Answer:
The equation of the plane is
8(x - 5) - 7(y - 4) - 5(z - 5) = 0
8x - 7y - 5z + 13 = 0
Step-by-step explanation:
Given 3 points, P(x₁, y₁, z₁), Q(x₂, y₂, z₂), and R(x₃, y₃, z₃).
We can calculate the equation of the plane through those points as
a(x - x₀) + b(y - y₀) + c(z - z₀) = 0, where (x₀, y₀, z₀) are the coordinates of any one of the points P, Q, or R, and <a,b,c> is a vector perpendicular to the plane.
The vector perpendicular to the plane is obtained by writing vector PQ and PR and taking the cross or vector product.
For this question,
P = (5, 4, 5)
Q = (-5, -1, -4)
R = (-2, 1, -2)
PQ = (-5, -1, -4) - (5, 4, 5) = (-10, -5, -9)
= (-10î - 5ĵ - 9ķ)
PR = (-2, 1, -2) - (5, 4, 5) = (-7, -3, -7)
= (-7î - 3ĵ - 7ķ)
PQ × PR is then
| î ĵ ķ |
|-10 -5 -9|
|-7 -3 -7|
= î [(-5×-7) - (-9×-3)] - ĵ [(-10×-7) - (-9×-7)] + ķ [(-10×-3) - (-7×-5)]
= î (35 - 27) - ĵ (70 - 63) + ķ (30 - 35)
= 8î - 7ĵ - 5ķ
Hence, (a, b, c) = (8, -7, -5)
And using point P as (x₀, y₀, z₀) = (5, 4, 5)
The equation of the plane is
a(x - x₀) + b(y - y₀) + c(z - z₀) = 0
8(x - 5) - 7(y - 4) - 5(z - 5) = 0
8x - 40 - 7y + 28 - 5z + 25 = 0
8x - 7y - 5z = 40 - 28 - 25 = -13
8x - 7y - 5z + 13 = 0
Hope this Helps!!!
Let f(x) = -2x + 7 and g(x) = -6x + 3. Find fg and state its domain.
Answer:
f(g(x))=12x+1
Step-by-step explanation:
f(g(x)) = -2(-6x+3)+7
f(g(x))= 12x-6+7
f(g(x))=12x+1
Domain: All real numbers
The functions r and s are defined as follows. r(x)=2x-1 s(x)=-2x^2-2 Find the value of s(r(-4)).
Answer:
s(r(-4)) = -164
Step-by-step explanation:
r(x) = 2x - 1
s(x) = -2x^2 - 2
r(-4) = 2(-4) - 1 = -8 - 1 = -9
s(r(-4)) = s(-9) = -2(-9)^2 - 2 = -2*81 - 2 = -162 - 2 = -164
Hope this helps!
Given that a = 5 , b = − 2 and c = − 2 work out 2 b − 3 a c
Answer:
26Step-by-step explanation:
[tex]a = 5 ,\\b = - 2 \\ c = - 2 \\ 2b - 3ac=?\\2(-2) -3(5)(-2)\\-4 +30\\= 26[/tex]
Answer:
-34
Step-by-step explanation:
2x-2-3(4)(-2)
which is -34
In a Washington town, the charge for commerical waste collection is $694.55 for 5 tons of waste and $1098.56 for 8 tons of waste. (a) Find a linear formula for the cost, C. of waste collection as a function of the weight, w, in tons.
Answer:
[tex] m =\frac{1098.56-694.55}{8-5}= 134.67[/tex]
And we can find the intercept like this:
[tex] 694.55 = 134.67*5 +b[/tex]
[tex] b = 694.55 -673.35= 21.2[/tex]
And the equation would be given by:
[tex] C = 134.67 w + 21.2[/tex]
Step-by-step explanation:
For this case we want a function given by:
[tex] C = mw +b[/tex]
Where C is the cost, m the slope, w the weight and b the intercept.
We have the following info (w=5, C= 694.55) and (w=8, C=1098.56) and we can find the slope with this formula:
[tex] m =\frac{1098.56-694.55}{8-5}= 134.67[/tex]
And we can find the intercept like this:
[tex] 694.55 = 134.67*5 +b[/tex]
[tex] b = 694.55 -673.35= 21.2[/tex]
And the equation would be given by:
[tex] C = 134.67 w + 21.2[/tex]
A linear function is a function that changes at a constant rate.
