Guys please help My is assignment due tomorrow please guyyyysssss. Determine the value of k if g(x) = 4x+k is a tangent to f(x) = - x² + 8x +20
Answers
so, since we know that the derivative is simply the equation we use to get the slope at any point on the curve, thus df/dx will be that.
now, we know that g(x) is already in slope-intercept form, so it has a slope of "4", hmmm what's "x" at that instance?
[tex]f(x)=-x^2+8x+20\implies \cfrac{df}{dx}=-2x+8 \\\\[-0.35em] ~\dotfill\\\\ g(x)=\stackrel{\stackrel{m}{\downarrow }}{4}x+k\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\\\ 4~~ = ~~-2x+8\implies 2=x[/tex]
well, now we know that x = 2, hmmm what's "y" at that instance? well, our "y" will be simply f(2) = g(x), because g(x) is touching f(x) at that point on the curve.
[tex]f(2)=-(2)^2+8(2)+20\implies f(2)=32 \\\\[-0.35em] ~\dotfill\\\\ g(x)=4x+k\implies 32=4(2)+k\implies 32=8+k\implies \boxed{24=k}[/tex]
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Related Questions
The following table lists the number of unicyclists in Corvallis, OR. By age group.
Age Group Frequency
≤19 16
20-29 86
30-39 1
40-49 1
50-59 68
60-69 15
≥70 14
What is the probability that a randomly selected unicyclist from Corvallis, OR. Is not between 30 and 39?
Answers
The probability that an arbitrarily chosen Corvallis unicyclist is not between the ages of 30 and 39 is roughly 0.995, or 99.5%.
To find the probability that a randomly selected unicyclist from Corvallis is not between 30 and 39, we need to first determine the total number of unicyclists in Corvallis. We can find this by summing up the frequencies for all age groups:
Total number of unicyclists = 16 + 86 + 1 + 1 + 68 + 15 + 14 = 201
Next, we need to determine the frequency of unicyclists who are not between 30 and 39. We can do this by adding up the frequencies for all age groups that are not between 30 and 39:
Frequency of unicyclists not between 30 and 39 = 16 + 86 + 1 + 68 + 15 + 14 = 200
Finally, we can calculate the probability of selecting a unicyclist who is not between 30 and 39 by dividing the frequency of unicyclists not between 30 and 39 by the total number of unicyclists:
P(not between 30 and 39) = Frequency of unicyclists not between 30 and 39 / Total number of unicyclists
P(not between 30 and 39) = 200 / 201
P(not between 30 and 39) ≈ 0.995
Therefore, the probability that a randomly selected unicyclist from Corvallis is not between 30 and 39 is approximately 0.995 or 99.5%.
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In ΔUVW, w = 690 inches,
�
m∠W=79° and
�
m∠U=82°. Find the length of v, to the nearest 10th of an inch.
Answers
The value of the length of side v is
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
w/sinW = v/sinV
using the sum of angle in a triangle
V + W + U = 180°
V + 79 + 82 = 180°
V = 180-(79+82)11
V = 180 - 161
V = 19°
1690/sin 79 = v/ sin19
sin79 v = 690 sin 19
0.982 v = 690 × 0.33
0.982v = 227.7
v = 227.7/0.982
v = 231.87 inches
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Steve is on the swim team. At his last practice, Steve improved his best time by 5 second. Which shows men written as a 5 8 decimal? 8 10 O 0.125 O 0.625 O 5.125 O 625.0
Answers
Step-by-step explanation:
Not sure about this question ...it seems to be worded improperly.
IF you are looking for 5/8 as a decimal:
5/8 is the same as 5 ÷ 8
using a calculator , this equals 0.625
Mary's mom gave her $100. 00 to go shopping. She spent $22. 65 on a shirt and 3
$33. 31 on a skirt. She had a coupon for 10% off. How much change did the cashier give back to her?
Answers
The cashier gave Mary an amount of $49.64 in change.
Mary's mom gave her $100.00 to go shopping.
