The scalar equation of the plane that contains given points and lines can be written as: (-4)(x-1) + 4(y-2) + (-10)(z-3) = 0.
What is equation of plane?
A given point p(x, y, z) that is located on the plane and a normal vector n define the equation of a plane. A plane's vector and scalar components can be used to formulate the equation for the plane.
The parametric form of line equation,
[tex]p = p_0 + t. \vec v[/tex]
On comparing with the given equation in question, we can say that,
p = {x, y, z}, p₀ = {0, 6, 1,}, vec(v) = {3, -2, -2}
The scalar equation can be given by,
[tex][ \vec \omega, p - p_1] = 0[/tex]
Here, p₁ = {1, 2, 3} and ω is perpendicular to v and to the segment p₁ - p₀ So,
[tex]\vec \omega = \vec v \times (p_1 - p_0) = ( 3, -2, -2 ) \times (1, -4, -2)[/tex]
then,
[tex]\vec \omega = (-4, 4, -10)[/tex]
Therefore, the scalar equation can be written as:
(-4)(x-1) + 4(y-2) + (-10)(z-3) = 0
It can also be written as:
26 - 4x + 4y - 10z = 0
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Complete Question
Find a scalar equation of the plane that contains the point (1,2,3) and contains the line represented by the vector equation r(t) = [3t, 6 - 2t, 1 -2t] ?
i need help please answer correctly
6. Applying the inscribed angle theorem, x = 33
7. m<ABP = 90°.
m<APB = 48°
What is the Tangent Theorem?The tangent theorem states that the tangent of a circle is perpendicular to the radius of that circle and therefore forms a right angle at the point of tangency.
What is the Inscribed Angle Theorem?An inscribed angle has a measure that is half the measure of the intercepted arc, according to the inscribed angle theorem.
Therefore:
Question 6:
Based on the inscribed angle theorem,
Measure of arc AB = 2(x + 3) = 2x + 6
108 + 2x + 6 = 180 [semicircle]
Solve for x
114 + 2x = 180
2x = 180 - 114
2x = 66
x = 33
Question 7:
Given that line PB is tangent to circle A, therefore, based on the tangent theorem, the measure of angle ABP = 90°.
m<APB = 180 - 90 - 42
m<APB = 48°
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Round 0.32 to the nearest ONE.Not the nearest tenth or hundredth..I asked for the one.
Answer:
0.32 rounded to the nearest 1 is 0.
Step-by-step explanation:
If the 0.1 decimal place is equal to 0.5 or higher, you round up but since this is 0.3, you round down.
PLSSSS HELP ASAPPP
Andrew has 34 coins in his pocket. His coins total $2.65. If he has dimes and nickels in his pocket, how many dimes does he have?
What does a scale factor less than 1 do to the image?
Answer:
Makes it smaller
Step-by-step explanation:
A scale factor less than 1 makes the image smaller than the preimage.
A scale factor of 1 makes the image the same size as the preimage.
A scale factor greater than 1 makes the image larger than the preimage.
The set of all possible values of the independent variables (x) in a function is called domain. The set of all possible values of the idependent variables (y) in a function. A graph of a function can be used to find its domain. If a value is outside the domain of a function, we can not use it in calculations of that function.
Option A. stating that the set of all possible values of the independent variables (x) in a function is called a domain.- is the correct answer as per the definition of a domain.
The domain of a function is the set of all the possible values of the independent variable. Or in simple words, we can say that the domain is the set of all possible x-values that makes up the function and gives out real y-values.
Hence, in the given question option A is the appropriate explanation of domain i.e The set of all possible values of the independent variables (x) in a function.
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The complete question is -
Select all correct answers about Domain.
A. The set of all possible values of the independent variables (x) in a function is called a domain.
B. The set of all possible values of the independent variables (y) in a function.
C. A graph of a function can be used to find its domain.
D. If a value is outside the domain of a function, we can not use it in calculations of that function.
A llama weighing 200kg needs to be transported on a stretcher, The upward acceleration on the stretcher is 0.63m/s². What net force is needed to accelerate the llama on the stretcher?
The net force is 126 kg m/s² needed to accelerate the llama on the stretcher.
To determine the net force needed to accelerate a llama weighing 200 kg on a stretcher with an upward acceleration of 0.63 m/s², we can use the formula F = ma, where F is the net force, m is the mass of the llama, and a is the upward acceleration of the stretcher.
As per the question, the mass of the llama is 200 kg and the upward acceleration of the stretcher is 0.63 m/s²,
So, the net force needed to accelerate the llama is:
F = 200 kg × 0.63 m/s²
F = 126 kg m/s².
Thus, the net force is 126 kg m/s² needed to accelerate the llama on the stretcher.
