Answer:
The first task in a word problem is to translate it into symbols.
First, give a name to each quantity:
Let w be the width of the rectangle
Notice the length = w+3
Let a be the area of the rectangle
Let p be the perimeter of the rectangle
Next, write down formulas relating the quantities
Step-by-step explanation:
a = w * (w+3)
p = 2w + 2(w+3)
We know p = 42, so
42 = 2w + 2(w+3)
im sure you know how to simplify and solve for w:
42 = 4w + 6
4w = 36
w = 9
now you’re ready to attack the area
a = w * (w+3) = 9 * (9+3)
can you take it from there?
If a total of 1100 square centimeters of material is to be used to make a box with a square base and an open top, find the largest possible volume of such a box.
Answer:
Step-by-step explanation:
Let x = base side length
y = side height
volume V = x²y
y = V/x²
surface area
A = x² + 4xy
A = x² + 4x(V/x²)
A = x² + 4V/x
Solving for volume
V = (A - x²)(x/4)
V = ¼(Ax - x³)
a maximum will occur when the derivative equals zero
V' = ¼(A - 3x²)
0 = ¼(A - 3x²)
0 = A - 3x²
3x² = A
3x² = 1100
x² = (1100 / 3)
x = √(1100/3)
V = (A - x²)(x/4)
V = (1100 - √(1100/3))²(√(1100/3)/4)
V = 3,510.56606...
V = 3510.6 cm³
The box height will be half of the base side length.
y = ½√(1100/3)
HELP
The perimeter of a rectangular pool is 740 yd. If the length is 30 yd less than four times the width, find the length and width.
The length of the rectangular pool is __ yd.
Use point-slope form to write the equation of a line that passes through the point (19,-17) with slop -5/3
Answer:
y +17 = -5/3(x -19)
Step-by-step explanation:
The point-slope form of the equation for a line is ...
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
You want a line with slope -5/3 through point (19, -17). Its equation is ...
y -(-17) = -5/3(x -19) . . . . . substitute the given values
y +17 = -5/3(x -19) . . . . . simplify
First round 0.69 to the nearest tenth.
Answer:
0.69 rounded to the nearest tenth is 0.7
thanks ill mark brainliest
If I'm watching Gossip Girl, then it is Monday.
Hope this helps you!
Answer:
if i am watching Gossip Girl then it is monday
Step-by-step explanation:
that is the common sense that everyone should know
hope this helps everyone and have a great summer!
correct?////////////////
Answer:
No solution
One solution
Many solutions
One solution
Step-by-step explanation:
Let's use y = mx + b
m = coefficient (or slope)
b = constant ( or y-intercept)
If they have different y-intercepts but they're both rising the same amount there would be no solution because they would never cross
If the slope was different but the same y-intercept they would cross on the y-axis, making them have one solution
Equal coefficients and constants is correct, there would be infinite solutions
Different slopes and different y-intercepts would make them cross randomly one, so one solution
Hope this helped! Comment if it does or not :)
i still need help finding angle 1 and 2
cost of 1 almirah is=$2345
what is the cost of 12 such almirah?
Answer:
28140Step-by-step explanation:
We can applyUnitary method to solve this :-cost of 1 almirah = $ 2345
therefore,cost of 12 such almirah = 2345 x 12.
= $28140...ans
Hope it helps you!!A company makes a profit of $y (in thousand dollars) when it produces x computers,
where y is given by the formula y = a(x - 100)(x - 200) for x 20 If 120
computers are produced, the profit will be $3,200,000.
a) Find the value of a.
b) What is the maximum profit the company can make? At this profit, how many
computers should be produced?
c) If the company targets to make at least $4,800,000, what is the range of the
number of computers to be produced?
Using quadratic function concepts, it is found that:
a) The value of a is -2000.
b) The maximum profit the company can make is of $5,000,000, when 150 computers should be produced.
c) Between 140 and 160 computers need to be produced.
