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
685,327 round to the nearest thousand
Answers
Answer:
685,000
Step-by-step explanation:
Answer:
685327.000
Step-by-step explanation:
What is the next number in the pattern
8.72, 8.52, 8.32 …
Answers
Answer:
3333
Step-by-step explanation:
3333
Answer:
8.12
Step-by-step explanation:
Because 0.20 is reduced after each number
8.72-0.20= 8.52
8.52-0.20=8.32
8.32-0.20=8.12
What is the value of w in the equation? 7w + 4 = 16 + 9 A.7 B.25 C.3 D.21
Answers
Answer: C
Step-by-step explanation:
16+9=25 so 25-4 is 21 and 7 times 3 is 21. This means that 7(3) + 4 is 25
Fill in the blank with a number to make a true statement. *
0.25 / ? = -0.25
Answers
What is 59.56 rounded to the nearest whole number?
Answers
Answer:
60
Step-by-step explanation:
A banker estimated a customer's worth to be $127,000. The customer was actually worth $120,000.
Find the percent error.
A. 5.5%
B. 5.6%
C. 5.7%
D. 5.8%
Get 50 points for an answer and brainlyiest for explination
Answers
Answer:
B
Step-by-step explanation:
pick a number, any number.
If it's even, divides it by 2. If it's odd, multiply it by 3 and add 1. Now repeat those steps again with your new number. Eventually, if you keep going, you'll eventually end up at 1 every single time
(please help me)
Answers
Answer: 1
Step-by-step explanation:
1 x 3 + 1=4
4/2=2
2/2=1
the same thing happens again,
1 x 3 +1=4
4/2=2
2/2=1
therefore the number is 1 when I first started
Answer: If this is a True or False Question the Answer is False
Step-by-step explanation:
Why? because if you pick -1 (negative one) the answer will always be negative.
Javad had a mix of yellow and red jellybeans as shown on the
graph. If there are 40 total jellybeans in his bag, how many
are red?
Answers
Hi there!!
The ratio of red jelly beans to yellow is 7:3.
There are 40 jelly beans.
7+3 is 10.
40/10 is 4.
7*4 is 28.
Therefore, 28 jelly beans are red.
Translate the following word phrase into an algebraic expression: Nine times a number y.
Answers
Answer:
9×y
Step-by-step explanation:
the
answer
of
the
given
is 9y
Which of the following describes a similarity between a solid and a gas
Answers
Answer:
they are both states of matterthey are both made up of atoms, molecules and ionsthey both have volumethe length of a rectangle is 10 meters more than the width. if the perimeter is 72 meters, what are the length and width?
Answers
Check the picture below.
Step-by-step explanation:
let's say a is length, and b is width:
a = 10 + b
after this, we can write:
2(a + b) = 72
2(10 + b + b) = 72
2(10 + 2b) = 72
20 + 4b = 72
4b = 72 - 20
4b = 52
b = 52 ÷ 4
b = 13
if b = 13, then a = 10 + b = 10 + 13 = 23
so: a = 23 and b = 13
6.
5. ¿Qué número tiene el mismo
valor que l centena, 7 decenas?
Answers
Answer:
7 Decenas = 70 Unidades espero que te ayude
Step-by-step explanation:
525, 650, 539, 643, 764, 539, 687
What is the interquartile range of these numbers
Answers
Answer:
148
Step-by-step explanation:
sorry, im not sure how to solve it, but its 148
hope this kinda helped :)
mark me brainliest :D
The water level in a lake was monitored and was noted to have changed -2 1/3 inches in one year. The next year it was noted to have changed -1 5/6 inches. What was the total change in the water level over the two years?
Answers
Answer:
The total change in water level over the past 2 years is [tex]\displaystyle -4 \frac{1}{6}[/tex].
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightFractions
Proper and ImproperNumbers
Least Common Multiple (LCM)Step-by-step explanation:
Step 1: Define
Identify
Year 1 water change: [tex]\displaystyle -2 \frac{1}{3}[/tex]
Year 2 water change: [tex]\displaystyle -1 \frac{5}{6}[/tex]
Step 2: Find Total Water Change
[Set up] Add yearly water changes: [tex]\displaystyle -2 \frac{1}{3} + -1 \frac{5}{6}[/tex][Fractions] Convert to improper: [tex]\displaystyle \frac{-7}{3} - \frac{11}{6}[/tex][Fraction] Rewrite [LCM]: [tex]\displaystyle \frac{-14}{6} - \frac{11}{6}[/tex][Order of Operations] Subtract: [tex]\displaystyle \frac{-25}{6}[/tex][Fraction] Convert to proper: [tex]\displaystyle -4 \frac{1}{6}[/tex]Find the lines of symmetry. Select all that apply. Thank you!
