We went to the market to buy some fruit. We decided to buy some apples, strawberries, and oranges. If we buy 2 apples, 3 boxes of strawberry, and 4 oranges, the fruit would cost $15.30. If we buy 1 box of strawberry, 4 apples, and 2 oranges, the fruit would cost $10.90. If we buy 1 orange, 5 apples and 2 boxes of strawberry, the fruit would cost $13.70. Use the Gaussian Elimination Method to solve for the price of each fruit.
Step-by-step explanation:
Let the amount of apples bought be x
Amount of strawberries bought be y and;
amount of oranges bought be z
If we buy 2 apples, 3 boxes of strawberry, and 4 oranges, the fruit would cost $15.30, then this will be expressed as;
2x+3y+4z = 15.30 ........... 1
If we buy 1 box of strawberry, 4 apples, and 2 oranges, the fruit would cost $10.90, this will be expressed as:
4x+y+2z = 10.90 ......... 2
If we buy 1 orange, 5 apples and 2 boxes of strawberry, the fruit would cost $13.70, this is expressed as:
5x+2y+x = 13.70 .......... 3
Solving the three equations simultaneously:
2x+3y+4z = 15.30 ........... 1
4x+y+2z = 10.90 ......... 2
5x+2y+z = 13.70 .......... 3
Reduce the number of equations
multiply equation 1 by 2 and subtract from equation 2
equation 1 * 2 will give:
4x+6y+8z = 30.6 ........... 4
eqn (4)-eqn(2)
6y-y + 8z-2z = 30.6-10.90
5y+6z = 19.7 ......... 5
Also multiply equation 2 by 5 and eqn 5 by 4 and subtract from each other.
eqn(2)* 5 will give:
20x+5y+10z = 54.5 .......... *
eqn(3) * 4 will give
20x+8y+4z = 54.8.......**
Subtsrct ** from *
8y-3y+(4z-10z)= 54.8-54.5
5y-6z = 0.3 .................. 6
Equate 5 and 6 and solve:
5y+6z = 19.7 ......... 5
5y-6z = 0.3 .................. 6
subtract:
6z+6z = 19.7+0.3
12z = 20
z = 20/12
z = 1.67
Substitute z = 1.67 into eqn 6
5y-6(1.67) = 0.3
5y - 10 = 0.3
5y = 10.3
y = 10.3/5
y = 2.06
Substitute z = 1.67 and y = 2.06 into equation 1
From 1:
2x+3y+4z = 15.30
2x+3(2.06)+4(1.67) = 15.30
2x+6.18+6.68 = 15.30
2x+12.86 = 15.30
2x = 15.30-12.86
2x = 2.44
x = 2.44/2
x = 1.22
Therefore 1 apple costs $1.22, 1 strawberry costs $2.06 and 1 orange costs $1.67
On a certain planet, Continent X has an area of 6.23*10^6 square miles and Continent Y has an area of 63,600,000 square miles. How many times larger is Continent Y than Continent X?
Answer:
Step-by-step explanation:
Continent X =6.23*10^6
Continent Y= 63,600,000
rounded = 60,000,000
Scientific notation = 6*10^7
Now round continent X= 6.23 or 6
Continent X= 6*10^6
6*10^7/ 6*10^6 = 1*10^(7-6)
= 1*10^1
= 1*10
= 10
So your answer would be 10.
I hope that helps
Answer:
Step-by-step explanation:Continent X =6.23*10^6
Continent Y= 63,600,000
rounded = 60,000,000
Scientific notation = 6*10^7
Now round continent X= 6.23 or 6
Continent X= 6*10^6
6*10^7/ 6*10^6 = 1*10^(7-6)
= 1*10^1
= 1*10
= 10
So, your answer would be 10 I would have done it this way too not trying to copy(:
Please help!!!!!!!!!!!
Find the measure of the exterior angle
Answer:
Im not sure but go with 24
exterior angle = sum of its opposite interior angles
Which means :-
[tex]x + 21 + 63 = 3x[/tex]
[tex]21 + 63 = 3x - x[/tex]
[tex]21 + 63 = 2x[/tex]
[tex]84 = 2x[/tex]
[tex]2x = 84[/tex]
[tex]x = 84 \div 2[/tex]
[tex]x = 42°[/tex]
Therefore , the correct option is :-
c) 42°Use the distributive property
to expand -4(-2/5+3x)
Which is an equivalent expression?
