The next two terms of the sequence based on the information given is 37 and 50.
How to illustrate the sequence?It should be noted that from the information given, the numbers illustrated are 5, 10, 17, and 26.
In this case, there is an addition of 2 to the previous difference.
Therefore, 26 - 17 = 9.
The next number will be:
= 26 + 9 + 2 =37
The following number will be:
= 37 + 11 + 2
= 50
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what is the answer to 20÷ 1683 pls
The function y=f(x is graphed below. What is the average rate of change of the function f(x)on the interval 0≤x≤5?
[tex]m = \frac{f(5) - f(0)}{5 - 0} [/tex]
[tex]m = \frac{ - 10 - 10}{5} = \frac{ - 20}{5} = - 4[/tex]
Step-by-step explanation:
the average rate of change is
(f(high interval end) - f(low interval end))/(high interval end - low interval end)
in our case here
(f(5) - f(0)) / (5 - 0)
(-10 - 10) / 5 = -20/5 = -4
(-4, 7), (-6,-4)
find the slope of the line through each pair of points
Answer:
slope = 11/2
Step-by-step explanation:
If you are given two points, you can find the slope using the point-slope equation. The equation looks like this:
y₁ - y₂ = m(x₁ - x₂)
In this form, "m" represents the slope, "x₁" and "y₁" represent the values from one point, and "x₂" and "y₂" represent the values from the other point. You can plug the values from the points into the equation and simplify to find the slope.
Point 1: (-4, 7) Point 2: (-6, -4)
x₁ = -4 x₂ = -6
y₁ = 7 y₂ = -4
y₁ - y₂ = m(x₁ - x₂) <----- Point-slope form
7 - (-4) = m(-4 - (-6)) <----- Insert values
11 = m(2) <----- Simplify
11/2 = m <----- Divide both sides by 2
[tex]\huge\boxed{\frac{11}{2}}[/tex]
The slope is equivalent to vertical change divided by horizontal change, otherwise known as "rise over run".
Therefore, the slope can be represented with the following equation, where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are your points:
[tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values and simplify to find the answer.
[tex]\dfrac{(-4)-7}{(-6)-(-4)}[/tex]
[tex]\dfrac{-4-7}{-6+4}[/tex]
[tex]\dfrac{-11}{-2}[/tex]
[tex]\boxed{\frac{11}{2}}[/tex]
consider function g. g(x) = { (1/2)^x +3, x< 0. -x^2 +2, x>_ 0
[tex]\square[/tex] The function is continuous. [False]
Both pieces of the function are continuous, so the overall continuity of [tex]g(x)[/tex] depends on continuity at [tex]x=0[/tex].
We have
[tex]\displaystyle \lim_{x\to0^-} g(x) = \lim_{x\to0} \left(\frac1{2^x} + 3\right) = 1 + 3 = 4[/tex]
and
[tex]\displaystyle \lim_{x\to0^+} g(x) = \lim_{x\to0} (-x^2+2) = 2[/tex]
The one-sided limits do not match, so [tex]g[/tex] is not continuous at [tex]x=0[/tex].
[tex]\square[/tex] As [tex]x[/tex] approaches positive infinity, [tex]g(x)[/tex] approaches positive infinity. [False]
[tex]g(x)[/tex] is a large negative number when [tex]x[/tex] is very large, so [tex]g(x)[/tex] is approaching negative infinity.
[tex]\boxed{\checkmark}[/tex] The function is decreasing over its entire domain. [True]
This requires [tex]g'(x) \le 0[/tex] on the entire real line. Compute the derivative of [tex]g[/tex].
[tex]g'(x) = \begin{cases}-\ln(2)\left(\dfrac12\right)^x & x<0 \\\\ ? & x=0 \\\\ -2x & x>0 \end{cases}[/tex]
• [tex]\left(\frac12\right)^x > 0[/tex] for all real [tex]x[/tex], so [tex]g'(x)<0[/tex] whenever [tex]x<0[/tex].
• [tex]x^2\ge0[/tex] for all real [tex]x[/tex], so [tex]-x^2\le0[/tex] and [tex]-x^2+2\le2[/tex]. Equality occurs only for [tex]x=0[/tex], which does not belong to [tex]x>0[/tex].
Whether the derivative at [tex]x=0[/tex] exists or not is actually irrelevant. The point is that [tex]g(b) < g(a)[/tex] if [tex]b>a[/tex] for all real [tex]a,b[/tex].
