Max and Toni’s flower bed is rectangular in shape. The length of the garden is 4 feet more than its width and the area of the flower bed is 96 square feet. If x represents the width of the flower bed, find the length and width of the old flower bed. Solve the quadratic equation using the quadratic formula. (20 points)
Answers
Answer: Width = 8ft, Length = 12 ft
Step-by-step explanation:
irst, let'Fs express the width of the garden as w (the unknown that we are trying to solve), since the length is 4 feet longer than it's width, we can express this as 4+w. Since the flowerbed is rectangular, the formula for the area is A=lw where l is it's length and w is it's width, replacing l with 4+w, then replace A for 96 sq.ft and we can begin solving for the unknown w. Multiplying 4+w and w, using the distributive property where a(b+c)=ab+ac, we will wind up with w^2 + 4w = 96, subtracting 96 and moving it to the other side, we end up with w^2 + 4w -96 = 0, now let's use the quadratic formula for the x intercepts where [tex]x = \frac{-b +/- \sqrt{b^2-4ac}}{2a}[/tex] , remember the quadratic equation has the form [tex]ax^2+bx+c[/tex], therefore our a value is 1, our b value is 4, and our c value is -96 (remember to put that negative!), we will get 2 answers, 8 and -12, a negative width is unreasonable and so 8 is the correct width, and since the length is 4 extra feet, this makes the length 12 feet for a total area of 96 feet. hope this helps! Its helpful to draw and visualize the problem!
Related Questions
Find the average rate of change of k(x) = x' over the interval [3, 9].
Answers
Answer:
y=6x×2/4
x=7
thanks for the points
The speed of an object is the ratio of its distance traveled to time. If the speed of a bicycle is 4.5 meters per second, what is the distance traveled in 9 seconds?
Answers
Answer:
40.5 meters
Step-by-step explanation:
4.5m/s • 9s = 40.5m
Evaluate each expression if x = 7, y = 1, and z = 8.
=
19. x + y + 2
20. x + 2z
21. 4y
22. 4x – 3z
23. 4x – 17
24. 62 – 52
shto The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.
25. 9y + (2x + 1)
26. 14 + 2z
27. 2 : 2
28. xz
29. y - x
30. 24y - 2
31. x2 – 2y + 8
32. 2xz
33. 30y - 40x – 1,000
Answers
20. 23
21. 2
22. 4
23. 11
24. 8
25. 19 1/2
26. 30
27. 4
28. 56
29. -6 1/2
30. 4
31. 63
32. 112
33. 3200
19, 15.5
20, 25
21, 1/16
22, 4
23, 11
24, 8
25, 19.5
26, 30
27, 4
28, 56
29, 6.5
30, 4
31, 21
32, 112
33, 3,200
here are they
A number n is a prime factor of 28 and 63
Answers
Answer:
7
Step-by-step explanation:
The factors of 28 and 63 are
28 : 1, 2, 4, 7, 14, 28
63 : 1, 3, 7, 9, 21, 63
The common factors are 1 and 7
7 is a prime factor of both 28 and 63
The sum of two numbers is 48. One numner is 3 times the other. Find the numbers.
Answers
Answer:
16 and 3?
Step-by-step explanation:
48÷3=16
hope this helps
Answer:
12 & 36
Step-by-step explanation:
According to the statement:
[tex]x+y=48[/tex]
[tex]x=3y[/tex]
Replace x= 3y:
[tex]3y+y=48[/tex]
[tex]4y=48[/tex]
[tex]y=48/4=12[/tex]
Then:
[tex]x=3y=3(12)=36[/tex]
Hope this helps
Find the distance between two points in the simplest radical form
Answers
Answer:
The answer will be 5.
Step-by-step explanation:
using the formula d=/(x2-x1)2 +(y2-y1)
Calculate the length of the circumference inscribed in the ABCD trapezium using the data shown in the figure
i need help :(
Answers
From the given figure,
Subtracting AB and DC, so,
[tex]6 - 3 = 3 \: cm[/tex]
As we know that :-
[tex]d = \sqrt{ {5}^{2} - {3}^{2} }[/tex]
[tex]→d = 4 π cm[/tex]
Since:-
[tex]c = πd[/tex]
[tex]c = 4πd[/tex]
So, Answer is 4 π d
X is the random number of times a coin with heads probability 1/4 is tossed till the first heads appears, find: g
Answers
write the fraction as a decimal use bar notatin if necessary
-2 5/22
Answers
Answer:
1.13
Step-by-step explanation:
to turn a fraction to a decimal divide the denomitator by the numerator [tex]\frac{-25}{22}[/tex] can also be written as -25÷22 which equals 1.13 or 1.136 with a line over it
Hope this helps!
