Answers
Answer:
(i) The area of the rabbit cage when the width is 5.2 m is 81.5 m²
(ii) The area of the rabbit cage if Wilson has 40 meters of wire mesh is 75 m²
Step-by-step explanation:
(i) The given relation of the area, A to the width P of the rabbit cage is A = 3·p²
The graph of the function between the values of 0 and 6 inclusive is found as follows;
A, 3·p²
0, 0
1, 1
2, 12
3, 27
4, 48
5, 75
6, 108
Please find attached the graph of A to 3·p²
From the graph, we have when the the width, p, of the rabbit cage = 5.2, the area, A ≈ 81.5 m²
The area of the rabbit cage when the width is 5.2 m = 81.5 m²
(ii) Also from the graph given that the total wire mess with Wilson = 40 meters, we have;
The formula for the perimeter of the cage = The formula for the perimeter of a rectangle = 2×length + 2×width
The formula for the perimeter of the cage = 2×3×p + 2× p = 8·p
Where the total length of the wire mesh available = 40 meters for the cage
The 40 meters of wire mesh will be used round the perimeter of the cage
∴ 40 m. = 8·p
p = 40/8 = 5 m.
At p = 5 m. the area is given as A = 75 m².
Therefore, the area of the rabbit cage if Wilson has 40 meters of wire mesh = 75 m².
Related Questions
Hi There! Can someone please help me with this Maths Question as soon as possible. I will mark the brainliest. Write each calculation as a single power. a) 8^5 multiplied by 8^4 b) 3^11 multiplied by 3 c)9^3 multiplied by 9^7 multiplied by 9^6 d) 7^7 ÷ 7 e) 12^10 ÷ 12^5 f) (6^3)^6
Answers
I'll be using the following properties about exponents:
[tex]a^b \times a^c=a^{b+c}[/tex]
[tex]a^b \div a^c=a^{b-c}[/tex]
[tex](a^b)^c=a^{bc}[/tex]
where a, b, and c are some positive integers
Part a:
[tex]8^5 \times 8^4 = 8^{5+4}=8^9[/tex]
Part b:
[tex]3^{11} \times 3 = 3^{11} \times 3^{1} = 3^{11+1} = 3^{12}[/tex]
Part c:
[tex]9^3 \times 9^7 = 9^{3+7}=9^{10}[/tex]
Part d:
[tex]7^7 \div 7 = 7^7 \div 7^1 = 7^{7-1}=7^6[/tex]
Part e:
[tex]12^{10} \div 12^5 = 12^{10-5}=12^5[/tex]
Part f:
[tex](6^3)^6 = 6^{6 \times 3} = 6^{18}[/tex]
These should be all the answers. Let me know if you need any clarifications, thanks!
what is an equation of the line passes through the points (8,-8) and (-5,-8)
Answers
Answer:
The answer is
y = - 8Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the line we must first find the slope
That's
Slope of the line using points
(8,-8) and (-5,-8) is
[tex]m = \frac{ - 8 + 8}{ - 5 - 8} = \frac{0}{ - 13} = 0[/tex]
So the equation of the line using point (8,-8) is
y + 8 = 0(x - 8)
y + 8 = 0
We have the final answer as
y = - 8Hope this helps you
Giải phương trình: 3x^2 + 3x - 6 = 0
Answers
Answer:
x=1
x=-2
Step-by-step explanation:
(3x-3)(x+2)
x=1
x=-2
The product of ages of a man 5 years ago and
5 years hence is 600, find his present age.
Answers
Answer:
25
Step-by-step explanation:
let his age be x, then
5 years ago his age was x - 5 and in 5 years will be x + 5 , thus
(x - 5)(x + 5) = 600 ← expand factors using FOIL
x² - 25 = 600 ( add 25 to both sides )
x² = 625 ( take the square root of both sides )
x = [tex]\sqrt{625}[/tex] = 25
Answer:
[tex]\boxed{Age \ of \ man = 25 \ years}[/tex]
Step-by-step explanation:
Let the age be x
Then, the given condition is:
(x-5)(x+5) = 600 [ x-5 for age 5 years ago and x+5 for age 5 years after ]
Using Formula [tex](a+b)(a-b) = a^2-b^2[/tex]
[tex]x^2-25 = 600[/tex]
Adding 25 to both sides
[tex]x^2 = 600+25[/tex]
[tex]x^2 = 625[/tex]
Taking sqrt on both sides
[tex]x = 25[/tex] years
When she subtracts 4 from both sides, Startfraction one-half EndFraction x equals negative StartFraction one-half EndFraction x. Results. What is the value of ?
