The plane 13x + 11y + 20z = 39 is where the line x = t, y = 1 + t, and z = 1 t cross (2,3,-1).
What is plane?A plane is an infinitely long, Euclidean, two-dimensional surface in mathematics. A plane is a point, a line, and three-dimensional space's equivalent in two dimensions. In geometry, a plane is a surface made up of all the straight lines connecting any two locations on it. It is, in other words, a level or flat surface. A plane is uniquely defined in a Euclidean space of any number of dimensions by one of the following: three non-collinear points are used.
Here,
13t+11(1+t)+20(1-t)=39
13t+11+11t+20-20t=39
4t+31=39
4t=8
t=2
x=2, y=3, z=-1
The line x = t, y = 1 + t, z = 1 − t intersects the plane 13x + 11y + 20z = 39 at (2,3,-1).
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Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answer: x = 25
Step-by-step explanation:
(x-7) = 36/2
x-7 = 18
x = 18 +7
x = 25
Answer: x = 1 and x = 13.
Step-by-step explanation: To solve the equation (x - 7)^2 = 36, we can first rewrite the equation as x^2 - 14x + 49 = 36.
Next, we can rewrite the equation as x^2 - 14x + 13 = 0.
To solve for x, we can then use the quadratic formula:
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
where a = 1, b = -14, and c = 13.
Substituting these values into the formula, we get:
x = (14 +/- sqrt(14^2 - 4(1)(13))) / 2
x = (14 +/- sqrt(196 - 52)) / 2
x = (14 +/- sqrt(144)) / 2
x = (14 +/- 12) / 2
The values of x are therefore 1 and 13.
Therefore, the correct answer is x = 1 and x = 13.
Simplify: 22-(8-2) + [6 (205) - 11]
Answer: 1,235 is your final answer!
Step-by-step explanation:
First we do what's inside the Parentheses always remember PEMDAS
P-Parentheses
E-Exponent
M-Multiplication
A-Addition
S-Subtraction
So first we do what's inside the brackets!
22-(8-2)+ (1230-11)
22-6+1219
16+1219
1235.
Follow the PEMDAS steps to simplify the answer!
6) A TV and external speakers cost $1,020. The cost of the TV is double that of the speakers.
How much do the TV and the speakers cost? Show your work.
Nicholas wants to buy a new computer that is on sale for $899. His parents will loan him the money if he repays them. He has $234 in his savings account and plans to work as a camp counselor to earn money during the summer. If he earns $35 per day, how many days will Nicholas have to work in order to fully repay his parents?
Answer: He will work for 19 days.
Step-by-step explanation:
If Nicholas has 234 dollars and the computer he wants to put is 899 dollars, you have to subtract to see how much he has to take the loan from his parents in order to buy the computer.
899 - 234 = 665
He took a loan of 665 dollars from his parents
To figure out how many days he needs to work to pay that amount, you divide the amount he earns each day with the amount of loan he took.
So 665 divided by 35 = 19
He has to work 19 days to pay off the 665 dollar loan he took from his parents.
We can check this answer by multiplying 35 x 19 , which equals to 665.
Hope this helps!
The number of students who are active in the computer club has jumped from 7 to 19. To the nearest percent, what is the percent increase?
You use a garden hose to fill a wading pool. if the water level rises 17 centimeters every 5 minutes and you record the data point of (15, y), what is the value of y? use slope to justify your answer.
The line has a 17/5 slope and y has a value of 51 which will be (15, 51).
What is the slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
The general equation for every straight line is y = MX + c, where m is the gradient (or degree of steepness) of the line and c is the y-intercept (the point in which the line crosses the y -axis).
So, the water level rises by 17 cm in 5 minutes.
Then in 15 minutes, the water will rise by:
15 * 17/5
3*17
51
Then (x, y) will be (15, 51).
Obtaining the slope as follows:
Formula: m = y1 - y2/x1 - x2
m = y2 - y1/x2 - x1
m = 17 - y/5 - x
m = 17/5
Therefore, the line has a 17/5 slope and y has a value of 51 which will be (15, 51).
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whenever a probability sample is drawn from a population, it is not enough to simply report the sample's descriptive statistics, for these measures contain a certain degree of error due to the sampling process. true false
Whenever a probability sample is drawn from a population, it is not enough to simply report the sample's descriptive statistics, for these measures contain a certain degree of error due to the sampling process.
Thus the answer is ‘ true’.
A population is any entire group that has at least one trait in common that is relevant to a given issue or experiment in statistics.
A probability sample is one that is drawn using a method of random selection that is compatible with the known odds for each member of the population to be selected, and that takes these probabilities into account when generating estimates from the sample.
If the chosen sample does not accurately reflect the total population of data, there has been a sampling error, which is a statistical error resulting from sampling.
