Answer:
90
bc i don't care about this
The equation of plane containing the points ABC is 13x+y-18z = 1035.
What is equation of plane?A plane in 3D coordinate space is determined by a point and a vector that is perpendicular to the plane. The equation of plane is defined as the position vectors and the Cartesian product of the vector perpendicular to the plane.
For the given situation,
The plane containing the points
A(10, 5, -50), B(15, 30, -45) and C(-5, 20, -60).
The equation of the plane in the form r.n=d can be represented as
[tex](r-a).[(b-a)[/tex] × [tex](c-a)]=0[/tex] ------ (1)
Let r = xi + yj +zk
a = 10i + 5j - 50k
b = 15i + 30j - 45k
c = -5i + 20j - 60k
[tex](r-a)=(x-10)i+(y-5)j+(z+50)k[/tex] ------- (2)
[tex](b-a)=(15-10)i+(30-5)j+(-45-(50))k[/tex]
⇒ [tex](b-a)=5i+25j+5k[/tex]
[tex](c-a)=(-5-10)i+(20-5)j+(-60-(50))k[/tex]
⇒ [tex](c-a)=-15i+15j-10k[/tex]
Now, [tex](b-a)[/tex] × [tex](c-a)[/tex]
⇒ [tex](5i+25j+5k)[/tex] × [tex](-15i+15j-10k)[/tex]
⇒ [tex]\begin{vmatrix}i&j&k\\5&25&5\\-15&15&-10\end{vmatrix}[/tex]
⇒ [tex]i(-250-75)-j(-50+75)+k(75+375)[/tex]
⇒ [tex]-325i-25j+450k[/tex] -------- (3)
Substitute all values in equation 1,
⇒ [tex][(x-10)i+(y-5)j+(z+50)k].[(-325i-25j+450k)]=0[/tex]
⇒ [tex]-325(x-10)-25(y-5)+450(z+50)=0[/tex]
⇒ [tex]-325x+3250-25y+125+450z+22500=0[/tex]
⇒ [tex]-325x-25y+450z=-22500-3250-125[/tex]
⇒ [tex]-325x-25y+450z=-25875[/tex]
On dividing by 25 and multiply with negative sign on both sides,
⇒ [tex]13x+y-18z=1035[/tex]
Hence we can conclude that the equation of plane containing the points ABC is 13x+y-18z = 1035.
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A podcast is 180 minutes long. During the podcast there are more than 48 minutes of commercials.
There are 8 commercial-free segments in the podcast that are each the same length.
In which inequality does a represent the possible length, in minutes, of each commercial-free segment of
the podcast?
Ms. Crane has a jar with 6 white marblos, 4 red marbles, and 5 blue marbles. If
she closes her eyes and picks one marble out of the jar, what is the probability
that it is not red?
A. 4/15
B. 2/5
C.11/15
D. 2/3
Answer:
11/15
Step-by-step explanation:
To find probability, you divide whatever you're looking for over your total. In this case, you have 11 marbles that are not red, and 15 marbles total, so your answer would be 11/15.
all i know is the answer isn’t 10. pls help
Answer:
X is 72 i think
Step-by-step explanation:
all triangle equal 180, triangle formula bxh/2, so i did that and got 72.
Synthetic Division to Find Zeros (Lev 1)
May 25, 1:20:18 PM
Watch help video
If ƒ(x) = x³ – 11x² + 26x — 16 and x – 1 is a factor of f(x), then find all of zeros
Consider two events such that P(A) = equals 3/5 , P(B) = 2/3 , and P(A ∩ B) = 1/5 . Are events A and B independent events?
Yes, they are independent because P(A) ⋅ P(B) = P(A ∩ B)
No, they are dependent because P(A) ⋅ P(B) ≠ P(A ∩ B)
Yes, they are independent because P(A) ⋅ P(B) ≠ P(A ∩ B)
No, they are dependent because P(A) ⋅ P(B) = P(A ∩ B)
Answer:
Option 2
Step-by-step explanation:
Checking whether P(A) × P(B) = P(A∩B) :
3/5 x 2/3 = 1/52/5 ≠ 1/5Since this does not obey the Multiplication rule of probability, these events are not independent.
