The length of a rectangle is 6 inches longer than its width. What are the possible widths if the area of the rectangle is at least 667 square inches?
Answers
Answer:
D, [tex]w\geq 23[/tex]
Step-by-step explanation:
The length is 6 inches longer than it's width, therefore:
[tex]l=w+6[/tex]
The area of the rectangle is AT LEAST 667 square inches, so:
[tex]lw\geq 667[/tex]
Now, we have a system of two equations:
[tex]\left \{ {{l=w+6} \atop {lw\geq 667}} \right.[/tex]
We want to isolate the width, so substitute the first equation into the second to eliminate the length.
[tex](w+6)w\geq 667[/tex]
Simplify:
[tex]w^2+6w\geq 667[/tex]
Since we now have a polynomial equation that needs to be factored, set the value of one side to 0.
[tex]w^2+6w-667\geq 0[/tex]
Now factor the equation:
[tex](w-23)(w+29)\geq 0[/tex]
Taking each factor individually, we find the following:
[tex]w\geq 23\\w\geq -29[/tex]
Since a negative width doesn't make any sense, we can eliminate that solution, and we are left with the correct answer!
[tex]w\geq 23[/tex]
Related Questions
PLEASE SHOW WORK
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Answers
it has two parallel and same sides
therefore multiply each side by 2 and add them
2(17.4x-0.8)+2(6x)
34.8x-1.6+12x
46.8x-1.6 is the perimeter
Answer:
Perimeter = 2(length) + 2(width)
Perimeter = 2(17.4x - 0.8) + 2(6X)
Perimeter = 34.8x - 1.6 + 12x
Perimeter = 46.8x - 1.6
The rhombus shown below has been dissected into smaller rhombuses and
equilateral triangles whose side lengths are all unequal positive integers.
Find the smallest possible perimeter of the rhombus.
Answers
Answer:
Hello,
Answer 176
Step-by-step explanation:
Very hard as problem.
1. we suppose 2 variables a and b.
we find that b=5a/6
2. One more variable c
we find c=13a/24
3. a must be a multiple of 24 and perimeter is 44*a/6 = 176a/24
can u explain why please, i need a explanation.
Answers
Explanation: a^2 + b^2 = c^2
a^2 + 18^2 = 82^2
a^2 = 6400
a = 80
how do i multiply fractions?
Answers
Answer:
The first step when multiplying fractions is to multiply the two numerator. The second step is to multiply the two denominators. finally, simplify the new fractions. The fractions can also be simplified before multiply by factoring out common factors in the numerator and denominator.
example equation: 3/4 x 2/5
1) line equation
3 2
_x_
4 5
2) nominators x nominators, denominators x denominators
3 2 6
_x_=_
4 5 20
4) simplify
6/20=3/10
good luck !!
help me please i do not understand this assignment
Answers
Answer: 164.53%
Step-by-step explanation:
105.3/64=1.6453125
1.6453125*100=164.53125
164.53125=164.53%
Notice the answer is greater than 100 percent. This is because 105.3 is greater than 64, meaning that 105.3 is greater than 100% of 64, so 105.3 will have a greater percent value.
Can someone please help me with this problem? 6 = |x| - 2
Answers
Answer:x=8
Step-by-step explanation:because you have to get the x by itself so add 2 to both sides so that's 8=x and its already x you dont have to divide so the answer is 8=x
hope this helps :}
Step-by-step explanation:
If it is absolutle vaules than there will be two solutions
First you want to get the absolute vaule of x by its self
After that you want to set up a postive and negative equation
[tex]8 = |x| [/tex]
[tex] - 8 = |x|[/tex]
Theres your two solutions.
Select the correct answer. Triangle is reflected across the y-axis and then dilated by a factor of centered at the origin. Which statement correctly describes the resulting image, triangle ? Image of right triangle ABC in a graph with vertices A (minus 4, minus 2), B (4, minus 2), and C (4, 4) A. Both the reflection and dilation preserve the side lengths and angles of triangle . B. Neither the reflection nor the dilation preserves the side lengths and angles of triangle . C. The dilation preserves the side lengths and angles of triangle . The reflection does not preserve side lengths and angles. D. The reflection preserves the side lengths and angles of triangle . The dilation preserves angles but not side lengths.
Answers
Answer: B (4 minus 2)
Write the equation in standard form given the following information (with solutions please)
1. The roots are 1/2 and -1/2
Answers
The Quadratic equation in standard form given the following roots are
f(x) = 2x^2 - 3x + 1
The root 1 is associated with the factor (x - 1).