[tex]\boxed{\checkmark}[/tex] The domain is all real numbers. [True]
There are no infinite/nonremovable discontinuities, so all good here.
[tex]\boxed{\checkmark}[/tex] The [tex]y[/tex]-intercept is 2. [True]
When [tex]x=0[/tex],
[tex]g(0) = -0^2 + 2 = 2[/tex]
to shift the graph of an equation a certain number of units down, you need to ______ the function equation
Answer:
Step-by-step explanation:
...You need to subtract that number of units from the function equation.
Example: given y = x^2, and wanting to shift the entire graph down 3 units, we subtract 3 from y = x^2, obtaining y = x^2 - 3.
A ball is thrown from an initial height of 5 feet with an initial upward velocity of 31 ft/s. The ball's height (in feet) after t seconds is given by the following.
h=5+31t-16t^2
Find all values of t for which the ball's height is 19 feet.
t= _ seconds
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
Solving a quadratic function, it is found that the ball has a height of 19 feet at t = 0.72 seconds and t = 1.22 seconds.
What is a quadratic function?A quadratic function is given according to the following rule:
[tex]y = ax^2 + bx + c[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]In which:
[tex]\Delta = b^2 - 4ac[/tex]
In this problem, the function is:
h(t) = -16t² + 31t + 5
The height is of 19 feet when h(t) = 19, hence:
19 = -16t² + 31t + 5
16t² - 31t + 14 = 0.
Then:
[tex]\Delta = (-31)^2 - 4(16)(14) = 65[/tex][tex]x_1 = \frac{31 + \sqrt{65}}{32} = 1.22[/tex][tex]x_2 = \frac{31 - \sqrt{65}}{32} = 0.72[/tex]More can be learned about quadratic functions at https://brainly.com/question/24737967
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The width of a rectangular house is 22 feet. What is the perimeter of this house if it has the same area as a house that is 33 ft wide and 50 ft long
1) 184 feet
2) 200 feet
3) 194 feet
4) 206 feet
Answer:
3) 194 feet
Step-by-step explanation:
The other house:
"a house that is 33 ft wide and 50 ft long"
area = LW = (33 ft)(50 ft) = 1650 ft²
This house:
LW = A
L × 22 ft = 1650 ft²
L = 75 ft
P = 2(L + W)
P = 2(75 ft + 22 ft)
P = 194 ft
Answer: 3) 194 feet
Answer:
3) P = 194 ft.
Step-by-step explanation:
[tex]A=wl[/tex]
[tex](30)(50)=22l[/tex]
[tex]1650=22l[/tex]
[tex]l=1650/22=75[/tex]
the dimensions of the house are: (22 × 75)
Perimeter:
[tex]p=2(22)+2(75)=44+150=194[/tex]
Hope this helps
Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800. A researcher from the admissions department at the University of New Hampshire is interested in estimating the mean math SAT scores of the incoming class with 95% confidence. How large a sample should she take to ensure that the margin of error is below 29?
Using the z-distribution, it is found that she should take a sample of 46 students.
What is a z-distribution confidence interval?
The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
The margin of error is:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800, hence, by the Empirical Rule the standard deviation is found as follows:
[tex]6\sigma = 800 - 200[/tex]
[tex]6\sigma = 600[/tex]
[tex]\sigma = 100[/tex]
The sample size is n when M = 29, hence:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]29 = 1.96\frac{100}{\sqrt{n}}[/tex]
[tex]29\sqrt{n} = 196[/tex]
[tex]\sqrt{n} = \frac{196}{29}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{196}{29}\right)^2[/tex]
n = 45.67.
Rounding up, a sample of 46 students should be taken.
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Melissa Costouras obtains a $3,000 loan for darkroom equipment. She makes six monthly payments of $511.18. Determine the APR.
Using the simple interest formula, it is found that the APR for the loan is of 4.472%.
What is the simple interest formula and when it is used?Simple interest is used when there is a single compounding per time period.
The amount of money after t years in is modeled by:
[tex]A(t) = A(0)(1 + rt)[/tex]
In which:
A(0) is the initial amount.r is the interest rate, as a decimal.The parameters for this problem are:
A(t) = 6 x 511.18 = 3067.08, A(0) = 3000, t = 0.5.
We solve the equation for r to find the APR.
[tex]A(t) = A(0)(1 + rt)[/tex]
[tex]3067.08 = 3000(1 + 0.5r)[/tex]
[tex]1 + 0.5r = \frac{3067.08}{3000}[/tex]
1 + 0.5r = 1.02236
r = (1.02236 - 1)/0.5
r = 0.04472.
