The coordinate vector of x relative to the basis b is:
[x]b = (2, −1/2, −1/2)
To find the coordinate vector [x]b of x relative to the given basis b, we need to solve the equation:
x = [x]b · b
where [x]b is the coordinate vector of x relative to b.
So, we need to find scalars a, b, and c such that:
x = a · b1 + b · b2 + c · b3
Substituting the values of x, b1, b2, and b3, we get:
3 −4 −3 = a · (1 −1 −4) + b · (−3 4 12) + c · (1 −1 5)
Simplifying, we get:
3 = a − 3b + c
−4 = −a + 4b − c
−3 = −4a + 12b + 5c
Solving these equations, we get:
a = 2
b = −1/2
c = −1/2
Therefore, the coordinate vector of x relative to the basis b is:
[x]b = (2, −1/2, −1/2)
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Describe a relationship that can be modeled by the function shown in the table, and explain how the function models the relationship.
x ------ f(x)
1 ------ 4
4 ------ 8
9 ------ 12
16 ------ 16
25 ------ 20
B: Identify and interpret the key features of the function in the context of the situation you described in part A
The relationship that can be modeled by the function shown in the table is y = 4·√x
How to illustrate the information?f(x) is defined as a product of 4 into √x
4 × √1 = 4
4 × √4 = 8
4 × √9 = 12
4 × √16 = 16
4 × √25= 20
Therefore, the relationship is defined as y is 4 times the square root of x that is, y = f(x) = 4√x
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Please help someone. {1,4,9,16...}
what are the next three members?
Answer:
The solution is 25, 36, 49
Step-by-step explanation:
a = 1
b = 3
c = 5-3
= 2
________________________________
Un = [tex]\sf a + (n-1) \times b + \frac{(n-1)(n-2)}{2} \times c[/tex]
Un = [tex]\sf 1 + (n-1) \times 3 + \frac{(n-1)(n-2)}{2} \times 2[/tex]
Un = [tex]\sf 1 + 3n-3 + (n-1)(n-2)[/tex]
Un = [tex]\sf 1 + 3n-3 + n^{2} - 2n - n + 2[/tex]
Un = [tex]\sf n^{2} + 3n - 2n - n + 2 + 1 - 3[/tex]
Un = [tex]\sf n^{2} + 0n + 0[/tex]
Un = [tex]\sf n^2[/tex]
________________________________
Un = n²
U5 = 5²
= 25
U6 = 6²
= 36
U7 = 7²
= 49
________________________________
So, the next three members are 25, 36, 49
Use the given information to find the unknown value. Y varies inversely with the cube of x. When x=5, then y=1. Find y when x=1
Answer:
125
Step-by-step explanation:
y = 1k/x^3 I am trying to find the constant k. I will use the information that I have been given to find k
1 = k/5^3
1 = k/125 Multiply both sides by 125
125 = k
Now, we will find y when x = 1
y = 125/1^3
y = 125
The value of y is 125 when x is 1.
Write the function y as a function of x, i.e., y = f(x), and then solve for x as a function of y, to determine the inverse of a function.
y = 1k/x^3 I am trying to find the constant k. I will use the information that I have been given to find k
1 = k/5^3
1 = k/125
Multiply both sides by 125
125 = k
Now, we will find y when x = 1
y = 125/1^3
y = 125
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Need to type in SSS, SAS, ASA, AAS, or HL
The triangles are congruent by SAS congruence theorem
How to determine the congruence theorem?From the figure, we have the following congruent sides
Sides AB and DBSides A F and D FAlso, both triangles share a common vertex at B
This means that:
<B = <B
Two sides and one angle are congruent in the triangles
Hence, the triangles are congruent by SAS congruence theorem
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Circle Q is shown. Secant L N and tangent P N intersect at point N outside of the circle. Secant L N intersects the circle at point M. Arc M P is y, arc L P is x, and arc M L is z.
Which equation is correct regarding the measure of ∠MNP?
m∠MNP = One-half(x – y)
m∠MNP = One-half(x + y)
m∠MNP = One-half(z + y)
m∠MNP = One-half(z – y)
By applying the Theorem of Intersecting Secant to circle Q, an equation which is correct about the measure of ∠MNP is: A. m∠MNP = One-half(x – y).
What is the Theorem of Intersecting Secant?The Theorem of Intersecting Secant states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.
