Answer:
Once we got
[tex]x=-1[/tex]
[tex]y=3[/tex]
[tex]z=2[/tex]
[tex]\boxed{\text{The sum is 4}}[/tex]
Step-by-step explanation:
Given the linear system:
[tex]\begin{cases} 2x + 3y-z = 5 \\ x- 3y + 2z = -6 \\ 3x + y - 4z = -8 \end{cases}[/tex]
Let's solve it using matrices. I will use Cramer's rule
[tex]M=\left[\begin{array}{ccc}2&3&-1\\1&-3&2\\3&1&-4\end{array}\right][/tex]
Considering determinant as D.
[tex]D=\begin{vmatrix}2&3&-1\\1&-3&2\\3&1&-4\\\end{vmatrix}=40[/tex]
[tex]M_x = \left[\begin{array}{ccc}5&3&-1\\-6&-3&2\\-8&1&-4\end{array}\right] \implies D_x = \begin{vmatrix}5&3&-1\\-6&-3&2\\-8&1&-4\\\end{vmatrix}=-40[/tex]
[tex]M_y = \left[\begin{array}{ccc}2&5&-1\\1&-6&2\\3&-8&-4\end{array}\right] \implies D_y = \begin{vmatrix}2&5&-1\\1&-6&2\\3&-8&-4\\\end{vmatrix}=120[/tex]
[tex]M_z = \left[\begin{array}{ccc}2&3&5\\1&-3&-6\\3&1&-8\end{array}\right] \implies D_z= \begin{vmatrix}2&3&5\\1&-3&-6\\3&1&-8\\\end{vmatrix}=80[/tex]
So, we have
[tex]$x=\frac{D_x}{D} =\frac{-40}{40}=-1 $[/tex]
[tex]$y=\frac{D_y}{D} =\frac{120}{40}=3$[/tex]
[tex]$z=\frac{D_z}{D} =\frac{80}{40}=2 $[/tex]
A lender will make an 80% loan-to-value loan on a property that is appraised for $72,250 and sells for $73,500. If the buyer has saved $14,450 for a down payment, how much more (if any) will he need in order to make the down payment required under the terms of this loan?
Answer:
$1,250
Step-by-step explanation:
We are given;
Loan to value ratio;LTV = 80% = 0.8
Appraised value of property = $72,250
Selling value of property = $73,500
Now, the formula for Loan to value ratio is;
LTV = Loan amount/Appraised value of property
0.8 = loan amount/72250
Cross multiply to get;
Loan amount = 0.8 × 72250 = $57,800
Now,we are told that he has saved $14,450.
Thus, total money raised including loan = $57,800 + $14,450 = $72,250
Since the selling value = $73,500, then,
Amount left for him to save in order to make down payment = $73,500 - $72,250 = $1,250
Inequalities with > or < symbols are graphed with a dashed line. Inequalities with an ≥or ≤ symbol line are graphed with a solid line. When graphing the inequalities in the example above. Which inequality would you graph using a dashed line? Select all that apply A B C D
Answer:
b and c
Step-by-step explanation:
both are just greater than or less than
In psychological theory, there are 6 types of basic instincts in a human being, and personality is determined by the
presence or absence (2 choices) of these 6 basic instincts.
How many different types of personalities can be identified?
15
O 64
O 36
O 30
Answer:
64
Step-by-step explanation:
Which best describe all possible classifications for the following set of numbers?
{0, 4, 25, 32}
I. Counting Numbers
II. Integers
III. Rational Numbers
IV. Whole Numbers
IV only
IV only
I and IV only
I and IV only
II, III, and IV only
II, III, and IV only
I, II, III, and IV
Answer:
| and |V only
Step-by-step explanation:
4, 25, and 32 are Counting numbers, while 0 is a whole number B)
M is the midpoint of line segment AB
Answer:
The coordinates of A would be (-1, 2)
Step-by-step explanation:
In order to find this, use the mid-point formula.
(xA + xB)/2 = xM
In this, the xA is the x value of point A, xB is the x value of point B, and xM is the x value of M. Now we plug in the known information and solve for xA.
