You are ordering shirts for the math club at your school. Short-sleeved shirts cost $10 each. Long-sleeved shirts cost $12 each. You have a budget of $300 for the shirts. The equation $10x+12y=300$ models the total cost, where $x$ is the number of short-sleeved shirts and $y$ is the number of long-sleeved shirts. a. Graph the equation. Interpret the intercepts
Answers
Answer:
a. i) Please see the included graph of the equation $10·x + $12·y = $300
ii) The intercepts give the maximum number of either short-sleeve (x-intercept) long-sleeved (y-intercept) that can be ordered
Step-by-step explanation:
The given information are;
The cost of each short-sleeved shirt = $10
The cost of each long-sleeved shirt = $12
The amount available in the budget = $300
The equation for the total cost = $10·x + $12·y = $300
Where;
x = The number of short-sleeved shirts
y = The number of long-sleeved shirts
Rewriting the equation given in slope and intercept form, we have;
$10·x + $12·y = $300
$12·y = $300 - $10·x
y = $300/$12 - $10·x/$12
y = 25 - 5/6·x
Please find attached, the graph of the equation made with Microsoft Excel
The values of the data that can calculated to plot the graph are;
x, y
(0, 25 )
(5, 20.83 )
(10, 16.67)
(15, 12.5 )
(20, 8.33)
(25, 4.17)
(30, 0 )
The x-intercept gives the number of short-sleeve shirts that can be purchased with the $300 available budget, while the y-intercept gives the number of short-sleeve shirts that can be purchased with the $300 available budget.
The graph of the equation is shown below.
The x-intercept is at point (30,0), which means the number of short-sleeved shirts is 30 when the number of long-sleeved shirts is 0.
The y-intercept is at point (0,25), which means the number of long-sleeved shirts is 25 when the number of short-sleeved shirts is 0.
Given:
Short-sleeved shirts cost $10 each.
Long-sleeved shirts cost $12 each.
The total budget is $300.
The given equation is:
[tex]10x+12y=300[/tex]
where [tex]x[/tex] is the number of short-sleeved shirts and [tex]y[/tex] is the number of long-sleeved shirts.
To find:
The graph of the given equation and the interpretation for the intercepts.
Explanation:
We have,
[tex]10x+12y=300[/tex]
Substitute [tex]x=0[/tex].
[tex]10(0)+12y=300[/tex]
[tex]12y=300[/tex]
[tex]y=\dfrac{300}{12}[/tex]
[tex]y=25[/tex]
So, the y-intercept is at point (0,25).
Substitute [tex]y=0[/tex].
[tex]10x+12(0)=300[/tex]
[tex]10x=300[/tex]
[tex]x=\dfrac{300}{10}[/tex]
[tex]x=30[/tex]
So, the x-intercept is at point (30,0).
Plot the points (30,0) and (0,25) on a coordinate plane and connect them by a straight line.
The x-intercept is at point (30,0), which means the number of short-sleeved shirts is 30 when the number of long-sleeved shirts is 0.
The y-intercept is at point (0,25), which means the number of long-sleeved shirts is 25 when the number of short-sleeved shirts is 0.
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Related Questions
Which of the following sets represents a function?
O [(1, 2), (3, 2), (5, 7))
O [(3,5),(-1,7), (3,9)}
O [(1, 2), (1,4), (1, 6)
Answers
Answer:
(1, 2), (1,4), (1, 6)
Step-by-step explanation:
They're adding the Y-axis
Kiran sells f full boxes and h half-boxes of fruit to raise money for a band trip. He earns $5 for each full box and $2 for each half-box of fruit he sells and earns a total of $100 toward the cost of his band trip. The equation 5f+2h=100 describes this relationship. Solve the equation for f.
Answers
Answer:
f = (100 - 2h) / 5
Step-by-step explanation:
Given:
5f + 2h = 100
Solve the equation for f.
5f + 2h = 100
Subtract 2h from both sides
5f + 2h - 2h = 100 - 2h
5f = 100 - 2h
Divide both sides by 5
5f / 5 = (100 - 2h) / 5
f = (100 - 2h) / 5
If f = 1 full box
h = 1/2 box
h = 1/2 of f
h = 1/2f
Substitute h = 1/2f into
f = (100 - 2h) / 5
f = {100 - 2(1/2f)} / 5
f = (100 - 2/2f) / 5
5f = 100 - f
5f + f = 100
6f = 100
f = 100 / 6
= 16.67
f = 16.67
The required value of f is 16.67.
Given that ;
Kiran sells full box of fruit cost for each box = f = $5
And Kiran sells half box of fruit cost for each = h = $2
According to the question ;
For full box cost + for half box cost = Total cost of his band trip
5f + 2h = 100
Solve the equation following equation for f .