The formula of the linear relationship is [tex]C = 134.67w + 21.2[/tex]
The given parameters are:
w = 5, C = 694.55 ---- Charges for 5 tonsw = 8, C = 1098.56 ---- Charges for 8 tonsStart by calculating the slope (m)
[tex]m = \frac{C_2 - C_1}{w_2 - w_1}[/tex]
This gives
[tex]m = \frac{1098.56 - 694.55 }{8- 5}[/tex]
Simplify
[tex]m = \frac{404.01}{3}[/tex]
This gives
[tex]m = 134.67[/tex]
The equation is then calculated as:
[tex]C = m(w -w_1) + w_1[/tex]
This gives
[tex]C = 134.67(w -5) + 694.55[/tex]
Expand
[tex]C = 134.67w -673.35 + 694.55[/tex]
[tex]C = 134.67w + 21.2[/tex]
Hence, the formula of the linear relationship is [tex]C = 134.67w + 21.2[/tex]
Read more about linear equations at:
https://brainly.com/question/14323743
"How much room is there to spread frosting on the cookie?" Clare says, "The radius of the cookie is about 3 cm, so the space for frosting is about 6 cm." Andre says, "The diameter of the cookie is about 3 inches, so the space for frosting is about 2.25 sq. in."
A. Is this question talking about area or circumference? Pick one. Why?
B. Which person is most likely correct, Clare or Andre? Why?
Answer:
(a)Area
(b)Andre is Right
Step-by-step explanation:
(a)Frost is spread on the surface of a cookie, therefore the question is talking about the area of the circular cookie.
(b)
Andre says, "The diameter of the cookie is about 3 inches, so the space for frosting is about 2.25 sq. in
Area of a Circle[tex]=\pi r^2[/tex]
Radius =Diameter/2 =3/2=1.5 Inches
Therefore, Space for frosting on the cookie
[tex]=\pi *1.5^2\\=2.25\pi$ in^2[/tex]
Andre is right.
What is the slope of the line that passes through the points (-3, -3) and
(-18, -23)? Write your answer in simplest form.
Answer:
work is shown and pictured
Given f(xl=x-7 and g(x)=x^2 find g(f(4))
Answer:
So we first need to solve for f(4) because thats what's inside g(_)
It should be 4-7 because I think its f(x)=x-7 you weren't very clear on it.
so that means that we need to solve for g(-3)
-3^2 = 9 because -3*-3 = 9
9 is answer
I need help pleaseeee help meee
Answer:
x>-1
Step-by-step explanation:
Answer:
x > -1
Step-by-step explanation:
First we need to determine what sign this inequality uses:
A closed circle represents greater than or equal to (≥) or less than or equal to (≤)An open circle represent greater than (>) or less than (<)Here we have an open circle so we know our sign will either be > or <
Our point is on the -1, and the arrow points in the direction of the sign as long as the variable x is on the left side of the answer
So the arrow is point to the right, indicating our sign will also be "pointing" to the right (>)
The inequality of this graph reads: x > -1
4x and 16y are like terms.
O A. True
O B. False
Answer for (12x+5)x-7x+2
Answer:
(12x2-2x+2)
Step-by-step explanation:
(12x)(x)+(5)(x)+-7x+2
12x2+5x+-7x+2
(12x2)+(5x+-7x)+(2)
12x2+-2x+2
A completely randomized design Group of answer choices has one factor and one block. has one factor and one block and multiple values. can have more than one factor, each with several treatment groups. has only one factor with several treatment groups.
Answer:
C. can have more than one factor, each with several treatment groups.
Step-by-step explanation:
A completely randomized design can be used in experimental research of a primary factor or multiple factors. The factors could have several treatment groups which are assigned in a random manner. For example, a researcher, could want to determine the effect of a drug against a disease on a class of people. To do this, he designs a treatment group with different concentrations of the drug and a placebo group. He then gets an equal number of subjects, randomly assigning them to each of the groups. The effect of both treatments are compared to know if the drug is indeed effective against the disease the researcher is experimenting on.