For this exercise, the following points should be noted:
x represents the major arc.y represents the minor arc.By applying the Theorem of Intersecting Secant to circle Q shown in the image attached below, we can infer and logically deduce that angle MNP will be given by this formula:
m∠MNP = One-half(x – y).
m∠MNP = ½(x – y)
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A single die is rolled twice. Find the probability of getting a 1 the first time and a 5 the second time. Express the probability as a simplified fraction.
The probability of first rolling a 1, then a 5, will be [tex]\frac{1}{36}[/tex].
What is probability?Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty. The greater the likelihood of an occurrence, the more probable it will occur.To find the probability of getting a 1 the first time and a 5 the second time:
Probability of getting 1 in 1st time = [tex]\frac{1}{6}[/tex]
Probability of getting 5 in 2nd time = [tex]\frac{1}{6}[/tex]
The probability of first rolling a 1, then a 5, will be = [tex]\frac{1}{6}[/tex] × [tex]\frac{1}{6}[/tex]
[tex]= \frac{1}{36}[/tex]
Therefore, the probability of first rolling a 1, then a 5, will be [tex]\frac{1}{36}[/tex].
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PLEASE HELP WILL GIVE YOU ALOT OF POINTS
Is (x-4) a factor of f(x)=x^3- 2x^2 + 5x +1. use either the remainder theorem or the factor theorem to explain your reasoning
If x - 4 is a factor then x = 4 is a root:
f(4) = 4^3 - 2 * 4^2 + 5 * 4 + 1
= 64 - 32 + 20 + 1
= 53
since f(4) is not zero then 4 is not a root of the f(x)
Also, x - 4 is not a factor
In algebra, the remainder theorem, or Bezout's small theorem, applies the principle of polynomial division. It states that the remainder of dividing the polynomial f (x) by the linear polynomial {\ display style x-r} is equal to {\ display style f (r). }
In algebra, a factor set is a set of factors and roots of. Polynomial. This is a special case of the remainder theorem. The factor theorem shows that the polynomial f (x) has a factor only if f = 0.
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Which expression is equivalent to 144 3/2
Answer:
144=12², so 144^3/2=(12²)^(3/2)=12³=1728.
this answer is not from the internet
go check yourselves
mark me brainliest
Find the volume of the solid to the nearest whole cubic unit. use a calculator, if needed. yellow solid v = ______
The volume of the cuboid is 132 cubic inches.
Given length of cuboid 7 1/3 inches, breadth being 6 2/3 inches , height being 2 7/10 inches.
Volume is amount of liquid a container can hold in its capacity. Cuboid is a 3 dimensional figure having length , breadth and height.Volume of cuboid is the product of length, breadth and height of cuboid.
We have to calculate volume of cuboid.
We have to make a simple fraction showing length , breadth and height.
Length=(3*7+1)/3=22/3
Breadth=(3*6+2)/3=20/3
Height=(10*2+7)/10=27/10
Volume=22/3*20/3*27/10
=11880/90
=132 cubic inches.
Hence the volume of cuboid having length of 22/3 inches, breadth of 20/3 inches and height of 27/10 is 132 cubic inches.
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Question is incomplete as it should include figure.
2. The lengths in centimeters of four line segments
are shown below.
3.12, 3.24, 31, √10
Write the lengths in order from least to greatest.
Answer:
I'm pretty sure it is √10, 3.12, 3.24, 31
Step-by-step explanation:
I don't know if you messed up but I got a question similar that is the length 31 in your quesion is actually 3 1/4 in my question. but i did the math and 31 is still the greatest number.
Graph and label each of the ordered pairs in the coordinate plane. Then state the quadrant
or axis in/on which the point is located.
55. A(2, 4)
56. B(0, -3)
57. C(1, -1)
59. E(-4,1)
61. G(-3,-2)
63. I(0, 2)
58. D(3, 3)
60. F(2,0)
62. H(-2, 3)
64. J(-1,-4)
and/or volume of the given figure.
d the perimeter & area:
The quadrants of the points that needs to be graphed are:
Quadrant 1- Points A and DQuadrant 2- Points E and HQuadrant 3- Points G and JQuadrant 4- Points Cx-axis- Point Fy-axis- Point B and IHow do you get the quadrants?Since the points that was given are:
A(2, 4) B(0, -3)
C(1, -1) E(-4,1)
G(-3,-2) I(0, 2)
D(3, 3) F(2,0)
H(-2, 3) J(-1,-4)
Then, we plot all the coordinate above on a graph (see image attached)
Hence, from the image attached graph, the categories that can be seen are:
Quadrant 1 is Points A and D
Quadrant 2 is Points E and H
Quadrant 3 is Points G and J
Quadrant 4 is Points C
x-axis- Point F
y-axis- Point B and I
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Which represents the inverse of the function f(x) = 4x?
the one you selected is correct
A sequence is defined by the recursive function f(n + 1) =1/3 f(n). if f(3) 9= , what is f(1)
Answer:
f(1) = 81
Step-by-step explanation:
f(n + 1) = 1/3 f(n)
⇔ f(n) = 3 × f(n + 1)
……………………………
if f(3) = 9 ⇒ f(2) = 3 × f(3) = 3 × 9 = 27
Then
f(1) = 3 × f(2) = 3 × 27 = 81
What is the area of the shaded portion of the figure? Express your answer in terms of pi.
