Answer:
a) length x = 45ftb) maximum area = 4050 ft²Step-by-step explanation:
Given the quadratic equation A=−2x2+180x that gives the area A of the yard for the length x, to maximize the area of the yard then dA/dx must be equal to zero i.e dA/dx = 0
If A=−2x²+180x
dA/dx = -4x + 180 = 0
-4x + 180 = 0
Add 4x to both sides
-4x + 180 + 4x = 0 + 4x
180 = 4x
x = 180/4
x = 45
Hence the length of the building that should border the yard to maximize the area is 45 ft
To find the maximum area, we will substitute x = 45 into the modelled equation of the area i.e A=−2x²+180x
A = -2(45)²+180(45)
A = -2(2025)+8100
A = -4050 + 8100
A = 4050 ft²
Hence the maximum area of the yard is equal to 4050 ft²
Can someone help me on this math question its confusing ill give brainly when right!!!
Find the arc length of the partial circle.
Answer:
arc length = 4π units
Step-by-step explanation:
The arc length is calculated as
arc = circumference of circle × fraction of circle
= 2πr × [tex]\frac{90}{360}[/tex]
= 2π × 8 × [tex]\frac{1}{4}[/tex]
= 2π × 2
= 4π units ← exact answer
Determine the vertex of the function f(x) = 3(x - 2)^2 + 1.
(2, 1)
(-2, 1)
(1,2)
(1,-2)
Answer:
The vertex is at (2,1)
Step-by-step explanation:
The vertex form of a quadratic is
y = a(x-h)^2 +k where (h,k) is the vertex
f(x) = 3(x - 2)^2 + 1.
The vertex is at (2,1)
The chemical element, silver, boils at a temperature of degrees Fahrenheit. What is the boiling point for silver in degrees Celsius? Round you answer to one decimal place.
Answer:
[tex]C=(x-32)\times\frac{5}{9}[/tex]
Step-by-step explanation:
The formula to convert the temperature in Fahrenheit to degrees Celsius is:
[tex]C=(F-32)\times\frac{5}{9}[/tex]
Here,
C = temperature in degrees Celsius
F = temperature in Fahrenheit
Suppose the boiling point for silver is x Fahrenheit, then then the temperature in degrees Celsius will be:
[tex]C=(x-32)\times\frac{5}{9}[/tex]
The internal dimension of a lidless wooden box is 48cm × 38cm × 32cm. If the thickness of the tank is 1 cm, find the volume of the wooden box
Step-by-step explanation:
this is confusing.
first the description says "the internal dimensions".
and then it tells us the thickness of the tank walls (1cm).
so, I am not sure what the given numbers describe.
in any case, the volume is length × width × height.
so, either
48×38×32
or
46×36×31 (as for length and width we need to consider 2 walls, one on each end, for the height only one wall, as the tank is open and lidless.
whatever you choose, make sure to mark the result as cm³.
PLS HELP- please look at the picture below
9514 1404 393
Answer:
1/3
Step-by-step explanation:
To find f(2), we need √(x+1) = 2. That means x+1 = 2^2, so x = 4-1 = 3.
Then f(2) = 1/x = 1/3.
Find the magnitude of the vector. Write your answer in simplified form.
hor
8
6
4
NO
Х
-10
-8
-6
-4
-2
0
2
4
6
8
10
-2
-4
-6
-8
-10
look
[tex] \sqrt{117} [/tex]
Find the value of x.
Answer:
Step-by-step explanation:
Bonsoir,
63°
The value of external angle x intercepted by two tangents is 63°
We have,
From the given figure,
External angle = x
From the definition of external angle intercepted by two tangents.
External angle = 1/2 x difference of the intercepted arc length
Now,
Difference of the arc length.
= 243 - (360 - 243)
= 243 - 117
= 126
Now,
Substituting the values.
External angle = 1/2 x difference of the intercepted arc length
= 1/2 x 126
= 63
Thus,
The value of external angle x is 63°
Learn mroe about intercepted arc here:
https://brainly.com/question/32892950
#SPJ6
Mathhhhhhhhhhhhhhhhhhhhhhhh Algebraaaaaaaa
Answer:
m=5/3
Step-by-step explanation:
Answer:
5/3 or 1 2/3
Step-by-step explanation:
First you subtract 4/3 from the left side. 23/6-4/3= 2 1/2
Then you multiply 2 on both sides, this simplifies the left side to be 3m and the right side 5.