Answer:
8/5-12x
Step-by-step explanation:
-4(-2/5+3x)
Multiply each term inside the parentheses by -4
-4 * -2/5 + -4 * 3x
8/5-12x
Answer:
-1.6+12x
Step-by-step explanation:
First you do -4*2/5 + -4*3x. Which will give you -1.6+ 12x
An animal reserve has 24,000 elks. The population increases by 12% a year. How long until the population is equal to 96,000,000
Answer:33,325,000
Step-by-step explanation:95,976,000÷2.88=33,325,000
Mr. Jones and Mr. Smith both plan to retire in 5 years. Mr. Jones has invested $250 per
month in a 401k retirement account for 20 years, and Mr. Smith has invested $500 a month
in a 401k retirement account for 10 years. Mr. Jones and Mr. Smith invested in the same
accounts yielding the same interest rate. Which statement about the retirement investments
of Mr. Jones and Mr. Smith is most likely to be true?
Mr.Smith will have more money saved because he invested more money each month.
Mr. Smith and Mr. Jones will have the same amount in their retirement funds.
Mr. Jones will have more money because he invested for a longer period of time.
cannot determine
Answer:
i don't know, i just want to know if you got it right
Step-by-step explanation:
The correct statement (C) "Mr. Jones will have more money because he invested for a longer period of time" is correct.
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
It is given that:
Mr. Jones and Mr. Smith both plan to retire in 5 years.
From the formula:
The rate of interest is the same for both cases.
The duration for Mr. Jones is 20 years
The Initial investment amount for Mr. Jones = $250
The duration for Mr. Smith is 10 years
The initial investment amount for Mr. Smith = $500
Mr. Jones will have more money because he invested for a longer period of time.
Thus, the correct statement (C) "Mr. Jones will have more money because he invested for a longer period of time" is correct.
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Which point is an example of a y intercept?
A. (-2, 8) B. (3, 4)
C. (0, -4)
D. (5,0)
what are the other ways two straight lines could intersect in the coordinate plane? How many solutions would each of these options have?
Answer:
what are the other ways two straight lines could intersect in the coordinate plane How many solutions would each of these options haver
Answer:
Step-by-step explanation:
On the 2nd equation, turn the slope the -3x. This creates two parralel lines.
Two linear equations will always be parallel and never intersect if their y-intersect is different and their slope is the same.
idkkk what it is I accidentally pressed a
The inequality will be x ≥ 2.
What is an inequality?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Given is an inequality, 4x - 3 ≥ 5,
We need to solve for x,
4x - 3 ≥ 5
Add 3 to both sides,
4x - 3 + 3 ≥ 5 + 3
4x ≥ 8
Divide the inequality by 4,
4x / 4 ≥ 8 / 4
x ≥ 2
Hence the inequality will be x ≥ 2.
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URGENT! 10 points
Solve for x then find DE
Answer:
14
Step-by-step explanation:
Answer:
11
Step-by-step explanation:
x+7+7=4x+2 simplify
The ratio of students who made
the honor roll to the total number
of students is 1:50. If there are
500 students in total, how many
made the honor roll?
Answer:
10 is the answer. 1:50 is 10:500 simplified
Step-by-step explanation:
500÷50=10.
Can someone please
Help w this?
The product of a number and is 3 Find the number.
Your answer
set up proportion and solve
Answer:
A.
Step-by-step explanation:
The Answer is A
At the ski shack, customers can rent,skis, snowboards, boots, and poles by the day Mrs.Alvarez is renting skis and poles she has a 18$ coupon off
which expression represents the total cost for Mrs.Alvarez to rent skis for s days and poles for p days
Answer:
48s plus 12p - 18
Step-by-step explanation:
Answer:
Add 48 + 12 and Subtract the sum from 18 (14+12-18)
Step-by-step explanation:
Sorry if I'm confusing you ;(
If T is the midpoint of SU what are ST, TU, and SU?
Answer:
x=7, SU=63, TU=63, SU=126
Step-by-step explanation:
The mid point of SU is T meaning, ST=TU
we find value of x as 7.
replace x by 7 and find the value of given lines.
