Answer:
[tex]\sqrt{(-\frac{806}{94}+8)^2+(-\frac{215}{94}-9)^2+ (-\frac{251}{94}-8)^2}[/tex] Whatever this number may be
Step-by-step explanation:
The distance will be on the plane containing the point, and perpendicular to the line - which exists as long as the point doesn't sit on the line, but in that case our distance will simply be zero. Good news, since the line is given in parametric equation, the equation of the plane is easy to write by simply computing the dot product between the vector generating the line - or any multiple of it! - and the vector joining a random point x y z of the space with our given point, and setting it equal to zero. The equation of our plane is thus
[tex]6(x-(-8)) + 3(y-9) -7(z-8) = 0\\6(x+8)+3(y-9)-7(z-8)=0[/tex]
We could multiply now or later, doesn't matter, so let's wait. Now, we need to know when the line passes through the plane, so let's plug the (parametric) coordinate of the line and let's see for which value of t that happens:
[tex]6(-2-6t+8) +3(1-3t -9) -7(-5+7t-8) =0\\6(6-6t) -3(8+3t)+7(13-7t)=0\\36-36t-24-9t+91-49t = 0\\t=103/94[/tex]
Found this value of t, we can use it to find the coordinate of the point in common between the line and the plane:
[tex](-2-6\frac {103}{94};1-3\frac {103}{94}; -5+7\frac {103}{94}) = (-\frac{806}{94};-\frac{215}{94};-\frac{251}{94})[/tex]
At this point it's simply a matter of calculating the distance between two points in 3D space, given by the usual [tex]\sqrt{\Delta x^2+\Delta y^2+\Delta z^2}[/tex], whatever abomination of a number it might become:
[tex]\sqrt{(-\frac{806}{94}+8)^2+(-\frac{215}{94}-9)^2+ (-\frac{251}{94}-8)^2}[/tex]
At this point is a simple exercise in number crunching which I refuse to entertain more - but please double check all calculation above in case I didn't notice something.
a carpenter has 6 boards that are each 7/8 yard long. how many 3/4 yard sections of board can he construct
The number of sections of board that he can construct will be equal to 7.
We are given that:
A carpenter has 6 boards.
Length of each board = 7 / 8 yard long
Now, we will use multiplication.
Total length of cardboards available = 7 / 8 × 6 yards
Total length = 42 / 8 yards
Total length = 21 / 4 yards.
Now, 3/4 yard sections of board that he can construct will be:
Number of sections of board = 21 / 4 ÷ 3 / 4
Number of sections of board = 21 / 3
Number of sections of board = 7
Therefore, the number of sections of board that he can construct will be equal to 7.
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1. Consider the following propositions
• P: 2+5=3
. Q: Warsaw is the capital of Poland.
. R: The US has the largest population in the world.
R= is incorrect
the answer is china :)
If the demand function for a commodity is given by the equation p2 + 16q = 1200 and the supply function is given by the equation 300 − p2 + 10q = 0, find the equilibrium quantity and equilibrium price. (Round your answers to two decimal places.)
The equilibrium quantity and equilibrium price are 34.62 and 25.42 respectively
How to find the equilibrium quantity and equilibrium price?The functions are given as
Demand: p^2 + 16q= 1200
Supply function: 300 - p^2 + 10q
Rewrite the demand function as
p^2 + 16q - 1200 = 0
At equilibrium, demand = supply
So, we have:
p^2 + 16q - 1200 = 300 - p^2 + 10q
Using a graphing calculator, we have:
p = 25.42 and q = 34.62
Hence, the equilibrium quantity and equilibrium price are 34.62 and 25.42 respectively
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Find the y-intercept, x- intercept and slope of the line with equation 8x +12y = 16.
(PLEASE EXPLAIN IN STEPS)
Answer juvhfVO"zohgvjozi nandish pro nbhvmno
Write and solve an inequality.
Twice a number x is more than the sum of that number x and 14.
[tex]\Large\textbf{Twice a number x is this: \textsf{2x}}\\\\\\\textbf{The sum of that number and 14 is this: \textsf{x+14}}\\\\\\\textbf{2x\textgreater x+14}\\\\\textbf{x\textgreater14}[/tex]
if LK=MK, LK=7x-10, KN=x+3, MN=9x-11, and KJ=28, find LJ
Congruent segments are LK=MK, LK=7x-10, KN=x+3, MN=9x-11, and KJ=28, the LJ will be-
LJ = 18 + 28 = 46
LJ = 18 + 28 = 46
These are Congruent segments
Let J, K, L, M, N are points on the same line.