(xA + 5)/2 = 2
xA + 5 = 4
xA = -1
Now we can do the same using the midpoint formula and the y values.
(yA + yB)/2 = yM
(yA + 10)/2 = 6
yA + 10 = 12
yA = 2
This gives us the midpoint of (-1, 2)
PORFAVOR ALLUDENME :( El estanque de combustible de un automóvil contiene x litros de gasolina, se consumen 25 litros en un primer viaje y 4/19 del resto en un segundo viaje, conservando finalmente 3 litros de gasolina. ¿Qué ecuación modela la situación planteada? a. 25 menos x menos estilo en línea fracción 4 entre 19 fin estilo paréntesis izquierdo 25 menos x paréntesis derecho igual 3 b. x menos 25 menos estilo en línea fracción 4 entre 19 fin estilo por 25 igual 3 c. x menos 25 menos estilo en línea fracción 4 entre 19 fin estilo paréntesis izquierdo x menos 25 paréntesis derecho igual 3 d. x menos 25 menos estilo en línea fracción 4 entre 19 fin estilo paréntesis izquierdo x más 25 paréntesis derecho igual 3
Responder:
c. x menos 25 menos estilo en línea fracción 4 entre 19 fin estilo paréntesis izquierdo x menos 25 paréntesis derecho igual 3
Explicación paso a paso:
Dado lo siguiente:
Cantidad original de gasolina en el tanque de combustible = x
Gasolina consumida en el primer viaje = 25 litros
Gasolina restante después del primer viaje = (x - 25) litros
Gasolina consumida en el segundo viaje = 4/19 de lo que queda, es decir;
(4/19) * (x - 25)
Gasolina restante después del segundo viaje = 3 litros
Cantidad inicial - cantidad consumida en el primer viaje - 4/19 de la cantidad restante después del primer viaje = 3
La gasolina que queda después del segundo viaje se puede modelar mediante la ecuación:
x - 25 - 4/19 (x - 25) = 3
Which number is a solution of the inequality 8 - 1/4 b > 27?
Answer:
b< -76
Step-by-step explanation:
8 - 1/4 b > 27 ⇒ add -8 to both sides-1/4b > 27 - 8 -1/4 b > 19 ⇒ multiply both sides by -4b < - 4*19 ⇒ change inequality sing to opposite due to multiplication to negative numberb < - 76 ⇒ answerAnswer is any number smaller than -76
Answer:
Answer:
b< -76
Step-by-step explanation:
8 - 1/4 b > 27 ⇒ add -8 to both sides
-1/4b > 27 - 8
-1/4 b > 19 ⇒ multiply both sides by -4
b < - 4*19 ⇒ change inequality sing to opposite due to multiplication to negative number
b < - 76 ⇒ answer
Answer is any number smaller than -76
Step-by-step explanation:
The Jammers basketball team had a
win to loss ratio of 5:1 during their
Season. They won 25 games. How many
games did they lose?
Answer:
5 Games
Step-by-step explanation:
Step 1: State what is known
We know for every 5 games the win they lose 1 game
They won 5 games
Step 2: Define your variables
Let x represent how many games the Basketball team lost
Step 3: Create equation
[tex]\frac{5}{1}=\frac{25}{x}[/tex]
Step 4: Solve for 'x'
Cross multiply to solve for 'x'
[tex]5x=25[/tex]
[tex]x=\frac{25}{5}[/tex]
x = 5
Therefore the will have lost 5 games
The pilot of a Boeing 747 is instructed to climb from 8000 ft to a cruising altitude of 29,000 ft. If the plane ascends at a rate of
3500 ft/min, how long will it take to reach the cruising altitude?
=======================================================
Explanation:
The plane needs to go up 29,000-8,000 = 21,000 feet
It does so at a rate of 3500 ft per min
So it needs 21000/3500 = 6 minutes to get to the proper height.
---------
You can think of it like the equation
3500x = 21000
where x is the number of minutes needed. Dividing both sides by 3500 solves to x = 6.