Completely randomized design has found application in agricultural and environmental researches.
what is the x-intercept of the line 10x-5y=40
Answer:
4
Step-by-step explanation:
The x-intercept occurs when y=0, if you think about it graphically. Plug y=o into your equation:
10x - 5(0) = 40
10x = 40 (divide each side by 10)
x=4
The point A (-7,5) is reflected over the line x = -5, and then is reflected over the line x= 2. What are the coordinates of
A?
o (7, 19)
O (10,5)
(7,5)
(10, 19)
Answer:
(7, 5) is the final reflection of the point.
Step-by-step explanation:
We are given point A(-7, 5) which is first reflected over the line [tex]x= -5[/tex].
The minimum distance of the point A(-7, 5) from the line [tex]x= -5[/tex] is 2 units across the horizontal path (No change in y coordinate).
Point A lies 2 units on the left side of the line [tex]x= -5[/tex].
So, its reflection will be 2 units on the right side of [tex]x= -5[/tex].
Let its reflection be A' which has coordinates as (-5+2,5) i.e. (-3, 5).
Now A'(-3, 5) is reflected on the line [tex]x=2[/tex].
The minimum distance of the point A'(-3, 5) from the line [tex]x=2[/tex] is 5 units across the horizontal path (No change in y coordinate).
Point A' lies 5 units on the left side of the line [tex]x=2[/tex].
So, its reflection will be 5 units on the right side of [tex]x=2[/tex].
Let its reflection be A'' which has coordinates as (2+5, 5) i.e (7, 5) is the final reflection of the point..
Please find attached image.
(7, 5) is the final reflection of the point.
Solve the inequality.
-3(x-1) > -3x - 2
Answer:
all real x
Step-by-step explanation:
-3(x-1) > -3x - 2
Distribute
-3x +3> -3x -2
Add 3x to each side
-3x +3 +3x > -3x+3x - 2
3 > -2
This is always true so the inequality is true for all x
What is the product of 4.672 and 8?
Answer:
12.672
Step-by-step explanation:
Answer: 37.376
Step-by-step explanation: Because 4.672 x 8 is 37.376
A family of five rents a kayak and splits the total time, k, equally. Each family member spent less than 25 minutes kayaking. Which values can be used to complete the math sentence below so that it accurately represents the situation?
Answer:
k ÷ 5 < 25
Step-by-step explanation:
Edg.
Answer:
k ÷ 5 < 25
Step-by-step explanation:
Which value of k makes 5-k+12=16 a true statement? Choose 1 answer: Choice A) k=1 (Choice B) k=2 (Choice C) k=3 (Choice D) k=4
Answer:
A) k=1
Step-by-step explanation:
5-k+12=16
17-k=16
k=1
Answer:
k=1
Step-by-step explanation:
5-k+12=16
Combine like terms
17 - k = 16
Subtract 17 from each side
17-k-17 = 16-17
-k = -1
Divide by -1
k = 1
a circle with circumference 20 has an arc at 72 central angle. what is the length of the arc
Answer:
4 units
Step-by-step explanation:
[tex] \because \: l = \frac{ \theta}{360 \degree} \times c \\ \\ \therefore \: l = \frac{72 \degree}{360 \degree} \times 20 \\ \\ \therefore \: l = \frac{72 \degree}{18\degree} \\ \\ \therefore \: l = 4 \: units[/tex]
15 POINTS & BRAINLIEST!!!
How do you find the axis of symmery in the form f(x) = 3(x - 4)^2 + 5?
Answer:
so the axis of symmetry is x=4
Answer: X = 4
Explanation: Hope it helps you♡
I WILLL GIVE BRAINLIEST ANSWER ASAP
Answer: 2ND ONE
Step-by-step explanation:
Answer:
-3
Step-by-step explanation:
5x+3=4x
5x-4x=-3
x=-3
Edit: Check by plugging in x = -3
5(-3)+3=4(-3)
-15+3=-12
-12=-12✅
Jeff rear-ended a car on his way to work and damaged his vehicle. He drove his car to the local body shop for an
estimate of the cost to repair his car. Jeff has a $500 deductible. The local body shop provided an estimate of $3725,
How much will Jeff have to pay?
A $3225
B $3725
C $4225
D $500
Answer:
A $3225
Step-by-step explanation:
Total = $3725
Dectuable = Able to be deducted
$3725 - $500 = $3225
A mountain bike is priced at $413. If the sales tax is 6.5 percent, what is the cost to purchase the mountain bike? Round to the
nearest cent if necessary.