Last year, wind turbines along a hilly ridge had an average output of 390 kilowatt hours per year. The turbines were upgraded, and now their average annual output is 30% more.
What is the new average yearly output?
kilowatt hours=
Answers
30% × 390 = 117
= 390 - 117
= 507 kw/h
In a particular country, 3% of the population is HIV positive. A test for HIV correctly
diagnoses 95% of those who have the condition, but incorrectly diagnoses 4% of those
who are not HIV positive as being HIV positive. A patient obtains a positive test result,
apparently indicating the presence of HIV. Determine the probability that the patient
really is HIV positive.
Answers
Using conditional probability, it is found that there is a 0.4235 = 42.35% probability that the patient really is HIV positive.
Conditional Probability
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened. [tex]P(A \cap B)[/tex] is the probability of both A and B happening. P(A) is the probability of A happeningIn this problem:
Event A: positive test.Event B: HIV positive.The percentages involving a positive test are:
95% of 3%(positive)4% of 100 - 3 = 97%(not positive).Hence:
[tex]P(A) = 0.95(0.03) + 0.04(0.97) = 0.0673[/tex]
The probability of both having a positive test and being HIV positive is:
[tex]P(A \cap B) = 0.95(0.03)[/tex]
Then, the conditional probability is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.95(0.03)}{0.0673} = 0.4235[/tex]
0.4235 = 42.35% probability that the patient really is HIV positive.
A similar problem is given at https://brainly.com/question/14398287
the interval [2, 4] is divided into n equal subintervals of length delta x. What is delta x (in terms of k and n)
Answers
Each subinterval would have length ∆x = (4 - 2)/n = 2/n
Eighteen greater than a number is 159. Find the number. Check your solution
The number is___
Answers
Answer:
let the number be x.
[tex]x + 18 = 159 \\ x = 159 - 18 = 141[/tex]
the number is 141
hope helpful <3
Evaluate the expression 16+1+2
Answers
Solve the following system of equations:y=x2−4x+3 y=2x−2
Answers
[tex]y = 2x -2 ~~~~.....(i) \\\\y = x^2 -4 x +3 ~~~~ .....(ii) \\\\\\x^2-4x +3 = 2x -2\\\\\implies x^2 -4x -2x +3 +2 =0\\\\\implies x^2 -6x +5 =0\\\\\implies x^2 -5x -x +5 =0\\\\\implies x(x-5) -(x-5) =0\\\\\implies(x-5)(x-1) =0\\\\\implies x = 5 ~~ \text{or}~~ x = 1 \\\\\\\text{Substitute x = 1 in equation (i):}\\\\y = 2 -2 =0\\\\ \text{Substitute x = 5 in equation (i):}\\\\\\y = 2(5) -2 = 10 -2 =8 \\\\\text{Hence,}~~ (x,y) = (1,0) ~ \text{and} ~ (x,y) = (5,8)[/tex]
Choose the correct answer below
Answers
Answer: B.
Step-by-step explanation:
brainliest me
00.5 divide 53.342 give solution right answer=brainliest=10 points
☢️⚠☢️nonsense report☢️⚠☢️
Answers
Answer:
Iᖴ 00.5÷53.342=0.009373476
Iᖴ 53.342÷00.5=106.684
Step-by-step explanation:
ᕼOᑭᗴ IT ᑕᗩᑎ ᕼᗴᒪᑭ YOᑌ ᒪOᐯᗴᒪOTՏ
when is a number divisible by 6?
Answers
what is the sum of 6/12 and 1/2
A.3/12
B.9/12
C.12/12
D.13/12
PLZZZZ HELP I WILL GIVE BRAINLIST
Answers
Answer:
1/2
Step-by-step explanation:6/12 is 1/2 of the fraction meaning that 6/12 is = to 1/2.
Answer:
12 / 12
Step-by-step explanation:
LCM of 12 and 2 = 12
1 / 2
= ( 1 / 2 ) x ( 6 / 6 )
= ( 1 x 6 ) / ( 2 x 6 )
= 6 / 12
6 / 12 + 1 / 2
= 6 / 12 + 6 / 12
= ( 6 + 6 ) / 12
= 12 / 12
The radius of a circle measures 10 yards what is the circumference of the circle
Answers
Answer:
62.8 yards
Step-by-step explanation:
The circumference would just be equal to diameter*3.14, and the diameter is 2 times the radius. 2x10=20, and 20x3.14 would equal 62.8 yards.
