Answer: f(10) = 290
Concept:
Here, we need to understand the idea of evaluation.
When encountering questions that gave you an expression with variables, then stated: "If x = a, y = b, z = c" (a, b, c are all constants), this means you should substitute the value given for each variable back to the expression.
Solve:
Given expression
f(x) = 3x² - x
Substitute values into the expression
f(10) = 3(10)² - (10)
Simplify exponents
f(10) = 3(100) - (10)
Simplify by multiplication
f(10) = 300 - 10
Simplify by subtraction
f(10) = [tex]\boxed{290}[/tex]
Hope this helps!! :)
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Find the sum Sn of the first n terms from the given sequence.
1, 1+2, 1+2+3, 1+2+3+4, ...
Please show your work and use Sigma Notation too. Thank you!
The Sequence:
1 , 1+2 , 1+2+3 , 1+2+3+4, ...
here, every term is an AP. finding the general formula for the sum of the elements of each term is:
Sₙ = [tex]\frac{x}{2}(2a + (x-1)d)[/tex] [where x = number of term, a = first term and d = common difference]
here, the first term is always 1 and so is the common difference.
Sₙ = [tex]\frac{x}{2}(2 +x-1)[/tex]
Sₙ = [tex]\frac{x}{2}(1 +x)[/tex] = [tex]\frac{1}{2}(x + x^{2})[/tex]
which is the formula for a general term in our series
now, we need to find the sum of the first n terms of this series
[tex]\displaystyle\sum_{x=1}^{n} [\frac{1}{2}(x + x^{2})][/tex]
[tex]\displaystyle\frac{1}{2} [\sum_{x=1}^{n} (x) + \sum_{x=1}^{n}(x^{2})][/tex]
in this formula, for the first term, it's just an AP from x = 1 to x = n
for the second term, we have a general formula [tex]\frac{n(n+1)(2n+1)}{6}[/tex]
[tex]\frac{1}{2}[\frac{n}{2}(2a + (n-1)d)+ \frac{n(n+1)(2n+1)}{6} ][/tex]
in this AP (first term), the first term and the common difference is 1 as well
[tex]\frac{1}{2}[\frac{n}{2}(2 + n-1)+ \frac{n(n+1)(2n+1)}{6} ][/tex]
[tex]\frac{1}{2}[\frac{n}{2}(n+1)+ \frac{n(n+1)(2n+1)}{6} ][/tex]
[tex][\frac{n}{4}(n+1)+ \frac{n(n+1)(2n+1)}{12} ][/tex]
[tex]\frac{n}{4}(n+1) [1+\frac{(2n+1)}{3} ][/tex]
[tex]\frac{n}{4}(n+1) [\frac{(3+2n+1)}{3} ][/tex]
[tex]\frac{n}{4}(n+1) [\frac{(2n+4)}{3} ][/tex]
[tex]\frac{n}{2}(n+1) [\frac{(n+2)}{3} ][/tex]
[tex]\frac{n(n+1)(n+2)}{6}[/tex]
which is the sum of n terms of the given sequence
Write -5i, 2, and 7 in the simplest polynomial function given the roots
Answer:
x^4-9x^3+39x^2-225x+350
Step-by-step explanation:
The simplest polynomial you can get with that roots are (x-5i)(x+5i)(x-2)(x-7)=x^4-9x^3+39x^2-225x+350
Calculate the length of segment AB on the graph below.
A. Square root of 5
B. Square root of 73
C. Square root of 65
D. Square root of 90
Answer:
D
Step-by-step explanation:
Substitute the co-ordinates if a and b in the distance formula and you will get the answer as sq root of 90 which is D
Solving equations involving vertical angles
Given the figure below, find the values of x and z.
Answer:
[tex]x=5\\z=94[/tex]
Step-by-step explanation:
As they are vertical angles
∴[tex]7x+51=86\\=>7x=35\\x=5[/tex]
And,
∴[tex]86+86+z+z=360\\=>2z=188\\z=94[/tex]
I have added an image for your further observation
Hope you have understood this.....
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if you rolled a die what is the probability that you would roll a 4 or 5
Answer:
1/3
a dice has 6 sides and the probability of getting 4 or 5 is just 2/6 which simplifies to 1/3
what is 98 divided by 5
Answer:
19.6
Step-by-step explanation:
the answer to the question is 19.6
Answer:
19.6
Step-by-step explanation:
We have to do long devision:
5 goes into 9 how many times? Once. So our first number will be one.
9 - 5(1) = 4
Bring the 4 down. Then bring the 8 from 98 down.
5 goes into 48 how many times? Nine times. So our second number will be nine.
48 - 5(9) = 3
Bring the 3 down. Since there is no numbers left from 98, add a decimal and then a zero to make the number 98.0.
