Qsn 1.4.1 have never done a problem of this kind before so will need background explanation for every step in the answer.
Answers
Answer
Maximum area = 4900 m²
Step-by-step explanation
1.4.1 The perimeter of a rectangle is calculated as follows:
[tex]P=2(l+w)[/tex]where l is the length and w is the width of the rectangle.
Substituting P = 280 m, l = 2x meters, and w = y meters, and solving for y:
[tex]\begin{gathered} 280=2(2x+y) \\ \frac{280}{2}=\frac{2(2x+y)}{2} \\ 140=2x+y \\ 140-2x=2x+y-2x \\ 140-2x=y \end{gathered}[/tex]The area of a rectangle is calculated as follows:
[tex]A=l\cdot w[/tex]Substituting l = 2x and w = y = 140 - 2x:
[tex]\begin{gathered} A=2x(140-2x) \\ A=2x(140)-2x(2x) \\ A=280x-4x^2 \end{gathered}[/tex]1.4.2 Given that Area's formula is a quadratic function, its maximum is placed at its vertex. The x-coordinate of the vertex is found as follows:
[tex]x_V=\frac{-b}{2a}[/tex]where a is the leading coefficient and b is the x-coefficient of the function. In this case, the coefficients are a = -4 and b = 280, then:
[tex]\begin{gathered} x_V=\frac{-280}{2(-4)} \\ x_V=\frac{-280}{-8} \\ x_V=35 \end{gathered}[/tex]Evaluating the Area at x = 35, the maximum Area is:
[tex]\begin{gathered} A=280(35)-4(35)^2 \\ A=4900\text{ m}^2 \end{gathered}[/tex]Related Questions
When we multiply or divide both sides of an inequality by a negative number, what happens to the inequality symbol?
Answers
Step-by-step explanation:
When we multiply or divide both sides of an inequality by a negative number, what happens to the inequality symbol?
Answer:
The sign flips.
≤ becomes ≥
and ≥ becomes ≤
the prime factorization is 3 to the power of 2 times 5 to the power of 2 what is the number
Answers
Answer:
225
Step-by-step explanation:
Kayla has $10 in a savings account. The interest rate is 5% per year and is not compounded. How much will she have in 2 years? Use formula i=p*r*t, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years
Answers
This is a question of Simple Interest. The simple interest is given by the formula:
[tex]I=P\cdot R\cdot T[/tex]That is:
Interest = Principal * Rate * Time
From the question, we have:
P = $10
R = 5% ---> 5/100 = 0.05
T = 2 years
Then, we have that the interest is (without units):
[tex]I=10\cdot0.05\cdot2\Rightarrow I=1[/tex]Therefore, the interest is $1.
However, Kayla will have in two years this interest plus the starting amount, that is:
$10 + $1 = $11.
Hence, Kayla will have $11 in two years in her savings account.
The figure below shows a circle with center J, diameter LT, secant TO, andtangents EB and IP. Which of the angles must be right angles? Select all thatapply.
Answers
Answer:
Explanation:
The angles that are right angles are the ones that measure 90 degrees.
These are:
angles formed at L
angles formed at E
Answer:
Explanation:
The angles that are right angles are the ones that measure 90 degrees.
These are:
angles formed at L
angles formed at E
Need help with 5 hurry I have to go somewhere in 5 minutes
Answers
Answer:
c. What is your favorite book?
Explanation:
A question is said to be biased when it is asked in such a way that it leads or skews people intentionally to a particular answer.
Looking at the given questions in the options, we can see that three of them have a particular person or thing mentioned in the question. These are examples of biased questions.
But the question, "What is your favorite book?" does not suggest a name of a particular book to the respondent which could influence their responses. This type of question is not biased.
Find the nth term of this
quadratic sequence
2, 8, 18, 32, 50, ..
Answers
Answer:
The nth term is 2n^2.
Step-by-step explanation:
We see that each term is twice a square number. So it follows that
[tex]a(n )= 2 {n}^{2} [/tex]
for n = 1, 2, 3,.....
