Given:
The length of a rectangle is one unit more than its width.
Area of rectangle = 56 units
To find:
The dimensions of the rectangle.
Solution:
Let, width of the rectangle be x.
Then, length of the rectangle = x+1
Area of a rectangle is
[tex]Area=length\times width[/tex]
[tex]56=(x+1)\times x[/tex]
[tex]56=x^2+x[/tex]
[tex]0=x^2+x-56[/tex]
By splitting the middle term, we get
[tex]x^2+8x-7x-56=0[/tex]
[tex]x(x+8)-7(x+8)=0[/tex]
[tex](x-7)(x+8)=0[/tex]
Using zero product property, we get
[tex]x-7=0[/tex] and [tex]x+8=0[/tex]
[tex]x=7[/tex] and [tex]x=-8[/tex]
Width cannot be negative. So, x=7.
Now,
Width = 7 units
Length = 7+1
= 8 units
Therefore, the length of the rectangle is 8 units and width is 7 units.
Answer:
7
Step-by-step explanation: POV: I got it right
WILL GIVE BRAINLIEST!!! Which equation is modeled below? 4 x tiles and 2 negative 1 tiles = 2 x tiles and 4 1 tiles. 2 x + (negative 2) = negative 2 x + 6 4 x + (negative 2) = negative 2 x + 6 2 x + 4 = 6 x + 2 Negative 2 x + 4 = 6 x + (negative 2)
Answer:
B
Step-by-step explanation:
4x+ (-2) =-2x+6
just took the quiz
Answer:
B) 4 x + (-2) = -2 x + 6
Step-by-step explanation:
if one leg of a right triangle is 12 and the other leg is 16, what is the length of the hypotenuse in this right triangle?
Answer:
20
Step-by-step explanation:
Since I am given two values of the triangle, I will input the equation a²+b²=c².
"c" represents the hypotenuse. First I plug in the values of the legs, 12²+16²=c². Next I simplify these values to 144+256=c², which is 400=c². Finally I take the square root from both the value and the variable: √400=√c² which is equivalent to 20=c. Therefore, the hypotenuse is 20. Hopefully this helps :)
What is the range of this (may be more than one answer)
ignore the answer chosen but does anyone know the answer to this pls asap!!
Answer:
The diagonals bisect each other
Step-by-step explanation:
2s = 10 s+5 = 10 FJ = JH
t+12 = 18 3t = 18 EJ = JG
A particle moves along the curve y = 5x^2 – 1 in such a way that the y value is decreasing at the rate of 2 units per second. At what rate is x changing when x = 1?
Decreasing one fifth unit/sec
Increasing one fifth unit/sec
Decreasing one tenth unit/sec
Increasing one tenth unit/sec
Answer:
The correct option is;
Increasing one fifth unit/sec
Step-by-step explanation:
The equation that gives the curve of the particle of the particle is y = 5·x² - 1
The rate of decrease of the y value dy/dt = 2 units per second
We have;
dy/dx = dy/dt × dt/dx
dy/dx = 10·x
dy/dt = 2 units/sec
dt/dx = (dy/dx)/(dy/dt)
dx/dt = dy/dt/(dy/dx) = 2 unit/sec/(10·x)
When x = 1
dx/dt = 2/(10·x) = 2 unit/sec/(10 × 1) = 1/5 unit/sec
dx/dt = 1/5 unit/sec
Therefore, x is increasing one fifth unit/sec.
A scientist uses a submarine to study ocean life she begins at C level which is at an elevation of 0 feet then she travel straight down for 90 seconds at a speed of 3.5 ft./s then she then travels directly up for 30 seconds how do you speed of 2.2 ft./s after this 120 seconds period how much time in seconds will it take for the sciences to travel back to see if level at the submarines maximum speed of 4.8 ft./s
9514 1404 393
Answer:
10.625 seconds
Step-by-step explanation:
distance = speed · time
We want the total of all distances to be zero.
(-3.5)(90) +(2.2)(120) +(4.8)t = 0
-315 +264 +4.8t = 0 . . . . . simplify
-51 +4.8t = 0 . . . . . . . . . . . simplify more
-10.625 +t = 0 . . . . . . . . . .divide by 4.8
t = 10.625 . . . . . . . . . . . . . add 10.625
It will take the scientist 10.625 seconds to reach sea level.