-----------
Or you could think of it like this
1 minute = 3500 feet
1/3500 minute = 1 foot (divide both sides by 3500)
1 foot = 1/3500 minute
21000 feet = 21000/3500 minute (multiply both sides by 21000)
21000 feet = 6 minutes
This shows that to go up 21000 feet, the plane needs 6 minutes to do so.
Name the line segments
Answer:
EF, FG, GH, EG, FH, EH
Step-by-step explanation:
These are all the ones under def. line segment.
See the attachment. It will be helpful.
In the game of roulette, a wheel consists of 32 slots numbered 00, 0, 1, 2, . . . , 30. To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. Complete parts (a) through (c).
(a) Determine the sample space. Choose the correct answer below.
A. The sample space is {00, 0, 1, 2, . . . , 30}.
B. The sample space is {00}.
C. The sample space is {00, 0}.
D. The sample space is {1, 2, . . . , 30}.
(b) Determine the probability that the metal ball falls into the slot marked 3 and Interpret this probability by choosing the correct answer below.
A. If the wheel is spun 100 times, it is expected about 31 of those times to result in the ball landing in slot 3.
B. If the wheel is spun 1,000 times, it is expected about 31 of those times to result in the ball landing not in slot 3.
C. If the wheel is spun 1,000 times, it is expected about 31 of those times to result in the ball landing in slot 3.
(c) Determine the probability that the metal ball lands in an odd slot and Interpret this probability by choosing the correct answer below.
A. If the wheel is spun 100 times, it is expected about 47 of those times to result in the ball landing in an odd number.
B. If the wheel is spun 1,000 times, it is expected about 31 of those times to result in the ball landing in an odd number.
C. If the wheel is spun 1,000 times, it
Answer:
(a) The sample space is {00, 0, 1, 2, . . . , 30}.
(b) If the wheel is spun 1,000 times, it is expected about 31 of those times to result in the ball landing in slot 3.
(c) If the wheel is spun 100 times, it is expected about 47 of those times to result in the ball landing in an odd number.
Step-by-step explanation:
We are given that in the game of roulette, a wheel consists of 32 slots numbered 00, 0, 1, 2, . . . , 30.
To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots.
(a) The sample space is {00, 0, 1, 2, . . . , 30} which means the metal ball can land on any of these numbers.
(b) As we know that there is an equal probability of the metal ball landing on any of the slots marked in the sample space.
Total number of slots = 32
Number of slots marked with 3 = 1
So, the probability that the metal ball falls into the slot marked 3 is given by = [tex]\frac{1}{32}[/tex] = 0.031 or 3.1%
This means that if the wheel is spun 100 times, it is expected about 3.1 of those times to result in the ball landing in slot 3.
So, if the wheel is spun 1,000 times, it is expected about 31 of those times to result in the ball landing in slot 3 because (0.031 [tex]\times[/tex] 1000) = 31.
(c) As we know that the odd slot in the given sample space is {1, 3, 5,......, 29}.
Total number of slots = 32
Number of odd slots = 15
So, the probability that the metal ball lands in an odd slot is given by = [tex]\frac{15}{32}[/tex] = 0.47 or 47%.
This means that if the wheel is spun 100 times, it is expected about 47 of those times to result in the ball landing in an odd number.
Square root of -72 in the form of a+bi
Answer:
[tex]0+6\sqrt{2}i[/tex]
or just [tex]6\sqrt{2}i[/tex]
Step-by-step explanation:
[tex]\sqrt{-72}[/tex] does not have a real part, it is a pure imaginary number.
Let's simplify.
First step:
[tex]\sqrt{-1}=i[/tex] is the imaginary unit.
So we have that we can write [tex]\sqrt{-72}=i \sqrt{72}[/tex].
Second step:
Let's simplify the factor [tex]\sqrt{72}[/tex] by looking for perfect squares of [tex]72[/tex].
[tex]72=2(36)=2(6^2)[/tex]
So [tex]36[/tex] is a perfect square because it can be written as [tex]6^2[/tex].
[tex]\sqrt{-72}[/tex]
[tex]i \sqrt{72}[/tex]
[tex]i \sqrt{2 \cdot 6^2}[/tex]
[tex]i \sqrt{2} \sqrt{6^2}[/tex]
[tex]i \sqrt{2} 6[/tex]
[tex]6 \sqrt{2}i[/tex]
We could write this as [tex]0+6\sqrt{2}i[/tex].
