If the sum of the base and the height are 30, then b+h=30 or h=b-30.
Remember that the area of any triangle is A=½bh.
If you substitute in b-30 for h, then you create a function for the area in terms of the base.
A = ½b(30-b)=15b-½b2
The maximum area would be at the vertex of the parabola that would result from the function. We can graph to find the max, but there is a simple formula for the x-coordinate of the vertex: -b/2a where b=the linear coefficient and a=the quadratic coefficient.
-15/2(-½)=15 meaning that a base of 15cm would provide the maximum area. The corresponding height would be 30-15 or 15cm as well.
Mark me as brainlest plz
The maximum area of a triangle where height plus base equals 30 cm occurs when both the base and height of the triangle are 15 cm each.
Explanation:This is a problem of maximization. It's based on the principle that a right triangle will have its largest area when the two legs (in this case, the base and the height) are equal. This maximizes the product of the two dimensions. As a result, both the base and the height of the triangle are each 15 cm.
Here are the steps to confirm this: let's denote the base as b and the height as h. The area (A) of a triangle is given by the formula A = 0.5*b*h. Given that the sum of base and height is 30 cm (b + h = 30), we can substitute h = 30 - b into the area formula, giving A = 0.5*b*(30 - b).
By applying the quadratic formula, you find that the maximum area of the triangle is achieved when b = 15 cm. Because the sum of base and height is 30, we then find that h = 15 cm.
So, for maximum area, both base and height should be 15 cm.
Learn more about Maximization here:https://brainly.com/question/36610486
#SPJ3
The table below shows the number of color pages a printer prints out over a period of time
Answer:
The constant of proportionality is 3/2
B is correct.
Step-by-step explanation:
We are given a table of Time (x) and Number of pages (y)
In x minutes printer prints y number of pages.
As we know the it would be direct proportion because if time increase number of printing page increase.
Thus, y=kx
x is time ( independent variable)
y is number of pages (dependent variable)
k is constant of proportionality.
From table we will take the value of x and y and to solve for k
x=2, y=3
3=2k
[tex]k=\dfrac{3}{2}[/tex]
Hence, The constant of proportionality is 3/2
Answer:
Option B) [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
We are given the following information in the question:
A table showing the number of pages printed(y) in time(x).
x: 2 6 8 18
y: 3 9 12 27
We have to find the constant of variation.
Constant of variation
It is the number that relates two variables that are directly proportional or inversely proportional to one another.y = kx, k is the constant of proportionality.Constant of variation =
[tex]\displaystyle\frac{y_2-y_2}{x_2-x_1}\\\\(x_1.y_1), (x_2,y_2)\text{ are the points belonging to the given table.}[/tex]
Putting the values, we get:
[tex]\text{Constant of variaion} = \displaystyle\frac{9-3}{6-2} = \frac{12-9}{8-6} = \frac{27-12}{18-8} = \frac{3}{2}[/tex]
Hence, the constant of variation is [tex]\frac{3}{2}[/tex]
Help me plzzzz I need more hw to do so help at least
5. Simple multiplication: 12 * 4 = 48 books in total
6. Simple multiplication: 29 * 4 = 116 cards in total
7. You could turn 5 * 198 into (5 * 200) - (5 * 10) using the Distributive Property and use mental math to solve
8. subtraction, multiplication
9. Simple multiplication: 5 * 78 = $3.90, so C
Twelve less than the one fifth of a number is -7
Answer:
[tex]\frac{1}{5} -12=-7[/tex]
Set builder notation of {0, 00, 10, 000, 010, 100, 110}?
Answer:
{0, 10, 100, 110} = {x : x = 10(n + k), n = 0, 10 and k = 0, 1}
Step-by-step explanation:
We have been given the set {0, 00, 10, 000, 010, 100, 110} which is in the Roster form.
Since repetition is not allowed in a set, let's rewrite the given set as:
{0, 10, 100, 110}
Note that the elements of the set are binary.
Now, let's write the set builder form of the above set as below:
{0, 10, 100, 110} = {x : x is an even binary number and its decimal equivalent is less than 7}
What is 3y plus 5x=-15 written in slope-intercept form?
To make an equation into slope intercept form, Y must have no coefficient.
So to solve
[tex]3y + 5x = -15\\3y = -5x-15\\y = -\frac{5}{3}x-3[/tex]
Answer:
I think it is Option C
y+5/3x-5Because if you do it then you get it XD
One number is 5 more than another. Five times the smaller equals 4 times the larger. Find the numbers
x = 5 + y
4x = 5y
Because we already have a value for x, we can solve for the exact value of y.