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The function P=48∙e^((.045t)) gives the number of bacteria in a population as a function of time in hours.
a) How many bacteria are there in t = 8 hours? *Accurate to four decimal.
b) How fast is this population growing in t = 8 hours? *Accurate to four decimals.
The number of bacteria when t = 8 is approximately 66 bacterias
Exponential functionsGiven the function that gives the number of bacteria in a population as a function of time in hour expressed as:
P=48∙e^((0.045t))
If the value of t is 8, hence;
P=48∙e^((0.045(8))
P = 48e^0.36
P = 65.933
Hence the number of bacteria when t = 8 is approximately 66 bacterias
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3(1-5x)=2(3x+1) find the solution set
Answer:
1/21
Step-by-Step Explanation:
Let's solve your equation step-by-step.
3(1−5x)=2(3x+1)
Step 1: Simplify both sides of the equation.
3(1−5x)=2(3x+1)
(3)(1)+(3)(−5x)=(2)(3x)+(2)(1)(Distribute)
3+−15x=6x+2
−15x+3=6x+2
Step 2: Subtract 6x from both sides.
−15x+3−6x=6x+2−6x
−21x+3=2
Step 3: Subtract 3 from both sides.
−21x+3−3=2−3
−21x=−1
Step 4: Divide both sides by -21.
-21x/-21=-1/-21
x=1/21
[tex]\boldsymbol{\sf{3(1-5x)=2(3x+1)}}[/tex]
Reorder terms
[tex]\boldsymbol{\sf{3(-5x+1)=2(3x+1) }}[/tex]Distribute
[tex]\boldsymbol{\sf{-15x+3=2(3x+1) }}[/tex][tex]\boldsymbol{\sf{-15x+3=6x+2 }}[/tex]Subtract 3x from both sides.
[tex]\boldsymbol{\sf{-15x+3-3=6x+2-3 }}[/tex]Simplify
[tex]\boldsymbol{\sf{-15x=6x+1}}[/tex]Subtract 6x from both sides.
[tex]\boldsymbol{\sf{-15x-6x=6x-1-6x }}[/tex]Simplify
[tex]\boldsymbol{\sf{-21x=-1 }}[/tex]Divide both sides by the same factor
[tex]\boldsymbol{\sf{\dfrac{-21x}{-21}=\dfrac{-1}{-21} }}[/tex]Simplify
[tex]\boxed{\boldsymbol{\sf{x=\frac{1}{21} }}}[/tex]The hospital in patient admission rate for employees of the ramsey
The computation shows that the the hospital in-patient admission rate for the employees of the Prendergast Corporation is 104.5 admissions per 1000 employees.
How to calculate the value?The in-patient admission rate for Ramsey Manufacturing company = 100 admissions per 1000 employees.
It is given that the in-patient rate of Prendergast will be 10% higher than Ramsey's.
So, in-patient rate of Prendergast:
= 100 + 10% of 100
= 110 admissions
Now, it is also given that out of total in-patients, 5% are for tonsillectomies (which are not in-patient).
So, in-patient admission rate for Prendergast:
= 110 - 5% of 110
= 110 - 5.5
= 104.5 admissions per 1000 employees
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Complete question:
The hospital in-patient admission rate for employees of the Ramsey Manufacturing Company is 100 admissions per 1000 employees per year.
The Prendergast Corporation has older employees and is told that its hospital in-patient admission rate will be 10% higher than Ramsey’s. At the same time, however, all tonsillectomies will be done in the hospital’s outpatient department instead of requiring the patient to be admitted as an in-patient. Given that 5% of all in-patient admissions are for tonsillectomies, what is the hospital in-patient admission rate for the employees of the Prendergast Corporation?
A. 110.0 B. 115.0 C. 109.5 D. 100.0 E. 104.5 F. 117.0
Determine what type of model best fits the given situation:
Answer:
B. quadratic function graph
Compare the monthly payments and total loan costs for the following pairs of loan options. Assume that both loans are fixed rate and have the same closing costs. You need a $200,000 loan Option 1 a 30-year loan at an APR of 10% Option 2 a 15-year loan at an APR of 9.5%. Find the monthly payment for each option. The monthly payment for option 1 is S The monthly payment for option 2 is S (Do not round until the final answer Then round to the nearest cent as needed) Find the total amount paid for each option The total payment for option 1 is S The total payment for option 2 is S (Use the answers from the previous step to find this answer Round to the nearest cent as needed) Compare the two options Which appears to be the better option? OA Option 2 will always be the better option B. Option 1 is the better option, but only if the borrower plans to stay in the same home for the entire term of the loan OC. Option 1 will always be the better option OD. Option 2 is the better option, but only if the borrower can afford the higher monthly payments over the entire term of the loan 0
The monthly payment for option 1 is $1755.144 and option 2 is $2088.97, total amount for option 1 is $631851.84 and option 2 is $376014.6, and on comparing option 2 will be better option.