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the registration fee for a car is 0.9% of the sale price of 5400$ how much is the fee
The registration fee is $60.
Given,
Sale Price = $5400
The value of the registration:
Registration fee = 0.9% of $5,400
= (0.9/100) * 5,400
= 60
Therefore, the registration fee is $60.
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JUSTIFY REASONING Consider the conjecture if two points are equidistant from a third point, then the three points are collinear is the
conjecture true or false? Justify your argument. If false, give a counterexample.
Select Choice if the two points create a straight angle that includes the third point, then the conjecture is Select ChoiceIf the two
points do not create a straight angle with the third point, then the conjecture is Select Choice
It is a supposition that it is true if two points are equally far apart from a third point and the three points are collinear.
Collinear points are what?If three or more points lie on a single straight line, they are said to be collinear. An axis is a term used to describe a line on which points are located, particularly if that line is connected to a triangle or other geometric shape. Since two points determine a line, two points are trivially collinear.
Collinear points are those that are situated along a identical straight line.
The supposition is correct since all three points are located on the same line.
if the two points create a straight angle that includes the third point, then the conjecture is true.
If the two points do not create a straight angle with the third point, then the conjecture is false.
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Find m
T 9 V 9 U 9
m
The measure of angle V i.e. [tex]m\angle V[/tex] is [tex]60^\circ[/tex].
For the triangle TUV ([tex]\triangle TUV[/tex]), all the sides are of same length i.e. 9. So we can consider this as an equilateral triangle.
We know for an equilateral triangle all of the angles are of same measure.
Now the sum of all angles of a triangle is [tex]180^\circ[/tex] and there are 3 angles in a triangle. So, each angle will be of measure [tex]60^\circ[/tex].
Therefore the measure of [tex]\angle V[/tex] i.e. [tex]m\angle V[/tex] is [tex]60^\circ[/tex].
Also the basic three properties of an equilateral triangle are:
All three sides are equal.All three angles are equal.The figure has three lines of symmetry.To learn more about angles,
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Hi Can some solve this with steps please
Answer:
- 51
Step-by-step explanation:
substitute x = - 2 into the expression
2x³ - 4x² + 8x - 3
= 2(- 2)³ - 4(- 2)² + 8(- 2) - 3
= 2(- 8) - 4(4) - 16 - 3
= - 16 - 16 - 19
= - 32 - 19
= - 51
Mrs. Jones makes scented candles and wax warmers. The table shows the ratio of the number of candles to the number of wax warmers she makes. Candles 7 14 21 28 77 OC. 55 OD. 75 Wax Warmers 5 10 15 20 ? How many wax warmers will she make when she makes 77 candles? O A. 69 O B. 40
Mrs. Jones will make 55 wax warmers when she produces 77 candles.
The given table shows the ratio of the number of candles to the number of wax warmers she makes.
Let's assume that "x" wax warmers will she make when she makes 77 candles
According to the given question, we can write the ratio would be as:
7 Candles : 5 Wax Warmers = 77 Candles : x Wax Warmers
⇒ 7/5 = 77/x
⇒ 7x = (77)(5)
Divided by 7 on both sides of the above equation,
⇒ x = (77)(5)/7
⇒ x = 11 × 5
Apply the multiplication operation, we get
⇒ x = 55
Thus, when she makes 77 candles, she will also produce 55 wax warmers.
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what is the estimated expected (mean) time for activity e? multiple choice 91 days 100 days 99 days 101 days 115 days
The estimate expected mean time for the given activity E from the give table data is equal to 101days.
As given in the question,
Let optimistic time be represented by [tex]T_{o}[/tex]
Most like time be represented by [tex]T_{m}[/tex]
And Pessimistic time be represented by [tex]T_{p}[/tex]
Optimistic time for activity E is equal to [tex]T_{o}[/tex] = 91
Most likely time for activity E is [tex]T_{m}[/tex] = 100
Ans Pessimistic time for activity E is [tex]T_{p}[/tex] = 115
Estimated expected mean time
= [tex]( T_{o} + 4T_{m} + T_{p} ) / 6[/tex]
= [ 91 + 4(100) + 115 ] / 6
= 606/6
= 101
Therefore, option d. 101days represents the estimated expected mean time for the given activity E.
The complete question is:
From the given table:
{ Time estimates (days)}
Activity Predecessor Optimistic Most likely Pessimistic
A A, B, C 30 50 62
B D 90 99 108
C E 85 105 115
D End 19 25 31
E F 91 100 115
F End 62 65 68
What is the estimated expected (mean) time for activity E?
Multiple choice
a. 91 days b. 100 days c. 99 days d. 101 days e.115 days
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how do you handle data in analytics to gain greater insights into our audience's behaviour? a partition b sample c segment d extract
By using the segment method, you handle data in analytics to gain greater insights into our audience's behavior.