Answers
Answer:
0Step-by-step explanation:
Given the expression after 4 has been subtracted from both sides as
1/2 x = - 1/2 x, the original expression will be gotten by adding back 4 to both sides of the resulting expression as shown;
1/2 x + 4 = - 1/2 x + 4
x/2 + 4 = -x/2 + 4
Find the LCM of both equation;
(x+8)/2 = (-x+8)/2
Multiplying both sides by 2 will give;
x+8 = -x+8
Collecting the like terms;
x+x = 8-8
2x = 0
x = 0/2
x = 0
Hence, the value of x is 0
Answer:
0
Step-by-step explanation:
listed below are the number of tech-supported questions successfully answered each day by misty and brock over a one week period, who is the more consistent employee?
Misty: 11,13,12,14,10,16,14
Brock: 8,15,10,11,16,10,9
Answers
Answer:
Misty is the more consistent employee
Step-by-step explanation:
The given data are
Misty: 11, 13, 12, 14, 10, 16, 14
Brock: 8, 15, 10, 11, 16, 10, 9
The mean of Misty's successfully answered questions = ∑x/n = 90/7 = 12.86
Misty's data standard deviation = √(∑(x - μ)²/n) = 1.884
The mean of Brock's successfully answered questions = ∑x/n = 79/7 = 11.29
Brock's data standard deviation = √(∑(x - μ)²/n) = 2.81
Therefore, based on the value of the standard deviation which is a measure of variability, whereby the standard deviation of Brock's number of successfully answered questions is larger than the standard deviation of Misty's number of tech supported successfully answered questions, Misty is the more consistent employee.
Which is a correct first step in solving 5 – 2x < 8x – 3? 5 < 6x – 3 3x < 8x – 3 5 < 10x – 3 2 – 2x < 8x
Answers
Answer:
5 < 10x – 3
Step-by-step explanation:
The inequality is 5 - 2x < 8x - 3.
5 < 6x – 3 is incorrect because 8x + 2x = 10x, not 6x.
3x < 8x – 3 is incorrect because 5 - 2x is not 3x, you can't subtract those terms as they are not like terms.
5 < 10x – 3 is correct because 8x + 2x = 10x.
2 – 2x < 8x is incorrect because 5 + 3 = 8, not 2.
Answer:
C on edg
Step-by-step explanation:
The function h(x) is defined as shown. h(x) = StartLayout Enlarged left-brace 1st row 1st column x + 2, 2nd column x less-than 3 2nd row 1st column negative x + 8, 2nd column x greater-than-or-equal-to 3 EndLayout What is the range of h(x)? –∞ < h(x) < ∞ h(x) ≤ 5 h(x) ≥ 5 h(x) ≥ 3
Answers
Answer: B
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
Your friend decides to flip a coin repeatedly to analyze whether the probability of a head on each flip is one half . He flips the coin 10 times and observes a head 4 times. He concludes that the probability of a head for this coin is four tenths equals0.40. Answer parts a and b below.
a. Your friend claims that the coin is not balanced, since the probability is not .50. What's wrong with your friend's claim?
b. If the probability of flipping a head is actually 1/2, what would you have to do to ensure that the cumulative proportion of heads falls very close to 1/2?
Answers
Answer and Step-by-step explanation:
a. As the friend claim is wrong as he flipped the coin very less i.e 10 only which reflects the number of time he flipped the coins. And we know that the probability is based on an imagination that could have a long series with respect to indefinite trails i.e unlimited
b. Since your friend flipped very less i.e only 10 which is not sufficient to get the nearest estimate your friend should flipped many times so that he would able to come very close.
change 651 to millilitres
Answers
Answer:
6510ml
Step-by-step explanation:
1cl = 10ml
651cl = ?
651 × 10 = 6510ml
Answer is 6510ml
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answers
Answer:
The function has two real roots and crosses the x-axis in two places.
The solutions of the given function are
x = (-0.4495, 4.4495)
Step-by-step explanation:
The given quadratic equation is
[tex]G(x) = -x^2 + 4x + 2[/tex]
A quadratic equation has always 2 solutions (roots) but the nature of solutions might be different depending upon the equation.
