Answer:
r(t) and s(t) are parallel.
Step-by-step explanation:
Given that :
the lines represented by the vector equations are:
r(t)=⟨1−t,3+2t,−3t⟩
s(t)=⟨2t,−3−4t,3+6t⟩
The objective is to determine if the following lines represented by the vector equations below intersect, are parallel, are skew, or are identical.
NOTE:
Two lines will be parallel if [tex]\dfrac{x_1}{x_2}= \dfrac{y_1}{y_2}= \dfrac{z_1}{z_2}[/tex]
here;
[tex]d_1 = (-1, \ 2, \ -3)[/tex]
Thus;
[tex]r(t) = \dfrac{x-1}{-1} = \dfrac{y-3}{2}=\dfrac{z-0}{-3} = t[/tex]
[tex]d_2 =(2, \ -4, \ +6)[/tex]
[tex]s(t) = \dfrac{x-0}{2} = \dfrac{y+5}{-4}=\dfrac{z-3}{6} = t[/tex]
∴
[tex]\dfrac{d_1}{d_2}= \dfrac{-1}{2} = \dfrac{2}{-4}= \dfrac{-3}{-6}[/tex]
Hence, we can conclude that r(t) and s(t) are parallel.
A biologist measured the length and mass of 20 reptiles. The equation y=0.3x - 2 is the line of best fit for the data, where x is the length, in centimeters, and y is the mass, is grams. Based on the equation what is the approximate length of a reptile that has a mass of 20.5grams
Answer:
It should be 75 cm if we're taking the same test.
Step-by-step explanation:
y=0.3x-2
20.5=0.3(75)-2
0.3*75=22.5
22.5-2=20.5
20.5=20.5
Using the line of best-fit, it is found that the approximate length of the reptile is of 75 centimetres.
-------------
The mass y, in grams, of a reptile with length of x centimetres is given by:
[tex]y = 0.3x - 2[/tex]
-------------
Mass of 20.5 grams means that [tex]y = 20.5[/tex]The length for this reptile is found solving the line of best-fit for x, thus:[tex]y = 0.3x - 2[/tex]
[tex]20.5 = 0.3x - 2[/tex]
[tex]0.3x = 22.5[/tex]
[tex]x = \frac{22.5}{0.3}[/tex]
[tex]x = 75[/tex]
The approximate length of the reptile is of 75 centimetres.
A similar problem is given at https://brainly.com/question/24141057
What two factors of 24 have a sum of 11
Answer:
8 and 3
Step-by-step explanation:
8+3=11
8*3=24
Which expression is equivalent to 9^36/9^3 ? A) 1/9^12 B) 9^33 C) 9^12 D) 9^39
Answer:
[tex]\huge\boxed{\dfrac{9^{36}}{9^3}=9^{33}\to\mathbb{B)}}[/tex]
Step-by-step explanation:
[tex]\text{Use}\ \dfrac{a^n}{a^m}=a^{n-m},\ \text{for}\ a\neq0.\\\\\text{We have}\ \dfrac{9^{36}}{9^3}=9^{36-3}=9^{33}[/tex]
ANSWER PLEASE! Hopefully someone can figure out.
Answer:
B
Step-by-step explanation:
The domain is the input values, that is the x- values
The range is the output, that is the y- values.
Thus using values from table
domain : {- 2, 0, 2 }, range : { - 1, 0, 1 }
POINTS......!!!!
Please answer!!!
Please state the width (part a)
And length (part b)
Answer:
(a) = 71 cm
(b) = 89 cm
Step-by-step explanation:
(a.)
perimeter of a rectangular field = 324 m
length (l) = 91 m
width (w) = ?
Now,
Perimeter Of Rectangle
= P = 2(l + w)
= 2(91 + w) = 324m
= 182 + 2w = 324m
= 2w = 324 - 182m
= 2w = 142m
= w = 142/2
= w = 71
(b.)
area of rectangular painting = 5696 cm²
width (w) = 64 cm
length (l) = ?