MK = MN + (-KN) = MN - KN = 9x - 11 - x - 3 = 8x - 14
As LK = MK and LK = 7x - 10, then
7x - 10 = 8x - 14
8x - 7x = -10 + 14
x = 4
LJ = MK + KJ
MK = LK = 7x - 10 = 7(4) - 10 = 28 - 10 = 18
LJ = 18 + 28 = 46
Congruent segments are segments which have the equal length. ≅ points that lie at the equal line are called collinear.
A theorem is a mathematical assertion that can be proved. The midpoint of a phase is a point that divides the phase into two congruent segments
If three or more points lie on a single straight line, they are said to be collinear. An axis is a term used to describe a line on which points are located, particularly if that line is connected to a triangle or other geometric shape. Since two points determine a line, two points are trivially collinear.
Two line segments are congruent if they have the same length. They do not need to have the same position or orientation
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Points L, M, and N are collinear. You are given LM = 21 and LN = 35.
What is a possible value of MN ?
The value of MN is 14 when the Points L, M, and N are collinear.
As per the question statement, we are supposed to find the possible value of MN when the Points L, M, and N are collinear.
Also, LM=21 and LN=35
As LN is greater than LM, point M has to be in between L and N for practicality and question existence.
[tex]LM+MN=LN\\MN=LN-LM\\LN=35\\LM=21\\MN=35-21\\MN=14[/tex]
Hence final answer is MN = 14
Collinear points: It is a set of points which has a thing in common i.e., they lie on the same line or when joined forms a straight line.To learn more, click on the link given below:
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what is 0.25x 2.6 pls help me this is hw
Answer:
0.65
Step-by-step explanation:
what is the answer to −4.2+3.3=
answer: -0.9
correct me if I'm wrong
Find the distance between the points A and B given below. (That is, find the length of the segment connecting A and B.) Round your answer to the nearest hundredth. 1 unit B
Answer:
theres no picture
Suppose that the world's current oil reserves is
R=1970 billion barrels. If, on average, the total reserves is decreasing by 24 billion barrels of oil each year, answer the following:
A.) Give a linear equation for the total remaining oil reserves, R, in terms of t, the number of years since now. (Be sure to use the correct variable and Preview before you submit.)
R=
B.) 12 years from now, the total oil reserves will be____billions of barrels.
C.) If no other oil is deposited into the reserves, the world's oil reserves will be completely depleted (all used up) approximately_______years from now.
(Round your answer to two decimal places.)
From the given situation, we have that:
A) The linear equation is R(t) = 1970 - 24t.
B) 12 years from now, the total oil reserves will be 1682 billions of barrels.
C) Approximately 82.08 years from now.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, the parameters are given as follows:
b = 1970, m = -24.
Hence the linear function is:
R(t) = 1970 - 24t.
For item b, the amount is of R(12), hence:
R(12) = 1970 - 24(12) = 1682.
12 years from now, the total oil reserves will be 1682 billions of barrels.
For item c, we have to solve for t when R(t) = 0, hence:
1970 - 24t = 0
24t = 1970
t = 1970/24
t = 82.08.
Approximately 82.08 years from now.
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What’s the volume of a 9ft rectangular prism
The volume of the prism with length as 9 feet will be 9 w h where w is the width and h is the height of the prism.
We are given a prism.
It is a rectangular prism.
We are also given that it if 9 feet.
We need to find the volume of this rectangular prism.
V = w × h × l
where
w = width of the prism
h = height of the prism
l = length of the prism
Now, we are given that l = 9 feet
So, V = w × h × l
V = 9 w h
Therefore, we get that the volume of the prism with length as 9 feet will be 9 w h where w is the width and h is the height of the prism.
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Violen crimes include grape, robbery, assault, and l=lomicide. The following is a summary of the violent-crime rate (violent crimes per 100,000 population) for all states of a country in a certain year. Complete parts (a) through (d).
, (c) The violent-crime rate in a certain state of the country in that year was. Would this be an outlier?
The lower fence is
enter your response here crimes per 100,000 population.
The upper fence is
enter your response here crimes per 100,000 population.
From the interquartile range of the distribution, the fences for non-outliers are given as follows:
Lower: 0.Upper: 657.65.What is the missing information?
The quartiles of the distribution are given as follows:
The interquartile range of a distribution is given by the difference of the third quartile by the first quartile, that is:
IQR = Q3 - Q1.
Outliers are given by:
1.5 IQR below Q1.1.5 IQR above Q3.For this problem, the IQR is:
IQR = 529.7 - 273.8 = 255.9.