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Kaden earns h dollars per hour working for a landscaper. He works 14 hours per week. He writes the expression 14 x h x 52 to represent how much money he earns in a year. Kaden's boss writes the expression 728h. Which person's expression tells you how many hours Kaden works per year? Explain your reasoning
Kaden's expression tells you how many hours Kaden works per year
How to determine which person's expression tells you how many hours Kaden works per year?Given: Kaden earns h dollars per hour working for a landscaper. He works 14 hours per week.
Kaden expression:
14 x h x 52
The 14 in this expression tells you how many hours Karen works per year. The 52 shows the number of weeks in a year
Kaden's boss expression:
728h
This does not tells how many hours Kaden works per year
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jar contains 6 quarters, 3 dimes, 4 nickels, and 10 pennies. if a coin is randomly selected from the jar, what is the probability that it will not be a dime or a penny?
Probability that a coin pulled at random from the jar will not be a dime or penny is 20 or 13.
Given that,
6 quarters, 3 dimes, 4 nickels, and 10 pennies are included in the jar.
We have to find what is the probability that a coin pulled at random from the jar won't be a dime or a penny.
We know that,
6 quarters, 3 dimes, 4 nickels, and 10 pennies are included in the jar.
6+3+4+10 =23
Probability that a coin pulled at random from the jar will not be a dime is 23-3=20
Probability that a coin pulled at random from the jar will not be a penny is 23-10=13
Therefore, Probability that a coin pulled at random from the jar will not be a dime or penny is 20 or 13.
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Please help me. It’s ASAP!
The interquartile range for the given data set 2.35, 1.56, 1.77, 2.45, 6.02, 4.38, 2.77, 5.23, 2.22, 3.26 is 2.16.
What is meant by interquartile range?The middle two-thirds of your data set—the interquartile range, or IQR—contain the second and third quartiles. The interquartile range, as opposed to range, provides the range of the middle half of a data set. Range provides the spread of the entire data set. The statistical dispersion, or spread of the data, is measured in descriptive statistics by the interquartile range. In addition to the IQR, other names for it include the mid spread, middle 50%, fourth spread, and H-spread. The distinction between the data's 75th and 25th percentiles is what is meant by this term.
Given the data set is,
2.35, 1.56, 1.77, 2.45, 6.02, 4.38, 2.77, 5.23, 2.22, 3.26
First we have to arrange data set in the ascending order:
1.56, 1.77, 2.22, 2.35, 2.45, 2.77, 3.26, 4.38, 5.23, 6.02
Here,
Median=(2.45+2.77)/2
Median=2.61
First Quartile Q₁=2.22
Third Quartile Q₃=4.38
Interquartile Range= Q₃- Q₁
=4.38-2.22
=2.16
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How do you calculate x value?
Answer: To calculate x in an equation, you can first look at the other numbers that aren't missing any values [say 2x + 60x = 248]. To find the value of x, bring the variable(s) to the left and bring all the remaining numbers to the right (I'm trying to explain this in a simple way)
Step-by-step explanation: math
Ethan buys a video game on sale. if the video game usually costs $39.99, and it was on sale for 20% off, how much did ethan pay? round to the nearest cent.
Answer:
The answer should be $31.99
100 POINTS HELP PLEASE Which of the following is a benefit of increased competition?
A. They access the same suppliers.
B. They attempt to win over your customers.
C. They make you improve your product quality.
the situation in which the value of the solution may be made infinitely large in a maximization linear programming problem or infinitely small in a minimization problem without violating any of the constraints is known as
The situation in which the value of the solution may be made infinitely large in a maximisation linear programming problem or infinitely small in a minimisation problem without violating any of the constraints is known as an unbounded solution
What is Linear Programming?
When a linear function is exposed to various constraints, it is maximised or reduced using the mathematical modelling technique known as linear programming.
Let's briefly define some situations
Infiniteness and semi-optimality, does not comply with what the situation exposes.
If there isn't a solution that satisfies all the requirements, the problem is said to be infeasible. As a result, this choice is not.
If the objective function can be improved indefinitely without going against the constraints and limits, then the problem is unbounded, and this is the right response.
The situation in which the value of the solution may be made infinitely large in a maximisation linear programming problem is known as an unbounded solution
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at the tesla automotive factory, a model s sedan is built using 4 tires, a main chassis, and 5 lithium-ion batteries. how many sedans can be made if there are 17 tires, 5 chassis, and 22 batteries?
The number of cars which can be made by using 4 tires, a main chassis, and 5 lithium-ion batteries are 4.