3 to the power of 2 divided by 3
Answers
Answer:
3
Step-by-step explanation:
3 to the power of 2 is nine because 3 x 3 = 9
9 / 3 is 3
Answer:
3
Step-by-step explanation:
3²÷3¹
=3²-¹
=3¹
=3
or
3²÷3¹
=9÷3
=3
Jason has three more than four times the amount of money Jeff has together they have $72 how much money does each person have
Answers
hello
determine the amount each of them have, let's write an equation to represent thier total amount
let x represent the amount Jason have
let y represent the amount Jeff has
now, we know that Jason has 3 more than 4 times the amount Jeff has
x = 4y + 3 .... equation 1
x + y = 72 .... equation 2
from equation 2,
make x the subject of formula
[tex]\begin{gathered} x+y=72 \\ x=72-y \end{gathered}[/tex]x = 72 - y .....equation 3
put equation 3 into equation 1
x = 4y + 3
72 - y = 4y + 3
solve for y
[tex]\begin{gathered} 72-y=4y+3 \\ \text{collect like terms} \\ 4y+y=72-3 \\ 5y=69 \\ y=\frac{69}{5} \\ y=13.8 \end{gathered}[/tex]we know y = 13.8
we can simply substitute the value into equation 2 and solve for x
[tex]\begin{gathered} x+y=72 \\ y=13.8 \\ x+13.8=72 \\ x=72-13.8 \\ x=58.2 \end{gathered}[/tex]therefore, Jason has $58.2 and Jeff has $13.8
Write an equation in point-slope form for the line that has a slope of 1/5 and contains the point (2,−9).
Answers
The equation is y+9=(1/5)(x-2).
What is a slope form?It is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point. The three major forms of linear equations are point-slope form, standard form, and slope-intercept form. The equation of the slope form is y-y₁ = m(x - x₁)
The formula for the point-slope is,
y-y₁ = m(x - x₁)
y₁ is the y-coordinate of the point in the line, x₁ is the x-coordinate of the point in the line and m is the slope.
y₁ = -9
m = 1/5
x₁ = 2
Substituting the above values in the above equation, we get
y-(-9) = (1/5)(x-2)
By simplifying the above equation, we get
y+9 = (1/5)(x-2)
Therefore, the equation is y + 9 = (1/5)(x-2).
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Find the value of the smaller angle. (Hint find the value of x first)
Answers
The sum of both angles must be 180°, therefore:
(2x+24) + (4x+36) = 180°
6x + 60 = 180°
6x = 120°
x = 120/6 = 20°
Then, the smaller angle is 2*20 + 24 = 64
Which equations are true equations? Select ALL correct answers.
Responses:
1.) 8^2−5^2=. 4^2−7
2.)24/2^2= 50−6^2−8
3.)39−3⋅6=. 6⋅10/4+4
4.)56÷8+3^2= 2⋅2^3
Answers
The system of equations which are correct are mentioned below:
2 ) [tex]24/2^2= 50- 6^2 - 8[/tex]
and 4 ) 56÷8+3^2= 2⋅2^3
The solution of all the system of equations are given below;
1 ) [tex]8^2 - 5^2= 4^2 - 7[/tex]
LHS = 64 - 25 = 39
RHS = 16 - 7 = 9
Since LHS is not equal to RHS the given equation is not correct.
2) [tex]24/2^2= 50- 6^2 - 8[/tex]
LHS = 24 / 4 = 6
RHS = 50 - 36 - 8 = 6
Since LHS = RHS the above system of equation is correct.
3 ) [tex]39 - 3 X 6=6 X 10/4+4[/tex]
LHS = 39- 18 = 21
RHS = 60 / 8 = 7.5
Since LHS is not equal to RHS the given system of equations is wrong
4 ) 56÷8+3^2= 2⋅2^3
LHS = 12
RHS = 12
Since LHS = RHS the above system of equations is correct.
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Emma is scrapbooking. She has 9 inches of paper and needs to cut it into 2/5 inch strips of paper. How many whole strips will she be able to make?
*
1 point
Answers
The number of strips Emma will be able to make 22.5 i.e. 22.
What is strips?The set of points in the plane between two parallel lines in the plane. The x,y coordinates plane of the points in the stripe satisfy the inequality C1 < . Ax + By < C2, where A, B, C1, C2 are certain constants and both A and B cannot be zero. The strip number is typically used in preparing the data for matching (or as a matching transformation within the matching processor). For text data that has numbers in the data but that you know are irrelevant, removing the numbers before matching is useful. As an abstract topological space, the Mobius strip can be embedded in three-dimensional Euclidean space in various ways. The twist is greater than 1 or the centerline is knotted.According to question
Total paper = Total strips × size of one
9 = n × 2/5
n = 22.5
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what is the answer to 3 1/8 ÷1 2/3
Answers
Answer: 3 1/8 ÷ 1 2/3 = 15/8. 15/8 as a simplified mixed number is 1 7/8
Step-by-step explanation: 15/8 is at it's simplist form and cannot be divided again that is why you convert it into a mixed number. I hope this helps!
