Answer:
[tex]\boxed{x = 4, ~y = -1,~ and~z = 3}[/tex]
.
Step-by-step explanation:
(eq-1) → x + y + z = 6
(eq-2) → x - y + z = 8
(eq-3) → x + y - z = 0
.
Eliminate eq-1 and eq-3
[tex]x + y + z = 6[/tex]
x + y - z = 0
[tex]2z = 6[/tex]
[tex]z = \frac{6}{2}[/tex]
[tex]z = 3[/tex]
.
Eliminate eq-1 and qe-2
[tex]x + y + z = 6[/tex]
x - y + z = 8
[tex]2y = -2[/tex]
[tex]y = \frac{-2}{2}[/tex]
[tex]y = -1[/tex]
.
Substitute the value of z and y to on of equations
[tex]x + y + z = 6[/tex]
[tex]x + (-1) + 3 = 6[/tex]
[tex]x + 2 = 6[/tex]
[tex]x = 6 - 2[/tex]
[tex]x = 4[/tex]
Answer:
The solution for the following system is: [tex]\mathbf{x=4, y=-1, z=3}[/tex]
Step-by-step explanation:
We need to find the solution to the following system.
[tex]x+y+z=6 \ and \ x-y+z=8 \ and \ x+y-z=0[/tex]
Let:
[tex]x+y+z=6 --eq(1)\\ x-y+z=8 --eq(2)\\ x+y-z=0--eq(3)[/tex]
Adding eq(1) and eq(2)
[tex]x+y+z=6 \\x-y+z=8 \\-------\\2x+2z=14 --eq(4)[/tex]
Adding eq(2) and eq(3)
[tex]x-y+z=8 \\ x+y-z=0\\-------\\2x=8\\x=8/2\\x=4[/tex]
We get value of x=4
Now, putting value of x in eq(4) to find value of z
[tex]2x+2z=14\\Put x=4\\2(4)+2z=14\\8+2z=14\\2z=14-8\\2z=6\\z=6/2\\z=3[/tex]
We get value of z=3
Now, putting value of x and z in eq(1) to find value of y
[tex]x+y+z=6\\Put \ x=4, z=3\\4+y+3=6\\y+7=6\\y=6-7\\y=-1[/tex]
So, value of y=-1
The solution for the following system is: [tex]\mathbf{x=4, y=-1, z=3}[/tex]
The science club went on a two-day field trip. The first day the members paid $62 for transportation plus $15 per ticket to the planetarium. The second day they paid $95 for transportation plus $12 per ticket to the geology museum. Write an expression to represent the total cost for two days for the n members of the club.
Answer:
(62 + 15n) + (95 + 12n)
Get that hundo!
You have 3/8 of a cake. You divide the remaining cake into 6 equal pieces. What fraction of the original cake is each piece? *
Im having difficulty with these problems. Can someone please help me out?
1) Solve 2cos x=1
2) Solve: tan x -2sin x tan x=0
3) Solve: cos (2x)= -3^(1/2)/2
Answer:
x=60° or 300°
Step-by-step explanation:
2cosx=1
cosx=1/2
cosx=cos60°,cos(360-60)°
cosx=cos60,cos300
either,
cosx=cos60
x=60
or,
cosx=cos300
x=300
the length of a rectangular sing is 5 time its width. if the sign perimeter is 24 inches. what is the sign area ?
Answer:
20 in²
Step-by-step explanation:
Assuming that the width of the sign is x, then from the question, we're told that the length is 5 times it's width, so
b = x inches
l = 5x inches
Again, we're told that the perimeter of the sign is 24 inches, and we know already that the perimeter of a rectangle is given as
Perimeter = 2(l + b), substituting this, we have
24 = 2(5x + x)
24 = 10x + 2x
24 = 12x
x = 24 / 12
x = 2 inches.
Since x is the width of the rectangle, and it's 2 inches, we use it to find the length of the sign.
l = 5 * 2
l = 10 inches.
Then, we are asked to find the area of the sign. Area of a rectangle is given as
A = l * b, so if we substitute, we have
Area = 10 * 2
Area = 20 square inches
Why did the feudal system rely on a high degree of local independence?
Answer:Feudalism helped protect communities from the violence and warfare that broke out after the fall of Rome and the collapse of strong central government in Western Europe. Feudalism secured Western Europe's society and kept out powerful invaders. Feudalism helped restore trade. Lords repaired bridges and roads.
Step-by-step explanation:
Nancy paid six dollars for two cans of soup. Determine the cost per can.
Answer:
3 dollars
Step-by-step explanation:
6 / 2 = 3
Answer:
3$ per can
Step-by-step explanation:
6$ divided by 2 cans of soup equals $3 per can :)
Helppppppppppppppppppp ASAP
Answer:
-2, 1, 3
Step-by-step explanation:
Evaluate h(t)=50-t/5
h(35)=
Csctheta x tantheta= sectheta
Answer:
TRUE
Step-by-step explanation:
That is true, you get 1/cos(Θ) which is sec(Θ)
please give thanks and hit that heart button :)
Which is the correct answer?
(explain how you got your answer)
Answer:
Option B. f¯¹(x) = ³√(– x – 9)
Step-by-step explanation:
From the question given above:
f(x) = – x³ – 9
f¯¹(x) =?
We can obtain the inverse f¯¹(x) of the above equation by doing the following:
f(x) = – x³ – 9
Replace f(x) with y
y = – x³ – 9
Interchange x and y
x = – y³ – 9
Make y the subject . This is illustrated below:
x = – y³ – 9
Rearrange
x + 9 = – y³
Multiply through by –1
–(x + 9) = y³
y³ = – x – 9
Take the cube root of both side
y = ³√(– x – 9)
Replace y with f¯¹(x)
f¯¹(x) = ³√(– x – 9)
Thus, the inverse of the function
f(x) = – x³ – 9
is
f¯¹(x) = ³√(– x – 9)
A farmer wants to fence a rectangular habitat for goats. The length (y) of the habitat has to be at least 80 feet. The farmer currently has 310 feet of fencing available to use on the habitat. The system of inequalities below models this problem situation, where x represents the width of the habitat (in feet) and y represents the length of the habitat (in feet). y≥80 2x+2y≤310 Which of the following is a true statement? a. If the farmer makes a rectangular habitat with a length of 60 feet, the width needs to be 80 feet. b. The farmer can make a habitat that is 75 feet long and 60 feet wide. c. The farmer does not have enough fencing to enclose a rectangular habitat that is 80 feet long. d. The farmer can make a habitat that is 40 feet wide and 100 feet long.
Answer:
d. The farmer can make a habitat that is 40 feet wide and 100 feet long.
Step-by-step explanation:
The attached graph shows the inequalities and the various answer choices. The existence of the doubly-shaded area shows that answer choice C is false.
The appropriate choice is ...
d. The farmer can make a habitat that is 40 feet wide and 100 feet long.
PLEASE HELP, BEEN STUCK FOR AN HOUR
How will you graph the function g(x) = (x – 4)+ 12 using the parent quadratic function, f (x) = x2?
9514 1404 393
Answer:
see below
Step-by-step explanation:
We assume your functions are ...
f(x) = x²
g(x) = (x -4)² +12
_____
You need to be able to recognize that g(x) matches a pattern:
g(x) = f(x-h) +k
where h = 4, and k = 12.
In this pattern, the value of h is the number of units the graph is translated to the right. The value of k is the number of units the graph is translated up.
So, g(x) is the same as the graph of f(x), but translated 4 units right and 12 units up.
From the definition of absolute value
3|x| = when x≥0
and
3|x| = when x<0.
Answer:
To answer your question use the code ICE on here to get your answer works every time for me hope this helps
A package states that there are 60 calories in 12 crackers
Answer: 5 calories = 1 cracker
Step-by-step explanation:
60:12 = 5:1
60 calories and 12 crackers = 5 calories and 1 cracker
I need a story problem to match the equation 36÷5=7 Remainder 1
Answer: sarah has 36 cookies but she has 5 friends. she doesnt know how much cookies go to her friends. Write a equation to solve the problem
Step-by-step explanation:
write and equation of the line that passes through 2,2 and is parallel to the line y=7x
Answer:
y = 7x+2
Step-by-step explanation:
Under typical conditions, 1 [tex]\frac{1}{2}[/tex] feet of snow will melt in 2 inches of water. How many inches of water will it take to melt 1 [tex]\frac{3}{4}[/tex] feet of snow?
Answer:
2[tex]\frac{1}{3}[/tex]inches
Step-by-step explanation:
First, I would try to get the mixed numbers into improper fractions. Then, I try to make them have the same denominator so it is easier.
1[tex]\frac{1}{2}[/tex]feet --- 2 inches
[tex]\frac{3}{2}[/tex]feet --- 2 inches
[tex]\frac{6}{4}[/tex]feet --- 2 inches
1[tex]\frac{3}{4}[/tex]feet --- ? inches
[tex]\frac{7}{4}[/tex]feet --- ? inches
[tex]\frac{7}{4}[/tex]feet --- [tex]\frac{7}{6}[/tex] × 2 inches
= 2[tex]\frac{1}{3}[/tex]inches
Is -27 greater than -28
(2,-3), slope = 4
What is the answer
We are given:
The line passes through (2,-3)
Slope of the line = 4
Finding the equation of the line:
We know that the general form of the slope-intercept form is:
y = mx + b [where m is the slope and b is the y-intercept]
y = 4x + b [since slope = 4]
Finding the y-intercept:
Now, we are given that the line passes through the points: (2,-3)
which can be written as: x = 2 and y = -3
Since the line passes through these points, these values must satisfy the equation
So,
y = 4x + b
-3 = 2(4) + b
-3 = 8 + b
b = -11 [subtracting 8 from both sides]
Hence, the y-intercept is -11
Equation of the line:
We wrote the equation of the line as:
y = 4x + b (where b is the y-intercept)
now that we know the value of b,
y = 4x - 11
Therefore, the equation of the line is: y = 4x - 11
f) -7x + 8x =
simplify
Answer:
The answer is: X
Step-by-step explanation:
-7x+8x = 1x
this means the answer is X
HELP PLEASE ASAP WILL GIVE BRAINLEIST
Answer:
PN = 10
Step-by-step explanation:
Base angles converse theorem states that a triangle with two congruent angles is isosceles. The sides opposite to the two congruent angles are the congruent sides. The side between the two congruent angles is the base.
