For the given rectangular playpen, the perimeter of rectangular playpen is 150 feet and its area is at least 1000 square feet. then the length of the rectangular playpen is equal to at least 17.35 feet and at most 57.66 feet.
As given in the question,
For the given rectangular playpen,
Perimeter of rectangular playpen is equal to 150 feet .
Area of the rectangular playpen is equal to at least 1,000 squared feet .
Area = length × width
Let x be the length of the rectangular playpen .
Then its width is equal to 1000 / x.
Substitute the value of length and width in perimeter we get,
Perimeter of rectangular playpen = 2 ( length + width )
⇒ 150 = 2 [ x + (1,000/x)]
⇒ 150 / 2 = ( x² + 1,000 ) / x
⇒ x² + 1000 = 75x
⇒ x² -75x + 1,000 =0
Simplify quadratic equation using discriminant we get,
x = [ -( -75) ± √(-75)² - 4(1) (1,000) ] / 2(1)
⇒ x = ( 75 ± √5625 - 4000) /2
⇒ x = (75 ± 40.31) / 2
⇒ x = 57.66 or 17.35
Therefore, for the given rectangular playpen, the perimeter of rectangular playpen is 150 feet and its area is at least 1000 square feet. then the length of the rectangular playpen is equal to at least 17.35 feet and at most 57.66 feet.
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Can someone help me with this
What is the product?
(-2x -9y^2) (-4x - 3)
A.-8^2 -6x -36xy^2 -27y^2
B.-14x^2 -36xy^2 +27y^2
C.8x^2+6x36xy^2 +27y^2
D.14x^2 + 36xy^2 + 27y^2
Answer:
C
Step-by-step explanation:
(-2x -9y^2) (-4x - 3)
= 8x^2+6x + 36y^2x+27y^2
Use the table to answer questions 9&10
Find constant k=
If you earned $17,500 how many monthes did you work for
The constant, k is $2500 and 7 months of work will be needed to earn $17,500.
According to the question,
We have the following information:
We have a table where months and the salary in dollars is given.
Now, the salary is increasing constantly with number of months.
So, we have the following expression:
9) Amount of dollars is directly proportional to number of months.
Dollars = k*months
2500 = k*1
k = 2500
10) Now, the amount given is $17,500.
So, we have:
k*months = 17,500
Months = 17500/2500
Months = 7
Hence, the constant, k is $2500 and 7 months of work will be needed to earn $17,500.
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Factor the perfect-square trinomial in y = (x2 2x 1) − 1− 1. y = (x )2 − 1 −1
Answer:x
2
−
2
x
+
1
=
x
2
−
2
x
+
1
2
=
(
x
−
1
)
2
A perfect square trinomial is the square of a binomial, so will take the form:
a
2
+
2
a
b
+
b
2
since
(
a
+
b
)
2
=
a
2
+
2
a
b
+
b
2
So a perfect square trinomial satisfies the following conditions:
(1) Two of the terms are squares.
(2) The other term is twice the product of the square roots (positive or negative) of the other two terms.
If the two square terms are
a
2
and
b
2
then the trinomial is either
(
a
+
b
)
2
or
(
a
−
b
)
2
depending on the sign of the third term.
For f(x) = −7x − 13, find f(x) when x = −1.
Answer:
-6
Step-by-step explanation:
-7 x -1 = 7
7 - 13 = -6
A group of friend wnat to go to the amuement park. They have no more than $110 to pend on parking and admiion. Parking i $8 and ticket cot $23 per peron including tax
Inequality: 23x + $8 ≤ $110
Inequality:
$110 = Amount of money they have
$8 = Parking Cost
$23 = Cost of tickets per person
23x + $8 ≤ $110
23x=$110-8
23x=$102
In mathematics, a courting among expressions or values that aren't the same as every other is referred to as 'inequality. This term is used to examine the significance, wide variety, and intensity of two values or expressions. Equations and inequalities are both mathematical sentences fashioned by using referring to two expressions for every difference. In an equation, the two expressions are deemed equal's shown with the aid of the symbol =.
whereas in inequality, the two expressions aren't necessarily the same that's indicated by means of the symbols: >, <, ≤ or ≥. Inequality is critical to poverty due to the fact the relative role of people or families in society is taken into consideration as a crucial aspect of their welfare.
