Answer:
The solutions I found to this system of equations are (1, 0) and (⁸/₁₅, -7).
I keep second guessing and recalculating the second point there, so I'd suggest double-checking it by going through the work yourself. The first one checks out though.
Step-by-step explanation:
Let's solve this by substitution, where one equation is solved for one variable and substituted in to the other. As the latter equation is already solved for y, we can simply substitute it into the other:
given:
y = 3x² - 4x + 1
3x - 5y = 3
then:
3x - 5(3x² - 4x + 1) = 3
Which we can then simplify and solve:
3x - 15x² + 20x - 5 = 3
-3x + 15x² - 20x + 5 = -3
15x² - 23x = -8
Now we can find find the solution by completing the square:
15(15x² - 23x) = 15(-8)
225x² - 345x = -120
225x² - 345x + (23/2)² = -120 + (23/2)²
225x² - 345x + 529/4 = -120 + 529/4
(15x - 11.5)² = -120 + 132.25
(15x - 11.5)² = 12.25
15x - 11.5 = ± √12.25
15x - 11.5 = ± 3.5
15x = 11.5 ± 3.5
x = (11.5 ± 3.5) / 15
x = 15 / 15, and 8 / 15
x = 1, and 0.5333...
Now that we have x, we can solve for y.
given: 3x - 5y = 3
for x = 1:
3 - 5y = 3
y = 0
for x = ⁸/₁₅:
3(⁸/₁₅) - 5y = 3
5y = 3(⁸/₁₅) - 3
5y = ²⁴/₁₅ - ⁴⁵/₁₅
5y = -²¹/₁₅
y = -²¹/₃
y = -7
So the solutions to this system of equations are (1, 0) and (⁸/₁₅, -7).
A store is having a sale where everything is discounted 30%. Find the discount and the sales price if a customer buys an item that normally sells for $365.
Discount = 365*30/100 = $109.5
sales price = 365*70/100 = $255.5
Do you understand what i am doing
Please HElp now no fake answers
Answer:
5.0 and 5.1
Step-by-step explanation:
√26 = 5.099019514 , it's from the calculator
Answer:
the square root of 26 must lie between 5 and 6
Step-by-step explanation:
5.099019514
At Chill Hill, there are 540 ways to make an ice cream sundae consisting of one flavor ice cream, one topping, and one type of syrup. If there are 9 ice cream flavors and 5 types of syrup, how many toppings are there?
Please explain for brainliest.
Answer:
12 toppings
Step-by-step explanation:
9x5=45
540/45=12
The length of a rectangular room is 4 more than three times the width. Find the perimeter and area of the room 16.
lyle has this juice box in his lunch. how much juice does it hold when its full?
A. 7/8ft^3
B. 3/14ft^3
C. 1/64ft^3
D. 1/14ft^3
combine like terms in the expression -4x+7x-2y+7y
Answer:
-4x + 7x - 2y + 7y =
3x + 5y
Step-by-step explanation:
Hope that this helps :)
A dress is on sale for 35\% off of the regular price.
If d represents the regular price of the dress, which expression represents the sale price of the dress?
A.
0.35d
B.
0.65d
C.
1.35d
D.
1.65d
PART B
Use the information from Part A to answer the question below. The regular price of a dress is $90, determine the sale price of the dress.
The sale price of the dress is $
.
Answer:
Expression that represents the sale price of the wedding dress is
Solution:
Given that, the dress is on sale for 35 % off the regular price
Let the regular price of dress be "w"
To find: Expression that represents the sale price of the wedding dress
Let "s" be the sale price of wedding dress
Sale price = Regular price - discount price
Discount price is given as:
Discount price = 35 % of regular price
Discount price = 35 % of w
Thus discount price = 0.35w
Expression for the sale price of the wedding dress:
Sale price = Regular price - discount price
s = w - 0.35
s = 0.65
s= 0.65
Thus expression that represents the sale price of the wedding dress is
s=0.56
Give the value of x. Explain how you got your answer OR which theorem you used.
100+75+70+x= 360° (sum of interior angles of quadrilateral)
x= 360-245= 115°
Complete the inequality with >, < or =
62
Answer:
4'3 = 6'2
=
Step-by-step explanation:
4 x 4 x 4 = 64
6 x 6 = 64
hope this helps
can someone help me with this please
Answer:
4
This figure has 4 lines of symmetry.