Given that for $200,000 loan Option 1 is a 30-year loan at an APR of 10% Option 2 is a 15-year loan at an APR of 9.5%.
A concept that implies that the future value of money will be lower than its present value due to several factors such as inflation is known as TVM(time of value money).
Monthly Payments
Option 1
Loan Amount = $200,000
Number of payments = 30×12 = 360
Monthly interest rate = 10%/12 = 0.008333333
Monthly payment = Loan amount (1+ monthly interest rate)ⁿ×monthly interest rate/[(1+monthly interest rate)ⁿ- 1]
Monthly payment=200,000×(1+0.008333333)³⁶⁰×(0.008333333)/[(1+0.008333333)³⁶⁰-1]
Monthly payment=33062.328/18.83739
Monthly payment=$1755.144
Option 2
Loan Amount = $200,000
Number of payments = 15 x 12=180
Monthly interest rate = 9.5%/12=0.00792
Monthly payment = 200,000(1+0.00792)¹⁸⁰(0.00792)/[(1+0.00792)¹⁸⁰-1]
Monthly payment=6553.096/3.137
Monthly payment=$2088.97
Total Payments
Option 1
As we've found out the monthly payments, we now need to multiply it by the number of months.
$1755.144×360 = $631851.84
Option 2
$2088.97×180 = $376014.6
Conclusion
Option 2 will always be the better option economically as it saves $255837.24 ($631851.84 - $376014.6) in total payments.
Hence, For $200,000 loan Option 1 a 30-year loan at an APR of 10% Option 2 a 15-year loan at an APR of 9.5% is the monthly payment for option 1 is $1755.144 and option 2 is $2088.97, total amount for option 1 is $631851.84 and option 2 is $376014.6, and on comparing option 2 will be the better option.
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A bank charges 12% simple interest p.a. on a cash loans for R10 000,must repay the loan over 4 years.
Calculate the interest which is gonna be paid to the loan?
Answer:
$4800
Step-by-step explanation:
Let's use the simple interest formula, P(1+rt), to find the final amount of the loan
10000(1+.12*4) = 14800, the final amount
14800 - 10000 = 4800 total in interest
Grocer Edwards graphs the relationship between the
diameter and heights of different cans in his store. The
graph is below.
Height (cm)
18-
D
16+
14+
12+
10+
8+
6+
4+
2+
2
Choose 1 answer:
4
●
6
8
A
●
10 12
What is the meaning of point A?
●
Diameter (cm)
●
14 16 18
A can with an 10 cm diameter has an 18 cm height.
A can with an 18 cm diameter has an 11 cm height.
A can with an 11 cm diameter has an 18 cm height.
A can with an 18 cm diameter has an 10 cm height.
Considering the given graph, the meaning of point A is given by:
A can with an 11 cm diameter has an 18 cm height.
What does the graph gives?The graph gives the height of the can as a function of the diameter. Both measures are in cm. Then, the axis are given as follows:
The x-axis is the diameter.The y-axis is the height.Point A has coordinates (11,18), that is, x = 11, y = 18, hence the interpretation is:
A can with an 11 cm diameter has an 18 cm height.
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Answer:
A
Step-by-step explanation:
just took the quiz and can confirm the other guy is valid :D
(7)/(3) of it is 5 (5)/(6)
let's firstly convert the mixed fraction to improper fraction and then take it from there, keeping in mind that the whole is "x".
[tex]\stackrel{mixed}{5\frac{5}{6}}\implies \cfrac{5\cdot 6+5}{6}\implies \stackrel{improper}{\cfrac{35}{6}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{3}x~~ = ~~5\frac{5}{6}\implies \cfrac{7}{3}x~~ = ~~\cfrac{35}{6}\implies 42x=105\implies x=\cfrac{105}{42} \\\\\\ x=\cfrac{21\cdot 5}{21\cdot 2}\implies x=\cfrac{21}{21}\cdot \cfrac{5}{2}\implies x=1\cdot \cfrac{5}{2}\implies x=2\frac{1}{2}[/tex]
The sun
of three numbers is 24. If two numbers are 16 and 22, what is the third?