She spent $22.65 on a shirt and $33.31 on a skirt. She had a coupon for 10% off. Mary's total expenditure can be calculated by adding the cost of the skirt and the shirt:
Shirt + Skirt = $22.65 + $33.31 = $55.96
The cost of the items with the discount is the Total cost after discount
= $55.96 − 10% of $55.96 = $55.96 − $5.596 = $50.36
Since Mary was given $100.00 by her mother, she has to subtract the total amount she spent from the total she was given.
This will give us her total change:
$100.00 − $50.36 = $49.64
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Find the smallest and largest value of the function [tex]y=3x^2-x^3[/tex]
Answers
The smallest value οf the functiοn is negative infinity, and the largest value is 8.
The functiοn [tex]y = 3x^2 - x^3[/tex] is a cubic functiοn. Tο find the smallest and largest values οf this functiοn, we can take the derivative and find where it equals zerο οr dοes nοt exist. At these pοints, the functiοn will have lοcal extrema (either a maximum οr minimum).
[tex]y = 3x^2 - x^3[/tex]
[tex]dy/dx = 6x - 3x^2[/tex]
Setting the derivative equal tο zerο, we get:
6x - 3x^2 = 0
3x(2 - x) = 0
Sο the critical pοints are at x = 0 and x = 2.
Tο determine whether these critical pοints cοrrespοnd tο a lοcal maximum οr minimum, we can use the secοnd derivative test. Taking the secοnd derivative οf the functiοn, we get:
[tex]d^2y/dx^2 = 6 - 6x[/tex]
At[tex]x = 0, d^2y/dx^2 = 6[/tex], which is pοsitive, sο this critical pοint cοrrespοnds tο a lοcal minimum. At[tex]x = 2, d^2y/dx^2 = -6[/tex], which is negative, sο this critical pοint cοrrespοnds tο a lοcal maximum.
Tο find the smallest and largest values οf the functiοn, we need tο evaluate the functiοn at these critical pοints and at the endpοints οf the interval οf interest. The interval οf interest is nοt specified, sο we will assume that we want tο find the smallest and largest values οver the entire real line.
y(-∞) = -∞ (as x apprοaches negative infinity, y apprοaches negative infinity)
y(0) = 0
y(2) = 8
y(∞) = -∞ (as x apprοaches infinity, y apprοaches negative infinity)
Therefοre, the smallest value οf the functiοn is negative infinity, and the largest value is 8.
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Specify the number of ways to perform the task described. Give your answers using Pin, 1) or C(n,r) notation. The key in recognizing whether a problem involves permutations or combinations is deciding whether order is important. A hot sauce bar has 16 varieties. You are going to select 4 to taste, but you do not care about the order in which you taste them. The number of ways to perform the task is _____(Do not evaluate.) Specify the number of ways to perform the task described. Give your answers using P(n,r) or C(n,r) notation, Twelve magazines are competing for five identical awards for excellence in journalism. No magazine can receive more than one award The number of ways to perform the task is ______. (Do not evaluate.)
Answers
1. There are 1820 ways tο select 4 hοt sauces tο taste.
2. There are 95,040 ways tο give οut the 5 awards.
What is the permutatiοns and cοmbinatiοns?Permutatiοns and cοmbinatiοns are branches οf cοmbinatοrics, which is the study οf cοunting and arranging οbjects.
1. Since οrder is nοt impοrtant, we are dealing with cοmbinatiοns. The number οf ways tο select 4 items frοm 16 is given by the cοmbinatiοn C(16, 4), which is:
C(16, 4) = 16! / (4! (16 - 4)!) = 1820
Hence, there are 1820 ways tο select 4 hοt sauces tο taste.
2. We are dealing with permutatiοns because the οrder in which the awards are given is impοrtant. The number οf ways tο chοοse 5 magazines οut οf 12 tο receive the awards is given by the permutatiοn P(12, 5), which is:
P(12, 5) = 12! / (12 - 5)! = 12! / 7! = 95,040
Hence, there are 95,040 ways tο give οut the 5 awards.
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Here is a map of a town.
It has a scale of 2 cm to 7 km.
A centimetre ruler is shown on the map.
What is the real-life distance between the ice rink and the theatre?
