Answer:
p = 6i -3j +9k
q = 3i -6j -3k
r = 2p +q
r = 5i -4j +5k
R(5, -4, 5)
Step-by-step explanation:
Given points P(6, -3, 9) and Q(3, -6, -3) and R that divides PQ in the ratio 1:2, you want ...
position vectors p and qr in terms of p and qr in terms i, j, and kthe coordinates of RPosition vectorThe vector from the origin to a point (x, y, z) will be ...
xi +yj +zk
where i, j, k are unit vectors in the direction of the x, y, and z axes, respectively.
Using this pattern, we find the position vectors p and q to points P and Q to be ...
p = 6i -3j +9k . . . . . . . . . . . . . position vector p
q = 3i -6j -3k . . . . . . . . . . . . . position vector q
DivisionPoint R divides PQ in the ratio 1:2, so its position vector will be the weighted sum of p and q:
r = (2p +q)/3 . . . . . . . . . . . . . . . . r in terms of p and q
Using the values of p and q from above, we find r to be ...
r = (2(6i -3j +9k) +(3i -6j -3k))/3 = ((2·6+3)i +(2(-3)-6)j +(2·9-3)k)/3
r = 5i -4j +5k . . . . . . . . . . r in terms of i, j, k
CoordinatesThe coordinates of R are the coordinates of the head of position vector r:
R(5, -4, 5) . . . . . . . . . . . . . coordinates of R
Determine the length of the missing sides for each special right triangle. Leave answer in exact (reduced radical) form. Geometry!! pls help!!
Answer:
[tex]a = 18 \sqrt{3} [/tex]
[tex]c = 36[/tex]
Which of the quotients are equivalent to -(48/17)
Answer:
Check the first box, third box and fifth box
Explanation:
1st box:
Rewrite the fraction: 48
- ----
17
Check equivalency: True
Answer: True
2nd box:
Check equivalency: False
Answer: False
3rd box:
Convert the improper fraction into a mixed number:
2 × 17 + 14
- -----------------
17
Calculate the product or quotient: 34 + 14
- -----------
17
Calculate the sum or difference: 48
- ----
17
Check equivalency: True
Answer: True
4th box:
Rewrite the fraction: 17
----
48
Check equivalency: False
Answer: False
5th box:
Rewrite the fraction: 48
- ----
17
Check equivalency: True
Answer: True
I hope this helps!
I WILL MARK BRAINLIEST PLEASE HELP !! Determine whether the two triangles are similar.
The two triangles are similar by SSA similarity. Option B is correct.
What is the triangle?A triangle is a three-sided polygon. It is one of the most fundamental geometric forms.
If the ratio of the sides are same as well as the one angle is common between the two triangles then in that condition there will be SSA similarity.
From the triangle ABC and DEC
The ratio of the sides is;
[tex]\rm \frac{10}{12}= \frac{8}{9.6} \\\\ \frac{5}{6}= \frac{5}{6}[/tex]
One angle c is common in the two triangles.
The two triangles are similar by SSA similarity.
Hence, option B is correct.
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4= 3/7(3x+14)
Solve for x in simplest form.
- Please see the attached picture for full solution!:)
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A local dry cleaner interviewed 15 candidates for the positions of cashier, washer, and delivery driver. How many ways can
they fill the 3 positions?
18
45
455
2,730
Answer:
D. 2730
Step-by-step explanation:
I just had this question on FLVS yesterday.
you use factorials for this:
15!/12!
15*14*13*12!/12!
15*14*13
2730
Number of ways in which 3 positions can be filled are 2730.
What is permutation and combinations?The number of ways in which objects from a set may be selected, generally without replacements, to form subsets. This selection of subset is called permutation when order of selection is a factor.
If n things taken r at a time and n! = n × (n-1) × (n-2) × (n-3)..........3 × 2 × 1
⇒Permutation,
[tex]P(n,r) =\frac{n!}{(n-r)!}[/tex]
Now it is given that number of candidates, n = 15
and number of position, r = 3
Hence number of ways positions can be filled-
[tex]P(n,r) =\frac{15!}{(15-3)!}[/tex]
⇒ [tex]P(15,3) =\frac{15!}{12!}[/tex]
⇒ P(15,3) = (15 × 14 × 13)12!/12!
