Answer:
The length is 46.05551275 inches, and the width is 26.05551275 inches.
Step-by-step explanation:
We know that the area must be 1200 square inches. Using this information, we can create an equation, where x is length and y is width:
x*y=1200
We know that its length must be 20 inches longer than its width. Therefore, x=y+20. Using this new information, we can replace 'x' in 'x*y=1200' with 'y+20':
(y+20)*y=1200
[tex]y^{2} +20y=1200[/tex]
[tex]y^{2} +20y-1200=0[/tex]
I have decided to use the quadratic formula, but you could also factor this equation into the 'intercept' form to determine the roots, which ultimately provides the same answer.
[tex]y=\frac{-b+\sqrt{b^{2} -4ac} }{2a}[/tex]
[tex]y=\frac{-(20)+\sqrt{(20)^{2} -4(1)(-1200)} }{2(1)}[/tex]
[tex]y=\frac{-(20)+\sqrt{400+4800} }{2}[/tex]
[tex]y=\frac{-(20)+\sqrt{5200} }{2}[/tex]
[tex]y=\frac{52.11102551 }{2}[/tex]
[tex]y=26.05551275[/tex] inches
[tex]x=y+20[/tex]
[tex]x=(26.05551275)+20[/tex]
[tex]x=46.05551275[/tex] inches
Therefore, the length is 46.05551275 inches, and the width is 26.05551275 inches.
PLEASE CORRECT BEFORE ANSWERING I AM HAVING TROUBLE GETTING THINNGS RIGHT SO PLEASE HELP
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Answer:
3
Step-by-step explanation:
AB is 1 unit long.
A'B' is 3 units long.
The scale factor is the ratio of these lengths:
scale factor = A'B'/AB = 3/1 = 3
ABC is dilated by a factor of 3 to get A'B'C'.
6. A boy pushes his little brother in a box with a force of 500 N for 324 m How much work is this if the force of
friction acting on the sliding box is (a) 100 N (6) 250. N?
Answer:
(a) 129600 J
(b) 81000 J
Step-by-step explanation:
The work done is given by the product of force and the displacement in the direction of force.
Force, F = 500 N
distance, d = 324 m
(a) friction force, f = 100 N
The work done is
W = (F - f) x d
W = (500 - 100) x 324
W = 129600 J
(b) Friction, f = 250 N
The work done is
W = (F - f) d
W = (500 - 250) x 324
W = 81000 J
in a group of boys the number of arrangments of boys 4 boys is 12 times the number of arrangment of 2 boys the number of boys in the group is
Answer:
4*12*2
Step-by-step explanation:
it will be the right answer
Answer:
There are 6 boys in group.
Step-by-step explanation:
Since we have given that
Number of arrangement of 4 boys = 12 times the number of arrangement of 2 boys.
So, Let the number of boys in the group be 'x'.
So, Number of boys in the group will be
\begin{gathered}x=\frac{12\times 2}{4}\\\\x=\frac{24}{4}\\\\x=6\end{gathered}
x=
4
12×2
x=
4
24
x=6
Hence, there are 6 boys in the group.
hope it helps you a follow would be appreciated
To the nearest 100th feet, find the volume of a hollow cylinder having inner radius =150 in, outer radius= 170 in and the height = 220 in
Answer:
R1 = 150 in = 12.5 ft
R2 = 170 in = 14.167 ft
H = 220 in = 18.333 ft
Volume of solid cylinder = Pi * R^2 * H
So the volume of a hollow cylinder must be V = Pi * H * (R2^2 - R1^2)
V = 3.142 * 18.33 * (14.17^2 - 12.5^2) = 2565 ft^3
.
Simplify (1 - sin x)(1 + sin x).
0 1
O cos^2 x
O sin^2 x
O tan^2 x
There are 84 students in a speech contest. Yesterday, 1/4 of them gave their speeches. Today, 3/7 of the remaining students gave their speeches. How many students still haven't given their speeches?
Answer:
36
Step-by-step explanation:
Total students un the contest = 84
Number of students who gave their speech yesterday:-
[tex] \frac{1}{4} \: of \: total \\ = \frac{1}{4} \times 84 \\ = 21[/tex]
so 21 students gave their speech yesterday
remaining students = 84 - 21= 63
Number of students who gave their speech today:-
[tex] \frac{3}{7} \: of \: remaining \\ = \frac{3}{7} \times 63 \\ = 27[/tex]
Number of students who have given their speech:-
= 21 + 27
= 48
Number of students who still haven't given their speech :-
= total - 48
= 84 - 48
= 36
Juan borrowed $ 3, 500 from a credit union for 6 years and was charged simple interest at a rate of 4.97 %. What is the amount of interest he paid at the end of the loan?
