1. Your school's Key Club decided to sell fruit baskets to raise
money for a local charity. The club sold a total of 80 fruit
baskets. There were three different types of fruit baskets.
Small fruit baskets sold for $15.75 each, medium fruit baskets
sold for $25 each, and large fruit baskets sold for $32.50
each. The Key Club took in a total of 52086.25. and they sold
twice as many large baskets as small baskets.
a. Formulate a system of three linear equations in three
variables to represent this problem situation. Be sure to
define your variables.
b. Solve the system of three linear equations using
technology with matrices. Write your answer in terms of
the problem situation.
c. Describe the solution in terms of the problem situation.
2. Is it always easier to solve a system of linear equations using
matrices? Explain your reasoning.
Answers
Let the small , medium and large baskets be denoted by s,m & l
Formulating the equations
s+m+l= 80--------- equation1
$15.75s+ $25 m + $32.5l = $2086.25------equation2
2s=l---------equation 3
Using the technology s=15, m=35 and l= 30
15+35+30= 80--------- equation1
$15.75(15)+ $25 (35)+ $32.5 (30) = $2086.25------equation2
2(15)=(30)---------equation 3
Yes because multiple variables can be easily calculated through matrices using technology
In Matrix form
[tex]\left[\begin{array}{ccc}1&1&1\\15.75&25&32.5\\-2&0&1\end{array}\right][/tex] [tex]\left[\begin{array}{c}s\\m\\l\end{array}\right][/tex] = [tex]\left[\begin{array}{c} 80\\2086.25\\0\end{array}\right][/tex]
Let A= [tex]\left[\begin{array}{ccc}1&1&1\\15.75&25&32.5\\-2&0&1\end{array}\right][/tex]
Z= [tex]\left[\begin{array}{c}s\\m\\l\end{array}\right][/tex]
B = [tex]\left[\begin{array}{c} 80\\2086.25\\0\end{array}\right][/tex]
Z= A⁻¹ B
A⁻¹= A mod/ det A
det A= -1
Using the technology s=15, m=35 and l= 30
15 small baskets,
35 medium baskets
30 large baskets were sold.
Part C:
15+35+30= 80--------- equation1
$15.75(15)+ $25 (35)+ $32.5 (30) = $2086.25------equation2
236.25+ 875+ 975=$2086.25
$2086.25=$2086.25
2(15)=(30)---------equation 3
Answer 2:
Yes because multiple variables can be easily calculated using technology.
N.B There is a typing error in question its $2086.25 not 52086.25
Related Questions
select the correct answer
which of these graphs represents a function?
Answers
Find the value of x. Round to the
nearest tenth.
35
Х
12
x = [ ? ]
Answers
Answer:
Step-by-step explanation:
[tex]Tan 35 = \dfrac{opposite \ side}{adjacent \ side}\\\\0.7=\dfrac{12}{x}\\\\0.7*x=12\\\\x=\dfrac{12}{0.7}\\\\x=17.1[/tex]
0<4K-5k
Can I get some help thanks
Answers
Answer:
0>k
Step-by-step explanation:
0<4k-5k
Combine like terms
0<-k
Multiply each side by -1, remembering to flip the inequality
0>k
Show work please
[tex]4 \sqrt{9} [/tex]
Answers
Answer:
12
Step-by-step explanation:
[tex]4 \sqrt{9} [/tex]
[tex] \sqrt{9} = \sqrt{ {3}^{2} } = 3[/tex]
[tex]4 \times 3[/tex]
[tex] = 12[/tex]
-2u+(-1)=-13
---------------
Answers
Answer:
Solution given
-2u+(-1)=-13
open bracket
-2u-1=-13
add 1 on both side
-2u-1+1=-13+1
-2u=-12
divide both side by -2
-2u/-2=-12/-2
u=6
[tex]\huge\text{Hey there!}[/tex]
[tex]\textsf{-2u + (-1) = -13}\\\textsf{-2u - 1 = -13}\\\large\text{ADD 1 to BOTH SIDES}\\\textsf{-2u - 1 + 1 = -13 + 1}\\\large\text{CANCEL out: -1 + 1}\\\large\text{KEEP: -13 + 1}\\\rightarrow\textsf{-2u = -12}\\\large\text{DIVIDE -2 to BOTH SIDES}\\\mathsf{\dfrac{-2u}{-2}= \dfrac{-12}{-2}}\\\textsf{CANCEL out: }\mathsf{\dfrac{-2}{-2}}\\\textsf{KEEP: }\mathsf{\dfrac{-12}{-2}}\\\mathsf{u = \dfrac{-12}{-2}}\\\mathsf{u = \bf 6}\\\huge\boxed{\mathsf{Answer: u = 6}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}\\\\\frak{Amphitrite1040:)}[/tex]
Can someone help me with problem 6 and 7? Please explain I am confused
Answers
Same with 7. They are each simplified already. I would suggest asking your teacher.
is 3/8 bigger or smaller than 3/5
Answers
3/8 is smaller than 3/5.