The product of a number x minus 5 and three less than twice x
Answer:
(x-5)(2x-3)
Step-by-step explanation:
key words:
product = multiplication
minus - subraction
x-5
and = first phrase times next phrase
less than = a number minus the number before the 'less than'
twice = 2 times a number
if we put it together we get x-5 times 2x-3. we put parenthesis because we dont want to multiply only 5 and 2x so our answer is (x-5)(2x-3).
i hope this helped :))
Isaaq put 2b + 3 dollars in the bank in the first week. The following week he doubled the first week’s savings and put that amount in the bank. The next week he doubled what was in the bank and put that amount in the bank. If he now has $477 in the bank, how much did he put in the bank the first week? Please add an numerical explanation
Answer:
The answer is $159
Step-by-step explanation:
2b + 3 - Day 1
4b + 6 - Day 2
6b + 9 - Day 3
477=6b+9
-9 -9
468=6b
78=b
(2x78) + 3 = 159
The answer is $159
*
ate: Find 8% of 40.
nt)
ASAP ,HELP ME PLS
Find the slope given these points:
(2,-4) & (3,1)
A. 5
B. -3
C. 3
D. -5
Answer:
A.
Step-by-step explanation:
What equation is graphed in this figure?
y-4= = -⅓(x+2)
y-3= ⅓(x + 1)
y+ 2 = -3(x - 1)
y - 5 = 3 (x - 1)
Answer:
y - 5 = 3(x - 1)
Step-by-step explanation:
Let the equation of the line passing through a point (x', y') and slope 'm' is,
y - y' = m(x - x')
Since slope of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] is represented by,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Therefore, slope of the line passing through (0, 2) and (1, 5) is,
m = [tex]\frac{5-2}{1-0}[/tex] = 3
Now equation of the line passing through a point (1, 5) and slope = 3 will be,
y - 5 = 3(x - 1)
Option (4) is the answer.
Answer:
y−5=3(x−1)
Step-by-step explanation:
What is the QUOTIENT of 16.8 and 4.4 ?
Answer:
3.81
Step-by-step explanation:
please help this is very urgent!!! :((((
Answer:
7
Step-by-step explanation:
x = 2
3x/2+4
3(2)/2 + 4
3+4
7
-2/5x=-5 What is this?
Answer:
25/2 or 12 1/2 or 12.5
Step-by-step explanation:
Use the distance formula to find the distance, to the nearest tenth, from S(5, −4) to W(−3, 7).
Answer:
185
Step-by-step explanation:
distance formula is d=√((x_2-x_1)²+(y_2-y_1)²
so it would be d=[tex]\sqrt{(-3-5)^{2} + (7-(-4))^{2} }[/tex]
where we see [tex](7-(-4))^{2}[/tex] will turn into [tex](7+4)^{2}[/tex]
[tex](-3-5)^{2} =64[/tex]
[tex](7+4)^{2} =121[/tex]
64+121= 185
Hope this helps...sorry if i'm wrong.
What is an equation for the line that passes through (6,-5) and (-8,16)
Answer:
y=mx
Step-by-step explanation:
i think thats the equation am pretty sure tho
Select the vector along which a translation of the plane would map point A to its image T (A).
Answer:MN
Step-by-step explanation:
I just did it lol
The vector [tex]\vec {MN}[/tex] that would map point A to its image T (A).
What is a vector?A vector is a quantity that possesses magnitude, direction, and adheres to the law of vector addition.
Given:
Two vectors [tex]\vec {PQ}[/tex] and [tex]\vec {MN}[/tex].
To map point A to its image T (A):
The translated map would be,
[tex]\vec {MN}[/tex].
Therefore, [tex]\vec {MN}[/tex] is the vector.
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The ratio of basketballs to volleyball in the gym is 3 to 5. If there are 60 volleyball in the gym, how many basketballs are there?
How much time will Alex need to walk to his school, which is 2 1/ 4 miles away from his house, if he would walk with the speed of …
3 mph
Please help!!!!
Answer:
Alex needs to walk for 45 minutes.
Step-by-step explanation:
2.25 / 3 = 0.75 hours
0.75 hours = 45 minutes
Five times the sum of a number n and seven
Hint- you need parenthesis
The equation of the problem is [tex]5(n+7)[/tex]
The sentence is asking 5 times the sum of n+7, so you are multiplying (n+7) by 5.