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[tex]12=\frac{c-6}{2}[/tex]
Answer: c = 30
Step-by-step explanation:
[tex]12=\frac{c-6}{2}\\ \\12(2)=c-6\\\\24=c-6\\\\c=24+6=30[/tex]
please help me I will give you brainiest, please
x + 9 = 13
3x = 12
x + 5 − 9 = 0
2x + 5 = 17
5x − 3 = 17
x − 3 = 1
7x = 35
[tex]\frac{4x}{4} =4[/tex]
3( x + 4) = 15
8 + x − 5 = 7
The values of the variables x in the equations are;
x = 4x = 4x = 4x = 6x = 4x = 4x = 5x = 4x = 1What is an equation?An equation is a mathematical statement that connects two mathematical expression with an equals sign.
x + 9 = 13
Subtracting 9 from both sides of the equation, we get;
x = 13 - 9 = 4
x = 43•x = 12
Dividing both sides of the equation by 3, we get;
x = 12 ÷ 3
x = 4x + 5 - 9 = 0
Subtracting (5 - 9) from both sides of the equation, we get;
x = 9 - 5 = 4
x = 42•x + 5 = 17
Subtracting 5 from both sides of the equation, we get;
2•x = 17 - 5 = 12
2•x = 12
Dividing both sides of the equation by 2, we get;
x = 12 ÷ 2 = 6
x = 65•x - 3 = 17
Adding 3 to both sides of the equation, we get;
5•x = 17 + 3 = 20
5•x = 20
Dividing both sides of the equation by 5, we get;
x = 20 ÷ 5 = 4
x = 4x - 3 = 1
Adding 3 to both sides of the equation, we get;
x = 1 + 3
x = 47•x = 35
Dividing both sides of the equation by 7, we get;
x = 35 ÷ 7 = 5
x = 5[tex]\frac{4\cdot x}{4} = 4 [/tex]
Multiplying both sides of the equation by 4 and dividing the result by 4, we get;
x = 4 × 4 ÷ 4 = 4
x = 43•(x + 4) = 15
Dividing both sides of the equation by 3, we get;
x + 4 = 15 ÷ 3 = 5
x + 4 = 5
Subtracting 4 from both sides of the equation, we get;
x = 5 - 4 = 1
x = 18 + x - 5 = 7
Adding 5 and subtracting 8 from both sides of the equation, we get;
x = 7 + 5 - 8 = 4
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The force of attraction, F of a body varies directly as its mass (m) and inversely as the square of the distance (d) from the body. When m=8kg and d=5meters, F=100 Newtons. Find F when m=2 kilograms and d=15 meters.
Answer:
Step-by-step explanation:
EQUATION: F = km / d²100 = k(8) / (5)²100 = k 8 / 25100 ÷ 8 / 25 = k 8 / 25 ÷ 8 / 25625 / 2 = kF = (625 / 2)(2) / (15)²F = 625 / 225F = 25 / 9
the student council sold $661$ t-shirts, some at $\$10$ and some at $\$12$. when recording the number of t-shirts they had sold at each of the two prices, they reversed the amounts. they thought they made $\$378$ more than they really did. how many t-shirts actually were sold at $\$10$ per shirt?
The student council sold $273$ t-shirts were sold at $\$10$ per shirt.
Let $x$ be the number of shirts sold at $\$10$
Let $y$ be the number of shirts sold at $\$12$
$x+y=661$
$10x+12y=3780$
$x=y+101$
$10y+12y=3780$
$22y=3780$
$y=172$
$x=172+101$
$x=273$
Hence $273$ t-shirts were sold at $\$10$ per shirt.