Which line contains the ordered pair (-4,-2)
Answer:
I think it is the line F..
Norris bought a television for $899. If the tax is 5.5%, how much sales tax will he pay?
Answer:
$49.445 or $49.5 if they round
Step-by-step explanation:
Answer:
$948.45
Step-by-step explanation:
■ Sales tax: $49.45
■ Cost/Price before ST: $899.00
■ Total Cost/Price including ST: $948.45
Write a polynomial that represents the area of the square.
(4c + 4d)² =
= (4c)² + 2 * 4c * 4d + (4d)² =
= 16c² + 32cd + 16d²
What does -4(3x-4)=44
What is x
Answer:
-7/3
Step-by-step explanation:
A small island country with less than 20,000 cars has decided to reissue the license plates for its cars and has decided on the following rules for assigning numbers and letters to the license plates. Each plate will have 7 character positions that each must be filled. The leftmost character position will hold a letter from the set {D, E, H, G, X}. The next three positions will hold integers from the set {0, 1, ..., 9} but none of the integers can be repeated. The rightmost three positions must be entirely from the set {I, V, X} or entirely from the set {P, Q, R}, with repetition allowed in either case. For example, a valid plate would be G 027 XXI and an invalid plate would be G 337 PQX (two rules violated). What is the maximum number of different license plates following the rules?
a. 270,000
b. 2,624,400
c. 3,645,000
d. 194,400
Answer:
The answer is "Choice d"
Step-by-step explanation:
Given data:
7 position [tex]5, 10 , 9, 8 , 2 \times 3^3[/tex]
calculating the left most filled by any of D, E, H, G, X
a possible way to fill =5
calculating the next 3 value that will be filled 0 to 10 without any repetition
possible way to fill [tex]=10 \times 9 \times 8[/tex]
calculting the last filled any if set [tex]\{I,V,X\} \ \ or \ \ \{P,Q,R\}[/tex] with repetation
possible way [tex]=2 \times 3^3[/tex]
Total different licence plates [tex]= 5 \times 10 \times 9 \times 8 \times 2 \times 3^3=194400[/tex]
all that make this true i need help
Answer:
D and E
Step-by-step explanation:
3(23+18)=123
6(18)=108. 6(19)=114. 6(20)=120. 6(22)=132. 6(24)=144
2x+y=5 y=x−1 system of equations please show your work
sub y = x - 1 into equation 1
2x + x - 1 = 5
3x = 6
x = 2
sub x = 2 into equation 2
y = 2 - 1
y = 1
1522 customers at a major retailer were surveyed whether or not they made a purchase and were satisfied with the service they received. The table below organized the responses
a) a total of 677 were not satisfied. Of these 494 made a purchase 494/677
b) a total of 624 made a purchase. Of these 494 were not satisfied 494/624
Which graph represents the function f(x)=0•2^x+3
Step-by-step explanation:
Literally, lets not waste anybody's time. Super simple fix, you'll thank me later!
Type in desmos graphing calculator.
dilation of 1.5 about the origin
Answer:
Step-by-step explanation:
use the rule they tell you of 1.5
so (x,y) ⇔1.5(x,y)
w = (2,0)
x = ( 0,2)
y = (-2, 1)
z = (0, -2)
1.5(x,y)
W' = (3,0)
X'= (0, 3)
Y' = ( -3, 1.5)
Z' = (0, -3)
nice :)
Cost, Revenue, Profit
Identify the relevant information given to you in the application problem below. Use that information to answer the questions that follow on cost, revenue and profit.
Round your answers to two decimal places as needed.
You decide to begin selling frozen bananas at the local park. Your cost for each frozen banana is $2.25 plus you have to pay a fixed weekly fee of $120 for the booth. Your plan is to sell each frozen banana for $3.51.