Answer:
$4543.70
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Simple Interest Rate Formula: [tex]\displaystyle A = P(1 + rt)[/tex]
P is principle amountr is ratet is timeStep-by-step explanation:
Step 1: Define
Identify
P = 3500
t = 6
r = 4.97% = 0.0497
Step 2: Find Interest
Substitute in variables [Simple Interest Rate Formula]: [tex]\displaystyle A = 3500(1 + 0.0497 \cdot 6)[/tex](Parenthesis) Multiply: [tex]\displaystyle A = 3500(1 + 0.2982)[/tex](Parenthesis) Add: [tex]\displaystyle A = 3500(1.2982)[/tex]Multiply: [tex]\displaystyle A = 4543.7[/tex]
I NEED MAJOR HELP WITH THIS QUESTION
Instriction; using the following image, solve for tbe trigonometry ratios of < D and < F .
Answer:
Kindly check explanation
Step-by-step explanation:
Since the triangle is right angled ; we can solve for x using Pythagoras :
x = hypotenus ; hence ;
x² = opposite² + adjacent²
x² = 15² + 8²
x² = 225 + 64
x² = 289
x = √289
x = 17
Using Trigonometry :
Sin D = side opposite D / hypotenus = 8/17
Cos D = side Adjacent D / hypotenus = 15 / 17
Tan D = side opposite D / Adjacent side = 8/15
Sin F = side opposite F / hypotenus = 15/17
Cos F = side Adjacent F / hypotenus = 8 / 17
Tan F = side opposite F / Adjacent side = 15/8
Robin will choose a movie from the Red Box when all movies are in stock. If she
randomly chooses a Romance, Comedy, or Action, what is the probability she will
choose a Romance?
What is the derivative of x^2?
Answer:
[tex]\displaystyle \frac{d}{dx}[x^2] = 2x[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationBasic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = x^2[/tex]
Step 2: Differentiate
Basic Power Rule: [tex]\displaystyle \frac{dy}{dx} = 2x^{2 - 1}[/tex]Simplify: [tex]\displaystyle \frac{dy}{dx} = 2x[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
The fourth term of an=(1/2)^n is
Answer:
[tex]1/16[/tex]
Step-by-step explanation:
The formula for the sequence [tex]a_n=\frac{1}{2}^n[/tex] is used to find the [tex]n[/tex]th term of the sequence.
To find the fourth term, substitute [tex]n=4[/tex]:
[tex]a_4=\left(\frac{1}{2})\right ^4,\\a_4=\frac{1^4}{2^4}=\boxed{\frac{1}{16}}[/tex]
Answer:
1/16
Step-by-step explanation:
the nth term is
[tex]a_{n} = (\frac{1}{2} )^{n}[/tex]
the 4th term is found by substituting n=4
[tex]a_{4} =(\frac{1}{2} )^{4} = \frac{1^{4} }{2^{4} } = \frac{1}{16}[/tex]
someone find x for me lol
Hi there!
[tex]\large\boxed{x = 60^o}[/tex]
We know:
∠AGB ≅ ∠DGC because they are vertical angles. They both are 90°.
∠AGE ≅ FGC because they are vertical angles, equal 30°.
∠BGF ≅ ∠DGE are vertical angles, both equal x.
All angles sum up to 360°, so:
360° = 90° + 90° + 30° + 30° + x + x
Simplify:
360° = 240° + 2x
Subtract:
120° = 2x
x = 60°
^please answer, thanks in advance ^
Answer:
There is not enough information to determine the mean, the median is 28.
There is not enough information to determine the mean absolute deviation, the interquartile range is 18
Step-by-step explanation:
The box plot given has a skewed distribution, this means that both the mean and median values are not the same. From a box plot, the median value Can be obtained as the point in between the box.
From the box plot given, the marked point in between the box is 28 cm
Hence, Median = 28 cm
The mean cannot be inferred from the skewed box plot.
There is also not enough information to determine the mean absolute deviation ;
The interquartile range:
(Q3 - Q1)
Q3 = upper quartile, the endpoint of the box = 40
Q1 = the starting point of the box = 22
IQR = Q3 - Q1
IQR = 40 - 22 = 18
Find the length of XW.
Answer:
XW = 78
Step-by-step explanation:
Both triangles are similar, therefore based on triangle similarity theorem we have the following:
XW/XZ = VW/YZ
Substitute
XW/6 = 104/8
XW/6 = 13
Cross multiply
XW = 13*6
XW = 78
6.) What are the coordinates of D, E and F after a reflection over the y-axis?