The profit is modeled by:
[tex]y = a(x - 100)(x - 200)[/tex]
Item a:
If 120 computers are produced, the profit will be $3,200,000, hence when [tex]x = 120, y = 3200000[/tex], and this is used to find a.
[tex]y = a(x - 100)(x - 200)[/tex]
[tex]3200000 = a(120 - 100)(120 - 200)[/tex]
[tex]-1600a = 3200000[/tex]
[tex]a = -\frac{3200000}{1600}[/tex]
[tex]a = -2000[/tex]
The value of a is -2000.
Item b:
We first place the quadratic function into standard form, thus:
[tex]y = -2000(x - 100)(x - 200)[/tex]
[tex]y = -2000(x^2 - 300x + 20000)[/tex]
[tex]y = -2000x^2 + 600000x - 40000000[/tex]
Which has coefficients [tex]a = -2000, b = 600000, c = -40000000[/tex].
Then, we have to find the vertex:
[tex]x_V = -\frac{b}{2a} = -\frac{600000}{2(-2000)} = 150[/tex]
[tex]\Delta = b^2 - 4ac = (600000)^2 - 4(-2000)(-40000000) = 40000000000 [/tex]
[tex]y_V = -\frac{\Delta}{4a} = -\frac{40000000000 }{4(-2000)} = 5000000[/tex]
The maximum profit the company can make is of $5,000,000, when 150 computers should be produced.
Item c:
We are working with a concave down parabola, hence the range is between the roots of:
[tex]y = -200x^2 + 600000x - 40000000[/tex]
[tex]4800000 = -200x^2 + 600000x - 40000000[/tex]
[tex]-200x^2 + 600000x - 44800000 = 0[/tex]
The coefficients are [tex]a = -200, b = 600000, c = -44800000[/tex].
Then:
[tex]\Delta = b^2 - 4ac = (600000)^2 - 4(-2000)(-44800000) = 1600000000[/tex]
[tex]x_1 = \frac{-b - \sqrt{Delta}}{2a} = \frac{-600000 - \sqrt{1600000000}}{2(-2000)} = 160[/tex]
[tex]x_2 = \frac{-b + \sqrt{Delta}}{2a} = \frac{-600000 + \sqrt{1600000000}}{2(-2000)} = 140[/tex]
Between 140 and 160 computers need to be produced.
A similar problem is given at https://brainly.com/question/24705734
QUIEN MONDA ME AYUDA A SOLUCIONA'
f(x)=(3x-4x)(-8x² + 3x)
POR FAVOR
Answer:
- x(- 8x^2 + 3x)
8x^3 - 3x^2
What is the value of x? Midsegments of triangles
Hi how u doin ?
[tex] \frac{16}{x + 4} = \frac{1}{2} \\ [/tex]
inverse both sides
[tex] \frac{x + 4}{16} = \frac{2}{1} \\ [/tex]
Multiply both sides by 16
[tex]16 \times \frac{x + 4}{16} = 16 \times 2 \\ [/tex]
[tex]x + 4 = 32[/tex]
Subtract both sides 4
[tex]x + 4 - 4 = 32 - 4[/tex]
[tex]x = 28[/tex]
There u go..... Have a great day ❤
this is just and addition to the great posting below, just supplementing.
keeping in mind that the midsegment of a triangle is half the length of the parallel base/side, Check the picture below.
Danielle's text messaging plan costs $8 for the first 550 messages and 15¢ for each additional text message. If she owes $8.60 for text messaging in the month of October, how many text messages did she send that month?
Answer:
Danielle sent 554 text messages that month.
Step-by-step explanation:
In Oct she owed: $8 + 60¢
Because 15¢ = 1 additional message => 60¢ = 4 additional messages
So Danielle sent 550 messages (=$8) and 4 additional messages (= 60¢)
=> She sent: 550 messages + 4 additional messages = 554 messages
Hope this helps!
Bradley is 27 years older than Madison seven years go, the sum of their ages was 59?