Now,
Area Of Rectangle
A = l × w
= l × 64 = 5696
= l = 5696/64
= l = 89 cm
VERIFICATION:-FOR (a)
= P = 2(l + w)
= P = 2(91 + 71) = 324 cm
FOR (b)
= l × w
A = 89 × 64 = 5696
3(3x-2)=39
Solve equation
27.2163 rounded to the nearest hundredth
Answer:
27.0000
Step-by-step explanation:
27.2163 rounded to the nearest hundredth is 27.0000 or 27 because the hundredth place held a 1 and 5 or above rounds up and 4 or below rounds down. The .2163 turned into zeros because the second number (the hundredths place) was a 1 so it rounded down, and hen it rounds down, all the numbers round to 0.
Find the mass of the lamina described by the inequalities, given that its density is rho(x, y) = xy. 0 ≤ x ≤ 2, 0 ≤ y ≤ 2
Answer: Mass of lamina = 4
Step-by-step explanation: A lamina is a plate in 2 dimensions, described by the plane it covers and its density function, [tex]\rho(x,y)[/tex].
To determine mass of the lamina:
mass (M) = [tex]\int {\int\limits_D \rho(x,y) \, dA[/tex]
where D is region bounded by the axis.
For the question:
M = [tex]\int\limits^2_0 {\int\limits^2_0 xy \, dy \,dx[/tex]
Calculating the double integral:
M = [tex]\int\limits^2_0 { x\frac{y^{2}}{2} \,dx[/tex]
M = [tex]\int\limits^2_0 { x(\frac{2^{2}}{2}-0)} \,dx[/tex]
M = [tex]\int\limits^2_0 { 2x} \,dx[/tex]
M = [tex]\frac{2.2^{2}}{2} - 0[/tex]
M = 4
The mass of lamina is 4 units.
(0.003s^2 +0.075 -0.027)•0.2
Answer:
0.0006s2+0.0096
Step-by-step explanation:
Perform the indicated operation(s). Write your answer in lowest terms.
7/10÷7/4 = ???
Answer:
76/86
Step-by-step explanation:
Answer:
76/86 is the answer it is the lowest term
Jan is painting a square canvas. The length of one side of the canvas is 4 feet. Write an equation to show how to show how to find the area of the canvas
Step-by-step explanation:
It is given that, Jan is painting a square canvas. The length of one side of the canvas is 4 feet.
We need to write an equation to show how to find the area of the canvas.
For a square, all its sides are equal. Let the side is x. The area of a square is given by :
[tex]\text{Area}=\text{side}^2\\\\A=x^2\\\\A=4^2\\\\A=16[/tex]
So, the equation that shows the area of the canvas is [tex]A=x^2[/tex].
Use the frequency distribution shown below to construct an expanded frequency distribution.
High Temperatures (°F)
Class
16-26
27-37
38-48
49-59
60-70
71-81
82-92
Frequency, f
17
45
66
67
82
66
22
Answer and Step-by-step explanation:
The calculation of midpoints, relative frequencies and cumulative frequencies are shown below:-
For Midpoint = [tex]\frac{Lower\ limit\ +\ Upper\ limit}{2}[/tex]
For Relative frequency = [tex]\frac{Frequency}{Total\ number\ of\ frequency}[/tex]
Class Frequency Midpoints Relative Cumulative
frequency frequency
16-26 17 21 0.047 0.047
27-37 45 32 0.123 0.17
38-48 66 43 0.181 0.351
49-59 67 54 0.184 0.535
60-70 82 65 0.225 0.76
71-81 66 76 0.181 0.941
82-92 22 87 0.060 1.001
Total 365
Therefore for computing the cumulative frequency we simply added relative frequency with previous cumulative frequency for class 27-37 and in the same manner of every class.
The rate at which something occurs over a particular period of time or in a given sample:
"An increase in the frequency of accidents due to increased overtime"
GivenUse the frequency distribution shown below to construct an expanded frequency distribution.
The formula to calculate the midpoint and relative frequency are given below.
[tex]\rm Midpoint = \dfrac{Lower \ limit + Upper \ limit }{2}[/tex]
[tex]\rm Relative \ frequency = \dfrac{Frequency}{total \ frequency}[/tex]
The frequency distribution to construct an expanded frequency distribution is given below.