Hence the fences are:
Lower: 273.8 - 1.5 x 255.9 = -110.05, negative numbers are not possible in the range of the question, hence the lower fence is of 0.Upper: 273.8 + 1.5 x 255.9 = 657.65.More can be learned about the interquartile range of a distribution at https://brainly.com/question/17083142
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Michael is trying to show that ABC to congruent to A'B'C
To find the reflection of ΔABC in the x-axis, the points would move as follows:
Point A would move 8 units Points B would remain at same point hence move 0 unitsPoint C would move 8 unitsUsing the original coordinates, Δ A'B'C' is a reflection of Δ ABC in the line?
line x = 4The triangles are?
The two triangles are congruentThe line of reflection Michael used is?
Michael used line x = 4What is reflection?
Reflection as used in geometry is the representation of an image in the mirror image copy. Reflection is done with respect to a line called line of reflection. Images formed are of equal distant to the line of reflection and the images are usually congruent.
Reflection as represented on a graph is most times in x axis or y axis. This axis shows the location of the line of reflection and it is very important when determining the position of the reflected image.
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Lena has to make 20 gallons of punch for a potluck. The punch is made of soda and fruit drink. The cost of the soda is $1.90 per gallon and the cost of the fruit drink is $2.10 per gallon. Lena’s budget requires that the punch cost $2 per gallon. How many gallons of soda and how many gallons of fruit drink does she need?
Answer:
10 for each
Step-by-step explanation:
1.90 x 10 = 19
2.10 x 10 = 21
so 19 + 21 = 30
What is the length of a rectangular holding pond with an area of 5 1/10 square miles and a width of 1/6 mile?
Suppose that you have 10 green cards and 5 yellow cards. The cards were well shuffled . You randomly draw two cards WITH REPLACEMENT (you draw, put the card back and draw again). Round your answers decimal
G1=The first card drawn is green
G2=the second card drawn is green
A. P(G1 and G2)=
B. P (at least one green=
C. P(G2) (G1)=
D. Are G1 and G2 independent
They are independent events or dependent event
The probability of P(G1 and G2) will be 1/5.
The probability of at least one green will be 3/10.
The probability for P(G2) (G1) will be 1/100.
They're dependent event
How to calculate the probability?G1= The first card drawn is green
G2= the second card drawn is green
The probability of P(G1 and G2) will be:
= 1/10 + 1/10
= 1/5.
The probability of at least one green will be:
= 1/10 + 1/5
= 3/10
The probability for P(G2) (G1) will be:
= 1/10 × 1/10
= 1/100
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b)
73cm
92cm
56 cm
What is the
the
area and perimeter
Answer:
Area=2044..... perimeter=221
Step-by-step explanation:
Step1:- Area =1/2×breath×height
1/2×73×56
1/2×4088
= 2044
Area =2044cm^2
Step2:- Perimeter= a+b+c
=73+56+92
=221
Perimeter=221cm
Lisa, Bree, and Caleb are meeting at an amusement park. They each enter at a different gate. On this diagram of the park, explain how the friends could calcuate the point that is equistant from all three gates
By joining the entry point of all three friends to form a triangle and then finding the centroid of this triangle , they can calculate the required point.
If Lisa, Bree, and Caleb are meeting at an amusement park and each enter at a different gate as shown in reference picture attached hereby, the friends could calculate the point that is equidistant from all three gates by the equation [(Distance between gate 1 and gate 2) = (Distance between gate 2 and gate 3) = (Distance between gate 1 and gate 3)]
As per question statement, Lisa, Bree, and Caleb are meeting at an amusement park and each enter at a different gate as shown in reference picture attached hereby.
We are required to determine to calculate the point that is equidistant from all three gates.
The required equation goes as [(Distance between gate 1 and gate 2) = (Distance between gate 2 and gate 3) = (Distance between gate 1 and gate 3)],
Where, they will have to use the distance formula to find the distances in between which goes as [tex]D=\sqrt{(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2} }[/tex], in the above mentioned equation.
Equation: In mathematics, an equation is a formula or a mathematical statement, that expresses the equality of two expressions, by connecting them with the "Equal To" sign.Complete question: Lisa, Bree, and Caleb are meeting at an amusement park. They each enter at a different gate. On this diagram of the park, explain how the friends could calculate the point that is equidistant from all three gates.
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Is 5.424 greater than 5.343
Answer:
Yes.
Step-by-step explanation:
Answer:
Yes
Step-by-step explanation:
The tenths place is 4 while 5.343 tenths place is 3
Hope It Helps
Sorry If I'm Wrong
❗❗100 POINTS FOR CORRECT ANSWER AND EXPLANATION❗❗~math question~
thanks)
Answer:
k = 110
Step-by-step explanation:
You want the integer multiple of pi that is the area of 300° of a donut with inner radius 8 cm and outer radius of 14 cm.