5 goes into 30 how many times? Six times. So our third number will be six. Don't forget to add the decimal before the six!
30 - 5(6) = 0
A wedding planner uses 72 ivy stems for 18 centerpieces. When sh arrives at the venue , she realizes she will only need 16 centerpieces. How many ivy stems should she use so that the ratio of ivy stems to centerpieces stays the same ?
Answer:
64 ivy stems
Step-by-step explanation:
72 ivy stems / 18 centerpieces = 4 ivy stems / 1 centerpiece
Create an equation with x being the amount of ivy stems needed.
x / 16 = 4
x = 64
Someone please help.
Hi there!
[tex]f(x)+f(x+1)=4f(x)[/tex]
There are 3 parts to this equation:
f(x)
f(x+1)
4f(x)
We must first determine these three parts separately.
1) f(x)
We're given that [tex]f(x)=3^x[/tex]:
⇒ [tex]f(x)=3^x[/tex]:
2) f(x+1)
Now, we must find f(x+1). To do so, add 1 to x in the original function [tex]f(x)=3^x[/tex]:
⇒ [tex]f(x+1)=3^x^+^1[/tex]
3) 4f(x)
To find 4f(x), multiply the original function [tex]f(x)=3^x[/tex] by 4:
[tex]4f(x)=4*3^x[/tex]:
4) Put it all together
Now, plug each of the three parts into the equation [tex]f(x)+f(x+1)=4f(x)[/tex]:
[tex]f(x)+f(x+1)=4f(x)[/tex]
[tex]3^x+3^x^+^1=4*3^x\\3^x+3^x*3=4*3^x[/tex]
Factor the left side
[tex]3^x*(1+3)=4*3^x[/tex]
Divide both sides by 3^x
[tex]1+3=4\\4=4[/tex]
Because this equation is true, [tex]f(x)+f(x+1)=4f(x)[/tex] is therefore true.
I hope this helps!
Can someone help me with this??
Carlos and Pamela are going on a road trip. They are driving a total of 650 miles in three days to reach the destination. They took it easy the first day. On the second day, they drove twice as many miles as the first day. On the third day, they drove 50 miles more than the second day. How many miles did they drive each day?
Answer:
Carlos and Pamela drove 120 miles on the first day, 240 miles on the second day, and 290 miles on the third day.
Step-by-step explanation:
Let x be the number of miles driven on the first day.
Then they drove twice as many miles, or 2x on the second day
and 50 miles more than the second day's, so 2x + 50
The total is 650 across all three days, so we'll take the sum.
x + 2x + (2x + 50) = 650
Combine like terms on the left
5x + 50 = 650
Subtract 50 on both sides
5x = 600
Divide by 5 on both sides
x = 120
Check work:
120 + 2(120) + 2(120) + 50 = 650
120 + 240 + 240 + 50 = 650
600 + 50 = 650
650 = 650
So they drove 120 miles on the first day
2*120 = 240 miles on the second day
and 2*120 + 50 = 240 + 50 = 290 miles on the third day
please help with these 5 math questions for 25 points!
Answer:
1)C 2)A 3)D
Step-by-step explanation:
(7x2 - 2x - 5)(3x2 + 2x - 3)
Answer:
21x4 + 8x3 - 40x2 + 15
Step-by-step explanation:
expand using distributive property.
how many axes of symmetry does a square have
Answer:
four lines axes of symmetry does a square have
can anyone help me please on this function.
USE (m a t h w a y) its real easy to use
Step-by-step explanation:
the heights of five basketball players are 184 cm, 190 cm, 198 cm, and 202 cm. what is the average height of the five players?
Answer:
93.5
Step-by-step explanation:
Also you only wrote down four numbers not 5 so I calculated it using those four numbers
Answer: 193.5
Step-by-step explanation:
184 + 190 + 198 + 202 = 774
first we add all the numbers together
774/4 = 193.5
then we divide the numbers by the amount of things we have in this case we have four players (last basketball player height not given) so we divide that by our added number and get 193.5cm
Find all y-intercepts of the following function. Express your answer as a coordinate
point in simplest form.