Recall that the general form of a quadratic equation is given by
[tex]a^2 + bx + c[/tex]
Comparing the general form with the given quadratic equation, we get
[tex]a = -1 \\\\b = 4\\\\c = 2[/tex]
The nature of the solutions can be found using
If [tex]b^2- 4ac = 0[/tex] then we get two real and equal solutions
If [tex]b^2- 4ac > 0[/tex] then we get two real and different solutions
If [tex]b^2- 4ac < 0[/tex] then we get two imaginary solutions
For the given case,
[tex]b^2- 4ac \\\\(4)^2- 4(-1)(2) \\\\16 - (-8) \\\\16 + 8 \\\\24 \\\\[/tex]
Since 24 > 0
we got two real and different solutions which means that the function crosses the x-axis at two different places.
Therefore, the correct option is the last one.
The function has two real roots and crosses the x-axis in two places.
The solutions (roots) of the equation may be found by using the quadratic formula
[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]
[tex]x=\frac{-(4)\pm\sqrt{(4)^2-4(-1)(2)}}{2(-1)} \\\\x=\frac{-4\pm\sqrt{(16 - (-8)}}{-2} \\\\x=\frac{-4\pm\sqrt{(24}}{-2} \\\\x=\frac{-4\pm 4.899}{-2} \\\\x=\frac{-4 + 4.899}{-2} \: and \: x=\frac{-4 - 4.899}{-2}\\\\x= -0.4495 \: and \: x = 4.4495 \\\\[/tex]
Therefore, the solutions of the given function are
x = (-0.4495, 4.4495)
A graph of the given function is also attached where you can see that the function crosses the x-axis at these two points.
A carnival is selling ride tickets 5 for $6, 10 for $12, or 15 for $18. What is
the cost per ticket?
Answers
Answer:
one ticket is $1.20
Step-by-step explanation:
6 / 5 = 1.2, then check it by multiplying 1.2 x 5. Its easier than you think. Im positive im correct. All you have to do is one but if u want to make sure you can do all of them
Answer:
$1.20
Step-by-step explanation:
If you divide the price of a ticket bundle by the amount of tickets, you get the individual ticket price.
5 tickets for $6.
6/5 = 1.2
10 tickets for $12.
12/10 = 1.2
15 tickets for $18
18/15 = 1.2
Please help...................
Answers
Answer:
30 degrees
Step-by-step explanation:
25 cm in length, radius 3.5cm
Which graph would result in a more accurate prediction? SAT vs. IQ because the data points are closer to the trend line. GPA vs. IQ because the data points are closer to the trendline. SAT vs. IQ because the rate of change is higher. GPA vs. IQ because the rate of change is higher.
Answers
Answer:
SAT vs. IQ because the data points are closer to the trend line.
Step-by-step explanation: The accuracy of linear model is based on the sum of the squared error between the actual and predicted data. Therefore in drawing our trend line, we want one in which gives the least sum of squared error(distance between trend line and the actual data point). With such a trend line, we'll get a more accurate prediction from our model. The rate of change does not rely dictate accuracy of a model, it only explains how a variable changes in relation to another. From both graphs, the data point on the SAT v IQ graph AR closer to the trend lines and as such will produce a lower sum of squared error than the GPA v IQ model.
Answer:
a
Step-by-step explanation:
find three rational number between under root 3 and root 5
Answers
do you know where is India
becz I am an Indian
Answer:
2,49/4,10/9
Step-by-step explanation:
[tex]1.\sqrt{4} =2\\2.\sqrt{x} =3+\frac{1}{2} =\frac{7}{2} \\x=\frac{49}{4} \\3.\sqrt{x} =3+\frac{1}{3} =\frac{10}{3} \\x=\frac{100}{9}[/tex]
n/2-3n/9+5n/9=21 (will mark brainiest)
Answers
Answer:
exact form: n=378/13
decimal form: n=29.0769....
mixed number form: n=[tex]29\frac{1}{13}[/tex]
Step-by-step explanation:
Answer:
n = 21
Step-by-step explanation:
[tex]\frac{n}{2}-\frac{3n}{9}+\frac{5n}{9}=21\\\\\frac{9n}{18}-\frac{6n}{18}+\frac{10n}{18}=21\\\\\frac{3n}{18}+\frac{10n}{18}=21\\\\\frac{13n}{18}=21\\\\13n=273\\\\n=21[/tex]
Steps:
1. Write as fractions
2. Make the fractions have the same denominator
3. Collect like terms
4. Collect like terms
5. Multiply both sides by 18
6. Divide both sides by 13.
5v2
By taking v2 = 1.414, find the value of
2
Answers
Answer:
1.999396
Step-by-step explanation:
2 = (√2)² = 1.414² = 1.999396
6 agents can sell 333 cars in 3 months.