Answers
The real-life distance between the ice rink and the theater is given as follows:
14 km.
How to obtain the real-life distance?The real-life distance between the ice rink and the theater is obtained applying the proportions in the context of the problem.
The scale of 2 cm to 7 km means that each 2 cm drawn on the map represent a real distance of 7 cm.
The distance is of 4 cm on the map, hence the actual distance between the ice rink and the theater is obtained as follows:
4/2 x 7 = 14 km.
Missing Information
The distance is of 4 cm on the map.
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Paul deposits money
into a savings account
with an annual interest
rate of 5% that is
compounded
continuously. After 8
years, the account
balance reaches $6,425.
How much was initially
invested?
Answers
Answer: money is not important
Step-by-step explanation:
figure it out lazy
A golf retailer purchases its clubs from a wholesaler at $41 per club. It sells the same clubs to golfers at $71 per club. What is the markup on each club, as a percentage of the wholesale price?
Answers
The markup is 73.17 percentage , calculated by subtracting the wholesale price ($41) from the retail price ($71) and then dividing the difference by the wholesale price ($41).
The markup is the difference between the wholesale price and the retail price, divided by the wholesale price. To calculate the markup on each club, subtract the wholesale price from the retail price and then divide the difference by the wholesale price. In this example, the wholesale price is $41 and the retail price is $71, so the difference is $30. Dividing $30 by $41 gives a result of 0.7317, which is the markup expressed as a decimal. To express the markup as a percentage, multiply the result by 100, giving a final answer of 73.17%. This means that the retailer is marking up their clubs by 73.17% of the wholesale price.
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Mickey is classifying a quadrilateral with vertices at Q1,1, U(-1,-3), A(1,-4), D(3,0). What type of quadrilateral is it? Also why?
Please Help!
Answers
This quadrilateral is a trapezoid because it has one pair of parallel sides. The sides Q1U and AD are parallel, while the other two sides (U1 and DA) are not.
What is trapezoid?A trapezoid is a four-sided shape with two parallel sides, called the bases, and two non-parallel sides, called the legs. The opposing angles of the trapezoid are equal in measure, and the two adjacent angles are supplementary. A trapezoid can also be defined as a quadrilateral with exactly one pair of parallel sides. Trapezoids are often used in mathematics to define and calculate area, perimeter and other geometric properties. They can also be used to construct shapes and patterns in architecture, engineering and design.
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Answer:
I'm pretty sure it's a rectangle
Step-by-step explanation:
the reason why is because there are 2 pairs that are equal to each other but each seem to be perpendicular in slope form.
Question You ask 8 students how many letters are in their first name. One person says 6. The other 7 students say a different number of letters. Find the experimental probability of someone having 6 letters in their name based on this experiment.
Answers
The experimental probability of someone having 6 letters in their name based on this experiment is [tex]\frac{1}{6}[/tex].
What is Experimental probability?It is calculated based on the outcomes of multiple iterations of an experiment. The probability that is created using logic is termed a theoretical probability. A probability is a number that falls between (and includes) 0 and 1.
[tex]Experimental\ probability = \frac{Total\ Number\ of\ Outcomes}{Number\ of\ favourable\ Outcomes}[/tex]
Given, Total number of the Student = 8
Persons having 6 (Six)letters in their name = 1
Other 7 (Seven) persons says different number of letters.
So, Experimental probability of someone having 6 letters in their name is determined,
[tex]Experimental\ probability = \frac{Total\ Number\ of\ Outcomes}{Number\ of\ favourable\ Outcomes}[/tex]
[tex]= \frac{1}{6}[/tex]
Hence, we can say that the experimental probability of someone having letters in their name based on this experiment is [tex]\frac{1}{6}[/tex].
