Answer:
The number of terms n in arithmetic series is n=25
Step-by-step explanation:
We are given:
a₁ = 13
d = 3
Sₙ = 1225
We need to find number of terms i.e n
The formula used will be: [tex]S_n=\frac{n}{2}(2a+(n-1)d)[/tex]
Putting values and finding n
[tex]S_n=\frac{n}{2}(2a+(n-1)d)\\1225=\frac{n}{2}(2(13)+(n-1)3)\\1225=\frac{n}{2}(26+3n-3)\\1225=\frac{n}{2}(23+3n)\\2(1225)=n(23+3n)\\2450=23n+3n^2\\3n^2+23n-2450=0[/tex]
Now, solving using quadratic formula to find value of n:
[tex]n=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Putting values: a=3, b=23 and c=-2450
[tex]n=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\n=\frac{-23\pm\sqrt{(23)^2-4(3)(-2450)}}{2(3)}\\n=\frac{-23\pm 173}{6}\\n=\frac{-23+ 173}{6}, n=\frac{-23- 173}{6}\\n=25, n=-\frac{98}{3}[/tex]
So, we get: [tex]n=25, n=-\frac{98}{3}[/tex]
Since number of terms can't be negative so, n= 25
So, the number of terms n in arithmetic series is n=25
Which of the following is NOT always true of a function and its inverse?
The statement that is not always true of inverse functions is (d) f-1(x) is a function
What are inverse functions?Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x); it also represents the opposite function
How to determine the statement that is not always true of inverse functions?As mentioned above,
The inverse functions are the opposite of an original equation
This means that:
If a function is f(x), then the inverse if f-1(x)
However, all inverse equation are relations, but not all inverse equations are functions
This means that the statement that is not always true of inverse functions is (d) f-1(x) is a function
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Which two points have the same absolute value?
P Q R S
_______________
-1 0 1
Answer:
-1 and 1
Step-by-step explanation:
Write the expression in simpliest form WILL GIVE GIVE BRAINLIEST
5 ( x - 1)
Answer:
5x-5
Step-by-step explanation:
pls give brainliest
Answer:
5x − 5
Step-by-step explanation:
Multiply x by 5, which will give you 5x
Then multiple 1 by 5, you get 5.
You end up with 5x - 5
PLEASE HELP WILL MARK BRAINLIEST NEED THE SMARTEST PEOPLE!!!
Answer:
-430
Step-by-step explanation:
evaluate using the values given :
3 pm; use m = 4, and p = 3
Answer:
36
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
3pm
m = 4
p = 3
Step 2: Evaluate
Substitute: 3(3)(4)Multiply: 9(4)Multiply: 36i need help with this
Answer: A.3x² - 2x - 6
Step-by-step explanation:
PLEASE ANSWER I NEED IT ASAP WILL AWARD BRAINLIEST AND GIVE POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
For 9:
1. Angle T and angle M are congruent because they are given
2. The line AH bisects angle THM because it is given
3. Angle 1 and angle 2 are congruent because of properties of angle bisection
4. The line AH is congruent to the line HA because of the reflexive property
5. Triangle TAH is congruent to triangle MHA because of AAS
6. The line TA is congruent to MA because of congruent triangles
For 10:
1. Angle H and angle J are congruent because it is given
2. G is the midpoint of FI because it is given
3. Angle 1 and angle 2 are congruent because they are vertical angles
4. Line HG is equal to line JG because of properties of midpoints
5. The triangles HIG and JFG are congruent because of AAS
6. The lines HI and JF are congruent because of congruent triangles
Suppose x = 9 is a solution to the equation f(x) = g(x). If a table of values for the equation y = f(x) contains an x-value of 9 and a corresponding y-value of 18, then which of these statements is correct about a table of values for the equation y = g(x)?
A
If it contains an x-value of 9, the corresponding y-value must be 9.
B
If it contains an x-value of 9, the corresponding y-value must be 18.
C
If it contains a y-value of 18, the corresponding x-value must be 9.
D
If it contains a y-value of 18, the corresponding x-value must be 18.
Answer:
I think it may be A
Step-by-step explanation:
how far away is earth from the sun?