Area of a circleThe area of a circle is given by the formula ...
A = πr²
Then the area of the outer circle is ...
A = π(14 cm)² = 196π cm²
The area of the inner circle is ...
A = π(8 cm)² = 64π cm²
Donut areaThe area of the whole donut is the difference of these areas:
whole donut area = (196 -64)π cm² = 132π cm²
Shaded areaThe shaded area of the figure represents 300° of the 360° full donut. The area is proportional to the central angle, so the shaded area is ...
shaded area = (300°/360°)×whole donut area
shaded area = 5/6 × 132π cm² = 110π cm²
Comparing this to the expression kπ cm², we see that ...
k = 110
Simplify negative 3 and 4 over 5 minus 5 and 2 over 3.
Answer:
-9 7/15
Step-by-step explanation:
I took the test lol. Also if your in advanced you should know this!
suppos there is a 1.2f drop in temperature for every thousand feet that an airplane climbs into the sky. if the temperature on the ground is 53.8f what will be the temperature when the plane reaches an altitude of 8,000ft?
The temperature will be 44.2f when the plane reaches an altitude of 8,000ft.
What exactly are mathematical operations?A function in mathematics that converts zero or even more input values (also known as "operands" or "arguments") to a well-defined output value is known as an operation.The number of operands determines the operation's arity.The most commonly studied operations are binary activities (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive direct opposite and multiplicative inverse.A constant is a zero-arity operation, also known as a nullary operation.An arity 3 operation, also recognized as a ternary operation, is the mixed product.So, there is a 1.2f drop in temperature for every thousand feet.
The plane is at 8000 ft then:
8000/1000 = 8So,
1.2 × 8 = 9.6The temperature at 8000 ft:
53.8 - 9.6 = 44.2Therefore, the temperature will be 44.2f when the plane reaches an altitude of 8,000 ft.
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Evaluate the function
f(x) = -2x^2 - 4x + 13
Find f(-7)
Answer:
g(-7) = 57
Step-by-step explanation:
note: the editor will not let me use eff of x. I have to use g(x)
Equation
g(x) = -2x^2 -4x + 13
Comment
y is the same thing as g(x) so you are really being asked to find y,
Given
x = - 7
g(-7) means that x is -7
Solution
g(x) = -2(-7)^2 - 4(-7) + 13 Substitute x = - 7 on the right
g(x) = -2*49 + 28 + 13 Combine
g(x) = -98 + 28 + 13
g(-7) = -57
If log y = 7, which is equal to y?
The value of the logarithm log y = 7 for y will be e⁷.
We are given the logarithm problem as:
log y = 7
We need to solve this to find the value of y.
We will use the properties of logarithm for this.
So, we get that
⇒ e ^ log y = e ⁷
Solving it, we will get that:
⇒ y = e⁷
So the value of the logarithm log y = 7 for y will be e⁷.
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The ratio of students with blond
hair to students with brown or
black hair is 1:2. If there are
212 students with brown or black
hair, how many students have
blond hair?
Answer: 106 students
Step-by-step explanation:
In a 1:2 ratio, we can see that there are 2x the amount of students with brown/black hair compared to students with blonde hair.
So taking 212 students, we can divide the number by half to get 106 students.
[tex]\frac{212}{2} = 106[/tex]
i have no idea how to do this
-3y+7y+4y^3-2y^2+6y^3-7y^3-5y
The sum of two numbers is 14. Using x to represent the smaller of the two numbers , translate "the sum of twice the smaller number and two more than the larger number" into a variable expression. Then simplify
The smaller number is 4 and the larger number is 10.
Given that, the sum of the two numbers is 14.
What is an equation?In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, x represents the smaller of the two numbers.
Then the larger number is
The sum of twice the smaller number and two more than the larger number = 2x+2
Now, x+2x+2=14
⇒3x+2=14
⇒3x=12
⇒x=4
So, 2x+2=10
Therefore, the smaller number is 4 and the larger number is 10.
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A family is planning their vacation to Disney World. They will drive from a small town outside New Orleans,
Louisiana, to Orlando, Florida, a distance of 700 miles. They plan to average a rate of 55 mph. How long will this
trip take?
The time taken for the trip will be 12.7 hours.
How to calculate the value?It should be noted that time taken is calculated as:
Time = Distance / Speed
Distance = 700 miles
Speed = 55 mph
Time = 700/55
Time = 12.7 hours.
Therefore, the time taken for the trip will be 12.7 hours.
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