Answers
========================================================
Explanation:
The old dimensions of the rectangle were 30 by 15.
The new dimensions are 30+x by 15+x, where x is some positive number.
The new rectangle dimensions multiply to 1000
(30+x)(15+x) = 1000
Use the FOIL rule to expand out the left side like so
(30+x)(15+x) = 1000
450+30x+15x+x^2 = 1000
450+45x+x^2 = 1000
x^2+45x+450
Then lets get everything to one side
x^2+45x+450 = 1000
x^2+45x+450-1000 = 0
x^2+45x-550 = 0
---------------------
From here we use the quadratic formula
Plug in a = 1, b = 45, and c = -550.
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(45)\pm\sqrt{(45)^2-4(1)(-550)}}{2(1)}\\\\x = \frac{-45\pm\sqrt{4225}}{2}\\\\[/tex]
[tex]x = \frac{-45\pm65}{2}\\\\x = \frac{-45+65}{2} \ \text{ or } \ x = \frac{-45-65}{2}\\\\x = \frac{20}{2} \ \text{ or } \ x = \frac{-110}{2}\\\\x = 10 \ \text{ or } \ x = -55\\\\[/tex]
Earlier we defined x to be a positive number. This means we ignore x = -55. It makes no sense to add on a negative amount to each dimension.
The only practical answer is x = 10.
So each dimension is increased by 10 feet.
--------------------------
If x = 10, then the old dimensions of 30 by 15 bump up to 30+10 = 40 by 15+10 = 25
Then note how 40*25 = 1000, which helps confirm we have the correct dimensions.
--------------------------
Now go back to the question at hand: we want to find the new width. The old width was 30 feet. The new width is 30+x = 30+10 = 40 feet
Related Questions
Alan travels eight and two thirds kilometers to get to school. He ran one and ten elevenths kilometers and walked the rest. How many kilometers were left to walk?
1.six and two thirty thirds kilometers
2.five and twenty five thirty thirds kilometers
3.six and twenty five thirty thirds kilometers
4.six and twenty thirty thirds kilometers
Answers
Answer:
3!
Step-by-step explanation:
8 2/3 - 1 10/11 = 223/ 33 (6 25/ 33)
Hope it helped!
A square has sides of length S inches. Suppose the perimeter of the square is P inches, and it's area is A square inches. If P = A, then what's the value of S? (Please show work I need help:(
Answers
Step-by-step explanation:
The answer has to be 4.
4×4=16
4+4+4×4=16
What is 2/5 ÷ 3 and 1/10
Answers
Answer:
0.13 and 0.1 hope it will help you..
Given g(x)=2x+3, solve for x when g(x)=3
Answers
Answer:
-3/2
Step-by-step explanation:
Find the domain and range of the function
Answers
Answer:
domain: (-∞ , ∞)
range: (-∞, 2]
Step-by-step explanation:
the domain is the set of values of what the x value can be. This function is parabolic and upside down, it can have a range of x values from - infinity to positive infinity. The function is most likely y=-x^2 +2
range is the output (y values) the function can possibly have. the max is 2 and includes 2 so we use bracket for that. The smallest y value can reach towards negative infinity.
Please give thanks by clicking the heart button! :)
Find rhe x- and y- intercerpts of the following relationships.(There may be more then one)
[tex]3x^{2} + 2y^2 = 24[/tex]
Answers
Answer:
see explanation
Step-by-step explanation:
Given
3x² + 2y² = 24
To find the x- intercepts , let y = 0 in the equation and solve for x
3x² + 2(0)² = 24, that is
3x² = 24 ( divide both sides by 3 )
x² = 8 ( take the square root of both sides )
x = ± [tex]\sqrt{8}[/tex] = ± 2[tex]\sqrt{2}[/tex] ← x- intercepts
To find the y- intercepts. let x = 0 in the equation and solve for y
3(0)² + 2y² = 24 , that is
2y² = 24 ( divide both sides by 2 )
y² = 12 ( take the square root of both sides )
y = ± [tex]\sqrt{12}[/tex] = ± 2[tex]\sqrt{3}[/tex] ← y- intercepts
Carmen is 5 1 ··4 years younger than Antoine. Katy is 11 1 ··2 years older than Carmen. To the nearest year, what is the difference in Antoine's age and Katy's age?