If they sold $661$ t-shirts in total, and they made a mistake when recording the amount of t-shirts sold at each price, then they actually sold more t-shirts at $\$10$ than they thought. This means that they thought they sold fewer t-shirts at $\$10$ than they actually did.
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(3.45 x 10^3)+ (6.11 x10^3
a.9.56 x 10^3
b.9.56 x 10^6
c.95.6 x 10^3
d.95.6 x 10^6
Answer:
a. 9.56 × 10^3
Step-by-step explanation:
You want the sum (3.45 × 10^3)+ (6.11 ×10^3).
Distributive property
The distributive property works when adding numbers in scientific notation:
(3.45 × 10^3)+ (6.11 × 10^3) = (3.45 +6.11) × 10^3 = 9.56 × 10^3
What is -5/2 times -41
The solution of the mathematical statement is 102.5
How to evaluate the expression?From the question, we have the following mathematical statement that can be used in our computation:
"What is -5/2 times -41"
This means that
-5/2 times -41
Express as numbers
So, we have
-5/2 * -41
Divide 5 by 2
So, we have
-2.5 * -41
Evaluate the product
102.5
Hence, the result is 102.5
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During hibernation, a bear's heart rate decreases to 62% of its usual rate. Alex says that means if a bear's heart rate during hibernation is 19 beats per minute, its usual heart rate is 31 beats per minute. Is Alex correct? Explain your reasoning.
Answer:
Yes, he is correct
Step-by-step explanation:
100% : x
62% : 19
Cross multiply
19*100% = 62%x
19 = 0.62x
19/0.62 = x
x = 30.645
Rounds up to 31
Find the circumference and area of the figure if each unit on the graph measures 1 centimeter. Round answers to the nearest tenth, If
necessary
g\one cannot tell whether a data set is close to symmetric or not by looking at a histogram. true false
False, one can tell if a data set is close to symmetric or not by watching a histogram.
The histogram exhibit a symmetrical distribution of given data. The data is symmetrical if we are able to draw a vertical line at some point in the histogram such that its shape on both sides of the left and the right of the vertical line exactly reflected images to each other. The mean, the median, and the mode are can be taken as examples to prove the symmetricity using histogram for these data.
In an altogether symmetrical distribution, the mean and the median are alike. Such as the mode has one mode (unimodal), and the mode is the alike as the mean and median.
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help! what does this mean?
n/16 lies between 4/16 and 8/16
So, n can be 5,6,7
Answer:
5, 6 , 7
Step-by-step explanation:
Change 1/4 and 1/2 to the values they would be if their denominator was 16
1/4 will become 4/16
1/2 will become 8/16
the values between these are 5/16, 6/16, 7/16
n can be 5, 6 or 7
how to read 8990 in decimal?
ONe tens decimal tenths Hundredths Thousandths Ten thousandths
Answer:
The answer has to be 8.999
A rectangular piece of wood measures 2.4 m by 60 cm by 80cm and has a mass of 32.5kg.
What is the density of the piece of wood?
( nearest 3 decimal places)
Answer:
0.282kg/m3
Step-by-step explanation:
density=mass/volume
mass=32.5kg
volume=lxbxh
volume=2.4mx60cmx80cm
convert 60cm and 80cm to m:
60cm=6m
80cm=8m
volume= 2.4mx6mx8m
volume=115.2m3
density=32.5/115.2m3
density=0.28211kg/m3
round to nearest three decimal places:
= 0.282kg/m3
Can slmeone please explain this and give me the answer ill be very grateful.
