The normal equation of the plane is: 20x - 48y + 56z = 0
To find the normal equation of the plane determined by points A(3, 0, -2), B(11, -5, 2), and C(3, 7, 4), we can use the cross product of the vectors formed by two sides of the plane.
Let's first find two vectors on the plane:
Vector AB = B - A = (11, -5, 2) - (3, 0, -2) = (8, -5, 4)
Vector AC = C - A = (3, 7, 4) - (3, 0, -2) = (0, 7, 6)
Next, we calculate the cross product of AB and AC:
N = AB × AC
The cross product is given by:
N = (AB_y * AC_z - AB_z * AC_y, AB_z * AC_x - AB_x * AC_z, AB_x * AC_y - AB_y * AC_x)
Substituting the values:
N = (8 * 6 - 4 * 7, 4 * 0 - 8 * 6, 8 * 7 - (-5) * 0)
N = (48 - 28, 0 - 48, 56 - 0)
N = (20, -48, 56)
Know more about equation of the plane here:
https://brainly.com/question/28456872
#SPJ11
food safety guidlines recommend that a beef rib roast should cook for 23 minutes per pound based on 325f oven setting. how many hours should it take to cook a 5.17 pound roast?
It should take approximately 1.98 hours, or around 1 hour and 59 minutes, to cook a 5.17 pound beef rib roast based on the recommended guideline of 23 minutes per pound at a 325°F oven setting.
To calculate the cooking time for a 5.17 pound roast, we can use the recommended guideline of 23 minutes per pound. First, we need to convert the weight from pounds to minutes, and then convert minutes to hours.
Cooking time in minutes = 5.17 pounds * 23 minutes/pound
Cooking time in minutes = 118.91 minutes
To convert minutes to hours, we divide the total minutes by 60:
Cooking time in hours = 118.91 minutes / 60
Cooking time in hours ≈ 1.98 hours
Therefore, it should take approximately 1.98 hours to cook a 5.17 pound beef rib roast based on the recommended guideline of 23 minutes per pound at a 325°F oven setting.
To know more about recommended guideline refer here:
https://brainly.com/question/28617982#
#SPJ11
Can anyone help me? I’ll give Brainly!!!
Answer:
Step-by-step explanation:
its 12 yd
Answer:
This is your answer. If I'm right so,
Please mark me as brainliest. thanks!!!
On a coordinate plane, a line goes through (0, negative 1) and (3, 1). a point is at (negative 3, 0). what is the equation of the line that is parallel to the given line and has an x-intercept of â€"3? y = two-thirdsx 3 y = two-thirdsx 2 y = negative three-halvesx 3 y = â€"three-halvesx 2
The equation of the line that is parallel to the given line and has an x-intercept of 3 is y = 2/3x - 2
What is the equation of the line that is parallel to the given line and has an x-intercept of 3?The given parameters are
Point =(0, -1) and (3, 1)
Calculate the slope using
m = (y₂ - y₁)/(x₂ - x₁)
Where m represents the slope
So, we have:
m = (1 -- 1)/(3 -0)
Evaluate
m = 2/3
Parallel lines have equal slopes
So, the slope of the other line is
m = 2/3
Linear equations are represented as:
y = mx + c
Where m represents the slope and c represents the y-intercept
So, we have
y = 2/3x + c
An x-intercept of 3 means
0 = 2/3 * 3 + c
So, we have
c = -2
Substitute c = -2 in y = 2/3x + c
y = 2/3x - 2
Hence, the equation of the line that is parallel to the given line and has an x-intercept of 3 is y = 2/3x - 2
Learn linear equations at
https://brainly.com/question/14323743
#SPJ4
precalculus b dba given a vertical asymptote and a horizontal asymptote, how would you begin to find an expression for a rational function?
By finding the vertical and horizontal asymptotes, you can use them to help find an expression for the rational function
To find an expression for a rational function given a vertical asymptote and a horizontal asymptote, start by recognizing that the general form of a rational function is f(x) = (ax + b)/(cx + d), where a, b, c, and d are all constants.
