Answer:
6 questions
Step-by-step explanation:
Take the total number of questions and divide by the number of days
150/28
5.357142858
You would need to round up to make sure that the packet is completed in time
6 questions
A rectangular field is to be fenced off, and then divided in two by a fence running parallel to one of the sides. If 996 meters of fencing can be used, find the dimensions of the field that will maximize the total area, and then find the maximum area. List the smaller dimension first.
Solution :
Maximize, S = xy
subject to 2x + 2y = 996
So,
2x + 2y = 996
2(x + y) = 996
x + y = 498
y = 498 - x
Therefore,
S = x (498 - x)
S = 498x - [tex]x^2[/tex]
S = [tex]-x^2 + 498x[/tex]
[tex]$S = -(x^2-498x + 249^2) + 300^2$[/tex]
[tex]$S= -(x-249)^2 + 249^2$[/tex]
S = x (498 - x)
S = 498x - [tex]x^2[/tex]
[tex]$\frac{dS}{dx}= 498 - 2x$[/tex]
[tex]$\frac{dS}{dx}= 0$[/tex]
498 - 2x = 0
2x = 498
x = 249
∴ y = 498 - x
y = 498 - 249
= 249
Answer:
A = 249 x 249 = 62001 square meter.
Side is L = 249 m
Step-by-step explanation:
Total length of the fence is 996 m.
Let the length is L and the width is W.
Perimeter = 2 (L + W)
996 = 2 (L + W)
498 = L + W
L = 498 - W ...... (1)
Let the area is
A = L W
A = (498 - W) W
A = 498 W - W^2
Differentiate with respect to W.
dA/dW = 498 - 2 W
Put it equal to zero.
498 - 2 W = 0
W = 249 m
Now, L = 498 - 249 = 249 m
Differentiate with respect to W again
[tex]\frac{d^2A}{dW^2} = - 2[/tex]
As it is negative so the area is maximum.
The maximum area is
A = 249 x 249 = 62001 square meter.
Side is L = 249 m
( x-3 ).( 2x-3 ) = 0
Answer:
Step-by-step explanation:
Assuming you want to find x, we can set two equations:
x-3=0
2x-3=0
This is so that we can individually find x within the two paranthesis and not have to do more work. It helps for standardized tests.
solve for x on both sides, and you get 3 and 1.5
Answer:
[tex]x=3, x=\frac{3}{2}[/tex]
Step-by-step explanation:
[tex]\left(x-3\right)\left(2x-3\right)=0[/tex]
The zero product theorem will be used here to solve this non-linear problem.
means that in the original equation, each variable component must be set to zero.
[tex]\begin{cases} x-3=0\\2x -3=0\end{cases}[/tex]
To solve this linear equation, we need to group all of the variable terms on one side of the equation and all of the constant terms on the other.
so, -3 will be moved to the right side
Notice that when a term moves from one side of the equation to the other, it changes sign.
[tex]\begin{cases} (x-3)+3=3\\(2x-3)+3=3 \end{cases}[/tex]
[tex]x\left \{ 3,\frac{3}{2} \}[/tex]
OAmalOHopeO
[tex](32)^{1/5}[/tex]
Answer:
2Step-by-step explanation:
[tex] {32}^{ \frac{1}{5} } [/tex]
[tex] = \sqrt[5]{32} [/tex]
[tex] = \sqrt[5]{2 \times 2 \times 2 \times 2 \times 2} [/tex]
= 2 (Ans)
how many line of symmetry is this figure
Answer:
There are sixteen lines.
is 1/5 a rational or irrational number (20 points pls help)
Answer:
rational
Step-by-step explanation:
Answer:
it's Rational Number
Step-by-step explanation:
since each integer can't be written in the fraction form or for this example it would be thus 5 so it would be a rational number
A video store charges $12 for used games and $25 for new games. Jonathan has saved $300 to spend on video games. This scenario is represented by a linear equation.
