There's only one system of equations here.
Let's eliminate x first,
x - y + z = -1
x = -1 + y - z
Substituting into x + y + 3z = -3 gives
(-1 + y - z) + y + 3z = -3
2y + 2z = -2
y + z = -1
Substituting for x into 2x-y+2z = 0 gives
2(-1 + y - z) - y + 2z = 0
-2 + 2y - 2z - y + 2z = 0
y = 2
Got lucky on that one.
z = -1 - y = -1 - 2 = -3
x = -1 + y - z = -1 + 2 - -3 = 4
Answer: x=4, y=2, z= -3
Check:
x-y+z = 4 - 2 + -3 = -1, good
x+y+3x = 4+2+3(-3) = -3, good
2x-y+2x = 2(4)-2+2(-3) = 0, good
After solving three equations, the result is x=4, y=2, and z=-3.
What is the definition of elimination?The elimination method involves removing one of the variables by combining the two equations. This method eliminates one variable, allowing you to solve for the other. Because there are two variables in a two-equation system, eliminating one simplifies the process of solving for the other. The addition property of equality is used in the elimination method for solving systems of linear equations. Each side of an equation can have the same value. So, if you have a system where x - 6 = 6 and x + y = 8, you can add x + y to the left side of the first equation and 8 to the right.Therefore,
Eliminate x first,
x - y + z = -1
x = -1 + y - z
Substituting into x + y + 3z = -3 gives
(-1 + y - z) + y + 3z = -3
2y + 2z = -2
y + z = -1
Substituting for x into 2x-y+2z = 0 gives
2(-1 + y - z) - y + 2z = 0
-2 + 2y - 2z - y + 2z = 0
y = 2
z = -1 - y
Simplifying the above equation then we get,
= -1 - 2
Z = -3
x = -1 + y - z
Substitute the value y and z the above equation,
= -1 + 2 - (-3)
Then we get
X = 4
Hence, The value of x = 4, y = 2, and z = -3
To learn more about eliminating, refer to:
https://brainly.com/question/28405823
#SPJ2
The equation of the graphed line is 2x – 3y = 12.
A coordinate plane with a line passing through (0, negative 4) and (6, 0).
What is the x-intercept of the graph?
–4
–Negative StartFraction 3 Over 2 EndFraction
StartFraction 2 Over 3 EndFraction
6
Step-by-step explanation:
Well, if you're trying to find the x-intercept, you should look where the line crosses the x-axis. If the line crosses at 6, then the x-intercept is 6. So what I'm saying is the answer is 6.
Btw, if you're trying to find the y-intercept, just look where the line crosses the y-axis, (vertical axis) and then that's your answer.
Example: If there is a line crossing through a 5 on the y-axis, that is your y-intercept.
Example: If there is a line crossing through a 5 on the x-axis, that is your x-intercept.
I hope this answers your question.
Answer:
6
Step-by-step explanation:
Find the m∠SAQ.
44°
46°
57°
77°
Answer:
X=57
Step-by-step explanation:
77+46+X=180
123+X=180
X=180-123
X=57
Answer:
57°
Step-by-step explanation:
Hope it helps you in your learning process
46° + m∠SAQ + 77° = 180° (straight line angles)
m∠SAQ + 123° = 180°
m∠SAQ = 180° - 123°
m∠SAQ = 57°
simplify 3x + 5 + 7 x - 3 - x + 2
Before we do this problem, let's go over a little algebra terminology.
The number in front of your variable is called your coefficient and notice that the x at the end of the problem does not have a coefficient.
When that happens, when there is no number in front of your variable, you can put a 1 there to fill that position. So -x can be thought of as -1x.
Next let's change all our minus signs to plus negatives.
So the problem reads 3x + 5 + 7x + -3 + -1x + 2.
Now let's simplify this by combining like terms.
We can combine our "x" terms first.
3x + 7x + -1x simplifies to +9x.
Now, 5 + -3 + 2 simplifies to 4.
So our answer is 9x + 4.
Answer:
10x-x+7-3
Step-by-step explanation:
The length of a rectangle is 3 more than the width. Find the length of the rectangle
if the perimeter is 98 in.
A gift box has the shape of a cube with an edge length of 4.5 in. What is the volume of the gift box? Enter your answer in the box. in³
Answer:
91.125 in^3
Step-by-step explanation:
4.5*4.5*4.5 = 91.125
plz help will give brainliest, thanks, and lots of points
Answer:
V = 687.28 cm ^3
Step by step explanation:
687.28 m ^3 is found in 3 steps.
Volume of a sphere = V=4/3πr3 = 268.8 m^3
Volume of a semi sphere = V = (2/3)πr. but i divide the top one by 2
= 268.8/2 = 134.4 m^3
Volume of a Cylinder prism = V=πr2h = 502.61 m^3
Volume of a cone V=(πr2 )h/3 = 50.27
We add 134.4 + 502.61 +50.27 = 687.28 m ^3
How to find Area;
We remember and compare to Area and other areas the values.
Area = 415m^2
circle is semi sphere A = π r2 h= 200.1 = /2 or *0.5 A=100.53 m^2
cylinder lateral A = 2πrh L = 251.327412 m^2 = 251 m^2
Cone lateral A=πrh2+r2 = 62.83 = 63 m^2
= 100.53 + 251.327412 + 62.83 =414.687412
or 101+251+63 = 415 m^2
Notes;
The best way is to find someway of not overwhelming yourself with the combined volume question and know what actually makes a cylinder being the central prism.
So write down all these values below onto a flashcard and title it Area of a composite Semi-sphere/cylinder/cone r = 4 / h= 10 r =4 / r= 4 h=3
and write these down.
Cylinder
lateral surface area L = 80 π m2
top surface area T = 16 π m2
base surface area B = 16 π m2
total surface area A = 112 π m2
Cone = 62.83
Semi sphere = 100.53
Area = 415 m2
2/3(p-12)=-(2p-1)+7
A. all real numbers
B. −6
C. –4
D. 4
Answer:
p=6
Was option B supposed to be 6 instead of -6?
Work:
2/3p-8=-2p+8
2p-24=-6p+24
8p=48
p=6
complete the equation describing how x and y are related
Answer:
y = 3x
Step-by-step explanation:
The difference between consecutive values of y are constant, that is
9 - 6 = 6 - 3 = 3 - 0 = 0 - (- 3) = - 3 - (- 6) = 3
This constant is the required multiplier, that is
y = 3x
Your dad is designing a new garden for your backyard. He has 26 feet of fencing to go around the garden. He wants the length of the garden to be 3 1/2 feet longer than the width. How wide should he make the garden?
Answer:
4.75 feet
Step-by-step explanation:
Perimeter for any rectangular shape is given by 2(length + width).
Fencing the garden means one wiring the garden along the perimeter.
Thus, it can be concluded that garden has perimeter of 26 feet as given in question.
__________________________________________
Let the width be x feet
given that, He wants the length of the garden to be 3 1/2 feet longer than the width
thus, length of garden = x + 3 1/2 feet = x + 3.5 feet
if length is x+3.5 feet and width is x feet.
Then perimeter = 2( x+3.5 + x) = 2(2x+3.5) = (4x + 7) feet.
This perimeter will be equal to 26 feet fence
thus,
(4x + 7) = 26
=> 4x = 26 - 7 = 19
=> x = 19/4 = 4.75 feet
x is width of garden.
Thus, he should make the garden 4.75 feet wide.
Answer:
4.75
Step-by-step explanation:
Plz lzplz plz plz plz help me plz ASAP
i think it is 4
hope this helps
Which expression can be used to find 17% of 58?
A. 58 = 0.17 B. 58 = 17
C. 58 x 0.17
D. 58 x 17
Answer:
58 times 0.17 which agrees with answer C in the given list of possible answers.
Step-by-step explanation:
Notice that 17% in math terms is 17/100 = 0.17
Now to find the 17% of the number 58, we need to multiply 58 by 17/100, which gives:
58 times 0.17
ANSWER AS SOON AS POSSIBLE;please and thank you/Gabby earns $30 per week. Her goal is to save 69,855 how long will it take for gabby to earn $69,855?
Answer:
2328.5 weeks or 6.4 years
Step-by-step explanation:
69855/30= 2328.5/365= 6.4
Find the area of the rhombus. Each indicated distance is half the length of its respective diagonal.
Answer:
24 square feet
Step-by-step explanation: There are four "triangles" of the rhombus. If you find the area of each triangle by multiplying the height by the width and divide by two, you get 6. You then multiply that by 4 to get 24.
for v =-3i+6j find unit vector u in the direction of v
Help pls so people say it’s none of these but idk I am confused.
Answer:
Volume = [tex]\pi r^2 h[/tex]
2512 = 3.14 × r^2 × 8
[tex]r^2 = \displaystyle\frac{314}{3.14}[/tex]
[tex]r^2 = 100[/tex]
[tex]r = 10 \ cm[/tex]
[tex]Diameter = 2r = 20 \ cm [/tex]
Dont get confused try to understand : )
Answer:
20 cm
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
We are given the volume and the height
2512 = pi r^2 *8
Divide each side by 8
2512/8 = pi r^2 *8/8
314 = pi r^2
Divide each side by pi
314/3.14 = 3.14 r^2 /3.14
100 = r^2
Take the square root of each side
sqrt(100) = sqrt(r^2)
10 = r
We want to find the diameter
d =2r
d =2(10)
d =20
The diameter is 20 cm
30PTS
ASAP: BRAINLEST FOR BEST ANSWER!
im stupid xD
Answer: $200-$75=$125
Answer:
125$
Step-by-step explanation:
$200-$75=125$
Help please !!!! I need this I don’t need a detailed explanation
Answer:
-6/5 (This is Answer c)
Step-by-step explanation:
Re-writing this equation in standard form, we get:
25x^2 + 60x + 36 = 0. The coefficients are a = 25, b = 60 and c = 36.
The discriminant, b^2 - 4ac, is 60^2 - 4(25)(36), or 3600 - 3600, or 0.
Because the discriminant is 0, we have two real, equal roots, corresponding to
-b -60
x = ------ = ---------- = -6/5 (This is Answer c)
2a 2(25)
Vocabulary Review List the five inequality symbols. Help me please
Answer:
Greater than, less, than, equal to, greater or equal to, less than or equal to
Step-by-step explanation:
Kali has a 6 meter ladder that she wants to use to get her cat out of a tree. She puts the base of the ladder 2
meters away from the base of the tree. How high into the tree will the ladder reach? Round your answer to the nearest tenth of a meter.
Answer:
5.7m
Step-by-step explanation:
the easiest way to solve for a side is to draw the question in a diagram (i have done this below). As it is a right-angled triangle and we know 2 of the side, we can use the Pythagoras theorem:
[tex]a^{2} +b^{2} =c^{2}[/tex]
sides a and b are the two shorter sides.
side c is the hypotenuse (longest side)
as shown in the picture below, because we know both sides c and b, we need to change the equation around:
[tex]c^{2} -b^{2} =a^{2}[/tex]
replace these sides with their numbers:
[tex]6^{2} -2^{2} = 32[/tex] (remember that 32 equals side a squared therefore we need to square root 32 to find the length of side a:
[tex]\sqrt{32} =5.65685...[/tex]
the question says to round to the nearest tenth meter:
Missing side = 5.7m
I hope this was helpful :-)
Answer:
5.7
Khan
Alright
Make me brainliest please just once.
Step-by-step explanation:
DUE NOW
The two-way table shows the number of students that do or do not do chores at home and whether they receive an allowance or not. Find the relative frequencies of students in the survey by rows. Round to the nearest hundredth.
Answer:
Relative frequencies
First row
0.8125 ,0.1875 ,16
Second row
0.555 ,0.444 ,9
third row
18 , 7 , 25
Step-by-step explanation:
Given data
allowance No allowance total
Chores 13 3 16
No chores 5 4 9
Total 18 7 25
Relative frequencies
allowance No allowance total
Chores [tex]\frac{13}{16} = 0.8125[/tex] [tex]\frac{3}{16} = 0.1875[/tex] 16
No chores [tex]\frac{5}{9} = 0.555[/tex] [tex]\frac{4}{9} = 0.444[/tex] 9
Total 18 7 25
Pure acid is to be added to a 5% acid solution to obtain 95L of 98% solution. What amounts of each should be used?
How many liters of 100% pure acid should be used to make the solution?
Answer:
Step-by-step explanation:
Equation:
acid + acid = acid
0.05x + 1.0(95-x) = 0.30*95
----
Multiply thr by 100 to get:
5x + 100*95 - 100x = 30*95
---
-95x = -70*95
---
x = 70L (amt of 5% solution needed)
---
95-x = 25L (amt of 100% solution needed)
==================================================
How many Liters of 100% acid should be used to obtain the solution?
need help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
y = -2x
Step-by-step explanation:
I used slope intercept form and took one of the answers and the slope hit (-2,4).
Find the area of the figure.
A triangle with base 8.2 cm and height 5.9 cm
The area equals ____ cm2.
So the right answer is 24.19 cm^2
Look at the attached picture
Hope it will help you
Good luck on your assignment
Answer:
[tex] = 24.19 {cm}^{2} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
PLS HELP What is the cos and sin for angle of rotation 30 degrees?
Answer:
cos 30=0.860254038
sin 30=0.5
Step-by-step explanation:
use a calculator
welp!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
~47%
Step-by-step explanation:
18 / 38 = 0.47368421053 = ~0.47 = 47%
wiil make braleast 10 pontsA circular wading pool has a radius of 12 feet.
What is the longest distance across the wading pool?
36 ft
12 ft
24 ft
48 ft
Answer:
24
Step-by-step explanation:
radius^2 = diameter
Answer:
24ft
Step-by-step explanation:
all you had to do is multiply 12x2
Which multiplication problem can be used to determine how many possible combinations there are for a lock
consisting of 3 digits from 0-9, if the digits can be repeated?
(3)(3)(3)
O (9/9/9)
O (10/9/8)
(10/10/10)
Intro
Done
4 of 11
What is the area of the trapezoid shown below?
A. 361 sq. units
B. 114 sq. units
C. 78 sq. units
D. 52 sq. units
Answer:
78
Step-by-step explanation:
7+8/2 multiply by 6
Answer:
C. 78 sq. units
Step-by-step explanation:
[tex]area \: of \: trapezoid \\= \frac{1}{2} \times (19 + 7) \times 6 \\ = 26 \times 3 \\ = 78 \: sq \: units[/tex]
If a dress costs $27.00 when it is on sale for 10% off, what is its original cost?
PLZ HELP IN A HUGE RUSH PLZ PLZ PLZ
Answer: 30
Step-by-step explanation:
simple
Select the quadrant or axis where each ordered pair is located on a coordinate plane.