Answer:
Y = x + 3
Step-by-step explanation:
The first equation has a slope of 1 so this new one must get the y intercept you must subtract 1 from both the x and the y. Then use the same slope.
Answer:
Y = x + 3
Step-by-step explanation:
The first equation has a slope of 1 so this new one must get the y intercept you must subtract 1 from both the x and the y. Then use the same slope.
A charity sells tickets for a fundraising dinner. Each adult's ticket cost $10 and each child's ticket cost $5. A total of $1050 was raised by selling 130 tickets. How many adult and child tickets were sold? Let x represent the number of adult tickets and y represent the number of child tickets.
Number of Adult Tickets Sold =
Number of Child Tickets Sold =
Answer:43
Step-by-step explanation:
The expression 4x − 2(5x − 1) is equivalent to the expression 2 + 6x.
True
False
It is false that the expressions 4x − 2(5x − 1) and 6x + 2 are equivalent expressions
How to determine the true statement?The expression is given as:
4x − 2(5x − 1)
Open the bracket
4x − 2(5x − 1) = 4x − 10x + 2
Evaluate the like terms
4x − 2(5x − 1) = − 6x + 2
− 6x + 2 and 6x + 2 are not equal expressions
Hence, 4x − 2(5x − 1) and 6x + 2 are not equivalent expressions
Read more about equivalent expressions at:
https://brainly.com/question/2972832
#SPJ2
1. 8x^2 + 10x - 9
2. 3x^4 - 14x^2 - 9
3. 4x^2 + 5x - 9
4. 8x^2 + 10x - 18
Answer:
4.
Step-by-step explanation:
(x^2 + 7x - 9) + (3x^2 - 2x) + (x^2 + 7x - 9) + (3x^2 - 2x)
x^2 + 7x - 9 + 3x^2 - 2x + x^2 + 7x - 9 + 3x^2 - 2x
Rearranging order:
3x^2 + 3x^2 + x^2 + x^2 + 7x + 7x - 2x - 2x - 9 - 9
Combine like terms
8x^2 + 10x - 18
What is 15 divided by 7.4?
The Shredder, Inc. produces two types of paper shredders, home and office. The office model requires 6 hours to assembly and 2 finishing work units for finishing work, the home model requires 4 hours to assemble and 12 finishing work units for finishing. The maximum number of assembly hours available is 96 per day, and the maximum number of finishing hours available is 96 per day.
Let
x = the number of office model shredders produced per day and
y = the number of home model shredders produced per day.
Write the system of inequalities that represents the maximum number of shredders that can be produced in one day.
NOTE: 4 inequalities are expected.
Answer:
4y + 6x ≤ 96
12y + 2x ≤ 96
Step-by-step explanation:
Paper shredders produced :
Home :
Assembling time = 4 hours
Finishing work unit = 12
Office :
Assembling time = 6 hours
Finishing work unit = 2
Maximum number of assembly hours = 96 / day
Maximum number of finishing hours = 96/ day
Let
x = the number of office model shredders produced per day and
y = the number of home model shredders produced per day
(office Assembly hours x Number of office model) + (Assembly hours * number home models)
OFFICE MODEL:
Assembly operation :
Home + office ≤ 96
4y + 6x ≤ 96
Finishing operation :
Home + office ≤ 96
12y + 2x ≤ 96
Help please !!!!! Thanks
Answer:
7) y = -2
8) x = 4
Step-by-step explanation:
Any straight horizontal/vertical line you find will be x= or y=. The vertical lines are always x= because they only touch the x axis. It's the opposite for horizontal lines. For example, on number 7, the line touches -2 on the y axis. That's why it's "y=-2". Same goes for 8. the line only touches 4.
I hope this helped and wasn't confusing!
How many factors are in a B + CD + EF + GH
The given expression is
=ab+cd+ef+gh
The meaning of expression is equal to terms which contains variables and constants and operation between them is Addition, Subtraction, Multiplication and Division.
→The expression consists of four terms which are, ab, cd, ef, and gh.
→Each term contains
Two factors.
plz mark as brainliest
Patrick is 5.432 feet tall, Ivan is 5.503 feet tall, Laura is 5.413 feet tall, and Daisy is 5.510 feet tall. Which of the following lists them in order from tallest to shortest?
Answer:
Daisy, Ivan, Patrick, Laura
Step-by-step explanation:
That's just the numbers biggest to smallest.
A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 10 cubic centimeters. Find the radius of the cylinder that produces the minimum surface area. (Round your answer to two decimal places.)