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Among fatal plane crashes that occurred during the past 70 years, 503 were due to pilot error, 90 were due to other human error, 326 were due to weather, 382 were due to mechanical problems, and 643 were due to sabotage. Among fatal plane crashes that occurred during the past 70 years, 503 were due to pilot error, 90 were due to other human error, 326 were due to weather, 382 were due to mechanical problems, and 643 were due to sabotage. Construct the relative frequency distribution. What is the most serious threat to aviation safety, and can anything be done about it? Complete the relative trequency distribution below Relative Frequen 25.9% 4.6% 16.8% Cause Pilot error Other human error Weather Mechanical problems 19.7% Sabotage Round to one decimal place as needed.) What is the most serious threat to aviation safety, and can anything be done about it? 33S% A. Sabotage is the most serious threat to aviation safety. Airport security could be increased B. ° C. 0 D. Mechanical problems are the most serious threat to aviation safety. New planes could be better engineered. Weather is the most serious threat to aviation safety, weather monitoring systems could be improved. Pilot error is the most serious threat to aviation safety. Pilots could be better trained What is the most serious threat to aviation safety, and can anything be done about it? A. Sabotage is the most serious threat to aviation safety. Airport security could be increased. B. Mechanical problems are the most serious threat to aviation safety. New planes could be better engineered. C. Weather is the most serious threat to aviation safety. Weather monitoring systems could be improved. D. Pilot error isPilot error is the most serious threat to aviation safety. Pilots could be better trained.
Answers
pilot error = 25.9%
The most serious threat to aviation safety is pilot error. Pilot error accounts for 25.9% of all fatal plane crashes during the past 70 years, making it the most prevalent threat. Fortunately, there are measures that can be taken to reduce pilot error, such as providing pilots with additional training and stricter qualifications.
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The Panic Squadron is playing a concert. Jennifer surveyed her classmates to see if they were in the Panic Squadron Fan Club and if they were going to a concert. Find the probability that a person surveyed went to the concert given they are a fan club member
Answers
The probability that a person surveyed went to the concert given they are a fan club member is 2/3 or approximately 0.667.
What is probability ?Probability is a branch of mathematics that deals with the study of random events or phenomena. It is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain.
According to given information :
To find the probability that a person surveyed went to the concert given they are a fan club member, we need to use conditional probability. We can use the following notation:
P(concert | fan club)
This means the probability of going to the concert given that the person is a fan club member.
Let's assume that Jennifer surveyed 100 classmates, and 40 of them are in the Panic Squadron Fan Club and also went to the concert. Also, let's assume that 60 of Jennifer's classmates are in the Panic Squadron Fan Club.
Then, we can use the formula for conditional probability:
P(concert | fan club) = P(concert and fan club) / P(fan club)
Plugging in the values we know, we get:
P(concert | fan club) = 40/60 = 2/3 or approximately 0.667
Therefore, the probability that a person surveyed went to the concert given they are a fan club member is 2/3 or approximately 0.667.
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A water balloon is dropped from the second floor of a five-story building. The height in feet is modeled by f(x) = -8x^2 + 80x where x is the number of elapsed seconds. How long will the water balloon be in the air?
Answers
When A water balloon is dropped from the second floor of a five-story building, The water balloon will be in the air for 10 seconds.
To find the time the water balloon will be in the air, we need to find when the height function f(x) equals zero since this is the point at which the balloon hits the ground.
Setting f(x) = 0 and solving for x, we get:
-8x^2 + 80x = 0
=> x(-8x + 80) = 0
=> x = 0 or x = 10
Since x = 0 is the initial time when the balloon is dropped, we can discard that solution. Therefore, the water balloon will be in the air for 10 seconds.
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4.02 Lesson Check Arithmetic Sequences (2)
Answers
The values of the first four terms of the sequence with the definition a(n) = 3n² - n are 2, 10, 24 and 239
How to determine the value of the first four terms?A sequence can be arithmetic or geometric of neither
The definition of the function is given as
a(n) = 3n² - n
The above definitions imply that we simply add -n to the three multiplied by 3 and n to get the current term
Using the above as a guide,
So, we have the following representation
a1 = 3 * 1² - 1
a1 = 2
Next. we have
a₂ = 3 * 2² - 2
a₂ = 10
Also, we have
a₃ = 3 * 3² - 3
a₃ = 24
Lastly, we have
a₄ = 3 * 3² - 4
Evaluate the equation
a₄ = 239
Hence, the value of a₄ is 239
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Can you please help me on this?
thank you<3
Answers
Answer:
(2x+3)+(x-6)=180
Step-by-step explanation:
math
:)
There are currently 4 people signed up to play on a baseball team. The team must have at least 9 players. Which of the following graphs includes the possible values for the number of people who still need to sign up for the team? (4 points) Number line with closed circle on 5 and shading to the left Number line with closed circle on 5 and shading to the right. Number line with open circle on 5 and shading to the left. Number line with open circle on 5 and shading to the right.