So, the answer is :
No, they are dependent because P(A) ⋅ P(B) ≠ P(A ∩ B)
Answer:
Option B
Step-by-step explanation:
Option A should be true if they are independent
P(A)P(B)3/5×2/32/5≠1/5So
They are dependant
Parallel lines p and q are intersected by transversal r, as show.
Using the corresponding angles theorem, the value of x is 150°
Calculating the measures of anglesFrom the question, we are to determine the value of the angle marked x°
From the diagram,
The angle that supplements the angle marked 30° is corresponding to angle x
Since corresponding angles are equal
Then, we can write that
∴ x = 180° - 30°
x = 150°
Hence, the value of x is 150°
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Donald bought a box of golf balls for $9.26. There were 18 golf balls in the box. About how much did each golf ball cost?
Answer:
$0.51 per golf ball.
Step-by-step explanation:
9.26 divided by 18 is 0.51.
Answer:
$1.94 dollars
Step-by-step explanation:
hehe
are all natural numbers also a rational number? (yes/no)
Answer:
Yes
Step-by-step explanation:
But not all rational numbers are natural numbers, so be careful of that.
Which expression is not equivalent to the other three?
Explanation:
Choice A simplifies to 9n-8 after combining the like terms -7n+16n to get 9n
Choice C simplifies to 9n-8 for similar reasoning. The n+8n turns into 9n
This shows choices A and C are equivalent to choice D. Choice B isn't the same because 9(n-8) = 9n-9*8 = 9n-72. Use the distributive property.
Answer:
B. 9(n - 8)
Step-by-step explanation:
- 8 - 7n + 16n
-8 (-7n + 16n or 16n - 7n)
-8 + 9n
9n - 8
9(n - 8)
9n - 72
n - 8 + 8n
9n - 8
9n - 8
Solve for the volume of the Sphere. ROUND TO THE NEAREST TENTH. 15 is the
radius.
Answer:
[tex]14137.8[/tex] to the nearest tenth
Step-by-step explanation:
write the equation of sphere volume:
[tex]\frac{4}{3} \pi r^{3}[/tex]
substitute the radius to the equation :
[tex]\frac{4}{3} \pi* 15^{3}[/tex]
solve by calculator:
[tex]\frac{4}{3} \pi* 15^{3}=14137.17\\[/tex]
≈[tex]14137.8[/tex] to the nearest tenth
What is the equation for an arithmetic sequence with a first term of 7 and a second term of 3? (5 points)
an = 7 − 4(n − 1)
an = 7 + 4(n − 1)
an = 7 − 3(n − 1)
an = 7 + 3(n − 1)
Answer:
1st option
Step-by-step explanation:
the equation for an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 7 and d = a₂ - a₁ = 3 - 7 = - 4 , then
[tex]a_{n}[/tex] = 7 - 4(n - 1)
Answer:
The answer is option A
Step-by-step explanation:
The solution is in the image
Type the correct answer in the box. use numerals instead of words. a population of beetles increases by 5% every year. if at the start of the year the population is at 10,000 beetles, what will its population be after three years? at the end of the third year the population of beetles will be .
At the end of the third year the population of beetles will be 11,576beetles
Exponential equationsThe standard form of an exponential function is given as:
y = ab^t
Given the following parameters
initial population 'a" = 10,000 beetles
Time = 3 years
rate b = 1.05
Substitute into the formula
y = 10,000(1.05)^3
y = 10,000(1.1576)
y = 11,576 beetles
Hence at the end of the third year the population of beetles will be 11,576beetles
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A spherical balloon is inflated so that its volume is increasing at the rate of 2.5 ft3/min. How rapidly is the diameter of the balloon increasing when the diameter is 1.3 feet?
Answer:
.9417 ft/min
Step-by-step explanation:
Sphere volume = 4/3 pi r^3
dv/dr = 4/3 pi * 3 r ^2 = 4 pi r^2
dv/dr * dr/dt = dv/dt = 4 pi r^2 dr/dt
2.5 = 4 pi (1.3/2)^2 dr/dt (Diameter is 1.3 , radius is 1.3/2)
dr/dt = .4709 ft/min
THIS answer is how fast the RADIUS is changing
the DIAMETER is changeing TWICE this:
2 x .4709 ft/min = .9417 ft / min = diameter/dt
a bus left town X at 6:30 and arrived at town Y at 1:00pm if the bus travelled 100km per hour calculate the distance from town X and Y
evaluate the following expression. you should do this problem without a calculator e^In3
The relation between the exponential and the logarithm is used. Then the expression [tex]e^{\ln3}[/tex] is given as 3.
What is a logarithm?Exponents can also be written as logarithms. A number base logarithm is similar to some other number. It is the exact inverse of the exponent expression.
The expression is given below.
[tex]\rightarrow e^{\ln3}[/tex]
We know the formula
[tex]\rm e^{\ln x} = x[/tex]
Then the expression can be written as
[tex]e^{\ln3} = 3[/tex]
More about the logarithm link is given below.
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What is the height of the cone below? a cone with base of 5 inches squared and volume of 45 inches cubed. 3 in. 9 in. 27 in. 75 in.
The cone is a three dimensional shape, and the value of the height of the cone is 27 inches
How to determine the height?The given parameters are:
Shape = ConeVolume, V = 45 in^3Base area, B = 5 in^2The volume of the cone is calculated using:
[tex]V = \frac13 Bh[/tex]
So, we have:
[tex]45 = \frac13 * 5 * h[/tex]
Divide both sides by 5
[tex]9 = \frac13 * h[/tex]
Multiply both sides by 3
h = 27
Hence, the value of the height of the cone is 27 inches
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Samantha and Mia each left Julia’s house at the same time. Mia walked north at 7 kilometers per hour. Samantha ran west at 11 kilometers per hour. How far apart were they after one hour? Round the answer to the nearest tenth.
Samantha and Mia are 13 km apart from each other.
What is Pythagoras theorem?The Pythagorean Theorem states that the sum of the squared sides of a right triangle equals the length of the hypotenuse squared.
As Mia walked 7km/h and she is 7 km north of Julia's house.
and, Samantha walked 11km/h and she is 11 km west of Julia's house.
The points where Mia and Samantha are after 1 hour as shown in figure, and Julia's house forms a right angled triangle.
the distance between the girls is shown by, hypotenuse of triangle
Using Pythagoras theorem,
[tex]H^{2} =P^{2} +B^{2}[/tex]
[tex]H^{2} =7^{2} +11^{2}[/tex]
[tex]H^{2} =49+121\\[/tex]
H= [tex]\sqrt{170}[/tex]
H= 13.038
H= 13 Km
They are 13 km apart from each other.
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Answer:
13.0 km
Step-by-step explanation:
What is the surface area of the solid that this net can form? a net has 2 rectangles. one rectangle has a base of 25 millimeters and a height of 21 millimeters. the other rectangle has a base of 41 millimeters and height of 5 millimeters. 730 square millimeters 875 square millimeters 1,000 square millimeters 1,444 square millimeters
The surface area of the solid is the sum of all the net shapes. The surface area of the solid that this net can form is 730mm²
Surface area of a solidThe surface area of the solid is the sum of all the net shapes.
Given the following parameters
The rectangle has a base of 25 millimeters and a height of 21 millimeters will have an area of 525mm²
The other rectangle has a base of 41 millimeters and height of 5 mm has an area of 205mm²
TSA = 525 + 205
TSA = 730mm²
Hence the surface area of the solid that this net can form is 730mm²
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treatment definition
Answer: Heyaa!
If you mean medicine treatment the definition is...
The management and care of a patient to combat disease or disorder.If you mean just basic treatment the definition is...
The manner in which someone behaves toward or deals with someone or something.Hopefully this helps you:
- Matthew
Need help with this problem
Find the gradient of the line joining (-1,9) and (3,5)
[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]
Find the gradient of the line joining (-1,9) and (3,5)
[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]
Use the slope formula:-
[tex]\boxed{\frac{y_2-y_1}{x_2-x_1}}[/tex]
Replace the letters with the numbers:-
[tex]\boxed{\frac{5-9}{3-(-1)}}[/tex]
[tex]\circ[/tex] On simplification,
[tex]\boxed{\frac{-4}{3+1}}[/tex]
[tex]\circ[/tex] On further simplification,
[tex]\boxed{\frac{-4}{4}}[/tex]
[tex]\circ\sf{SLOPE=-1}[/tex]
Good luck with your studies.[tex]\rule{300}{1}[/tex]
What is the equation of the line that passes through the point (2,5) and has a slope of 5?
- - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\diamond\large\textsf{\textbf{\underline{\underline{Question:-}}}}\diamond[/tex]
What is the equation of the line that passes through the point (2, 5) and has a slope of 5?
[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}\diamond[/tex]
First let's write the equation of the line in point-slope form:-
[tex]\sf{y-y_1=m(x-x_1)}[/tex]
Substitute 5 for y₁, 5 for m and 2 for x₁:-
[tex]\sf{y-5=5(x-2)}[/tex]
That's the equation of the line in Point-slope form.
Now let's convert it into slope-intercept:-
[tex]\sf{y-5=5x-10}[/tex]
Adding 5 to both sides results in our slope intercept equation, which looks like this:-
[tex]\dashrightarrow\bigstar\boxed{\boxed{\bold{\underline{y=5x-5}}}}\bigstar\dashleftarrow[/tex]
Good luck.- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
I need help with this math problem brainliest for the best answer
Answer:
It is the first one
Hope this helps!
Answer:
I believe it is 4x+10y=200, x+y=38
Explanation:
On the map at the right, the public swimming pool can be represented by the point (-6, 5) and Tim’s house can be represented by the point (1, 5). If each unit on the graph represents 0.5 miles, how many miles is Tim’s house from the pool
The distance between the swimming pool and Tim's house is 3.5 miles.
How to find the distance?
First, we need to find the distance between the two points, and then we multiply that by 0.5 miles.
The distance between the points (-6, 5) and (1, 5) is:
[tex]d = \sqrt{(-6 - 1)^2 + (5 - 5)^2} = 7[/tex]
Now, changing to miles, we get:
d = 7*0.5mi = 3.5mi
So the distance is 3.5 miles
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what is 2 17/18 divided by 6 as a fraction
Sam is thinking of retiring from his job after many years of faithful service. during the last 35 years at his job, his annual salary averages to $37,991. every month, his bills total $1,755. how much money would sam need each month to supplement his monthly social security benefit (assuming his annual benefit is 42% of his salary average) and still be able to pay his bills? a. at least $81.23 b. at least $425.32 c. at least $1,410.92 d. at least $3,019.67
Using proportions, the amount of money that Sam would need each month to pay his bills is of:
b. at least $425.32.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, his annual social security benefit is of 42% of $37,991, hence:
A = 0.42 x 37991 = $15,956.22.
Hence the monthly amount is given by:
M = 15956.22/12 = $1,329.68
He needs $1,755 monthly, hence the amount he needs is of at least:
An = 1755 - 1329.68 = $425.32.
Which means that option b is correct.
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Please answer
ALMN AQRS. Solve for y. L 2x+11 /(y+10)° N (2y-40) Q S M R 3x-9
Answer:
50
Step-by-step explanation:
Since it's given that these are similar triangles then the measure of angles are equal
2y - 40 = y + 10 transfer like terms to the same side of equation
2y - y = 10 + 40 do the calculation (notice how the terms changes sign from + to - and from - to + when they are transferred)
y = 50
Pls help]ppppppppp me
Answer:
a. (2x - 3)(x - 4)
b. 17 m, 6 m
c. 46 m
Step-by-step explanation:
a.
2x² - 11x + 12 = (2x - 3)(x - 4)
b.
2x - 3 = 2(10) - 3 = 17
x - 4 = 10 - 4 = 6
c.
P = 2L + 2W = 2(17) + 2(6) = 46
does anyone know proof without words ?
Step-by-step explanation:
it shows that all the small triangles that together make the complete square (c²) under the Hypotenuse consist of exactly all the composing triangles of the squares above the legs (a² and b²).
we find the 2 purple, the 2 orange, the 2 yellow and the 2 blue triangles there.
so, the area of c² must be the same as the sum of the areas of a² and b².
Write each of the following expressions without using absolute value. |z−7|−|z−9|, if z<7
Answer:
-2
Step-by-step explanation:
z - 7 ≥ 0
z ≥ 7
| z - 7 | = z - 7, z ≥ 7
| z - 7 | = -z + 7, z < 7
z - 9 ≥ 0
z ≥ 9
| z - 9 | = z - 9, z ≥ 9
| z - 9 | = -z + 9, z < 9
| z - 7 | = -z + 7
| z - 9 | = -z + 9
|z - 7| - |z - 9|
-z + 7 - (-z + 9)
-z + 7 + z - 9
= -2