Can you rewrite a sum as a product!!!??? QUICK ANSWER PLEASE
Answers
yes of course it can surely be
Answer:
Yes, you can factor out common factors to write equivalent algebraic expressions.
[from edge's summary video script]
estimate 6 and five ninths times sixty eight and 1 third
Answers
To estimate this, let's first translate to figures.
We have:
[tex]\begin{gathered} \text{Five ninths = }\frac{5}{9} \\ \\ Sixty\text{ eight = 68} \\ \\ 1\text{ third = }\frac{1}{3} \end{gathered}[/tex]Let's estimate, we have:
[tex]undefined[/tex]Find the trigonometric form of the complex number. Hint: Graph the complex number first to give yourself a visual representation.
Answers
First, let's graph the complex number:
The trigonometric form will be given by:
[tex]-2-2i=r(\cos \theta+i\sin \theta)[/tex]The angle θ here is 225° (5π/4), the r-value will be
[tex]\begin{gathered} r=\sqrt[]{(-2)^2+(-2)^2} \\ \\ r=\sqrt[]{4+4} \\ \\ r=\sqrt[]{8}=2\, \sqrt[]{2} \end{gathered}[/tex]Now we have the trigonometric representation:
[tex]-2-2i=2\, \sqrt{2}\mleft(\cos \mleft(\frac{5\pi}{4}\mright)+i\sin \mleft(\frac{5\pi}{4}\mright)\mright)[/tex]Therefore the correct answer is the letter D.
Please look at picture! thank you!
Answers
Answer:
16
Step-by-step explanation:
write the equation for a3
a3 = a2 + 3(3) -> eq1
now find what is a2, write equation for a2
a2 = a1 + 3(2) -> eq2
you know a1=1, replace that into eq2
a2 = 1 + 3(2) = 1 + 6 = 7
replace a2 into eq1
a3 = 7 +3(3) = 7 + 9 = 16
Perform the following food service calculation.
Meat served: chicken with a bone
Pounds of chicken available: 48 lbs.
How many guests can be served?
Answers
The number of guests that can be served is 12
How to determine the number of guests?From the question, we have the following parameters that can be used in our computation:
Meat served: 4 lbs chicken with a bone
Pounds of meat available: 48 lbs.
The number of guests needed is calculated using the following equation
Number of guests = Pounds of meat available/Meat served
Substitute the known values in the above equation, so, we have the following representation
Number of guests = 48/4
Evaluate the quotient
Number of guests = 12
Hence, 12 guests can be served with the available meat
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Possible question
Perform the following food service calculation.
Meat served: 4 lbs chicken with a bone
Pounds of meat available: 27 lbs.
How many guests can be served?
Please read in round your answer to the nearest whole number do not round any intermediate calculations
Answers
Solution
Total space
[tex]337+240+173+180=930[/tex]Probability
[tex]Probability\text{ =}\frac{Possible\text{ outcome}}{Total\text{ sample}}=\frac{337}{930}[/tex]Now for the next thin crust of 2000 pizza
[tex]\frac{337}{930}\times2000=724.7311[/tex]The final answer
[tex]725[/tex]Given the following sequence of numbers find the recursive formula, and the appropriate sequence formula,(arithmetic or geometric) and find the next three numbers in the sequence.5, 9, 13, 17, 21,
Answers
We can say that it's an arithmetic sequence since it has a common rate of change or common difference of 4.
Arithmetic sequences are represented by the following formula:
Recursive formula:
[tex]\begin{gathered} a_n=a_{n-1}+d \\ \text{Explicit formula:} \\ a_n=a_1+(n-1)d \\ \text{The next three numbers would be: }a_6,a_7,a_8 \end{gathered}[/tex]an= nth term
a1= 1st term
n= number of terms
d= common difference
[tex]\begin{gathered} a_6=5+(6-1)\cdot4 \\ a_6=25 \\ a_7=5+(7-1)\cdot4 \\ a_7=29_{} \\ a_8=5+(8-1)\cdot4_{} \\ a_8=33 \end{gathered}[/tex]A shoe store was having a back to school sale where you could buy 6 pairs of shoes for $52.62. If a large family decided to buy 3 pairs of shoes, how much would it cost them?
