Answer:
Length = 90 feet
Width = 70 feet
Step-by-step explanation:
The area of a rectangle is found by finding the product of the length. Therefore, the following formula equation can be made:
[tex]A=lw[/tex]
The problem tells us that the area of the garden is 6,300 square feet and that the length is 20 feet longer than the width. Therefore, our equation can be rewritten as such:
[tex]6300=(w+20)(w)~or~6300=w(w+20)[/tex]
Now that there are no longer two different variables, we can solve for w.
[tex]6300=w(w+20)\\\\6300=w^2+20w\\\\0=w^2+20w-6300[/tex]
We are left with a trinomial so we'll use the quadratic formula to further solve for w.
[tex]w=\frac{-20\pm\sqrt{20^2-4(1)(-6300)} }{2(1)}\\\\w=\frac{-20\pm\sqrt{400+25200} }{2}\\\\w=\frac{-20\pm\sqrt{25600} }{2}\\\\w=\frac{-20\pm160}{2}\\\\\\w=70\\or\\w=-90[/tex]
Since distance cannot be negative, w = -90 cannot be a solution for this problem. Therefore, the width of the rectangular garden is 70 feet.
Now that the width has been found, we know the length is 20 feet longer than it. Therefore, the length is 90 feet.
314. Find the area under the graph of f(t) = t/(1+t^2) where t is
between t= 0 and t = x. where a > 0 and a does not equal 1 is
fixed, and evaluate the limit as x → .
Infinity
Answer:
Check the attached image for the sake of my sanity typing integrals in these.
Notes on the red marks.
1. From the first to the second passage I multiplied top and bottom by 2. The bottom one stood outside the integral by linearity, the top got inside to get the derivative of the denominator.
2. Quick y substitution, it's a dy/y which should get integrated as the logarythm of the absolute value. This is a situation where you can skip it since you know that you are dealing with positive values (1 is positive, and 1 plus something squared is even greater than 1 which was positive already).
The area as x diverges also diverges
Find the error(s) and solve the problem correctly. Be sure to explain and show your work. Where did the "wrong answer" come from? sin 52° Answer: sin 52 = .9866
The error of the evaluation comes from the fact that Sin 52° = 0.7880.
According to the question;
we are required to determine what's wrong with the evaluation..By evaluation;
Sin 52° when evaluated by means of a scientific calculator or tables gives; 0.7880.The error can be determined by evaluating; the inverse sine of 0.9866.
Sin-¹ .9866 = 80.6.Read more;
https://brainly.in/question/14817452
Solve: m = 5 – (-10).
Answer:
m=15
Step-by-step explanation:
Any help would be great!
Answer:
Step-by-step explanation:
67.5
Solve for r.
17r–13r=20
r=
Answer:
Step-by-step explanation:
Solve for r.
17r–13r=20
4r = 20
r = 20 : 4
r = 5
What is the final cost of a $40 item after a 8% tax is applied
A dog park is divided into sections for large and small dogs. The ratio of the perimeter of the small dog section to the perimeter of the entire dog park is 7 : 12. Find the area of each section.
Answer:
58
Step-by-step explanation:
This diagram models 3 friends who are sharing 2 turkey sandwiches equally.
How much does each friend get?
1/3 sandwich
2/3 sandwich
11/3 sandwiches
11/2 sandwiches
Answer:
2/3 sandwich.
Step-by-step explanation:
No Explanation
Robert baked 6 pies to donate to a charity dinner before he ran out of sugar. With each additional cup of sugar he buys, he can bake 1 more pie.
Write an equation that shows how the total number of pies Robert can bake, y, depends on the number of cups of sugar he buys, x.
Y=
Answer:
y=4x+6
Step-by-step explanation:
slope intercept form y=mx+b
The total number of pies Robert can bake, y, depends on the number of cups of sugar he buys, x, according to the following equation:
y = 6 + x
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
According to the following equation, the total number of pies Robert may bake, y, is determined by the number of cups of sugar he purchases, x:
y = 6 + x
This equation can be read as: "The number of pies Robert can bake, y, is equal to the number of pies he baked before he ran out of sugar, which is 6, plus the number of additional cups of sugar he buys, x."
For example, if Robert buys 2 additional cups of sugar, he can bake a total of 6 + 2 = 8 pies.
If he buys 3 additional cups of sugar, he can bake a total of 6 + 3 = 9 pies, and so on.