3/8 is smaller than 3/5
Find the LCD of both fractions:
Multiples of 8:
8, 16, 24, 32, 40, 48, 56, 64, 72, …
Multiples of 5:
5, 10, 15, 20, 25, 30, 35, 40, 45, …
40 is the LCD of denominators 5 and 8.
Multiply both denominators by a number that makes it 40, multiply that same number by each numerator:
3/8:
3 x 5 = 15
8 x 5 = 40
15/40
3/5:
3 x 8 = 24
5 x 8 = 40
24/40
15/40 < 24/40
Hope this helps
In a hotel, 40 people occupy excatly 26 rooms. Each room is occupied by either one or two people. How many rooms are occupied by exactly one person?
Answers
Explanation:
Let's say that the first 26 people will occupy each of the 26 rooms. This means that, so far, there's one person per room.
There are 40-26 = 14 people left. Let's say those 14 people occupy the first 14 rooms. This means that the first 14 rooms now have 2 people in them per room. The remaining 26-14 = 12 rooms still have one person per room.
Amela put 15x- 4 gallons of gas in her car at the beginning of the week. She used 7x-3 gallons driving to work. Which of the following choices represents the
number of gallons left in her car?
A) 22x+7
B) 22x-7
C) 8x+1
D) 8x-1
Answers
Answer:
D) 8x - 1
Step-by-step explanation:
Let's say that x = 5. That would mean Amelia put 15(5) - 4 gallons of gas in her car, which equals 71 gallons. She used 7(5) - 3 gallons driving to work, which is 32 gallons used. 71 - 32 = 39 gallons left.
What else equals 39, you might ask?
8(5) - 1
40 - 1
39.
Answer:
D is the answer
Step-by-step explanation:
if f(x)=x-4 find the value if f(x)+f(-x)
Answers
Answer:
2x
Step-by-step explanation:
f(x) = x -4
Step 1:
y = x - 4
Step 2: Replace y with x
x = y - 4
Step 3: Find y
x + 4 = y
f(-x) = x + 4
f(x) + f(-x) = (x - 4)+ (x + 4) = 2x
سر
.
A particular satellite is 15 m wide. A model
of it was built with a scale of 1 cm: 5 m.
How wide is the model?
Answers
Answer:
3cm
Step-by-step explanation:
A particular satellite is 15 m wide
Model of it was built with a scale of 1 cm: 5 m
=> scale of the model will be: 1/500cm and A particular satellite is 1500 cm wide
=>1500*1/500=3(cm)
If m ZABD = 83º, what are mZABC and m ZDBC?
3x+33° D
(Ex-6)°
B
mZABC = °
Answers
Answer:
∠ ABC = 48°
Step-by-step explanation:
∠ ABC + ∠ DBC = ∠ ABD , that is
6x - 6 + 3x + 8 = 83
9x + 2 = 83 ( subtract 2 from both sides )
9x = 81 ( divide both sides by 9 )
x = 9
Then
∠ ABC = 6x - 6 = 6(9) - 6 = 54 - 6 = 48°
Aisha wants to paint the wall of the room. She knows that each can of the paint contain one gallon. A half gallon will completetly cover a 55 square feet of wall. Each of the four wall of the room is 10 feet high. Two of the walls are 10 feet wide and two of the walls are 15 ft wide. How many one gallons buckets of paint does aisha need to buyin order to paint the room ?
Answers
Answer:
It doesn't say what to do with that 0.1 of a gallon. I would buy another gallon or dilute what I had so it came to exactly 9.1 gallons. In math, I suppose the answer is 9.
In reality it would be 10.
You have to choose. What has been done with other questions like this.
Step-by-step explanation:
1 can covers 55 square feet.
h = 10
w1 = 10 feet
w2 = 10 feet
w3 = 15 feet
w4 = 15 feet
Total area = Area of wall 1 + wall 2 + wall 3 + wall 4
Total area = 10*10 + 10*10 + 10*15 + 10* 15
Total area = 100 + 100 + 150 + 150
Total area = 500 feet^2
1 gallon / 55 ft^2 = x / 500 ft^2 Cross multiply
55 * x = 500 Divide by 55
x = 500/55
x = 9.1 gallons.
In real life you would buy another gallon.
What is the percentage change from 305 to 395
Answers
Answer:
29.51%
Step-by-step explanation:
The change from 305 to 395 is the difference between the two numbers. So, it would be 395 - 305 or 90. Now, to find the percentage of change, we need to find what part of the original amount is the change. In other words, we would have to divide 90 by 305. By putting this in a calculator you get about 0.2951. To convert this decimal into a percent, we would multiply by 100 giving us 29.51%.
1. How much interest
will Hannah earn in 4 years if she
deposits $630 in a savings account at
6.5% simple interest?
Answers
Answer:
$163.8 more.
Step-by-step explanation:
Let's use the formula Principle × Rate × Time, or PRT to find our simple interest. Let's fill in the blanks. Our principle is $630. Our rate is 6.5% and our time is 4 years. Next, we multiply all this. $630 × 13/200 × 4. Our answer would be 163.8. I hoped this helped.
How tall are redwood trees? ( statistical not statistical
Answers
Answer:
It's a statistical question.
and there between 250-300 feet.