Answer:
D
Step-by-step explanation:
Since Δ QTS is isosceles then the base angles are congruent , that is
∠ TQS = ∠ QST = y
∠ QST and ∠ RST are a linear pair and sum to 180° , that is
∠ QST + ∠ RST = 180
y + ∠ RST = 180 ( subtract y from both sides )
∠ RST = 180 - y
the sum of the 3 angles in Δ TRS = 180° , that is
∠ RTS + ∠ TRS + ∠ RST = 180
∠ RTS + x + 180 - y = 180 ( subtract 180 from both sides )
∠ RTS + x - y = 0 ( subtract x - y from both sides )
∠ RTS = y - x
Erin solved 3 word problems in 10 minutes.
If she were to solve the remaining 8 word problems at the same rate, how long would it take to the nearest minute?
O Carys gets to Norwich station at 0750. How long will she have to wait for a train directly to Colchester? minutes
O Carys gets to Norwich station at 0750. To know how long will she have to wait for a train directly to Colchester.
Lets assume the values to be
a = 0848
b = 1 hour 2 minutes
c = 5 minutes
And let us look into it in detail as below
a = The first train arrive in London is 0848
b = Norwich to Colchester gets the trains in 1 hour 2 minutes
c = Carys gets to Norwich at 0750
So she need to wait for 5 minutes in a a train to get directly to Colchester.
Hence the answer is 5 minutes.
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What is the series sum calculator?
Answer:
Series calculator is a free online tool that gives the summation value of the given function for the given limits.
please make my answer as brainelist
Two sides of a parallelogram are 38 feet and 88 feet. The measure of the angle
between these sides is 132º. Find the area of the parallelogram to the nearest square
foot.
Answer:
Area under the curve f (x) = 38 on interval [88, 132]: 38 132 -3344 (Decimal: 1672)
Step-by-step explanation:
problem 1 use polar coordinates for finding dxda, where d is the region in the first quadrant that lies between the circles x2 y2
The first quadrant that lies between the circle x² + y² =4 is 1.09587
The graph of x² +y² = 4 is a circle of radius 2, centered at (0, 0). In polar coordinates, this equation becomes simply r = 0.
The second equation requires a bit more work. To convert it to a polar equation, we
substitute, r cos θ for x and r sin θ for y:
r²cos ²θ + r²sin ²θ
= 2r cos Ф
⇒r² = 2r cos θ
⇒r = 2 cos θ
This is the polar equation for a circle of radius 1, centered at the point (x, y) = (1, 0). (This can be seen directly from the original equation by completing the square, which results in the equation (x − 1)²+ y² = 1.)
To describe the region between the circles in polar coordinates, we can let θ range from 0 to π/2. Our values for r should range from the smaller circle to the larger one
Recalling again that x = r cos θ and dA = rdrdθ, our integral becomes
∫ ∫ₐ x DA = 8/3 - π/2
We can get a rough check of this answer as follows. The area of the region D is easily computed to be π/2. The average value of the function x in the region is somewhat less than 1, since D is thicker on the left. Doing these sorts of visual estimates can be very tricky, but let’s say the average value of x in D is about 0.70. Thus
∫∫ₐ x dA ∼=π/2· 0.70 ∼= 1.09956
Since 8/3 − π/ 2∼= 1.09587, this estimate agrees quite well with our answer.
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The volume of a cylinder is 300 cm³. What would be the volume of a cone which has the
same radius and depth?
The volume of a cone having the same radius and same height as that of the cylinder is equal to 100 cm³.
Given that:
The volume of a cylinder is 300 cm³.
We assume that,
The radius of the cylinder = radius of the cone = r cm.
Height of cylinder = height of cone = h cm.
We have to find the volume of a cone having the same radius and same height as that of the cylinder.
The formula for the volume of a cylinder is = π x radius² x height
The formula for the volume of a cylinder is = πr²h cm³ = 300 cm³ ..... (1)
We know that,
The formula for the volume of cone = (1/3) x π x (radius)² x h
Volume of cone = (1/3) x π x (radius)² x h
Volume of cone = (1/3) x (πr²h)
Putting the value of πr²h from equation (1).
Volume of cone = (1/3) * 300
Hence, the volume of the cone is equal to 100 cm³.