Answers
Let, age of Carmen, Antoine and Katy is C, A and K.
And it is given that :
[tex]A - C = 5\dfrac{1}{4}[/tex] …1)
[tex]K-C = 11 \dfrac{1}{2}[/tex] ...2)
We need to find the difference in Antoine's age and Katy's age.
Subtracting equation 2) from 1), we get :
[tex]( A - C ) - ( K-C) =5\dfrac{1}{4} - 11\dfrac{1}{2}\\\\A - K = -6\dfrac{1}{4}\\\\K-A = 6\dfrac{1}{4}[/tex]
Therefore, Katy is [tex]6\dfrac{1}{4}[/tex] years older than Antoine.
which of the following statements best describes the graph of x + y =2?
A) it is a line which intersects the y-axis at (2,2).
B) it is aligned joining the points whose x- and Y- coordinates add up to 2.
C) it is a line which intersects the x-axis at (2,2).
D) it is a line joining the points whose x- and Y- coordinates add up to 4.
Answers
Step-by-step explanation:
so x+y=2
a line would have to go 0,2 2,0
so the answer would be D
Garrys H is one less than three times is Sister's age Girl ❤️ Gary's age is one less than three times is Sister‘s age Girl ❤️ Gary is 11 years old how old is his sister
Answers
Answer:
4 years old
Step-by-step explanation:
His sister is x years old.
Gary is 1 year less than 3 times her age, so his age is
3x - 1
His age is 11, so we can write an equation.
3x - 1 = 11
Add 1 to both sides.
3x = 12
Divide both sides by 3.
x = 4
Answer: She is 4 years old.
Answer:
4
Step-by-step explanation:
Leah has an account balance of –150 dollars. Which of the following represents a debt greater than –150 dollars?
Answers
Answer:
-175
Step-by-step explanation:
bc its farther than -150 from the 0
PLEASE HELP!!
just look at the picture
Answers
Answer:
its the math that solve
Step-by-step explanation:
1.The [ ] of an Isosceles triangle is the side included between the pair of congruent angles
Answers
Answer:
Base
Step-by-step explanation:
A triangle is a polygon with three sides and three angles. There are different types of triangles which are scalene triangle, isosceles triangle,, equilateral triangle etc..
An isosceles triangle is a triangle in which two of the sides are equal, also two angles are equal. The two equal sides of the isosceles triangle are called base while the other side is the base.
The base of an Isosceles triangle is the side included between the pair of congruent angles.
z = y + x + m , solve for x
step by step
Answers
I hope this helps you
Good luck
You got this :)
m= -1/3
b=4
y=
I need to find how to do the equation
Answers
Answer:
y= -1/3x + 4
Step-by-step explanation:
m in this case is (-1/3)
and b is (4)
knowing that you can just plug them into the equation (y=mx+b)
(-11/6) + m= -2/9
SOLVE FOR M
Answers
Answer:
29/18
Step-by-step explanation:
Add -11/6 to both sides of the equation
m=-2/9+11/6 = -4/18+33/18=29/18
Find the value of k, if x + 3 is a factor of 3x² + kx + 6. *
Answers
Hope it help
6. Which expression is equivalent to (14442,6 for all positive values of k and r? OF 12kr7 O G.726?-14 OH 144kry O J. 126-14
Answers
Answer:
the answer is 12k²r¹⁴.........
WILL GIVE BRAINIST!!!
AND 20 POINTS:)
Answers
Ummmm its not clear so
Alexis bought 2 bags of apples for the fruit salad for her party. Each bag contained 13 apples. If she cuts each apple into 8 pieces, how many apple pieces would she have?
Answers
Answer:
2 times 13 is 26 and 26 times 8 is 206
Step-by-step explanation:
Let p(x)=x^3+15x^2-8x+2. What is the remainder when p(x) is divided by x-2?
