Answer:
-divide both sides by -2
-2x-y=-9
2x+3y=15
-sum the equations vertically to
eliminate at least one variable
2y=6 divide both sides of the equation
by 2
y=3
-substitute the given value of y into the simplest equation
2x+3*3=15
-solve for x
x=3
-the solution of the system is the ordered pair (x,y)
(x,y)= (3,3)
Check √
-check if the given ordered pair is a solution of the system of equations
{4*3+2*3=18
{2*3+3*3=15
simplify the inequalities
{18=18
{15=15
-since all of the equalities are true the ordered pair is the solution of the system
Step-by-step explanation:
Calculate.
(10.4)2 =
20.16
100.16
108.16
20.8
Ethan is conducting an experiment to determine whether a new medication is effective in reducing sneezing. He finds 1,500 volunteers with sneezing issues and divides them into 2 groups. The control group does not receive any medication; the treatment group receives the medication. The patients in the treatment group show reduced signs of sneezing. What can Ethan conclude from this experiment?
The center of a circle is located at (5, −5) . The radius of the circle is 3.
What is the equation of the circle in general form?
x2+y2−10x+10y+41=0
x2+y2+10x−10y+47=0
x2+y2+10x−10y+41=0
x2+y2−10x+10y+47=0
Answer:
I did this twice to help anyone who might have missed from the same question I answered earlier. Have a nice day! Stay safe! And this is really good for k12 students!
Step-by-step explanation:
A coyote 43 mph while rabbit can man up to 35 mph right to equivalent expressions in then find how many more miles a coyote can run in six hours then a rabbit these rates
Answer:
(6x43)+(6x35)
6•43+6•35
48 miles
Step-by-step explanation:
Charlene has nine different necklaces, and she wears four at a time. How many different ways can Charlene wear four necklaces?
A building in san fransico is shaped like a square pyramid. It has a slant height of 856.1 feet and each side of its base is 145 feet long. Find the lateral area of the building.
A trading token is in the shape of a trapezoid and has an area of 25 square centimeters. If the bases are 3 and 7 centimeters, What is the height of the token
Answer:
5 cm
Step-by-step explanation:
The formula for the area of a trapezoid gives a relation that can be used to find the height.
A = 1/2(b1 +b2)h . . . . b1, b2 are base lengths, h is the height
__
Filling in the given information, we have ...
25 cm² = 1/2(3 cm +7 cm)h
25 cm²/(5 cm) = h = 5 cm . . . . . . . divide by the coefficient of h
The height of the token is 5 cm.
A new sidewalk will be 4 ft wide, 280 ft long, and filled to a depth of 9 inches (0.75 ft) with concrete. How many cubic yards of concrete are needed?
Answer:
Volume of the pit is [tex]31.11[/tex] cubic yards.
Step-by-step explanation:
First lets change all the values to yards.
1 yard = 3 foot
Width in yards = [tex]\frac{4}{3}[/tex] yards
Length in yards = [tex]\frac{280}{3}[/tex] yards
Depth in yards = [tex]\frac{0.75}{3}[/tex] yards
Volume of the pit = Length * Width * Depth
=[tex]\frac{4}{3} *\frac{280}{3} *\frac{0.75}{3}[/tex]
=[tex]\frac{4*280*0.75}{3*3*3}[/tex]
=[tex]\frac{840}{27}[/tex]
=[tex]31.11[/tex] cubic yards.
Volume of the pit is [tex]31.11[/tex] cubic yards.
A plumbing contractor receives proceeds of $4,713.54 on a 12.5% simple discount note with a face value of $5,000. Find the time of the note in days. (Assume a 360-day year.) Do not round intermediate calculations!
The time of the note in days is calculated using the simple discount formula, and by substituting the values of proceeds, face value, and discount rate, the result is 164.99856 days.
The question involves finding the time in days for which a simple discount note is held, given the proceeds, face value, and discount rate. The note's face value is $5,000 and the proceeds received are $4,713.54. The simple discount rate is 12.5%. Assuming a 360-day year, we need to calculate the time period for the note.
Firstly, we need to determine the amount of the discount, which is the difference between the face value and the proceeds: $5,000 - $4,713.54 = $286.46. The discount, given the simple discount formula, is equal to the face value multiplied by the discount rate and the time (in years). The simple discount formula can be expressed as: Discount = Face Value × Discount Rate × Time. Rearranging this formula to solve for time, we get: Time = Discount ÷ (Face Value × Discount Rate).