Answer:
[tex]r = 1.34[/tex]
Step-by-step explanation:
Given
Solid = Cylinder + 2 hemisphere
[tex]Volume = 10cm^3[/tex]
Required
Determine the radius (r) that minimizes the surface area
First, we need to determine the volume of the shape.
Volume of Cylinder (V1) is:
[tex]V_1 = \pi r^2h[/tex]
Volume of 2 hemispheres (V2) is:
[tex]V_2 = \frac{2}{3}\pi r^3 +\frac{2}{3}\pi r^3[/tex]
[tex]V_2 = \frac{4}{3}\pi r^3[/tex]
Volume of the solid is:
[tex]V = V_1 + V_2[/tex]
[tex]V = \pi r^2h + \frac{4}{3}\pi r^3[/tex]
Substitute 10 for V
[tex]10 = \pi r^2h + \frac{4}{3}\pi r^3[/tex]
Next, we make h the subject
[tex]\pi r^2h = 10 - \frac{4}{3}\pi r^3[/tex]
Solve for h
[tex]h = \frac{10}{\pi r^2} - \frac{\frac{4}{3}\pi r^3 }{\pi r^2}[/tex]
[tex]h = \frac{10}{\pi r^2} - \frac{4\pi r^3 }{3\pi r^2}[/tex]
[tex]h = \frac{10}{\pi r^2} - \frac{4r }{3}[/tex]
Next, we determine the surface area
Surface area (A1) of the cylinder:
Note that the cylinder is covered by the 2 hemisphere.
So, we only calculate the surface area of the curved surface.
i.e.
[tex]A_1 = 2\pi rh[/tex]
Surface Area (A2) of 2 hemispheres is:
[tex]A_2 = 2\pi r^2+2\pi r^2[/tex]
[tex]A_2 = 4\pi r^2[/tex]
Surface Area (A) of solid is
[tex]A = A_1 + A_2[/tex]
[tex]A = 2\pi rh + 4\pi r^2[/tex]
Substitute [tex]h = \frac{10}{\pi r^2} - \frac{4r }{3}[/tex]
[tex]A = 2\pi r(\frac{10}{\pi r^2} - \frac{4r }{3}) + 4\pi r^2[/tex]
Open bracket
[tex]A = \frac{2\pi r*10}{\pi r^2} - \frac{2\pi r*4r }{3} + 4\pi r^2[/tex]
[tex]A = \frac{2*10}{r} - \frac{2\pi r*4r }{3} + 4\pi r^2[/tex]
[tex]A = \frac{20}{r} - \frac{8\pi r^2 }{3} + 4\pi r^2[/tex]
[tex]A = \frac{20}{r} + \frac{-8\pi r^2 }{3} + 4\pi r^2[/tex]
Take LCM
[tex]A = \frac{20}{r} + \frac{-8\pi r^2 + 12\pi r^2}{3}[/tex]
[tex]A = \frac{20}{r} + \frac{4\pi r^2}{3}[/tex]
Differentiate w.r.t r
[tex]A' = -\frac{20}{r^2} + \frac{8\pi r}{3}[/tex]
Equate A' to 0
[tex]-\frac{20}{r^2} + \frac{8\pi r}{3} = 0[/tex]
Solve for r
[tex]\frac{8\pi r}{3} = \frac{20}{r^2}[/tex]
Cross Multiply
[tex]8\pi r * r^2 = 20 * 3[/tex]
[tex]8\pi r^3 = 60[/tex]
Divide both sides by [tex]8\pi[/tex]
[tex]r^3 = \frac{60}{8\pi}[/tex]
[tex]r^3 = \frac{15}{2\pi}[/tex]
Take [tex]\pi = 22/7[/tex]
[tex]r^3 = \frac{15}{2 * 22/7}[/tex]
[tex]r^3 = \frac{15}{44/7}[/tex]
[tex]r^3 = \frac{15*7}{44}[/tex]
[tex]r^3 = \frac{105}{44}[/tex]
Take cube roots of both sides
[tex]r = \sqrt[3]{\frac{105}{44}}[/tex]
[tex]r = \sqrt[3]{2.38636363636}[/tex]
[tex]r = 1.33632535155[/tex]
[tex]r = 1.34[/tex] (approximated)
Hence, the radius is 1.34cm
The radius of the cylinder that produces the minimum surface area is 1.34cm and this can be determined by using the formula area and volume of cylinder and hemisphere.