4(5 + y) = 5y
Distributive property.
20 + 4y = 5y
Subtract 4y from both sides.
y = 20
Now that we have the exact value of y, we can solve for x.
x = 5 + 20
x = 25
which is larger 5.034, 5.34, or 5.043
5.34, because the 3 is in the tenths place
To find the largest number among 5.034, 5.34, and 5.043, let's compare these numbers one-by-one:
1. First, we compare 5.034 and 5.34. Since 0.34 is larger than 0.034, therefore, 5.34 is larger than 5.034.
2. Next, we need to compare this larger number (5.34) with the remaining number 5.043. Here, 0.34 is also larger than 0.043.
So, after these comparisons, we see that 5.34 turns out to be the largest number among the three numbers 5.034, 5.34, and 5.043.
100 POINTS BRAINLIEST QUESTION ATTACHED
-1 plz mark brainliest
Find 4 on the x-line (the horizontal line).
Find where the red line crosses through that is where the 4 is at.
Once you find it, trace the line in which the 4 is x, and find the y.
The line gives (4, -1)
Find the slope of the line.
(4, -1) = (x₁ , y₁)
(0, 2) = (x₂ , y₂)
slope = (y₂ - y₁)/(x₂ - x₁) = (2 - (-1)/(0 - 4) = 3/-4
y = (-3/4)x + b
Plug in a point, for example (0, 2)
2 = (-3/4)0 + b
Simplify
2 = 0 + b
b = 2
Plug in 2 for b
---------------------------------------------------------------------------------------------------------------------------
f(x) = (-3/4)x + 2 is your equation.
Now, plug in 4 for x (as you are solving for x.
f(x) = (-3/4)(4) + 2
Simplify
f(x) = -3 + 2
f(x) = -1
-1 is your function when x = 4
hope this helps
In 1999, bus fare in Atlanta was $4.70. In 1979, the fare was 2/5 the fare in 1999. What was the fare in 1999?
Answer:
The fare in 1979 was $1.88.
Step-by-step explanation:
In 1999, bus fare in Atlanta was $4.70.
In 1979, the fare was 2/5 the fare in 1999.
This means the fare in 1979 was 2/5 of $4.70.
This means [tex]\frac{2}{5}\times4.70= 1.88[/tex] dollars
Hence, the fare in 1979 was $1.88.
it costs a manufacturer $60 per dozen to make a specific sweater and a manufacturer sells 3000 dozen at $100 per dozen
The company makes a $40 profit per dozen sweaters sold. With selling 3000 dozen, they make a total profit of $120,000. Economies of scale are not determinable with the given information.
Explanation:The subject of this question is Business, specifically related to cost, revenue, and profit calculations. In this case, the cost to manufacture a dozen sweaters is $60, and these are sold for $100 per dozen, creating a profit of $40 per dozen. If the manufacturer sells 3000 dozen, the total revenue is the number of items sold times the price, which is 3000 dozen * $100 per dozen = $300,000. The total cost is the number of items made times the cost to manufacture each item, which is 3000 dozen * $60 per dozen = $180,000. Subtracting the total cost from the total revenue gives the total profit, which in this case is $300,000 - $180,000 = $120,000.
Economies of scale, as shown in Figure 7.9, shows how the cost of manufacturing decreases as more items are produced. In this scenario, however, we are not given sufficient information to determine if the sweater manufacturer enjoys economies of scale.
Learn more about Cost, Revenue and Profit here:https://brainly.com/question/32710282
#SPJ3
PLLZ HELP! Solve each given equation and show your work. Tell whether it has on solution, and infinite number of solutions, or no solutions, and identify each equation as an identify, a contradiction, or neither.
(a) 2x + 3x - 6 = 10 + 4x
(b) 17 + 5x = 23 + 4x - 6 + x
(c) 7x + 4 = 5x + 8 + 2x - 10
a. 2x+3x-6=10+4x
5x-6=10+4x
5x-4x=10+6
x=16
one solution
b. 17+5x=23+4x-6+x
17+5x=17+5x
infinite number of solutions
c. 7x+4=5x+8+2x-10
7x+4=7x-2
no solution
(a) 2x + 3x - 6 = 10 + 4x ---> Answer: x = 16, it has one solution, it is an identity.