Please help me with question 5!!!!!!!!!
Answers
Answer:
a)2,3,4,5,6
b)-3,-1,1,3,5
Step-by-step explanation:
a) y(-2)=-2+4=2
y(-1)=-1+4=3
y(0)=0+4=4
y(1)=1+4=5
y(2)=2+4=6
b)y=2x+1
y(-2)=2*(-2)+1=-3
y(-1)=2*(-1)+1=-1
y(0)=2*0+1=1
y(1)=2*1+1=3
y(2)=2*2+1=5
y: 2* 3* 4* 5* 6*
x: -2 -1 0 1 2
y: -3* -1* 1* 3* 5*
an elevator in a tall building goes up 7 floors, then down 9 floors, down 4 floors, up 8 floors, anddown 2 floors. now it is on floor 14 on what floor did the elevator start
Answers
Answer:
It started on the same floor, floor 14
Step-by-step explanation:
if it went up 7 then down 9, so negative 2 kinda, then down another 4, so negative 6, then up 8 so positive 2, then down 2, it would've started on floor 14
Answer:
14
Step-by-step explanation:
Let the floor started be 'x'
Equation:-
=> x + 7 - 9 - 4 + 8 - 2= 14
x + (+7) + (-9) + (-4) + (+8) + (-2) = 14
x + 7 - 9 - 4 + 8 - 2 = 14
x + 15 - 15 = 14
x = 14
Therefore, elevator started from 14th level.
If the average annual CPI of a career goes from 124.0 to 130.7 what is the inflation rate (don't forget to put % in your answer).
Answers
Answer:
(new-old)/old * 100%
130.7-124/124 = .054 = 5.4%
Step-by-step explanation:
We can calculate the volume V of a rectangular prism using V = lwh, where l is the length, w is the width, and h is the height of the
prism. Suppose that a prism has a volume of 200 cm and l = 2w.
a. Select all of the equations that rewrite the volume formula by making substitutions for V and l.
200 = 2w²h
200 = 4wh
V = 22
2w xwxh = 200
Answers
Answer:
Step-by-step explanation:
200=2w²h
The equations are -
200 = 2[tex]w^{2}[/tex]h
2w x w x h = 200
We have a prism and the formula to calculate its volume is given.
We have to select all of the equations that rewrite the volume formula by making substitutions for V = 200 cubic centimeter and L = 2w.
What is Prism ?A Prism is a three-dimensional shape, which consists of two identical polygons, which do not lie in the same axis.
According to the question, we have -
Volume of Prism = 200 cubic centimeter
L = 2w
The formula to calculate the volume of prism equals to -
V = Lwh
Substituting values, we get -
200 = 2[tex]w^{2}[/tex]h
or
2w x w x h = 200
Hence, the equations are -
200 = 2[tex]w^{2}[/tex]h
2w x w x h = 200
To solve more questions on prism, visit the link below-
https://brainly.com/question/17619973
#SPJ2
bài 5: rút gọn
(x +1)^2 – (2x + 1)^2
Answers
[tex](x+1)^2-(2x+1)^2=\\\\=(x^2+2\cdot x\cdot1+1^2)-((2x)^2+2\cdot2x\cdot1+1^2)=\\\\=(x^2+2x+1)-(4x^2+4x+1)=\\\\=x^2+2x+1-4x^2-4x-1=\\\\=x^2-4x^2+2x-4x+1-1=\boxed{-3x^2-2x}[/tex]
Are a total of 127 Cars And trucks on a lot. If there. For more than twice the number of trucks, then cars, how many cars and trucks are on the lot?
Answers
Answer:
41 cars and 86 trucks
Step-by-step explanation:
C+T=127
2C+4=T
C+(2C+4)=127
3C+4=127
3C=123
C=41When C=41,
41+T=127
T=127-41
T=86
Im bad at money :/ do please help me
Answers
The third answer
1 quarter, 6 dimes, 1 nickel, 7 pennies
what is the LCM of 4489
Answers
Answer:
plz mark me brainliest
Step-by-step explanation:
thanks for question
can someone help I need help lol
Answers
2^3/3^3=
8/27
Hope helps u
A student’s incorrect attempt to simplify an exponential expression is show in the box
What is his mistake!!!!!
Answers
Answer:
A
Step-by-step explanation:
x^a/x^b=x^(a-b). General rule of exponents
for the math experts again!
Answers
Answer:
985
Step-by-step explanation:
The absolute value of a number is its distance from 0. This means a number would be itself if it was positive and if it was negative it would be its opposite. Since 985 is positive, |985| would just be 985.
blake and josh are both saving money for a new bike. the ratio of blake,s saving to josh saving is 3:1 if they have saved 400$, how much has each boy saved
Answers
Answer:
200 each.
Step-by-step explanation:
400 divided by 2 is 200
Evaluate –3² + (2 – 6)(10).
Answers
Answer:
-49
Step-by-step explanation:
Y=DB-3 solve for d. These equations are still tricky for me.
Answers
then divide both sides by b, this gives (y + 3)/b = d