Next, use the given information to solve for a, b, c, and d in the equation. The vertical asymptote represents the x-values at which the denominator of the equation equals zero, so set cx + d equal to zero and solve for x. Similarly, the horizontal asymptote can be found by setting ax + b equal to the asymptote’s y-value.
Once both equations are solved for x, substitute the x-values back into the equation for the rational function and solve for the corresponding a, b, c, and d values.
A vertical asymptote occurs when the denominator of the rational function is equal to zero, so you can set the denominator equal to zero and solve for the variable to find the vertical asymptote.
A horizontal asymptote occurs when the degree of the numerator and denominator are equal, so you can look at the leading coefficients of the numerator and denominator to find the horizontal asymptote.
Know more about asymptotes here:
https://brainly.com/question/4138300
#SPJ11
Kaun ha R 5,400. 00 on hand to be depoited in two account. He ha depoited part
of it in a fixed depoit at 3% annual interet and the ret in a aving account that earn
2% annual interet. If the imple interet earned from both account i R 140. 00 for
the year, then how much doe he have in each account
Based on simultaneous equations, Kaun has deposited in each account the following:
Account A = R 3,200Account B = R 2,200.What are simultaneous equations?When two or more algebraic equations are solved concurrently, we call them simultaneous equations.
We can solve simultaneous equations by graphing, elimination, or substitution methods.
The total deposit in the two accounts = R 5,400
The annual interest in Account A = 3% or 0.03
The annual interest in Account B = 2% or 0.02
The total interest earned from both accounts for the year = R 140
Let Account A be designated as a and Account B be designated as b.
Equations:a + b = 5,400 ... Equation 1
0.03a + 0.02b = 140 ... Equation 2
Eliminate a by multiplying Equation 1 by 0.03:
0.03a + 0.03b = 162 ... Equation 3
Subtract Equation 2 from Equation 3:
0.03a + 0.03b = 162
-
0.03a + 0.02b = 140
= 0.01b = 22
b = 2,200
From Equation 1, substitute b:
a + 2,200 = 5,400
a = 3,200 (5,400 - 2,200)
Check:
In equation 2:
0.03a + 0.02b = 140
0.03(3,200) + 0.02(2,200) = 140
96 + 44 = 140
140 = 140
Learn more about simultaneous equations at https://brainly.com/question/185757
#SPJ1
may u answer this with equation im very confused pls
Answer:
See explanation below.
Step-by-step explanation:
1. (-1, -1) and (2, -2)
m = -2+1 / 2+1
m = -1/3
2. (-1, -4) and (0, -1)
m = -1+4 / 0+1
m = 3/1
m = 3
3. (-4, 0) and (-2, -3)
m = -3-0 / -2+4
m = -3/2
4. (2, 0) and (0, -3)
m = -3-0 / 0-2
m = -3/-2
m = 3/2
5. (-1, 2) and (-4, -3)
m = -3-2 / -4+1
m = -5/-3
m = 5/3
6. (4, 3) and (1, -4)
m = -4-3 / 1-4
m = -7/-3
m = 7/3
I need help on this question!
Answer:
110 cookies in 180 minutes
Step-by-step explanation:
To solve the system of linear equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 by using the linear combination method, Henry decided that he should first multiply the first equation by –3 and then add the two equations together to eliminate the x-terms. When he did so, he also eliminated the y-terms and got the equation 0 = 0, so he thought that the system of equations must have an infinite number of solutions. To check his answer, he graphed the equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 with his graphing calculator, but he could only see one line. Why is this?
Henry could only see one line since both lines had the same slope, which means that the graphs of both equations will be identical and hence overlap.
Identify the linear equation?Linear equations in a system 3x + 2y = 4, and 9x + 6y = 12
We must demonstrate why Henry could only make out one line when he plotted the equations 3x-2y=4 and 9x-6y=12 on a graph.
Take the provided linear equation system into consideration.
3x - 2y = 4 ................(1)
9x - 6y = 12 ..................(2)
Due to the fact that equation (2) is a multiple of equation (1), 3 (3x - 2y = 4) = 9x - 6y = 12
The slopes of the provided equations are also same.
