Andrea is buying some new shirts and sweaters. She is able to buy 3 shirts and 2 sweaters for $114, or she is able to buy 2 shirts and 4 sweaters for $164. How much does a shirt cost? How much does a sweater cost ?
Answers
Answer:
The cost of a shirt is $16 and the cost of a sweater is $33
Step-by-step explanation:
Let
x -----> the cost of a shirt
y -----> the cost of a sweater
we know that
[tex]3x+2y=114[/tex] -----> equation A
[tex]2x+4y=164[/tex]----> equation B
Solve the system by graphing
Remember that the solution of the system is the intersection point both graphs
The solution is the point (16,33)
see the attached figure
therefore
The cost of a shirt is $16 and the cost of a sweater is $33
Answer:
The cost of each shirt is 16$ and the cost of each sweater is 33$
Solution:
Let us consider “x” as the cost of each shirt and “y” as the cost of each sweater.
From question, Andrea has bought 3 shirts and 2 sweaters for 114$. Hence we form equation as,
3x + 2y = 114 ------ eqn 1
Similarly, Andrea has bought 2 shirts and 4 sweaters for $164. Hence we form equation as,
2x + 4y = 164 ----- eqn 2
By solving equation 1 and equation 2, we get the value of “x” and “y”.
On multiplying equation 1 by 2,we get
6x + 4y = 228 -------- eqn 3
Now solving eqn 2 and eqn 3
6x + 4y = 228
-2x - 4y = -164
4x + 0y = 64
4x = 64
[tex]x = \frac{64}{4}[/tex]
x = 16
Substituting the value of x in eqn 1, we get
3(16) + 2y = 114
48 + 2y = 114
2y = 114 - 48
2y = 66
[tex]y = \frac{66}{2}[/tex]
y = 33
Thus the values of x and y are 16 and 33. So the cost of each shirt is 16$ and the cost of each sweater is 33$
Related Questions
My first number is -2 my fifth number is 26 what’s my third number
Answers
Answer:
Answer:
12
Step-by-step explanation:
28 / 4 = 7
1) -2
2) -2+7=5
3) 5+7=12
4) 12+7=19
5)19+7=26
My first number is -2 my fifth number is 26
My third number is 12
Given :
My first number is -2 my fifth number is 26
Lets assume the given numbers are in arithmetic sequence
First term is -2 and fifth term is 26
[tex]a_1=-2\\a_5=26[/tex]
Formula for nth term is
[tex]a_n=a_1+(n-1)d[/tex]
where d is the difference and n is the number of terms
[tex]a_5=a_1+(5-1)d\\a_5=-2+4d\\26=-2+4d\\26+2=4d\\28=4d\\divide \; by \;4 \\d=7[/tex]
Common difference is 7
First term is -2
second term is [tex]-2+7=5[/tex]
Third term is [tex]5+7=12[/tex]
So , the third number is 12
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Last month haos dog ate 40 cans of dog food in 30 days how many cans hao buy to feed his dog for the next 6 days?
Answers
A company packs boxes at a constant rate of 3/4 of a box every of a box every
1/2 minute. What is the number of boxes per
A company packs boxes at a constant rate of
minute the company packs?
Answers
Answer:
1 1/2 boxes per minute
Step-by-step explanation:
The company packs boxes at a rate of 3/4 of a box every 1/2 minute. By multiplying this rate by the reciprocal of the time (2/1), we find that the company packs 1.5 boxes per minute.
The student's question involves finding out the rate at which a company packs boxes. The company packs boxes at a constant rate of 3/4 of a box every 1/2 minute.
To find how many boxes are packed per minute, we need to adjust the given rate to reflect the number of boxes packed in one full minute. We can do this by dividing the number of boxes (3/4) by the fraction of the minute (1/2) during which they are packed.
Here's a step-by-step explanation:
Multiply the number of boxes by the reciprocal of the time fraction: (3/4) × 2/1.Simplify the result: 3/4 × 2 = 6/4, which reduces to 3/2 or 1.5.Therefore, the company packs 1.5 boxes per minute.
Is the number 4.333..... rational or irrational?
Answers
Answer:
Irrational number
The number 4.333.... is a rational number because it can be expressed as the fraction 13/3. An irrational number, like Pi, cannot be expressed as a fraction of two integers.
Explanation:The number 4.333..... is an example of a rational number. Rational numbers can be expressed as a fraction of two integers, and in this case, 4.333.... can be expressed as 13/3. In contrast, an irrational number cannot be expressed as a fraction of two integers. For example, the number Pi is an irrational number because it can not be accurately expressed as a fraction.
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which property is shown? 4/5+(-4/5)=0
Answers
Answer:
Inverse Property
Step-by-step explanation:
Any number X plus the negative of itself = 0
What is my number?
Clue 1 My number is a multiple of 2 and 7.