Change the word sentence into a mathematical equation. Tell what each variable represents.
1. A music club membership costs $17.00 and $7.00 per CD.
2. The total cost of a carpet is $3.00 times the number of square feet.
3. The amount of money you earn for allowance is $20 times the number of months.
4. The cost of belonging to a fitness club is $200 to join and $30 a month in membership dues.
Answer:
1. $17 + $7C.
This equation provides the total cost if you want to purchase a music CD along with a music club membership. C represents the amount of CDs you wish to purchase, and since each CD costs $7, the amount of money you would need to purchase C amount of CDs is $7C.
2. $3A.
This equation provides the total cost of the area of carpet you want to purchase. A represents the area of the carpet that you want to purchase, measured in square feet as provided by the question, and since each square foot costs $3, the total cost is $3A.
3. $20M.
This equation provides the total money you earn for allowance after M months. M is the number of months that have passed, and since you earn $20 for allowance every month, the total allowance you have earned is $20M.
4. $200 + $30M.
This equation provides the total cost for joining and staying in a fitness club for M months. The initial cost, $200, is applied no matter how many months you join, so we add it from the start; since each month, M, you have to pay $30, the total amount of membership dues is $30M.
Step-by-step explanation:
Hope this helped!
Someone please help me!
Answer:
A. [tex] x \leq -16[/tex]
B. b > 11
C. [tex] c \leq -13 [/tex]
D. [tex] x \geq -9[/tex]
Step-by-step explanation:
Given the following algebraic expression;
A. [tex] \frac {3x}{4} \leq 12 [/tex]
We would simplify the equation by multiplying all through by 4;
[tex] 4 * \frac {-3x}{4} \leq 12 * 4[/tex]
[tex] -3x \leq 48[/tex]
Divide both sides by -3;
[tex] x \leq -16[/tex]
B. 5b - 28 > 27
Rearranging the equation, we have;
5b > 27 + 28
5b > 55
Divide both sides by 5
b > 11
C. [tex] 13c \leq -169[/tex]
Divide both sides by 13
[tex] c \leq -13 [/tex]
D. [tex] 3x - 7 \geq 4x + 2[/tex]
Collecting like terms, we have;
[tex] 3x - 4x \geq 2 + 7[/tex]
[tex] -x \geq 9[/tex]
Divide both sides by -1
[tex] x \geq -9[/tex]
what is 281.4/10*0?
No steps needed just answer
Answer:
0
Step-by-step explanation:
Answer:
0
Step-by-step explanation:
Solve for x. 4x^2 – 2x + 3 = 0
Answer:
[tex]x=\frac{1\pm i\sqrt{11}}{4}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Standard Form: ax² + bx + c = 0Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]Algebra II
Imaginary Roots: √-1 = iStep-by-step explanation:
Step 1: Define Equation
4x² - 2x + 3 = 0
Step 2: Identify Variables
a = 4
b = -2
c = 3
Step 3: Solve for x
Substitute [Quad Formula]: [tex]x=\frac{2\pm\sqrt{(-2)^2-4(4)(3)} }{2(4)}[/tex]Evaluate Exponents: [tex]x=\frac{2\pm\sqrt{4-4(4)(3)} }{2(4)}[/tex]Evaluate Multiplication: [tex]x=\frac{2\pm\sqrt{4-48} }{8}[/tex]Evaluate Subtraction: [tex]x=\frac{2\pm\sqrt{-44} }{8}[/tex]Factor Radical: [tex]x=\frac{2\pm\sqrt{-1} \sqrt{44} }{8}[/tex]Simplify Radicals: [tex]x=\frac{2\pm 2i\sqrt{11} }{8}[/tex]Factor Numerator GCF: [tex]x=\frac{2(1\pm i\sqrt{11}) }{8}[/tex]Simplify: [tex]x=\frac{1\pm i\sqrt{11}}{4}[/tex]Steven and Brittney are both starting lawn mowing businesses to save money to buy a dog. Steven charges $20 a yard and $6 an hour. Brittney charges $28 a yard and $5 an hour. How many hours will they need to work to have the same amount of money? If the cost of the dog is $300, who will be able to buy it first? Pick two correct statements only.