с
A
F
OA. 56 T
OB. 22 T
728
Oc.
45
π
112°
OD. 56 T
ㅠ
E
B
AE = 4 cm
AB= 6 cm
The given radii of 4 and 6 and the sector angle of 112°, gives;
[tex] C.\: \frac{56 \cdot \pi}{9} [/tex]
How can the measure of the shaded portion be found?The possible figure that relates to the question can be described as follows;
Two concentric circles having radii of AE = 4, and AB = 6, respectively.
Sector of the circles formed by lines AC and AB, with angle of sector = 112°
The shaded portion is described by arcs FE and CB
Therefore;
Area of the sectors are found as follows;
[tex]AFE = \frac{112 ^\circ}{360 ^\circ} \times \pi \times {4}^{2} = \frac{224 \cdot \pi}{45} [/tex]
[tex]ACB = \frac{112 ^\circ}{360 ^\circ} \times \pi \times {6}^{2} = \frac{56 \cdot \pi}{5} [/tex]
Area of the shaded portion, A is therefore;
[tex] A= \frac{56 \cdot \pi}{5} - \frac{224 \cdot \pi}{45} =\frac{56 \cdot \pi}{9} [/tex]
[tex] Shaded \: area, \: A= \frac{56 \cdot \pi}{9} [/tex]
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To eliminate the x terms and solve for y in the fewest steps, by which constants should the equations be multiplied by before adding the equations together? first equation: second equation:
Answer:
See below.
Step-by-step explanation:
Here is an example:-
Solve by elimination:
2x - 3y = 0
3x + 2y = 13
To eliminate the y terms Multiply the first equation by 2 and the second by 3. This gives:
4x - 6y = 0
9x + 6y = 39 Adding the 2 equations:
13x + 0 = 39
13x = 39
x = 39/13 = 3
Finally we find y by plugging x = 3 into the first equation:
2(3) - 3y = 0
3y = 2(3) = 6
y = 2.
What is the slope of the line through (-3, 3) and (-1, -1)?
(-3, 3)
-3 -2 -1
(-1,-1)
4
3
2
You
1
-1
2.
y
1 2
3
4
X
Answer:
The slope is -2
Step-by-step explanation:
To find the slope, we can use the slope formula
m = ( y2-y1)/(x2-x1)
= (-1 -3)/(-1 - -3)
= ( -1-3)/(-1+3)
= -4/2
= -2
The slope is -2
In a group of 75 student 20 like football only 30 like circket ony and 18 didn't like any of wo game
(i) 57students liked at least one game.
(ii) 7 students who liked both the games.
(iii) 27 students liked football.
(iv) 37 students liked cricket.
(v) Below we represented the result in a Venn diagram.
What is Venn diagram?
John Venn popularized the Venn diagram in the 1880s, which is a type of diagram that displays the logical relationship between sets. The illustrations are used in probability, logic, statistics, linguistics, and computer science to demonstrate basic set relationships and to teach rudimentary set theory.
Part (i)- We have to get number of people who like at least one game, there are total 75 students and only 18 did not like any of two games, so students who like at least one game are-
75-18 = 57
Part (ii)- There are 57 students who like at least one game, from the question statement we know that 20 students like football only and 30 liked cricket only, so student who like both games are-
57-20-30 = 7
Part (iii)- There are 7 students who liked both games and 20 who liked football only, so student who liked football are-
20+7 = 27
Part (iv)- There are 7 students who liked both games and 30 who liked cricket only, so student who liked cricket are-
30+7=37
Part (v)- Venn Diagram will look like-
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Complete Question- In a group of 75 students, 20 liked football only, 30 liked cricket only and 18 did not like any of two games? (i) How many of them liked at least one game? (ii) Find the number of students who liked both the games. (iii) How many of them liked football? (iv) How many of them liked cricket? (v) Represent the result in a Venn diagram.
What is the x-intercept of p(x) = -x + 8?