Lastly, you divide by 3 to isolate the variable m.
And you get 5/3, which also equals 1 2/3
I order 700 notebooks by accident. I only need 3⁄7 of my order. How many notebooks do I return?
I have to return 400 notebooks.
Here, we have,
given that,
I order 700 notebooks by accident. I only need 3⁄7 of my order.
To determine how many notebooks you need to return, you can calculate 4/7 of your order, which represents the portion you don't need.
Let's calculate it step by step:
Calculate the number of notebooks you don't need:
4/7 * 700 = 400
we have,
I only need 3⁄7 of my order.
so, i need = 3/7 * 700
= 300
Subtract the number of notebooks you need from the total order to find the number of notebooks you should return:
700 - 300 = 400
Therefore, you should return 400 notebooks.
To learn more on subtraction click:
brainly.com/question/2346316
#SPJ2
[tex]B=(\frac{-3}{16} x^{2} y) . (4x^{4}y^{3})[/tex]
Answer:
[tex]B=-\frac{3}{4}x^6y^4[/tex]
Step-by-step explanation:
One is given the following equation:
[tex]B=(\frac{-3}{16}x^2y)(4x^4y^3)[/tex]
Multiply each term in one of the parenthesis by its like term in the other. Bear in mind, since all of the operations in this equation are multiplication, one doesn't have to multiply every single term by another in the parenthesis, one only has to multiply like terms to simplify.
[tex]B=(\frac{-3}{16}x^2y)(4x^4y^3)[/tex]
[tex]B=(\frac{-3}{16})(4)(x^2)(x^4)(y)(y^3)[/tex]
Simplify further, remember, when multiplying two terms with the same base, one can add their exponents to simplify,
[tex]B=(\frac{-3}{16})(4)(x^2)(x^4)(y)(y^3)[/tex]
[tex]B=(\frac{-3*4}{16})(x^2^+^4)(y^1^+^3)[/tex]
[tex]B=(\frac{-3*4}{16})(x^6)(y^4)[/tex]
Now simplify the fraction, remove like terms found in both the numerator and denominator. Remember, (4) is a factor of both (4) and (16):
[tex]B=(\frac{-3*4}{16})(x^6)(y^4)[/tex]
[tex]B=(-\frac{3}{4})(x^6)(y^4)[/tex]
[tex]B=-\frac{3}{4}x^6y^4[/tex]
What number could be added to 0.40 mL for the level pf precision to be 0.01mL?
Answer:
-0.39mL
Step-by-step explanation:
Let x be the number.
The expression would be: 0.40 + x = 0.01
Apply algebra to the equation to solve for x. You can subtract 0.40 from each side to simplify the expression. Here's what it should look like after applying algebra: x = -0.39
Therefore the answer is -0.39mL
The city soccer club has thirteen new members and fifty-two returning members. If they break up into teams of eleven players, how many complete teams would there be?
Answer:
5
Step-by-step explanation:
The easiest way to do this is to add the new members to the old and then divide by 11. Ignore the remainder.
13 + 52 = 65
65 / 11 = 5 with 10 left over. Ignore the 10. That's not a complete team.
The answer is 5
A square has a perimeter of 32 and one vertex at (6,8). what could be the location of another vertex of this shape?
PLEASE HELP I AM IN A RUSH!!!
Answer:
6,5
Step-by-step explanation:
Answer:
(6,0),(-2,8),(-2,0)
20. Find the midpoint between the given points.
(3, -8) and (-5, -13)?
I need an answer fast! help if you can!
Hi there! :)
Answer:
[tex]\huge\boxed{(-1, -10.5)}[/tex]
Use the midpoint formula to solve for the midpoint:
[tex](x_{m}, y_{m}) = (\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2}}{2})[/tex]
Plug in the points:
[tex](x_{m}, y_{m}) = (\frac{-5+3 }{2} , \frac{-13 -8}{2})[/tex]
Simplify:
[tex](x_{m}, y_{m}) = (\frac{-2 }{2} , \frac{-21}{2})[/tex]
[tex](x_{m}, y_{m}) = (-1 , -10.5)[/tex]
A retailer allowed 4%. discount on her his
goods to make 20 %profit and sold a refrigerator
for Rs.10848 with 13%. VAT . By how much
is the discount percent to be increased so that
she lhe gained only 15 % profit ?