⇒ P(15,3) = (15 × 14 × 13)
⇒ P(15,3) = 2730
∴ Number of ways in which 3 positions can be filled are 2730.
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Please help me with this LINEAR INEQUALITIES question:
Please enter 3 inequalities with the correct symbols. I'd really appreciate it!
The system of linear inequalities which satisfy the region R are:
y < x - 3.y ≤ -2x + 5.y ≥ x.How to find the inequalities?Mathematically, the standard equation of a straight line is given by y = mx + b.
In order to determine the system of linear inequalities that satisfy the region R, we would identify the points through which the lines passes through.
For the broken line, we have:
y-intercept = 3.
x-intercept = -3.
Points (x, y) = (0, 3) and (-3, 0).
Since the line is broken (not equal to), the inequality is given by:
y < x - 3.
For the other line, we have:
y-intercept = 5.
x-intercept = -5/2.
Points (x, y) = (0, 5) and (-5/2, 0).
(x/-5/2) + y/5 ≤ 1
-2x + y ≤ 5
y ≤ -2x + 5
For the line passing through the origin, we have:
y - x ≥ 0
y ≥ x.
In conclusion, the system of linear inequalities which satisfy the region R are:
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A distance travaled by train in three hours with a constant speed of r miles per hour
The distance travelled by the train with constant speed of r miles will be 3r.
What is Speed?The most crucial scientific notion is measurement. Base or physical fundamental units are used to quantify a wide range of quantifiable quantities. One such measurable metric is speed, which calculates the ratio between the distance an object travels and the time needed to cover that distance. Let's explore speed in-depth in this session. The pace at which an object's location changes in any direction. When an object travels the same distance in the same amount of time, it is said to be moving at a uniform speed. When an object travels a different distance at regular intervals, it is said to have variable speed.We know the formula of distance linking the speed and the time.
Distance = speed × time
Substituting the given values to get:
Distance = r × 3
Distance = 3r
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Figure ABCD is transformed to figure A prime B prime C prime D prime, as shown below:
A coordinate grid is shown from negative 5 to 0 to 5 on both x -and y-axes. A polygon ABCD has A at ordered pair 1, 3, B at ordered pair 3, 4, C at ordered pair 2, 1, D at ordered pair 1, 1. A polygon A prime B prime C prime D prime has A prime at ordered pair negative 3, 3, B prime at ordered pair negative 5, 4, C prime at ordered pair negative 4, 1, D prime at ordered pair negative 3, 1.
Which of the following sequences of transformations is used to obtain figure A prime B prime C prime D prime from figure ABCD?
Reflection over the x-axis followed by a translation to the right by 2 units
Reflection over the y-axis followed by a translation to the left by 2 units
Counterclockwise rotation by 90 degrees about the origin followed by a translation to the right by 2 units
Counterclockwise rotation by 90 degrees about the origin followed by a translation to the left by 2 units
The figure ABCD reflected over the y-axis followed by a translation to the left by 2 unit to form figure A'B'C'D'
What is a transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.
Dilation is the increase or decrease in the size of a figure.
The figure ABCD reflected over the y-axis followed by a translation to the left by 2 unit to form figure A'B'C'D'
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Use the following set of data: 78, 78, 83, 85, 89, 91, 95, 98 what is the median for the set of data? (a) 85 (b) 89 (c) 87 (d) 98 please help!!!!!!!!!!!!!1
bill is replacing his 15ft long by 12 ft wide deck. his new deck will add 5 feet to the length and 4 feet to the width. if a drawing of the new deck uses a scale of 1 inch =2.5 feet, fin the dimensions of the deck in the drawing
The dimensions i.e. length and width of the deck in the drawing is 8 and 6.4 inches respectively.
Given that the length of the previous deck = 15 feet
The width of the previous deck = 12 feet
Since the new deck will add 5 feet to the length and 4 feet to the width,
The length of the new deck = 15 + 5 = 20 feet
The width of the new deck = 12 + 4 = 16 feet
Also given that a drawing of the new deck uses a scale of 1 inch = 2.5 feet.