Answer:
x-intercept = 8
Step-by-step explanation:
Hello!
An x-intercept is when the y-value is 0, or when the graph intersects the x-axis.
We can replace p(x) with 0 and solve for x.
Solve for x[tex]p(x) = -x + 8[/tex][tex]0 = -x + 8[/tex][tex]-8 = -x[/tex][tex]8 = x[/tex]The x-intercept is 8.
A car dealer acquires a used car for $7,000, with terms fob shipping point. compute total inventory costs assigned to the used car if additional costs include
$290 for transportation-in.
$190 for shipping insurance.
$1,000 for car import duties.
$200 for advertising.
$1,400 for sales staff salaries.
$190 for trimming shrubs.
Shipping points are independent organizational entities within which processing and monitoring of the deliveries, as well as goods issue, is carried out. A delivery is processed by one shipping point only.
"FOB shipping point" or "FOB origin" means the buyer is at risk once the seller ships the product. The purchaser pays the shipping cost from the factory and is responsible if the goods are damaged while in transit. "FOB destination" means the seller retains the risk of loss until the goods reach the buyer.
Please check the attached file for a complete answer.
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PLEASE HELP
Graph the triangle with the given vertices. Find the length and the slope of each side of the triangle. Then find the coordinates of the midpoint of each side. Is the triangle a right triangle? isosceles? Explain (Assume all variables are positive and m ≠ n)
D (0,n), E(m,n), F(m,0)
The given triangle is a right triangle
The length and slopeThe coordinates are given as:
D (0,n), E(m,n), F(m,0)
The length is calculated using:
[tex]l=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2[/tex]
So, we have:
[tex]DE=\sqrt{(0-m)^2 + (n-n)^2} = m[/tex]
[tex]DF=\sqrt{(0-m)^2 + (n-0)^2} = \sqrt{m^2 + n^2[/tex]
[tex]EF=\sqrt{(m-m)^2 + (n-0)^2} = n[/tex]
The slope is calculated using:
[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
So, we have:
[tex]DE = \frac{n -n}{0- m} = 0[/tex]
[tex]DF = \frac{n -0}{0- m} = -\frac nm[/tex]
[tex]EF = \frac{n -0}{m- m} = \mathbf{unde fined}[/tex]
The coordinates of the midpointsThis is calculated using
[tex]m = 0.5 * (x_1 + x_2, y_1 + y_2)[/tex]
So, we have:
[tex]DE = 0.5 * (0 + m, n+ n)=(0.5m, n)[/tex]
[tex]DF = 0.5 * (0 + m, n+ 0)=(0.5m, 0.5n)[/tex]
[tex]EF = 0.5 * (m + m, n+ 0)=(m, 0.5n)[/tex]
The type of triangleIn (a), we have:
Lengths
[tex]DE= m[/tex]
[tex]DF = \sqrt{m^2 + n^2[/tex]
[tex]EF= n[/tex]
Slope
[tex]DE = 0[/tex]
[tex]DF = -\frac nm[/tex]
[tex]EF = \mathbf{unde fined}[/tex]
The sides are not equal.
However, the 0 and the undefined slope implies that the triangle is a right triangle because the sides are perpendicular
It should be noted that the triangle cannot be graphed because the coordinates are not numeric
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Ayudaaaaaaa es para hoy:
Necesito saber cuanto es 389 pesos mexicanos con un 12% de rebaja,ayuda plis
El precio resultante con descuento de 12 % es igual a 342.32 pesos.
¿Cómo hallar el precio resultante con descuento?
En este problema tenemos que determinar el precio resultante, el cual es igual al precio inicial menos el descuento. A continuación, se presenta la siguiente expresión:
x = 389 · (1 - 12/100)
x = 389 - 46.68
x = 342.32
El precio resultante con descuento de 12 % es igual a 342.32 pesos.
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Bd=16 and ac is the perpendicular bisector of bd. 2x-14 37-x d 2y-2 3 y=[?] enter
The value of y from the given expression is 5
Perpendicular Bisector
Given:
BD = 16
BC = 2y - 2
CD = y + 3
Since AC is a perpendicular bisector of BD:
BC = CD
2y - 2 = y + 3
2y - y = 3 + 2
y = 5
Hence, the value of y from the given expression is 5
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can someone please help mee (will give brainliest 20 points!!!)
[a] x = 175 - 7.5p
For a, we are isolating the x variable to one side of the equation.