Class Frequency Midpoints Relative frequency Cumulative frequency
16-26 17 21 0.047 0.047
27-37 45 32 0.123 0.17
38-48 66 43 0.181 0.351
49-59 67 54 0.184 0.535
60-70 82 65 0.225 0.76
71-81 66 76 0.181 0.941
82-92 22 87 0.060 1.001
Total 365
To know more about Frequency click the link given below.
https://brainly.com/question/17740069
Evaluate : 9⁴xa⁷b⁴/ 3⁵xa⁴b⁴
Answer:
27a³
Step-by-step explanation:
9⁴xa⁷b⁴ / 3⁵xa⁴b⁴
(3²)⁴xa⁷b⁴ / 3⁵xa⁴b⁴
3⁸xa⁷b⁴ / 3⁵xa⁴b⁴
3³a³
27a³
Based on the graph which statement is true
A. He needs1 cup of flour for 1 batch
B. He needs 1 cup of flour for 8 batches.
c. He needs 4 cups of flour for 8 batches
He needs 6 cups of flour for 3 batches
How many flour cups are needed per batch of cookie?
1
1.5
2
2.5
Answer:
D. He needs 6 cups of flour for 3 batches
Find x, if 3x − 5(y + x ) ^2 = 16 and 4x + 2(y + x )^ 2 = 30
Answer:
x = 7
Step-by-step explanation:
Start by solving for [tex](y+x)^2[/tex] which is a common expression for both equations. Then in the first equation:
[tex]3\,x5\,(y+x)^2=16\\3x-16=5\,(y+x)^2\\(y+x)^2=\frac{3\,x-16}{5}[/tex]
and in the second equation:
[tex]4\,x+2\,(y+x)^2=30\\2\,(y+x)^2=30-4\,x\\(y+x)^2=15-2\,x[/tex]
Now we make the two [tex](y+x)^2[/tex] expressions equal so we get:
[tex]\frac{3\,x-16}{5} =15-2\,x\\3\,x-16=75-10\,x\\13\,x=75+16\\13\,x=91\\x=7[/tex]
() and () are inverses of one another and drawn on the same graph with the same scale on both the horizontal and vertical axis. Which of the following would be true?
A.
By reflecting the entire coordinate grid over the line =, () would land on ().
B.
() is the same as (), translated up 3 units.
C.
By rotating () 90° clockwise around the origin you would get ().
D.
By rotating () 180° clockwise around the origin you would get ().
Answer: Option A.
Step-by-step explanation:
We have the functions f(x) and g(x), that are inverses between them.
This means that if:
f(x) = y
then:
g(y) = x.
now, remember that:
When we have a point (x, y), and we reflect it over the line y = x, our new point will be (y, x).
So before we whe had:
f(x) = y.
and now in that same place, we have:
g(y) = x.
So the old graph of f(x) now coincides with the graph of g(x). (And the old graph of g(x) now coincides with the graph of f(x) )
So A is true.
B) This depends on the function:
if we have f(x) = x + 1.5
then f(0) = 1.5
now we want that:
g(1.5) = 0, then we can write:
g(x) = x - 1.5
Now f(x) and g(x) are inverses, and we would have that:
f(x) = g(x) + 3.
So f(x) is g(x) translated up by 3 units, but this is a particular case, not a general one, so B is not always true.
C and D) When we do rotations of 90° or 180°, we are effectively changing the quadrant of our point. so rotations will cause not only changes as the reflection over the x = y line, those will also cause changes in the sign of our variables, so, while for some functions f(x) and g(x) we can have that the rotations will map one into the other, this is not the general case.
f(x)=x2–5x+7, find f(3)
Answer:
[tex]f(3) = 1[/tex]Step-by-step explanation:
f(x) = x² - 5x + 7
To find f(3) substitute the value of x that's 3 into f(x) that's replace every x in f (x) by 3
We have
[tex]f(3) = {3}^{2} - 5(3) + 7 \\ = 9 - 15 + 7 \\ = - 6 + 7[/tex]We have the final answer as
[tex]f(3) = 1[/tex]Hope this helps you
3b^2+6b-28
which of the following describes 3 in the expression above
A. quotient
B. coefficient
C. sum
D. product
Answer:
3 is a coefficient. (Option B)
Step-by-step explanation:
A coefficient in a term is the number placed before the variable. The coefficient multiplies the variable.