At this rate, how many cars can 3
agents sell in 6 months?
Answers
Answer:
333 cars
Step-by-step explanation:
Assuming among 6 agents, the working efficiency is the same and constant. Fixing number of agents:
6 agents can sell 333 cars in 3 months.
=> 6 agents can sell 333/3 cars in 3/3 month.
=> 6 agents can sell 111 cars in 1 month.
Fixing number of months:
=> 6/2 agents can sell 111/2 cars in 1 month.
=> 3 agents can sell 111/2 cars in 1 month.
Then considering that 3 agents worked in 6 months:
=> 3 agents can sell 6 x 111/2 cars in 6 x 1 months.
=> 3 agents can sell 333 cars in 6 months.
Which sum or difference is modeled by the algebra tiles?
Answers
Answer:
(C)[tex]x^2+4x-2-(-x^2+2x-4)=2x^2+2x+2[/tex]
Step-by-step explanation:
The expression represented by the upper tiles is: [tex]x^2+4x-2[/tex]
The expression represented by the lower tiles is: [tex]x^2-2x+4[/tex]
Adding the two
[tex]x^2+4x-2+(x^2-2x+4)=2x^2+2x+2[/tex]
Writing it as a difference, we have:
[tex]x^2+4x-2-(-x^2+2x-4)=2x^2+2x+2[/tex]
The correct option is C.
Answer:
yeah, what newton said :]
In isosceles triangle the length of the base is twice shorter than the length of a leg. The perimeter of this triangle is 50 cm. Find the lengths of all sides.
Answers
Answer:
The base is 10cm. The other two sides are 20cm each
Step-by-step explanation:
I believe that "the base is twice shorter" means that the two equal sides of the iscosceles triangle are twice the length of the base.
Using the equation x + 2x +2x = 50 where x is the length of the base, we can simplify it to
5x=50. Then divide both sides by 5 to get the results:
x=10 for the base and
2x=20 for the other two sides.
Which kind of symmetry does the word TOOT have?
Answers
Answer:
Linear symmetry.
Step-by-step explanation:
The word 'TOOT' can be reflected in y-axis if a point (0,0) on cartesian plane divides the words' TO' and 'OT' equally.
Karina uses the system of equations below to compare the monthly utility costs in July and December for electricity, x, and natural gas, y. 750x + 17y = 141.61 300x + 30y = 75.90 Karina solves the system using linear combination and arrives at the equation 116y = 96.28. She then solves this equation for y. Which statement explains Karina’s solution?
Answers
Answer:
d. The cost of natural gas (y) = $0.83 per unit
Step-by-step explanation:
The explanation is shown below:-
the equation of system is:
750x + 17y = 141.61 (i)
300x + 30y =75.90 (ii)
as x indicates the cost of electricity and y indicates the costs of natural gas.
we will solve the both equation with the help of multiplication for (i) by 30 and for (ii) 75
[tex]30\times (750x + 17y) 30\times 141.61\\\\[/tex]
after solve the above equation we will get
22,500x + 510y = 4248.3 (iii)
[tex]75\times (330x + 30y) = 75\times 75.90[/tex]
after solve the above equation we will get
22500x + 2250y = 5692.5 (iv)
After deducting the equation (iii) and (iv) we will get
1740 y = 1444.2
After Dividing by 15 both sides,
116y = 96.28
So, Katrina simplify the above system using linear equation and reach at the equation that is
116 y = 96.28
By Division property of equality defines that divide the equal no. of both sides of an equation:
by Division of 116 to both sides of an equation, to get y:
[tex]\frac{116y}{116} = \frac{96.28}{116}[/tex]
y = 0.83
So, the natural gas is $0.83 per unit
Answer:
d
Step-by-step explanation:
6 root 5 plus 6 root 5
Answers
Answer:
12√5
Step-by-step explanation:
6√5 + 6√5 = (6 + 6) * √5 = 12 * √5 = 12√5.
Answer:
12 [tex]\sqrt{5}[/tex]
Step-by-step explanation:
When you add the surds which are the same type, (both are root 5), just add the integers before them together.
i will give brainliest.The product of 5 and the sum of 12 and a certain number is 10. What is the number
Answers
Answer: x=-10
Step-by-step explanation:
5*(12+x)=10
Distribute
60+5x=10
Subtract(60)
5x=-50
x=-10
Hope it helps <3
Answer:
Heeyyy hope it helps
Step-by-step explanation:
Ok, so the product is the answer to a multiplication problem.
