Answer:
y = 1/3x -2
Step-by-step explanation:
the equation for slope intercept form is y= mx + b.
m is the slope and b is where the line crosses the y-axis which is called the y-intercept.
to find the y-intercept plug in a coordinate on the line (6,0)
0 = 1/3(6) + b
then solve for b by first multiplying 1/3 by 6
0 = 2 + b
subtract 2 from both sides
-2 = b
and then you can plug b into the equation
y = 1/3x - 2
It’s time to lock down the design details for the redesigned Brick and Egyptian candles. Because of manufacturing constraints, the base length for each candle has to be at least 2 cm and can be no more than 10 cm. Make a recommendation for the base dimensions of each candle. Explain how you determined your base dimensions. Your reasoning does not have to be all math related.
Answer:
THE SMALLEST FORMS:
- smallest prism ---> the cube with all sides 2 ==> the volume is 2*2*2 = 8 cm^3
- smallest pyramid number one ---> the pyramid with base sides 2 and the height also 2 ==> the volume is (1/3)*2*2*2 = 8/3 cm^3
- smallest pyramid number two ---> the pyramid with base sides 2 and the lateral sides also 2 ==> the radius of the base is sqrt(2) ==> [pyramid_height]^2 = [lateral_side]^2 - [base_radius]^2 = 2^2 - sqrt(2)^2 = 4 - 2 = 2 ==> pyramid_height = sqrt(2) ==> the volume is (1/3)*2*2*sqrt(2) = 4*sqrt(2)/3 cm^3
- smallest cylinder --> the cylinder of diameter 2 and height also 2 ==> the radius is diameter/2 = 2/2 = 1 ==> the volume is pi*(radius^2)*height = pi*(1^2)*2 = pi*1*2 = 2*pi cm^3
The lesser volume is the volume of the smallest pyramid number two. ==> it's wax cost is approximately 0.0075 * 4 * 1.42 / 3 $ per candle = 0.014 $ per candle ==> the total cost per candle is approximately 0.014 + 1.6 = 1.614 $ per candle.
THE BIGGEST FORMS:
- biggest prism ---> the cube with all sides 10 ==> the volume is 10*10*10 = 1000 cm^3
- biggest pyramid number one ---> the pyramid with base sides 10 and the height also 10 ==> the volume is (1/3)*10*10*10 = 1000/3 cm^3
- biggest pyramid number two ---> the pyramid with base sides 10 and the lateral sides also 10 ==> the radius of the base is 5*sqrt(2) ==> [pyramid_height]^2 = [lateral_side]^2 - [base_radius]^2 = 10^2 - [5*sqrt(2)]^2 = 100 - 50 = 50 ==> pyramid_height = 5*sqrt(2) ==> the volume is (1/3)*10*10*5*sqrt(2) = 500*sqrt(2)/3 cm^3
- biggest cylinder --> the cylinder of diameter 10 and height also 10 ==> the radius is diameter/2 = 10/2 = 5 ==> the volume is pi*(radius^2)*height = pi*(5^2)*10 = pi*25*10 = 250*pi cm^3
The bigger volume is the volume of the biggest prism (the side-10 cube). ==> it's wax cost is 0.0075 * 1000 $ per candle = 7.5 $ per candle ==> the total cost per candle is 7.5 + 1.6 = 9.1 $ per candle
The range of the cost is the interval [1.614 ; 9.1]. Depending on other prices on the market, you greed, and other factors you will put a profit margin: maybe 20% of the cost ; maybe a fixed margin like 5$. So the price per candle will be the cost per candle plus the profit margin per candle.
If I were to choose the base length I would have to say 6 because it is the arithmetic mean between 2 and 10: (2+10)/2 = 12/2 = 6. 2cm is too small, and 10cm is too big.
Also if you start with a rectangle of length 10 and width 2 and you have to find the rectangle with the largest area by being allowed to increase the width and decrease the width with the same quantity you get this:
Area of the new rectangle is (10-x)(2+x) = -x^2 + 8x + 20 = -x^2 + 8x -16 + 36 = -(x^2 - 2*x*4 + 4^2) + 36 = -(x-4)^2 + 36 = 36 - (x-4)^2 which has the maximum value of 36 because out of 36 you subtract a positive value. You get the maximum when (x-4)^2 = 0 ==> x-4=0 ==> x=4
The new length is 10-4=6 and the new width is 2+4=6.
Next I would choose the height of the prism (I like prisms :P) to be [the_golden_ratio]*[base_side] which is approximately 1.618 * 6 = 9.708 which I would round up to 10. ==> The volume would be 6*6*10 = 360 cm^3. ==> the cost would be 0.0075*360 + 1.6 = 2.7 + 1.6 = 4.3 $ per candle. And because my candle is so perfect I'd put the profit margin to be 5.69 $ per candle so I can proudly show it in the store with the price of 4.3 + 5.69 = 9.99 $ :)
Simplify:
3-2i
-11-8i
Answer:
1i and -19i
Step-by-step explanation:
3-2=1, therefor: 1i
-11-8=-19, therefor: -19i
what is the surface area of the square pyramid (pic attached)
Answer:
18ft2
Step-by-step explanation:
4m + 7 = -3m + 49 what does this
Answer: m = 6
Step-by-step explanation:
first, move the terms.
