You go shopping at a local department store with your friend and cousin. You buy one pair of jeans, four pairs of shorts, and two shirts for $84. Your friend buys two pairs of jeans, one pair of shorts, and three shirts for $76. Your cousin buys one pair of jeans, two pairs of shorts, and one shirt for $52. How much does each item cost?
Answer: Cost per pair of jeans = $ 20
Cost per pair of shorts = $12
Cost per shirt = $8
Step-by-step explanation:
Let x= cost per pair of jeans
y = Cost per pair of shorts
z= cost per shirt.
For you, total cost = x+4y+2z= 84
For your friend, total cost = 2x+y+3z=76
For cousin, total cost = x+2y+z= 52
Required system:
[tex]x+4y+2z=84\ (i)\\ 2x+y+3z=76\ (ii)\\ x+2y+z=52\ (iii)[/tex]
from (i), [tex]x=84-4y-2z[/tex] (*)
put this in (ii) and (iii) we get
[tex]2\left(84-4y-2z\right)+y+3z=76\\\Rightarrow\ -7y-z+168=76\ (iv)\\\\ 84-4y-2z+2y+z=52\\\Rightarrow\ -2y-z+84=52 \ (v)[/tex]
from (iv), [tex]y=-\frac{z-92}{7}\ (vi)[/tex]
[tex]\mathrm{Subsititute\:}y=-\frac{z-92}{7}\ \text{in}\ (v)[/tex]
[tex]-2\left(-\frac{z-92}{7}\right)-z+84=52\\\\\Rightarrow\ -2\left(-\frac{z-92}{7}\right)-z=-32\\\\\Rightarrow\ -\frac{5z}{7}-\frac{184}{7}=-32\\\\\Rightarrow\ -5z-184=-224\\\\\Rightarrow\ -5z=-40\\\\\Rightarrow\ z=8[/tex]
[tex]\mathrm{Subsititute\:}z=8\text{ in (vi)}[/tex]
[tex]y=-\frac{8-92}{7}\\\\\Rightarrow \ y=12[/tex]
[tex]\mathrm{Subsititute\:}z=8,\:y=12\text{ in (*)}[/tex]
[tex]x=84-4\cdot \:12-2\cdot \:8\\\\\Rightarrow\ x= 20[/tex]
Hence, x= 20, y= 12 , z=8
So, Cost per pair of jeans = $ 20
Cost per pair of shorts = $12
Cost per shirt = $8
HELP QUICK
Find the y-intercept of the graph of the equation given. Write your answer as an ordered pair.
-5x+2y=10
what is the positive square root of 9/16
Answer: |√9/16| = ¾ or .75
PLz mark brainliest:)
Sue has 18 sweets
Tony also has 18 sweets
sue gives Tony x sweets
Answer:
18 sweets?
Step-by-step explanation:
Not much info to help me answer it
Strip malls appear to popping up everywhere. The relationship between the actual price of a strip mall and the listing price is modeled in the least-squares regression line Ĉ = 0.2 + 1.011. Both amounts are in hundred-thousands of dollars. Let L represent the listing price and C represent the sales price. Which of the following is the best interpretation of the slope of the regression line?
A)For each hundred-thousand-dollar increase in the listing price, the sales price will increase by $1.01.
B)For each hundred-thousand-dollar increase in the listing price, the sales price will increase by $101,000,
C)For each hundred-thousand-dollar increase in the listing price, the sales price will decrease by $101,000.
D)For each hundred-thousand-dollar increase in the listing price, the sales price is predicted to increase by $1.01.
E)For each hundred-thousand dollar increase in the listing price, the sales price is predicted to increase by $101,000.
Answer:
The correct option is;
E) For each hundred-thousand dollar increase in the listing price, the sales price is predicted to increase by $101,000
Step-by-step explanation:
Whereby the relationship between the actual price of a strip mall and the listing price is modeled according to the least squares regression line as follows;
C = 0.2 + 1.01·L
Where;
L = The listing price
C = The sales price
Where both amounts are in hundred-thousands of dollars;
Therefore, given that the slope is 1.01, we have that for an increase of $100,000 for the listing price, L, which is 1 unit increase the sale price increases as follows
C₁ = 0.2 + 1.01 × 1 = 1.21
While for an increase of an extra $100,000, to make the listing price. $200,000 or 2 units, we have;
C₂ = 0.2 + 1.01 × 2 = 2.22
The increase is C₂ - C₁ = 2.22 - 1.21 = 1.01
C₂ - C₁ = $100,000 × 1.01 = $101,000
The increase is C = $101,000
Whereby, the equation is a linear regression line which is a model for prediction, we have;
The predicted increase in the sale price is $101,000 for each $100,000 increase in the listing price.