In the given expression, 3 would be the coefficient in [tex]3b^2[/tex].
A, C, and D are answers to an expression depending on the expression's operation.
In this case, option B would be the correct answer.
Hope this helps.
Answer:
[tex]\huge \boxed{\mathrm{B. \ coefficient}}[/tex]
Step-by-step explanation:
[tex]3b^2[/tex]
[tex]b^2[/tex] is being multiplied by 3.
A coefficient is a number used to multiply a variable.
Solve for x: |4x + 12| = 16 (5 points) x = 7, x = −7 x = 1, x = −1 x = 1, x = −7 x = −1, x = 7
Answer:
x =1 x = -7
Step-by-step explanation:
|4x + 12| = 16
Absolute value equations have two solutions, one positive and one negative
4x+12 = 16 4x+12 = -16
Subtract 12 from each side
4x+12-12 = 16-12 4x+12-12 = -16-12
4x =4 4x =-28
Divide by 4
4x/4 = 4/4 4x/4 = -28/4
x =1 x = -7
5x - 10 less than it equal to 20
In one day, a book store earned $199 in sales for 4 copies of a new cookbook and 5 copies of a new science fiction novel. On the next day, it earned $152 in sales for 3 copies of the cookbook and 4 copies of the science fiction novel. What was the price of each book?
Answer:
The cookbook costs $36 per copy while the science fiction costs $11 per copy
Step-by-step explanation:
Here in this question, we are interested in calculating the price of the cookbook and the price of the science fiction novel.
Since we do not know the price of each, we start by assigning variables to stand in for these unknown prices.
Let the price of the cookbook be $x , while the price of the science fiction be $y
Now, on the first day, 4 copies of the cookbook and 5 copies of the fiction;
mathematically that would be 4 * x and 5 * y
We add both and sum to be $199
Thus we have;
4x + 5y = 199 ••••••••••(i)
On the second day;
3 copies of cookbook 3 * x = 3x with 4 copies of science fiction 4 * y
Adding both yielded 152;
Thus, we have ;
3x + 4y = 152••••••••••(ii)
So we need to solve both equations simultaneously to get the values of x and y
4x + 5y = 199
3x + 4y = 152
Multiply equation i by 3 and equation ii by 4
3 * 4x + 5y = 199
4 * 3x + 4y = 152
12x + 15y = 597
12x + 16y = 608
Now, subtract multiplied equation ii from multiplied equation i
(12x-12x) + (15y-16y) = (597-608)
-y = -11
y = 11
To get x, simply substitute in any of the equations;
let’s use equation 1
4x + 5y = 199
4x + 5(11) = 199
4x + 55 = 199
4x = 199-55
4x = 144
x = 144/4
x = 36
. Suppose the coordinate of A is 0 and AR = 5 and AT = 7.
a. What are the possible coordinates of R? Of T
==================================================
Explanation:
If we're on a number line, then R could be at either R = 5 or R = -5. This is so the distance from A to R is 5 units. Distance is never negative. You count out the spaces to get the distance, or use subtraction and absolute value.
Saying "distance from A to R is 5" can be written as AR = 5. Meaning segment AR is 5 units long.
Now if AT = 7, then T could be at 7 or -7 on the number line. The reasoning as similar as to why R could be at -5 or 5.
Convert 2.54 x 10^6 into standard notation
Which number line represents the solution |2x|-12 =
Answer:
Third option, last one
Step-by-step explanation:
Let's solve for x first.
|2x| - 12 = -2
|2x| = 10
2x = 10 or -2x = 10
x = 5 or x = -5
The number line that represents this is the last one.
when bisecting an angle, one of the steps is to draw an arc centered on a point on a ray of the angle. in particular this angle is to be drawn on the interior of the angle, why must The Arc be drawn in the interior of the angle?