1. Write a function, Cin), to represent your total costs for the week if you sell n frozen bananas. C(n) 2.25 + 120
2. Write a function, R(n), to represent the revenue from the sale of n frozen bananas during the week. R(n) 3,5ln
3. Write a function, P(n), that represents the profits for selling n frozen bananas in a given week. P(n) 1.26n - 120
1. How many frozen bananas must you sell in order to make a positive profit? Write your answer as a whole number. 95.23809524 frozen bananas
2. Complete the following sentence to explain the meaning of #1:
In order to make a profit, I have to sell a minimum of________
Answer:
1. C(n) = 2.25n + 120
2. R(n) = 3.51n
3. P(n) = 1.26n - 120
1. 96 frozen bananas must be sold in order to make a positive profit.
2. In order to make a profit, I have to sell a minimum of 96 frozen bananas.
Step-by-step explanation:
1. Write a function, C(n), to represent your total costs for the week if you sell n frozen bananas.
Total cost is the addition of total variable cost and total fixed cost. Therefore, the function is as follows:
C(n) = 2.25n + 120
Where 2.25n is the total variable cost while 120 is the total fixed cost.
2. Write a function, R(n), to represent the revenue from the sale of n frozen bananas during the week.
Revenue is equal to selling price per unit multiplied by the number of units sold. Therefore, the function is as follows:
R(n) = 3.51 * n
R(n) = 3.51n
Where 3.51 is the selling price per unit while n the number of units sold.
3. Write a function, P(n), that represents the profits for selling n frozen bananas in a given week.
Profit is equal to total revenue minus total cost. Therefore, the function can be derived as follows:
P(n) = R(n) - C(n)
P(n) = 3.51n - 2.25n + 120
P(n) = 1.26n - 120
1. How many frozen bananas must you sell in order to make a positive profit? Write your answer as a whole number.
This can be obtained by equating the profit function to zero and solve for n as follows:
P(n) = 0 => 1.26n - 120 = 0
Therefore, we have:
1.26n = 120
n = 120 / 1.26
n = 95.2380952380952 frozen bananas
Writing it as a whole number, we have:
n = 95 frozen bananas
However, using this whole number will result in a negative profit by substituting it into the profit function as follows:
P(n) = (1.26 * 95) - 120 = -$0.30
Therefore, n has to be increased by one to 96 which is also a whole number to have a positive profit as follows:
P(n) = (1.26 * 96) - 120 = $0.96
Therefore, 96 frozen bananas must be sold in order to make a positive profit.
2. Complete the following sentence to explain the meaning of #1:
In order to make a profit, I have to sell a minimum of 96 frozen bananas.
We’ve built a machine that follows these instructions:
Add 4
Multiply by 2
Subtract 3
If we put 10 into this machine, what will come out?
A certain species of bird is in danger of becoming extinct. There were 1500 of these birds in 2010 and they are decreasing at an annual rate of 6.5%. If this trend continues, how many birds will be left in 2025?
A 12m by 12m square garden has a 1m wide path through the centre, parallel to one side of the square. calculate the area of the garden left for planting.
Answer:
132 m²
Step-by-step explanation:
overall area = 12 m x 12 m = 144 m²
area of path = 1 m x 12 m = 12 m²
144 m² - 12 m² = 132 m²
Erin is making fruit punch for a party. The bowl currently has 2 1/4 cups of punch. Write and solve an equation to find the number of cups of fruit punch that were added to the bowl. -Be sure to define your variable as specially as possible.
Answer: x+2 1/4
Step-by-step Explanation: It does not tell you how much you had before they added 2 1/4 cups of water. all you need is a variable to represent the unknow number. A variable is a letter that represents something, A-Z.
will mark brainliest if fast
Sector area can be found with the formula [tex]A = \frac{\theta}{360} \pi r ^2[/tex] where [tex]\theta[/tex] is the central angle.
