Answer:
[tex]\left[\begin{array}{ccc}1&0\\0&4\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\y\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}5\\3\end{array}\right][/tex]
Step-by-step explanation:
A matrix is an algorithm that has many applications. It is composed of a series of numbers (typically coefficients of variables) organized in a pattern. When dealing with a matrix, one must always remember the rule (rows by columns). One such application is that a matrix can facilitate the process by which one solves a system of equations.
When given the following system:
y = 5
4x = 3
One can see that not all of the equations have all variables in them. Yet, bear in mind that any number times zero is zero, therefore, one can rewrite the equation such that it has all of the variables if one ensures that the coefficient of the missing variable is (0).
y + 0x = 5
0y + 4x = 3
Now organize this in the form of a matrix, the coefficients of the variable go in a (4 x 4) since there are now (4) elements. The variables are vertically arranged in a (2 x 1), and the equation results are also vertically arranged in a (2 x 1).
[tex]\left[\begin{array}{ccc}1&0\\0&4\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\y\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}5\\3\end{array}\right][/tex]
Expand the function.
f(x) = (3x - 1)3
Answer:
[tex](a-b)^3 = a^3 - b^3 - 3a^2b + 3ab^2\\\\a = 3x, \ b = 1\\\\(3x-1)^3 = (3x)^3 - (1)^3 - 3(3x)^2(1) + 3(3x)(1)^2\\\\[/tex]
[tex]= 27x^3 - 1-3(9x^2)+ 9x\\\\=27x^3 -27x^2 +9x -1[/tex]
The expanded form of the function f(x) = (3x - 1)³ is 27x³ - 9x² + 9x - 1.
We have,
To expand the function f(x) = (3x - 1)³, we can use the binomial expansion formula, which states:
(a + b)³ = a³ + 3a²b + 3ab² + b³
In this case,
a = 3x and b = -1.
Substituting these values into the formula, we get:
[tex](3x - 1)^3 = (3x)^3 + 3(3x)^2(-1) + 3(3x)(-1)^2 + (-1)^3[/tex]
Simplifying further:
(3x - 1)³ = 27x³ - 9x³ + 9x - 1
Therefore,
The expanded form of the function f(x) = (3x - 1)³ is 27x³ - 9x² + 9x - 1.
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129,454,475,954 Which digit is in the hundred-thousands place?
Answer
129,454,475,954
Step-by-step explanation:
it is the four in bold
Answer:
4 is in the hundred-thousands place.
Explanation:
129,454,475,954
(the one that I bolded and underlined out)
HELP!
If the volume of the pyramid is 216 cm, and the length of s is 6 cm, what is the length of the altitude, h?
A. 42cm
B. 36cm
C. 35cm
D. 18cm
The height of the altitude h is 18 cm.
What is an altitude?Altitude is the vertical height of an object above some chosen level.
To calculate the length of the altitude h, we use the formula below
Formula:
h = 3v/l²................ Equation 1Where:
v = Volume of the pyramidl = Length of the baseh = length of the altitudeFrom the question,
Given:
v = 216 cm³l = 6 cmSubstitute these values into equation 1
h = 3×216/6²h = 18 cmHence, the right option is D. 18 cm.
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A parallelogram has a base of 9 km and a height of 5 km. A triangle has a base of 6 km and a height of 3 km. How many times greater is the area of the triangle?
Answer:
Parallelogram has greater area.
Step-by-step explanation:
Given:
Base of parallelogram = 9 km
Height of parallelogram = 5 km
Base of triangle = 6 km
Height of triangle = 3 km
Find:
Greater area
Computation:
Area of parallelogram = Base x Height
Area of parallelogram = 9 x 5
Area of parallelogram = 45 km²
Area of triangle = (1/2)(b)(h)
Area of triangle = (1/2)(6)(3)
Area of triangle = (1/2)(18)
Area of triangle = 9 km²
Parallelogram has greater area.
4 people can stay in a hotel for 5 days for $ 240. Find the bill for 5 people staying in
the hotel for a week
Answer:
$420
Step-by-step explanation:
Divide to isolate the cost
240 / 4 = 60 - amount per person (for 4 people)
60 / 5 = 12 - amount per person per day (5 days)
Multiply using that cost and new values.
12 x 5 = 60
60 x 7 = 420
Please help I will give brainliest
Answer:
52, 60, 68, 76..
Step-by-step explanation:
complete:
a 20% x ____ = $30
Answer:
20/100*x=$30
20x/100=$30
x/5=$30
x=$30*5
x=$150
Step-by-step explanation:
20 percent of 150 equals 30 so 150 times 20 percent would give you 30
There are 15 plates in the kitchen cabinet. The diameter of each plate is either 9 inches or 12 inches. The diameter of all 15 plates combined is 150 inches.
