Answers
Answer:
4 ( a+2)
Step-by-step explanation:
The average rate of change is
(f(a) - f(2))/(a-2)
f(a) = 4a^2 -8
f(2) = 4*2^2 -8 = 4*4 -8 = 16-8 = 8
(4a^2 - 8 - 8))/(a-2)
(4a^2 -16) / (a-2)
Factor the numerator
4( a^2 -4) / (a-2)
4( a-2)(a+2) / (a-2)
Cancel
4 ( a+2)
Related Questions
Simplify the given expression. Assume x doesn’t = 0. (20x^-3/10x^-1)^-2
X^4/2
X^4/4
X^2/4
Answers
Answer:
X^4
------
4
Step-by-step explanation:
The simplified expression is 1/4x²
What is a polynomial expression?Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is an expression composed of variables, constants, and exponents, combined using mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial. For example P(x) = x²-5x+11
Given here, the expression is (20x⁻³ / 10x⁻¹)⁻² =2⁻²× x⁻²
= 1/4x²
Hence, the simplified expression is 1/4x²
Learn more about polynomial expression here:
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Use the equation and type the ordered-pairs. y = log 2 x {(1/2, a0), (1, a1), (2, a2), (4, a3), (8, a4), (16, a5)}
Answers
Answer:
the answer is 1/2,a0
Step-by-step explanation:
Find the median of the following set of data: 4, 7, 2, 1, 4, 6,
2,6
Answers
Answer:
(4+4)/2 = 4
Hope this helps
Answer:
4
Step-by-step explanation:
1,2,2,4,4,6,6,7
The median is the number in the middle however there are an even amount of numbers so you get the number between 4 and 4 which is just 4
Only answer if you know geometry or if you know this
Answers
Answer:
SAS
Step-by-step explanation:
the angles are congruent, and the 2 pairs of sides are proportional.
200/150 is 4/3 and 320/240 is 4/3 as well.
therefore Side-Angle-Side
If the selected consumer is 70 years old, what is the probability that he/she likes crunchicles
Answers
Answer:
The probability that a selected consumer, given that is 70 years old, likes Crunchicles is 12.78%.
Step-by-step explanation:
The question is incomplete:
Three hundred consumers were surveyed about a new brand of snack food, Crunchicles. Their age groups and preferences are given in the table.
18–24 25–34 35–55 55 and over Total
Liked Crunchicles 4 9 3 23 39
Disliked Crunchicles 5 27 28 64 124
No Preference 7 27 10 93 137
Total 16 63 41 180 300
One consumer from the survey is selected at random. If the selected consumer is 70 years old, what is the probability that he/she likes crunchicles .
If the consumer is 70 years old is included in the category "55 and over" from this survey. There are 180 subjects in that category.
The number that likes Crunchicles and are 55 and over is 23.
If we calculate the probability as the relative frequency, we have:
[tex]P(\text{L }|\text{ 55+})=\dfrac{P(\text{L \& 55+})}{P(5\text{5+})}=\dfrac{23}{180}=0.1278[/tex]
L: Likes Crunchicles.
The probability that a selected consumer, given that is 70 years old, likes Crunchicles is 12.78%.
What is the solution set of the quadratic inequality x2+x-2
Answers
Answer:
The solution set is x = 1 and x = -2
Step-by-step explanation:
Help plzzzzzzzssssss
Answers
Answer:
16
Step-by-step explanation:
There are three possible equations: the first is used for inputs (x-values) in between negative infinity and -7, the second for inputs in between -7 and 2, and the third for inputs in between 2 and infinity. 7 is in between 2 and infinity so the third equation is applicable.
[tex]g(x)=(x+1)(x-5)[/tex]
[tex]g(7)=(7+1)(7-5)[/tex] Plug in the values
[tex]g(7)=(8)(2)[/tex] Simplify
[tex]g(7)=16[/tex]
hope this helped
An orange is shot up into the air with a catapult. The function h given by
h(t) = 15 + 60t – 16t2 models the orange's height, in feet, 1 seconds after it was
launched.
Question 5 What is the initial speed at which the orange is shot in the air?
Answers
Answer:
Velocity = 59 feet/second
Step-by-step explanation:
h(t) = 15 + 60t – 16t2
Time t = 1 second
Let's substitute time into the equation to get the distance
h(t) = 15+60(1)-16(1)²
h(t) = 15 + 60 - 16
h(t) = 59 feet
Speed or velocity = distance/time
Distance = 59 feet
Time = 1 second
Velocity = 59/1
Velocity = 59 feet/s
Write the point slope form of an equation of the line through the points (-2,6) and (3,-3)
Answers
Answer:
A.