Clue 2 My number is less than 100 but greater than 50.
Clue 3 My number is the product of three different prime numbers.
Answers
Answer:
56 is the correct answer
Step-by-step explanation:
50<X<100 it could be 56,70,84,98
56=2*7*5 V
70=2*7*6 X
84=2*7*7 X
98=2*7*8 X
The number that satisfies all the given clues is 84.
Explanation:The number that satisfies all the given clues is 84.
Clue 1: The number is a multiple of 2 and 7. The least common multiple of 2 and 7 is 14. So, any multiple of 14 will be a valid answer.Clue 2: The number is less than 100 but greater than 50. 84 satisfies this condition.Clue 3: The number is the product of three different prime numbers. Prime factorizing 84 gives 2 × 2 × 3 × 7, which are different prime numbers.Therefore, the number that meets all the given clues is 84.
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The amount of money,
A
(
t
)
A(t)
in a savings account that pays 3% interest, compounded quarterly for
t
t
yesrs, when an initial investment of $2000 is made, is given by
A
(
t
)
=
2000
(
1.0075
)
4
t
A(t)=2000(1.0075)4t
.
Answers
good luck man i hate having to do this kind of thing in class
The formula [tex]\(A(t) = 2000(1.0075)^{4t}\)[/tex] represents the amount of money in a savings account with quarterly compounding interest over time.
The formula [tex]\(A(t) = 2000(1.0075)^{4t}\)[/tex] describes the amount of money, [tex]\(A(t)\),[/tex] in a savings account over time, where [tex]\(t\)[/tex] represents the number of years. The initial investment is $2000, and the account earns interest at a rate of 3%, compounded quarterly.
The term [tex]\((1.0075)^{4t}\)[/tex] represents the growth factor of the investment over time.
The base, [tex]\(1.0075\),[/tex] represents the factor by which the investment grows each quarter, considering the 3% annual interest rate.
Since the interest is compounded quarterly, it is raised to the power of [tex]\(4t\)[/tex] to account for the total number of quarters over [tex]\(t\)[/tex] years.
Multiplying the initial investment by this growth factor yields the total amount of money in the account after[tex]\(t\)[/tex]years.
As time increases, the exponential term increases, leading to exponential growth in the account balance.
This formula provides a mathematical model for calculating compound interest and understanding how investments grow over time.
hi i need help please
Answers
last week at the business where you work,you sold 120 items.the business paid $1 per item and sold them for $3 each.what profit did the business make from selling the 120 items?
Answers
Answer:
The business would get 240$
Step-by-step explanation:
120$ is the amount you would of made for the the 120 items. The business gets 3$ per item. 120 x 3 would be 360, subtracted by 120 which is what they give you. The business would end up with 240$, or 2/3rds of the money.
Answer:
240
Step-by-step explanation:
since you get the items for 1 dollar and sell them for 2 you need to subtract 3-1 to get your profit which is 2. since you sold 120 items, multiply 120x2 to get your profit of 240.
What is the solution to the following equation?
|3x - 6| = 10
Answers
Answer:
B
Step-by-step explanation:
1) Set up the following two equations, because of the absolute value:
3x-6=10
3x-6=-10
2) Solve both equations:
3x=16
3x=-4
3) Divide both sides by 3:
x=16/3
x=-4/3
4) Make fractions proper:
x=5 1/3
x=-1 1/3
if y varies direrectly as x and inversely as the square of z. y=52 when x=16 and z=2. find y when x=18 and z=3.
Answers
Answer:
y = 26
Step-by-step explanation:
Given y varies directly as x and inversely as the square of z then the equation relating them is
y = [tex]\frac{kx}{z^2}[/tex] ← k is the constant of variation
To find k use the condition y = 52, x = 16, z = 2
k = [tex]\frac{yz^2}{x}[/tex] = [tex]\frac{52(4)}{16}[/tex] = 13
y = [tex]\frac{13x}{z^2}[/tex] ← equation of variation
When x = 18 and z = 3, then
y = [tex]\frac{13(18)}{9}[/tex] = 26
how do you solve the following equation:
6(3x-5)=21
Answers
Answer:
17/6
2 5/6
Step-by-step explanation:
18x-30=21
18x=51
x=51/18
x=17/6
Sketch and prove the following for the two congruent triangles ∆ABC and ∆DEF.
The medians drawn from vertex A and D are congruent.