So, The length of the deck in the drawing = 20/2.5 inches = 8 inches
The width of the deck in the drawing = 16/2.5 inches = 6.4 inches
Therefore, the dimensions i.e. length and width of the deck in the drawing is 8 and 6.4 inches respectively.
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Triangle N T M is shown. Angle N T M is a right angle. An altitude is drawn from point T to point U on side N M to form a right angle. The length of N T is y, the length of T M is 6, the length of N U is 9, and the length of U M is 3.
What is the value of y?
3 StartRoot 3 EndRoot units
6 StartRoot 3 EndRoot units
9 StartRoot 3 EndRoot units
12 StartRoot 3 EndRoot units
Answer:
6 StartRoot 3 EndRoot units
Step-by-step explanation:
65. Extensions
Find the equation of the line that passes through the following points: (a, b) and (a, b +1 )
Answer:
The equation for the line which passes through the points given as (a, b) and (a, b+1), is x=a, which represents a vertical line.
Step-by-step explanation:
It is given that a line passes through the points whose coordinates are (a, b) and (a, b+1).
It is asked to find the linear equation which passes through the given points.
To do so, first determine the slope of the given line using the coordinates and the formula for the slope. Accordingly, proceed to find the equation of the given line.
Step 1 of 2
Determine the slope of the line.
The points through which the line passes are given as (a, b) and (a, b+1). Next, the formula for the slope is given as,
[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
Substitute b+1&b for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex] respectively, and a&a for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,
[tex]m=\frac{b+1-b}{a-a}$\\ $m=\frac{1}{0}$[/tex]
b+1. So the equation of the line cannot be found using the general point-slope form equation.
Step 2 of 2
Write the equation of the line.
So, by definition, the line that passes through the given points is a vertical line. Now, as its x- coordinate is a, so the equation of the line is given as x=a.
Solve the equation f(x)=x3+2x2+4x+8 given that one of its roots is x=−2.
Okay, first you need to understand that function of x, (or f(x)) is y.
We now plug in x.
f(-2) or y=-2(3)+(2•2)+4(-2)+8
f(-2)=-6+4+-8+8
f(-2)=-2
When x=-2, y=-2. Lets plug it back in to see if its true.
-2=-2(3) + (2x2) + (4(-2)) + 8
-2 = -6 + 4 + -8 + 8
-2 = -2.
Heart if it helps, comment if you need help.
Can someone help me out on this problem and show work
Step-by-step explanation:
1. multiply by 8
2. divide by 2
Answer:
4096, 125
Step-by-step explanation:
In the first sequence, notice that each term increases by a factor of 8 (multiplied by 8 each time). Therefore, the fourth term would be 64*8 = 512, so the fifth term is 512*8 = 4096.
In the second sequence, each term decreases by a factor of 2 (divided by 2 each time). The fourth term would be 500/2 = 250, so the fifth term is 250/2 = 125.
PLS help asap!!!!!
Which equation represents the line that is perpendicular to y = 6 and passes through (-8,-2)?
Answer:
The answer is a since non of the other answer would go throught that point
Hope This Helps!!!
The graph shows the heights, y (in centimeters), of a plant after a certain number of weeks, x. Donna drew the line of best fit on the graph.
A graph titled Plant Height shows Number of Weeks on x axis and Height of Plant in cm on y axis. The scales on both x and y axes are shown from 0 to 5 at increments of 5. The graph shows dots at the ordered pairs 0, 1 and 0.5, 1.5 and 1, 2 and 1.5, 2.5 and 2, 2.8 and 2.5, 3 and 3, 3.4 and 3.5, 3.5 and 4, 4 and 4.5,4.5 and 5, 5. A straight line joins the ordered pairs 0, 1 and 5, 5
What would most likely be the approximate height of the plant after 8 weeks?
11.0 centimeters
9.25 centimeters
8.8 centimeters
7.4 centimeters
(Please show your work)
Thank you!
Using the given linear function of best-fit, the most likely approximate height of the plant after 8 weeks would be of 7.4 centimeters.
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.The line of best-fit goes through points (0,1) and (5,5). Point (0,1) means that the y-intercept is of b = 1. The slope is given as follows:
m = (5 - 1)/(5 - 0) = 4/5 = 0.8.