Difference with regard to x for equation (1) yields,
additional to equation (2),
With regard to x, we can differentiate to get,
The graphs of both equations will overlap since both lines have the same slope and hence have the same appearance on the graph.
To learn more about linear equations refer to:
https://brainly.com/question/2030026
#SPJ1
based on the following results, conclude whether to reject or not reject h0. h0 : p=0.75; ha : p>0.75 α=0.05 (significance level) the test statistic is 2.59. the critical value is z0.05=1.65.
Reject H0.
To determine whether to reject or not reject H0 (null hypothesis), we compare the test statistic to the critical value. In this case, the test statistic is 2.59, and the critical value at a significance level of 0.05 is 1.65.
Since the test statistic is greater than the critical value, we have sufficient evidence to reject the null hypothesis. This suggests that there is significant evidence to support the alternative hypothesis (Ha: p > 0.75).
The result indicates that the proportion being tested is significantly greater than the hypothesized value of 0.75.
For more questions like Hypothesis click the link below:
https://brainly.com/question/31319397
#SPJ11
is 132 divisible by 3
Answer:
yes clearly
Step-by-step explanation:
using rules of divisibility it is divisible
using your calculator it is divisible
the answer is 44
pls hurry. 10. Select all numbers that represent a solution of the equation below.
\(x^2=196\\x=-\sqrt{196} \vee x=\sqrt{196}\\x=-14 \vee x=14\)
Therefore, it's A and D.
Help now Twenty-seven is 25% of a0.
Answer:
27 is 25 % of 108
Step-by-step explanation:
x*25/100=27 or x=(27*100)/25=108
11.) The sum of four consecutive even
integers is 68. Find the four consecutive
even integers. What is the 3rd integer
in the sequence?
Answer:
Four consecutive even integers are 14, 16, 18 and 20Step-by-step explanation:
Let N be the first even integer
Each consecutive integer is 2 away from the previous integer
Next consecutive integer = N + 2, next one = N+4 and the last one = N +6
Add these expressions together, set them equal to 68 to solve for N
==> N + (N +2) + (N +4) + (N + 6) = 68
==> N + N +2 + N +4 + N + 6 = 68
==> 4N + 12 = 68
==> 4N = 68-12
==> 4N = 56
N = 56/4 = 14
So the integers are 14, 16, 18 and 20
Third integer in the sequence is 18
What is the value of -112.84-54.14-(29.18)?
−196,16
.....................
In exponential growth functions, the base of the exponent must be greater than 1. How would the function change if the base of the exponent were 1
If the base of the exponent in an exponential growth function were 1, the function would become constant, with a fixed value of 1 regardless of the value of x.
In exponential growth functions, the base of the exponent represents the factor by which the function grows at each step. When the base is greater than 1, the function experiences exponential growth, with the values increasing rapidly over time. However, if the base of the exponent were 1, the function would change significantly.
When the base of the exponent is 1, the function becomes constant. This is because any number raised to the power of 1 remains unchanged. Therefore, if the base is 1, the exponential function will have a constant value and will not exhibit any growth or decay.
Mathematically, an exponential function with a base of 1 can be represented as:
f(x) = 1^x
No matter what value of x is used, the result will always be 1. For example, if we substitute different values for x, such as x = 2 or x = -3, we get:
f(2) = 1^2 = 1
f(-3) = 1^(-3) = 1
In both cases, the result is always 1.
For more such question on exponent. visit :
https://brainly.com/question/13669161
#SPJ8
Hannah has liabilities totaling $30,000 (excluding her mortgage of $100,000 ). Her net worth is $45,000. What is her debt-to-equity ratio? 0.75 0.45 0.67 1.30 1.00
Hannah's debt-to-equity ratio when her liabilities was $30,000 (excluding her mortgage of $100,000 ) and her net worth is $45,000 is 0.75.
Debt-to-equity ratio is a financial ratio that measures the proportion of total liabilities to shareholders' equity. To calculate the debt-to-equity ratio for Hannah, we need to first calculate her total liabilities and shareholders' equity.
We are given that Hannah has liabilities of $30,000 excluding her mortgage of $100,000. Therefore, her total liabilities are $30,000 + $100,000 = $130,000.