Learn more about the equations here:
brainly.com/question/10413253
#SPJ2
Solve for b.
b+23=114
Enter your answer as a fraction in simplest form in the box.
b =
An equation is a collection of variables and constants. The value of b for the given equation b + 23 = 114 will be 91.
What is the equation?There are many different ways to define an equation.
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
More than one variable may be present inside a linear equation.
As per the given equation,
b + 23 = 114
Add -23 both sides
b + 23 - 23 = 114 - 23
b + 0 = 91
b = 91
Hence "An equation is a collection of variables and constants. The value of b for the given equation b + 23 = 114 will be 91".
For more about the equation,
brainly.com/question/10413253
#SPJ3
Evaluate x? - x + 8 for x = -2.
=
Answer:
tan
(
x
)
,
x
=
−
π
3
x
+
2
y
+
z
x
+
y
+
z
,
x
=
2
,
y
=
3
,
z
=
1
csc
(
x
)
,
x
=
π
Answer:
6
Step-by-step explanation:
X+8 first substitute x
-2+8 solve
=6
What is the 5th term of the linear sequence? 1,7,13,19,25,...
Answer : 31
Explanation : Every numbers have a gap of 6 as you can see:
1 + 6 = 7
7 + 6 = 13
13 + 6 = 19
19 + 6 = 25
So,
25 + 6 = 31
Hope This Helps You!
WILL GIVE YOU BRILLIANT
State whether the graph of the linear relationship is a solid line or a set of unconnected points. Complete the explanation of your reasoning. The relationship between the number of $5 lunches you buy with a $145 school lunch card and the money remaining on the card because you select ) The relationship is a select ) buy a (select
Answer:
The relationship will be a solid line.
Step-by-step explanation:
The relationship between the number of $4 lunches you buy with a $100 school lunch card and the money remaining on the card.
The relationship will be a solid line as it is a linear and common slope. Each time you buy lunch, the amount in the card will decrease by $4.
Let the number of lunches you buy be = x
Let the amount remaining in the card be = y
So, equation forms:
When you buy 1 lunch, or x = 1
When x = 2
When x = 3
We can see that the decrease is gradual and same.
You can also see the graph attached that a straight line is formed.
represent each solution on a number line 3
I don't know how to represent it on a nomberline
I
Which of the following is a solution to the given equation? y = -3x - 7
Answer:y = 3(-2) - 7
Step-by-step explanation:
What is the algebraic expression for the following word phrase: the product of 7 and the difference of x and y?
Answer:
7(x-y)
Step-by-step explanation:
difference of x and y=x-y
product of 7=7 times the expression
so,
Answer is 7(x-y)
Suppose that $50,000 is invested at 9% interest. Find the amount of money in the account after 8 years if the interest is compounded annually.
Answer:
50,000(1+0.09)^8
50000(1.99256)
A=99,628.13
Please HELP ME!!!
[tex]x=1+i[/tex] is a solution to which of the following equations?
a: [tex]x^{2}+1=0[/tex]
b:[tex]x^{2} -2x+2=0[/tex]
c: [tex]x^{2} -2x+1=0[/tex]
d:[tex]x^{2} -1=0[/tex]
If you could please share you're thought process and work with me as well, so I can better understand how you found the answer. Thanks a bunch!
Answer:
b. x² - 2x + 2 = 0Step-by-step explanation:
Solve each to confirm answer
a.
x² + 1 = 0x² = - 1x = √ -1x = iFALSEb.
x² - 2x + 2 = 0(x - 1)² + 1 = 0(x - 1)² = - 1x - 1 = √-1x - 1 = ix = 1 + iTRUEc.
x² - 2x + 1 = 0(x - 1)² = 0x - 1 = 0x = 1FALSEd.
x² - 1 = 0x² = 1x = √1x = ± 1FALSEAnswer:
Option B
Step-by-step explanation:
[tex]\\ \sf\longmapsto x^2-2x+2=0[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{-(-2)\pm\sqrt{(-2)^2-4(1)(2)}}{2(1)}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{2\pm\sqrt{4-8}}{2}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{2\pm\sqrt{-4}}{2}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{2\pm 2i}{2}[/tex]
[tex]\\ \sf\longmapsto x=1\pm i[/tex]
Verified
You buy a $266,000 home with a down payment of 21%. Find the amount of the down payment and the mortgage amount.
down payment
$
mortgage
$
Answer:
down is #0.21 while mortage is
Is this correct way to solve the problem?
