Given:
The terms of a sequence are:
[tex]-6,-\dfrac{11}{2},-5[/tex]
To find:
The number of terms whose sum is -25.
Solution:
We have, the given sequence:
[tex]-6,-\dfrac{11}{2},-5[/tex]
Here, the first term is -6.
[tex]-\dfrac{11}{2}-(-6)=-5.5+6[/tex]
[tex]-\dfrac{11}{2}-(-6)=0.5[/tex]
Similarly,
[tex]-5-(-\dfrac{11}{2})=-5+5.5[/tex]
[tex]-5-(-\dfrac{11}{2})=0.5[/tex]
The difference between consecutive terms are same. So, the given sequence is an arithmetic sequence with common difference 0.5.
The sum of n terms of an arithmetic sequence is:
[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
Where, a is the first term, d is the common difference.
Putting [tex]S_n=-25,a=-6,d=0.5[/tex], we get
[tex]-25=\dfrac{n}{2}[2(-6)+(n-1)0.5][/tex]
[tex]-50=n[-12+0.5n-0.5][/tex]
[tex]-50=-12.5n+0.5n^2[/tex]
[tex]0=0.5n^2-12.5n+50[/tex]
Splitting the middle term, we get
[tex]0.5n^2-2.5n-10n+50=0[/tex]
[tex]0.5n(n-5)-10(n-5)=0[/tex]
[tex](0.5n-10)(n-5)=0[/tex]
Using zero product property, we get
[tex](0.5n-10)=0[/tex] and [tex](n-5)=0[/tex]
[tex]n=\dfrac{10}{0.5}[/tex] and [tex]n=5[/tex]
[tex]n=20[/tex] and [tex]n=5[/tex]
Therefore, the sum of either 5 or 20 terms is -25.
Only answer if you’re sure :) thank yew
Can someone solve this?
Answer:
u=4
v=2√3
Step-by-step explanation:
The 30-60-90 triangle theorem states that the shortest side of a triangle is half of the hypotenuse, so 2*2=4. So, the hypotenuse, u, is 4.
The longest leg is √3 times greater than the shortest leg, so 2*√3=2√3. So, the longest leg, v, is 2√3.
can someone please help me with this math question?
9514 1404 393
Answer:
D. 0, 1, or 2 solutions
Step-by-step explanation:
The line represented by g(x) may intersect the parabola represented by f(x) in 0, 1, or 2 places, as illustrated in the attachment. The curves are different shapes, so cannot overlap to give infinite solutions.
The system may have 0, 1, or 2 solutions.
If ∠WOZ and ∠WOX are supplementary angles and ∠WOX and ∠XOY are complementary angles, then what is the value of x and m∠XOY?
Answer:
b.) x= 6, m∠XOY= 18
Step-by-step explanation:
comment if u need explanation :))
Length of insect is 23mm and length of drawing is 85mm. So what is Magnification
Answer:
The magnification is the ratio of the size of the image to the size of the object. In this case, the length of the insect is the size of the object, and the length of the drawing is the size of the image.
To find the magnification, we can divide the size of the image by the size of the object:
Magnification = size of image / size of object
Plugging in the values, we have:
Magnification = 85mm / 23mm
Calculating, we find that the magnification is approximately 3.7. This means that the length of the drawing is 3.7 times the length of the insect.
Step-by-step explanation:
An Item costs $450 Before tax. and the sales tax is $31.50
Find the sales tax rate. Write your answer as a percentage
The tax rate of an Item that costs $450 Before tax. and the sales tax is $31.50 is 7%
What is tax rate?The tax rate is the percentage of an income or an amount of money that has to be paid as tax.
To find the tax rate of $31.50 from $450
The formula is
Amount taxed/Principal amount x 100
= $31.50/$450 x100
=$3150/450
=7%
Hence, the tax rate is 7%
Learn more about tax rate at : https://brainly.com/question/28526221
#SPJ1
A 3kg cart moving with a speed of 4m/s collides with a 1 kg cart at rest
The speed of the carts after collision is 3 m/s.
What is the velocity after collision?We have to note that in this case, we would need to apply the principle of the conservation of linear momentum. This implies that the momentum before collision would have to be the same as the momentum after collision.
Then we have;
Momentum before collision = Momentum after collision thus;
(3 * 4) + ( 1 * 0) = (3 + 1) v
Note that the two carts are said to stick together and move with a common speed
Hence;
12 = 4v
v = 12/4
v = 3 m/s
Learn more about momentum:https://brainly.com/question/24030570
#SPJ1
The scatter plot shows the number of chin-ups and push-ups completed by a sample of fourth grade students.
What is the median number of chin-ups for all students?