4m + 3m = 49 - 7
then, collect like terms and calculate.
7m = 42
then divide both sides.
m = 6
Answer:
m=42
Step-by-step explanation:
simplifying both sides of the equation then isolating the variable.
Plz help me with this
Answer:
The first choice
Step-by-step explanation:
It says that its decreasing so the slope is negative.
It also starts of with 565 so that's the y intercept
In the equation, f(x)=2x-4(x+1), what is the value of f(-14)?
A. 32
B. -32
C. 5
D. 24
Answer:
D. 24
Step-by-step explanation:
Plug in -14 to the equation:
f(x) = 2x - 4(x + 1)
f(-14) = 2(-14) - 4(-14 + 1)
Simplify:
f(-14) = -28 - 4(-13)
f(-14) = -28 + 52
f(-14) = 24
So, D is the correct answer.
[tex] \sqrt[3]{( \frac{1}{8} - x)} = - \frac{1}{2} [/tex]
what is the answer?
∛(1/8 - x) = -1/2
Take the 3rd power of both sides and solve:
(∛(1/8 - x))³ = (-1/2)³
1/8 - x = -1/8
2/8 = x
x = 1/4
Match each table to the slope it represents
Answer:
I dont see anything how am I supposed to
In the given figure, ABCD is a trapezium in which AD || BC,
ABC = 90°, AD = 16 cm, AC = 41 cm and BC = 40 cm. Find the
area of the trapezium,
Answer:
252 cm²
Step-by-step explanation:
Find AB:
AB² = 41² - 40²
AB² = 81
AB = √81
AB = 9 cm
Area of the trapezium = ½(a + b) × h
Where,
a = 16 cm
b = 40 cm
h = 9 cm
Area = ½(16 + 40) × 9
Area = ½(56)×9
Area = 252 cm²
A soup can has a height of 4 cm and a radius of 3 cm
Answer:
what's the question
................
1/3^3= 1/27 I will need this answer soon as possible plz
Reduce by cancelling the common factors.
(13)x−1=27 Convert the exponential equation to a logarithmic equation using the logarithm base (13) of the right side (27) equals the exponent (x−1)log13(27)=x−1
3/4 square feet in 1/4 hour
Answer:
ill assume you're asking the answer for 1 hour
Step-by-step explanation:
multiply each side by 4. then, 12/4(3)=1
so 3 square feet and hour
Maurice has a paper bag with three hard candies: two blueberries and one green apple. Yvonne and Kate ask if they can each have one. Yvonne closes her eyes and picks a candy from the bag, hoping for a blueberry. What are the chances she will pick a blueberry candy?
Answer:
The chances of Yvonne to get a blue berry candy in the two cases are 1 and 1/2 in case 1 and 2/3 in the case 2.
Step-by-step explanation:
Maurice has a paper bag with three hard candies
2 blueberries and 1 green apple
Yvonne and Kate want 1 candy each
It is not mentioned that ether Kate has taken a candy already before Yvonne or not so we will consider both the cases
Case 1
If Kate has picked a candy before Yvonne
If Kate gets an Apple green candy then the probability or Yvonne to get a Blueberry will be = 2/2 = 1 ( as there will 2 blueberry candy left in the bag)If Kate has taken a Blueberry candy then there will be 1 blueberry and 1 apple green candy in the bag so the probability of Yvonne to get a Blueberry candy will be = 1/2Case 2
If Kate has not taken any candy from the bag before Yvonne
Probability that Yvonne will get a blueberry candy will be = 2/3
Therefore the chances of Yvonne to get a blue berry candy in the two cases are 1 and 1/2 in case 1 and 2/3 in the case 2.
17q=476 Solve for q
Answer: The answer is q = 28.
Please answer correctly !!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!!
Answer:
For every 2 boys in class, there is 1 girl in class
Step-by-step explanation:
(0,0)
M is the midpoint of CD. If the midpoint M
is (-3, 5) and C is (2,3), then what are the
coordinates of D?
O
(-1/2,4)
(-8,7)
o
(-4,1)
Answer:
The answer is (3-,5) watch is C cause if you do that but in math form it's the same
By which rule are these triangles congruent?
A) AAS
B) ASA
C) SAS
D) SSS
Answer:
A) AAS
Step-by-step explanation:
solve 3^x+3=30 (will give brainlest for the correct answer)
Answer:
x=3
Step-by-step explanation:
3^x+3=30
3^x=27
3^3=27
x=3
Answer:
Step-by-step explanation:
3 x 3 = 9 + 3 = 12
30 divided by 12
= 2.5
Find the value of k , if one of the two roots of the equation : x2 + k X – 98 = 0 is double
the additive inverse of the other.