Answers
Answer: The family would buy the three pairs of shoes for $26.31 because you have to divide $52.62 in half since they bought half the amount of pairs of shoes that are given in the sale.
Answer:
$26.31
Step-by-step explanation:
3 × [tex]\frac{52.62}{6}[/tex]
3 × [tex]\frac{5262}{600}[/tex]
3 × [tex]\frac{877}{100}[/tex]
[tex]\frac{3 *877}{100}[/tex]
[tex]\frac{2631}{100}[/tex]
= 26.31
Name the coordinates of Q(6, -4) under a reflection in the x-axis.
Answers
The coordinates of Q(6, -4) under a reflection in the x-axis is Q'(6,4)
The coordinates of x will remain the same for reflection in the X axis, while y will change with the opposite sign.
From the question, we have
The coordinates of Q(6, -4) under a reflection in the x-axis is Q'(6,4).
Reflection:
A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another. The reflected picture should have the same size and shape as the original, but it faces the opposite way. Changes in position during contemplation may also result in translation. Pre-image and image are terms used to refer to the same thing in this context. ABC and A'B'C are used to represent the pre-image and image, respectively. The coordinate system may be referred to by the reflection transformation (X and Y-axis).
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a stationary shop had an equal number of pens and notepads at first. after selling 1250 pens and 380 notepads, there were 4 times as many notepads as pens left. how many pens did the stationary shop have at first
Answers
The stationary shop had 90 pens with them initially.
Let,
The number of pens initially at the stationary shop=x
The number of pens and the number of notepads are said to be equal. Therefore, The number of notepads initially at the stationary shop=x
After selling,
The number of pens = x-1250
The number of notepads = x-380
The number of pens was four times the number of the number of notepads. Modelling the linear equation for the situation:
x-1250=4(x-380)
x-1250=4x-1520
x=4x-270
-3x=-270
x=90
The stationary shop had 90 pens initially.
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Where can I calculate the shaded area of this diagram?
Answers
We are asked to find the area of the shaded region.
Notice that the overall figure is a rectangle and the missing area is a triangle.
The area of the rectangle is given by
[tex]A_{\text{rect}}=w\cdot l[/tex]Where w is the width and l is the length of the rectangle.
width = 7 m
length = 16 m
[tex]A_{\text{rect}}=w\cdot l=7\cdot16=112\; \; m^2[/tex]So, the area of the rectangle is 112 m²
The area of the triangle is given by
[tex]A_{\text{tri}}=\frac{1}{2}\cdot b\cdot h[/tex]Where b is the base and h is the height of the triangle.
base = 7 m
height = 8 m
[tex]A_{\text{tri}}=\frac{1}{2}\cdot b\cdot h=\frac{1}{2}\cdot7\cdot8=28\; \; m^2[/tex]So, the area of the triangle is 28 m²
The area of the shaded region can be found by subtracting the area of the triangle from the area of the rectangle.
[tex]\begin{gathered} A=A_{\text{rect}}-A_{\text{tri}} \\ A=112-28 \\ A=84\; \; m^2 \end{gathered}[/tex]Therefore, the area of the shaded region is 84 m²
Given below is a number written in factored form. Use this representation to determine the following. Factored Form 7.7.7.7.7.7 Enter the number in exponential form. Enter the number in standard form.
Answers
Given number in factored form 7.7.7.7.7.7 can be represented in the following way :
Exponential form : 7⁶
Standard form. : 11.7649 × 10⁴
As given in the question,
Given number in factored form is equal to 7.7.7.7.7.7
Represent the given factored form number into exponential form and standard form is written as :
Exponential form is given by :
7.7.7.7.7.7
= 7¹⁺¹⁺¹⁺¹⁺¹⁺¹
= 7⁶
Standard form is given by :
7.7.7.7.7.7
= 117649
= 11.7649 × 10⁴
Therefore, given number in factored form 7.7.7.7.7.7 can be represented in the following way :
Exponential form : 7⁶
Standard form. : 11.7649 × 10⁴
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Choose the graph of this equation. y = 2.5x
Answers
Answer:
1
Step-by-step explanation:
A real estate licensee leased a building for 10 years at an annual rent of$48,000. she will receive a commission of 7.5 % for the first 5 years, 5% for the next there years and 3.5% for the final two years. what will her income be from this commission over the life of the lease?