r = 8m , [tex]\theta[/tex] = 135º
[tex]A = \frac{135}{360} \pi (8)[/tex] m^2
Arc length formula is [tex]s = 2\pi r (\frac{\theta}{360} )\\[/tex]
[tex]s = 2\pi (8)(\frac{135}{360} )\\[/tex] m
The director of training for an equipment manufacturing company is interested in determining whether different training methods have an affect on the productivity of assembly line employees. She randomly assigns 42 newly hired employees into two groups of 21. The first group receives an on-line training program and the second receives a team based training program. At the end of the training, the employees are evaluated on the time (in seconds) that it takes to assemble a part. The results follow. A hypothesis test is made to see if there is a significant difference in the mean assembly times. What is the null hypothesis?On-Line19.4 16.7 20.7 19.3 21.8 16.8 14.1 17.7 16.1 19.8 16.819.3 14.7 16.0 16.5 17.7 16.2 17.4 16.4 16.8 18.5Team22.4 13.8 18.7 18.0 19.3 20.8 15.6 17.1 18.0 28.2 21.720.8 30.7 24.7 23.7 17.4 23.2 20.1 12.3 15.2 16.0
Answer:
The null hypothesis is that there is no difference between the mean time it takes an online trained employee or a team-based trained employee to assemble the given part
Step-by-step explanation:
The information the director of the equipment manufacturing company is interested in determining is weather the productivity of assembly line employees is affected by the method used in their training
The total number newly hired employees in the sample = 42
The number of newly hired employees that receive training online = 21
The number of newly hired employees that receive training in a team = 21
The given data of the result of the time it takes an employee to assemble a part is presented as follows;
On-Line 19.4, 16.7, 20.7, 19.3, 21.8, 16.8, 14.1, 17.7, 16.1, 19.8, 16.8, 19.3, 14.7, 16.0, 16.5, 17.7, 16.2, 17.4, 16.4, 16.8, 18.5
Team; 22.4, 13.8, 18.7, 18.0, 19.3, 20.8, 15.6, 17.1, 18.0, 28.2, 21.7, 20.8, 30.7, 24.7, 23.7, 17.4, 23.2, 20.1, 12.3, 15.2, 16.0
The mean time for the of the on-line trained employee, [tex]\overline x_1[/tex] = 17.55714
The standard deviation of the time for the of the on-line trained employee, s₁ = 1.93328
The mean time for the of the team based trained employee, [tex]\overline x_2[/tex] = 19.89048
The standard deviation of the time for the of the team based trained employee, s₂ = 4.5667
The null hypothesis, H₀: [tex]\overline x_1[/tex] = [tex]\overline x_2[/tex]
The alternative hypothesis, Hₐ: [tex]\overline x_1[/tex] ≠ [tex]\overline x_2[/tex]
[tex]t=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{\dfrac{s_{1}^{2} }{n_{1}}-\dfrac{s _{2}^{2}}{n_{2}}}}[/tex]
Therefore, we have;
[tex]t=\dfrac{(19.89048 - 17.55714)}{\sqrt{\dfrac{4.57667^{2}}{21} - \dfrac{1.93328^{2} }{21}}} \approx 2.5776[/tex]
The degrees of freedom, df = n₁ - 1 = 21 - 1 = 20
At 95% confidence level, we have α = 1 - 0.95 = 0.05, and t = 2.086
Therefore, given that the test statistic is larger than the critical 't' value, we reject the null hypothesis. There is sufficient statistical evidence to show that there is a difference between the mean time of assembly value for the on-line trained and team-based employee
Find the slope of the line -2,-6 and -4,8
Answer:
dhkmbhuigago katangina mo
Answer:
hope help you stay happy
A company has a maximum advertising budget of $100,000 for the year. It
will be using two different platforms of advertising: online ads and billboards. Each online ad purchased will cost $15,000 for the year, and each billboard will cost $10,000 for the year. The company will not spend more than 60% of its overall budget on one of the platforms.Given that x represents the number of online ads purchased and y represents the number of billboards purchased, create a system of inequalities modeling the scenario. Select all that apply.
Answer:
Step-by-step explanation:
The graph shows the relationship between the distance a car is driven and the number of gallons of gasoline used. Identify the value of d in the point (1, d). What does that point represent?
A. d=25; the unit rate is 25 miles per gallon
B. d=25; the unit rate is 25 gallons per mile
C. d=50; the unit rate is 50 miles per gallon
D. d=50; the unit rate is 50 gallons per mile
Answer:
B
Step-by-step explanation:
The "x" coordinate goes before the y coordinate. For example, it is (x, y)
To solve:
When the x coordinate, or the gasoline used (In gallons) is 1, then we need to find what d is.
On the graph, d = 25 miles per gallon.
So, the answer is B.