The root 1/2 is associated with the factor (x - 1/2), which in turn is equivalent to (2x -1)
The quadratic in question is f(x) = (x - 1)(2x - 1). To write this in standard form, perform the indicated multiplication:
f(x) = 2x^2 - 2x - x + 1, or f(x) = 2x^2 - 3x + 1
What is Quadratic equation?Any equation in algebra that can be written in standard form as where x is an unknown and a, b, and c denote known numbers, where a 0 is a quadratic equation.
An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as a[tex]x^{2}[/tex] + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.
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the cost of a can of coca-cola in 1960 was $ 0.10 . the function that models the cost of a coca-cola by year is c ( t )
Answers
The cost of the Coca-Cola can will be $1 in the year 2000.
Given that the cost of a can of Coca-Cola can in 1960 = $0.10
The function which models the cost of a Coca-Cola by year 't' is
c(t) = [tex]0.10e^{0.0576t}[/tex].
Here, 't' denotes the number of years since 1960.
c(t) is an exponential function.
We have to find the year in which the cost of a can will be $1.
So substitute c(t) = 1, we get,
1 = [tex]0.10e^{0.0576t}[/tex]
⇒ [tex]10 = e^{0.0576t}[/tex]
We have, [tex]ln(e^x) = x[/tex] .
Taking logarithm on both sides, we get,
log(10) = 0.0576t
⇒ [tex]t=\frac{ln(10)}{0.0576}[/tex] = 39.97 ≈ 40 years .
Thus the cost of a can of Coca-Cola will be $1 in the year, 1960 + 40 = 2000.
The question was incomplete. Find the complete question at:
The cost of a can of Coca-Cola in 1960 , was $0.10. The function that models the cost of a Coca-Cola by year is C(t)=0.10e^(0.0576t) , where t is the number of years since 1960 . In what year is it expected that a can of Coca-Cola will cost $1.00 ?
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what meets a segment at its midpoint at a 90 degree angle?
Answers
Answer:
The right angle's vertex.
Step-by-step explanation:
A right angle is 90 degrees. The vertex is at the middle of the angle, so that point is used to draw a segment in the middle of the right angle.
what type of measurement scale is used for operating system? nominal scale ordinal scale interval scale ratio scale
Answers
We can actually deduce here that the type of measurement scale that is used for operating system is: Nominal scale.
What is nominal scale?A nominal scale is actually known to be a measurement scale whereby numbers are used as “tags” or “labels” only in order to identify, locate or classify an object.
This measurement scale actually deals only with non-numeric variables. It can be used where numbers have no value.
Other measurement scales include:
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Given the function g(x) = x² − 3, find the value of g (−2).
Answers
Explanation:
g(-2)= -(2*2) - 3
g(-2)= -4 -3
At the beginning of the day, the stock market goes down 70 1/2 points and stays at this level for most of the day. At the end of the day the stock market goes up 80 3/4 points from the low at the beginning of the day. What is the total change in the stock market from the beginning of the day to the end of the day?
Answers
The change for the day is 10 1/4
In this problem, we are expected to calculate the change in the price of a particular stock
Given that the days high is 80 3/4
and also that the days low is 70 1/2
we can calculate the change by subtracting the days low from the days high
i.e 80 3/4- 70 1/2= 323/4-141/2= (323-282)/4= 41/4
hence the change for the day is 41/4 =10 1/4
Also we can calculate the percentage change as
%change = (high-low)/low*100
%change= 80 3/4- 70 1/2/70 1/2*100= 41/4/70 1/2 *100
%change= 41/4*2/141*100
%change= 0.00145=0.145%
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arc xylocated on circle ahas a length of 40 centimeters. the radius of the circle is 10 centimeters. what is the measure of the corresponding central angle for xy⌢in radians?
Answers
We know that an arc is a part of the entire perimeter of a circle.
Radian is defined as a unit of plane angular measurement that is equal to the angle subtended by the circle at the center by an arc that is of the length equal to the radius
We also know that the circle as a whole contains 2π radians
Now first we are required to find the perimeter of the circle
Perimeter of the circle is given by the formula 2πr
Hence, perimeter of the circle = 2πr= 2π x 10 =20π=62.851cm
Hence value of arc in radians = 40/62.851 x 2π =0.636 x 2 π =1.272π
Radian can be converted to degree by multiplying the radian measure by 180/π
Therefore, angle subtended by arc in degrees =1.272 π x 180 /π =229.1 °
Hence the angle subtended by arc is 229.1°
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Which of the following is the solution to 3 | x-1 | > 12?