Answers
We have the lease of a building is for 10 years with an annual rent of $48 000.
We first determine the 7.5% for the first 5 years, for that we add the cost of the rent for 5 years, that is:
[tex]5(48000)=240000[/tex]In 5 years the rent will be of $240 000, now we find the 7.5%:
[tex]c_5=\frac{240000\cdot7.5}{100}\Rightarrow c_5=18000[/tex]Her commision for the first 5 years is going to be of $18 000.
Now we determine the 5% for the next 3 years, for this we determine the rent for 3 years:
[tex]3(48000)=144000[/tex]The rent for 3 years adds $144 000, now we determine the 5%:
[tex]c_3=\frac{144000\cdot5}{100}\Rightarrow c_3=7200[/tex]From this we have that the commission for the next 3 years will be of $7200.
And finally, we determine the rent for the two remaining years:
[tex]2(48000)=96000[/tex]We have that the last two years the rent will be of $96000, now we determine the 3.5% of her commission during that time:
[tex]c_2=\frac{96000\cdot3.5}{100}\Rightarrow c_2=3360[/tex]From this we have her commission for the last two years will be of $3360.
Finally we add all of the values of the commissions she will get:
[tex]c_t=18000+7200+3360\Rightarrow c_t=28560[/tex]From this we have that the total commision money she will be getting during those 10 years will be $28 560.
Find an equation for the line that passes through the points (5, 2) and (1, 4).
Answers
The equation of the line that passes through the points (5,2) and (1,4) is given by [tex]y=-\frac{x}{2} +\frac{9}{2}[/tex].
Let the points [tex](5,2) = (x_{1} , y_{1} )[/tex] and [tex](1,4) = (x_{2} , y_{2} ).[/tex]
The two-point form of the equation of a line is given by,
[tex]y-y_{1} =\frac{y_{2} -y_{1} }{x_{2}- x_{1} } (x-x_{1} )[/tex]
Substituting the values of [tex]x_{1} , x_{2}, y_{1}[/tex] and [tex]y_{2}[/tex] in the above equation, we get,
[tex]y-2=\frac{4-2 }{1-5 } (x-5 )\\\\ y-2 = \frac{2 }{-4 } (x-5 )\\\\ y-2=-\frac{1}{2} (x-5)\\ \\y-2=-\frac{x}{2} +\frac{5}{2} \\ \\y=-\frac{x}{2} +\frac{5}{2} +2\\ \\y=-\frac{x}{2} +\frac{9}{2}[/tex]
Thus the equation of the line is [tex]y=-\frac{x}{2} +\frac{9}{2}[/tex].
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PLEASE HELP ASAP!!!!!!!! (NO BOTS OR LINKS- WILL BE REPORTED)
Answers
The minimum number of tiles will be 122 that Imane needs to cover the floor.
How to Convert Square Feet to Square Inches?Multiply the area by the conversion ratio to convert a square foot measurement to a square inch measurement. Because one square foot equals 144 square inches, you may use the following easy formula to convert:
square inches = square feet × 144
The area in square inches is equal to the square feet multiplied by 144.
The floor she wants to cover has an area of 216 square feet.
The required area in square inches is :
216 × 144 = 31,104 sq in
Each tile covers an area of 256 square inches.
The minimum number of tiles = 31,104 sq in / 256 sq in
The minimum number of tiles = 121.5 ≈ 122
Thus, the minimum number of tiles will be 122 that Imane needs to cover the floor.
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Suppose S and T are mutually exclusive events. Find P(S or T) if P(S)= 6/11 and P(T)= 1/10
A. 71/110
B. 3/55
C. 1/3
D. 71/21
Answers
The value of P(S or T) is 71/110.
What is mutually exclusive event?
If two events cannot happen simultaneously, they are mutually exclusive or discontinuous. The results of a single coin flip, which can result in either heads or tails but not both, serve as an obvious illustration.
As given,
S and T are mutually exclusive events. P(S)= 6/11 , P(T)= 1/10.
By using,
P(S ∪ T) = P(S) + P(T) - P(S ∩ T)
= 6/11 + 1/10 - P(S ∩ T)
= 71/110 - P(A ∩ T)
But the events S and T are mutually exclusive events.
therefore, P(S ∩ T) = 0.
So,
P(S ∪ T) = 71/110
Therefore, value of P(S or T) is 71/110.
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