1. 8 hrs to have the same amount of money
2. 18 hrs to have the same amount of money
3. Brittney will be able to buy the dog first
4.Steven will buy will be able to buy the dog first
Answer:
https:brainly.com/question/20068899
evaluate
Evaluate-8÷2+12×9-4×6
Answer:
Step-by-step explanation:
Use PEDMAS {Parenthesis ; Exponent ; Division ; Multiplication ; Addition; Subtraction }
8÷2 + 12*9 - 4*6 = 4 + 12*9 - 4*6 {Division}
= 4 + 108 - 24 {Multiplication}
= 112 - 24 {Additon}
= 88
Answer: 88
Step-by-step explanation:
Evaluate using PEMDAS.
P = Parenthesis; There are no parenthesis in this expression
E = Exponents; There are no exponents in this expression
M = Multiplication; 12 x 9 = 108, 4 x 6 = 24
D = Division; 8/2 = 4
A = Addition; 4 + (12 x 9) = 112
S = Subtraction; (4 + (12 x 9)) - (4 x 6)
112 - 24 = 88
2) A big league pitching coach tries to limit his pitchers to 110
pitches per game. If the pitcher has already thrown 52
pitches, write and solve an inequality to find how many more
pitches he can throw before reaching the limit.
i have a c please help it will mean alot
[tex]\Large\boxed{\tt Answer: 5\frac{2}{3} }[/tex]
[tex]\tt Step-by-step~explanation:[/tex]
We can solve this by dividing both numbers by four.
[tex]\tt 8\div4=2\\12\div4=3\\\frac{2}{3}[/tex]
We then add that to 5 to get our answer.
Pls help i need to fnsh
Answer:
(1,0)
Step-by-step explanation:
Step-by-step explanation:
Are you here??..........
Help PLEASE ASAP, Algebra question, need steps
Answer: x=2
Step-by-step explanation: I download and I see your work and that my answer up there, hope this help
pls, help hurry! a⁴-9
and explain pls
Answer:
[tex] {a}^{4} - 9 \\ = {a}^{ {2}^{2} } - {3}^{2} \\ let \: {a}^{2} \: be \: y \\ = {y}^{2} - {3}^{2} \\ from \: difference \: of \: squares \\ = (y - 3)(y + 3) \\ substitute \: for \: y \\ = ( {a}^{2} - 3)( {a}^{2} + 3)[/tex]
Answer:
100 POINTS! (50 split up) PLSSSSSSSSSS HELP!!! I REALLY NEED IT SO MUCH :( I PROMICE2 g. Describe your results in terms of precision and accuracy. Explain your answer in a paragraph for the best grade.
Step-by-step explanation:
NEED HELP ASSP!! please help!!??
Answer:
Step-by-step explanation:
this is a 30 60 90 triangle.. b/c 2 of the angles are given and you know the total is 180 around a triangle so the last angle is 30
also you know the hypotenuse of this triangle is 10 so use cos and sin to figure out the other sides
Use SOH CAH TOA to remember how the sin and cos functions fit on the triangle
CAH = Cos(Ф) = Adj/ Hyp we are given the Ф angle and we know the hypotenuse so solve for the Adj side
Hyp*Cos(Ф)= Adj
10 * Cos(60) = Adj
5 = Adj = y
Use Sin for the other side and the mnemonic to remember how it fits on the triangle and solve for the Opposite , since we don't know that .. yet
Sin(Ф) = Opp/ Hyp
Hyp * Sin (Ф) = Opp
10 * Sin(60) = Opp
10 *[tex]\sqrt{3}[/tex]/2 = Opp
5*[tex]\sqrt{3}[/tex] = Opp = x
:) I know Sin(60) = [tex]\sqrt{3}[/tex]/2 from a table and also my memory .. know that one from memory
A square has a perimeter of 36 millimeters.
What is the area of the square?