5f + 2h = 100
Subtract 2h from both sides
5f + 2h - 2h = 100 - 2h
5f = 100 - 2h
Divide both sides by 5
[tex]\frac{5f}{5} = \frac{100}{5} - \frac{2h}{5}[/tex]
f = 20-2h
For full box f = 1 full box
For half box h = 1 half box
It means h = [tex]\frac{1}{2}[/tex] of f
h = [tex]\frac{1}{2}f[/tex]
Substitute the value of h
[tex]f = \frac{(100-2h)}{5} \\f = \frac{100-2(\frac{1}{2f} )}{5}[/tex]
[tex]f = \frac{100-f}{5}[/tex]
5f = 100 - f
5f + f = 100
6f = 100
[tex]f = \frac{100}{6}[/tex]
f = 16.67
The required value of f is 16.67.
For more details about the making equation click the link given below.
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I need help please, can you help me?
Answers
Answer:
x= 16 degrees
Step-by-step explanation:
the angles can be a little hard to remember but just know that the angles that are outside of the transversal are exterior angles and if they are on the opposite sides of the line that passes through the parallel lines then they're alternate exterior angles and those angles that are inside are interior angles and if they are on the opposite sides of the line passing through the parallel then they are alternate interior angles .
M= 1/2
M= 2
M= -1/2
M=-2
Answers
Answer:
It should be 1/2
Step-by-step explanation:
On a coordinate plane, a line is drawn between points (negative 4, negative 3) and (negative 1, 4).
Use the Pythagorean theorem to find the distance on the coordinate plane.
a2 + b2 = c2
What is the distance between the two points?
StartRoot 20 EndRoot
StartRoot 40 EndRoot
StartRoot 45 EndRoot
StartRoot 58 EndRoot
Answers
Answer:
StartRoot 58 EndRoot
Step-by-step explanation:
Given the coordinates (-4, -3) and (-1, 4)
To get the distance between the two points, we will use the formula:
D =√(y2-y1)²+(x2-x1)²
From the coordinates, x1 = -4, y1 = -3, x2 = -1 and y2 = 4
Substitute
D =√(4-(-3))²+(-1-(-4))²
D = √(4+3)²+(-1+4)²
D = √7²+3²
D = √49+9
D = √58
Hence the correct option is D
StartRoot 58 EndRoot
Answer:
D. 58
Step-by-step explanation:
A quarterback dropped back 5 yards behind the lone of scrimmage. Then, he passed the ball 14 yards. How far past the line of scrimmage did the ball travel? (Write an equation to represent this problem)
Answers
Answer:
9 yards
Step-by-step explanation:
-5 + 14 = 9
Multi-step Equations
5) 5n + 34 = -2(1 - 7n)
Answers
Distribute -2 so -2(1 - 7n) = -2 + 14n
Add 2 to each side 5n + 36 = 14n
Subtract 5n from each side 36 = 9n
Divide each side by 9 so 4 = n
Answer:
4
Step-by-step explanation:
if you do all the steps right you should get 4
What is an equation that is equivalent to -3/4x+1/8=-3/8?
Also the / is not a division symbol. The numbers with a / are fractions.
Answers
Hope this helps! Follow my Instagram trlamb822!
What’s 19,975 divided by 25 show your work
Answers
the answer to the question is 799
helpp ill mark u as brainlist
Answers
Answer:
Assuming you want slope formula for this, it's y= (5/9)x -1
Which of the q-values satisfy the following inequality?
6-3q≤1
Answers
Answer:
[tex]q\ge \frac{5}{3}\\\\q\geq 1\frac{2}{3}[/tex]
Step-by-step explanation:
[tex]6-3q\leq 1\\\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\\\6-3q-6\le \:1-6\\\\Simplify\\\\-3q\le \:-5\\\\\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\\\\\left(-3q\right)\left(-1\right)\ge \left(-5\right)\left(-1\right)\\\\Simplify\\\\3q\ge \:5\\\\\mathrm{Divide\:both\:sides\:by\:}3\\\\\frac{3q}{3}\ge \frac{5}{3}\\\\Simplify\\\\q\ge \frac{5}{3}\\\\q\geq 1\frac{2}{3}[/tex]
any luck of help? I'll brainlist uu promise . I really need it for correction :)
Answers
Answer:
the cist of entry for x adults
Answer:
i think it would be d)
Step-by-step explanation:
cuz like, it says to write an expression. for an expression, most of the time you need more than one like number and variable
hope this helped :)
Which best represents the change in the vertices of rectangle ABCD to form rectangle A'B'C'D'?