Answer:
The Third would be 72
Step-by-step explanation:
The sum of the two is 16+22=38. the third one is 72-38=34
I’m confused in the exponential
These are the laws of indices. You just have to memorise it, sorry : (
Hope it helps : )
HELP!!!!!!!!!!!!!!!!!!!!!!!!
The recursive formula for f(n) is f(n) = 4.25 + f(n - 1), f(0) = 2.25.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let f(n) represent the total cost of shoe rentals for n games, hence:
The recursive formula for f(n) is f(n) = 4.25 + f(n - 1), f(0) = 2.25.
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In 2016, Alberta had about 4.2 million people.
Assuming they follow the same population
growth rate, it is predicted they will have 6.65
million people in 20 years. At what rate is the
province's population growing?
The province's population is growing at the rate of 58.34 %
Rate of change is used to mathematically describe the percentage change in value over a defined period of time, and it represents the momentum of a variable. The calculation for ROC is simple in that it takes the current value of a stock or index and divides it by the value from an earlier period.
Given:
Initial Population = 4.2 million
Population after 20 years = 6.65 million
Change in population = 6.65 - 4.2 = 2.45 million
Rate at which the province's population growing is
= [tex]\frac{Change in population}{Inital Population}[/tex] x100 %
= [tex]\frac{2.45}{4.2}\\[/tex] x 100%
= 58.34 %
Thus the province's population is growing at the rate of 58.34 %
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solve asap please!!!
The length of a rectangle is two more than double the width. If the perimeter is 100 inches, find the
dimensions.
Answer:
width = 34 inches
length = 16 inches
Step-by-step explanation:
Given:
1.)The length of a rectangle is two more than double the width
2.)The perimeter is 100 inches
Let's analyze the first part,
The length is 2 more than double the width so if we let x represent the length the width would be 2x + 2
Now the second part,
the perimeter is calculated by the following formula:
2*(w+l)
(w: width, l: length)
2*(x+2x+2) first do inside the parenthesis by adding like terms
x+2x+2 = 3x + 2 now multiply both terms with 2
2*(3x+2) = 6x + 4 this is the perimeter of the rectangle, now write another equation using this
6x + 4 = 100 subtract 4 from both sides
6x = 96 divide both sides by 6
x = 16 this the length and the width would be
2x + 2 = 2*16 + 2 = 34
Consider the function f denoted by:
[tex]f(x) = ln(x) [/tex]
Find the nth derivative of f(x) denoted by:
[tex]f {}^{(n)} (x ) [/tex]
Irrelevant answers will be reported immediately.
Step-by-step explanation:
Let take the first derivative
[tex] \frac{d}{dx} ln(x)) = x {}^{ - 1} [/tex]
The second derivative
[tex] - {x}^{ - 2} [/tex]
The third derivative
[tex]2 {x}^{ - 3} [/tex]
The fourth derivative
[tex] - 6 {x}^{ - 4} [/tex]
The fifth derivative
[tex]24 {x}^{ - 5} [/tex]
Let create a pattern,
The values always have x in it so
our nth derivative will have x in it.
The nth derivative matches the negative nth power so the nth derivative so far is
[tex] {x}^{ - n} [/tex]
Next, lok at the constants. They follow a pattern of 1,2,6,24,120). This is a factorial pattern because
1!=1
2!=2
3!=6
4!=24
5!=120 and so on. Notice how the nth derivative has the constant of the factorial of the precessor
so our constant are
[tex](n - 1)[/tex]
So far, our nth derivative is
[tex](n - 1)!x {}^{ - n} [/tex]
Finally, notice for the odd derivatives we are Positve and for the even ones, we are negative, this means we are raised -1^(n-1)
[tex] - 1 {}^{n -1} (n - 1) ! {x}^{-n} [/tex]
That is our nth derivative
A sample of a radioactive isotope had an initial mass of 440 mg in the year 1990 and decays exponentially over time. A measurement in the year 1998 found that the sample's mass had decayed to 40 mg. What would be the expected mass of the sample in the year 2001, to the nearest whole number?
Using an exponential function, the expected mass of the sample in the year 2001 would be of 16 mg.
What is the exponential function for the amount of a substance?The function is:
[tex]A(t) = A(0)e^{-kt}[/tex].