We are also given that her net worth is $45,000. The net worth is calculated by subtracting the total liabilities from the total assets. Therefore, the shareholders' equity is $45,000 + $130,000 = $175,000.
Now we can calculate the debt-to-equity ratio by dividing the total liabilities by the shareholders' equity.
Debt-to-equity ratio = Total liabilities / Shareholders' equity = $130,000 / $175,000 = 0.74 (rounded to two decimal places)
Therefore, Hannah's debt-to-equity ratio is 0.74, which is closest to option 0.75.
Learn more about Debt-to-equity ratio here: https://brainly.com/question/27993089
#SPJ11
Solve the equation for x. 2/3x-1/9+5=20
Answer: x = 68/3
Step-by-step explanation: 2/3x - 1/9 + 5 = 20
Combine the fractions: 5 - 1/9 = 44/9
44/9 + ⅔x = 20
Subtract 44/9 from both sides: 44/9 + ⅔x - 44/9 = 20 - 44/9
Simplify: ⅔x = 136/9
Multiply both sides by 3: 3 x ⅔x = 136 x 3 divided by 9
Simplify: 2x = 136/3
Divide both sides by two: 2x/2 = 136/3 divided by two
Simplify: x = 68/3
Lebron runs 3 miles in 14 minutes at a constant speed . Stephon runs 1 mile in (3/4) the amount of time Lebron runs 1 mile . How long does it take for Stephon to run 1 mile ?
Speed generally refers to the rate at which an object moves, typically measured in units of distance per unit of time, such as miles per hour or meters per second.
To solve this problem, we need to first figure out how long it takes LeBron to run one mile. We know that he runs three miles in 14 minutes, so we can set up a proportion:
3 miles / 14 minutes = 1 mile / x minutes
Cross-multiplying, we get:
3x = 14
x = 4.67 minutes
So LeBron runs one mile in 4.67 minutes.
Next, we need to figure out how long it takes Stephon to run one mile. We know that he runs one mile in (3/4) the amount of time it takes LeBron to run one mile, so we can set up another proportion:
(3/4)x = 1
Cross-multiplying, we get:
3x = 4
x = 4/3 = 1.33 minutes
So it takes Stephon 1.33 minutes to run one mile.
In summary, LeBron runs one mile in 4.67 minutes and Stephon runs one mile in 1.33 minutes.
To know more about Speed visit:
https://brainly.com/question/28224010
#SPJ11
solve the system of equations y=8x+5 y=6x+25
Answer:
(10,85)
Step-by-step explanation:
x=10
y=85
For a science experiment, maria threw an egg 88.2 meters in 3 seconds. what was the average rate of speed of the egg? a. 88.2 m/sec. b. 44.1 m/sec. c. 29.4 m/sec. d. 9.8 m/sec.
Answer: its not A its b c or d sorry i could not help more
Answer:
The answer is C. 29.4 m/sec.
Step-by-step explanation:
I got it right ^w^
HELP!!!
WHAT IS THE AREA OF THE POLYGON IN SQUARE UNITS?
A- 180 square units
B- 108 square units
C- 70 square units
D- 64 square units
Answer: C
Step-by-step explanation:
area of rectangle = (5--2) × (2--2) = 7 × 4 = 28
area of triangle = ((12-5) × (6--6)) ÷ 2 = (7 × 12) ÷ 2 = 84 ÷ 2 = 42
total area = 28 + 42 = 70
the t distribution is a family of similar probability distributions T/F
The statement "the t distribution is a family of similar probability distributions" is True.
The t-distribution is indeed a family of similar probability distributions. It is used in statistics to model the distribution of a random variable when the sample size is small and the population standard deviation is unknown. The shape of the t-distribution depends on the degrees of freedom, which is determined by the sample size. As the degrees of freedom increase, the t-distribution approaches the shape of the standard normal distribution.
The t-distribution is symmetric and bell-shaped like the normal distribution, but it has heavier tails, which means it has more probability in the tails and less in the center compared to the normal distribution. The t-distribution plays a crucial role in hypothesis testing and constructing confidence intervals when working with small samples.