Label medians MA and ND ; then △ABM≅△
by reason
Answers
Answer:
See explanation
Step-by-step explanation:
Given: ΔABC ≅ ΔDEF
AM, DN - medians
Prove: AM ≅ DN
Proof:
1. Congruent triangles ABC and DEF have congruent corresponding parts:
AB ≅ DE;BC ≅ EF;∠ABC ≅ ∠DEF.2. BM ≅ MC - definition of the median AM;
3. EN ≅ NF - definition of the median DN;
4. AB ≅ 2BM, EF ≅ 2EN
BM ≅ 1/2 AB,
EN ≅ 1/2 EF,
thus, BM ≅ EN
5. Consider two triangles ABM and DEN. In these triangles \:
AB ≅ DE (see 1));BM ≅ EN (see 4));∠ABM ≅ ∠DEN (see 1).So, ΔABM ≅ ΔDEN by SAS postulate.
6. Congruent triangles ABM and DEN have congruent corresponding sides BM and DN.
9 divided by 4/9 in simplest form
Answers
Answer:
The answer is [tex]\frac{81}{4}[/tex]
Step-by-step explanation:
The formula is: [tex]\frac{a}{b} \div \frac{c}{d} = \frac{ad}{bc}[/tex]
In this case we have: [tex]\frac{9}{1} \div \frac{4}{9} = \frac{9\times 9}{1\times 4} = \frac{81}{4}[/tex]
Since 81 y 4 do not have common divisors. The fraction [tex]\frac{81}{4}[/tex]
is in its simplest form.
Final answer:
9 divided by 4/9 equals 81/4 or 20.25. This is done by multiplying 9 by the reciprocal of 4/9, resulting in 81/4, which is already in simplest form.
Explanation:
To calculate 9 divided by 4/9, we can rewrite the division as a multiplication by the reciprocal of 4/9. Here's the step-by-step explanation:
First, identify the reciprocal of 4/9, which is 9/4.Next, multiply 9 by the reciprocal of 4/9: 9 × (9/4).Perform the multiplication: 9 × 9 = 81 and keep the denominator 4.Now you have the fraction 81/4.Therefore, 9 divided by 4/9 equals 81/4 or 20.25 in decimal form. Since the problem asks for the simplest form, 81/4 is the final answer and cannot be simplified further because 81 and 4 have no common factors other than 1.
how many times does 26 go into 80
Answers
Answer:
80/26 = 3.07
Step-by-step explanation:
Answer: 3 times!
Step-by-step explanation:
80 divided by 26 is 3.07 but you can round it to 3
Please help me idk this
Answers
Answer:
it would be 2.8150
Step-by-step explanation:
since there is a one in the tenths place it rounds down to 0 with makes it 50
-1/4 in decimal form
Answers
Answer:
-0.25
Step-by-step explanation:
During the first year it is in business, another candy company sells
100 times as many boxes as the Cricket Candy Company. How
many boxes are sold by both companies during that first year?
Answers
BRAINLIEST FIRST TO ANSWER! Which property is shown in this example? (8.1+7.9)+5.4=8.1+(7.9+5.4)
Identity/ Commutative/ Associative/ Distributive/
Answers
Answer: Associative
Associative says it doesn't matter what is added or multiplied first, and this question shows this
Hope this helps!
Answer: Associative
Step-by-step explanation:
Sophie and $18 for working 2 1/4 hours how much did she earn per hour
Answers
Answer:
8 dollars per hour
Step-by-step explanation:
2 1/4=2.25
18/2.25=8
(Sorry I read the question wrong at first above answer should be able to help you. I apologize)
Answer:
As of the 2010 census, there were 3,669 people living in Marlboro, New York. Brooklyn, New York, has 681 times as many people. How many more people live in Brooklyn than in Marlboro?
Answers
Answer:
2,494,920
Step-by-step explanation:
We have been given that in 2010 census, there were 3,669 people living in Marlboro, New York. Brooklyn, New York, has 681 times as many people.
[tex]\text{People live in Brooklyn}=681\times 3,669[/tex]
[tex]\text{People live in Brooklyn}=2,498,589[/tex]
Now, we will subtract 3,669 from 2,498,589 to find the number of people more in Brooklyn than Marlboro.
[tex]\text{People more in Brooklyn than Marlboro}=2,498,589-3,669[/tex]
[tex]\text{People more in Brooklyn than Marlboro}=2,494,920[/tex]
Therefore, there are 2,494,920 more people live in Brooklyn than in Marlboro that is 680 times the people in Marlboro.
@ 4x +(2x - 1) = x +5+x-6
Answers
Answer:
I believe the answer is 4 but im not sure because I skipped the @ but I didnt know what it meant
Step-by-step explanation:
4x +(2x - 1) = x +5+x-6
pretend that there is a 1 in front of the bracket
4x+1(2x-1)= x+5+x-6
Mutiply the bracket by 1
(1)(2x)= 2x
(1)(-1)= -1
4x+2x-1=x+x+5-6( combine like terms)
6x-1= 2x-1
move 2x to the other side
sign changes from +2x to -2x
6x-2x-1= 2x-2x-1
4x-1=-1
move -1 to the other side
4x-1+1= -1+1
4x= 0
divide by 4 for both sides to get x by itself
4x/4= 0/4
Cross out 4 and 4, divide by 4 and then becomes 1*1*x= x
x= 0/4
Answer: x= 0
what is the smallest number that rounds to 40
Answers
Answer: 2
Step-by-step explanation:
Answer:35
Step-by-step explanation: the reason this is true is because 5is the smallest number that can round up to ten
Write an exponential growth function and explain the growth pattern it models. Use complete sentences?