A. x≤-3 or x >5
B. x > -3 or x > 5
C. x < -3 and x > 5
D. X > 5
Answers
Answer:
7
Step-by-step explanation:
8-9-6
What are the sides of ∠JBA ?
Answers
The sides of angle JBA is ray BJ and BA.
What is an angle ?In the geometry, angle is defined as the geometry formed by the multiple rays. Or we can say that the angle is the figure formed by two rays which has same initial point. These rays are also known as the sides of an angle. A angle can have two rays.
Some common terms related to angle :
Endpoint : It is the point where the rays met to each other.
Ray : Ray is the side or line segment on which angle is formed.
Curve : It is a line but not straight i.e. a bended line.
Tangent : A line which touches the surface of curve.
In the given question, as ∠JBA is made between two lines or rays i.e. ray BJ and ray BA . Therefore sides of this angle are BJ and BA.
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At most, Alana can spend $40 on carnival tickets. Ride tickets cost $4 each, and food tickets cost $2 each. Alana buys at least 16 tickets. The system of inequalities represents the number of ride tickets, r, and the number of food tickets, f, she buys.
r + f ≥ 16
4r + 2f ≤ 40
A graph shows r on the x-axis, from 0 to 18, and f on the y-axis, from 0 to 20. Two solid lines are shown. The first line has a negative slope and goes through (0, 20) and (10, 0). Everything to the left of the line is shaded. The second line has a negative slope and goes through (0, 16) and (16, 0). Everything above the line is shaded.
What is the maximum number of ride tickets she can buy?
4
6
10
12
Answers
The maximum number of ride tickets that she can buy is A. 4.
How to illustrate the information?It should be noted that the system of inequalities represents the number of ride tickets, r, and the number of food tickets, f, she buys.
r + f ≥ 16
4r + 2f ≤ 40
The two inequalities are first shown on the graph as seen in the attachment. The graph demonstrates where the two in-equations intersect (4,12).
Consequently, we can observe that r has a maximum value of 4. This was illustrated in the graph.
In conclusion, the correct option is A.
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if the least common multiple of $a$ and $b$ is $1575$, and the ratio of $a$ to $b$ is $3:7$, then what is their greatest common divisor?
Answers
The greatest common divisor of two given numbers is 15.
Given that, the least common multiple of A and B is 1575 and A: B=3: 7.
We need to find what is their greatest common divisor.
What is the least common multiple?The least common multiple is also known as LCM (or) the lowest common multiple in math. The least common multiple of two or more numbers is the smallest number among all common multiples of the given numbers.
We know that the product of the GCF and the LCM of two numbers is always the product of the two numbers.
Let the GCF of two numbers be x.
Then A×B=1575×x
Take A:B=3k:7k
Now, 3k×7k=1575×x
⇒21k²=1575x
⇒k²=75x
x must be expressed as a square divided by 75.
Now, 75=3×5×5
If we multiply 3 to the above product we get the perfect square number.
So, k²=225
⇒k=15
Now, 3k=45 and 7k=105
45=3×3×5 and 105=3×5×7
So, GCD=3×5=15
Therefore, the greatest common divisor of two given numbers is 15.
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Your question is incomplete, probably the complete question/missing part is:
If the least common multiple of A and B is 1575, and the ratio A of B to 3 is 7 , then what is their greatest common divisor?
Answer: 75
Step-by-step explanation:
Since the ratio of A to B is 3:7:
There is an integer k for which A=3k and B=7k.
Moveover, k is the greatest common divisor of A and B, since 3 and 7 are relatively prime.
Recalling the identity lcm(A,B)*gcd(A,B)=AB, we find that 1575k=(3k)(7k), which implies k=1575/21=75.
The surface area of a cube is 96 cm².
Work out the volume of the cube in cubic centimetres.
Answers
The volume of cube in cm is (4cm)
Volume of cube is =96 CM^2
Let's consider he as the edge of cube
Surface area of is =6
That is symbol cube as (e^2)
As per the given question the surface are of cube is given as 96 cm^2
As we know
96=6^2
e^2=96/6
e^=16
e=√16
e=4cm
The volume of cube in centimetre is 4cm
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write as a power of a prime
a) 64
b) 169
c) 625
Answers
Answer:
64:2⁶
169:13²
625:5⁴..................