The product of 5 and the sum of a number(X) and 3 is
5(X + 3) = 12
5X + 15 = 12
5X = 12 - 15
5X = -3
X = -3/5
[tex]Expand $(a + 2)(3a^2 + 12)(a - 2).$[/tex]
Answers
Answer:
3[tex]a^{4}[/tex] - 48
Step-by-step explanation:
Given
(a + 2)(3a² + 12)(a - 2)
= (a + 2)(a - 2)(3a² + 12) ← expand the first pair of parenthesis using FOIL
=(a² - 4)(3a² + 12) ← expand using FOIL
= 3[tex]a^{4}[/tex] + 12a² - 12a² - 48 ← collect like terms
= 3[tex]a^{4}[/tex] - 48
Hailey paid \$13$13dollar sign, 13 for 1\dfrac3{7} \text{ kg}1 7 3 kg1, start fraction, 3, divided by, 7, end fraction, start text, space, k, g, end text of sliced salami.
Answers
Answer:
1kg of salami cost $9.1
Step-by-step explanation:
Hailey paid $13 for 1 3/7 kg of sliced salami.
What was the cost per kilogram of salami?
Cost of 1 3/7 kg of sliced salami=$13
1 3/7 kg=10/7kg
Let x=1 kg of sliced salami
10/7 kg of x=$13
$13=10/7x
13=10/7*x
x=13 ÷ 10/7
=13×7/10
=91/10
=9.1
x=$9.1
Therefore, 1kg of salami cost $9.1
plzzz helpp ASAP 1. Why is it important to know what the limitations of a particular model are? A. so you can create a prototype based on your model B. so you don't make the mistake of confusing an object and a system C. so you can revise your model to represent every property of the real thing D. so you don't confuse properties of the model with properties of the real thing
2. Mathematical and computer models are similar because both involve _____. A. using calculations to represent an object or system B. comparisons between an object or system and something familiar C. building a complex object or system isolated from the natural world D. creating real-life objects that show features of the modeled object or system
3. Some models can illustrate a system. What does the term system refer to? A. a collection of interacting things B. a set of rules or laws about things C. something with advantages and limitations D. something illustrating parts of a real-life thing
4. J.J. Thomson's Plum Pudding Model is an example of _____. A. a picture B. an analogy C. a prototype D. a mathematical model
5. An advantage of describing a cell as being like a factory is that it _____. A. makes cells easier to understand B. shows the limitations of cells clearly C. prevents having to study the complexities of cells D. is cheaper to do experiments in a factory than on a cell
6. Scientists like using models because they are often _____ than the real thing. A. more accurate B. more enjoyable to study C. cheaper and more complex D. cheaper and easier to work with
7. An advantage of J.J. Thomson's Plum Pudding Model was that it _____. A. was a much less expensive way to study atoms B. simplified the calculations necessary to describe an atom C. clearly explained where electrons were located in an atom D. is much less expensive to bake a plum pudding than to look at an atom
8. A small clay model of a volcano is an example of _____. A. an analogy B. a prototype C. a physical model D. a computer model
9. An advantage of using a model instead of the real thing is that models _____. A. include better detail B. can be easier to change C. are much more interesting to study D. don't include any features of the real thing
Answers
Answer:
D. so you don't confuse properties of the model with properties of the real thing.
2-Mathematical and computer models are similar because both involve using calculation to represent an object or system
3- Some models can illustrate a system. What does the term system refer to
A. a collection of interacting things
4-J.J. Thomson's Plum Pudding Model is an example of _____B. an analogy
5. An advantage of describing a cell as being like a factory is that it _____
A. makes cells easier to understand
6- C. cheaper and more complex
7-C. clearly explained where electrons were located in an atom
8-C. a physical model
9-B. can be easier to change
GOOD LUCK
Instructions: Find the missing side. Round your answer to the
nearest tenth
Answers
Answer:
x = 20Step-by-step explanation:
To find x we use cosine
That's
cos ∅ = adjacent / hypotenuse
From the question
The adjacent is x
The hypotenuse is 28
So we have
cos 43 = x / 28
x = 28 cos 43
x = 20.477
x = 20 to the nearest tenth
Hope this helps you
answer choice D) The graph crosses the y-axis at (0,5), increasing from x=-10 to x=2 and decreasing from x=2 to x=10
Answers
Answer:
(A) see the attachments
Step-by-step explanation:
The graph is constant from x=2 to x=10. This eliminates all descriptions except A, which is the correct one.
plz help will give brainliest
Answers
Answer:
77
Step-by-step explanation:
slope equation