Which system of equations can be used to find the number of 9-inch plates, x, and the number of 12-inch plates, y, that are in the cabinet?
Answer:
Step-by-step explanation:
The important thing to remember here is that the number of plates is a different equation from the one that uses the diameter of the plates. The number of plates will make up one equation; the diameter of the plates will make up the other equation. As far as the number of plates go, we have 15 total. Let's call the 9" plates x and the 12" plates y according to the instruction given. If we have a mixture of 9 and 12 inch plates and we have a total of 15 plates, the first equation regarding the number of plates is
x + y = 15
Now on to the diameters. The 9" plates are x's and the 12" plates are y's and the inches refer to the diameter, of which the total is 150". Therefore, the second equation regarding the diameter of the plates is
9x + 12y = 150
Those 2 equations make up the system. It doesn't say you have to solve it, but if you did, you would find that there are 10 9" plates and 5 12" plates in the cabinet.
which of the following is equal to |-8+4|?
Answer:
-8+4=-4
sign of bigger number, and -×+=-
Which of the following best describes area?
A. Distance
B. Cover
C. Fill
D. Time
Answer:
I dont know
Step-by-step explanation:
oop
Answer:
I think it would not be fill since i think that would be referring to volume so it would most likley be B.cover
Answer- Cover
Step-by-step explanation:
none really
help me plzz pllz help now im on a time line
Answer:
Oki, mizuki here to help!
Hi there user, looks like you need help!
Anyways, option B is the correct answer!
Step-by-step explanation:
How to find average speed: distance/time
Since the graph shows 480 meters in 6 seconds, option B should be the correct answer!
Hope this helped!
Step-by-step explanation:
we know that
Speed = Distance/ Time
so the correct answer is B
what is 20% of 90???
Answer:
answer :
18
Step-by-step explanation:
use calculator it's easy to solve
Answer:
18
Step-by-step explanation:
20% of 90 = (20/100 )* 90
= 1/5 * 90
= 18
Which number is the closest approximation of 39?
Answer:
Because 39 is significantly closer to 36 than it is 49, the approximation of the square root of 39 to the nearest whole number would be 6
Step-by-step explanation:
Please help me with this.
Answer:
M1=35, M2=77, M3=49, M4=77, M5=62, M6=28
Step-by-step explanatio
Answer:
Angle 1) 35
Angle 2) 77
Angle 3) 49
Angle 4) 77
Angle 5) 62
Angle 6) 28
Step-by-step explanation:
Start with angle 3)
You have 2 angles for this one already, 90 and 41
All angles in a triangle have the sum of 180, therefore
Angle 3 = 180 - 90 - 41
Angle 3 = 49
Next is Angle 6)
You have Angle 3 and 103
Angle 6 = 180 - 49 - 103
Angle 6 = 28
Now Angle 2)
Angle 2 is on the same line as 103 and are supplementary, the sum is 180
Angle 2 = 180 - 103
Angle 2 = 77
Angle 4)
2 and 4 are vertical opposites with the same measurement, so 77
Angle 1)
Using Angles 1 and 2 and 68, they have a sum of 180
Angle 1 = 180 - 77 - 68
Angle 1 = 35
Angle 5)
Now with Angle 4 and 41 thats given, Angle 5 is
180 - 77 - 41 = 62
A running track has two semi-circular ends with radius 29m and two straights of length 91.3m as shown. Calculate the total area of the track rounded to 1 DP.
Answer:
13617.2 m^2
Step-by-step explanation:
5281.5
Work out the circumference of a circle with radius 6.5cm
Answer:
circumference=13π cm (see below if you need π approximated)
Step-by-step explanation:
Hi there!
The formula for the circumference of a circle is given as 2πr, where r is the radius and π is pi
we are given that the radius of the circle is 6.5 cm
substitute what we know into the equation:
circumference=2πr
circumference=2π*6.5
circumference=13π cm
some places will accept the answer as 13π, but others ask to have π substituted, usually as 3.14 or 22/7
if you need π substituted as 3.14, the answer will be 40.82 cm
if you need π substituted as 22/7, the answer will be about 40.86 cm
Hope this helps! :)
The function f (x) = 2* and g(x) = f(x) + k. if k = 2, what can be concluded about the graph of
g(x)?
the graph of g(x) is shifted vertically
Select a Value
the graph of g(x) is shifted horizontally
Select a Value
Answer:
g(x) shifted vertically by 2, no horizontal shift
Step-by-step explanation:
Any addition outside the function creates a vertical shift of the same value. Addition within the function moves the graph in the horizontal direction but opposite.
