Answer:
See Explanation
Step-by-step explanation:
The function is not properly given. So, to solve this question I'll assume it is:
f(x) = x² + 3
Required
Calculate the average rate of change on −1 ≤ x ≤ 3.
[The average rate of change (R) is calculated using:]
R = (f(b) - f(a))/(b - a)
[Where]
a ≤ x ≤ b = −1 ≤ x ≤ 3.
[This means that]
a = -1
b = 3
[Solving f(b); We have]
f(x) = x² + 3
[Substitute b for x]
f(b) = b² + 3
[Substitute 3 for b]
f(3) = 3² + 3 = 9 + 3 = 12
[Solving f(a); We have]
f(x) = x² + 3
[Substitute a for x]
f(a) = a² + 3
[Substitute -1 for b]
f(-1) = (-1)² + 3 = 1 + 3 = 4
[So, the equation becomes]
R = (f(b) - f(a))/(b - a)
R = (12 - 4)/(3 - (-1)
R = 8/(3+1)
R = 8/4
R = 2
[Hence, the average rate of change is 2]
An exercise bike increased in price from $415 to $498 find the percent increase in the cost of the exercise bike
Answer:
20%
Step-by-step explanation:
((498/415)-1)*100
= (1.2-1)*100
= 0.2*100
= 20
Write a polynomial function of least degree with real coefficients in standard form that has the given zeros. –2, –4, –3 + 4i
Given:
Zeroes of a polynomial are –2, –4, –3 + 4i.
To find:
The polynomial function of least degree with real coefficients in standard form.
Solution:
According to the complex conjugate root theorem, if a complex number a+ib is a zero of a polynomial, then its conjugate a-ib is also a zero of than polynomial.
–3 + 4i is zero of the polynomial. So, by complex conjugate root theorem -3-4i is also a zero of required polynomial.
If c is a zero of p(x), then (x-c) is a factor of p(x).
–2, –4, –3 + 4i, -3-4i are zeroes of the polynomials. So, (x+2), (x+4), (x+3-4i), (x+3+4i) are the factors of the required polynomial.
Let the required polynomial be p(x), so
[tex]p(x)=(x+2)(x+4)(x+3-4i)(x+3+4i)[/tex]
[tex]p(x)=(x^2+4x+2x+8)((x+3)^2-(4i)^2)[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
[tex]p(x)=(x^2+6x+8)(x^2+6x+9-16i^2)[/tex] [tex][\because (a+b)^2=a^2+2ab+b^2][/tex]
[tex]p(x)=(x^2+6x+8)(x^2+6x+9-16(-1))[/tex] [tex][\because i^2=-1][/tex]
[tex]p(x)=(x^2+6x+8)(x^2+6x+9+16)[/tex]
[tex]p(x)=(x^2+6x+8)(x^2+6x+25)[/tex]
[tex]p(x)=x^2(x^2+6x+25)+6x(x^2+6x+25)+8(x^2+6x+25)[/tex]
[tex]p(x)=x^4+6x^3+25x^2+6x^3+36x^2+150x+8x^2+48x+200[/tex]
Combining like terms, we get
[tex]p(x)=x^4+(6x^3+6x^3)+(25x^2+36x^2+8x^2)+(150x+48x)+200[/tex]
[tex]p(x)=x^4+12x^3+69x^2+198x+200[/tex]
Therefore, the required polynomial is [tex]p(x)=x^4+12x^3+69x^2+198x+200[/tex].
Please do it I don’t know how to
Answer:
Step-by-step explanation:
I'm that's hard to do
Find the distance between the two points. Write your answer as a decimal rounded to the hundredths place if needed.