X-4
F(x)=————————
X^2+5x-36
Step-by-step explanation:
to find y intercept, put x to be 0
hence,y int is -36
also, to find x int put y to be 0 and factorise the equation
hence, x are - 9 and 4
finally, the answer in a co ordinate are
(4,-36) , (-9,-36)
600 miles/day into miles per hour
C^-24 times c^9 times c^-87 answer using positive exponents
Answer:
1/c^102
Step-by-step explanation:
C^-24 * c^9 * c^-87
When we multiply exponents with the same base, we add the exponents
c^(-24+9+-87)
c^(-102)
We know that a^-b = 1/a^b
1/c^102
Answer:
Step-by-step explanation:
[tex]a^{m} *a^{n} = a^{m+n}\\\\\ a^{-m}=\dfrac{1}{a^{m}}\\\\\\c^{-24}*c^{9}*c^{-87}=c^{-24+9-87}\\\\=c^{-102}\\\\=\dfrac{1}{c^{102}}[/tex]
By rationalizing the denominator of
[tex] \frac{ \sqrt{2} }{ \sqrt{5 + \sqrt{3} } } [/tex]
Salma got the answer as:
a)
[tex] \frac{ \sqrt{2} }{ \sqrt{5 - \sqrt{3} } } [/tex]
b)
[tex] \frac{ \sqrt{2( \sqrt{5 - \sqrt{3)} } } }{2} [/tex]
c)
[tex] \frac{ \sqrt{2( \sqrt{5 + \sqrt{3}) } } }{2} [/tex]
d)
[tex] \sqrt{5 - \sqrt{3} } [/tex]
Answer:
D
Step-by-step explanation:
What is 7 divided by 329
Answer:
47
Step-by-step explanation:
Do long division.
7 goes into 32, 4 times.
32 - 28= 4
7 goes into 49, 7 times.
Therefore 47 is correct.
can any one solve this please....I kinda need this
9514 1404 393
Answer:
t₂ = 2t₃ = 2Step-by-step explanation:
The given expression says ...
[tex]t_n+1=3\\\\t_n=2\qquad\text{for any value of n}\\\\t_2=2\\\\t_3=2[/tex]
Answer:
[tex]here \: tn + 1 = 3 \\ tn = 2 \\ put \: n = 1 \\ t1 = 2 \\ n = 2 \\ t2 = 2 \\ n = 3 \\ t3 = 2 \\ for \: all \: n \: values \: = 2 \\ thank \: you[/tex]
on a number line to suppose point it has a coordinate of two and EG equals eight what are the possible coordinates of point G
Answer:
I don't understand please can you explain to me
This diagram was created by starting with points A and
B and using only straightedge and compass to construct
the rest. All steps of the construction are visible.
Describe precisely the straightedge and compass moves
required to construct the line CD in this diagram.
The drawing instruments required for a construction, is dependent on the type of construction performed
The straightedge and the compass moves required to construct the line CD in the diagram are;
Move 1: Place the compass at point A and draw circle A with center at A and radius ABMove 2: Place the compass at any point of the circumference of circle A and label the point, at point B. Draw a second circle with the same radius AB and center at point B with the compassMove 3: Label the point the two circles intersect as points C and DMove 4: Place the straightedge at points C and D and construct the straight line CDLearn more about technical drawing here:
https://brainly.com/question/157137
Answer:
Move 1: Place the compass at point A and draw circle A with center at A and radius AB
Move 2: Place the compass at any point of the circumference of circle A and label the point, at point B. Draw a second circle with the same radius AB and center at point B with the compass
Move 3: Label the point the two circles intersect as points C and D
Move 4: Place the straightedge at points C and D and construct the straight line CD
Step-by-step explanation:
if this trapezoid is moved through the translation (x+3,y-2) what will the coordinates of B` be
Answer:
-2, 2
Step-by-step explanation:
Find the exact solution of -x^2+3x+7=0 by using the Quadratic Formula?
what is the opposite of
A) 7 & B) -3
A -7 , -3
B -7 -3
C -7 , 3
D 7 , 3
Melany wants to hang a canvas, which is 8 feet wide, on his wall. Where on the
canvas should Melany mark the location of the hangers if the canvas requires a
hanger every 1/5 of its length, excluding the edges? Justify your answer.
The length of the canvas where Melany will mark the position of the hanger is 1.6 feet.
The given parameters:
length of the canvas = 8 feet
dimension of the hanger = [tex]\frac{1}{5} \ of \ the \ shoe's \ length[/tex]
To find:
the length of the canvas where Melany will mark the position of the hanger.The length of the canvas where Melany will mark the position of the hanger is calculated as follows:
[tex]location \ of \ the \ hanger = \frac{1}{5} \times 8\ ft\\\\location \ of \ the \ hanger = 1.6 \ ft[/tex]
Thus, the length of the canvas where Melany will mark the position of the hanger is 1.6 feet.
Learn more here: https://brainly.com/question/17765207
A _______ is a collection of values.
A. data summary
B. data volume
C. data summation
D. data set
pls help
A data summation is a collection of values.
Pls help me in this my math exam is Tom and I wanna know how to solve theese
Step-by-step explanation:
[tex]thank \: you[/tex]
if a=3x and b = 3x-4i, find the value of a3b In fully simplified form
Kai took a trip from Stratford to Paris in 2013, and needed to exchange 500 British
pounds for euros. The exchange rate was 1 pound to 1.23 euros. How many euros did Kai
receive in this exchange?
Answer:
500pounds×1.23euros
=615euros