Answer:
8%
Step-by-step explanation:
Let the cost price of the goods be $y. Let us assume the selling price of the goods is $x. The retailer sold at 4% discount, this means it was sold for 0.96x (100% - 4% = 96%). Since the goods was sold to make 20% profit, therefore it was sold for 1.2y (100% + 20% = 120%).
The refrigerator was sold at 13% VAT at Rs. 10848:
1.2y + 13%(1.2y) = 10848
1.2y + 0.13(1.2y) = 10848
1.2y + 0.156y = 10848
1.356y = 10848
y = 8000
The cost price is Rs 8000.
The selling price is:
0.96x = 1.2y
0.96x = 1.2(8000)
x = 10000
The selling price is Rs. 10000
For a profit of 15%, that is 1.15(8000) = 9200, the discount is:
(1 - discount)10000 = 9200
1 - discount = 0.92
Discount = 1 - 0.92 = 0.08
Discount = 8%
A student decided to research primate psychology for their science project. They measured how long it took gorillas to adapt to their new habitat when moved from one zoo to another. They measured how long it took the new gorilla to interact regularly (more than 3 times per day) with the gorillas that already live there. Seven different cases were examined and the data collected. What can be said about the data?
The question is not complete, so i have attached it.
Answer:
Option A - The data may not be reliable because there is an outlier.
Step-by-step explanation:
Looking at the question attached and the number of the gorrila vis - a - vis the time to interact, we can see that majority of the time to interact falls between 2.5 and 3.4.
However, we have a time of 8.3 days which is for gorrila 3.
This 8.3 is far higher than the range of the other values. Thus, we have an outlier because an outlier is a value is much more smaller or larger than most of the other values in a set of given data.
Thus, the data may not be reliable because there is an outlier.
A plumber’s apprentice needs to cut a 54-inch length of pipe so that one piece is twice the length of the other piece. How far from the endpoint should the apprentice cut the pipe?
Answer:
18 inches
Step-by-step explanation:
To to this you would just divide 54 by 3 and you would get how far away from the endpoint which is 18 inches
the x-intercept of the function f(x)=x^2-81
Answer:
hendoebhdjdbdjjsjsnsnns
jskebeuejbeiwnwvgwvshcc
Answer:
x=9
x=-9
Step-by-step explanation:
The x intercept or roots are x values that makes the f(x) equal 0. So in order words, to find the x intercept. Set the equation equal 0.
[tex] {x}^{2} - 81 = 0[/tex]
We can approach this problem 2 ways
Way 1: Differnece of Squares
Recall that
[tex]a {}^{2} - {b}^{2} = (a + b)(a - b)[/tex]
Since x^2 and 81 are both perfect squares and 81 is negative, we can say that
[tex](x + 9)(x - 9) = 0[/tex]
Set each equation to zero
[tex]x = 9[/tex]
[tex]x = - 9[/tex]
Way 2: Take square root of both sides
[tex] {x}^{2} - 81 = 0[/tex]
[tex] {x}^{2} = 81[/tex]
Next step, take square root of both sides. Square root produce negative and positive solutions so
[tex]x = 9[/tex]
or
[tex]x = - 9[/tex]
Determine the quadrant(s) in which (x, y) could be located. (Select all that apply.) x > 0 and y < 0 Quadrant I Quadrant II Quadrant III Quadrant IV none of these
Answer:
Quadrant IV
Step-by-step explanation:
If x is greater than 0, then it will remain on the right side, on quadrants I and IV. If y is less than 0, then it will be on the bottom, so we are left with quadrant IV:
x is greater than 0, so all possible values are positive
y is less than 0, so all possible values are negative
(x,-y)
Following are the description of the wrong choice:
In the first Quadrant, (x,y) both -axis values are positive that's why it is wrong.In the second Quadrant, the x-axis has a negative value and the y-axis has a positive value that's why it's wrong.In the third Quadrant, (x,y) both -axis has the negative value that's why it is wrong.That's why the "Quadrant IV" is the correct answer.