To know more about t-distribution, refer here:
https://brainly.com/question/32675925#
#SPJ11
3. The x-intercept of a line is -5 and the y-intercept is -2. What is the equation of the line?
A y = -5/2x -5
B y = 2/5x +2
C y = 5/2x -2
D y = -2/5x -2
4. What is the slope- intercept form of the equation y- 7 = -5/2(x+4)?
A y - 2 = -5/2(x+2)
B y + 7 = -x + 5/2
C y = -4/7 +2
D y = -5/2x -3
5. What is the standard form of the equation y = -3/2x +5?
A 3x + 2y = 10
B 3x - 2y = 10
C -2y - 3x = 26
D 3x + 2y = 26
Answer:
1)D
2)D
3)A
Step-by-step explanation:
A plane flies from Dubbo on a bearing of 139° for 852 km, then turns and flies on a bearing of 285° until it is due west of Dubbo. How far from Dubbo is the plane, to the nearest km?
Answer:
Step-by-step explanation:
So first you add them together which gives you infinity and then you divide infinity by (139+285) then keep doing it until you realise this is a scam
please help asap, it's for homework
Answer:
The slope is 10/1 so +10
Step-by-step explanation:
Hope this helps !!!
Answer:
10.
Step-by-step explanation:
Picking out 2 convenient points, (3, 30) and (0, 0):
Slope = (30-0)/(3-0)
= 30/3
= 10.
Karen exchanged BDS$2000 and received EC$2700. How much is the value of one BDS$ in EC$
Answer:
Bds$ 1 EC$ 1.34
Step-by-step explanation:
Which property can be changed to affect the natural frequency of an object?
responses
color
length
elasticity
pressure
Length can be changed to affect the natural frequency of an object. (option 2).
The natural frequency of an object refers to the frequency at which it vibrates when subjected to a disturbance. It is determined by the object's mass and stiffness, with a long object having a lower natural frequency than a shorter one. Changing the length of an object directly affects its mass, stiffness, and natural frequency.
For example, if a spring is made longer, its natural frequency will decrease, causing it to oscillate more slowly. Conversely, if the length of a spring is reduced, its natural frequency will increase, making it oscillate more quickly. Other properties such as color, elasticity, and pressure do not affect the natural frequency of an object in the same manner as length.
Learn more about natural frequency here:
https://brainly.com/question/12936127
#SPJ4
Complete Question:
Which property can be changed to affect the natural frequency of an object?
colorlengthelasticitypressureplz i need help for my exam 100 points
What is the solution to this system?
x= 7 - 2y
2x + y = 5
(3,1)
(4,-1)
(1,3)
(-1,4)
The temperature at noon was 5.6 F. During the afternoon the temperature dropped 2.8 F and then dropped another 2.2 F in the evening.
Part A: Estimate the new temperature
Part B: Find the actual new temperature
Part C: Peter got an exact new temperature of 11.63 F. Explain how peter can use the estimate to determine that his answer is wrong
-If the answer is correct, I'll give brainiest
Which value of x makes this equation true? -12x - 2(x+9) = 5(x+4)
x = -2
−12x−2(x+9)=5(x+4)
Use the distributive property to multiply −2 by x+9.
−12x−2x−18=5(x+4)
Combine −12x and −2x to get −14x.
−14x−18=5(x+4)
Use the distributive property to multiply 5 by x+4.
−14x−18=5x+20
Subtract 5x from both sides.
−14x−18−5x=20
Combine −14x and −5x to get −19x.
−19x−18=20
Add 18 to both sides.
−19x=20+18
Add 20 and 18 to get 38.
−19x=38
Divide both sides by −19.
x=
−19
38
Divide 38 by −19 to get −2.
x=−2
The required simplified value of x for the given equation is -2/19.
To determine the value of x that makes equation -12x - 2(x + 9) = 5(x + 4) true.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
-12x - 2(x + 9) = 5(x + 4)
-12x -2x - 18 = 5x + 20
-14x - 18 = 5x + 20
-14x - 5x = 20 - 18
-19x = 2
x = -2/19
Thus, the required simplified value of x for the given equations is -2/19.
Learn more about simplification here: https://brainly.com/question/12501526
#SPJ2