Hence the equation that gives the approximate height after x weeks is:
y = 0.8x + 1.
After 8 weeks, the expected height is:
y = 0.8 x 8 + 1 = 6.4 + 1 = 7.4 centimeters.
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9. Find all function values f(x) such that the distance
from f(x) to the value 8 is less than 0.03 units.
Express this using absolute value notation.
Answer: [tex]|f(x)-8| < 0.03[/tex]
Can someone do this whole page please? I REALLY NEED IT!
Answer:
1. A(-8,3) B(-8,-2) C(-4,-2)
2. A'(8,3) B'(8,-2) C'(4,-2)
3. A"(-12,1.5) B"(-12,-3) C"(-6,-3)
4. they give you the coordinates, haha. Just graph and connect the dots.
5. Coordinates of ABC: A(-8,3) B(-8,-2) C(-4,-2)
Coordinates of A'''B'''C''': A'''(-3,10) B'''(-3,5) C'''(1,5)
The correct coordinates for a 90 degree rotation is: A''''(3,8) B''''(-2,8) C''''(-2,4)
Most of these are formulas so I hope you have this memorized in preparation for tests! Good luck!
An arithmetic sequence has this recursive formula:
a1= 5
an= an-1-4
The explicit formula for the sequence is an = 5 + (n - 1)(-4)
Explicit rule of a sequenceThe formula for calculating the nth term of an arithmetic sequence is expressed as:
an = a + (n - 1)d
where
a is the first term
d is the common difference
n is the number of terms
From the given data
a = 5
a2 = a1 - 4
a2 = 5 - 4
a2. = 1
d = a2 - a
d = 1 - 5
d = -4
Substitute
an = 5 + (n - 1)(-4)
Hence the explicit formula for the sequence is an = 5 + (n - 1)(-4)
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Can someone help me out and show work
Answer: [tex]5(3)^{n-1}[/tex]
Step-by-step explanation:
The common ratio is 15/3 = 5.
The first term is 3.
So, the explicit rule is [tex]5(3)^{n-1}[/tex]
Write down a multiple of 9 that is between 60 and 80
Answer:
72
Step-by-step explanation:
9×8 = 72 which means that 72 is a multiple of 9 lying between 60 and 80.
Do not forget to mark as brainliest if u like my answer.
Complete the point-slope equation of the line through-8,-8) and (7, 9)
Answer:
[tex]y = \frac{17}{15}x + \frac{16}{15}[/tex]
Step-by-step explanation:
So the slope-intercept form is given as: y=mx+b where m is the slope and b is the y-intercept (since if you plug in 0 as x, mx will be 0 leaving only b). You can calculate the slope with the slope formula: [tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex] which is essentially [tex]\frac{rise}{run}[/tex]. So for this example (-8, -8) will be ([tex]x_1, y_1[/tex]) and (7, 9) will be ([tex]x_2, y_2[/tex]).
Plug values into equation:
[tex]\frac{9 - (-8)}{7 - (-8)}[/tex]
cancel out negatives
[tex]\frac{9+8}{7+8}\\[/tex]
Simplify
[tex]\frac{17}{15}[/tex]
The fraction is in the most simplified form unless you want to have a mixed fraction, otherwise you can't do anything else to the fraction.
so now we have the slope we have one part of the equation: [tex]y=\frac{17}{15}x + b[/tex], but now we need to solve for b. This can be done by using either of the points and plugging in x and y, but for this example I'll use (7, 9).
Plug in (7, 9) as (x, y)
[tex]9 = \frac{17}{15}(7) + b[/tex]
Multiply
[tex]9 = \frac{119}{15}+b[/tex]
Subtract
[tex]9-\frac{119}{15}=b[/tex]
Rewrite 9 as a fraction
[tex]\frac{135}{15} - \frac{119}{15} = b[/tex]
Subtract numerators
[tex]\frac{16}{15} = b[/tex]
now we have both pieces of information
[tex]y = \frac{17}{15}x + \frac{16}{15}[/tex]
10. Which is the equation of a line that is perpendicular to the line represented by y=3/4x-1/2
What is the measure of RCD?