What is the value of x? A. 36 B. 12 C. 32 D. 28
Answer:
the answer is D I hope this helps
Casey and David both ride all-terrain vehicles on trails every weekend for fun each month KC rides for a total of 2x hours at an average speed of x miles per hour David rides for more hours a month in KC but at an average speed that is 3 miles per hour less than Casey's average speed write the standard form of the function which describes the total distance of miles that David rides each month
Answer:
(x - 3)mph * > 2x
Step-by-step explanation:
KC's total rides in hours = 2x
KC's average speed = x
David's average speed :
3 mph less than KC's average speed = (x - 3)mph
David's total ride in hours in a month is more than KC's, that is ( >2x)
From the equation:
Speed = distance / time
Distance = speed * time
Total distance of miles David rides each month:
(x - 3)mph * > 2x
A man drove 8 miles directly east from his home, made a left turn at an intersection, and then traveled 8 miles due north to his place of work. If a road was made directly from his home to his place of work, what would its distance be? ______ miles
Answer:
11.3 miles
Step-by-step explanation:
We can use the pythagorean theorem to find the distance from his home to work, since the 3 roads form a right triangle where the new road is the hypotenuse.
a² + b² = c²
8² + 8² = c²
128 = c²
= approx. 11.3 miles
The distance between his home and his work of place is 11.31 miles.
Given,
A man drove 8 miles directly east from his home, made a left turn at an intersection, and then traveled 8 miles due north to his place of work.
A road was made directly from his home to his place of work.
We need to find what would its distance be in miles,
How to construct direction?We have,
North
West <----- ⇅ -------> East
South
What is the Pythagorean theorem?In a right triangle,
The square of the hypotenuse is equal to the sum of the square of the other two sides.
Find the direction of the given statement.
A man drove 8 miles directly east from his home:
8 miles
Home ------------------->East
Made a left turn at an intersection, and then traveled 8 miles due north to his place of work:
North Work
⇅ Left
⇅ 8 miles
Home ------------------->East
⇅
Right
If a road was made directly from his home to his place of work:
Work
Home North
West <------------------⇅ --------------->East
South
A (Work)
/ ║
/ ║
/ ║ 8 miles
/ ║
(Home) B /___________║C
8 miles
Find the distance between home and place of work.
AB = distance between home from work
Applying the Pythagorean theorem.
AB² = BC² + AC²
AB² = 8² + 8²
AB² = 64 + 64
AB² = 128
AB = ±√128
The distance can never be negative here so,
√128 = 11.31
AB = 11.31 miles.
Thus the distance between his home and his work of place is 11.31 miles.
Learn more about justifying the distance Formula using the Pythagorean Theorem here:
https://brainly.com/question/11099
#SPJ2
The diameter of the inscribed circle in a regular hexagon is 4√3 inches long. What is the perimeter of this regular hexagon?
Answer:
12√3 inches or 20.785 inches.
Step-by-step explanation:
A regular hexagon can be defined as a polygon with 6 sides.
The formula for the perimeter of a regular hexagon =
6 × the length of the sides of the hexagon.
From the above question, we are told that there is an inscribed circle I'm the hexagon with a diameter of 4√3 inches long
Step 1
Find the radius of the circle
Radius of the circle = 4√3/2 = 2√3 inches
Step 2
The radius of the inscribed circle = Length of one of the sides of a regular hexagon.
Hence, the perimeter of the regular hexagon = 6 × 2√3
= 12√3 inches
= 20.784609691 inches.
Approximately 20.785 inches
write the desimales 3.17 in word form
Answer:
Three point one seven is your answer.
Step-by-step explanation:
Hope it will help you:)
Factor completely:
3x² (x²+6) - 4(x2+6)
Answer:
(x² + 6)(3x² - 4)
Step-by-step explanation:
factor out (x² + 6)
(x² + 6)(3x² - 4)
Dean has a piece of wood that is 3/4 of a foot long, He
needs to cut pieces of the wood into 1/16 of a foot long, How
many pieces can Dean cut? How do you know?
