Final answer:
The implicit equation of the plane is 2x + y + 3z - 14 = 0, found using the direction vector of the line as the normal vector for the plane and the given point to determine the specific plane equation.
Explanation:
To find an implicit equation for the plane passing through the given point (-1,-4,5) and perpendicular to the given line, we need to determine the direction vector of the line which will also serve as the normal vector to the plane. The equation of the line is given as l(t) = <1+2t, 1+t, 5+3t>, which suggests that the directional vector of the line (and thus the normal vector of the plane) is <2, 1, 3>.
Now, the general equation of a plane in 3D space can be given by Ax + By + Cz + D = 0, where <A, B, C> is the normal vector to the plane. Thus, substituting the normal vector and the given point into this equation will allow us to find the value of D and hence the implicit equation of the plane. In this case, the equation is given by:
2(x + 1) + 1(y + 4) + 3(z - 5) = 0, simplifying this gives:
2x + y + 3z - 14 = 0,
which is the implicit equation of the desired plane.
Final answer:
The implicit equation of the plane passing through the point (-1, -4, 5) and perpendicular to the line ℒ(t) is 2x + y + 3z - 9 = 0.
Explanation:
To find an implicit equation for a plane that is perpendicular to a given line, we first need the direction vector of the line. The line ℒ(t) = <1+2t, 1+t, 5+3t> has a direction vector of <2, 1, 3>, which also serves as the normal vector of the plane. The normal vector (A, B, C) and a point (x0, y0, z0) on the plane can provide an equation via the dot product: A(x - x0) + B(y - y0) + C(z - z0) = 0.
For the given point (-1, -4, 5), the equation becomes 2(x + 1) + 1(y + 4) + 3(z - 5) = 0. Simplifying, we get:
2x + 2 + y + 4 + 3z - 15 = 0
2x + y + 3z - 9 = 0
This is the implicit equation of the plane that passes through the point (-1, -4, 5) and is perpendicular to the given line.
The price of an item has dropped to $46 today yesterday was $115 find the percent decrease
Answer:
percent decrease = 40%
Step-by-step explanation:
The price of an item yesterday = $115
Today the price of the item has dropped to = $46
The percent decrease = [tex]\frac{46}{115}\times 100[/tex]
= 0.40 × 100
= 40%
The percent decrease would be 40%.
(9-13)-(56-65) =5
Replace the question mark to create a TRUE STATEMENT.
The product of 1.3×10^-4 and a number n results in 2.6×10^12 , what is the value of n?
Answer:
2x10^16
Step-by-step explanation:
ik im late but in case anyone still needs it
also tell me if u want an explanation
Factor −1/3
out of −1/3x−8
Answer:
The factor form is [tex]-\frac{1}{3}x-8=-\frac{1}{3}(x+24)[/tex]
Step-by-step explanation:
To find : Factor [tex]-\frac{1}{3}[/tex] out of [tex]-\frac{1}{3}x-8[/tex]
Solution :
Taking the term common means we the number multiply inside give you the same result.
Taking [tex]-\frac{1}{3}[/tex] out of [tex]-\frac{1}{3}x[/tex] is left with
[tex]\frac{-\frac{1}{3}x}{-\frac{1}{3}}=x[/tex]
Taking [tex]-\frac{1}{3}[/tex] out of [tex]8[/tex] is left with
[tex]\frac{8}{-\frac{1}{3}}=-8\times 3=-24[/tex]
So, [tex]-\frac{1}{3}x-8=-\frac{1}{3}(x-(-24))[/tex]
[tex]-\frac{1}{3}x-8=-\frac{1}{3}(x+24)[/tex]
The factor form is [tex]-\frac{1}{3}x-8=-\frac{1}{3}(x+24)[/tex]
write an equivalent expression for 3 (1-7)
Patrick is reading a book about forest animals. He has read 3/4 of the 100 pages in his book. Nicholas has read 2/3 of the 120 pages about alpine flowers. who has more pages to read in his book?
Final answer:
Upon calculating, Nicholas, who is reading about alpine flowers, has more pages left to read (40 pages) in his book compared to Patrick, who is reading about forest animals and has 25 pages left.