Evaluate 5 + (-4) + (-7) +2
Answer:
5+(-4)+(-7)+2
5-4-7+2
5-11+2
5+2-11
7-11
-4
Don Luis, el carpintero, desea construir un mueble para estantería, el cual es in- dispensable que tenga dos áreas cuadradas, donde el cuadrado mayor mida por lado, una unidad menor que el doble del largo del cuadrado menor. El área total del mueble será de 121 pies cuadrados.
Answer:
El área de un cuadrado de lado L es:
A = L*L
Y sabemos que si el cuadrado menor tiene lado de largo L, entonces el cuadrado mayor tiene lado de largo 2*L - 1ft
Área menor = L*L = L^2
Área mayor = (2L - 1ft)*(2L - 1ft)
El área total es igual a la suma de ambas áreas:
121 ft^2 = L^2 + (2L - 1ft)*(2L - 1ft) = L^2 + 4*L^2 - 2ft*L + 1ft^2
Ahora podemos resolver esto para L.
121 ft^2 = 5*L^2 - 2ft*L + 1ft^2
0 = 5*L^2 - 2ft*L - 120 ft^2.
Usando la formula de Bhaskara, las soluciones son:
[tex]L = \frac{2ft +- \sqrt{(2ft)^2 - 4*5*(-120ft^2)} }{2*5} = \frac{2ft +- 49ft}{10}[/tex]
Las dos soluciones son:
L = (2ft + 49ft)/10 = 51ft/10 = 5.1ft
L = (2ft - 49ft)/10 = -4.7 ft
Como estamos hablando de el largo de algo, la única opción que tiene sentido es la positiva.
Entonces el largo de los lados del cuadrado menor es L = 5.1 ft
El largo de los lados del cuadrado mayor es M = 2*5.1ft - 1ft = 9.2ft
what is 5 divided 1/3
Answer:
15
Step-by-step explanation:
basic math.
Answer:
its 15 i believe
Step-by-step explanation:
Is each pair of equations equivalent? explain.
4y+2x=-7
2y-6x=8
What is the slope of 1.5x+4.5y=18 ,and how do you know?
Answer:
m=-1/3
Step-by-step explanation:
The slope of this line is m=-1/3 because if you use the slope-intercept formula, y=mx+b, m is the slope. If you take this equation and plot two points on a line that has this equation, the slope will be negative if the line forms an obtuse angle on the 0 line. In this case, m=-1/3 as the line goes back 1/3 unit for every unit in this equation. Hope it helps!
Answer: the slope is -0.33... The does means that 3 is repeating.
Step-by-step explanation:
First we will convert the equation into slope intercept form, which is the same way of solving for y in the equation.
1.5x + 4.5y = 18 Solve for y by first subtracting 1.5x from both sides
-1.5x -1.5x
4.5y = 18 - 1.5x Now divide both sides by 4.5
y= 4- 0.33x
y= -0.33x + 4 Now the slope is the coefficient of the variable x which is the number that comes after the variable.
In this case, the slope is -0.33...
Who was Genghis Khan and how did he and
his Mongol armies impact Japan?
Answer:
Genghis Khan, the leader of the Mongolian army, began his campaign to take over the known world in 1206 CE. Within 50 years, Genghis Khan and his ferocious mounted warriors had extended their Mongolian empire throughout China and Korea in the east and as far as Poland and Russia in the west. After awhile, lost power as many warlords fell into bankruptcy.
Which equation represents the graphed function?
–3x + 2 = y
–x + 2 = y
x – 3 = y
2x – 3 = y
Answer:
-x-3 = y
Step-by-step explanation:
Taylor bought a necklace for each of her three sisters. She paid $7.50 for each necklace. Supposed she had $9 left. How much money did she have initially to spend on each sister?
Answer:31.50$
Step-by-step explanation:
what is the inverse of the function f(x) = 2x+ 1?