Substituting the known values we have: Time = $286.46 ÷ ($5,000 × 0.125) = $286.46 ÷ $625 = 0.458336 years. To convert years to days, we multiply the time in years by the number of days in a year (assuming a 360-day year): 0.458336 years × 360 days/year = 164.99856 days. Since we're instructed not to round intermediate calculations, the time of the note is 164.99856 days.
A merchant can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment, he sent a total of 96 boxes. If there are more large boxes than small boxes, how many cartons did he ship?
Lamar purchased n notebooks. They were 5 dollars each. Write an equation to represent the total cost c that Lamar paid.
A woman has 7 keys. only one of them will open her door. when seh arrives at the door there is no sufficient light for her to find the correct key. if she tries one key at a time and discards the keys that don't work, what is the probability that she will open the door with the first key she picks? what is the probability that it will take exactly three attempts to open the door? suppose that the first three attempts to open the door have been unsuccessful. what is the probability that she will pick the right key the fourth time?
The chance of the woman opening the door with the first key she picks is 1/7, or approximately 14.29%. The probability that it takes exactly three tries to find the correct key is also 1/7 or 14.29%. If the first three tries are unsuccessful, the probability that the fourth key is the correct key is 1/4, or 25%.
The probability that the woman will open the door with the first key she picks is 1 out of 7 keys, or about 14.29%. This is because each key has an equal chance of being the correct one, and there is only one correct key among the seven.
For the probability that it will take exactly three attempts to open the door, we need to consider the sequence of events: She picks a wrong key first (6 out of 7 chances), and then picks another wrong key from the remaining six (5 out of 6 chances), and then finally picks the correct key from the remaining five (1 out of 5 chances). We multiply these probabilities: (6/7) * (5/6) * (1/5) = 1/7 or about 14.29%.
If the first three attempts have been unsuccessful, we are now left with four keys, one of which is the correct one. Therefore, the probability that she will pick the right key on the fourth attempt is 1 out of 4, or 25%.
Hazel has an assortment of red, blue, and green balls. The number of red balls is the number of blue balls. The number of green balls is more than the number of blue balls. In total, she has balls.
An equation created to find the number of blue balls will have?
When finding the number of blue balls in the scenario described, the equation will have x + x + x + 1 = 9, where x represents the number of blue balls.
An equation created to find the number of blue balls will have:
Let x be the number of blue balls.
The equation will be x + x + x + 1 = 9.
Solving the equation, we get x = 2.67.
How do I solve the y= x/11- 11x
d/dx ( x/11- 11/x)
uka and Anja each measured the height of their friend three times. Their friend is 59 inches tall. They recorded their measurements as shown. Luka: 59 in., 58, in., 58 in. Anja: 59.3 in., 59.6 in., 58.2 in. Which statement is true? Luka’s measurements are more precise and more accurate. Anja’s measurements are more precise and more accurate. Luka’s measurements are more precise, but Anja’s measurements are more accurate. Luka’s measurements are more accurate, but Anja’s measurements are more precise.
Luka’s measurements are more precise, but Anja’s measurements are more accurate.
What is measurement?In the study of science and mathematics, measurement is a fundamental concept. The characteristics of an object or event that we can compare to other things or events are quantified by measurement. When discussing the division of a quantity, the term "measurement" is the one that is used the most frequently. Also, when it takes a certain number of things to complete a certain task. We frequently encounter various length, weight, and time measurement types in our daily lives.
Given actual height of their friend is 59 inches
Luka recording 59 in, 58 in, 58in
Anja recording 59.3 in, 59.6 in, 58.2 in,
Accuracy is how close a measured value is to the actual value.
Precision is how close the measured values are to each other.
Accuracy:
Luka: ( 59 + 58 + 58 ) / 3 = 58.33
Anja: ( 59.3 + 59.6 + 58.2 ) / 3 = 59.03 ( closer to 59 )
Precision:
Luka : 59 - 58 = 1 ( subtract the lowest from the highest result )
Anja: 59.6 - 58.2 = 1.4
Luka's measurements are more precise, but Anja's measurements are more accurate.
Hence option C is correct.
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Equipment was acquired at the beginning of the year at a cost of $75,720. The equipment was depreciated using the straight-line method based on an estimated useful life of six years and an estimated residual value of $7,920. What was the depreciation expense for the first year?
Final answer:
The annual depreciation expense for the equipment is calculated by subtracting the estimated residual value from the cost to find the depreciable base, and then dividing by the useful life. The first-year depreciation expense is $11,300.