In which:
A(0) is the initial amount.k is the decay rate.The information given is as follows:
A(0) = 440, A(8) = 40.
Hence:
[tex]A(t) = A(0)e^{-kt}[/tex].
[tex]40 = 440e^{-8k}[/tex].
[tex]e^{-8k} = 0.09090909[/tex]
[tex]\ln{e^{-8k}} = \ln{0.09090909}[/tex]
[tex]-8k = \ln{0.09090909}[/tex]
[tex]k = -\frac{\ln{0.09090909}{8}[/tex]
k = 0.29973691
Then the function is:
[tex]A(t) = 440e^{-0.29973691t}[/tex]
2001 is 11 years after 1990, hence the amount is:
[tex]A(11) = 440e^{-0.29973691 \times 11} = 16[/tex]
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On a piece of graph paper, plot the following points: A (3, 1), B (1, 5), C (9, 9), and D (11, 5). These coordinates will be the vertices of a quadrilateral. How would you use the distance formula and the slope formula to prove that this figure is actually a rectangle?
The given coordinates are actually a rectangle
How to determine the quadrilateral type?
The coordinates are given as:
A (3, 1), B (1, 5), C (9, 9), and D (11, 5).
Calculate the distance between the coordinates using:
[tex]d = \sqrt{(x_2 -x_1)^2 +(y_2 -y_1)^2[/tex]
So, we have:
[tex]AB = \sqrt{(3 -1)^2 +(1-5)^2} =\sqrt {20[/tex]
[tex]BC = \sqrt{(1 -9)^2 +(5-9)^2} =\sqrt {80[/tex]
[tex]CD = \sqrt{(9 -11)^2 +(9-5)^2} =\sqrt {20[/tex]
[tex]DA = \sqrt{(11 -3)^2 +(5-1)^2} =\sqrt {80[/tex]
The above shows that the opposite sides are congruent
Next, we calculate the slopes using:
m = (y2- y1)/(x2- x1)
So, we have:
AB = (1- 5)/(3-1) = -2
BC = (5- 9)/(1-9) = 1/2
CD = (9- 5)/(9-11) = -2
DA = (5- 1)/(11-3) = 1/2
The slopes of adjacent sides are opposite reciprocals.
This means that the sides are perpendicular
Hence, the given coordinates are actually a rectangle
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What is the domain and range of the quadratic function given by the equation /(x) = 2(x-4)] - 2
The domain of the function is the set of all real numbers and the range of the function is the set of all values greater than -2
How to determine the domain and the range?The function is given as:
f(x) = 2(x -4)^2 - 2
A quadratic function can take any real number as its input.
So, the domain of the function is the set of all real numbers
The vertex of the above function is:
Vertex = (4, -2)
And the leading coefficient is:
a = 2
The y value of the vertex is;
y = -2
Because the value of a is positive, then the vertex is a minimum.
This means that the range of the function is the set of all values greater than -2
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If f(x) = -4x-8 and g(x)=3x²+x, then f(-1)g(2) =
Answer:
b
Step-by-step explanation:
(-4(-1)-8)(3(2)^2+2=4-8×12+2
-4×14=-56
Which expression is equivalent to (z−3)4z−6 for all values of z where the expression is defined?
The equivalent of the expression [ (z−3)4z−6 ] is 4z² - 12z - 6.
What is the equivalent of the expression?
Given the expression; (z−3)4z−6
First, we apply distributive property.
(z−3)4z−6
(z−3)4z−6
z(4z) - 3(4z) - 6
We remove the parentheses
4z² - 12z - 6
Therefore, the equivalent of the expression [ (z−3)4z−6 ] is 4z² - 12z - 6.
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Factor completely 2x3y4 − 8x2y3 + 6xy2.
Answer:
[tex]2xy^2(xy-1)(xy-3)[/tex]
====================
Given expression
[tex]2x^3y^4-8x^2y^3+6xy^2[/tex]
The greatest common factor of all three terms is [tex]2xy^2[/tex].
Factor this out:
[tex]2xy^2(x^2y^2-4xy+3)[/tex]
Complete the square:
[tex]2xy^2(x^2y^2-4xy+4-1)=[/tex]
[tex]2xy^2((xy-2)^2-1)[/tex]
Factorize further using the identity for the difference of squares:
[tex]2xy^2(xy-2+1)(xy-2-1)=[/tex]
[tex]2xy^2(xy-1)(xy-3)[/tex]