Given :
A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 10 cubic centimeters.The volume of a cylinder is given by:
[tex]\rm V = \pi r^2 h[/tex]
The total volume of the two hemispheres is given by:
[tex]\rm V' = 2\times \dfrac{2}{3}\pi r^3[/tex]
[tex]\rm V' = \dfrac{4}{3}\pi r^3[/tex]
Now, the total volume of the solid is given by:
[tex]\rm V_T = \pi r^2 h+\dfrac{4}{3}\pi r^3[/tex]
Now, substitute the value of the total volume in the above expression and then solve for h.
[tex]\rm 10 = \pi r^2 h+\dfrac{4}{3}\pi r^3[/tex]
[tex]\rm h = \dfrac{10}{\pi r^2}-\dfrac{4r}{3}[/tex]
Now, the surface area of the curved surface is given by:
[tex]\rm A = 2\pi r h[/tex]
Now, the surface area of the two hemispheres is given by:
[tex]\rm A'=2\times (2\pi r^2)[/tex]
[tex]\rm A'=4\pi r^2[/tex]
Now, the total area is given by:
[tex]\rm A_T = 2\pi rh+4\pi r^2[/tex]
Now, substitute the value of 'h' in the above expression.
[tex]\rm A_T = 2\pi r\left(\dfrac{10}{\pi r^2}-\dfrac{4r}{3}\right)+4\pi r^2[/tex]
Simplify the above expression.
[tex]\rm A_T = \dfrac{20}{r} + \dfrac{4\pi r^2}{3}[/tex]
Now, differentiate the total area with respect to 'r'.
[tex]\rm \dfrac{dA_T}{dr} = -\dfrac{20}{r^2} + \dfrac{8\pi r}{3}[/tex]
Now, equate the above expression to zero.
[tex]\rm 0= -\dfrac{20}{r^2} + \dfrac{8\pi r}{3}[/tex]
Simplify the above expression in order to determine the value of 'r'.
[tex]8\pi r^3=60[/tex]
r = 1.34 cm
For more information, refer to the link given below:
https://brainly.com/question/11952845
What is the simplest form for 15:25
Answer:
3/5
Step-by-step explanation:
Both can be divided by 5. So, 15 divided by 5 is 3, and 25 divided by 5 is 5! Hoped this helped :)
What comes between 1/2 and 2/3
Answer:
3/5
Step-by-step explanation:
1/2 can be written as 50%
2/3 can be written as 66.66%
3/5 can be written as 60%
Here
Step-by-step explanation:
The example fractions of 1/2, 2/3 and 3/4 with common denominators become 6/12, 8/12 and 9/12. The numerator 8 is between 6 and 9, so the fraction you created – 8/12, or 2/3 when simplified – is between the two fractions you started with.
The sum of a first and second number is 130. If the second number is 20 less than four times the first number, find the two numbers. Let x represent the first number and y represent the second number.
Write the System of Equations used to solve this problem.
The system of equations used to solve this problem are: x+y=130 and
y=20-4x. For this system x=-110/3 and y=500/3.
System of Linear Equations
System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.
You should convert the text into a math expression:
x+y=130 (1)
y=20-4x (2)
Thus, you should replace the value of y given in equation 2, into equation 1. The,
x+20-4x=130
-3x=130-20
3x=-110
x= - 110/3
Therefore, y will be:
y=20-4*(- 110/3 )
y=20+440/3
y=60/3 +440/3
y=500/3
Learn more about the system of equations here:
brainly.com/question/384631
#SPJ2
Martin is interested in joining a gym and has researched the cost of two gyms close to his
house Gym A has a $50 registration fee and costs $30 per month. Gym B has a $100
registration fee and costs $10 per month. The cost of joining each gym can be modeled by the
expressions below, where m represents the number of months.
• Gym A: 30m + 50
• Gym B: 10m + 100
Answer:
I suppose that you want to find which gym will be cheaper for you.
We have two equations:
• Gym A: 30m + 50
• Gym B: 10m + 100
First, let's find the value of m such that both gyms cost exactly the same:
30*m + 50 = 10*m + 100
Let's solve this for m
30*m - 10*m = 100 - 50
20*m = 50
m = 50/20 = 2.5
now:
for m < 2.5, Gym A will be cheaper, because the y-intercept is smaller.
for m > 2.5, Gym B will be cheaper, because the slope is smaller,
Then depending on the number of months that Martin wants to go to the gym, he can se the info above to pick the one that is cheaper.
88) 4 times a number decreased by 8 equals 40
A) x=80 B) x = 40 C) x=8
D) x = 12
solve the following formula for H. r=n/2(b+H)
Answer:
See below.