Explanation:
The question asks who has more pages to read in his book between Patrick, who is reading about forest animals, and Nicholas, who is reading about alpine flowers. To determine this, let's calculate the pages each has already read and then subtract that from the total number of pages in their respective books.
For Patrick: He has read 3/4 of the 100 pages. This means he has read 75 pages (since 3/4 of 100 is 75), leaving him with 25 pages to read.
For Nicholas: He has read 2/3 of the 120 pages. This means he has read 80 pages (since 2/3 of 120 is 80), leaving him with 40 pages to read.
Comparing the pages left to read, Nicholas has more pages to read in his book about alpine flowers than Patrick does in his book about forest animals.
Let f(x)=2x^2+7x-5 and g(x)=-8^2-3x+5. What is g(x)+f(x)?
Using addition of two polynomials, f(x) + g(x) = 2x² +4x - 64
What is polynomials?Polynomials are "algebraic expressions that may comprise of exponents which are added, subtracted and multiplied".
According to the question,
f(x) = 2x² + 7x - 5
g(x) = -8² - 3x + 5
f(x) + g(x) = 2x² +4x - 64.
Learn more about polynomials here
https://brainly.com/question/21199523
#SPJ
Martha placed $2,500 in a college savings account with a simple interest rate of 5% when when Ryan was born. How much will be in the account in 18 years when her son is ready to go to college?
A. crystal lund has been your trusted employee for 25 years. she performs all cash-handling and accounting duties. crystal just purchased a new lexus and a new home in an expensive suburb. as owner of the company, you wonder how she can afford these luxuries because you pay her only $42,000 a year and she has no sources of outside income
HELP PLZ Which math expression represents the phrase? 9 times the sum of a number and 7 A. 9 · n + 7 B. 9 · (n + 7) C. 9 · (n – 7) D. 9 · (n · 7)
60 minutes is 20% of blank kilometers
13+8 POINTS!!!! PLEASE HELP ME PLEASE!!!!! DUE TODAY PLEASE HELP!!!
Complete the coordinate proof of the theorem.
Enter your answers in the boxes.
The coordinates of parallelogram ABCD are A(0, 0) , B(a, 0) , C(??), and D(c, b) .
The coordinates of the midpoint of AC¯¯¯¯¯ are (, b2 ).
The coordinates of the midpoint of BD¯¯¯¯¯ are ( a+c2 , ).
The midpoints of the diagonals have the same coordinates.
Therefore, AC¯¯¯¯¯ and BD¯¯¯¯¯ bisect each other.
Answer:
Step-by-step explanation:
1). Coordinates of point C will be
x - coordinates = [Distance of B from the origin + Distance of D from y axis]
= (a + c)
y - coordinates = (Distance of D from x - axis)
= b
Therefore, coordinates of C will be [(a + c), b]
2). Coordinates of the midpoint of AC = [tex][\frac{(a+c)+0}{2}, \frac{b+0}{2}][/tex]
= [tex][\frac{(a+c)}{2}, \frac{b}{2}][/tex]
[Since coordinates of the midpoint of (x, y) and (x', y') are denoted by ([tex]\frac{x+x'}{2},\frac{y+y'}{2}[/tex])]
3). Coordinates of the midpoint of BD = [tex][\frac{(a+c)}{2}, \frac{b+0}{2}][/tex]
= [tex][\frac{(a+c)}{2}, \frac{b}{2}][/tex]
The following table gives the scores of 30 students in a mathematics examination. Scores 90–99 80–89 70–79 60–69 50–59 Students 3 7 12 4 4 Find the mean and the standard deviation of the given data. Hint: Assume that all scores lying within a group interval take the middle value of that group. (Round your answers to two decimal places.)
Which is a valid proportion?
A. 3/4=21/28
B. 5/6=29/30
C.4/7=16/49
D.2/5=12/15
The level of calcium in the blood of healthy young adults follows a normal distribution with mean $\mu=10$ milligrams per deciliter and standard deviation $\sigma=0.4$. a clinic measures the blood calcium of 25 healthy pregnant young women at their first visit for prenatal care. the mean of these 25 measurements is $\bar{x}=9.6$ we want to test the hypotheses $h_0$: $\mu=10$ vs. $h_a$: $\mu<10$ what does it mean if the p-value is 0.0002.