$26.85
$28.91
$437.78
$439.85
answer: D) 439.85
Step-by-step explanation:
we are given the price of the bike which is $413.
we are also given the sales tax which is 6.5%.
sales tax is added to the original price to give us our total. so in order to find the total cost we need to find what the 6.5% sales tax is and add it to our original price. to find the sales tax number in dollars we need to set up our formula. The easiest formula is to use a proportion. X is out of 413 = 6.5% is out of 100%. X/413=6.5/100. We can then cross multiply then divide. 6.5 times 413=2,684.5. then divide 2684.5÷100= 26.845.
we need to round up to the nearest cent since we are working with dollars and cents 26.85. 26.85 is 6.5% of the price of the bike which is 413. Now we just simply add the tax to the original price and we get the cost. 413+26.85=439.85
Answer: The answer is D) 439.85
Step-by-step explanation:
A mail carrier can deliver mail to 36 houses in 30 minutes. Mark wants to determine how many houses the carrier can deliver mail to in 7.5 minutes at this rate. He thinks that to find the answer, he should do the following.
1. First divide 36 houses by 30 minutes to find a unit rate of 1.2 houses per minute.
2. Then multiply 1.2 houses per minute by 7.5 minutes to get 9 houses.
Which statement is correct?
-Mark’s method is wrong, because it is impossible to deliver mail to 1.2 houses in a minute. The carrier can only deliver to a whole number of houses.
-Mark’s method is wrong, because it is impossible to deliver mail for 7.5 minutes. The carrier can only deliver mail for a whole number of minutes.
-Mark’s method is correct, because even though it is impossible to deliver mail to 1.2 houses in a minute, 1.2 represents the unit rate of houses per minute.
-Mark’s method is correct, because it is possible to deliver mail for 7.5 minutes; 7.5 represents the unit rate of 7.5 minutes per house.
The correct answer is C. Mark’s method is correct because even though it is impossible to deliver mail to 1.2 houses in a minute, 1.2 represents the unit rate of houses per minute.
Explanation:
To begin Mark should determine the rate of delivery (number of houses the carrier can deliver in 1 minute). This can be found by dividing the houses by the minutes (36 / 30 = 1.2 houses per minute). This means the 1.2 rate found by Mark is correct; also, in this case, it is important to clarify, the carrier will not deliver to 1.2 houses at the same time, but this is the delivery rate or number used to understand the relationship between the number of houses, and the time.
Moreover, you can use this rate, and multiply it by 7.5 and this will show you how many houses the carrier can deliver in this time (7.5 (minutes) x 1.2 (delivery rate) = 9 houses). Thus, the method is correct, and in it, 1.2 represents the unit rate, this is why even when it is not possible to deliver to 1.2 houses all the process is correct.
Answer:
c
Step-by-step explanation:
i took the test
In right triangle $ABC,$ $\angle C = 90^\circ.$ Median $\overline{AM}$ has a length of $19,$ and median $\overline{BN}$ has a length of $13.$ What is the length of the hypotenuse of the triangle?
Answer:
AB = 2√106 ≈ 20.591
Step-by-step explanation:
The Pythagorean theorem says the square of the hypotenuse is equal to the sum of the squares of the legs.
For median AM, we have ...
AM² = CM² +AC² = (BC/2)² +AC²
For median BN, we have ...
BN² = CN² +BC² = (AC/2)² +BC²
The sum of these two equations is ...
AM² +BN² = BC²/4 +AC² +AC²/4 +BC² = (5/4)(AC² +BC²)
AM² +BN² = (5/4)(AB²)
The hypotenuse of triangle ABC is then ...
AB = √(4/5(AM² +BN²))
AB = 2√((19² +13²)/5)
AB = 2√106 ≈ 20.591
Amar wants to make lemonade for a birthday party. He wants to mix 12 tablespoons of sugar in water. He only has a teaspoon which needs to be used 4 times to be equivalent to one tablespoon. At this rate, how many teaspoons of sugar will Amar need to make the lemonade?
Answer:48
Step-by-step explanation:
Given
Amar wants 12 tablespoons of sugar in water.