Step-by-step explanation:
So first you need to find the slope:
[tex]\frac{-2-6}{3+2} =-\frac{8}{5}[/tex]
Since it's point slope, you have to use a point:
It's either:
[tex](y - 6)=-\frac{8}{5}(x+2)[/tex]
or
[tex](y+2)=-\frac{8}{5}(x-3)[/tex]
Check which answer has those:
A.
The solution is Option A.
The equation of line is y - 6 = ( -8/5 ) ( x + 2 ) where the slope is -8/5
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( -2 , 6 )
Let the second point be Q ( 3 , -2 )
The slope of the line between the point is given by m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 6 - ( - 2 ) ) / ( -2 - 3 )
On simplifying the equation , we get
Slope m = ( 8 / -5 ) = -8/5
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 6 = ( -8/5 ) ( x - ( -2 ) )
On simplifying the equation , we get
y - 6 = ( -8/5 ) ( x + 2 )
Hence , the equation of line is y - 6 = ( -8/5 ) ( x + 2 )
To learn more about equation of line click :
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URGENT!! EASY IM DUMB MY LAST QUESTION WILL FOREVER BE GRATEFUL PLS HELP WILL GIVE BRANLIEST!! AT LEAST TAKE A LOOK!!!! PLS I AM BEGGING!!!
YOU HAVE TO LOOK CLOSLY TO SEE THE NUMBERS ON THE TRIANGLE
IN CASE YOU CANNOT ON THE LEFT IT IS 15CM AND ON THE BOTTOM IT IS 14 CM
Find the unknown side of the triangle below (round to the nearest tenth).
A) 20.5 cm
B) 210.5 cm
C) 5.4 cm
D) 16 cm
Answers
Answer:
A. 20.5
Step-by-step explanation:
We can use the Pythagorean theorem to solve this equation for the missing side length, X.
a^2 + b^2 = c^2
We have a and b, we just need c, the hypotenuse.
14^2 + 15^2 = c^2
196 + 225 = c^2
421 = c^2
Now, we will square both sides:
The answer is about 20.5
What’s the Midpoint of (2,-1) and (1,-2)
Answers
Answer:
(3/2,-3/2)
Step-by-step explanation:
The midpoint of (2,-1)(1,-2) is (3/2,-3/2)
Answer:
(1.5,-1.5)
You have to remember the formula to find mid-point and that is:
[tex]midpoint = ( \frac{x1 + x2}{2} ,\frac{y1 + y2}{2} )[/tex]
please see the attached picture for full solution
Hope it helps
Good luck on your assignment
Jacob put his 731 Marbles and 37 bags if he puts the same amount in each bag how many marbles were in each bag how many marbles were left out of the backs
Answers
Answer:
19 marbles in each bag 28 left over
Step-by-step explanation:
the first step to this problem is to find out the number of marbles in each bag.
if there were 731 marbles and 37 bags, we need to divide 731 by 37.
731/37 = 19[tex]\frac{28}{37}[/tex]
therefore there are 19 marbles in each bag.
the second part of the question is to determine how many are left out or in other words how many numbers are "left over"
since the fraction is 28/37 there are 28 marbles that are left out of the bag.
feel free to ask questions, hope this helped you!
what are the solutions
Answers
Answer:
2 and -8
Step-by-step explanation:
[tex]x^2+6x-6=10 \\\\x^2+6x-16=0 \\\\(x+8)(x-2)=0 \\\\x=2, -8[/tex]
Hope this helps!
А
What is the measure of ZDAB?
&
B
Enter your answer in the box.
D
96°
C
Next
Answers
Answer:
84°
Step-by-step explanation:
Adjacent angles in a parallelogram are supplementary:
∠A = 180° -96°
∠A = 84°
What is the y coordinate of the point that divides the directed line segment from j to k into a ratio of 2 to 3
Answers
Answer:
y = [tex]y_{1}[/tex] + rise * 2/5
Step-by-step explanation:
5.44 Teaching descriptive statistics: A study compared five different methods for teaching descriptive statistics. The five methods were traditional lecture and discussion, programmed textbook instruction, programmed text with lectures, computer instruction, and computer instruction with lectures. 45 students were randomly assigned, 9 to each method. After completing the course, students took a 1-hour exam. (a) What are the hypotheses for evaluating if the average test scores are different for the different teaching methods?
Answers
Answer:
The null hypothesis is that all the different teaching methods have the same average test scores.
H0: μ1 = μ2 = μ3 = μ4 = μ5
The alternative hypothesis is that at least one of the teaching methods have a different mean.
Ha: at least one mean is different. (μ1 ≠ μi)
Step-by-step explanation:
The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.
For the case above, let μ represent the average test scores for the teaching methods:
The null hypothesis is that all the different teaching methods have the same average test scores.