Explanation:
To calculate the depreciation expense for the first year using the straight-line method, we first need to determine the depreciable base of the equipment. The depreciable base is the cost of the asset minus its estimated residual value. For the equipment mentioned, the cost is $75,720 and the estimated residual value is $7,920.
Depreciable base = Cost - Residual Value
= $75,720 - $7,920
= $67,800
Next, we divide the depreciable base by the useful life of the asset to calculate the annual depreciation expense:
Depreciation Expense = Depreciable base / Useful life
= $67,800 / 6 years
= $11,300 per year
Therefore, the depreciation expense for the first year is $11,300.
Find the volume of a frustum of a right circular cone with height 25, lower base radius 32 and top radius 15.
Jenny has $25 and she earns $10 for each lawn that she mows. Jenny wants to buy a concert ticket that costs $65. Enter the minimum number of lawns Jenny needs to mow to be able to buy the concert ticket. $$
Answer:
4 Lawns
Step-by-step explanation:
Jenny wants to buy a concert ticket that costs = $65.00
Jenny has $25.00.
She needs more to buy a concert ticket = 65 - 25 = $40.00
For each lawn that she mows she earns = $10.00
For $40 she needs to mow = 40 ÷ 10 = 4 lawns
Jenny needs to mow 4 lawns to be able to buy the concert tickets.
Which shows a correct order to solve this story problem? Kent and Curtis went to the state fair. They had to pay a total of $7.18 sales tax on everything they bought. They spent $22.50 for each admission ticket and $35.50 altogether for food. They split all the costs evenly. How much did each boy pay? A. Step 1: Calculate the price of 2 admission tickets. Step 2: Add that amount to the amount spent on food and the tax. Step 3: Divide by 2. B. Step 1: Double the amount for 1 admission ticket. Step 2: Take half of the amount spent on food and add the total from Step 1 plus the tax. Step 3: Divide by 2. C. Step 1: Add $22.50 and $35.50. Step 2: Divide the total by 2. Step 3: Add the amount of the tax.
a collection of dimes and nickels is worth $4.70 there are 60 coins in all how many of each are there?
Answer:
26 nickels34 dimesStep-by-step explanation:
If all were nickels, the value would be 60×$0.05 = $3.00. Their $4.70 value is $1.70 more than that. For each nickel replaced by a dime, the value goes up by $0.05, so there must be 1.70/0.05 = 34 replacements. That is, ...
... there are 34 dimes and 60-34 = 26 nickels.
_____
Using an equation
In mixture problems, it often works well to let the variable represent the quantity of the largest contributor. Here, we can let "d" represent the number of dimes, the coin with the greatest value. Then 60-d will be the number of nickels, and the total value of the coins (in dollars) is ...
... (60 -d)×0.05 + d×0.10 = 4.70
... 0.05d + 0.05×60 = 4.70 . . .simplify
... 0.05d = 4.70 -3.00 . . . . . . . subtract 3.00
... d = 1.70/0.05 = 34 . . . . . . . . divide by the coefficient of d
There are 34 dimes and 26 nickels.
The sequence of math steps should look a lot like the sequence of steps described in words, above.
_____
As a mixture problem
The average coin value is 4.70/60 = 0.07833... = 7 5/6¢. Then the proportion that are dimes is given by ...
... (7 5/6 - 5)/(10 - 5) = (2 5/6)/5 = 17/30 . . . . . 10 and 5 are the cents values of the coins in the mix
Multiplying by the 60 coins, we find (17/30)×60 = 34 are dimes. The remaining 26 are nickels.
- - -
The formula used above is ...
... proportion of highest contributor = ...
... ((mix value) - (least contributor)) / ((greatest contributor) - (least contributor))
This is the generic solution for any mixture problem.
Math question
Algebra 2, Fundamental Theorem of Algebra, Stste the number of complex roots and the possible number of real and imaginary roots for each equation. Then find all roots. One root has been given.
x^6 - 3x^5 + 2x^4 - 6x^3 - 15x^2 + 45x = 0; 3
(if possible please provide work)
A class has 50 students. use the third row of digits in the random number table below to select a simple random sample of three students. if the students are numbered 01 to 50, what are the numbers of the three students selected
To select a simple random sample of three students from a class of 50 students using the third row of digits in the random number table, you would use the digits in the third row to determine the numbers of the selected students.
Explanation:To select a simple random sample of three students from a class of 50 students using the third row of digits in the random number table, you would start by numbering the students from 01 to 50.
Then, you would use the digits in the third row of the random number table to select the students.
For example, if the digits in the third row are 579362814, you would select the students with the corresponding numbers: 05, 79, and 36.