Step-by-step explanation:
What you wrote means:
[tex] r = \dfrac{n}{2}(b + H) [/tex]
If that is what you meant, then the answer is:
[tex] \dfrac{2r}{n} = b + H [/tex]
[tex] H = \dfrac{2r}{n} - b [/tex]
On the other hand, if this is what you meant:
[tex] r = \dfrac{n}{2(b + H)} [/tex]
then the answer is:
[tex] 2r(b + H) = n [/tex]
[tex] 2rb + 2rH = n [/tex]
[tex] 2rH = n - 2rb [/tex]
[tex] H = \dfrac{n - 2rb}{2r} [/tex]
Answer:
Step-by-step explanation:
[tex]\frac{n}{2}(b + H) = r\\\\b +H = r * \frac{2}{n}\\\\b + H = \frac{2r}{n}\\\\H = \frac{2r}{n} - b[/tex]
A large tank is partially filled with 100 gallons of fluid in which 20 pounds of salt is dissolved. Brine containing 1 2 pound of salt per gallon is pumped into the tank at a rate of 6 gal/min. The well-mixed solution is then pumped out at a slower rate of 4 gal/min. Find the number of pounds of salt in the tank after 35 minutes.
Answer:
Step-by-step explanation:
From the given information:
[tex]R_{in} = ( \dfrac{1}{2} \ lb/gal) (6)\ gal /min \\ \\R_{in} = 3 \ lb/min[/tex]
Given that the solution is pumped at a slower rate of 4gal/min
Then:
[tex]R_{out} = \dfrac{4A}{100+(6-4)t}[/tex]
[tex]R_{out}= \dfrac{2A}{50+t}[/tex]
The differential equation can be expressed as:
[tex]\dfrac{dA}{dt}+ \dfrac{2}{50+t}A = 3 \ \ \ ... (1)[/tex]
Integrating the linear differential equation; we have::
[tex]\int_c \dfrac{2}{50 +t}dt = e^{2In |50+t|[/tex]
[tex]\int_c \dfrac{2}{50 +t}dt = (50+t)^2[/tex]
multiplying above integrating factor fields; we have:
[tex](50 +t)^2 \dfrac{dA}{dt} + 2 (50 + t)A = 3 (50 +t)^2[/tex]
[tex]\dfrac{d}{dt}\bigg [ (50 +t)^2 A \bigg ] = 3 (50 +t)^2[/tex]
[tex](50 + t)^2 A = (50 + t)^3+c[/tex]
A = (50 + t) + c(50 + t)²
Using the given conditions:
A(0) = 20
⇒ 20 = 50 + c (50)⁻²
-30 = c(50) ⁻²
c = -30 × 2500
c = -75000
A = (50+t) - 75000(50 + t)⁻²
The no. of pounds of salt in the tank after 35 minutes is:
A(35) = (50 + 35) - 75000(50 + 35)⁻²
A(35) = 85 - [tex]\dfrac{75000}{7225}[/tex]
A(35) =69.6193 pounds
A(35) [tex]\simeq[/tex] 70 pounds
Thus; the number of pounds of salt in the tank after 35 minutes is 70 pounds.
A large bucket of 200 golf balls is divided into 4 smaller buckets. How many golf balls are in each small bucket?
Answer:
50 golf balls
Step-by-step explanation:
200/4 is 50. I did that because it says the golf balls are DIVIDED into 4 smaller buckets.
To check the answer you do 50 times four.
Answer:
50 in each small bucket
A school newspaper estimates that their academic team will win 25 out of 30 matches for the season. After 15 matches, they have won 12. If the team continues winning at this rate, what will be the percent error of the newspaper's estimate once the season is over? Round to the nearest percent
Answer:
4
Step-by-step explanation:
The percent error of the newspaper's estimate once the season is over will be 4%.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
A school newspaper estimates that their academic team will win 25 out of 30 matches for the season.
Then the percentage will be given as,
P = (25 / 30) x 100
P = 0.8333 x 10
P = 83.33%
After 15 matches, they won 12. Then the percentage will be given as,
P = (12 / 15) x 100
P = 0.80 x 100
P = 80%
If the team continues winning at this rate. Then the percent error of the newspaper's estimate once the season is over will be
P = [(83.33 - 80) / (83.33)] x 100
P = 0.04 x 100
P = 4%
More about the percentage link is given below.
https://brainly.com/question/8011401
#SPJ5
12 1/2 percent multiple 64
Answer: The answer is 384 if your question is 12x1/2x64
If a car travels 23 miles in 20 min what is the. car speed in miles per hour?