(-9,1) and (-10, -11)
Answer:
12.04Step-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{ ({x_1 - x_2})^{2} + ({y_1 - y_2})^{2} } \\[/tex]
From the question we have
[tex]d = \sqrt{ ({ - 9 - - 10})^{2} + ({1 - - 11})^{2} } \\ = \sqrt{ ({ - 9 + 10})^{2} + ({1 + 11})^{2} } \\ = \sqrt{ {1}^{2} + {12}^{2} } \\ = \sqrt{1 + 144} \\ = \sqrt{145} \: \: \: \: \: \: \: \: \\ = 12.041594[/tex]
We have the final answer as
12.04 to the nearest hundredthHope this helps you
simplify fully: (9(x+7)^2)/(3(x-1)(x+7))
Step-by-step explanation:
9(x + 7)² divided by 3(x - 1)(x + 7)
= 3(x + 7)/(x - 1).
Before Cam broke his right arm, he was able to type 9 words per minute on his phone. After he broke his arm, he had to use his left hand for a while, and he could only type 6 words per minute. What is the difference between the number of words he could type in 5 minutes before and after he broke his arm.
Answer:Before he broke his arm: 45 words in 5 minutes
After he broke his arm: 30 words in 5 minutes
9*5=45 6*5=30
Hope this helps... mark as Brainliest plz
Step-by-step explanation:
plzzzzzzzzzzzzzzzzzzzzzzzz
If six people share 4 pints of lemonade equally, how much lemonade will each person receive?
Answer:
1.5
i think
Step-by-step explanation:
Which ordered pair is a solution of the equation?
y = -6x+1
Answer:
2,-11
Step-by-step explanation:
create an x/y table and plug in #s for ordered pairs
-6x + 1 = y [plug in 2 for x]
-12 + 1 = -11 [ordered pair is 2, -11]
Answer:
Both (-2, 13) and (-1, 7)
Step-by-step explanation:
Got it from Khan
Someone please help me!
the points (-5,4)and (1,r) lie on a line with slope -1. Find the missing coordinates r.
Answer:
R has to be -2
Step-by-step explanation:
So to find a slope the formula is written as
Y2-Y1/ X2 -X1
We know X1 and X2 and Y1.
If we plug those in and put Y2 as the variable ”r”
You’ll get
[tex]\frac{r-4}{1+5}[/tex]
Now make that equal to -1 since thats the slope
If you solve the equation it should get you -2
If the perimeter of a rectangle is 34 cm and the area is 60 square cm, then what are the dimensions of the
rectangle?
Answer: 12 by 12 by 5 by 5
Step-by-step explanation: 12*5 = 60
12+12+5+5
=34
Is it true that Terms with no variables are like terms?
Answer:
yes
Step-by-step explanation:
What is the equation of the line that passes through the point (4,5) with a zero slope?
Answer:
x=5
Step-by-step explanation:
Since there is no slope, there must be a constant y.
The constant y for this coordinate is 5.
When we have the equation x=5, that creates a straight line through all coordinates with 5 as a y-value.
Harry earned d dollars mowing lawns. He put 20% of his earnings in the bank and paid back $50.00 to his father. He spent one-fifth of the re mb ainig money on a video game. Which expreesion represents the amount he spent on the video game _,_,_,_
The question is incomplete.
Complete Question
Harry earned d dollars mowing lawns. He put 20% of his earnings in the bank and paid back $50.00 to his father. He spent one-fifth of the remaining money on a video game. Which expression represents the amount he spent on the video game?
(0.20 - 10) dollars
(0.20 - 50) dollars
(0.160 + 10) dollars
(0.160 - 10) dollars
Answer:
(0.160 - 10) dollars
Step-by-step explanation:
Let the total number of earnings be represented by d
Harry earned d dollars mowing lawns. He put 20% of his earnings in the bank
Amount in the bank = 20% of d = 0.20d
He paid back $50.00 to his father.
The amount left = 1d - 0.20d = 0.80d
He paid back his father
Hence:
= (d - 0.20d) - $50
= 0.80d -$50.00
He spent one-fifth of the remaining money on a video game.
The amount remaining
= 0.80d -$50.00
Hence, the amount he spent on video games =
1/5(0.80d - $50.00)
(0.16d - $10.00)
= (0.16d - 10)
= (0.16 - 10) dollars
Can someone help me
Answer:
ok sooo just go over the grfat and mm count it up to the dot.