H0: μ1 = μ2 = μ3 = μ4 = μ5
The alternative hypothesis is that at least one of the teaching methods have a different mean.
Ha: at least one mean is different. (μ1 ≠ μi)
What is X=
5/6 = 10/2x−3
Answers
Answer: x= 23/30
Step-by-step explanation:
[tex]\frac{5}{6}[/tex] = [tex]\frac{10}{2}x -3[/tex] reduce 10/2 to 5 because 10/2 is 5.
5/6 = 5x -3
+ 3 +3
23/6 = 5x divide both sides by 5.
x= 23/30
Use the distributive property to remove the parentheses .
-8(y-v-3)
Answers
Answer:
-8y +8v +24
Step-by-step explanation:
-8(y-v-3)
Multiply each term inside the parentheses by -8
-8y -v*-8 -3*-8
-8y +8v +24
___________________________________
Hey!!!
solution,
-8(y-v-3)
= -8y+8v+24
_________________________________
Here,
You have to remember these things:
(+)*(+)=(+)(+)*(-)=(-)(-)*(-)=(+)(-)*(+)=(-)Hope it helps.
Good luck on your assignment
If the measure of the angle in the southwest corner of the intersection of Broadway and 21st Street is approximately 105ºwhat is the measure of the angle in the southwest corner of the intersection of Broadway and 22nd Street?
A: 85 degrees
B: 95 degrees
C: 120 degrees
D: 105 degrees
Answers
Answer:
95°
Step-by-step explanation:
The angle on the 20TH street and 22ND street must add up to 180° so the answer is 95°
Answer:
This isnt right. Good try though
Step-by-step explanation:
Anyone know the answer?
What is the length of AC
Answers
Answer:
5.8
Step-by-step explanation:
The angle bisector makes the triangle sides on either side of it proportional.
AC/CD = AB/BD
AC = CD·AB/BD
AC = 2(8.1/2.8) = 8.1/1.4 ≈ 5.7857 . . . . substitute shown values, evaluate
AC ≈ 5.8
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answers
Answer:
D. It would be less steep
Step-by-step explanation:
The first graph moves at a rate of 5/1 which is a greater fraction than 3/4
The second graph is shallow due to the close points in x and y that are able to be conducted The first Graph rapidly increases at a way higher rate making it VERY steepWhile both are linear the second strays away in terms of plot linesadiocarbon dating of blackened grains from the site of ancient Jericho provides a date of 1315 BC ± 13 years for the fall of the city. What is the relative amount of 14C in the old grain vs the new grain in 2007 AD? (A0 = original radioactivity; At = radioactivity in 2007 AD).
Answers
Answer:
[tex]\left(\frac{m(t)}{m_{o}} \right)_{min} \approx 0.659[/tex] and [tex]\left(\frac{m(t)}{m_{o}} \right)_{max} \approx 0.661[/tex]
Step-by-step explanation:
The equation of the isotope decay is:
[tex]\frac{m(t)}{m_{o}} = e^{-\frac{t}{\tau} }[/tex]
14-Carbon has a half-life of 5568 years, the time constant of the isotope is:
[tex]\tau = \frac{5568\,years}{\ln 2}[/tex]
[tex]\tau \approx 8032.926\,years[/tex]
The decay time is:
[tex]t = 1315\,years + 2007\,years \pm 13\,years[/tex] (There is no a year 0 in chronology).
[tex]t = 3335 \pm 13\,years[/tex]
Lastly, the relative amount is estimated by direct substitution:
[tex]\frac{m(t)}{m_{o}} = e^{-\frac{3335\,years}{8032.926\,years} }\cdot e^{\mp\frac{13\,years}{8032.926\,years} }[/tex]
[tex]\left(\frac{m(t)}{m_{o}} \right)_{min} = e^{-\frac{3335\,years}{8032.926\,years} }\cdot e^{-\frac{13\,years}{8032.926\,years} }[/tex]
[tex]\left(\frac{m(t)}{m_{o}} \right)_{min} \approx 0.659[/tex]
[tex]\left(\frac{m(t)}{m_{o}} \right)_{max} = e^{-\frac{3335\,years}{8032.926\,years} }\cdot e^{\frac{13\,years}{8032.926\,years} }[/tex]
[tex]\left(\frac{m(t)}{m_{o}} \right)_{max} \approx 0.661[/tex]
TIVITY MODULE
The length of a rectangle is eight centimeter less than
twice the width. The area of the rectangle is 24
centimeters squared. Determine the dimensions of the
rectangle in centimeters.