Answer:
the earth is 93.111 million miles away from the sun
f(x) = x² + 3x
f(-4)=
evaluate the function
Answer:
4
Step-by-step explanation:
f(x) = x² + 3x
f(-4) = (-4)^2 + 3×(-4)
= 16 - 12
= 4
this is an arithmetic progression. please help!
A graduate is required to pay his education loan of RM3960 in 24 monthly instalments, with the first instalment being RM 50. Subsequent instalments are increased by RM 10 each month. What is the amount of the last instalment?
Answer:
The last installment is RM 280
=========================
GivenAP with:
The first term a = 50,Common difference d = 10,Number of terms n = 24.SolutionUse the nth term equation of AP to find the last installment:
[tex]a_n=a_1+(n-1)d[/tex][tex]a_{24}=50+(24-1)(10) = 50+23*10=50+230=280[/tex]Which expression could be used to determine the product of -4 and 342
o(-4)(3)(-4)
x (
0 (-4)(3) + (-4)
0 %)(-4)=(3 ()
(3)(-4) + (3)
Answer:
the second answer
Step-by-step explanation:
.........
PLEASE HELP WILL MARK BRAINLIEST Question 8
Which pair of equations show below would have infinite solutions?
Answer
A Y = -2 + 8
y = 4x - 7
B y = x - 4
y = 3x - 2
C) x
x – 3y = -3
x – 3y = 6
D 3x +y = 3
6x + 2y = 6
Answer:
Step-by-step explanation:
a)y=-2x+8
y=4x-7
solution
b)y=x-4
y=3x-2
solution
c)x – 3y = -3
x – 3y = 6
no solution
d)3x +y = 3
6x + 2y = 6
infinite.
Answer: D
Step-by-step explanation:
I NEED HELP WITH BUMBER 3 PLEASE ASAP ILL LOVE U FOR EVER AND IF YOU CANT SEE THE WORDS VERY WELL THAN U CAN JUS ZOOM IN
Answer: i can't see it sorry to blery
Step-by-step explanation:
Maria drove 520 miles in 8 hours. How many miles per hour did she drive?
Answer:
65 mph
Step-by-step explanation:
520/8 is 65
Find the difference: -15 - 47
Answer:
-62
Step-by-step explanation:
One easy way to subtract two negative numbers like this (for me anyway) is to factor out the minus sign and add:
- (15 + 47)
- (62)
Remove the parentheses
-62
PLSSS HELP ANSWER, THE QUESTION IS IN THE SCREENSHOT
We know that f(x) is a positive, decreasing, and concave down function.
Therefore, the order, from least to greatest is:
right endpoint (since you're considering the smallest values)actual areamidpoint trapezoidalright endpointWhat is the slope of a line perpendicular to the line whose equation is
4x – 3y = –27. Fully reduce your answer.
Answer:
-3/4
Step-by-step explanation:
We can rearrange the equation to get 3y = 4x + 27. Then we can find the slope intercept form: y = 4x/3 +9. You find the perpendicular slope by solving for the opposite and reciprocal of the current slope 4/3. So we would get -4/3, and then -3/4.
Which of the following is divisible by 3?
Answer:
108 and 150
Step-by-step explanation:
108/3=36
150/3=50
-2/3(3x - 4) +3x =5/6
What is X
X= -19/6
X= -11/6
X = 21/6
X=29/6
The value of x from the given linear function is -11/6
Linear equationLinear equations are expression that has a leading degree of 1
Given the linear equation below
-2/3(3x - 4) +3x =5/6
Expand
-2/3(3x) - 2(-4) + 3x = 5/6
-2x + 8/3 + 3x = 5/6
Collect the like terms
x = 5/6 - 8/3
x = (5-16/6
x = -11/6
Hence the value of x from the given linear function is -11/6
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Please help someone anyone please help
Answer:
if 135 calories represents 1/4 then a whole cup is 540 calories so two cups is 540 times 2 which is 1080
Step-by-step explanation:
Answer:
1080 calories
Step-by-step explanation:
135x8=1080
Which value is closest to 0 on the number line?
A. 20
B. -21
C. |2|
D. |-3|
2
u r the very much welcome
Answer:
The answers C
Step-by-step explanation:
hope this helps
Easy math problems!!!!!!!!