Analytics:
Analytic refers the field of computer science that uses math, statistics, and machine learning to find meaningful patterns in data.
Given,
Here we need to find how do you handle data in analytics to gain greater insights into our audience's behavior.
In order to find the solution for this one, we must know the definition for the terms of the following,
Audience's behavior - attitudes that affect the behavior of an audience towards a brand or category.
Data - information that has been translated into a form that is efficient for movement or processing.
Insights - the capacity to gain an accurate and deep understanding of someone or something.
Here we have divide the full question into segment to solve this.
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Solve the problem using an equation and check the solution.
1. Bank teller Darrin Wentworth counted a deposit with 72 five-, ten- and one-hundred-dollar bills. After counting, Darrin found that the value of the bills was $3,500. He noticed that there was an equal number of five- and ten-dollar bills. How many of each bill was in the deposit?
Answer:
Step-by-step explanation:
20 5 dollar
20 10 dollar
32 hundred dollar
7. A watch loses 8 seconds every hour. It was set to read the correct time at 1100 h on Sunday. Determine the time, in a 12-hour system, the watch will show on the following Thursday when the correct time is 0500 h.
On Thursday when the correct time is 5:00h, watch shows 4:24h.
What is ratio?Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
The watch is set at 11:00 h on Sunday.
Also, the watch loses 8 seconds in every hour.
To determine the time in watch on Thursday,
In one day total hours = 24 hours.
from Sunday 11:00 to Thursday 11:00
Total hours = 24 x 4 = 96 hours
And 11:00 to 5:00, total = 6 hours
Total hours = 96 + 6 = 102 hours
Since, watch loses 8 seconds in 1 hour
So in 102 hours watch losses = 102 x 8 = 816 seconds
816 seconds = 816/60 minutes = 13.6 minutes
The watch loses 13.6 minutes in 102 hours.
So the exact time will be, 4 : 24.
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P(x) = 6x³-5x² - 4x + 4;-3
The value of P(-3) =-191 if the given polynomial function is
P(x) = 6x³-5x² - 4x + 4
What is meant by polynomial?A polynomial is an expression made up of exponents, constants, and variables that are combined using addition, subtraction, multiplication, and division in mathematics, according to the definition of a polynomial. Polynomials are frequently employed in both mathematics and science. For example, they are employed to define polynomial functions, which are present in a range of fields ranging from elementary physics and chemistry to economics and social science. From straightforward word problems to intricate scientific conundrums, polynomial equations are utilized to represent a broad variety of topics. In high mathematics, polynomials are used to build algebraic varieties and polynomial rings, which are essential concepts in algebra and algebraic geometry.
Given,
P(x)= 6x³-5x²-4x+4
P(-3)=6(-3)³-5(-3)²-4(-3)+4
=6(-27)-5(9)+12+4
=-162-45+16
=-191
So, the value of P(-3)= -191
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help please this is confusing me i only need number 7
Answer:
24.98 units
Step-by-step explanation:
You want the perimeter of triangle ABC with vertices A(-5, 4), B(1, -2), and C(3,6).
Distance formulaThe distance between two vertices can be found using the formula ...
d = √((x2 -x1)² +(y2 -y1)²)
ApplicationThe distance between A and B is ...
d = √((1 -(-5))² +(-2 -4)²) = √(6² +(-6)²) = 6√2 ≈ 8.485
The attached spreadsheet performs the same calculation on all the pairs of points. (The distance from each point to the one below it is listed.)
PerimeterThe perimeter of the triangle is the sum of the segment lengths. That is also shown in the spreadsheet.
P = AB +BC +CA
P = 8.485 +8.246 +8.246 ≈ 24.98
The perimeter of triangle ABC is about 24.98 units.
__
Additional comment
When calculations are repetitive, we like to let a spreadsheet do them.
what is the answer i need answers now I'm going to fail
Answer:
3
Step-by-step explanation:
this problem we need to subtract
There is 6 1/2 grape juice and 3 1/3 orange juice
6 1/2 3 1/3
We get common denominators and one is 6
6 3/6 3 2/6
And now we subtract
3 1/6
And rounded down is 3
Hopes this helps please mark brainliest
can anyone help me with the 5"c" and "d"
Answer:
see explanation
Step-by-step explanation:
(c)
ratio of
boys : total students
= 182 : 260 ( divide both parts by 26 )
= 7 : 10
number of girls = 260 - 182 = 78
ratio of
girls : total students
= 78 : 260 ( divide both parts by 26 )
= 3 : 10
A figure i made up of a emicircle and triangle. The diameter of the emicircle i 10ft, the bae of the triangle i 8 ft and the height i 6 ft. What i the area of the figure
The area of the figure that is made up of a semicircle and a triangle is 63.25 square feet .