A. h(x) = 1/2x -1/2
B. h(x) = 1/2x + 1/2
C. h(x) = 1/2x - 2
D. h(x) = 1/2x + 2
[tex]f(x) = 2x + 1[/tex]
[tex]y = 2x + 1[/tex]
Subtract sides -1
[tex]y - 1 = 2x + 1 - 1[/tex]
[tex]y - 1 = 2x[/tex]
[tex]2x = y - 1[/tex]
Divided sides 2
[tex] \frac{2}{2}x = \frac{y - 1}{2} \\ [/tex]
[tex]x = \frac{1}{2}y - \frac{1}{2} \\ [/tex]
Thus ;
[tex] {f}^{ - 1} = h(x) = \frac{1}{2}x - \frac{1}{2} \\ [/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
So the correct answer is (( A )) .
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Dominic bought a new video game that was on sale for 35% off. If the original price is 29.95, what will the amount be that Dominic pays?
Answer:
19.47
Step-by-step explanation:
Sandy evaluated the expression below.
(-2) (6-3)-5(2+3)
(-2) (3) -5(5)
8(3) - 25
24-25
-1
What was Sandy's error?
Sandy should have evaluated (-2) as-8.
O Sandy should have not multiplied 5 and 5.
O Sandy did not add 2 and 3 correctly.
O Sandy should have not subtracted 3 from 6 first
Answer:
answer A
Step-by-step explanation:
i got it right on the test
solve the equation. check your solution 6(5-2v)=-4(3v+1)
2.7.4 practice on Apex in GEOMETRY
REALLY CONFUSED!
The 2.7.4 practice on Apex in geometry focuses on the Pythagorean theorem and its applications. Students are assessed on their ability to apply the theorem to solve problems involving distances, heights, and lengths in right triangles.
The concept of 2.7.4 practice on Apex in geometry is a crucial topic that students must understand to excel in the subject. Geometry is the study of shapes, sizes, positions, and angles of objects and figures in space. The 2.7.4 practice on Apex in geometry mainly focuses on the Pythagorean theorem and its applications.
The Pythagorean theorem is a mathematical formula that is used to calculate the length of a right triangle's hypotenuse. It states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
The Pythagorean theorem is one of the most fundamental concepts in geometry, and it is essential to understand how to apply it in problem-solving. The 2.7.4 practice on Apex in geometry provides students with an opportunity to test their understanding of the Pythagorean theorem.
Students are expected to apply this theorem to solve problems related to distance, height, and length. The practice tests are designed to assess students' ability to use the Pythagorean theorem to calculate the length of the hypotenuse in a right triangle.
For more questions on Pythagorean theorem
https://brainly.com/question/343682
#SPJ8
2x + 7 = - 4x + 11
what’s the answer?
Answer:x=2/3
Step-by-step explanation:
(16,3) ,(16,-80) is it zero slope undefind slope negative slope or positive slop
Help me plz!!!!!!!!!!!!!!!
Answer:
$2.40
Step-by-step explanation:
sales tax = 30 * .08 = $2.40
Someone please help me
PLEASE HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
How many yards are there in 2.00 feet? (3 ft = 1 yd)
Answer: .667 yard
Step-by-step explanation:
Hope this helps
Answer:
0.66666666667 Yards
Step-by-step explanation:
google is always right
PLEASE HELP it’s literally easy
Answer:
it would be 4 right (the last one)
Step-by-step explanation:
PLEASE HELP.!! ILL GIVE BRAINLIEST *EXTRA POINTS* DONT SKIP.!! :((
-59, -41, -23, -11.
I can see how this can be confusing, Just remember if its a negative number, the bigger it is, the smaller the quantity, if that makes sense.
HELP I NEED THIS RIGHT KNOW!!!!!!!
Explain what
m(4)=90 means in context. (1pts)
Answer:
[tex]m(4)=90 \\ m = \frac{90}{4} \\ m = 22.5[/tex]
Evaluate 1/3 x 5/6.
A. 1/15
B. 6/15
C. 5/18
D. 3/30
Answer:
C
Step-by-step explanation:
1x5=5
3x6=18
and you can't simplify 5/18.
Answer:
5/18
Step-by-step explanation:
1 times 5 equals 5. 3 times 6 equals 18.
10 : 35 fraction in simplest from
What is 10/35 Simplified? - 2/7 is the simplified fraction for 10/35.
-BBBM
What is the greatest four-digit multiple of 18?
Please help me
Answer:
9990.
Step-by-step explanation: