Answer:
The order of operations IS crucial because it will assist us in performing equations.
Step-by-step explanation:
Solve the system.
3x + 2y + 4z = 11
2x – y + 3z = 4
5x – 3y + 5z = -1
Enter your answer as an ordered triple.
Someone help please!!
Answer: (x, y, z) = (-3, 2, 4)
In other words, x = -3, y = 2 and z = 4.
You'll enter the number only into each box.
===============================================================
Explanation:
There are a few routes we can take to solve this. I'll use substitution.
First let's isolate y in the second equation.
2x - y + 3z = 4
2x + 3z = 4+y
4+y = 2x+3z
y = 2x+3z-4
This is then plugged into the first equation
3x+2y+4z = 11
3x+2( y )+4z = 11
3x+2( 2x+3z-4)+4z = 11 .... replace y with 2x+3z-4; since y = 2x+3z-4
3x+4x+6z-8+4z =11
7x+10z-8 = 11
7x+10z = 11+8
7x+10z = 19 .... we'll call this equation (4) and come back to this later
--------------------------------------
Move onto the third equation (of the original equations given)
Plug in y = 2x+3z-4
5x - 3y + 5z = -1
5x - 3( y ) + 5z = -1
5x - 3( 2x+3z-4 ) + 5z = -1
5x - 6x - 9z + 12 + 5z = -1
-x - 4z + 12 = -1
-x - 4z = -1-12
-x - 4z = -13 ..... let's call this equation (5)
--------------------------------------
To recap, we found equation (4) and equation (5) to be
7x+10z = 19-x - 4z = -13We can then solve for x in equation (5) like so
-x - 4z = -13
-x = -13 + 4z
-x = 4z - 13
x = -(4z - 13)
x = -4z + 13
This is then plugged into equation (4)
7x+10z = 19
7(-4z+13)+10z = 19 .... note how we now have one variable
-28z+91+10z = 19
-18z+91 = 19
-18z = 19-91
-18z = -72
z = -72/(-18)
z = 4
We can use this value of z to find x
x = -4z+13
x = -4(4)+13
x = -16+13
x = -3
Use the values of x and z to find y. We'll revisit the first equation in which we isolated y
y = 2x+3z-4
y = 2(-3)+3(4)-4
y = -6+12-4
y = 6-4
y = 2
So overall, the solution to this system is (x, y, z) = (-3, 2, 4)
-------------------------------
Checking the answer:
We'll replace x,y,z with the values we found.
In the first equation, 3x+2y+4z = 11 becomes 3(-3)+2(2)+4(4) = 11 and that simplifies to 11 = 11. In other words, the expression 3(-3)+2(2)+4(4) turns into 11. This confirms the first equation.Repeat the same idea for the second equation. We have 2x-y+3z=4 turn into 2(-3)-2+3(4) = 4 and that simplifies to 4 = 4. The answer is verified here. The third equation 5x-3y+5z = -1 becomes 5(-3)-3(2)+5(4) = -1 which simplifies to -1 = -1. We get a true equation here as well.Since all three equations are true when (x, y, z) = (-3, 2, 4), this verifies the answer completely. This is the only solution to the system. The system is independent and consistent.
Find the length of side x in simplest radical from with a rational denominator.
Answer:
4
Step-by-step explanation:
The value of the hypotenuse x will be equal to √6.
What are trigonometric identities?Equations involving trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities. The Pythagorean Theorem serves as the basis for some of the most popular trigonometric identities, including.
The study of correlations between triangles' side lengths and angles is known as trigonometry.
Given that the angles are 45 and the base is √3 the hypotenuse will be calculated as,
cosθ = Base / Hypotenuse
cos45 = √3 / x
x = √3 / ( 1 / √2)
x = √6
Therefore, the value of the hypotenuse x will be equal to √6.
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please help!! i really need it.
ill give brainilest!!
Answer:
14
Step-by-step explanation:
i think it's 14. i hope i helped :)
The cost to rent a raft is $7 per person. A raft can hold up to 6 people. There is a $3 launch fee per raft. What is the total cost for a group of 6?
Before you tell me the answer tell me how do I explain how I got my answer :{
Answer:
$42 [$7/person*6 people]+$6[$3 launch fee/raft*2 rafts]
Step-by-step explanation:
$48 total
PLEASE MARK BRAINLIEST
NEED IT FOR A NEW RANK
ty in advance:D
HELP ASAP. pls ❤️ if u do this i’ll luv u 4ever
Answer:
A' ( 2,3)
B' ( 5,5)
C ( 7,3)
D'(5,2)
cube root(8+ 3 root 21)+ cube root (8-3 root 21)
plese give good answer with explanation or I will report
Answer:
[tex]\sqrt[3]{8+3\sqrt{21} } + \sqrt[3]{8-3\sqrt{21} }[/tex] = 1Step-by-step explanation:
Given[tex]\sqrt[3]{8+3\sqrt{21} } + \sqrt[3]{8-3\sqrt{21} }[/tex]To find The value of the expressionSolutionLet's rewrite the given as:
[tex]\sqrt[3]{3\sqrt{21} + 8} - \sqrt[3]{3\sqrt{21} - 8}[/tex]Let the value is m and the expressions under 3rd roots are a and b, then we have
a = 3√21 + 8, b = 3√21 - 8m = ∛a - ∛bCube the both sides:
m³ = (∛a - ∛b)³m³ = a - b - 3[tex]\sqrt[3]{a^2b}[/tex] + 3[tex]\sqrt[3]{ab^2}[/tex]Simplify in bits:
a - b = 3√21 + 8 - 3√21 + 8 = 16ab = (3√21 + 8)(3√21 - 8) = 9*21 - 64 = 125∛ab = ∛125 = 5So the expression becomes:
m³ = 16 - 3[tex]\sqrt[3]{125a} + \sqrt[3]{125b}[/tex]m³ = 16 - 15∛a + 15∛bm³ = 16 - 15(∛a - ∛b)m³ = 16 - 15mSolve for m:
m³ + 15m - 16 = 0m³ - 1 + 15m - 15 = 0(m - 1)(m² + m + 1) + 15(m - 1) = 0(m - 1)(m² + m + 16) = 0m - 1 = 0, m² + m + 16 = 0m = 1 is the only real root, the quadratic equation has no real rootsThe answer is 1
help would be great during these troubling times
Answer:
117 - 120 < -3
-3 < -3
False no
because it is not above -3
Step-by-step explanation:
Answer: No
Step-by-step explanation:
x = 9
y = 6
13x - 20y < -3?
Substitute the values of x and y
13(9) - 20(6) < - 3?
117 - 120 < -3?
-3 </ -3
-3 = -3
(9, 6) is not a solution
How do I do this please help me
Answer:
Answer of first one is. = angle 3
answer of second one is = angle 4
answer of third one is = angle 2
angle of fourth one is = 5
and last.one is angle 1
Which relation is a function?
A. (1, 0), (3.0), (1.1), (3, 1) (1.3)
B. (1, 1), (2, 2), (3, 3), (4, 4). (5, 8). C. ( 2, 7), (6,5), (4.4), (3, 3), (2, 1)
D. (9. -3), (19, 3) (4, -2), (4, 2), (0, 0)
Answer:
A
Step-by-step explanation:
A function is a relationship between inputs where each input is related to exactly one output.
A function can be one-to-one and many-to-one but can not be one-to-many.
The relation that is a function is
(1, 1), (2, 2), (3, 3), (4, 4). (5, 8). C. ( 2, 7),
Option B is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
A function can be one-to-one and many-to-one but can not be one-to-many.
A. (1, 0), (3.0), (1.1), (3, 1) (1.3)
This is not a function because we have one-to-many.
(1, 0) and (1, 1) are one-to-many.
B. (1, 1), (2, 2), (3, 3), (4, 4). (5, 8).
This is a function because it satisfies the function.
The given relation are one-to-one.
C. ( 2, 7), (6,5), (4.4), (3, 3), (2, 1)
This is not a function because we have one-to-many.
(2, 7) and (2, 1) are one-to-many relations.
D. (9. -3), (19, 3) (4, -2), (4, 2), (0, 0)
This is not a function because we have one-to-many relations.
(4, -2) and (4, 2) are one-to-many relations.
Thus,
The relation that is a function is
(1, 1), (2, 2), (3, 3), (4, 4). (5, 8). C. ( 2, 7),
Option B is the correct answer.
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Jaxson drives 15 miles in 10 minutes. If he drove one hour in total at the same rate, how far did he go?
Answer:
90 miles
Step-by-step explanation:
15 miles/10 minutes = x miles/60 minutes
10*6=60 so 15*6=90
My lil sister said she needs help with ALL of the questions..........if you help i will give you brainliest
Answer:
MONDAY: 2 hours
Tuesday: $34.65
Thursday: -54
Friday: 5 complete bags
Sorry that I did not do the question below wednesday but I still hope this helps.
Pls mark me brainliest.
Can you guys help me? please
Answer:
3 square root 2.
Step-by-step explanation:
I think the answer is b (3 square root 2). the Pythagorean therom states that B^2+ B^2= C^2. we know that c squared is 36. 3 square root 2 is approximately 4.24. ( this squared is 17.98). 17.98 + 17.98 = 35.96. If i round this up, it is 36.
Find the slope of the line y=-6x-4. Type your answer as an integer.
Answer:
The slope is -6
Step-by-step explanation:
In the slope intercept form, it is y=mx+b, where m is the slope and b is the y-intercept
Therefore, -6 is slope and -4 is y-intercept
HELP PLS I GIVE BRAINLIEST
Answer:
1. $200
2. $65
3. $70
Step-by-step explanation:
1. 4x50=200
2. 200-135= 65
3. 135-65= 70
Find the Surface Area of the following figure:
16 ft
10 ft
7 ft
Answer:
1120
Step-by-step explanation:
please help
travelling 14m to the right first and travelling 19m to the left . calculate the final position
Answer:
5 meters to the left
Step-by-step explanation:
Given that :
First travel : 14 meters to the right
Second travel : 19 m to the left
Final position :
First travel - Second travel.
(14 m - 19m)
Final position = - 5 m
-5m = 5 meters to the left.
Find the length of AB.
140°/6 in
19%
AB = [ ? ]in
B
Round your answer to the nearest hundredth.
Answer: 14.66 in
Step-by-step explanation:
A hollow cylinder has solid hemisphere in one end and on the other end it is closed with a flat circular plate. The height of water is 10cm when flat circular surface is downward. Find the level of the water, when it inverted upside down, common diameter is 7cm and height of the cylinder is 20 CM.
Answer:
this will be the correct answer
What is the answer to 2 1/3 ÷ (-3 2/3) ?
Answer:
2 1/3 / (-3 2/3) = -0.636363636 AKA 0.636
Step-by-step explanation:
Step-by-step explanation:
[tex]2 \frac{1}{3} \div ( - 3 \frac{2}{3} )[/tex]
[tex] \frac{7}{3} \div ( - \frac{11}{3} )[/tex]
[tex] \frac{7}{3} \times ( - \frac{3}{11} )[/tex]
=
[tex] - \frac{7}{11} [/tex]
. A and B are vertical angles. If mA = (5x – 28) and
mB = (3x + 4)º, find the measure of each angle.
Answer:
measure of both angles is 52°
x = 16
Step-by-step explanation:
5x - 28 = 3x + 4
2x - 28 = 4
2x = 32
x = 16
Plug in 16 for 'x': 3(16) + 4 = 48 + 4 = 52°
Answer:
Both are 56°
Step-by-step explanation:
5x-28=3x+4
x=16
5(16)-28= 56°
p is an odd number
explain why p^2 + 1 is always an odd number
The point (2, 20) lies on the graph of y = kx'. Write the value of k.
Step-by-step explanation:
Y = 20 , X = 2
put in the equation
Y = KX ( given )
20 = K × 2
20/2 = K
10 = K
What is the slope of a line parallel to the line with equation 2x+4y=8
Answer:
m = [tex]\frac{-1}{2}[/tex]
Step-by-step explanation:
To find the slope of most lines, we should rearrange the equation into the slope-intercept form or y = mx + b.
So,
2x + 4y = 8
4y = -2x + 8
[tex]y=\frac{-2x +8}{4}[/tex]
[tex]y=\frac{-2}{4}x+\frac{8}{4}[/tex]
[tex]y=\frac{-1}{2}x+2[/tex]
The slope is the coefficient of the x term, so
m = [tex]\frac{-1}{2}[/tex]
Answer:
[tex]-\frac{1}{2}[/tex]
Step-by-step explanation:
2x+4y=8
4y = -2x +8
y = [tex]-\frac{2}{4}[/tex]x + [tex]\frac{8}{4}[/tex]
y = [tex]-\frac{1}{2}[/tex]x + 2
y=mx+b so the slope is m=[tex]-\frac{1}{2}[/tex].
parallel lines have the same slope.
What is the slope of the line that passes through the points (10,8) and (-15,18) wrote the answer in simplest form
Answer:
-2/5
Step-by-step explanation:
A number w increased by 6 is at least 24. Using an inequality
Answer:
x<24
Step-by-step explanation:
[tex]w + 6 \geqslant 24[/tex]
Find the missing angle measurement of a triangle with these angles:
45°, 35.8°, x°
a = 45 b = 35.8 c = 57.503
Tera can jog 5.5 miles in 1
hour. At the same rate, how face can she jog in 2 hours
Answer:
11 miles
Step-by-step explanation:
if she can jog 5.5 miles in 1 hour, than in 2, she can jog 11 miles, because 5.5(miles) x 2 (hours) = 11
hope this helps :)
a brainliest would be appreciated
Simplify: (9a* - 5a'-1)+7a*
Answer:
The answer is -2a because first you multiple the number and eliminate redundant perenthese then last combine like terms and that how you get -2a
Will give brainliest if your right
A scientist conducts an experiment to observe the half-life period of the radioactive element barium. He starts the experiment with 200 grams of barium and records the mass at the end of every thirteen day. After how many days is the mass of barium closest to 1.5 grams?
Answer:
It would be 91 days
Step-by-step explanation:
Hope this helps :)
A snail travels at an average speed of 0.1 feet per hour for 15 minutes. How many feet will the snail travel?
Answer:
1.5 Feet
Step-by-step explanation:
15 x .1 = 1.5