2. If freezing rain is falling, then the air temperature is 32°F or less.
Converse:
Inverse:
Contrapositive:
Answers
Answer:
Converse: If the air temperature is 32°F or less, then freezing rain is falling.
Inverse: If freezing rain is not falling, then the air temperature is not 32°F or less.
Contrapositive: If the air temperature is not 32°F or less, then freezing rain is not falling.
Explanation:
Statement: If p, then q.
Converse: If q, then p.
Inverse: If not p, then not q.
Contrapositive: If not q, then not p.
money marilyn is going on a class outing to an amusement park. she has $40 to spend. the admission price is $20. she plans to buy a sandwich for $5. a cup of lemonade costs $3.00. write an inequality to show how many cups of lemonade, c, she can buy.
Answers
Money Marilyn can buy 1≤ x≤5 (more than or equal to one and less than or equal to five) cups of lemonade from the rest of the money.
Here we have,
Total money to spend= $40
Admission price= $20
Sandwich= $5
Add all expenses to find the money spent by Money Marilyn.
Total expense= admission price + sandwich
Total expense = $20 + $5 = $25
Amount left with her= $40-$25 = $15
The number of cups when each cup's cost is $3
Total lemonade(x) = $15/$3 = $5
In an equality,
Money Marilyn can buy 1≤ x≤5 (more than or equal to one and less than or equal to five) lemonades from the rest of the money.
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What is 1,837 + 1,283?
Answers
Answer:
3,120
Step-by-step explanation:
Does this need an explanation?
Answer:
1,837+1,283= 3,120
Step-by-step explanation:
Hope It Helps
Sorry If I'm Wrong
assuming that the value of x is 4, and the value of y is 6, what is the value of the following expression? (x - y)**2 > y
Answers
The result of the expression "(x - y)**2 > y" is -4>6 and it is false.
Information about the problem:
(x - y)**2 > yx = 4y = 6To solve this problem, we have to substitute the values of (x) and (y) and solve the equation:
(x - y)**2 > y
(4 - 6)**2 > 6
-2 ** 2 > 6
-4 > 6
The expression is false because - 4 is not higher than 6. The correct expression is:
(x - y)**2 < y
-4 < 6
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
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Which number is Irrational?
a
square root 9
b
0.123123123....
c
5/9
d
0.2535455565....
Answers
Answer:
Step-by-step explanation:
d. Square root of 9
you’re welcome :)
The irrational number is 0.2535455565.....
The correct option is D.
Given, that identify the irrational number.
Irrational number : Irrational numbers are non terminating and non repeating.
1) Square root of 9: √9
= 3
It is rational number.
2) Number : 0.123123123....
It is Non terminating but repeating thus it is not an irrational number.
3) Fraction : 5/9
5/9 = 0.555555..
It is a repeating number thus its is not an irrational number.
4) Number: 0.2535455565....
The number is non terminating as well as non repeating. Thus it is an irrational number.
Therefore option D is correct.
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jackie has a checking account. For each day that her checking account balance falls below zero, she is charged by the bank a fee of $7.50 per day. Her current balance in the account is –$12.50. If she does not make any deposits or withdrawals, what will be the new balance in her account after 2 days? Show your work.
Answers
The new balance will be -27.50.
How to illustrate the expression?It should be noted that for each day that her checking account balance falls below zero, she is charged by the bank a fee of $7.50 per day.
Since her current balance in the account is –$12.50, the new balance after 2 days will be:
= -12.50 + (-7.50 × 2)
= -12.50 + -15
= -27.50
The balance is -27.50
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I need help asap!!!!!
Answers
Answer:
last one
Step-by-step explanation:
6 3x2/8x2= 6 6/16
6 +5=11
6/16+11/16=17/16
11 17/16
What is the image of the point (-1, -4) after a rotation of 90° counterclockwise
about the origin?
Answers
Answer:
(4, -1)
Step-by-step explanation:
See attached image.
on her desk.
Susan has a box for paperclips
The box is 6 centimeters long, 3 centimeters
wide, and 2 centimeters high. What is the
volume of the box?
Answers
Answer:
36 cm³
Step-by-step explanation:
6x3x2 = (36 cm³)
Length x Width x Height
pls help will give brainliest !!!!!!!!!
Answers
have a good day