Answer:
1. 12 pieces of wood
2. How to determine the number of pieces of wood Dean cut is by dividing the total length of wood by length of each piece of wood
Step-by-step explanation:
Total length of wood=3/4 of a foot
He needs to cut pieces of the wood into 1/16 of a foot long
How many pieces can Dean cut
Let x= number of pieces of wood Dean needs to cut
x=Total length of wood / length of each piece
=3/4 ÷ 1/16
=3/4 × 16/1
=48/4
=12 pieces
Number of pieces of the wood Dean can cut =12 pieces
How to determine the number of pieces of wood Dean cut is by dividing the total length of wood by length of each piece of wood
That is,
3/4 ÷ 1/6
Then follow the procedures in question 1
What is the value of the y-coordinate of point A
Answer: [tex]-\dfrac{1}{2}[/tex]
Step-by-step explanation:
The coordinate at -30° (-30° = 330°) = [tex]\bigg(\dfrac{\sqrt3}{2},-\dfrac{1}{2}\bigg)\\[/tex]
the x-value is [tex]\dfrac{\sqrt3}{2}[/tex]
the y-value is [tex]-\dfrac{1}{2}\\[/tex]
Answer:
-0.5
Step-by-step explanation:
What is an equation of the line that passes through the point (-2, -3) and is
parallel to the line 5x + 2y = 14?
Answer: 2y + 5x + 16 = 0
Step-by-step explanation:
To solve this you need to understand the principle/ conditions for parallelism and perpendicularity.
for two lines to be parallel to each other, their gradients or slopes (m) must be equal, that is m₁ = m₂
Now from the given equation,
5x + 2y = 14 , we need to rearrange it to conform to the equation of a straight line so that the gradient could be established. ie
y = mx + c where m is the gradient
2y = -5x + 14
y = -5x/2 + 14/2
y = ⁻⁵ˣ/₂ + 7 , therefore , m₁ = ⁻⁵/₂ and m₂ = ⁻⁵/₂ ( parallelism Rule )
The next step is to find the value of C using the coordinate ( -2, -3 )
-3 = ⁻⁵/₂ ˣ ⁻² + C,
-3 = ¹⁰/₂ + C
-3 = 5 + C
C = -8.
Now to find the equation of the line that passed through the coordinate
y = mx + c
y = ⁻⁵ˣ/₂ - 8
2y = -5x - 16
2y + 5x + 16 = 0.
Someone plz help.The temperature started at 35°F. If the temperature went down 4°F and then up 2°F, whats is the temperature difference relative to the high temperature? A) -2°F B) -1°F C) 1°F D) 2°F
Answer:
The temperature difference relative to the high temperature is -2°F.
Step-by-step explanation:
We are given that the temperature started at 35°F. The temperature went down 4°F and then up 2°F.
Firstly, the original temperature = 35°F
Now, it is stated that the temperature went down 4°F, this means that the temperature decreases by this amount.
So, the new temperature = 35°F - 4°F = 31°F
Now, the temperature went up by 2°F, this means that the temperature increases by this amount.
So, the final temperature = 31°F + 2°F = 33°F
Now, the final temperature difference relative to the high temperature is given by = 33°F - 35°F = -2°F.
{Here, the maximum temperature is 35°F}
Find the surface area of the composite figure. need help asap. Thank You
Answer: A=276.52 cm²
Step-by-step explanation:
To find the surface area of the figure, we can find the surface area of the rectangular prism and hemisphere. Then we would add them together.
Rectangular Prism
A=2(lw+hl+hw)
Since we are given the length, width, and height, we can directly plug them into the equation and solve.
[tex]A=2((10*5)+(4*10)+(4*5))[/tex]
[tex]A=2(50+40+20)[/tex]
[tex]A=2(110)[/tex]
[tex]A=220 cm^2[/tex]
The surface area for the rectangular prism is 220 cm².
----------------------------------------------------------------------------------------------------------------
Hemisphere
A=2πr²
This formula above is derived from the formula for surface area of a sphere.