12x + 25y = 300
x = number of used games
y = number of new games
How many games can Jonathan buy if he spends all his money on used games?
Answer:
25 used games
Step-by-step explanation:
Divide his money by the price for one used game
300/12
25
Answer:
y=0
12x=300
X=300/12
X=25
he can buy 25 used games .
Step-by-step explanation:
What is the percent change from 75 to 14?
Answer:
the change is -81.33% (the 3 is repeating)
A circle is represented by the equation below:
(x − 9)2 + (y + 8)2 = 16
Which statement is true?
a) The circle is centered at (−9, 8) and has a radius of 8.
b) The circle is centered at (9, −8) and has a diameter of 8.
c) The circle is centered at (9, −8) and has a radius of 8.
d) The circle is centered at (−9, 8) and has a diameter of 8.
Answer:
The center is (9,-8) and the diameter is 8
Step-by-step explanation:
(x − 9)^2 + (y + 8)^2 = 16
A circle is in the form
(x − h)^2 + (y -k)^2 = r^2 where (h,k) is the center and r is the radius
(x − 9)^2 + (y - -8)^2 = 4^2
The center is (9,-8) and the radius is 4
The diameter is 2 times the radius so the diameter is 8
The center is (9,-8) and the diameter is 8
help find the height
Answer:
A
Step-by-step explanation:
Heron's formula finds the area of any triangle.
Area = sqrt(s*(s - a)*(s-b)*(s-c) )
s = (a + b + c)/2
a = 8
b = 16
c = 12
s = 36/2 = 18
s-a = 18 - 8 = 10
s-b = 18 - 16 = 2
s-c = 18 - 12 = 6
Area = sqrt(18*10*2*6) = sqrt(2160)
Area = 12*sqrt(15)
Area = 46.4758
Now x is easily found. It is the altitude to 16
Area = 1/2 16 * h
46.4758 * 2 / 16 = h
h = 3*sqrt(15)/2
h= 5.81
If a school camp has enough food for 150 students over 5 days
How long would the food last for is only 100 students are there
Answer:
It is over 7 days
hope it helps
what is the scale factor from figure A to figure B
Answer:
scale facor is 1/3
Step-by-step explanation:
help me with this math question pls!! Find the value of x
Answer:
x = 3
Step-by-step explanation:
using the mid segment formula since quadrilateral WZYP is similar to that of MZYT, this is expressed as;
29 = 1/2(23 +11x+2)
Cross multiply
2(29) = 23+11x+2
58 = 25 + 11x
11x = 58 - 25
11x = 33
Divide both sides by 11
11x/11 = 33/11
x = 3
Hence the value of x is 3
Rút gọn bthuc
7x(4y-x) + 4y(y-7x) - (4y^2 -7x)
¢✓¢==¢=
Step-by-step explanation:
==`==¢=¢✓%✓™€✓✓€=€✓€✓
dbshhshs
shhsshsh
Sweatshirts at the school store cost $30. They currently sell about 4 shirts per month. They have decided to decrease the price of the shirts. They found the for each each $1.50 decrease, they will sell 2 more shirts per month. How many decreases in prices will give the max value?
A. 30
B. 9
C. 363
D. 16.50
g(x) = x3 + 2x2 - x - 2 to answer all the questions in Part II. 1. Use synthetic division to show that x = -2 is a zero of the polynomial.
Answer:[tex]x^{2} -1[/tex]
Step-by-step explanation:
Given :[tex]g(x)=x^{3} +2x^{2} -x-2[/tex]
Factor x+2,x=-2
Using synthesis division:
-2 ) 1 2 -1 -2
-2 0 2
1 0 -1 0
[tex]x^{2} +0x-1[/tex]
Yes, x = -2 is a zero of the polynomial.
Given that,
The function g(x) = x³ + 2x² - x - 2 is divided by (x + 2)
Now apply the synthetic division to show that x = -2 is a zero of the polynomial.
When we divide by using synthetic division as shown in the attached image.