Adding the like terms on the same side of the equation to solve for x:
2x + 3x - 4x = 10 + 6
x = 16
(b) 17 + 5x = 23 + 4x - 6 + x ---> Answer: it has infinite number of solutions, it is a contradiction
Adding the like terms on the same side of the equation to solve for x:
5x - 4x - x = 23 - 17 - 6
5x - 5x = 6 - 6 (this equation is cancelling everything on each side so it can not be true no matter what value we assign, therefore it has infinite number of solution)
(c) 7x + 4 = 5x + 8 + 2x - 10 ---> Answer: no solution, its a contradiction.
Adding the like terms on the same side of the equation to solve for x:
7x - 5x - 2x = -10 + 8 - 4
7x - 7x = -6 (the terms of x are cancelled by each other, therefore no solution.
Which system of linear inequalities is graphed?
Answer:
The last ONE!!!
Step-by-step explanation:
In the attachment!
Answer:
y > -3.
5y ≥ -4x -10.
Step-by-step explanation:
Given : Graph.
To find : Which system of linear inequalities is graphed.
Solution: We have given graph with two line one is dotted and other is solid.
Both the line are shaded up.
For dotted line :
We show the line by y = mx + b
Where, m = slope of line and b = y intercept .
The dotted line represent by the greater sign , slope of dotted line is zero and y intercept is -3.
So, equation would be y > 0x - 3.
y > -3.
For solid line : It represented by the greater than equal to sign for solid and shaded up. y intercept of solid line is -2.
Then equation would be 5y ≥ -4x -10.
Therefore, Equation would be y > -3.
5y ≥ -4x -10.
AnimeBrainly PleaseHelp!
1. Tom and his best friend Edward are seeking to join a gym. Tom saw on television that Platinum Gym was having a grand opening in a few months. Tom is considering a membership at Platinum Gym. Platinum Gym charges a one-time registration fee of $60, and membership is $20 a month. Tom's best friend Edward says he plans to join Super Fit because Super Fit only charges $10 a month but has a one-time registration fee of $150.
(a) Write an expression to represent the membership cost of Platinum Gym for x months.
(b) Write an expression to represent the membership cost of Super Fit for x months.
(c) If Tom decides to join Platinum Gym and Edward joins Super Fit, who would pay less during the first month of membership? Who would pay less after a year of membership? Show your work.
(d) Is there a membership period for which Tom and Edward would pay the same amount? If so, how long would this membership be and how much would it cost? Show your work.
(e) Which gym membership is a better deal? Explain why.
1.
Platinum Gym charges a one-time registration fee of $60, and membership is $20 a month.
Super Fit charges a one-time registration fee of $150, and membership is $10 a month.
(a) Write a expression to represent the membership cost of Platinum Gym for x months.
Let x = months
20x + 60 is your expression
(b) Write an expression to represent the membership cost of Super Fit for x months
Let x = months
10x + 150 is your expression
(c) You are solving for both one month and twelve months of membership.
One month: Plug in 1 for x.
20(1) + 60 = 20 + 60 = 80
10(1) + 150 = 10 + 150 = 160
Platinum Gym is cheaper overall for one month by $80
One year: There are twelve months in a year. Plug in 12 for x.
20(12) + 60 = 240 + 60 = 300
10(12) + 150 = 120 + 150 = 270
Super Fit is cheaper than Platinum Gym overall for one year by $30
(d) Set the two expression equal to each other.
20x + 60 = 10x + 150
Isolate the x. Subtract 10x and 60 from both sides
20x (-10x) + 60 (-60) = 10x (-10x) + 150 (-60)
20x - 10x = 150 - 60
Simplify
20x - 10x = 150 - 60
10x = 90
Isolate the x. Divide 10 from both sides
10x/10 = 90/10
x = 9
It takes 9 months for the cost to be the same.
(e) It really depends on how long you want to work out at a gym. If you are working out for less than a year, than Platinum Gym is the better choice. If more than a year, then Super Fit is the better choice.
---------------------------------------------------------------------------------------------------------------------
hope this helps
flowers unlimited has two spring floral arrangements, the easter bouquet and the spring bouquet. the easter bouquet requires 10 jonquils and 20 daisies and produces a profit of $1.50. the spring bouquet required 5 jonquils and 20 daisies and yield a profit of $1. how many of each type of arrangement should the florist make to maximize the profit if 120 jonquils and 300 daisies are available? (assume that all bouquets will be sold)
Answer:
The florist should make 9 Easter bouquet and 6 Spring bouquet to maximize the profit.