D'(-3,-3) E (5,0) F (2,2)
D'(3,3) E'(-5,0) F'(-2,-2)
D'(3,-3) E (0,5) F'(-2,2)
The value of a car will “depreciate” over time. For example, a car that was worth $24 000 when it was new, is being sold for $13 500 three years later. Determine the annual depreciation rate on this car. Express your final answer as a percent, rounded to one decimal place.
Answer:
The car will depreciate at a rate of 21.14% per year.
Step-by-step explanation:
Given that the value of a car will “depreciate” over time, and, for example, a car that was worth $ 24,000 when it was new, is being sold for $ 13,500 three years later, to determine the annual depreciation rate on this car the following calculation must be performed:
13,500 x (1 + X) ^ 1x3 = 24,000
13,500 x (1 + 0.2114) ^ 3 = 24,000
X = 21.14%
Therefore, the car will depreciate at a rate of 21.14% per year.
The average cost when producing x items is found by dividing the cost function, C(x), by the number of items,x. When is the average cost less than 100, given the cost function is C(x)= 20x+160?
A) ( 2, infinit)
B) (0,2)
C) (-infinit,0) U (2,infinit)
D) (- infinit,0] U [2,infinit)
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Answer:
A) (2, ∞) . . . . or C) (-∞, 0) ∪ (2, ∞) if you don't think about it
Step-by-step explanation:
We want ...
C(x)/x < 100
(20x +160)/x < 100
20 +160/x < 100 . . . . . separate the terms on the left
160/x < 80 . . . . . . . subtract 20
160/80 < x . . . . . multiply by x/80 . . . . . assumes x > 0
x > 2 . . . . . . simplify
In interval notation this is (2, ∞). matches choice A
__
Technically (mathematically), we also have ...
160/80 > x . . . . and x < 0
which simplifies to x < 0, or the interval (-∞, 0).
If we include this solution, then choice C is the correct one.
_____
Comment on the solution
Since we are using x to count physical items, we want to assume that the practical domain of C(x) is whole numbers, where x ≥ 0, so this second interval is not in the domain of C(x). That is, the average cost of a negative number of items is meaningless.
Which of the following functions is graphed below?
20
15
10
-8-84
-2
42
-5
-10
-15
-20
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Answer:
D.
Step-by-step explanation:
The linear portion of the curve is in the region x ≥ 2. The only function defined that way is the one in choice D.
PLEASE HELP ME ASAP (72 POINTS)
Answer:
d=10.45t
Step-by-step explanation:
The last one is the answer.
Hope this helps!
--Applepi101
Answer:
D) d=10.45t
Step-by-step explanation:
His distance(d) was 100. And his time(t) was 9.58 seconds.
So 100=9.58x
x≈10.44
The answer is D, because 10.45 is greater than 10.44.
I hope this helps!
Responde las preguntas 10 y 11 con base al siguiente gráfico. A 10. ¿Cuáles son los nombres de los ángulos de color azul y rojo respectivamente? A. Obtuso y llano. B. Llano y obtuso. C. Obtuso y agudo. D. Agudo y llano. 11. ¿Cuáles son los colores de un ángulo agudo y uno recto respectivamente? A. Naranja y verde. B. Morado y rojo. C. Morado y naranja. D. Verde y naranja. firmaciones ac
Answer:
10) Los ángulos en azul y rojo son llano y obtuso, respectivamente. (Respuesta: B)
11) Los ángulos agudo y recto están diferenciados por los colores morado y naranja, respectivamente. (Respuesta: C)
Step-by-step explanation:
Basándonos estrictamente en lo descrito en la figura, tenemos la siguiente clasificación por colores:
Agudo - Morado.
Plano o Recto - Naranja.
Obtuso - Rojo.
Llano - Azul.
Completo - Negro.
A continuación, se consigna las respuestas en forma de oración:
10) Los ángulos en azul y rojo son llano y obtuso, respectivamente. (Respuesta: B)
11) Los ángulos agudo y recto están diferenciados por los colores morado y naranja, respectivamente. (Respuesta: C)
An office manager booked 55 airline tickets. He booked 6 more tickets on Airline A than Airline B. On Airline C, he booked 5 more than twice as many tickets as on Airline B. How many tickets did he book on each Airline?
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Answer:
A: 17B: 11C: 27Step-by-step explanation:
If we let a, b, c represent tickets booked on airlines A, B, C, respectively, then we have ...
a + b + c = 55
a - b = 6
-2b + c = 5
Using the last two equations to write expressions for a and c, we have ...
a = b +6
c = 5 +2b
These can be substituted into the first equation to give ...