The p-value of 0.0002 indicates strong evidence against the null hypothesis and suggests that the mean blood calcium level in pregnant young women is less than 10 milligrams per deciliter.
The p-value of 0.0002 indicates the probability of obtaining a sample mean as extreme as 9.6, assuming the null hypothesis (μ = 10) is true.
A p-value of 0.0002 is less than the commonly used significance level of 0.05, which suggests strong evidence against the null hypothesis.
Therefore, we reject the null hypothesis in favor of the alternative hypothesis (μ < 10).
This means that there is sufficient evidence to suggest that the mean blood calcium level in pregnant young women is less than 10 milligrams per deciliter.
The probable question may be:
The level of calcium in the blood of healthy young adults follows a normal distribution with a mean (\(\mu\)) of 10 milligrams per deciliter and a standard deviation (\(\sigma\)) of 0.4. A clinic measures the blood calcium of 25 healthy pregnant young women at their first prenatal care visit, resulting in a sample mean (\(\bar{x}\)) of 9.6.
Now, we want to test the hypotheses \(H_0: \mu = 10\) versus \(H_a: \mu < 10\). If the computed p-value is 0.0002, what does this indicate in the context of hypothesis testing?
Solve the equation what is 2y-3y=5
When simplified, what is the value of square root of negative 45 end square root,if i2 = −1?
What is the scale factor of Triangle ABC to Triangle DEF?
Answer:
1
Step-by-step explanation:
skylar paid $18 to park at the airport. she bought 4 plane tickets for her family.each plane ticket cost the same. altogether she paid $610 for the plane tickets and parking
Using only the values given in the table for the function, f(x) = x3 – 3x – 2, what is the interval of x-values over which the function is decreasing? (–4, 1) (–4, –1) (–1,1) (–1, 2)
Using only the values given in the table for the function , f(x) = x3-3x-2 , what is the interval of x-values over which the function is decreased. Advertisement ... 3 = 3(x² - 1) We know, any Function f(x) decrease s in interval [a, b] when f'(x) < 0 ... -1 < x < 1. Hence, function f(x) = x³ - 3x - 2 , is decreased in (-1, 1).
The interval of x-values over which the given function is decreasing is (-1,1) and this can be determined by differentiating the given function.
Given :
[tex]\rm f(x) = x^3-3x-2[/tex]
The following steps can be used in order to determine the interval in which the given function is decreasing:
Step 1 - Write the given function.
[tex]\rm f(x) = x^3-3x-2[/tex]
Step 2 - Now, differentiate the above function with respect to 'x'.
[tex]\rm f'(x) = 3x^2-3[/tex]
Step 3 - Now, equate the above expression to zero.
[tex]\rm x^2 = 1[/tex]
x = 1 or -1
Therefore, the correct option is C).
For more information, refer to the link given below:
https://brainly.com/question/24062595
b. Yesterday, Gina again mixed red and white paint and made the same amount of paint, but she used one more pint of red paint than she used last week. Predict how the new paint color will compare to the paint she mixed last week
Karyn proofreads 15 pages in 2 hours for $40. What is her proofreading rate in pages per hour?
………………………………………………………………
When solving -1/3 (x − 15) = −4, what is the correct sequence of operations? Please help!! 15 points
-1/3(x-15) = -4
1st step distribute(multiply) the -1/3 with what is inside parenthesis
-1/3x + 5 = -4
2nd step subtract 5 from both sides of the equation
-1/3x = -9
3rd step divide both sides of the equation by -1/3 to get x
x = -9 / -1/3
x = 27
About 22/40 of a lawn is planted with Kentucky bluegrass. What percent of the lawn is planted with Kentucky bluegrass
What is the length y of the remaining, vertical side of the 30-60 right triangle?
The length of side y in the right triangle, with a hypotenuse of 14 cm and legs measuring 7 cm and y cm is determined to be 16.16 cm.
The triangle has a hypotenuse of 14 cm, and the other two sides are 7 cm and y cm.
Setting up the Equation for sin 60°:
In the given figure, sin 60° is defined as the ratio of the side opposite the angle to the hypotenuse.