Answers
Answer: Length: 4, width: 6
Step-by-step explanation:
Let the length be x and width be y
Then x=2y-8 and xy=24
Substitute to get 2y-8 * y = 24, so 2y^2-8y=24 or y^2-4y=12, then solve to get y=6 or y=-2. Since width is positive y=6.
Substitute y=6 into xy=24 to get x=4.
Length: 4, width: 6
Hope that helped,
-sirswagger21
When the health department tested private wells in a county for two impurities commonly found in drinking water, it found that 10% of the wells had neither impurity, 90% had impurity A, and 20% had impurity B. (Obviously, some had both impurities.) If a well is randomly chosen from those in the county, find the probability distribution for Y, the number of impurities found in the well.
Answers
Answer:
P(Y= 0) = 0.1
P(Y= 0) = 0.7
P(Y= 0) = 0.2
Step-by-step explanation:
Let Y be number of impurities that can be found in the well,
Let A denote the event that impurity A is randomly found in the well
Here Y can have three values i.e 0 , 1 and 2
✓It will take take the value of 0 when there is no impurity found in the well
✓It will take the value of 1 when when exactly one impurity vis found in the well
✓It will take the value of 2 when when both impurities vis found in the well
CHECK THE ATTACHMENT FOR DETAILED EXPLATION
Patrick’s luck had changed over night – but not his skill at mathematical reasoning. The day after graduating from college he used the $20 that his grandmother had given him as a graduation gift to buy a lottery ticket. He knew his chances of winning the lottery were extremely low and it probably was not a good way to spend this money. But he also remembered from the class he took in business analytics that bad decisions some-times result in good outcomes. So he said to himself, "What the heck? Maybe this bad decision will be the one with a good outcome." And with that thought, he bought his lottery ticket.The next day Patrick pulled the crumpled lottery ticket out of the back pocket of his bluejeans and tried to compare his numbers to the winning numbers printed in the paper. When his eyes finally came into focus on the numbers they also just about popped out of his head. He had a winning ticket! In the ensuing days he learned that his share of the jackpot would give him a lump sum payout of about $500,000 after taxes. He knew what he was going to do with part of the money, buy a new car, pay off his college loans, and send his grandmother on an all expenses paid trip to Hawaii. But he also knew that he couldn’t continue to hope for good outcomes to arise from more bad decisions. So he decided to take half of his winnings and invest it for his retirement. So what do you think? Who is right, Josh or Peyton? And more important, why?
Answers
Answer:
I assume Josh and Peyton are his friends and both gave him advice on what to do with half of the money from the big lottery win.
Let's say Josh said "save it or invest it for your retirement" and Peyton said "use it to keep playing the lottery.
We will now look at the sense in each piece of advice!
Step-by-step explanation:
JOSH
By investing the $250,000 (half of the money won), Patrick will be sure that the money is available for him anytime and would even have gotten interest, by the time he's ready to use it.
PEYTON
By playing the lottery continuously, Patrick could get lucky once in a while and win big again. How big though?
Analyzing with the figures given,
$20 gets Patrick a lottery ticket.
$250,000 will get him 12,500 lottery tickets!
Whether he's buying the tickets at once or he'll play the lottery once in a while, I'll say he has good chances of winning big again.
So if the probability of winning big after purchasing up to 12,500 tickets is close to 1, Patrick should play the lottery with the $250,000
If the probability of winning big after purchasing 12,500 lottery tickets is close to 0 (closer to 0 than it is to 1) then Patrick should invest the $250,000 in retirement.
Find the volume of the prism.
The volume is cubic meters.
Answers
Given the diagram below, what is m
Answers
where is m?
if it was asking for angle A the answer would be D.
Answer:
D. 70
Step-by-step explanation:
because the D side is the same line as A and the D side is also 70
which equation represents a line perpendicular to the line shown on the graph
Answers
Answer:
y = 1/4x + (any number)
Step-by-step explanation:
m = -8/2 = -4, the equation shown is y = -4x + 8
perpendicular is y = 1/4x + (any number), you didn't say where the line was perpendicular.
Choose the function that is a "parent function".
Answers
Answer:
f(x)=√x
Step-by-step explanation:
A parent function is something simple with just x
Answer:
f(x)=Square Root of x (choice B or the second one down)
Step-by-step explanation:
All the other choices have either a plus 3 or minus 3. A parent function is not going to have any type of number being added or subtracted to it.
Please answer this correctly
Answers
Answer:
0
Step-by-step explanation:
No one is there which satisfies the condition
Answer:
0 or 0/9 of the club members
Step-by-step explanation:
The only part of the data of members that have logged more than 1 1/5 but less than 1 3/5 hours is the members that logged 1 2/5 hours. There are no members that have logged 1 2/5 hours so our answer is 0 or 0/9.