1/5 divided by 2 = ___
Answer:
0.1
Step-by-step explanation:
According to my calculator lol
Answer:
1/10
Step-by-step explanation:
1/5 / 2/1
1*1/5*2
=1/10
The answer please for my online class
Answer:
B. -500
Step-by-step explanation:
[tex] \dfrac{(2a^4)^2}{a^0a^5} = [/tex]
[tex] = \dfrac{2^2a^8}{a^5} [/tex]
[tex] = 4a^3 [/tex]
[tex] = 4(-5)^3 [/tex]
[tex] = 4(-125) [/tex]
[tex] = -500 [/tex]
Does (8,4) make the equation y = x true?
Answer:
false
Step-by-step explanation:
(8,8) or (4,4)
Two angles are supplementary. One angle is twenty less than four times the other angle. Find the measure of the larger angle.
180°
140°
130°
40°
NO LINKS
If two angles are supplementary, then they add up to 180.
Angle 1 = twenty less than four times the other angle
Angle 2 = the other angle
Angle 2 = 1x
Angle 1 = 4x - 20
Next, we can add up angles 1 and 2 and set the sum equal to 180.
x + 4x - 20 = 180
5x - 20 = 180
5x = 200
x = 40
Now that we know x, we can find the values of our angles.
Angle 1 = 4(40) - 20 = 160 - 20 = 140 degrees
Angle 2 = 40 degrees
Hope this helps!! :)
Find the area of the triangle
Answer:
Hello! answer: 84 sq mm
Step-by-step explanation:
To find triangle area we would do
base × height × 1/2 or
base × height ÷ 2 So...
14 × 12 = 168 168 ÷ 2 = 84 therefore the area is 84 sq mm HOPE THAT HELPS!
what are the points when you graph y = -7x -1
Answer: I believe you mean x and y intercepts? They are (0, -1) and (-1/7, 0)
Step-by-step explanation:
Plug in 0 for x and y (one at a time) for each intercept. eg The x intercept is at y=0 and the y intercept is at x=0.
23% of what number is 46?
Answer: 200
Step-by-step explanation:
first, you set up your proportion. (23% at the top right, 100 at the bottom right, 46 at the top left, and x and the bottom left.) next, you multiply x * 23% = 23x then 46*100 = 4600. 4600 divided by 23 = 200. therefore, x = 200. please let me know if you have further questions!
Good luck !
Question: Find the area of the orange shaded region in terms of pi.
Answer:
84π sq. units
Step-by-step explanation:
radius of little orange circles = 2
There is a total of 3 little orange circles (1 + 1 + 1/2 + 1/2).
Total area of 3 little orange circles = 3*π*2^2 = 12π
radius of 4 medium white circles = 3
Total of area of 4 medium white circles = 4*π*3^2 = 36π
radius of middle white circle = 6
Area of middle white circle = π*6^2 = 36π
Radius of the big circle = 12
Area of the big circle = π*12^2 = 144π
Area of orange = area of big circle - area of middle white circle - area of 4 medium white circles + area of 3 little orange circles = 144π - 36π - 36π + 12π = 84π
A rectangular-shaped school courtyardhas a length of 280 feet and a width of150 feet wide. What is the approximatelength of a diagonal of the courtyard tothe nearest tenth?
Answer:
317.6 feet
Step-by-step explanation:
the length of the diagonal can be determined using Pythagoras theorem
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
280² + 150²
= 78,400 + 22,500
= 100,900
take the square root of 100,900
= 317.648 feet
the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero
317.6 to the nearest tenth
The simple interest on 400 invested for 4 month was 12.what is the yearly rate of interest
Answer:
9%
Step-by-step explanation:
If you get 12 for 4 months, then you get 36 for the year/12 months
Annual interest is $12 x 3 Months =36
36/400=9%.
the sum of three consecutive natural number is 30 find the numbers
Answer:
9 + 10 + 11
Step-by-step explanation:
guess and check
Answer:
9,10,and 11
Step-by-step explanation:
Pls, help with this question
Answer:
[tex]m\text{ arc BC} =32\\m\angle 2=16\\m\angle3=74\\m\angle4=74\\m\angle5=16[/tex]
Step-by-step explanation:
Arc BC is the intercepted arc for the central angle COB, so its measure is the same as the central angle.
Angle 2 is an inscribed angle, so its measure is half the measure of the intercepted arc BC.
Angles 3 and 4 are congruent inside an isosceles triangle (OB = OC, both radii), and the sum of all angles in triangle COB is 180 degrees, so
180 - 32 = 148 (sum of angles 3 and 4)
Each of angles 3 and 4 measure half that remaining 148 degrees.
Angle 5 is one of two congruent angles in an isosceles triangle AOC (OA = OC) so its measure is that of angle 2.
An n-sided polygon has one interior angle of 90°. The other interior angles are all equal.
If the size of one of the equal angles is 150°, calculate the value of n.