Answer:
how old is Madison right then I can't really help u solve it with that little info
Can someone answer this
Answer:
Step-by-step explanation:
multiply by 6
4-24x+21=-54x+5
54x-24x=5-4-21
30x=-20
x=-20/30=-2/3
pls answer this .............
Answer:
Do the same thing for the other exercises and you should find the results. They are all complimentary angles, that means if you sum the two equations representing the angles of each exercise they will be equal to 180º always
Step-by-step explanation:
3. notice 2x is complimentary of 2x + 80 because 2x is opposed to that blank space that compliments it.... I'm bad at explaining, I'll just show.
2x + 2x + 80 = 180
4x + 80 = 180
4x = 180 - 80
4x = 100
x = 25º
so then:
2x = 2*25
2x = 50º
and:
2x + 80 = 50 + 80
2x + 80 = 130º
5. Hamza chopped up
pineapple and gave į to his
mum. He also ate half himself.
How much was left to give to
his dad?
Answer:
depends how much he chopped up
Step-by-step explanation:
Answer:
Nothing
Step-by-step explanation:
"5. Hamza chopped up
pineapple and gave ½ to his
mum. He also ate half himself.
How much was left to give to
his dad?"
1 - 1/2 - 1/2 = 2/2 - 1/2 - 1/2 = 1/2 - 1/2 = 0
Answer: There was nothing left for him.
A ladybug crawls around the outside of a rectangle that measures 7.5 cm by 8.5 cm. The ladybug stays exactly 3.9 cm from the rectangle at all times to form a larger figure. What is the area of the new rectangle bound by the path of the bug?
Answer:
185.64 [tex]cm^{2}[/tex]
Step-by-step explanation:
Width =7.5+3.9*2 = 15.3 cm
Length = 8.5+3.9*2=16.3 cm
Big Area = 15.3*16.3 = 249.39 [tex]cm^{2}[/tex]
Small Area = 7.5*8.5 = 63.75 1 [tex]cm^{2}[/tex]
area bounded by the path of the bug = 249.39-63.75 = 185.64 [tex]cm^{2}[/tex]
find the missing side length. giving BRAINLIEST.
Answer:
15 degrees
Step-by-step explanation:
It is a right angle!
61 + 14 = 75
90 - 75 = 15
Hope this helps!!! :))
An airline with two types of airplanes, P1 and P2, has contracted with a tour group to provide transportation for a minimum of 400 first class, 900 tourist class, and 1500 economy class passengers. For a certain trip, airplane P1 costs $10,000 to operate and can accommodate 20 first class, 50 tourist class, and 110 economy class passengers. Airplane P2 costs $8500 to operate and can accommodate 18 first class, 30 tourist class, and 44 economy class passengers. How many of each type of airplane should be used in order to minimize the operating cost?
The relationship between airplane 1 and airplane 2 is an illustration of objective function
14 of airplane 1 and 7 of airplane 2 should be used to minimize the operation cost
How to determine the number of each type of airplane?Represent P1 and P2 with x and y, respectively.
From the question, we ave have the following parameters:
x y Minimum
First class 20 18 400
Tourist 50 30 900
Economy 110 44 1500
Cost 10000 85000
So, the objective cost function to minimize would be:
C = 10000x + 8500y
And the constraints are:
20x + 18y ≥ 400
50x + 30y ≥ 900
110x + 44y ≥ 1500
x, y ≥ 0
Next, we plot the graphs of the constraints
From the graph (see attachment), we have the following feasible solutions
(x,y) = {(4.9,21.8), (8.5,12.7), (14,6.7)}
Substitute these values in the objective function.
C(5,22) = 10000 * 5 + 8500 * 22 = 237000
C(9,13) = 10000 * 9 + 8500 * 13 = 200500
C(14,7) = 10000 * 14 + 8500 * 7 = 199500
The minimum value is:
C(14,7) = 199500
Hence, 14 of airplane 1 and 7 of airplane 2 should be used to minimize the operation cost
Read more about objective function at:
https://brainly.com/question/16826001
100 points, Please help!