In this problem, it is given that <P = <O, hence ΔNOP is isosceles, because of base angles theorem. OP is the base, and hence NO is one of the congruent sides and therefore has to be congruent to PN. Which means that PN is 10.
According to an accepted chemistry reference, the
heat of vaporization of water is 540 calories per
gram. A student determined in the laboratory that
the heat of vaporization of water was 620 calories
per gram. The student's results had a percent error
of
Answer:
14.8%
Step-by-step explanation:
Step 1: Given data
True value for the heat of vaporization of water (ΔH°vap(T)): 540 cal/g
Experimental value for the heat of vaporization of water (ΔH°vap(E)): 620 cal/g
Step 2: Calculate the experimental percent error
To determine the experimental percent error we will use the following expression.
%E = |ΔH°vap(T) - ΔH°vap(E)|/ΔH°vap(T) × 100%
%E = |540 cal/g - 620 cal/g|/540 cal/g × 100%
%E = 14.8%
Michelle and her roommate rent an apartment for $798 a month. Each of them pays half. Because there are about 4 weeks in a month, Michelle estimates her share of the rent is about $100 a week. Is that a good estimate?
Yes
No, it is much high
Not, it is much low
Answer:
yes
Step-by-step explanation:
half of $798 is $399. $100 a week × 4 = $400. 400 is very close to 399, so yes it would be a food estimate. Hope this helps! :)
Roxanne started making sugar cookies for her friends at 11:35 A.M. It took her 50 minutes to make the dough and 50 minutes to bake all of the cookies. Then, Roxanne spent 40 minutes decorating the cookies with icing and sprinkles. What time was it when Roxanne finished making the cookies?
Include A.M. or P.M. in your answer .Please help me fast !!!
Answer: 1:55Pm
Step-by-step explanation:
Answer:
1:55 P.M
Step-by-step explanation:
You would add 50 and 50 together it 100 add 40 equal 140.2 hours and 20 mins. 11:35 P.M add 2 hours is 1:35 add 20 mins equal 1:55 P.M
Find the equation of the line through point (-3, 8) and perpendicular to y = x + 14. Use a forward slash (i.e. "M) for
fractions (e.g. 1/2 for 3).
Answer:
y+x = 5
Step-by-step explanation:
Given the equation y = x + 14
Get the slope first
The slope m = 1
Since the required equation is perpendicular to the line, the required slope will be M = -1/1 = -1
Get the required equation using the equation y-y0 = m(x-x0)
(x0, y0) = (-3, 8)
y - 8 = -1(x-(-3))
y-8 = -(x+3)
y-8 = -x-3
y+x = -3+8
y+x = 5
Hence the required equation of the line is y+x = 5
Rewrite the following equation in exponential form.
log49 (7)=1/2
Answer:
49^1/2 =7
Step-by-step explanation:
log49(7)=1/2
in exponential form
49^1/2 =7
Monica went shopping for holiday presents. She bought boxes of chocolates and boxes of ornaments for her
coworkers. Boxes of chocolate cost $10 each and boxes of ornaments cost $12 each. She buys a total of 14
boxes and spends $156. How many boxes of chocolates and how many boxes of ornaments does she buy?
Use C for number of chocolate boxes and for number of ornament boxes.
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The number of chocolate boxes is 6.
The number of ornament boxes is 8.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 5 is an equation.
We have,
Number of chocolate boxes = C
Number of ornaments boxes = B
The total cost of 14 boxes = $156
Cost of one box of chocolate = $10
Cost of one box of ornaments = $!2
Now,
C + B = 14 ______(1)
10C + 12B = 156 _______(2)
From (1) we get,
C = 14 - B ______(3)
Putting (3) in (2) we get,
10 (14 - B) + 12B = 156
140 - 10B + 12B = 156
140 + 2B = 156
2B = 156 - 140
2B = 16
B = 16/2
B = 8
Now,
C = 14 - B
C = 14 - 8
C = 6
Thus,
The number of chocolate boxes is 6.
The number of ornament boxes is 8.
Learn more about equations here:
https://brainly.com/question/17194269
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Write an integer for loss of 18 pounds
PLEASE HELP
So a loss is negative it will be -18 on the number line.
UwU hope this helps
Find all values of X which make the equation below true | 3x + 5 | = 8
Answer:
x= -13/1,1
3x+5=8
-(3x+5)=8
x=1
x=-13/3
x=-13/3,1
Answer:
x and equal 1 or -13/3
Step-by-step explanation:
this is an absolute value equation so the equation can either equal 8 or -8. if you set up two equations that are 3x+5=8 and 3x+5 = -8 and just isolate the x, you get 1 and -13/3.
correct solution to the inequality x+1>5?