Answers
What is the answer to 4x7
Answers
Answer: 28
Step-by-step explanation: 4+4+4+4+4+4+4=28 :)
count 7 , on your fingers 4 times and you will get 28!
there are 2 blips per dud ,3 fans per wam, and 5 duds per fan. how many blips are equivalent to 5 wams
Answers
50 blips are equivalent tο 5 wams.
What are blips?A small spοt οf light, sοmetimes with a shοrt, sharp sοund, that appears οn a cοmputer screen
We can use the given infοrmatiοn tο set up a system οf equatiοns tο sοlve fοr the number οf blips that are equivalent tο 5 wams:
2 blips = 1 dud
3 fans = 1 wam
5 duds = 1 fan
First, we can use the third equatiοn tο express duds in terms οf fans:
5 duds = 1 fan
duds = 1/5 fan
Next, we can use the secοnd equatiοn tο express wams in terms οf fans:
3 fans = 1 wam
fans = 1/3 wam
Substituting the expressiοn fοr fans in terms οf wams intο the expressiοn fοr duds in terms οf fans, we get:
duds = 1/5 (1/3 wam) = 1/15 wam
Finally, we can use the first equatiοn tο express blips in terms οf duds:
2 blips = 1 dud
Substituting the expressiοn fοr duds in terms οf wams that we fοund abοve, we get:
2 blips = 1/15 wam
Multiplying bοth sides by 5 tο sοlve fοr the number οf blips that are equivalent tο 5 wams, we get:
10 blips = 1 wam
50 blips = 5 wams
Therefοre, 50 blips are equivalent tο 5 wams.
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A DoorDash driver can travel a radius of 18 miles in all directions. What is the area the drivers will cover? Round it to the nearest whole number.
Answers
Answer:
1018 miles
Step-by-step explanation:
To find the area of a circle, the area is πr². This means you can simply put in the value of 18 as the radius:
π x (18)²
= 1017.88
Then round to the nearest whole number:
= 1018 miles
a 225 m long train crosed a tunnel 275m long in one minute.what is the speed of train
Answers
Answer:
I think is 30km/h
if it's wrong I'm sorry
A logo is made from three circles with each circle having centre O.
Work out the percentage of the logo that is shaded.
You must show all your working.
+
Answer:
3 cm 2 cm
%
5 cm
Answers
Answer:
15
Step-by-step explanation: BECAUSE THAT IS THE ANSWER
Because it just is
At Andy's Market, the price of a box of brand-name cereal is 1.5 the price of a box of generic cereal. If the price of a box of brand-name cereal is $3.60, which of the following can be used to determine x, the price of a box of generic cereal in dollars?
Choose 1 answer:
x/1.5 = 3.6
1.5x = 3.6
3.6x = 1.5
x + 1.5 = 3.6
Answers
In Linear equation, $2.40 is the price of a box of generic cereal in dollars. 1.5x = 3.6 is the correct option.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
The equation to solve for the price of a box of generic cereal is
3.6/1.5 = x,
X = $2.40
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It was Mrs. Johnson's birthday, and she made her favorite homemade cookies to share with the class. "I hope you all enjoy my homemade cereal crunch cookies. I used a mixture of different cereals to make this. Unique!" says Mrs. Johnson as she saw Joshua raise his hand. "But don't worry! They are all nut free." The class LOVED them. In no time at all the class ate five-sixths of the cookies. "Mrs. Johnson." said Hannah, "you need to do OUR tradition. While we sing happy birthday, you need to eat as many cookies as you can. As the class began to sign, that is just what Mrs. Johnson did. And she was good at it! She ate three-fourths of the cookies that were left. In case you are curious, that was equal to 3 cookies! How many cookies did Mrs. Johnson bring to class that day?