Step-by-step explanation:
Suppose, the number of the Easter bouquet is [tex]x[/tex] and the number of Spring bouquet is [tex]y[/tex].
The Easter bouquet requires 10 jonquils and 20 daisies, and the Spring bouquet requires 5 jonquils and 20 daisies.
So, the total number of jonquils required [tex]=10x+5y[/tex]
and the total number of daisies required [tex]=20x+20y[/tex]
Given that, there are total 120 jonquils and 300 daisies are available. So, the constraints will be........
[tex]10x+5y\leq 120;\\ \\ 20x+20y\leq 300;\\ \\ x\geq 0; y\geq 0[/tex]
(As the number of each type of bouquet can't be negative)
Now, each Easter bouquet produces a profit of $1.50 and each Spring bouquet produces a profit of $1. So, the profit function will be: [tex]P=1.50x+1y[/tex]
If we graph the constraints now, then the vertices of the common shaded region are: [tex](0,0), (12,0), (9,6)[/tex] and [tex](0,15)[/tex]
For (0, 0) ⇒ [tex]P=1.50(0)+1(0)=0[/tex]
For (12, 0) ⇒ [tex]P=1.50(12)+1(0)=18[/tex]
For (9, 6) ⇒ [tex]P=1.50(9)+1(6)=13.50+6= 19.50[/tex]
For (0, 15) ⇒ [tex]P=1.50(0)+1(15)=15[/tex]
So, the profit will be maximum when [tex]x=9[/tex] and [tex]y=6[/tex]
Thus, the florist should make 9 Easter bouquet and 6 Spring bouquet to maximize the profit.
Please Help. I'll give you BRAINLIEST.
Stan, Liam, and Louise are competing in a cooking competition. They all used different amounts of flour from a can containing 5 pounds of flour.
Stan used 12% of the total flour in the can.
Liam used 0.11 of the total flour in the can.
Louise used 0.7 pound of the total flour in the can.
Who used the greatest amount of flour from the can? Show your work and explain your answer in words.
Answer:
Louise used the most flour.
Step-by-step explanation:
Okay so first off 12% of 5 pounds would be 0.6 pounds. So we can put that Stan used 0.6 pounds. Then 0.11 of the total flour would be the same as 11% of 5 pounds, which is 0.55 pounds. So Liam used 0.55 pounds. We already know that Louise used 0.7 pounds of flour so we can order it like this.
Louise=0.7 Pounds
Stan=0.6 Pounds
Liam=0.55 Pounds
Answer:
Louise used the most flour.
Louise = 00.70 Pounds
Stan = 00.60 Pounds
Liam = 00.55 Pounds
PLZ GIVE BRAINLYEST!!!
During 7 1/2 months of hibernation, a black bear experienced a weight loss of 64.4 pounds. On average, what was the bear's weight change per month? Round to the nearest tenth. Enter your answer in the box.
The bear lost an average of 8.6 pounds per month during hibernation. This was calculated by dividing the total weight loss (64.4 pounds) by the total duration of hibernation (7.5 months).
Explanation:The student's question pertains to determining an average over a period of time. In this case, the black bear's average weight loss per month during hibernation. Given that the bear lost a total of 64.4 pounds in 7 1/2 or 7.5 months, we find the average by dividing the total weight loss by the total months. So, 64.4 pounds ÷ 7.5 months = approximately 8.59 pounds. When rounded to the nearest tenth, the black bear lost an average of 8.6 pounds per month during hibernation.
Learn more about Average Weight Loss here:https://brainly.com/question/33456548
#SPJ3
What is the quotient of 1180 and 5
That would be 236. Quotient means divide the numbers from one another.
Hope I could help! :)
Answer,
1,180/5 = 235
Hope this helps :-)
Need help please please
I'll give brainliest! Whats the value of r that makes the equation true? r+(-0.16)=0.37
A)-0.53
B)-0.21
C)0.21
D)0.53
The answer is D Because -0.16 + 0.53 = 0.37
What is the value of x? 34x+5−12x=3
The value of x is [tex]-1/11[/tex]
To find the value of xin the equation [tex]34x-12x+5=3[/tex], follow these steps:
1. Combine like terms on the left-hand side:
[tex]34x-12x+5=3[/tex]
2. Simplify the equation:
[tex]22x+5=322x + 5 = 322x+5=3[/tex]
3. Subtract 5 from both sides to isolate the term with xxx:
[tex]22x=3-522x = 3 \\- 522x=3-5 22x\\=-222x = -222x=−2[/tex]
4. Divide both sides by 22 to solve for xxx:
[tex]x=−222x \\= \frac{-2}{22}x=22-2 x\\=-111x =\frac{-1}{11}x=\\-1/11[/tex]
So, the value of x is [tex]-1/11[/tex]
what is the lengh of the line segmant between (-3,8) and (7,8)
Answer:
Length = 10
Step-by-step explanation:
Normally you would use
d = sqrt( (x2 - x1)^2 + (y2 - y1)^2 )
But the 2 y values are the same so y2 - y1 = 0.