In the question ,
it is given that ,
a figure is made up of a semicircle and a triangle ,
the diameter of the given semicircle is = 10 ft ,
So , the radius of the given semicircle is = 10/2 = 5 ft .
hence the area of the semicircle will be = (πr²/2)
= 3.14×(5)²/2
= 39.25 square feet
the base of the triangle is given to be = 8 ft ,
the height of the triangle is given to be = 6 ft ,
So , the area of the triangle is = (1/2)×b×h = (1/2)×8×6 .
= 4 × 6
= 24 square feet .
So , the area of the figure = area of semicircle + area of triangle
= 39.25 + 24
= 63.25 .
Therefore , the area of the figure is = 63.25 square feet .
The given question is incomplete , the complete question is
A figure is made up of a semicircle and triangle. The diameter of the semicircle is 10ft, the base of the triangle is 8 ft and the height is 6 ft. What is the area of the figure ?
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An item is regularly priced at $81. Shen bought it on sale for 45% off the regular price
Use the ALEKS calculator to find how much Shen paid.
For this problem there are $44.55 Shen paid.
What is sale price?
The cost following a discount applied to the original cost. This item is being sold for $8.00. We must first calculate the discount amount if the discount is a percentage: • Original price x discount rate equals the discount amount.
Given:
An item is regularly priced at $81.
Shen bought it on sale for 45% off the regular price.
The formula for calculating the sales price of an item is:
s = p - (p x d)
Where:
s is the sales price: what we are calculating in this problem.
p is the regular price of the item: $81 for this problem.
d is the discount rate: 45% for this problem. "Percent" or "%" means "out of 100" or "per 100", Therefore 45% can be written as 45/100.
Substituting and calculating s gives:
[tex]s = 81 - (81 *\frac{45}{100}) \\s = 81 - (36.45)\\s = 44.55[/tex]
s = $44.55
Hence, for this problem there are $44.55 Shen paid.
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find the value of unknown; chapter matrices
please help me out on these questions below! thnak u
with full explanations and working please
Answer:
Step-by-step explanation:
what is x + 5x -6 < 12?
Answer:
x<3
Step-by-step explanation:
;)
Graph the equation
-Show your work
The graph of the equation, y = -50x + 300, is given in the attachment below.
How to Graph the Equation of a Line?The equation of a line, where m is the slope or unit rate, and b is the y-intercept or starting value, is expressed as y = mx + b in the slope-intercept form.
Given the situation above, first determine the value of the starting value / y-intercept (b) and that of the slope / unit rate (m).
The starting value / y-intercept is b = 300.
The slope / unit rate is m = - 50 [this is negative because the distance from home reduces as she drives at the speed of 50 mph]
To write the equation, substitute m = -50 and b = 300 into y = mx + b:
y = -50x + 300.
Thus, the graph of this equation, y = -50x + 300 is shown in the mage attached below.
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What is the domain and range 5,0, 12,4, 3,-3
Answer:
domain=5,12,3
range=0,4,-3
Irma wa in charge of keeping attendance for a local ummer camp each year. Summer camp attendance
Year Kid
2018 93
2019 92
2020 78
2021 75
2022 78
According to the table, what wa the rate of change between 2018 and 2021?
The rate of change in the attendance of students between 2018 and 2021 is 1.24.
What is the rate of change?The term "rate of change" (ROC) describes the rate at which something changes over time.
Thus, it is not the number of individual changes themselves but rather the acceleration or deceleration of changes (i.e., the rate).
The rate of change is a tool used in finance to comprehend price returns and spot trend momentum.
Divide the change in y-values by the change in x-values to determine the average rate of change.
Identifying changes in measurable values like average speed or average velocity calls for the knowledge of the average rate of change.
So, according to the given table:
The rates of change between 2018 and 2021 are:
2018/2021
93/75
1.24
Therefore, the rate of change in the attendance of students between 2018 and 2021 is 1.24.
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Help and wright a step by step explanations
Answer:
The total surface area is 3860 ft^2
The total volume is 22,500 ft^3
Step-by-step explanation:
See attached worksheet.
The house needs to be broken up into separate rectangles and triangles, as shown on the worksheet. Individual calculations of the area and volume are then added for a total number for both volume and surface area.
Quick question, how would you answer if someone tells you : "keep dreaming :)"
If someone tells me "keep dreaming :)", I would likely respond by thanking them for their encouragement and expressing my determination to continue pursuing my dreams. I might also share some of my aspirations and plans for achieving them, and encourage the other person to do the same. Depending on the context and tone of the conversation, I might also make a joke or offer a playful response, such as "I will, and I'll make sure to dream big!"
HELP THIS IS MY LAST QUESTION
Answer:
associative property of multiplication
Step-by-step explanation: