Given:
A plane is normal to the vector = -2i+5j+k
It contains the point (-10,7,5).
To find:
The component equation of the plane.
Solution:
The equation of plane is
[tex]a(x-x_0)+b(y-y_0)+c(z-z_0)=0[/tex]
Where, [tex](x_0,y_0,z_0)[/tex] is the point on the plane and [tex]\left< a,b,c\right>[/tex] is normal vector.
Normal vector is -2i+5j+k and plane passes through (-10,7,5). So, the equation of the plane is
[tex]-2(x-(-10))+5(y-7)+1(z-5)=0[/tex]
[tex]-2(x+10)+5y-35+z-5=0[/tex]
[tex]-2x-20+5y-35+z-5=0[/tex]
[tex]-2x+5y+z-60=0[/tex]
[tex]-2x+5y+z=60[/tex]
Therefore, the equation of the plane is [tex]-2x+5y+z=60[/tex].
write the number that is 6 less then 8000
Answer:
8000-6=7994 is the required number
Jake feeds some chickens 1/8 of a bag of chicken feed each day. If he has 8 bags of feed, how many days will the feed last?
Answer:
1/2
Step-by-step explanation:
because if he has 8 bags he wil only have half a bag left
Really need help . Find the missing value that makes the two expressions equivalent
Answer:
1. 4
2. 5
3. 9
Step-by-step explanation:
1.
4(x+3y)
4x+12y=4x+12y
2.
5(7x+10y)
35x+50y=35x+50y
3.
9(2x+y)
18x+9y=18x+9y
i hope this helps!
Mutations happen at a steady rate.
True
False
In ΔOPQ, PQ = 17, QO = 9, and OP = 15. Which statement about the angles of ΔOPQ must be true?
Answer:
All angles are different.
Internal angles can be acute, obtuse, or right angle.
The smallest side is opposite to the smallest angle and the longer side is opposite to the larger angle.
Step-by-step explanation:
Given - In ΔOPQ, PQ = 17, QO = 9, and OP = 15.
To find - Which statement about the angles of ΔOPQ must be true?
Proof -
As given,
In ΔOPQ, PQ = 17, QO = 9, and OP = 15.
As all the sides of the given triangle is different, So the given triangle is a Scalene triangle.
Now,
We know that , In Scalene triangle -
All sides are different.
All angles are different.
Internal angles can be acute, obtuse, or right angle.
The smallest side is opposite to the smallest angle and the longer side is opposite to the larger angle.
Smallest angle: ∠P
Opposite shortest side.
Middle angle: ∠O
Opposite middle side.
Largest angle: ∠Q
Opposite longest side.
Therefore:
m∠P<m∠O<m∠Q
Less than symbol goes from smallest to largest
Here's a better Explanation!!!!!!
Find angle picture below.
Answer:
Angle M = 63
Angle N = 96
Step-by-step explanation:
By exterior angle of triangle:
Angle M + Angle N = 159
(4y+3)+(6y+6)=159
y = 15
Angle M = 4y + 3 = 4(15) + 3 = 63
Angle N = 6y + 6 = 6(15) + 6 = 96
The flag football league eventually had 72 kids sign up for the spring season after putting six teams together from the original amount of sign ups they took took it off of everything to make the final rosters how many kids were on the original rosters before removing some players
draw a tape diagram and write an equation to match the situation then solve the equation and put your answer in the context of the situation
Answer:
each team has 12
Step-by-step explanation:
The frequency table shows the scores from rolling a dice.
Score
Frequency
Answer:
The median is 3.5
Step-by-step explanation:
We want to find the median of the set of values.
First, we need to write the set in ascending order.
We get:
1 five times
2 three times
3 five times
4 two times
5 seven times
6 four times
The median will be the midle value (for example in a set of 5 elements, the middle element is the third one) of this set, then the first part is to write the set, we get:
{1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6}
In this set we have
5 + 3 + 5+ 2 +7 + 4= 26 values
So we will not have a middle value, we need to take the mean of the two middle values (the 13th value and the 14th value)
We can see in the set above that these values are:
3 and 4.
Then we want to take the mean between 3 and 4.
We get:
M = (3 + 4)/2 = 3.5
The median of this set is 3.5
Decrease 1428g by 38.5%
Answer:
1428 (1-0.385) = 878.22
Step-by-step explanation:
g The population of Little Townville in 2005 was 13,625 people. In 2009 the population grew to 15,325 people. Assume that this trend is linear and the population has been growing like this since 2000. a. Write a function for the population, P, in terms of the number of years since 2000, ????. (6 points) b. What is the slope of the function and what does it represent in the context of the problem. Include units. (5 points) c. What is the vertical intercept of the function and what does it represent? Include units (5 points) d. What do you believe the population was in 2015?
Answer:
a) [tex]P(t) = 11500 + 425t[/tex]
b) The slope is of 425 people, which is by how much the population increases each year.
c) The vertical intercept is of 11500 people, and it represents the population of Little Townville in the year 2000.
d) 17,875 people.
Step-by-step explanation:
A linear function that measures population after t years has the following format:
[tex]P(t) = P(0) + at[/tex]
In which P(0) is the vertical intercept, which represents the initial population, and a is the slope, which represents the yearly population.
a. Write a function for the population, P, in terms of the number of years since 2000.
The first step is finding the slope.
Finding the slope:
The slope is the change in the output divided by the change in the input, during a period of time.
The population of Little Townville in 2005 was 13,625 people. In 2009 the population grew to 15,325 people.
This means that in 2009 - 2005 = 4 years, the population increased by 15325 - 13625 = 1700.
So the slope is
[tex]a = \frac{1700}{4} = 425[/tex]
So
[tex]P(t) = P(0) + 425t[/tex]
Finding the initial population:
We want to find P(0), which is the population in 2000. The population of Little Townville in 2005 was 13,625 people, which means that [tex]P(5) = 13625[/tex]. So
[tex]P(t) = P(0) + 425t[/tex]
[tex]13625 = P(0) + 425*5[/tex]
[tex]P(0) = 13625 - 425*5[/tex]
[tex]P(0) = 11500[/tex]
So
[tex]P(t) = 11500 + 425t[/tex]
b. What is the slope of the function and what does it represent in the context of the problem. Include units.
The slope is of 425 people, which is by how much the population increases each year.
c. What is the vertical intercept of the function and what does it represent? Include units
The vertical intercept is of 11500 people, and it represents the population of Little Townville in the year 2000.
d. What do you believe the population was in 2015?
2015 is 2015 - 2000 = 15 years after 2000, so this is P(15).
[tex]P(15) = 11500 + 425*15 = 17875[/tex]
17,875 people.
HELP PLZ I HAVE LIKE 20-30 MINUTES PLZ I BEG ILL MARK YOU BRAINLIEST
Answer:
.........(loading)....................
Step-by-step explanation:
...........................
Milton spilled some ink on his homework paper. He can't read the coefficient of $x$, but he knows that the equation has two distinct negative, integer solutions. What is the sum of all of the distinct possible integers that could be under the ink stain
Answer:
[tex]Sum = -81[/tex]
Step-by-step explanation:
See the comment for complete question.
Given
[tex]c = 36[/tex] ----- Constant
No coefficient of x^2
Required:
Determine the sum of all distinct positive integers of the coefficient of x
Reading through the complete question, we can see that the question has 3 terms which are:
x^2 ---- with no coefficient
x ---- with an unknown coefficient
36 ---- constant
So, the equation can be represented as:
[tex]x^2 + ax + 36 = 0[/tex]
Where a is the unknown coefficient
From the question, we understand that the equation has two negative integer solution. This can be represented as:
[tex]x = -\alpha[/tex] and [tex]x = -\beta[/tex]
Using the above roots, the equation can be represented as:
[tex](x + \alpha)(x + \beta) = 0[/tex]
Open brackets
[tex]x^2 + (\alpha + \beta)x + \alpha \beta = 0[/tex]
To compare the above equation to [tex]x^2 + ax + 36 = 0[/tex], we have:
[tex]a = \alpha + \beta[/tex]
[tex]\alpha \beta = 36[/tex]
Where: [tex]\alpha, \beta <0[/tex] and [tex]\alpha \ne \beta[/tex]
The values of [tex]\alpha[/tex] and [tex]\beta[/tex] that satisfy [tex]\alpha \beta = 36[/tex] are:
[tex]\alpha = -1[/tex] and [tex]\beta = -36[/tex]
[tex]\alpha = -2[/tex] and [tex]\beta = -18[/tex]
[tex]\alpha = -3[/tex] and [tex]\beta = -12[/tex]
[tex]\alpha = -4[/tex] and [tex]\beta = -9[/tex]
So, the possible values of a are:
[tex]a = \alpha + \beta[/tex]
When [tex]\alpha = -1[/tex] and [tex]\beta = -36[/tex]
[tex]a = -1 - 36 = -37[/tex]
When [tex]\alpha = -2[/tex] and [tex]\beta = -18[/tex]
[tex]a = -2 - 18 = -20[/tex]
When [tex]\alpha = -3[/tex] and [tex]\beta = -12[/tex]
[tex]a = -3 - 12 = -15[/tex]
When [tex]\alpha = -4[/tex] and [tex]\beta = -9[/tex]
[tex]a = -4 - 9 = -13[/tex]
At this point, we have established that the possible values of a are: -37, -20, -15 and -9.
The required sum is:
[tex]Sum = -37 -20 -15 - 9[/tex]
[tex]Sum = -81[/tex]
Suppose you have a tablet with a capacity of gigabytes. For a plain text book, one byte typically corresponds to one character and an average page consists of 2000 characters. Assume all gigabytes are used for plain text books.
a. How many pages of text can the tablet hold?
b. How many 500 page books can the tablet hold?
Answer:
tablet can hold 500000 pages of text .
tablet can hold 1000 books of 500 pages
pls help. whats 6¹⁵÷6¹⁰=?
Answer:
6^5 or 7776
Step-by-step explanation:
When you divide exponentials you minus the exponents. 15-10=5
6^5 = 7776
Answer:
6^5 = 7776
Step-by-step explanation:
6^15 /6^10 = 6^(15-10) = 6^5 = 7776
Explain how to determine whether two quantities are proportional.
please help :)
Answer:
* Ratios are proportional if they represent the same relationship.
*If the reduced fractions are the same, your ratios are proportional.
*If two ratios are proportional is to write them as fractions and then reduce them.
Hope its helpful
Thank you
Use least common multiple or greatest common divisor to solve the problem.
Three clocks chime every 15 minutes, 39 minutes, and 65 minutes,
respectively. If the three clocks chime together, how much time must pass
before they will chime together again?
Answer:
Step-by-step explanation:
3) 15,39,65
_________
5 )5,13,65
--------------
13 )1,13,13
----------------
| 1,1,1
L.C.M.=3×5×13=195
They will chime together after 195 minutes.
Rectangle M was dilated to form rectangle M'.
6
4
WA
M
2
M'
What ratio is the scale factor?
Answer:
3/2 or answer D
Step-by-step explanation:
just took it on edg
tres carpinteros juan alberto y luis se encargaron de hacer 6 mesas iguales por lo que recibieron $600 pesos juan hizo una mesa alberro hizo 2 mesas y luis 3 mesas cuanto dinero corresponde a cada uno
Answer:
primero divides 600 entre 6 te da 100
entonces cada mesa vale 100 pesos así que
100x1:100 así que a juan le tocan 100 pesos
100x2:200 así que Alberto le tocan 200 pesos
100x3:300 así que a Luis le tocan 300 pesos
Me das coronita plispleaseee somebody tell me the answer.
Answer:
aprx. 50.24 inches
Step-by-step explanation:
I hope this helps! :)
☁️☁️☁️☁️☁️☁️☁️
If f(x)=3x-1 find the following f(3) f(2)
Answer:
(4(f(2)
Step-by-step explanation:
If f(x(=3x-1 then f(3)f(2)
what is 1 x 5555 + -6779 . 55555
Answer:
−376601790
Step-by-step explanation:
1
⋅
5
5
5
5
−
6
7
7
9
⋅
5
5
5
5
5
5
5
5
5
−
6
7
7
9
⋅
5
5
5
5
5
Answer:
it's -1,224.55555
Step-by-step explanation:
1 x 55,555 = 55,555
55,555 + -6779.55555 = -1224.55555
hope this helps...
Subtract. (12+8i)−(7+4i) Enter your answer in the box.
Answer:
5+12i
Step-by-step explanation:
So 12-7 = 5 and 8i+4i=12i and that equals 5+12i
how do you solve problems like 6.45/0.25
Answer:
25.8
Step-by-step explanation:
divide
Answer:
divide like i said
Step-by-step explanation:
The original price, p, of a single scoop of ice cream has increased by 7%. The new price can be represented as 1.07p. Which expression is also equivalent to the new price? *
Answer:
107%p
not much explanation needed here, just conversion of units.
Jenny earns $30 a day working part time at a supermarket. Write an expression to represent the amount of money she will earn in d days.
Answer: d($30)
Explanation: $30 times d which d is the number of days.
Find dy/dx by implicit differentiation.
cot(y) = 9x – 7y
dy/dx = ?
Answer:
Step-by-step explanation:
Write these decimals in order from least to greatest.
0.6 0.8 0.55 0.125 0.875
Then explain how you know.
Answer:
0.125, 0.55, 0.6, 0.8, 0.875
Using complete sentences, describe the net of a rectangular prism with a length of 12 centimeters, a width of 9
centimeters, and a helght of 5 centimeters.
s
WRITER
Answer:
The description is as follows:
Step-by-step explanation:
The description of the net of a rectangular prism is as follows:
The length i.e. 12 centimeters would be multiplied by width of 9 and then it added to the height i.e. 5 centimeters
The above represent the description of the net of a rectangular prism
PLEASE HURRY I WILL MARK BRAINIEST
The new wing of an art
museum has 3 times
as many windows as
the old wing. Together,
both wings have
32 windows. How many
windows are in
the new wing?
Answer: 24
Step-by-step explanation:
32/4 = 8
3 * 8 = 24
24 + 8 = 32
There are 24 windows in the new wing.
Hope this helped! :)
(4 1/4x + 8) + (-1 1/2x - 12)
Answer:
(19x-290)/(4(x+2)(x-6)
Step-by-step explanation:
Apply Fraction Rule:
(41)/(4x+8)-(11)/(2x-12)
Factor:
(41)/4(x+2)-(11)/(2x-12)
Factor:
(41)/4(x+2)-(11)/2(x-6)
LCM:
(41)(x-6)/(4)(x+2)(x-6)-(22(x+2))/(4)(x+2)(x-6)
Expand:
= (19x-200)/4(x+2)(x-6)