Answers
Answer:
Step-by-step explanation:
Using synthetic division, the zeros goes into the box, which would be -1
-1 | 1 -3 -1 24
-1 4 -3
1 -4 3 21
The remainder is 21
Help! Algebra 1! Will mark brainliest!
What is the solution to -3/4x+2_<-7?
PICTURE IS ATTACHED.
Answers
Answer:
x ≥ 12
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define
-3/4x + 2 ≤ -7
Step 2: Solve for x
Subtract 2 on both sides: -3/4x ≤ -9Divide -3/4 on both sides: x ≥ 12please help ASAP due tomorrow!!!
Answers
Answer:
1. b =1/2 (4)(3.5)
v=(14)(8)
2.b= 1/2 (9)(12)
V=(54)(13)
3.b= 1/2(7)(6.1)
v= (21.35)(9)
9x+16
3
<7
solve each inequality
Answers
Step-by-step explanation:
9+16×+3
28×<7
35x it's answer can I help
this is a sat practice. need help
Answers
Answer:
The answer is A) -1 + 12i
Step-by-step explanation:
(7 + 3i) + (-8 + 9i)
(7 - 8) + (3 + 9)i
7 - 8 = - 1
3 + 9 = 12
- 1 + 12
(7+3i)+(-8+9i)
You go ahead and rewrite it like this
7-8+3i+9i
And then combine like terms
-1+12i
So your answer is A
A cookie recipe requires 2.5 cups of sugar for every 10 cups of flour. If a
baker makes enough cookies to use 16 cups of sugar, how many cups
of flour would be used?
HELP FAST THIS IS A TEST AND ITS ABOUT TO END SOOOONNNNN
Answers
Answer:64
Mr. Molier is figuring out the the semester averages for his history students. He can calculate the average of 20 students in an hour. How long does it take him to figure the average for each student? Explain your answer.
Answers
36 is what percent of 100?
A. 0.36%
B. 2.78%
C. 277.8%
D. 36%
Answers
Answer: it B. 2.78%
Step-by-step explanation: if it wrong sorry
Answer:
D
Step-by-step explanation:
we know how to find a percent by making it a fraction out of 100
36/100 is 36% so D
whats is 10000000000000000+00+0000000++000000+0000000010000000000001010101010102010202010200100202020202020.
jk, here is a gift from me Merry Christmas :)
Answers
Answer:
aww I find this so cutee
Step-by-step explanation:
Merry Christmas :) :) ^ ^
Answer:
its past t but it never too late to celebrate christmas happy christmas past and future
Step-by-step explanation:
Mrs. Nally's swimming pool is 10 feet by 6 feet. She paves the area around it with a sidewalk x feet wide, using 80 square feet of a new type of non-slip concrete. How wide is the sidewalk? A. The sidewalk is 20 feet wide. B. The sidewalk is 4 feet wide. C. The sidewalk is 10 feet wide. D. The sidewalk is 2 feet wide.
Answers
Answer:
The sidewalk is 2 feet wide
Step-by-step explanation:
The area of the sidewalk is given as 80 square feet
The length and width of pool
including side walks will be;
10 + 2x and 6 + 2x
To get the area of the side walk
That will be area of total minus area of the pool
That will be ;
(10 + 2x)(6 + 2x) - 10(6) = 80
60 + 12x + 20x + 4x^2 - 60 = 80
4x^2 + 32x -80 = 0
x^2 + 8x -20
x^2 + 10x - 2x - 20 = 0
x(x + 10) -2(x + 10) = 0
(x-2)(x + 10) = 0
x = 2 or -10
since width cannot be negative;
The sidewalk is 2 feet wide
Carlos is picking 6/384 apples. Mateo is picking oranges of 10. How much did Mateo pick?
Answers
Question might be incomplete or incorrect so we'd have to assume Mateo took apples
Answer:
5/189 apples
Step-by-step explanation:
If Carlos picks 6/384 apples then there must be 384 apples available to pick from. Amount of apples left after Carlos picks =384-6=378 apples
If Mateo picks 10 apples after Carlos then how much apples Mateo has taken would depend on the number of apples available, hence the fraction of apples Mateo has taken = 10/378
Reduce to lowest terms to get 5/189 apples