Answer:
A=81
Step-by-step explanation:
Answer:
81
Step-by-step explanation:
36/4=9
9*9=81
what is the simplified form of 4x - 7 + x - 10
Answer:5x-17
Step-by-step explanation:
4x - 7 + x -10 = 0
4x + x - 7 - 10 = 0
5x - 17 = 0
5x = 17
x = 17/5
PLEEAAASE IIIIIIIIIII NNNNNNNNNEEEEEEEEEEEEDDDDDDDD HEEEEEEEEEEEEEEEELLLLLLLLLLLPPPPPPPPPPPP
Answer:
9
Step-by-step explanation:
In order for this problem to have more than one solution, one will have to make it such that the two sides are equal. Call the unknown quantity "x", and solve this equation like a literal equation;
5u + 3(4u - 6) = -3u - 27 + 20u + x
Simplify, (distribute and combine like terms);
5u + 12u - 18 = 17u - 27 + x
17u - 18 = 17u - 27 + x
Inverse operations;
17u - 18 = 17u - 27 + x
-17u - 17u
-18 = -27 + x
+27 + 27
9 = x
Answer: 9
Step-by-step explanation:
evaluate daw ito
9x2+25, for x = 1/3
Answer:
25
Step-by-step explanation:
9×(1/3)²+25=9×1/9+25=25
Eric rented a truck for one day the base fee was 16.95 for additional charge of .76 cents for each mile driven eric had to pay 152.23 when he returned the truck how many miles did he drive
Answer:
178 miles
Step-by-step explanation:
Let Eric has driven d miles.
As the rate of charge of driving the truck = 76 cents /mile
So, the charge of driving the truck for d miles = 76d cents= $0.76d
The base fee of the truck was $16.95.
Total money paid at the time of returning the truck = $152.23
So, 16.95+0.76d=152.23
0.76d= 152.23-16.95=135.28
d=135.28/0.76
d=178
Hence, he drives 178 miles.
Answer and ill mark u as brainlist with an explaination
Answer:
d
Step-by-step explanation:
PLEASE ANSWER FAST
On 1 September, Leila starts to go swimming every day.
She swims 30 lengths of the swimming pool every day. The swimming pool is 20m long.
Work out the date when Leila has swum a total of 10 km.
Answer:
22 November
Step-by-step explanation:
First we have to find the total length she swims in 1 day
= 2(length of the swimming pool) x no. of lengths she swims in 1 day
=2x30x20
=120m she covers in 1 day
10km = 10,000m
no of days= total distance/ distance she covers in 1 day
=10000/120
=83.3 days
A farmer is selling apples from his orchard. He uses the equation c = 1.6pto calculate the total cost, c, for every pound of apples, p.
a.) How much does a customer pay for 1 pound of apples?
b.) How much would 8.5 pounds of apples cost?
c.) A customer spent $5.20. How many pounds of apples did they purchase?
Answer:
A) $1.60
B) $13.60
C) 3 1/4 lb
Step-by-step explanation:
What we know:
A farmer uses the equation c = 1.6p to calculate the total cost, c, for p pounds of apples.
A) 1 pound would cost $1.60, as that is the unit rate.
B) 8.5 * 1.6
8.5 + (0.6 * 8.5)
8.5 + 5.1 = $13.60 for 8 1/2 lbs of apples.
C) 5.2/1.6
52/16
13/4 = 3 1/4 lbs of apple for $5.20
A. Explain why ABC and ADBE
are similar
B. What is the height of the building?
Step-by-step explanation:
This figure is not the best, but I'll try my best here
Since BC is parallel to BE (BC is part of BE) and BA is part of BD, two sides are parallel, making two angles congruent and the triangles therefore similar.
Since BA correlates to BD (they are parallel), we can use the knowledge that BA is 7 and BD is 42 to find the scaling factor to be 42/7 =6 from ABC to DBE. Since BC correlates to BE, BC = 10, and the scaling factor is 6, BC*6=BE= 60 = height
Look at the photo pick A B C D either one explanation not needed thank you! <3
Answer:
A?
Step-by-step explanation:
I will mark brainliest for the best and first answer .......:
Answer:
its the first one
Step-by-step explanation:
Another name for 3/3 is
OA) 0
OB) 3
OC) 1