Amar has teaspoon whose four times is equivalent to 1 tablespoon
i.e. [tex]4\ \text{teaspoon}\equiv 1\ \text{tablespoon}[/tex]
therefore
[tex]12 tablespoon is 4\times 12[/tex]
[tex]\Rightarrow 4\times 12[/tex]
[tex]\Rightarrow 48\ \text{teaspoons}[/tex]
So, amar need to add [tex]48\ \text{teaspoons}[/tex] for lemonade
Answer:6328565394729
Step-by-step explanation:213
sorry
The fraction of students ages 10 to 17 who favor math or science is
Answer:
So if 17/25 of the students like math, science, and art and 3/20 of the students like art only. We first need to find common demoninator. 68/100 and for the second one 15/100. Subtract them both
68-15 = 53/100 of the students factor math, and science or 53%
f(x)<0 over (-∞, -3) and what other interval?
O (-2.4, - 1.1)
O (-3, - 1.1)
O (-1.1, 2)
O (-1.1, 0.9)
Answer:
Option (4). (-1.1, 0.9)
Step-by-step explanation:
In a graph of any function, values of f(x) are represented by the values on the y-axis for the different input values on x-axis.
For the given graph, values of f(x) are less than zero.
That means interval in which the values of the function are negative for the different values of x.
Negative values of the given function are in the intervals (-∞, -3), (-1.1, 9).
Therefore, from the given options, Option (4) will be the answer.
Answer is (-1.1,0.9)
Step-by-step explanation:
Want Brainliest? Get this Correct The x-values in the table for f(x) were multiplied by -1 to create the table for g(x) What is the relationship between the graphs of the two functions? A. They are reflections of each other across the y-axis B. They are reflections of each other across the x-axis C. The graphs are not related D. They are reflections of each other over the line x = y
Answer:
Option (A).
Step-by-step explanation:
We choose a point from table of f(x), that is (-2, -31)
1). If this point is reflected across x-axis, rule to be followed,
(x, y) → (x, -y)
That means y coordinate of the point gets changed with opposite notation.
If (-2, -31) is reflected over the x-axis,
(-2, -31) → (-2, 31) ----------(1)
2). When a point is reflected over the y-axis,
Rule to be followed,
(x, y) → (-x, y)
(-2, -31) → (2, -31) ----------(2)
3). When a point is reflected over the line y = x
Rule to be followed,
(x, y) → (y, x)
(-2, -31) → (-31, -2) -----------(3)
By comparing f(x) and g(x) we find the relation between the functions as,
f(-2, -31) → g(2, -31)
Rule between the functions f and g matches with the rule number (2).
Therefore, function 'f' has been reflected across y axis to get the function 'g'.
Option (A) will be the answer.
Find the equation of the line passing through the point (4,−1) that is parallel to the line 2x−3y=9 Find the slope of the line 2x−3y=9. Use a forward slash (i.e. "/") for all fractions (e.g. 1/2 for 12). m=____ What would the parallel slope be? m=______ Use the slope to find the y-intercept of the parallel line. b= _____
Answer:
Step-by-step explanation:
2x - 3y = 9
-3y = -2x + 9
[tex]y=\frac{-2}{-3}x + \frac{9}{-3}\\\\y=\frac{2}{3}x-3\\[/tex]
Parallel lines have same slope.So,
Slope m = 2/3
(4 , -1)
Equation: y - y1 = m(x - x1)
[tex]y-[-1]=\frac{2}{3}(x - 4)\\\\y+1=\frac{2}{3}*x - \frac{2}{3}*4\\\\y+1=\frac{2}{3}x-\frac{8}{3}\\\\y=\frac{2}{3}x-\frac{8}{3}-1\\\\y=\frac{2}{3}x-\frac{8}{3}-\frac{3}{3}\\\\y=\frac{2}{3}x-\frac{11}{3}[/tex]
b = -11/3
Simplify the following expression and then write down the coefficient of x²: x² + x² + x² + x²
Answer:
The expression is 4x² and coefficient is 4.
Step-by-step explanation:
All have the same variables, x², so you add up together :
[tex] 1{x}^{2} + 1{x}^{2} + 1{x}^{2} + 1{x}^{2} [/tex]
[tex] = 4 {x}^{2} [/tex]