Answer:
Look if you say 100 points. Give a hundred points. If you want an answer be honest~ and say fifty points
Step-by-step explanation:
1=17
2=97
Answered:
1 = 17
2 = 97
What type of correlation does the data set display?
х
y
2
13
5 11
7 10
9
8
11
2
A. Negative
O B. No correlation
C. Positive
Answer:
B-NO CORRELATION.....
When a divisor divides the dividend exactly without leaving remainder then the divisor and quotient are
pls answer
Answer:
The divisor is called a factor of the dividend.
Step-by-step explanation:
Hope this helps
(Brainliest is appreciated)
Answer:
If a divisor divides the dividend exactly and leaves no remainder, this divisor is also called a factor of that dividend. Therefore, all factors of a number are divisors, but not always all factors have to be factors of a number The factors of 8 are for example 1, 2, 4 and 8, because 8 can be divided exactly by 1, 2, 4, 8.
Step-by-step explanation:
Hope this helps :)
Bài 4: 350 Cho tam giác ABC nhọn, hai đường cao BD, CE cắt nhau tại H. M là trung điểm của BC. K đối xứng với H qua M. a) Chứng minh tứ giác BHCKlà hình bình hành b) Chứng minh BK LAB và CK AC. c) Gọi 0 là trung điểm của AK. Chứng minh OM IBC d) Gọi N là điểm đối xứng với H qua BC. Chứng minh BNKC là hình thang cần
Help me poeaseeeeeeeeeeee
Answer:
C. Hope It's Help :)))))
Answer:
4.5
Step-by-step explanation:
∛100 = ?
100 = 2 x 2 x 5 x 5
∛100
= ∛ ( 2 x 2 x 5 x 5 )
= 4.642
4.642 ~ 4.5
The approximation 4.642 can also be written as 4.5
Therefore,
∛100 = 4.5
Solve for t in the following equation.
10 + 4–2 = 2–2( + 4)
A. =−1 B. =−35
C. =35
Answer:
the answer would be 35...
Step-by-step explanation:
Dont know how to explain it on here
The labor cost for a certain dish is $40 per hour. If it takes 45 minutes to make the dish, what is the labor cost for this particular dish?
In the 7th grade, 30% of students wear a medium size shirt. If 93 students wear a medium, how many total students are there in the 7th grade?
Answer:
310
Step-by-step explanation:
Answer:
310
Step-by-step explanation:
is/of = % / 100
[tex]93/x = 30/100[/tex]
93 * 100=9300
9300/30 = 310
shola earns #750 every month. if she spends 4/5 of her salary and saves the rest, how much does she save every month?
Answer:
250
Step-by-step explanation:
Amount she earns = 750
amount she spend = ⅘ of 750 = ⅘×750= 600
amount she saves = 750-600
Shola saves $150 every month.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is multiplied by 3, or 2 is added 3 times.
Given:
Shola earns $750 every month.
She spends 4/5 of her salary.
That means,
4/5 of $750.
And 4/5 of $750 = 4/5 x 750
= 4 x 150
= 600
She spends $650 per month.
Saved amount,
= $750 - $600
= $150
Therefore, $150 is her monthly savings.
To learn more about the multiplication;
https://brainly.com/question/19634536
#SPJ2
Homework: Week 3 - Ratios...
Question 13, 1.4.39
O Points: 0 of 1
The ratio of female students to male students at a particular college is 3 to 2 If there are 3375 female students at the college, what is the total number of students at the college?
The total number of students at the college is (Simplify your answer)
Answer:
5,625
Step-by-step explanation:
divide 3375 by 3 and get 1125 now multiply that by two and get 2250. Add 3375 by 2250 to get 5625 students
4 lbs of tomato’s cost $14 complete the double number line so that it shows how much it will cost for up to 8 lbs of tomato’s
Answer:
the answer is 28$ because since the lbs get doubled so ypu also have to double the cost