Answer:
2√23
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Trigonometry
[Right Triangles Only] Pythagorean Theorem: a² + b² = c²Step-by-step explanation:
Step 1: Define
We are given a right triangle. Therefore, we can use PT to solve for the missing length.
Step 2: Identify Variables
Leg a = √88
Leg b = 2
Hypotenuse c = x
Step 3: Solve for x
Substitute: (√88)² + 2² = x²Exponents: 88 + 4 = x²Add: 92 = x²Isolate x: √92 = xSimplify: 2√23 = xRewrite: x = 2√23Answer:
Mm did you do this already its been 4 days just want to make sureee
Step-by-step explanation:
32. Which of the following best describes the relationship between AABC and ADEF? (1 point)
B
E
A
TH
D
F
O AACBAFED
O AABC ADEF
O AABC AEFD
O AABC ADFE
Answer:
2) tri ABC is congreunt to tri DEF
Step-by-step explanation:
you would have to make sure you name the traingles in a specific order so the congruent angles in both triangles are listed in the same order :))
The option that best describes the relationship between AABC and ADEF is AABC ~ ADEF, the correct option is B.
What are similar triangles?
All similar triangles are triangles that share these two features presented as follows;
1. Congruent angle measures.
2. Proportional side lengths.
We are given that;
AB is similar to DE: BC is similar to EF; AC is similar to DF; ZA is similar to ZD; ZB is similar to ZE; ZC is similar to ZF.
Now,
The relationship between two similar triangles is that their corresponding angles are equal and their corresponding sides are proportional1. This means that if AABC and ADEF are similar, then:
∠A = ∠D
∠B = ∠E
∠C = ∠F
AB/DE = BC/EF = AC/DF
To describe this relationship, we can use a notation that shows which angles and sides correspond to each other. For example, we can write:
AABC ~ ADEF
This means that triangle ABC is similar to triangle DEF and the order of the letters shows how they match up. The first letter of each triangle corresponds to the first angle, the second letter corresponds to the second angle, and so on.
Therefore, by similar triangle properties the answer will be AABC ~ ADEF.
More can be learned about similar triangles at; brainly.com/question/14285697
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Transformations of functions and domain
by looking at the graph given we can see that:
The graph is decreasing in (-∞, -5]The graph is increasing in [5, ∞)And the function is never constant.
How to determine in which intervals the function increases, decreases or is constant?
Here our function is:
f(x) = √(x^2 - 25)
And we have a graph of it.
First, remember that the argument of a square root needs to be zero or larger, so the interval (-5, 5) is not in the domain of our function.
We also can see that this is a square root, so there are no interval where the function is constant.
Finally, by looking at the graph given we can see that:
The graph is decreasing in (-∞, -5]The graph is increasing in [5, ∞)If you want to learn more about domains:
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Someone, please help me!! I don't understand
Solve Ax − By = C for x
Helpppppp
And elephant's heart beats 28 times per minute. Complete
the product to find how many times its heart beats in 30
minutes.
beats X
minutes =
beats
1 minute
1
Answer:
840 beats in 30 minutes
Step-by-step explanation:
if its 28 a minute than you just need to multiply that by the number of minutes
Im on a test and i need the answer really bad please help me out
Max puts a stopper in the bathtub and turns on the faucet at t=0. After 5 minutes, there are 11 gallons of water in the tub and after 10 minutes, there are 22 gallons in the tub. Write an equation that relates the number of gallons, g, to the time, t. Does the relationship represent a linear function? Justify your response.
Answer:
y = 2.2x
Yes, it represents a linear function
Step-by-step explanation:
Given that :
Stopper applied at t = 0
At t = 5 minutes ; water in tub = 11 gallons
At t = 10 minutes ; water in tub = 22 gallons
General form of a linear function :
y = mx + c
Where c = intercept ; m = Slope ; y and x are dependent and independent variables respectively
The intercept = gallon of water at t = 0 ; this is not given and will be taken as 0
Slope = change in y / charge in x
Slope = (22 - 11) / (10 - 5)
Slope = 11 / 5
Slope = 2.2
Hence ;
y = 2.2x + 0
y = 2.2x
Yes, it represents a linear function