The surface area of a sphere is A=4πr². Since the picture displays half of a sphere, we divide that by 2. This gives us A=2πr².
Since we have the radius, all we have to do is plug it in.
[tex]A=2\pi (3)^2[/tex]
[tex]A=2\pi (9)[/tex]
[tex]A=18\pi[/tex]
[tex]A=56.52 cm^2[/tex] *Note I used 3.14 instead of π.
----------------------------------------------------------------------------------------------------------------
Now that we have the surface area of the hemisphere and rectangular prism, we add them together to find the surface area of the entire prism.
A=220+56.52=276.52 cm²
John Maynard Keynes and Karl Marx would agree most about the answer to
which question?
O A. Should governments take total control over economies?
B. Are precious metals a good measure of economic strength?
O C. Do free market economies create problems for workers?
D. Is it right for strong countries to control weaker colonies?
Answer:
Option C: Do free market economies create problems for workers?
Step-by-step explanation:
There was a law called Say's law which states that capitalist production generates its own markets, and therefore, there can't possibly be any gluts or overproduction of goods in relation to market demand.
Now, keynes and marx rejected this say's law because they both believed that gluts or overproduction may likely occur.
They believed that this law would make capitalists own nothing but the right to sell their labor in exchange for wages.
That due to the capitalists competition with themselves for profits, it would squeeze as much work as possible out of the working class people at the lowest possible price and that this competition would cause some capitalist firms to fail, and thereby increasing unemployment among the working class.
Thus, it's clear this was an answer to the question on whether free market economies create problems for workers.
Answer:
A.Should government take total control over economies
Step-by-step explanation:
If one chip is randomly selected from each bag, what is the probability that a chip with a B on it and a chip with a 2 on it will be selected?
Answer:
it has a 1% chance.
Step-by-step explanation:
Because of the whole there is one chip in it that has a 2 on it so it has a 1% chance out of 100%
Solve for x...
Z = 8(x-h)
X = ????
Please state what X is...
This is equivalent to x = z/8 + h or x = (1/8)z + h
=================================================
Work Shown:
z = 8(x-h)
z = 8x-8h ... distribute
8x-8h = z
8x = z+8h .... adding 8h to both sides
x = (z+8h)/8 .... dividing both sides by 8
x = z/8 + 8h/8
x = z/8 + h
x = (1/8)z + h
Factoring Trinomials in Standard form x^2+2x=-1
Answer:
(x + 1)(x + 1) = 0 OR (x + 1)^2 = 0
Step-by-step explanation:
First, we need to get the trinomial x^2 + 2x = -1 all on one side of the equation.
x^2 + 2x = -1
x^2 + 2x + 1 = -1 + 1
x^2 + 2x + 1 = 0
Now that the trinomial is on the left-hand side, let's factor the equation.
x^2 + 2x + 1 = 0
(x + 1)(x + 1) = 0
We can simplify this factored trinomial further to be:
(x + 1)(x + 1) = 0
(x + 1)^2 = 0
Cheers.
NEED HELP ASAP!! Angles of Elevation and Despression! Need to find x! Round to the nearest tenth!!
Greetings from Brasil...
Using sine, we will be able to find the value of X
SEN 17 = X/47
X = 47 · SEN 17
X = 47 · 0,29237
X = 13,741
X ≈ 13.7Solve for x, please help
Answer:
the answer 18 because:
40=2X+4
choose all the equations for which x=2 is a solution
a. x+3=5
b. x+2=8
c. x+1=1
d. x-2=4
e. x-7=-5
Answer:
Option A and Option E
Step-by-step explanation:
Option A.
x + 3 = 5
(x + 3) - 3 = 5 - 3
x = 2
Option B.
x + 2 = 8
(x + 2) - 2 = 8 - 2
x = 6
Option C.
x + 1 = 1
(x + 1) - 1 = 1 - 1
x = 0
Option D.
x - 2 = 4
(x - 2) + 2 = 4 - 2
x = 2
Option E.
x - 7 = -5
(x - 7) + 7 = -5 + 7
x = 2
Therefore, Option (A) and Option (E) are the correct options.