Answer:
69 miles per hour
Step-by-step explanation:
car travels 23 miles in 20 min
So 20 min=20/60hour
=1/3. hour
Speed of the car=23÷1/3
=69 miles/hour
So the final answer is 69miles/hour
Frank wants to go bowling. The bowling alley charges $4 per game and a one-time charger of $3 for bowling shoes. Look at the information below:
y = 4x + 3
y is the total cost of bowling
x is the number of games bowled
Based on the information, which statement is true?
Report that other guy smh... but im not quite too sure but i believe the answer you were looking for was C. The total cost will increase by 4$ every 3 games bowled :D
The weights of broilers (commercially raised chickens) are approximately normally distributed with mean 1395 grams and standard deviation 200 grams. Use the TI-84 Plus calculator to answer the following. (a) What proportion of broilers weigh between 1160 and 1250 grams?(b) What is the probability that a randomly selected broiler weighs more than 1510 grams? (c) Is it unusual for a broiler to weigh more than 1610 grams? Round the answers to at least four decimal places.
Answer:
a) 0.0977
b) 0.3507
c) No it is not unusual for a broiler to weigh more than 1610 grams
Step-by-step explanation:
Mean = 1395 grams
Standard deviation = 200 grams. Use the TI-84 Plus calculator to answer the following.
We solve using z score formula
z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.
(a) What proportion of broilers weigh between 1160 and 1250 grams?
For x = 1160
z = 1160 - 1395/300
= -0.78333
Probability value from Z-Table:
P(x = 1160) = 0.21672
For x = 1250 grams
z = 1250 - 1395/300
z = -0.48333
Probability value from Z-Table:
P(x = 1250) = 0.31443
The proportion of broilers weigh between 1160 and 1250 grams is
0.31443 - 0.21672
= 0.09771
≈ 0.0977
(b) What is the probability that a randomly selected broiler weighs more than 1510 grams?
For x = 1510
= z = 1510 - 1395/300
z = 0.38333
Probability value from Z-Table:
P(x<1510) = 0.64926
P(x>1510) = 1 - P(x<1510) = 0.35074
Approximately = 0.3507
(c) Is it unusual for a broiler to weigh more than 1610 grams?
For x = 1610
= z = 1610 - 1395/300
z = 0.71667
Probability value from Z-Table:
P(x<1610) = 0.76321
P(x>1610) = 1 - P(x<1610) = 0.23679
No it is not unusual for a broiler to weigh more than 1610 grams
What’s the equation of a line that is perpendicular to -x +2y =4 and passes through the point (-2,1)
Answer:
y = -2x - 3
Step-by-step explanation:
Given:
Equation of -x +2y =4
Point of (-2,1)
-x + 2y = 4
y = x/2 + 2 or y = 1/2x + 2
Which means the equation's slope is m = 1/2.
The slope of the perpendicular line is negative inverse which is m = -2.
Now we have an equation of y = -2x + a.
Use (-2, 1) to find a:
1 = (-2)(-2) + a
a = -3
y = - 2x - 3
the length of a rectangle is increased by 15% while its perpendicular height is decreased by 15%. determine, if any, the percentage change in its area.
No change in area if sides of rectangle are equal.
Hope this helps.
(GIVING BRAINLIEST!!)
Solve the equation using equivalent fractions. SHOW YOUR WORK
6/15 + 3/10 + 3/5
Answer:
1 3/10
Step-by-step explanation:
Find the common denominator.
6/15 times 2
12/30
3/10 times 3
9/30
3/5 times 6
18/30
Add.
12/30 + 9/30 + 18/30 = 39/30
Simplify
13/10 = 1 3/10
4xº
(2x – 6°
33°
A. x= 31, y = 91
B. x= 31, y = 116
C. x = 56, y=91
D. x= 56, y = 116
Find the arc length of the partial circle.
What function represents the amount of change given from a $10 bill, f(x), based on x, the number of bagels purchased? f(x) = 4x + O f(x) = -x + 10 Of(x) = x + 10 O f(x) = -x + 10
Answer:
the answer is c
Step-by-step explanation:hope this helps
Answer:
C or the third option, 3/4 x + 10
Step-by-step explanation:
100% correct please mark brainlist. HAVE A GREAT DAY
if owen has a collection of nickels and quarters worth $8.10. if the nickles were quarters and the quarters were nickels, the value would be 17.70 find the number of each coin?
2
If the mean of a positively skewed distribution is 70, which of these values
could be the median of the distribution?
Answer:
65
Step-by-step explanation:
just took the quiz.com