Answers
Answer:
l and n
Step-by-step explanation:
Which equations are true? Select all that apply.
A.
66
÷
10
1
=
6
.
6
B.
660
÷
10
0
=
66
C.
6
,
600
÷
1
,
000
=
0
.
66
D.
0
.
66
÷
10
1
=
0
.
066
E.
6
÷
100
=
0
.
06
Answers
Answer:
a b d e
Step-by-step explanation:
i just took the test and got a hundred
Equations A, B, and E are true, i.e 66: 10 = 6.6, 660: 10° = 66, 6: 100 = 0.06.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
Make sure your equation is correct by comparing the values on either side of the equals sign to create a true equation. A true equation must have the same numerical values on both sides of the "=" sign. One real equation is, for instance, 9 = 9. A valid equation is 5 + 4 = 9.
As a result, the true equations are,
66: 10 = 6.6
660: 10° = 66
6: 100 = 0.06
Thus, equations A, B, and E are true, i.e 66: 10 = 6.6, 660: 10° = 66, 6: 100 = 0.06.
Learn more about the equation here,
https://brainly.com/question/10413253
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Answer fast please!!!
Answers
The correct answer is C. 58
Hope this helps!
Step-by-step explanation:
the answer is 58 this is the result I hope I've helped
please answer it fast .......^-^......
Answers
Answer:
990- YES, YES, NO,YES, YES, NO, YES, YES, YES
1586- YES, NO, NO, NO, NO, NO, NO, NO, NO
275- NO, NO, NO, YES, NO, NO, NO, NO, YES
6686- YES, NO, NO, NO, NO, NO, NO, NO, NO
639210- YES, YES, NO, YES, YES, NO, NO, YES,YES
429714- YES, YES, NO, NO, YES, NO, YES, NO, NO
2856- YES, YES, YES, NO, YES, YES, NO, NO, NO
3060- YES, YES, YES, YES, YES, NO, YES, YES, NO
406839- NO, YES, NO, NO, NO, NO, NO, NO, NO
Step-by-step explanation:
hope this helped<3
Use properties to evaluate 1/3 (-15 ÷ 1/2 ) 1/4?
A. - 5/2
B. 5/8
C. - 5/8
D. 5/2
Answers
see the attachment for explanation
hope it helps[tex]\huge\textbf{Hey there!}[/tex]
[tex]\mathbf{\dfrac{1}{3}(-15 \div \dfrac{1}{2})(\dfrac{1}{4})}\\\\\mathbf{= \dfrac{1}{3}(-15\div 0.5)(0.25)}\\\\\mathbf{= \dfrac{1}{3}(-30)(0.25)}\\\\\mathbf{= -10(0.25)}\\\\\mathbf{= \boxed{\bf -\dfrac{5}{2}}\approx -2.5}\\\\\\\\\\\\\huge\text{\bf Therefore, your answer is: \boxed{\mathsf{Option\ A. -\dfrac{5}{2}}}}\huge\checkmark[/tex]
[tex]\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}[/tex]
~[tex]\bf{Amphitrite1040:)}[/tex]
Help plz I don’t understand how to do this math below
Answers
The graph below represents the function f(x) and the translated function g(x).
AVA
2x
/g(x)
a
If f(x) = x, which of the following functions could be an algebraic representation of g(x)?
Answers
Answer:
letter A.g(x)=x2+b that's the answer cause g(x) is in the positive
2. (a) Use a prove by contradiction to show that if a and b are nonzero integers such that a divides b and a + b is odd, then a is odd. (b) Prove that if n is a positive integer, then n² does not equal 2(mod 4).
Answers
a. Assume a is even, so a = 2k for some integer k. Now let a and b be integers such that a divides b and a + b is odd.
Since a divides b, b = an for integer n, and in turn b = 2nk, which means b is even and hence a + b is also even. But this contradicts our initial assumption, so a must be odd.
b. Let n be even, so that n = 2k for some integer k. Then
n² = (2k)² = 4k²
so that n² ≡ 0 (mod 4).