Student Name
Label
Number of Chin-ups and Push-ups
10-
9
А
B
H
B
8
Jared
Tonya
Alex
Rishab
L
D
G
с
7-
F
D
K к
Gao
E
E
А
с
F
Riki
Anne
5-
4-
3
2-
G
Amira
H
12
/
Samuel
Lily
0
J
1
6
8
9
10
Abdu
K
2
Chin-ups
Mike
Answer:
9
Step-by-step explanation:
One did 10,one did 9, and 1 did 8 and 9 is the median number of those 3 numbers.
Answer:
Abdu, Tonya, Gao, Lily, Mike, Rishab
Step-by-step explanation:
he average movie admission price for a recent year was $7.18. The population variance was 3.81. A random sample of 15 theater admission prices had a mean of $8.02 with a standard deviation of $2.08. At α = 0.05, is there sufficient evidence to conclude a difference from the population variance? Assume the variable is normally distributed.
Answer:
Since the calculated value of z= 1.6279 does not fall in the critical region Z ≥ ±1.96 we conclude that there is no difference between the population variance and the sample variance.
Step-by-step explanation:
The data given is
Population mean μ= $ 7.18
Population variance= σ²= 3.81
Population Standard Deviation = √σ²= √3.81= 1.952
Sample Mean= x`= $ 8.02
Sample Standard Deviation =s = $ 2.08
Sample Size = 15
Significance Level = ∝= 0.05
The null and alternate hypotheses are
H0: σ1=σ2 against the claim that Ha: σ1≠ σ2
where σ1 is the population variance and
σ2 is the sample variance
The rejection region is Z ≥ ±1.96 for two tailed test at ∝= 0.05
The test statistic z is used
z= x`- μ/ σ/√n
Putting the values
Z= 8.02-7.18/1.952/√15
z= 0.84/0.51599
z= 1.6279
Since the calculated value of z= 1.6279 does not fall in the critical region Z ≥ ±1.96 we conclude that there is no difference between the population variance and the sample variance.
Two lines, A and B, are represented by equations given below:
Line A: y = x − 2
Line B: y = 3x + 4
Which of the following shows the solution to the system of equations and explains why?
Group of answer choices:
A) (−3, −5), because the point does not lie on any axis
B) (−3, −5), because the point satisfies both equations
C) (−4, −8), because the point satisfies one of the equations
D) (−4, −8), because the point lies between the two axes
The point (0,0) is located on a line with slope of 3/4. which point could also be located on the line?
Answer:
Below
Step-by-step explanation:
The equation of the line will be y = 3/4 x pick ANY value of 'x' to find the corresponding 'y' value
Say x = 8 then y = 6 8,6 is a point on the line
Answer:
(1 , 0.75)
(2 , 1.5)
(3 , 2.25)
(4 , 3)
(5 , 3.75)
(4 , 3)
(6 , 4.5)
(7 , 5.25)
(8 , 6)
(9 , 6.75)
(10 , 7.5)
(11 , 8.25)
(12 , 9)
Step-by-step explanation:
To find the other points we must put the given information into the slope-intercept form: [tex]y=mx+b[/tex] m = slope and b = y-intercept
[tex]y=\frac{3}{4} x+0[/tex] or [tex]y=\frac{3}{4} x[/tex]
Then just simply start inputting any numbers for x so you can solve for [tex]y=\frac{3}{4} x[/tex] to get the other points of the line.
describe the translation of the figure ABCD. Complete the sentence to explain your answer
What is 46% of 388
Please help me
Answer:
178.48
Step-by-step explanation:
We are asked what is 46 percent out of 388.
To solve this, we need to follow the formula when finding the percentage of a number.
P being the percentage
X being the number
Y being the answer, the forumla is
Y = P * X
Substitute :
Y = 46% * 388
Convert the percentage into a decimal,
46%/100
0.46
Y = 0.46 * 388
Multiply :
178.48 = 0.46 * 388
178.48
your welcome btw
Given m | n, find the value of x and y.
m
(2y+17) (4x-3)°
(7x+18)°
n
Answer:
the first one is scamer
Step-by-step explanation:
help me report that userWhat is 46-2004asdfgh
Answer:
if it is 46-2004 then the answer is -1958
Step-by-step explanation:
Solve this math problem.
Therefore ,the value of a given fraction is equal to 10/12, which equals 5/6, after resolving the given problem.
What exactly is a fraction?To represent a whole, divide it into any number of comparable parts, or fractions. How many units of a particular size there are is expression using fractions in standard English. 8, 3/4. Parts of a whole are included. Numbers in mathematics are stated as a ratio of the excess to the denominator. These are each simple fractions that represent an integer. A fraction is contained in the fraction or reduction of a complex fraction. When a fraction is true, its numerators are less than its denominators. An amount that makes up a fraction of a whole is called a fraction. You can assess the whole by dissecting it into smaller pieces.