Step-by-step explanation:
The arc drawn must be in the interior side of the angle to be bisected because while constructing the angular bisector, we make an arc cutting both the rays of the angle, so in order to cut the angle in to two equal part, we should make arcs in the interior part of the angle subtended so that it bisects the angle in two equal parts.
How many solutions are there for the system of equations shown on the graph?
Answer:
Hey there!
These lines only intersect at one point, so there is only one solution.
Let me know if this helps :)
Answer:
one solution
Step-by-step explanation:
The solutions are where the graphs intersect
There lines cross at one point (0,3), so there is one solution
A population of bacteria is growing rapidly. The population at any hour, h, can be represented
by the function f(h) = 2 • 4h. What is the population of bacteria after 4 1/2 hours?
Answer:
36
Step-by-step explanation:
Function is:
f(h) = 2*4hAfter 4 1/2 hours, h = 4 1/2 = 4.5
f(4.5) = 2*4*4.5 = 36Answer:
36
Step-by-step explanation:
4×4.5=18
18×2=36
when factoring 6x^2 -7x-20 by grouping , how should the middle term be rewritten
Answer: -7x should be written as -15x+8x or 8x-15x
===============================================
Explanation:
Multiply the first coefficient 6 and the last term -20 to get -120
We need to find factors of -120 that add to the middle coefficient -7
Through trial and error you should find that
-15 + 8 = -7
-15 * 8 = -120
Therefore, we break the -7x into -15x+8x
----------------------------
Extra info: if you want to fully factor by grouping, then follow these steps
6x^2 - 7x - 20
6x^2 - 15x + 8x - 20 ... break up -7x
(6x^2 - 15x) + (8x - 20) .... group into pairs
3x(2x - 5) + 4(2x - 5) .... factor each group
(3x + 4)(2x - 5) ..... pull out the overall GCF 2x-5
So 6x^2-7x-20 fully factors to (3x+4)(2x-5)
We can check the answer by FOILing out the last expression above to get the original expression back again. The box method works as well. So does the distributive property.
The length of a rectangle is shown below: (look at the picture) If the area of the rectangle to be drawn is 12 square units, where should points C and D be located if they lie vertically below the line that connects B and A, to make this rectangle? C(−2, −1), D(1, −1) C(−2, −4), D(1, −4) C(−2, −2), D(1, −2) C(−2, −5), D(1, −5)
================================================
Explanation:
The distance from B to A, or vice versa, is 3 units. You can count out the spaces between the points, or you could subtract the x coordinate values then use absolute value
|B - A| = |-2-1| = |-3| = 3
or
|A - B| = |1-(-2)| = |1+2| = |3| = 3
Whichever method you prefer, the distance between the two points is 3 units.
----------
The area of the rectangle is 12 square units, and we know one dimension of the rectangle is 3 units. The other dimension must be 12/3 = 4 units.
Point C is directly below point B. Specifically C is 4 units below B.
Start at B(-2,2) and move down 4 units to get to C(-2,-2). Then move to the right 3 units to get to D(1,-2)
Or you could start at A(1,2) and move 4 units down to get to D(1,-2) and then move 3 units to the left to get to C(-2,-2)
Answer:
Answer choice = B - C(−2, −4), D(1, −4)
in the following graph, AABC is congruent to AA'B'C'. A teacher asks a student Janine to state the
translation rule for this transformation janine focuses on point and states that the translation rule is
(x,y) (x-2, y-6). In other words, to shift from the blue to the red triangle, you must shift each point two
units left and six units down
State whether Janine's answer was correct or incorrect. In at least three sentences, support your
response with a brief explanation. Be sure to use the term transformation in your explanation
Answer:
Janine's answer is incorrect.
Step-by-step explanation:
Rigid transformations are methods by which the image of a given figure or object can be produced either by rotation, translation, dilation or reflection.
Since Janine used translation method for the transformation, the dimension of the shape is preserved but not its initial position. To translate AABC to AA'B'C', each point should shift three units left and five units down.
Therefore, the appropriate translation rule is:
(x, y) ⇒ (x + 3, y + 5)