Remainder = 0
Hence, this shows that x = -2 is a zero of the polynomial.
Therefore, x = -2 is a zero of the polynomial.
To learn more about the divide visit:
https://brainly.com/question/28119824
#SPJ4
50 points and brainly
Trinas you company charges $0.86 per pound to ship toys. Part A: Write an equation to determine the totals cost, c, to ship p pounds of toys. Use your equation to determine the cost of shipping 2 pounds of toys. Path B: if the company reduces the cost to ship toys by $0.05 per pound, write an equation to determine the total cost, c, to ship p pounds of toys with the reduced cost.
Answer:
Part A:
c = .86*p
c =1.72 for 2 lbs
Part B:
c =.81p
Step-by-step explanation:
Part A:
Total cost = cost per pound * number of pounds
c = .86*p
Let p = 2
c = .86*2
c =1.72
Part B:
Total cost = cost per pound * number of pounds
c = .(.86-.05)*p
c =.81p
Is the quotient of a rational number and
an irrational number always irrational?
Explain.
HELP ASAP
Answer = No,It can be either rational or irrational.
________________________________
Prroof —
4 ÷ √8 = √2 { Which is an irrational number }
________________________________
Now, Here comes a twist,
We know that — 0 is a rational number.
And, 0 ÷ √56666 = 0 ________________________________
Note—
But, √56666 ÷ 0 = Error ( Lol )
________________________________
A cylinder has a volume of 132x cubic feet and height of 4 feet. What is the area of the base?
* Square feet
Answer:
33π square feet
Step-by-step explanation:
Volume = base area × height
132π = base area × 4
or, base area = 132π/4
or, base area = 33π
Answered by GAUTHMATH
In this 3x3 square, you can use only numbers from 1-9, to make all the rows and columns equal to 15. Good luck to the person solving this and just know that I and lots more people thank you for solving this!
Answer:
Hello,
Step-by-step explanation:
The well-known magic square. (first apparition in China).
Here it the methode du Marquis de Liouville: (odd square:3,5,7,9,11,13,...)
We are going to put successively the number from 1 to n² (here n=3)
We imagine that the square is put on a sphere;
We begin in the middle of the last line where we put 1
ICI:
We move in direction SE of one case and put le next number
until we reach of multiple of n
After have reached a multiple of n, we move verticaly of one case
and we go to ICI until we reach n²
2. find out the h.c.f
2a , 1st exp= a2 + ab
= a(a+b)
2nd exp = a2-b2
= (a+b) (a-b)
HCF = (a+b)
b, 1 st exp= (a+b)2
= (a+b)(a+)
2 nd exp = a2-b2
= (a+b) ( a-b)
HCF = (a+b)
c, 1 st exp= (a-1)2
= (a+1) (a-1)
2nd exp= a2-1
= (a+1)(a-1)
HCF = (a-1)
d, 1st exp= (x-2)(x-3)
= x(x-3)-2(x-3)
= x2 - 3x - 2x + 6
= x2- 5x+ 6
= x2 - (3+2)x + 6
=x2 -3x-2x+ 6
= x(x-3) -2(x-3)
=(x-3)(x-2)
2 nd exp = (x+2) (x-3)
= x( x-3) + 2 (x-3)
= x2 - 3 x+ 2x -6
= x(x-3) + 2(x-3)
=(x-3) ( x+ 2)
HCF = (x-3)
In right triangle ABC, if AC = 5/13 and AB = 1, what is the length of BC?
Answer:
BC = [tex]\frac{12}{13}[/tex]
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
BC² + AC² = AB²
BC² + ([tex]\frac{5}{13}[/tex] )² = 1²
BC² + [tex]\frac{25}{169}[/tex] = 1 ( subtract [tex]\frac{25}{169}[/tex] from both sides )
BC² = [tex]\frac{169}{169}[/tex] - [tex]\frac{25}{169}[/tex] = [tex]\frac{144}{169}[/tex] ( take square root of both sides )
BC = [tex]\sqrt{\frac{144}{169} }[/tex] = [tex]\frac{12}{13}[/tex]
Maya just bought a refrigerator for $642. She paid $160.40 in a down payment and will pay the rest in 4 equal installments. How much does she need to pay for each installment?