d then becomes sqrt(x2 - x1)^2
d = (x2 - x1) because the square root of (x2 - x1)^2 is just (x2 - x1)
x2 = 7
x1 = -3
d = (7 - - 3) = 10
Q25. A ladder AP of length 10m is kept against a wall AB such that it reaches a window at A, 6m high from the ground. The same ladder reaches another window at C when it is rested against the wall opposite to AB. If the walls are 14 m apart. Find the height of the window at C from the ground.
Answer:
Step-by-step explanation:
Given a ladder AP of length = 10m is kept against a wall AB such that it reaches a window at A, such that AB=6m .
Consider a triangle ABP
By Pythagoras theorem,
[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2\\\\i.e.\ (10)^2=(6)^2+(BP)^2\\\Rightarrow100=36+(BP)^2\\\Rightarrow(BP)^2=64\\\Rightarrow\ BP=8\ m[/tex]
Now,The same ladder reaches another window at C when it is rested against the wall opposite to AB .
Let D be a point which represent the foot of the second building CD on the ground which is 14 m away from B.
∴ BD = BP+ PD
⇒ 14 = 8+PD
⇒PD =14-8 = 6m
Now consider another triangle CPD
Again by Pythagoras theorem,
[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2\\\\i.e.\ (CP)^2=(CD)^2+(PD)^2\\\Rightarrow\ (10)^2=(CD)^2+(6)^2\\\\\Rightarrow100=(CD)^2+36\\\Rightarrow(CD)^2=64\\\Rightarrow\ CD=8\ m[/tex]
Therefore, the height of the window at C from the ground CD=8m
a line that passes through the point (1, –1) and parallel to another line whose slope is 1.
if 1000 35 year old women were to pay and insurance company $140/month for 20 years , how much money would the insurance company recieve
Find out how much money one woman would pay a year by multiplying $140 and 12 months together like this.
140×12=1680
Next, find out how much she'd be paying for 20 years by multiplying the product by the years like this.
1680×20=33600
Now, to find out how much money all 1000 women are paying for the 20 years, multiply the previous product with the number of women.
33600×1000=3600000
Therefore, all 1000 women would be paying $3,600,000 total during the 20 year time period.
HOPE THIS HELPS!
Write the answer in scientific notation (5.4 × 10 to the power of 8) (3.2 × 10 to the power of 6)
Answer:
1,728 × 10 to power twelve
Step-by-step explanation:
(5.4 × 100000000)(3.2×1000000)
(540,000,000)(3,200,000)
1,728,000,000,000,000
1,728 × 10 to power twelve
the sum of 10 and a number divide by four is 17.find the number
To find the unknown number, one must solve the equation (10 + x) / 4 = 17, which simplifies to x = 58.
The student has asked to find a number such that when 10 is added to this number and the sum is divided by four, the result is 17. This can be written as an equation: (10 + x) / 4 = 17, where x represents the unknown number. To solve for x, we first multiply both sides of the equation by 4 to get rid of the denominator, resulting in 10 + x = 68. Then, we subtract 10 from both sides to isolate the variable, yielding x = 68 - 10. Therefore, x equals 58.
simplify -16+8y+{-3}
-16 + 8y + {-3} =
-16 + 8y - 3 =
8y - 19
nine less than a number is no more than 8 and is no less than 3
X<17, if i got it correct
Answer:
3 is less than or equal to x-9 is less than or equal to.
3<= x-9<=8
<= these mean less than or equal to.
hope I helped you!
Which value of x is in the solution set of the inequality -3x+5>17?
-3x + 5 > 17 |subtract 5 from both sides
-3x > 12 |change the signs
3x < -12 |divide both sides by 3
x < -4|-19| - |+17|. I hate math
The absolute value of -19, expressed as |-19|, is +19. That of |+17| is 17. We are thus left with +19 - 17, or 2.