0.4x + 3p = 70
0.4x = - 3p + 70
x = - 7.5p + 175
[b] x = 115
For b, we are solving for x when p = 8.
x = - 7.5p + 175
x = - 7.5(8) + 175
x = 115
Annel sells a phone which costs $180 and earns $9 commission. If he sells $640 worth of phones the following days, how much will he earn in commission?
The percentage of the cost of the phones Annel earns in commission is 5%. If he sells $640 worth, the amount he earns as percentage will be $32.
How can the amount Annel earns be found?The amount in commission Annel earns when he sells the phone worth $180 = $9
The percentage of the amount sold, Annel earns as commission is therefore;
[tex] \frac{9}{180} \times 100 = 5\%[/tex]
The amount earned as commission if he sells $640 worth of phones is found as follows;
Amount earned = 5% × 640 = 32
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Find the original price if the price was:
$520 after a 30% increase
(Please Help with explanation that makes sense...will mark brainliest)
Given that price was $520 after a 30% increase, the original price was $400.
What is the the original price?Given that;
Percentage increase = 30%Price after the increase = $520Original price = x
To determine the original price, we say;
x × ( 100% + 30% ) = $520
x × ( 130% ) = $520
x × (130/100) = $520
130x / 100 = $520
130x = $52000
x = $52000 / 130
x = $400
Given that price was $520 after a 30% increase, the original price was $400.
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What is the domain of the function graphed below?
X<7
x≤7
-2
all real numbers
Answer:
x < 7
Step-by-step explanation:
The domain encompasses all the "x" values (or inputs) of a function.
The arrow on the left line symbolizes that the function continues into the negative region for infinity. As such, this eliminates option C.
Closed dots are points whose "x" values are included in the function. Open-dots are on points whose "x" values are not included in the function. Although the open-dot on the left line at x = -1 generally means it is not included in the function, the closed dot on the right line overrides this. Therefore, x = -1 is in the domain. The value x = 7 is not within the domain of the function due to the open-dot. This eliminates option B and option D.
With this said, the domain of the function is x < 7.
Select the statement that describes the expression 5 + (3 x 6) − 4. 5 times the sum of 3 and 6, then subtract 4 Add 5 to the product of 3 and 6, then subtract 4 Add 5 to the product of 3 and 6, then add 4 Add 5 to the quotient of 3 and 6, then subtract 4
Answer: Add 5 to the product of 3 and 6, then subtract 4
Step-by-step explanation:
We will use the order of operations. Looking at 5 + (3 x 6) − 4, we would:
[1] Multiply 3 x 6
[2] Add 5 to that product
[3] Subtract 4 from that value
This means the answer to your question is:
Add 5 to the product of 3 and 6, then subtract 4
Answer: B
i DiD tHe TeSt
PLEASE HELP
Quentin is using paper folding to find the center of a circle. He draws triangle ABC on a sheet of patty paper and folds the paper so that vertex A is lined up on vertex B. He then repeats the process twice so that vertex A is lined up on vertex C and vertex B is lined up on vertex C.
Blank one: angle OR perpendicular
Blank two: lies on OR is the center of
blank three: inscribed OR circumscribed
The necessary solution that would be used to fill in the blanks would be
perpendicularis the center ofCircumscribedHow to find the center of the circleThe way that Quintin would be able to do this would be the center of the circumferential triangle is equidistant from the vertices.
The center is going to be the intersection of the bisectors of the three sides of the given triangle.
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perpendicular bisectors, is the center of, circumscribed
Answer:
In the image
Hope this helps!
Step-by-step explanation:
1. perpendicular
2. is the center of
3. circumscribed
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar.
The focus of a parabola is (0, -1). The directrix is the line y=0. What is the equation of the parabola in vertex form?
Check the picture below, so the parabola looks more or less like so, with the vertex half-way from the focus point and the directrix.
Now, the distance from the directrix to the focus point is only 1 unit, so half that, or namely the "p" distance is 1/2 unit, and since the parabola is opening downwards, "p" is negative, so
[tex]\textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=0\\ k=-\frac{1}{2}\\[1em] p=-\frac{1}{2} \end{cases}\implies 4\left( -\frac{1}{2} \right)\left( ~~y-\left( -\frac{1}{2} \right) ~~ \right)~~ = ~~(x-0)^2 \\\\\\ -2\left( y+\frac{1}{2} \right)=x^2\implies y+\cfrac{1}{2} =\cfrac{x^2}{-2}\implies y = -\cfrac{1}{2}x^2-\cfrac{1}{2}[/tex]
now, we could also write that as either
[tex]y = -\cfrac{1}{2}(x^2+1)\qquad or\qquad y = \cfrac{1}{2}(-x^2-1)[/tex]