Answer:
120.40 per payment
Step-by-step explanation:
Subtract the down payment
642 - 160.40
481.60
Divide this by 4
481.60 / 4
120.40
find the area of triangle
i. b=6cm ,h=4cm
ii. b=5cm ,h=7cm
iii. b=8.4 cm ,h=5cm
answer
[tex]i.12cm {}^{2} [/tex]
[tex]ii.17.5cm {}^{2} [/tex]
[tex]iii.21cm {}^{2} [/tex]
Answer:
Step-by-step explanation:
What are we supposed to do? You already have the answers and they’re all correct if that’s what you wanted to know
8. The value of [3 - 4 * (3 - 4) ^ 4] ^ 3 is
a) 1
b) -1
c)0
d) 7
help me please
Answer:
-1
Step-by-step explanation:
[3-4(-1)^4]^3
=>(3-4)^3
=>(-1)^3
=>-1
Answer From Gauth Math
Answer:
-1
Step-by-step explanation:
[tex][3-4*(3-4)^4]^3[/tex]
[tex](3-4)^4= 1\\Therefore, [3-4*1]^3= -1^3\\So, -1^3= -1\\\\[/tex]
Cube of any negative integer will be negative, or, a negative integer raised to any odd number will be negative. Likewise, a negative integer raised to an even number will be positive.
please HELP ME!!! (16 POINTS) due today :)))
Answer:
Step-by-step explanation:
I'm not sure what the question is asking, but if you mean the angles in the blue lines
First one, we know that the full length is 90, and it has gacen us 80, so the angle would be 10
Second one, we see that the angle is still 90, and since the given degree is 30, the unkown angle would be 60
Third one, the given angle is 75 so 90-75=15.
The answers would be 10, 60, and 15.
What is the value of 2.3 + 8 – 1/2?
a ) 10.8
b) 10.03
c) 9.8
d) 9.5
Answer:
9.8
Step-by-step explanation:
2.3 + 8 – 1/2
Rewriting the fraction as a decimal
2.3 + 8 – .5
9.8
What is the difference between 15% of 7 and of 7?
The circumference of a circle is 14 meters. Which of the following represents the area of the circle
Answer:
A = 49/pi
Step-by-step explanation:
C = 2 * pi *r
14 = 2 * pi *r
Divide each side by 2 pi
14/2pi = r
7/pi = r
The area is given by
A = pi r^2
A = pi ( 7/ pi)^2
A = pi * 49 / pi^2
A = 49/pi
Answer:
[tex]area = {15.61m}^{2} [/tex]
explanation is attached to the picture
Hope this helps you
Please help me ill give brainliest!!
Answer:
3744.64
Step-by-step explanation:
To know the answer to this question you need to know the formulas to find the volume of the cylinder and the rectangular prism. The volume of a cylinder is pi*r^2*h while the volume of the rectangular prism is l*w*h. The cylinder is 1808.64 cubic in while the rectangular prism is 1936 cubic. Together, they are 3744.64 cubic in.
Answer:
cylinder= A=πr²h
=3.14×4²×9
=452.16
rectangle=A=l×w×h
=19×11×11
=2299
total area=452.16+2299
=2751.16
Step-by-step explanation:
how many permutations can be made with the letters in the word Metallica
===============================================
Explanation:
There are 9 letters in "Metallica", so there would be 9! = 9*8*7*6*5*4*3*2*1 = 362880 different permutations; however, this is only the case if we could tell the letters L and A apart.
We have two copies of each of those repeated letters, so we have to divide by 2!*2! = (2*1)*(2*1) = 4 to account for these repeats.
Because we can't tell the repeated letters apart, we really have (9!)/(2!*2!) = (362880)/(4) = 90720 different permutations.