Here,
Given : 5/8 X 4/3
=> 5/8 X 4/3 = 20/24
on condensing,
10/12 = 5/6
To know more about fraction visit:
brainly.com/question/10354322
#SPJ1
a tee junction occurs when a connection meets an existing pipe of header at what angle? A 180 degree, B 30 degree, C. 90 degree, D.45 degree
Tee welding joints are formed when two members intersect at a 90-degree angle that makes the edges come together in the center of a plate or component
the ratio of the number of goat to the number of sheep is 3:1. The sheep are 10 in numbers. how many goats are in the gardens and many animals are there?
Answer:
30 goats, and 40 animals
Step-by-step explanation:
so since the problem says 10 goats are in the garden, and the ratio of sheep to goats is 3:1 you do 3*10. it's basically saying for every 1 goat you have 3 sheep. so if you take away the 0 from 30 and 10 you get 3:1. : )
Rewrite 12x4y3 − 48x3y4 using a common factor.
Answer: 12x^3 y^3 (x − 4y)
(GCF is: 12x^3 y^3)
Step-by-step explanation:
This is the best I can do, sorry that I don't have an explanation.
a rectangular table is 5 1/4 feet by 3 3/4feet. what is the area of the table?
Answer:Area = Length times Width
5 1/4 times 3 3/4
5 x 4 + 1 = 21
21/4
3 x 4 +3 = 15
15/4
21/4 x 15/4 = 315 / 16 or 19 11/16 ft^2
Step-by-step explanation:
1+1+1+1=4
2+2+2+2=16
3+3+3+3=?
Answer:
12
Step-by-step explanation:
write the equation 0.3x^2+5x-7=0 in standard form and then choose the value of “b”
70
50
5
Answer:
b = 5
Step-by-step explanation:
The given equation is :
[tex]0.3x^2+5x-7=0[/tex] .......(1)
It is in the form of quadratic equation. The general form of a quadratic equation is as follows :
[tex]ax^2+bx+c=0[/tex] .....(2)
Comparing equations (1) and (2), we get :
a = 0.3, b = 5 and c = -7
Hence, the value of b is equal to 5.
solve y=(1/2)x exponential graph
The value of the exponential graph y = ( 1/2 )ˣ is graphed
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
y = ( 1/2 )ˣ be equation (1)
On simplifying the equation , we get
y = 1 / (2ˣ)
Now , the graph of the function y = ( 1/2 )ˣ will be a slanting line which will not touch the x axis and passes through the point y = 1
The graph of the function y = ( 1/2 )ˣ is given below
Hence , the function is solved and the graph is plotted
To learn more about exponents click :
https://brainly.com/question/28966438
#SPJ1
Please please help!!!!
Answer:
280 inches
Step-by-step explanation:
8 x 8 = 64
9 × 24 = 216
64 + 216 = 280
Shirt Prices
$50, $35, $48,
$31, $34
What is the median price of the five shirts?
Answer: 35 would be the median
Step-by-step explanation: Put the numbers in order and whichever one is the middle value is the median
Answer:
35
Step-by-step explanation:
The median is the middle price when listed from smallest to largest
31, 34, 35, 48, 50
The middle price is 35
The median is 35
Any help please, - What is the area for this?
Answer:
109.18
Step-by-step explanation:
Subtract 13.4-7.2 then solve the triangle (base x height) getting 32.86. Next solve the rectangle getting 76.32. Then add all of it concluding in 109.18.
Using elimination, what is the solution to the following system?
2x+4y=16
-2x-3y=-13
Answer:
x=2, y=3. (2, 3).
Step-by-step explanation:
2x+4y=16
-2x-3y=-13
-----------------
y=3
2x+4(3)=16
2x+12=16
2x=16-12
2x=4
x=4/2
x=2
pls help and give only correct answers
Answer:b
Step-by-step explanation:
i took that test
Simplify the expression 3a² + 1/4a + 3 + a² + 4 + 1/4a
The Correct answer while simplifying the given algebraic expression is: 4a²+1/2a+7
What are Algebraic Expressions?The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.
Method to simplify any algebraic Expressions are :
By multiplying factors, remove any grouping symbols like brackets and parenthesis.If the words contain exponents, use the exponent rule to eliminate grouping.Add or subtract like terms to combine them.Add the constants togetherGiven:
=3a²+1/4a+3+a²+4+1/4a
=(3a²+a²)+(1/4a+1/4a)+(3+4)
=4a²+1/2a+7
So the Answer is
=4a²+1/2a+7
To know more about algebraic Expressions visit:
brainly.com/question/27029970
#SPJ1
Suppose f is a function. If f(6) = -9, give an ordered pair of numbers that is a solution of the function.
The ordered pair solution to the function f(x) is (6, -9) because f(6) = -9,
What is an equation?An equation is an expression relating numbers and variables.
A function is a rule that defines the relationship between the dependent and independent variable. Dependent variables are variables that depends on others variable while independent variables are variables that does not depends on others variable
A solution to a function is the values of the variable that makes the equation true.
Given the function f(x) have solution of f(6) = -9. The ordered pair is (6, -9)
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1