Now let n be odd, so n = 2k + 1 for integer k. Then
n² = (2k + 1)² = 4k² + 4k + 1
so that n² ≡ 1 (mod 4).
Therefore n² is never congruent to 2 (mod 4).
find the prime factorization of each number. 52, and 41
Answers
Step-by-step explanation:
We will first find the prime factorization of 41 and 52. After we will calculate the factors of 41 and 52 and find the biggest common factor number .
Step-1: Prime Factorization of 41
Prime factors of 41 are 41. Prime factorization of 41 in exponential form is:
41 = 411
Step-2: Prime Factorization of 52
Prime factors of 52 are 2, 13. Prime factorization of 52 in exponential form is:
52 = 22 × 131
Pls heeellllppppp me pls no links pls no fake answers and pls answer both questions
Answers
Answer:
I think it's True
Step-by-step explanation:
When you multiply a negative and positive, it equals a negative: (-)x(+)=(-)
^-2/5x > -8
Then multiply both sides of the inequality by ^-5/2 and flip the inequality sign
Which gives you:
x < 20
Answer:
Step-by-step explanation:
one would flip the sign on (-2/5)x > -8 because you would be multiplying by a negative number (- 5/2) to get positive x standing alone. It resolves to
x < 20
You would also flip the sign on
-x + ¾ < 10
-x + ¾ - ¾ < 10 - ¾
-x(-1) > 9¼(-1) multiplying by a negative number flips the sign.
x > - 9¼
I need answers 1 through 5 please
Answers
Answer:
1) first & last option
2) x=10
3) x=15
4) acute, acute, obtuse. right
5)
Step-by-step explanation:
(8)^2+(6)^2=(x)^2
64+36=x^2
square root of 100= square root of x^2
x= 10
A waiter carried 6 baskets with 5 dinner rolls in each
basket. How many dinner rolls did he carry? Show
your work.
Answers
Answer:
30 dinner rolls
Step-by-step explanation:
There are 5 dinner rolls per basket and there are 6 baskets
So there are 6 groups of 5:
5 + 5 + 5 + 5 + 5 + 5
In other words, multiply 5 and 6
5 dinner rolls x 6 = 30 dinner rolls
Each basket has five rolls so you have to do 5+5+5+5+5+5 which equals 30
Please help! How to do this? Ill give brainly
Answers
Answer:
c=60
d=45
Step-by-step explanation:
3c=180
c=60
4d=180
d=45
find the area of the triangle. 20ft, by 21ft. by 29ft.
Answers
Answer:
a=210ft²
The area of the triangle is 210 square feet.
Step-by-step explanation:
This is a right triangle, as shown by the Pythagorean theorem:
[tex]20^{2} +21^{2} =29^{2} \\400+441=841\\841=841[/tex]
The 2 perpendicular legs of a right triangle are also the base and height of a rectangle of the same size. A right triangle is exactly half of that rectangle, and therefore the area of a right triangle is exactly half of the area of that rectangle.
The area of that rectangle is:
[tex]a=b*h\\a=20*21\\a=420[/tex]
And then the area of the triangle is:
[tex]a=\frac{420}{2}\\a=210[/tex]
I make $20 an hour but I love 30% to taxes. How much do I take home each hour after taxes?
Answers
Answer:
$14
Step-by-step explanation:
We can make an equation
30%. . . . . .X
--------- = ---------
100. . . . . . .20
Now we cross multiply
100x = 600
x = 6
Now we subtract to find how much we will take home.
20 - 6 = $14 every hour will be made
Compare the expressions 7+3^2-2⋅5 and (3/4+1/8)÷1/8 using , =, or . Show your work. Answer:
Answers
[tex]A=7+3^2 -2 \cdot 5 = 7 + 9 - 10 = 9-3=6\\\\\\B = \left(\dfrac 34 + \dfrac 18\right) \div \dfrac 18 = \dfrac 78 \times 8 =7\\\\\\B>A[/tex]
The expression relation is 7+3²-2⋅5 > (3/4+1/8)÷1/8.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
First, 7+3²-2⋅5
Solving the above expression
= 7 + 9 -2.5
= 16 - 2.5
= 13.5
Second,
(3/4+1/8)÷1/8
= (6/8 + 1/8) ÷ 1/8
= 7/8 ÷ 1/8
= 7/8 x 8/1
= 7
Hence, 7+3²-2⋅5 > (3/4+1/8)÷1/8.
Learn more about Inequality here:
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