5(2x-2)=30
10x-1030
10x=30+10
10x=40
(-10x)=(40)
x=-4
help me plz
Answer:
10x=40
x=40/10
x=4
4 is the answers, not -4
Step-by-step explanation:
pls mark as brainliest
The circumference (C) of a swimming pool is 47 feet. Which formula can you use to find the radius (r) if you know that C = 2πr ?
Answer:
The answer is 7.48 or 7.5
Step-by-step explanation:
If the circumference is C which is equal to 47 feet, what you have to do is divide it by pi, or 3.14 for an estimate. After that, you'll get the diameter and then divide it by 2. Now you have your radius.
plz help me plz need your help plz help
Step-by-step explanation:
a+b^2 =a^2+b^2+2ab
-2ab and+2ab cut
To find the equation of a regression line, ý = ax + b, you need these formulas:
8=13
--
b= y - az
S
A regression line has a slope of 2.334. If the mean of the x-coordinates of the
data points is 6.607, and the mean of the y-coordinates is 10.738, what is the
y-value of the y-intercept of the line to three decimal places?
A. -18.455
B. -4.683
C. 4.683
D. 18.455
Answer:-4.683
Step-by-step explanation:
Took the test
Please help me , fast
Answer:
0.3 with the hat ? the answer is first no, then it's a repeated decimal.
Step-by-step explanation:
At a pumpkin stand, Fei bought 3 pumpkins: one large, one medium, and one small. The large pumpkin cost twice as much as the medium one, and the medium pumpkin cost three times as much as the small one. Fei spent $20 in total. How much did the large pumpkin cost?
Answer:
Step-by-step explanation:
lets put the small pumpkin as x that means medium is 3x and large is 6x
so we have a equation
x+6x+3x=20
combine them
10x=20
divide by 10
x=$2
Answer:
2
Step-by-step explanation:
you really should stop the noetic tests
Help quick 20points please please
Answer:
AB = 23.6
BC = 18.5
CD = 23.6
DA = 18.5
Step-by-step explanation:
4.
Both sets of opposite sides are parallel, so this is a parallelogram.
In parallelogram ABCD:
AB≅CD
AD≅BC
Knowing that, you can write 2 equations with the given information:
[tex]2a-20.4=a+1.6\\a-3.5=18.5[/tex]
You can solve whichever one you want, but I'll do both to be sure.
[tex]2a-20.4=a+1.6\\2a=a+1.6+20.4\\2a-a=1.6+20.4\\a=22[/tex]
Now for the second one:
[tex]a-3.5=18.5\\a=18.5+3.5\\a=22[/tex]
a = 22, so now you can solve for the side lengths.
[tex]2(22)-20.4=23.6\\22-3.5=18.5\\22+1.6=23.6\\18.5=18.5[/tex]
What is the distance between the two points (4,7) and (4, -2)?
a. 5
12.04
b. 9
d. 12.53
C.
Answer:
9 unitsStep-by-step explanation:
Given two points:
(4, 7) and (4, - 2)The distance between them is the difference of y- coordinates since x- coordinates are same:
7 - (- 2) = 7 + 2 = 9
Given the function h (x) = –22 - 4, the value of h(-5) would be?
Answer:
At the value of x = 3 the function H(x) is undefined. (answer is 3)
Step-by-step explanation:
h (x) = 1/(x-5)2 + 4 (x-5) +4
Solution :
We know that for the values of x where denominator is zero the function H(x) is not define.
(x -5)2 +4 (x -5 ) +4 = 0
x2 -6x +9 =0
x2 - 3x - 3x +9 = 0
(x - 3)2 = 0
So x= 3
At x = 3 the function H(x) is undefined. (3 is your answer)
I really need help this is due in a little bit and I need to finish
Answer:
The correct form is [tex]y = -2x + 24[/tex]
Step-by-step explanation:
First we need to interpret the equation of Nolan.
The [tex]y[/tex] means the current value in the bank accountThe [tex]x[/tex] means the past days-2 means that spend each dayand 12 the initial amount in the bankHow you can see the initial amount in the bank is incorrect because Nolan started with 24 instead of 12.
So the correct form of the equation is:
[tex]y = -2x + 24[/tex]
A patient has an illness that typically lasts about 24 hours. The temperature, T, in degrees Fahrenheit, of the patient t hours after the illness begins, is given by: T(t) = -0.013t^2 + 0.3172t +98.6. When does the patient reach its maximum value? what is the patient's maximum temp?
Answer:
no entiendo, perdóname, suerte