The equation is set up as sin 60° = y / 14.
Substituting the Value of sin 60°:
The sine of 60 degrees is known to be √3/2.
Substitute sin 60° with √3/2 in the equation: √3/2 = y / 14.
Isolating y in the Equation:
Multiply both sides of the equation by 14 to isolate y: √3y = 28.
Solving for y:
Divide both sides of the equation by √3 to solve for y: y = 28/√3.
Rationalizing the Denominator:
Multiply the numerator and denominator of y by √3 to rationalize the denominator: y = (28√3)/3.
Simplifying the Expression for y:
The final step simplifies the expression by dividing both numerator and denominator by 3: y = 16.16 cm.
Therefore, the length of side y in the given right triangle is 16.16 cm.
A hypotenuse of 14 cm and legs of 7 cm and y cm, the length of side y in a right triangle is calculated to be 16.16 cm.
The triangle's two other sides are 7 cm and y cm, and its hypotenuse measures 14 cm.
Configuring the Equation for 60° Sin:
As seen in the illustration, sin 60° is the side opposite the angle divided by the hypotenuse.
The formula is written as follows: sin 60° = y / 14.
Replacing the Value of Sin 60° with:
It is known that the sine of sixty degrees is √3/2.
Replace √3/2 with sin 60° in the equation: y / 14 = √3/2.
Calculating y in the Equation: To isolate y, multiply both sides by 14: √3y = 28.
Finding y':
To find y, divide both sides of the equation by √3. y = 28/√3.
Making Sense of the Denominator
To rationalize the denominator, multiply both the numerator and denominator of y by √3. y = (28−3)/3.
The Expression for y Simplified:
In the last stage, the formula is made simpler by dividing the denominator and numerator by three: y is equal to 16.16 cm.
As a result, side y in the supplied right triangle has a length of 16.16 cm.
What does h(40) = 1400 mean in terms of the problem
Answer:
The correct option is B.
Step-by-step explanation:
From the given table it is clear that left column represents the hours of training and the right column represents the Monthly pay.
Here, left column is input (x) and right column is output (y). It means a worker with x hours of training is paid $y per month.
[tex]h(40)=1400[/tex]
In this equation the value of y is 1400 at x=40.
A worker with 40 hours of training is paid $1400 per month.
Therefore, correct option is B.
If someone sleeps 8 hours a day for 75 years how many hours did that person sleep in his lifetime?
Jenny read 3 books in 7.5 hours. At this rate, how many books can Jenny read in one hour?
Solve the system of linear equations. separate the x- and y- values with a coma.
7x-7y=7
14x-4y=74
A survey of 100 people found that 35 people exercise in the morning, 45 people exercise in the afternoon, and 20 people exercise at night. Tara claims that 35:55, 45:80, and 20:65 are possible ratios from this data. Jim claims that 35:100, 45:100, and 20:100 are possible ratios from this data. Who is correct? Explain.
Jim is correct as he has shown the ratio of people exercising at various times to total people in survey , correctly.
It is given that total 100 people participated in a survey and data of people doing exercises in morning , evening and at night is given.
We have to find out who is correct , if Tara and Jim has shown the possible ratios.
What do you mean by ratio ?
A ratio is defined as the relative sizes of two or more values i.e., 12 : 24 or 13 : 26 , etc.
As per the question ;
Total no. of people in survey = 100
People exercising in morning = 35
People exercising in afternoon = 45
People exercising at night = 20
and
Possible ratio claimed ;
According to Tara is ;
35:55, 45:80, and 20:65
and
According to Jim is ;
35:100, 45:100, and 20:100
Let's check who has got it correct ;
So ;
Ratio of people exercising in morning to total people in survey will be ;
= 35 : 100
and
Ratio of people exercising in afternoon to total people in survey will be ;
= 45 : 100
Ratio of people exercising at night to total people in survey will be ;
= 20 : 100
So ;
We found that Jim has shown the correct possible ratio.
Thus , Jim is correct as he has shown the ratio of people exercising at various times to total people in survey , correctly.
To learn more about ratios click here ;
brainly.com/question/25866844
#SPJ2