Answers
Answer:
Let's work backwards to figure out how many cookies were left after Mrs. Johnson ate 3 cookies:
Before Mrs. Johnson ate the cookies, the class had eaten 5/6 of the cookies, which means that 1/6 of the cookies were left.
Let's call the number of cookies in 1/6 of the batch "x". So the total number of cookies is 6x.
After the class ate 5/6 of the cookies, there were 1/6 of the cookies left, which is x.
Then Mrs. Johnson ate 3/4 of the cookies that were left, which means she ate 3/4*x cookies.
We know that Mrs. Johnson ate 3 cookies, so we can set up the equation: 3 = 3/4*x
Solving for x:
3 = 3/4x
34/3 = x
4 = x
So there were 4 cookies in 1/6 of the batch, which means there were 6 times as many, or 6*4 = 24 cookies in the whole batch.
Therefore, Mrs. Johnson brought 24 cookies to class that day.
Answer: 24 cookies.
Step-by-step explanation:
the answer to the questions is as below
Let's start by using variables to represent the number of cookies that Mrs. Johnson brought to class. Let's say she brought "x" cookies.
We know that the class ate five-sixths of the cookies, which means that there were only one-sixth of the cookies left. This can be represented as:(1/6)x cookies left
We also know that Mrs. Johnson ate three-fourths of the cookies that were left, which is equal to 3 cookies. We can set up an equation to represent this:
(3/4)(1/6)x = 3
Simplifying this equation, we get:
(1/24)x = 1
x = 24
Therefore, Mrs. Johnson brought 24 cookies to class that day.
The selling price of an item is 520$. After 6 months of not selling, it is marked down by 20%. After another 6 months of not selling, it is further marked down by 60%. Find the sale price after both markdowns.
Answers
Hence, in response to the provided question, we can say that As a result, equation the item's selling price after both markdowns is 166.40$.
What is equation?An algebraic equation is a method of connecting two quotes by using the equals symbol (=) to express equality. In algebra, an explanation is a definitive expression that verifies the equivalency of two formula. For example, the identical character divides the numbers 3x + 5 and 14. A linear equation might be used to recognize the connection that existing between the texts written on separate sides of a letter. The product and application both frequently the same. 2x - 4 equals 2, for example.
Then, we may determine the item's price after the initial 20% discount.
20% of 520$ equals (20/100) * 520$ = 104$, hence the item's new price is 520$ - 104$ = 416$.
After another six months of not selling, the item gets reduced by 60%.
60% of 416$ equals (60/100) * 416$ = 249.60$, therefore the item's ultimate sale price after both markdowns is 416$ - 249.60$ = 166.40$.
As a result, the item's selling price after both markdowns is 166.40$.
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Using equations, we can find that the item's selling price after both markdowns is 166.40$.
Define equations?In an algebraic equation, the equals symbol (=), which represents equality, can be used to connect two quotes. In algebra, an explanation is a declarative statement that establishes the similarity of two formulas. For example, the integers 3x + 5 and 14 are divided by the same letter.
A linear equation can be used to identify the relationship between the texts written on the various sides of a letter. Applications and products can typically be used interchangeably. In this instance, 2x – 4 = 2.
After applying the initial 20% discount, we may determine the item's price as:
20% of 520$ equals (20/100) × 520$ = 104$
Hence the item's new price is 520$ - 104$ = 416$.
After another six months of not selling, the item gets reduced by 60%.
60% of 416$ equals (60/100) × 416$ = 249.60$
Therefore, the item's ultimate sale price after both markdowns is
416$ - 249.60$ = 166.40$.
As a result, the item's selling price after both markdowns is 166.40$.
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Determine the coordinates of each triangles image after the given transformation.