Answers
The growth pattern is multiply by two consecutively for every y, when moving from left to right on the x axis
The function which grows or decreases at a constant % growth rate is known as an exponential function, and further discussion can be defined as follows:
This equation can be written as [tex]\bold{ f(x) = a(1 + r)^x\ or\ f(x) = ab^x}[/tex], where [tex]\bold{b = 1 + r}[/tex].These functions were frequently used to represent real-world applications.These bacterial growth & decay, demographic growth or decline, and compound interest.Growth curve modeling is a statistical technique for examining change over time using observational studies.Learn more:
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Gabe Amodeo, a nuclear physicist, needs 30 liters of a 60% acid solution. he currently has a 40% solution and a 70% solution. how many liters of each does he need to make the needed 30 liters of 60% acid solution?
Answers
To make 30 liters of a 60% solution from 40% and 70% solutions, set up two simultaneous linear equations representing volume and concentration; solve them to find the required volumes.
Explanation:To solve the question posed by Gabe, a nuclear physicist, we will need to use the concept of mixtures in Mathematics. The total volume he needs is 30 liters of a 60% acid solution, and he has available 40% and a 70% acid solutions.
The solution to this problem involves setting up two equations, one for the total volume and second for the amount of acid.
Let's denote the volume of the 40% solution by x and the volume of the 70% solution by y. Our first equation based on volume is: x + y = 30 (because total volume needed is 30 liters).
Our second equation represents the fact that the volume times the percentage of acid present (converted to a decimal) for each solution should match up to the total volume times the overall percentage of acid (also converted to a decimal) in the final 60% solution. This gives us: 0.4x + 0.7y = 30*0.6.
Solving these two linear equations simultaneously using methods such as substitution or elimination will give us the value of x and y, which are the required liters of 40% solution and 70% solution respectively.
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Miguel says that to create rectangle F' he reflected rectangle F across the y-axis, dilated the reflection by a scale factor of 3, and translated the dilated figure to the right 2 units.
What mistake did Miguel make in describing the steps of his transformation?
A. He gave the incorrect scale factor.
B. He named the incorrect axis of reflection.
C. He gave the incorrect direction of translation.
D. He gave the incorrect number of units of translation.
Answers
Answer:
A. He gave the incorrect scale factor.
Step-by-step explanation:
The scale factor is the Multiplicative Inverse of 3, which is ⅓:
F → 12 × 6
F' → 4 × 2
This is a genuine statement because according to the graph, each block is worth 2, and ⅓ of 6 is 2, and ⅓ of 12 is 4.
I am delighted to assist you anytime my friend.
Answer:
the answer is A
Step-by-step explanation:
Miguel gave an incorrect scale factor. The shape decreased in size meaning it would have a scale factor under 1 but he put 3 meaning the shape got larger when really it shrunk. This means A is the correct answer
BRAINLIEST!!!!!!!!!!!!!!!
Answers
Answer:
all the ekements of set A lies in set B
Answer: were is the question and how do you put down brainliest
Step-by-step explanation:
Randy's football team had the ball on the zero yard line.On their first play they gained 6 yards.On the second play they lost 4 yards.On what yard line is the ball now?
Answers
Answer:
2 yard line
Step-by-step explanation:
It starts at the 0 yard line then goes up to the 6 yard line
0 + 6 = 6
After, from the 6 yard line they go back 4 yards
6 - 4 = 2
Now they're at the 2 yard line.
is the function even, odd, or neither?
Answers
If the graph is symmetric to the y-axis then it’s even, if the graph is symmetric to the origin it’s odd.
If it doesn’t fit within these then it’s neither.
Rewrite the radical expression with a rational exponent
3✔️ x7.
A. X21
B. X4
C. X 7/3
D. 3/7
Answers
Answer:
[tex]x^{\frac{7}{3} }[/tex]
Step-by-step explanation:
The given expression is
[tex]\sqrt[3]{x^{7} }[/tex]
There's a exponent which relates fractional exponents and roots, that is
[tex]\sqrt[n]{x^{m} } = x^{\frac{m}{n} }[/tex]
So, if we apply this property, the results would be
[tex]\sqrt[3]{x^{7} }=x^{\frac{7}{3} }[/tex]
Therefore, the right answer is the third choice [tex]x^{\frac{7}{3} }[/tex]
Answer:
c
Step-by-step explanation:
i took the test