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Find the smaller angles between the hour hand and the minute hand of a clock at half past 8
The angle of half past eight between the hour and minute hands of a clock is 255°.
Given that,
We have to find look for the smaller angles half past eight between the hour and minute hands of a clock.
We know that,
The clock is in circle.
A clock has 12 different parts. Between any two divisions, there is a 30° angle. Each division is then divided into 5 equal pieces, each of which is divided by an angle of 60° and equals 1 minute.
We know the total angle of the circle is 360°.
So, 12 hours is 360°.
Then 1 hours is
1 hour= 360/12=30°
So, 1 hour is 30°
60mins=1 hour
60 mins = 30°
1 min =30/60
1 min=1/2
So,
8 hour and 30 min
(8× 1 hour)+( 30×1 min)
(8×30)+(30×1/2)
240+15
255°
Therefore, The angle of half past eight between the hour and minute hands of a clock is 255°.
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Aidan buys used bicycles, fixes them up, and sells them. His average cost to buy and fix each bicycle is $47. He also incurred a one-time cost of
$840 to purchase tools and a small shed to use as his workshop. He sells bikes for $75 each. Use this information for the exercises.
WRITE Write revenue and cost functions R(x) and C(x) for Aidan's situation, where x is the number of bicycles. How do you include the one-time
cost in C(x)?
WRITE Write a profit function P(x) such that P(x) = R(x)-C(x). In words, what does P(x) represent?
PERSEVERE List key features for the profit function P(x). Then use the key features to sketch a graph, on a separate sheet of paper, that shows
the profit P(x) as a function of x bicycles.
ANALYZE Which key feature of the graph represents Aidan's break-even point (profit = 0)? Explain how to use your graph to find the most
accurate value for this feature.
Answer:
P(x) = $31x - $840
Step-by-step explanation:
Let x be the number of bicycles. The total cost for purchasing and repairing the bikes is $47x, plus a one-time purchase of $840 for a workshop and tools. Total cost, C is therefore:
C(x) = $47x + $840
We learn Aidan sells the bikes for $75 each. Total revenue, R, is:
R(x) = $75x
Profit, P, would be the difference of revenue, R, and costs, C:
P(x) = R(x) - C(x) or $75x -($47x + $840)
P(x) = $75x -$47x - $840
P(x) = $31x - $840
P(x) represents the total profit for x bicycles.
See the attached graph. Note the key features of the graph are the breakeven (27 bikes) and the initial investment (-$840). We can find the breakeven point by looking for the value of x when the profits are $0. A more accurate determination can be found by solving the equation we developed for the case in which P(x) = $0:
P(x) = $31x - $840
0 = $31x - $840 for P(x) = 0 (breakeven)
$31x = $840
x = 27.1 units. We need to round to 27 units since 0.1 of a bicycle makes no sense in this context.
look at the table. is the relationship between x and y a proportional relationship?
yes or no
Answer:
Yes, the relation is proportional
Step-by-step explanation:
For a proportional relation, the ratio of X/Y (and thus Y/X) should be constant. You can verify, for examply dividing each Y by the corresponding X:
9 / -3 = -3
6 / -2 = -3
-3 / 1 = -3
-6 / 2 = -3
-9 / 3 = -3
As you can see, the ratio is the same, so the relation is proportional.
Construct rectangle ABCD in which b) BC = 5.4 cm and BCA = 45°
Step-by-step explanation:
Please refer to photo for drawing
Tell which ordered pair is a solution of the inequality y < x + 12.
(−4, 12)
(−7, 9)
(−5, 8)
(−3, 5)
Answer:
(-3,5)
Step-by-step explanation:
we just plug the solutions in the equation to see if it’s true
y<x+12
12<-4+12
12<8
Not true 12 is not less than 8
9<-7+12
9<5
not true 5 is not greater than 9
8<-5+12
8<7
Not true 8 is not less than 7
5<-3+12
5<9
true 5 is less than 9
Hopes this helps please mark brainliest