Using hit and trial method :
→ assuming tires as limiting substance
4 tires → 1 car
17 tires → 17/4 ×1 car
= 4.25 cars {reducing it to greatest integer value}
→ Assuming chassis as limiting theorem:
1 chassis → 1 car
5 chassis → 5 cars
→ Assuming batteries as limiting theorem substance:
5 batteries → 1 car
22 batteries → 22/5 × 1 car
= 4.4 → 4 cars
Therefore, 4 cars can be made by the given substance.
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How do you dilate an image?
To dilate an image , multiple the scale factor with the coordinates
The process of dilation entails scaling or changing a thing. It is a transformation that uses the specified scale factor to make the objects smaller or larger.
The resizing happens from a point called the center of dilation. It is the center of dilation from which the objects/figures are expanded or contracted.
Scale factor is a number by which the size of any geometrical figure can be changed with respect to its original size.
Follow the steps below to dilate an image.
Step 1: Determine the scale factor and the dilation centre.
Step 2: Identify an image vertex. Draw a line through one of the image's vertices from the centre of dilation.
Step 3: Determine the horizontal and vertical distances between the dilation centre and the vertex.
To find the horizontal and vertical distances from the centre of dilation to a new vertex, multiply the distances by the scale factor.
Step 4: Determine the new horizontal and vertical distances from the centre of dilation. Make a point plot.
Step 5: Join the new vertices together to create the dilated image.
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How do you solve 4 linear equations?
Steps to solve linear equations;
Clear fractions or decimals. Remove parentheses from each side of the equation and combine similar phrases to make it simpler. Remove the variable term from the equation's other side. Divide each side of the equation to find the solution. Check your solution.Given,
Linear equations;
Ax + By = C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x + 3y = 5. When an equation is given in this format, finding both intercepts is rather simple (x and y).
Here,
The steps to solve linear equations are;
Clear fractions or decimals. Remove parentheses from each side of the equation and combine similar phrases to make it simpler. Remove the variable term from the equation's other side. Divide each side of the equation to find the solution. Check your solution.Learn more about linear equations here;
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Andrew has $20 saved and is working for $8
an hour. How many hours does he have to
work to save a total of at least $140?
Answer:
15 hours
Step-by-step explanation:
Firstly, Andrew has 20$ saved, right? So we should minus that by our goal, $140.
140-20=120
That leaves us with $120 to earn. Andrew works for $8 an hour. So we should divided 120 by 8 to get the number of hours he needs to work to get $140.
120÷8=15 hours
Which means that Andrew has to work for 15 hours to get a total of $140.
a group of fish is called a school . there are twenty-five in the small school.there are one hundered twelve fish in the big school. how many fewer fish are in the small school
There are 87 fewer fish in small school compared to big school.
We solve addition and subtraction problems by focusing on either the action (joining or separating) or the relationship in the problem. Many problems involve monetary relationships.
This week, we looked at COMPARISON problems, which involve determining the similarities and differences between sets.
Difference Unknown: One type of compare problem entails determining how many more items are in one set than another. James, for example, has six mice. Joy has eleven mice. Joy has how many more mice than James?
Given,
Number of fish in small school = 25
Number of fish in big school = 112
then,
Number of fewer fish does small school have 112 -25 = 87
Thus, there are 87 fewer fish in school than big school.
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A school has 1 teacher
for every 24 kids.
How many teachers for 72 kids?
Answer:
There should be around three teachers.
Step-by-step explanation:
72/24 = 3
or
24 x 3 =72
Another way you could do it is three circles put one dot in each circle until you reach 72.
Hope this helped
Find cos (A) given the triangle
[tex]\cos A=\frac{21}{75}[/tex] since cosine is (adjacent)/(hypotenuse).
can someone pls help me with exercise 7 in algebra
Answer: Ok so the slope is always going to be m and the y intercept will be the b.
Step-by-step explanation: For example the slope form in y=mx+b. Whatever is in that b spot is going to be the y-intercept. So for number one on exercise 7 the slope will be 2/3 and the y- intercept will be -4. Same for number 2 remember take your time and know that m is the slope and b is your y-intercept. I really hope this helps you.
The diameter of the circle is 18 m. Eugene incorrectly says that the circumference of the circle is about
113.04 m. What is the circumference of the circle? What mistake did Eugene make?
Answer: 3.14
Step-by-step explanation:
1. go home
2. sleep
3. poop
4. eat
Leah can make one dozen cookies every hour. How many cookies can she make in a four hour period of time?
Answer:
42
Step-by-step explanation:
1 dozen equals 12 so 12 x 4 would be 42
College administrators at a small, private college noticed that students who had higher high school gpas tend to have higher college gpas. What are the explanatory variable and response variable for this relationship?.
The explanatory variables and response variables for this relationship are;
b. Explanatory variable: high school GPA
Response variable: college GPA
What are explanatory variables?