Find length CD first, which is the hypotenuse of the triangle.
PD = opposite
Opposite & hypotenuse = SOH or sin
Sin(27) = 15/H
x h, then ÷ sin(27)
H = 15/sin(27)
H = 33.04....
Move to triangle CDR:
15 is length opposite the angle we're after.
So far, we've got the hypotenuse (which we just found to be 33.04....) & the opposite of our triangle
Hypotenuse & opposite = SOH
Sin(x) = 15/33.04... but, to find the angle we do inverse of sin
sin-1(15/33.04...) = x
x = 27
(33.04... means I used the full numbers displayed on my calculator)
Thus, RCD is 27 degrees
Hope this helps!
Mikal is proving that AE ≅ CE .
Triangles A B E and C D E are connected at point E. Angles A B E and E D C are right angles. The lengths of A C and D C are congruent.
Which reason does the ♣ represent in Mikal’s proof?
SAS
SSS
ASA
AAS
The reason that this represent in Mikal’s proof regarding the triangle is SAS.
How to illustrate the triangle?It should be noted that a triangle is a shape that has three sides and angles.
The SAS implies the side angle side. It shows that any two sides and angles that are included between the sides of an angle are equal to the other two sides.
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Answer:
AAS
Step-by-step explanation:
2022 edge
solve for n (please help i’ll do my best to get everyone the answers points)
Answer:
N = 18Step-by-step explanation:
Both triangles are similar by SAS property,
that means corresponding sides are proportional,so,
5/6 = 15/N
= 6/5 = N/15
N = (6×15)/5
N = 6×3
N = 18
What is the fourth row of Pascal’s triangle?
Answer:
14641
Step-by-step explanation:
[tex]formular \: for \: the \: digits \: in \: each \\ row \: of \: a \: pascal \: triangle \: is \: = 11 {}^{n} \\ row \: 0 = \: 11 {}^{0} = 1 \: \\ row \: 1 \: = 11 {}^{1} = 11 \\ row \: \: 2 \: = 11 {}^{2} = 121 \\ row \: 3 = \: 11 {}^{3} = 1331 \\ row \: 4 = 11 {}^{4} = 14641 \\ therefore \: the \: fourth \: row \: is \: 14641[/tex]
could you show me what sin D is?
Answer:
sin D = 28/53
Step-by-step explanation:
sin D = opp/hyp
For angle D, the opposite leg is FE with length 28.
The hypotenuse is DE with length 53.
sin D = 28/53
Answer: sinD=28/53.
Step-by-step explanation:
[tex]sinD=\frac{FE}{DE} =\frac{28}{53} .[/tex]
Consider the following equation.
x^2-3x+2= √ x-2 + 2
Approximate the solution to the equation using three iterations of successive approximation. Use the graph below as a starting point.
please I really need this and I don't have more points to give but I will definitely MARK BRAINLIEST
The approximate solution of the above equation is: 55/15 (Option A). This is solved using the quartic formula, not quadratic equation.
What is the Quartic Formula?
The quartic formula has up to four various solutions including real and imaginary numbers. Read on for more explanation.
What is the solution to the above question?
First we restate the above equation:
x²-3x+2= √(x-2) + 2
Next we remove square roots
[tex]x^{4}[/tex] - 6x³ + 9x² = x - 2
Add two to both sides
→ [tex]x^{4}[/tex] - 6x³ + 9x²+2 = x - 2 +2
→ [tex]x^{4}[/tex] - 6x³ + 9x²+2 = x
Subtract X from both sides
→ [tex]x^{4}[/tex] - 6x³ + 9x²+2 -x = x -x
→ [tex]x^{4}[/tex] - 6x³ + 9x²+2 - x= 0
Using the Quartic formula to solve the fourth order equation:
a[tex]x^{4}[/tex] + bx³ + cx² + dx + e
The resolution of x is given as:
x = 2.691085, 3.346753
Because the fraction nearest to 3.4 is 55/16
hence, the correct answer is Option A.
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The slope of the line below is -3. Which of the following is the point-slope form of the line?
Answer:
Step-by-step explanation:
Is there a graph or more information?