State the rules for multiplying integers.
Answers
Answer:
If they are the same integer, then the answer is always positive. However, if the integer are different, the answer is negative.
they are sixty four thousand people at a football game 80% of the people were supporting the home team how many people were supporting the home team
Answers
Answer:
51200
Step-by-step explanation:
64000×80%=51200
[tex]\huge\mathfrak{question}[/tex]
they are sixty four thousand people at a football game 80% of the people were supporting the home team how many people were supporting the home team
[tex] \huge \mathfrak step \: by \: step[/tex]
First we will look for how much 80% of 64,000 is.
Lets put our equation
[tex]64000 \times 80 \div 100[/tex]
solve it and we get
[tex]{{\boxed{{51200}}}}}[/tex]
as our answer
please what is measurement BAC
Answers
Answer:
54 degrees? I'm not an expert, but judging by the pic, I would say 54 degrees.
Anyone able to help with this?
Answers
[tex]W = 23.7°[/tex]
Step-by-step explanation:
The formula given is the statement of Snell's law of refraction. We are given the following:
[tex]I_a = 1.0003[/tex]
[tex]I_w = 1.3[/tex]
[tex]A = 31.5°[/tex]
So we need to find the angle of refraction W. Starting with Snell's law,
[tex]\dfrac{I_w}{I_a} = \dfrac{\sin A}{\sin W} \Rightarrow \sin W = \left(\dfrac{I_a}{I_w}\right)\sin A[/tex]
Plugging in the given values, we get
[tex]\sin W = \left(\dfrac{1.0003}{1.3}\right)\sin{31.5°} = 0.402[/tex]
Solving for the angle W, we then get
[tex]W = \sin^{-1}(0.402) = 23.7°[/tex]
hi can you please answer this question 20 points if u do
Answers
Answer:
Step-by-step explanation
just multiply
like 1x2=2
so 60x2=120
2x5=10
120x5=600
and on and on
What is a circle define and illustrate The following in figures
Answers
Answer:
Circle is a closed geometric figure having an infinite number of sides.
Step-by-step explanation:
A circle ⭕ has infinite number of sides want to know how then try and experiment.
First draw a pentagon of five sides, then a hexagon of six sides and keep on increasing the number of sides and then you will notice the shape being close of a circle.
Complete the sentences to make true statements
6 is 100 times ____.
0.06 is 10 times ____.
60 is 1/100 of ____.
Answers
Answer:
6 is 100 times 0.06
0.06 is 10 times 0.006
60 is 1/100 of 6,000
Step-by-step explanation:
Since 6/100 is equal to 0.06, we can say that 6 is the result of multiplying 0.06 by one hundred (0.06 x 100 = 6).
On the other hand, since 0.06 / 10 is equal to 0.006, it is correct to say that 0.006 x 10 is equal to 0.06 (0.006 x 10 = 0.06).
Finally, 60 is one hundredth of 6000, since multiplying 60 x 100 the result is 6,000 (6,000 / 100 = 60).
hope this really helped!!
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The complete sentences are:
6 is 100 times 0.06 .
0.06 is 10 times 0.006.
60 is 1/100 of 6,000.
"6 is 100 times greater than 0.06":
This means that if you multiply 0.06 by 100, you get 6.
So, 6 is indeed 100 times larger than 0.06.
"0.06 is 10 times greater than 0.006":
In this case, if you multiply 0.006 by 10, you get 0.06.
Thus, 0.06 is 10 times larger than 0.006.
"60 is 1/100 of 6,000":
This means that if you divide 6,000 by 100, you get 60.
So, 60 is a hundredth (1/100) of 6,000.
Hence, 6 is 100 times 0.06
0.06 is 10 times 0.006
60 is 1/100 of 6,000
To learn more on Number system click:
https://brainly.com/question/1763119
#SPJ3
A father wants to buy a total of five milk drinks for his son and spend $7.95. Eggnog costs $1.55 and a peanut punch costs $1.65. Determine the number of each milk drink bought
Answers
Answer:
2
Step-by-step explanation:
$ 1.55 + $1.65 = $3.11
the budget is $7.95
$7.95 ÷ $3.11 = 2.5 but since you can't get half a milk it's 2
what led to the creation of the free-soil party?
A. To stop immigrants from entering the United States
B. To promote slavery across the West
C. To stop the spread of slavery
D. To achieve Manifest Destiny
Answers
Answer:
The answer is C
Step-by-step explanation:
brainliest plss
pls help
i will appreciate it if you could help
Answers
Answer:
I think it is 20 percent
Step-by-step explanation:
Sorry if this is wrong