Learn more:
quadrant: brainly.com/question/7196054Black Diamond Ski Resort charges $25 for ski rental and $10 an hour to ski. Bunny Hill Ski Resort charges $50 for ski rental and $5 an hour to ski. Create an equation to determine at what point the cost of both ski slopes is the same.
Answer:
25 + 10h = 50+5h
Step-by-step explanation:
Black Diamond Ski Resort
25 + 10h
Bunny Hill Ski Resort
50+5h
We want when they are equal
25 + 10h = 50+5h
Answer:
10x + 25 = 5x + 50
Step-by-step explanation:
Solve for x 3x - 4 = 2x - 10
Answer:
-6
Step-by-step explanation:
To solve this problem, you should move all of the variables onto one side, and all of the constants onto the other side as such:
3x-4=2x-10
+10 +10
3x+6=2x
-3x -3x
6=-x
/-1 /-1
x=-6
Hope this helps!
P.S. Please give me brainliest. Thanks :)
Answer:
[tex]x = -6[/tex]
Step-by-step explanation:
Looking at the expression [tex]3x - 4 = 2x - 10[/tex], our goal is to get rid of the x term on one side.
To do this, we can subtract 2x from both sides which gets us
[tex]x - 4 = -10[/tex]
Add 4 to both sides:
[tex]x = -6[/tex]
Hope this helped!
what is 45/99 simply
Answer:
5/11
Step-by-step explanation:
divide numerator and denominator by 9
5/11
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
Answer:
5/11
Step-by-step explanation:
45/99
Divide the top and bottom by 9
45/9 = 5
99/9 = 11
5/11
In March, Mateo ran 19 miles. In April, he ran twice as many miles as he ran in March. In May, he ran four times as many miles as he did in April. How many total miles did Mateo run in the three months? Enter your answer in the box.
Answer:
209
Step-by-step explanation:
march = 19 miles
april = 19 times 2 = 38
may = 38 times 4 = 152
so that'd be 19 + 38 + 152 = 209 miles in total.
209 miles Mateo ran in the three months.
What is Simplification?Simplification in mathematical terms is a process to convert a long mathematical expression in simple and easy form.
Given that,
Mateo ran in March = 19 miles,
Also,
Mateo ran in April = 2 times of ran in March = 2 x 19 = 38 miles
Mateo ran in May = 4 times of ran in April = 4 x 38 = 152 miles.
Total distance ran by Mateo in all three months
= ran in March + ran in April + ran in May
= 19 + 38 + 152
= 209 miles.
Mateo ran 209 miles in all three months.
To know more about Simplification on :
https://brainly.com/question/2804192
#SPJ2
Can someone plz help me ASAP!!!!!!!!
Answer:
A) The number halfway between -2 and 6 is 2.
B) -10 is halfway between -18 and 8
Combine like terms to create an equivalent expression. 3.4-2.8d+2.8d-1.3
Answer:
2.1Step-by-step explanation:
[tex]3.4-2.8d+2.8d-1.3\\\\\mathrm{Add\:similar\:elements:}\:-2.8d+2.8d=0\\\\=3.4-1.3\\\\\mathrm{Subtract\:the\:numbers:}\:3.4-1.3\\\\=2.1[/tex]
if f(x) =7x+5/3-x, then show that fof power -1(x) is an identity function
Answer:
please see the steps in the picture
Write as an equation: Sara spent $2 more than Lauren, and together they spent $19.
Answer:
Equations:
a + b = 19
a = b + 2
a = Money that spent Laura
b = Money that spent Laureen
then:
(b+2) + b = 19
2b + 2 = 19
2b = 19-2
2b = 17
b = 17/2
b = 8.5
a = b + 2
a = 8.5 + 2
a = 10.5
Check:
10.5 + 8.5 = 19
What is the value of m that makes the equation true? 18m- 2+ 7m- 8= -60
Answer:
m = -2
Step-by-step explanation:
First, let's move all variables to one side of the equation. (Don't forget to change the signs when you move the numbers to the other side.)
18m + 7m = -60 + 2 + 8
Now we simplify to get this:
25m = -50
Now we divide -50 by 25 which gets us -2.
Therefore, m = -2
Hope this helps!
I am an odd two-digit number. The sum of my two digits is 10 and the difference of my two digits is 0. What number am I?