Mr. champing travels 20 km duo East and then 25 km due west. respect to find his position with respect to his starting point.