«+
C
Given:
[tex]x^2+kx-98=0[/tex]
One of the two roots of the given equation is double the additive inverse of the other.
To find:
The value of k.
Solution:
Let two roots of the given equation are [tex]\alpha[/tex] and [tex]\beta[/tex].
According to the question,
[tex]\beta=2(-\alpha)[/tex] (Additive inverse of [tex]\alpha[/tex] is [tex]-\alpha[/tex])
[tex]\beta=-2\alpha[/tex]
If [tex]\alpha[/tex] and [tex]\beta[/tex] are roots of the quadratic equation [tex]ax^2+bx+c=0,[/tex] then
[tex]\alpha+\beta=-\dfrac{b}{a}[/tex]
[tex]\alpha\beta=\dfrac{c}{a}[/tex]
We have,
[tex]x^2+kx-98=0[/tex]
Here, a =1, b=k and c=-98.
[tex]\alpha+\beta=-\dfrac{k}{1}[/tex]
[tex]\alpha-2\alpha=-k[/tex] [tex][\because \beta=-2\alpha][/tex]
[tex]-\alpha=-k[/tex]
[tex]\alpha=k[/tex] ...(i)
Now,
[tex]\alpha\beta=\dfrac{c}{a}[/tex]
[tex]\alpha(-2\alpha)=\dfrac{-98}{1}[/tex] [tex][\because \beta=-2\alpha][/tex]
[tex]-2\alpha^2=-98[/tex]
Divide both sides by -2.
[tex]\alpha^2=49[/tex]
Taking square root on both sides.
[tex]\alpha=\pm \sqrt{49}[/tex]
[tex]\alpha=\pm 7[/tex]
Using (i), we get
[tex]k=\pm 7[/tex]
Therefore, the value of k is either -1 or 1.
I NEED HELP ASAP
A student wrote and simplified an expression for the perimeter of the rectangle. (Using the picture provided.)
perimeter
Explain the mistake that was made in the simplified expression. Include the correct simplified expression in your explanation. Be sure to use math vocabulary words.
Answer:
Step-by-step explanation:
Last one
helpppppppppppppppppppppppp meeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: The answer is C
Step-by-step explanation:
2. Solve:
у = 3х
x = -2y + 70
Answer: (10,30)
Step-by-step explanation:
y = 3x
x = -2y + 70
Solve by using the substitution method. Substitute the value for x into the first equation and solve for y.
y = 3(-2y + 70) Multiply it out
y = -6y + 210 Add 6y to both sides
+6y +6y
7y = 210
y = 30
Since y is equal to 30, input the value for y into the equation and solve for x.
30 = 3x Divide both sides by 3
x = 10
The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1500 after 1 day, what is the size of
the colony after 3 days? How long is it until there are 80,000 mosquitoes?
The size of the colony after 3 days is approximately mosquitoes.
Answer:
There are 2,500 misquitos after 3 days and it takes 158 days to reach 80,000 mosquitos.
PLS HELP MATHH!!! FIVE STARS!!!
Polynomials are closed under subtraction.
Question 22 options:
True
False
Answer:
True
Step-by-step explanation:
sry if it wrong
A student can run 100 yards in 15 seconds. Convert this speed to miles per hour.
what two numbers add up to be 116.5
Answer:
58.25
Step-by-step explanation:
116.5 / 2
= 58.25
Hope this helps!!
58.25+58.25
Those are the two numbers that add up to that number (116.5)
Btw there are also MULTIPLE numbers that add up to 116.5, I'm just putting the one that makes the most sense.
(｡ŏ﹏ŏ)
Miri
I give Brainlliest! 15 pionts!
Write the decimal as a percent.
0.768 =
Answer:
76.8%
Step-by-step explanation:
All you have to do is multiply the decimal by 100.
Answer:
76.8%
Step-by-step explanation:
I just did a thing and got the answer -v-
plz help me if you see this
Quantity
0-20 pairs
21-40 pairs
41-60 pairs
61-80 pairs
81 or more pairs
Wholesale Price
(per pair)
$25.00 each
$23.00 each
$21.00 each
$19.00 each
$17.00 each
a) Write an equation that could be used to find the retail price for each range.How do you know the equation will work consistently for each range? plz help me if you see this
Answer:
I am confused on what you are asking but I think the answer is y=12345x
Step-by-step explanation:
its correct
Element X is a radioactive isotope such that every 20 years, its mass
decreases by half. Given that the initial mass of a sample of Element X is 410
grams, how long would it be until the mass of the sample reached 270 grams,
to the nearest tenth of a year?
Answer:
12.1
Step-by-step explanation:
y=a(1/2)^t/h
270=410(1/2)^t/20
Divide both sides by 410
0.6585365854 = (1/2)^t/20
Log Both sides
Log(0.6585365854) / Log(1/2)
.6026645024= t/20
20 x .6026645024 = t
12.05329005 to the nearest tenth is 12.1 = t
Probability question 2
A number cube is rolled once....