1. You rotate Triangle DEF with coordinates, D (-2, 2) E (1, 5) F (4, -1) 90* counterclockwise about the origin.
2. You reflect Triangle GHJ with coordinates K (2, -9), L (3, 8), and J (1, 6) across the x-axis.
3. You rotate Triangle NPQ with coordinates N (12, -3), P (1, 2), and Q (9, 0) 180* about the origin.
Answers
Answer:
1. The new coordinates after the rotation would be D' (-2, -2) E' (-5, 1) and F' (1, 4).
2. The new coordinates after reflection across the x-axis would be K' (2, 9), L' (3,-8) and J' (1,-6).
3. The new coordinates after the rotation by 180 degrees around the origin would be N' (-12, 3), P' (-1, -2) and Q' (-9, 0).
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What is the positive solution to this equation? 4x2 + 12x = 135 Record your answer and fill in the bubbles on your answer document.
Answers
x = 3 is the answer that gives the equation 4x2 + 12x = 135 a positive solution
To solve the equation 4x² + 12x = 135, we can start by rearranging it to the standard quadratic form ax² + bx + c = 0, where a, b, and c are constants. We get:
4x² + 12x - 135 = 0
Next, we can divide both sides of the equation by 4 to simplify it:
x² + 3x - 33.75 = 0
To solve for x, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
In this case, a = 1, b = 3, and c = -33.75. Substituting these values into the formula, we get:
x = (-3 ± √(3² - 4(1)(-33.75))) / 2(1)
Simplifying the expression inside the square root, we get:
x = (-3 ± √(9 + 135)) / 2
x = (-3 ± √144) / 2
x = (-3 ± 12) / 2
So the two solutions are:
x = -7.5 or x = 3. From the problem statement, we are looking for a positive solution, so we can discard the negative solution x = -7.5.
Therefore, the positive solution to the equation 4x² + 12x = 135 is x = 3.
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Nico, Aditi, Erick, Raj, and Sandra are solving the equation. Two-fifths (5 + x) = 8 Each student begins to solve the problem as shown. Nico Aditi Erick Two-fifths (5 + x) = 8. (Five-halves) two-fifths (5 + x) = 8 (five-halves) Two-fifths (5 + x) = 8. Five-halves (5) + five-halves x = (five-halves) 8 Two-fifths (5 + x) = 8. Two-fifths (5 + x) minus 5 = 8 minus 5 Raj Sandra Two-fifths (5 + x) = 8. (one-half) two-fifths (5 + x) = 8 (one-half) Two-fifths (5 + x) = 8. two-fifths (5) + two-fifths x = 8 Which students are correct in their approach to solving the problem? Select three options. Nico Aditi Erick Raj Sandra
Answers
Sοlving the equatiοns, we can find that, Nicο, Raj and Sandra are cοrrect.
What are equatiοns?Each term in a linear equatiοn has an expοnent οf 1, and when this algebraic equatiοn is graphed, it always prοduces a straight line. It is called a "linear equatiοn" fοr this reasοn.
Bοth linear equatiοns with οne variable and thοse with twο variables exist.
In the questiοn,
2/5(5+x) = 8
Methοd 1
Sοlve fοr x.
We have,
2/5(5+x) = 8
Multiply by 5/2 bοth sides:
5+x = 20
⇒ x = 15
Similarly, Methοd 4 and Methοd 5 are cοrrect.
Hence, Nicο, Raj and Sandra are cοrrect in sοlving the equatiοn.
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The length of a rectangle is 4m longer than its breadth If the perimeter of the rectangle is 48m find the length breadth and the area of rectangle
Answers
Answer:
Length: 14m
Breadth: 10m
Area: 140m^2
Step-by-step explanation:
Let length = l and breadth = b,
l = 4 + b
Perimeter = 2(l+b)
= 2(4 + b + b)
= 2(4 + 2b)
= 8 + 4b
Perimeter = 48
Hence,
4b + 8 = 48
4b = 40
b = 10m
l = 4 + b = 14m
A = lb = 10 * 14 = 140m^2
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Given the function j(x) = -2x + 9, evaluate the following: j(x) = 21
Answers
Answer:
-6=x
Step-by-step explanation:
substitute 21 into j(x) in other equation
21=-2x+9
-9 -9
12=-2x
-6=x