(b +6) +b +(5 +2b) = 55
4b +11 = 55
4b = 44
b = 11
a = b+6 = 17
c = 5 +2b = 27
He booked 17 tickets on Airline A, 11 tickets on Airline B, and 27 tickets on Airline C.
Which choice is equivalent to the fraction below? (Hint: Rationalize the
denominator and simplify.)
2-√2
2 + 2
A. 2.
B. 2-3
o
C. 3-2.12
D. 6 - 42
(2/3)x-1=27/8,find x
Answer:
x = 105/16
Step-by-step explanation:
2/3x - 1 = 27/8
Add 1 to each side
2/3x - 1+1 = 27/8+1
2/3x = 27/8 + 8/8
2/3x = 35/8
Multiply each side by 3/2
3/2 * 2/3x = 35/8 *3/2
x = 105/16
A car travels 1/8 mile in 2/13 minutes. What is the speed in terms of miles per minute?
Answer:
13/16 miles per minute
Step-by-step explanation:
Take the miles and divide by the minutes
1/8 ÷ 2/13
Copy dot flip
1/8 * 13/2
13/16 miles per minute
Simplify the expression3x 3√648x4y8
Answer:
= 1296x √ xy
Step-by-step explanation:
Apply exponent rule: a^b . a^c = a^b + c 3 . 3 = 3^ 1 + 1
= x . 3^1+1 √648x . 4y . 8
Add the numbers: 1 + 1 = 2
= x . 3^2 √648x . 4y . 8
= 3^2 . 144x √ xy
Refine
= 1296x √ xy
Can someone explain how to solve this step by step? Thank you
Answer:
x=10
Step-by-step explanation:
Using the Rational Roots Test, we can say that the potential rational roots are
± (1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90).
Unfortunately, there doesn't really seem to be an easy way to figure out which numbers are actually roots outside of guess and check. Therefore, to solve this, we'll have to go through numbers until we hit something.
To make the process faster, I wrote a Python script as follows:
numbers = [1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90]
negative_numbers = [i * (-1) for i in numbers]
numbers = numbers + negative_numbers
for i in numbers:
if (i**3 - 10*(i**2) + 9*i-90) == 0:
print(i)
The result comes out as 10, meaning that 10 is our only rational root. Using the Factor Theorem, we can say that because 10 is a root, (x-10) is a factor of the polynomial. Using synthetic division, we can divide (x-10) from the polynomial to get
10 | 1 -10 9 -90
| 10 0 90
_________________
1 0 9 0
Therefore, we can say that
(x³-10x²+9x-90)/(x-10) = (x²+0x+9), so
x³-10x²+9x-90 = (x-10)(x²+9)
As the only solution to x²+9=0 contains imaginary numbers, x=10 is the only solution to x³-10x²+9x-90 = (x-10)(x²+9) = 0
In a large sample of customer accounts, a utility company determined that the average number of days between when a bill was sent out and when the payment was made is with a standard deviation of days. Assume the data to be approximately bell-shaped.
Required:
a. Between what two values will approximately 68% of the numbers of days be?
b. Estimate the percentage of customer accounts for which the number of days is between 18 and 46.
c. Estimate the percentage of customer accounts for which the number of days is between 11 and 53.
p and q are two numbers.whrite down an expression of. a.) the sum of p and q. b) the product of p and q
The cost function in a computer manufacturing plant is C(x) = 0.28x^2-0.7x+1, where C(x) is the cost per hour in millions of dollars and x is the number of items produced per hour in thousands. Determine the minimum production cost.
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Answer:
$562,500 per hour
Step-by-step explanation:
The cost will be a minimum where C'(x) = 0.
C'(x) = 0.56x -0.7 = 0
x = 0.7/0.56 = 1.25
The cost at that production point is ...
C(1.25) = (0.28×1.25 -0.7)1.25 +1 = -0.35×1.25 +1 = 0.5625
The minimum production cost is $562,500 per hour for production of 1250 items per hour.
_____
Additional comment
This is different than the minimum cost per item. This level of production gives a per-item cost of $450. The minimum cost per item is $358.30 at a production level of 1890 per hour.
Solve the following system of equations
x^2+2y^2=59
2x^2+y^2=43
Answer: x = (-3,3), y = (-5,5)
Step-by-step explanation:
Add both of the equations together, for [tex]3x^{2}+3y^{2} = 102[/tex]. Now we can divide both sides by 3, getting[tex]x^2+y^2=34[/tex]. we subtract the first equation from our equation we just got, getting [tex]y^2=25[/tex] y= (5,-5). once we plug that in, we get [tex]50+x^2 = 59[/tex], [tex]x^2 = 9[/tex] x = (-3,3)