Step-by-step explanation:
Allison can sew three scarves in 75 minutes how many scarves can she sew in 4 hours?
Answer: 9
Step-by-step explanation:
I think this is the answer based off a estimate
help is much appreciated!!
Find the value of T.
A. 12 B. 5 C. 4 D. 16
On a trip last summer, I used 20 gallons of gas to travel 600 miles. At this rate, how much gas
would I need to go 1500 miles?
Answer:
45,000
Step-by-step explanation:
You should divide 20 by 600 to see how many miles he would run per mile
and you take 30 x 1,500 to get your answer
-
What is the slope of the line Perpendicular to y = -x- 10
-4
04
o
o Zero
Need help
Answer:
A. -4
Step-by-step explanation:
Perpendicular lines have negative slopes
so you would have to flip the fraction and change the sign
so 1/4x = -4/1x or -4x
1/4 , 1, 4, 16, 64, ________, ________, ________
Answer:
256, 1024, 4096
Step-by-step explanation:
Multiply the number by 4 to get the next one.
Brainliest please
Five friends decided to get together to bake cookies for a fundraiser. In total, they baked 144 cookies and packaged them in dozens. How many packages of cookies did they bake?
.........................................................I am d u m b
What type of lines are coplanar and do not intersect?
A) Parallel
B) Perpendicular
C) Segments
D) Transversal
Answer:
A(parallel
I hope this helps you
A carpenter has 10 ½ feet of wooden plank. He cuts off 4 ¼ feet to replace the slat of deck and 3 ⅔ feet to repair a bannister. He uses the rest of the plank to fix a stair. How many feet of wood does the carpenter use to fix the stair?
Cobra Kai yehdhehdhehehebdhdhdvdgdhdhdhdbdhdbdh
Whether a team had zero, one, or two Liberos for the first
sets of the match, they may designate new Liberos for the
deciding set.
Answer:
Whether a team had zero, one, or two Liberos for the first
sets of the match, they may designate new Liberos for the
deciding set.
sheet at the start of the match. If zero or one Libero is designated on the line-up sheet, the coach may select a different Libero for subsequent sets, but may not have two Liberos. If two Liberos are designated on the line-up sheet for Set 1, those are the only two Liberos who may play for that team for the match. b.
Step-by-step explanation:
No. Whether a team designates one or two Liberos for the start of the match, the player(s) designated as Libero prior to the match will be the only players who may participate as a Libero in the match, except in the cases where re- designation is permitted
2) A big league pitching coach tries to limit his pitchers to 110
pitches per game. If the pitcher has already thrown 52
pitches, write and solve an inequality to find how many more
pitches he can throw before reaching the limit.
Solve the equation: [tex]5^x^(^x^-^1^)=1[/tex]
The concept:
We are given the equation:
[tex]5^{x(x-1)} = 1[/tex]
Which can be simplified as:
[tex]5^{x^{2} - x} = 1^{1}[/tex]
Since any number to the power '0' is 1
x² - x must be equal to 0 for the given equation to be true
Solving for x:
x² - x = 0
x(x-1) = 0
now, we can divide both sides by either x OR x-1
So we will see what we get for either choice:
x = 0/(x-1) x-1 = 0/x
x = 0 x = 1
Hence, the value of x is either 0 or 1
2x +18 = 9x + 14 for x.
Answer:
X= 4/7
Step-by-step explanation:
I used a calculator :)
Simplify: 3(2x+7)-2(x+5)
Answer:
=4x+11
Step-by-step explanation:
Answer:
4x - 11
Step-by-step explanation:
3(2x+7)-2(x+5)
6x + 21 - 2x - 10
combine like terms
4x - 11
Hope this helps!!
PLEASE HURRY
Which equation has only one solution?
O-5|=-1
O6-2x| =8
O 5x+ 10| =10
O-6x+ 3| = 0
Answer:
D
Step-by-step explanation:
|-6x+3|=0
-6x+3=0
-6x=-3
x=-3/-6
x=1/2