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Jimmy is a partner in an internet-based coffee supplier. The company offers gourmet coffee beans for $14 per pound and regular coffee beans for $7 per pound. Jimmy is creating a medium-price product that will sell for $9 per pound. The first thing to go into mixing bin was 18 pounds of the gourmet beans. How many pounds of the less expensive regular beans should be added?
To create a blend that sells for $9 per pound, when Jimmy has already added 18 pounds of the gourmet beans, he needs to add approximately 36 pounds of the regular coffee beans.
Explanation:This is a problem of mixtures in mathematics. Jimmy is attempting to create a new blend of coffee for his business that will have a price point between the regular beans and the gourmet beans.
First, let's understand the goal: A new blend worth $9 per pound. He has already added 18 pounds of gourmet beans which costs $14 per pound. To bring the overall cost down to $9 per pound, we need to add cheaper beans, worth $7 per pound.
Let's denote the weight of the regular beans needed as 'x'. We set up the equation based on weights and costs:
(18*$14 + x*$7) / (18 + x) = $9
Solving this equation, we find x to be around 36 pounds. So, Jimmy should add approximately 36 pounds of the regular beans to his mixture to reach the target price of $9 per pound.
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Jaws made his figure from six congruent squares the edge of each square was 8 inches which figure did Josh construct what is the surface area of his figure
Looking at the waves on an ocean beach, a girl notices that the waves reach the shore at the same time apart. She also notices that the distance between waves looks the same. In science, what do we call the distance between waves? A) amplitude B) frequency C) period D) wavelength
Answer:
D) Wavelength
Step-by-step explanation:
The correct answer is wavelength. Wavelength is defined as the distance between two identical points on the waves.
Amplitude is the maximum/minimum height reached by the wave. Frequency is defined as the number of waves passing through a point in 1 sec. Period or Time period is the reciprocal of Frequency and it represents time taken for the wave to complete its one cycle.
Therefore, from the given options, Wavelength is the best possible answer.
Answer: THE ANSWER IS D)WAVELENGTH
Step-by-step explanation:
What is the range of f(x) = (3/4)x – 4?
{y | y > –4}
{y | y > 3/4}
{y | y < –4}
{y | y < 3/4}
Answer:
A- {y | y > -4}
Step-by-step explanation:
Since the range is x - 4 the range will only go down to - 4. It will not go past the - 4 mark. Therefore the range should be anything greater then -4 to infinity.
SO-
A- {y | y > -4}
Need the rate of change!!!
Two points: (30, 14) and (34, 17)
A farmer wishes to fence a rectangular area behind his barn. The barn forms one end of the rectangle and the length of the rectangle is three times the width. How many linear feet of fence must he buy if the perimeter of the rectangle is 320 feet?
Final answer:
The farmer needs to buy 320 linear feet of fence to enclose the rectangular area behind his barn.
Explanation:
Let's represent the width of the rectangle as x. Since the length is three times the width, we can represent the length as 3x. The perimeter of a rectangle is calculated by adding up all four sides, so we have the equation:
2(x + 3x) = 320
Simplifying, we get:
2(4x) = 320
8x = 320
x = 40
So the width of the rectangle is 40 feet, and the length is 3 times that, which is 120 feet. The perimeter is calculated by adding up all four sides: 40 + 120 + 40 + 120 = 320 feet. Therefore, the farmer needs to buy 320 linear feet of fence.
Why do the functions f(x) = sin−1(x) and g(x) = cos−1(x) have different ranges?
In this exercise we want to explain why two more similar functions have different ranges, like this:
the values of the range are different because the domain in which the inverse function exists are different .
In this exercise we know that we are dealing with two distinct functions, like this:
What is the function of sine?The sine function is considered an odd function, as there is a symmetry in the graph with respect to the bisector of the odd quadrants. When a function is considered odd, we have that f (x) = -f (x), that is, sin (-x) = -sin (x).
What is the function of cosine?Cosine is a trigonometric function, used in a right triangle to define the ratio of the side adjacent to and the hypotenuse of this triangle.
So we can see that the reason the two functions have different ranges is associated with them having different domains.
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What is the truth value of p ∨ q?
Answer:
T T T F
Step-by-step explanation:
suppose that p is true and q is true then the truth value of p∨q is true .
when p is true and q is false then the truth values of p∨q is true
when we take p is false and q is true then the truth value is p∨q is true
when we take p is false and q is false then the truth value is p∨q is false .
if any value of p or q is true then truth value of p∨q is true and if both are false then the truth value of p∨q is false .