When it comes to an experiment, a researcher-manipulated variable is an explanatory variable. It acts as a gauge of the transformation the response variable underwent.
Explanatory variables are frequently referred to as predictor variables or independent variables. A response variable is the variable that a researcher is asking a specific question about.
Numerous variables, referred to as explanatory variables, might have an impact on the response variable.
Therefore, the correct option is b, Explanatory variable: high school GPA, Response variable: college GPA.
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Complete question:
College administrators at a small, private college
noticed that students who had higher high school
GPAs tend to have higher college GPAs.
What are the explanatory variable and response
variable for this
relationship?
Explanatory variable: size of college
Response variable: college GPA
Explanatory variable: high school GPA
Response variable: college GPA
Explanatory variable: college GPA
Response variable: high school GPA
Explanatory variable: type of college (public)
Response variable: college GPA
There are 1000 rabbits and chickens on a farm, and together they have 3150 legs. How many rabbits and how many chickens are there on the farm?.
The number of rabbits on the farm is 575 and the number of chickens is 425.
Here we have to find the number of rabbits and the number of chickens on the farm.
Data given:
Total number of rabbits and chicken = 1000
Number of legs = 3150
Let x be the number of rabbits and y be the number of chickens.
So we have
x + y = 1000 -------(1)
4x + 2y = 3150
A rabbit has 4 legs and a chicken has 2 legs.
2x + y = 1575 ------(2)
Substrating equation (1) from (2) we have:
x = 575
Now put in equation (1) we have:
575 + y = 1000
y = 425
Therefore the number of rabbits is 575 and the number of chickens is 425.
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You have 1. 50 in dime you exchange all your dime for quarter how many quarter do you have
Answer:
2
Step-by-step explanation:
quarter = 25
2 quarter = 50
Aim receive 18 dollar from hi father in a week. The ratio of the amount of money he pend to the amount of money
As per the given Ratio difference between the amount of money spent and the amount of money saved in a week is $2.
In mathematics, what is a ratio?A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion is an equation that sets two ratios equal to each other.
What exactly is the ratio formula?The ratio formula can be used to represent a ratio as a fraction. For any two quantities, say a and b, the ratio formula is a:b = a/b. Because a and b are separate amounts for two portions, the total quantity is given as (a + b).
et 5x be the money he spends and 4x be the amount he saves
therefore, 5x+4x= 18
9x= 18
x= 18/9= 2
Tom spends, 5×2 = $10
and he saves, 4×2= $8
Difference, = $10-$8= $2
Therefore, as per the given ratio in the question difference between the amount of money spent and the amount of money saved in a week is $2.
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Tom receives $18 from his father in a week. The ratio of the amount of
the money he spends to the amount of money he saves in a week is 5:4
What is the difference between the amount of money spent and
amount of money saved in a week?
Las coordenadas del punto (-2, 3) despues de una reflexion sobre el eje y son:
Responden: Original Answer Language (Spanish)
Las coordenadas del punto (-2, 3) después de una reflexión en el eje y son: (2,3). Se explica en la imagen.
Answer: Traducir el idioma de la respuesta (inglés)
The coordinates of the point (-2, 3) after a reflection on the y-axis are: (2,3). It is explained in the image.
11. Which expression is equivalent to
-5.2v + (-2.8) + 1.1 + (-2.6v)?
A-9.5v
B-3.9v
-7.8v 1.7
-
D-7.8v+3.9
Answer:
C. −7.8v −1.7
Step-by-step explanation:
add like terms
-5.2v + (-2.6v) = −7.8v
(-2.8) + 1.1 = -1.7
Answer:
C ) −8v−1.7
Step-by-step explanation:
1 ) − 5.2v − 2.8 + 1.1 −2.6v
2) = − 5.2v + −2.8 + 1.1 + − 2.6v
Combine Like Terms:
3 ) = − 5.2v + − 2.8 + 1.1 + − 2.6v
4 ) = ( − 5.2v + − 2.6v ) + ( −2.8 + 1.1 )
5 ) = − 7.8v + − 1.7
Hope this helps! :)
at the 0.01 significance level, do women save more money than men? what is the value of the test statistic for this hypothesis test?
Both means are approximately equal at 1% level of significance.
What is significance level?
A finding has statistical significance in statistical hypothesis testing when it is highly unlikely to have happened given the null hypothesis.
H0: Mean of mean = mean of women
Ha: means of men < mean of women
(Left tailed test)
Since population std deviation is known but sample sizes are small t test is used.
The mean of Men minus Women equals -5.00
standard error of difference = 2.201
t = 2.2721
df = 53
p value= 0.0136
since p >0.01 at 1% significance level we fail to reject H0.
Both means are approximately equal at 1% level of significance.
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