F) (x, y ) → (2x, 2y)
G) (x, y ) → (1.5x, 1.5y)
H) (x, y ) → (3x, 3y)
J) (x, y ) → (4x, 4y)
Answers
Answer:
F
Step-by-step explanation:
Two uniformly charged, infinite, nonconducting planes are parallel to a yz plane and positioned at x " #50 cm and x " )50 cm. The charge densities on the planes are #50nC/m2 and )25 nC/m2 , respectively. What is the magnitude of the potential difference between the origin and the point on the x axis at x " )80 cm? (Hint: Use Gauss’ law.)
Answers
Two uniformly charged, infinite, nonconducting planes are parallel to a yz plane and positioned at x = -50 cm and x = +50 cm. The charge densities on the planes are -50 nC/m² and +25 nC/m², respectively. What is the magnitude of the potential difference between the origin and the point on the x axis at x = +80 cm? (Hint:Use Gauss’ law.)
Answer:
ΔV = 2520 V
Step-by-step explanation:
We are given;
Charge density 1; σ1 = -50 nC/m² = -50 × 10^(-9) nC/m²
Charge density 2; σ2 = +25 nC/m² = +25 × 10^(-9) nC/m²
Now, formula for electric field strength is;
E = -(½ε)(|σ1| ± |σ2|)
ε is vacuum permittivity with a constant value as 8.85 × 10^(−12) C²/N.m²
|σ1| and |σ2| means we are taking the absolute values and would therefore not use the negative sign attached to them.
Now, in between x = 0 cm(0 m) and 50 cm (0.5 m), electric field generated by both charge densities would be in the same direction and thus;
E_in = -(½ε)(|σ1| + |σ2|)
E_in = -(½ × 8.85 × 10^(−12)) × [(50 × 10^(-9)) + (25 × 10^(-9))]
E_in = -4200 V/m
In contrast, when x ≥ 50 cm (0.5 m), electric field generated by both charge densities would be in opposite directions and thus;
E_out = -(½ε)(|σ1| - |σ2|)
E_out = -(½ × 8.85 × 10^(−12)) × [(50 × 10^(-9)) - (25 × 10^(-9))]
E_out = 1400 V/m
The magnitude of the potential difference from the origin to x = 80 cm(0.8 m) is calculated as attached;
From the attachment, we see that;
ΔV = 2520 V
I do not understand this
Answers
Answer:
It would be C. The hexagon.
Answer:It would be C because you have 3 sides for the triangle than 4 sides for the rectangle, 5 sides for the pentagon, and 6 sides for the hexagon
Step-by-step explanation:
what is the value of the expression 12 - k
if k = (-3)
Answers
Answer:
15
Step-by-step explanation:
12-k
12- (-3)
12+3
=15
Answer:
15
Step-by-step explanation:
Substitute the variable, "k" into "12-k" from the equation "k=(-3).
12-k
12-(-3)
12+3---> two negatives make a positive
15
Alonso plans to buy a new kayak that costs $2,100. But he needs to pay a 8.5% tax. What is the total cost of the kayak?
Answers
Answer:
$ 2,273.25
Step-by-step explanation:
Is this graph of a function yes or no
Answers
Answer: It could be, just add two dots at the smiley face, BOOM! The function of Facial muscles in humans.
Step-by-step explanation:
what percentage is equal to 32/100
Answers
Answer:
32%
Step-by-step explanation:
32/100 is 32%
{(5²)} ³×5⁴}÷5⁷ simplify and express the following as exponent
Answers
Answer:
The answer is 5³.
Step-by-step explanation:
You have to apply Indices Law :
[tex] {a}^{m} \times {a}^{n} ⇒ {a}^{m + n} [/tex]
[tex] {a}^{m} \div {a}^{n}⇒ {a}^{m - n} [/tex]
[tex] { ({a}^{m} )}^{n} = {a}^{mn} [/tex]
So for this question :
[tex]( {( {5}^{2}) }^{3} \times {5}^{4} ) \div {5}^{7} [/tex]
[tex] = ( {5}^{6} \times {5}^{4} ) \div {5}^{7} [/tex]
[tex] = {5}^{10} \div {5}^{7} [/tex]
[tex] = {5}^{3} [/tex]
Help me please.
Write a ratio expressing the slope of the line passing through (5,7) and (-3,-2).
Answers
Answer:
9/8
Step-by-step explanation:
change in y/change in x= slope
so in this case -9/-8 or 9/8 bc the negatives cancel out
Lily drew 37 hearts and 36 circles. What is the ratio of hearts to circles?
Simplify your answer if possible.
Answers
Answer:
37: 36
Step-by-step explanation:
You can not simplify. Have a good day!
help me with this please
Answers
Answer:
26
Step-by-step explanation:
square root of 81 is 9, 9*2 is 18, square root of 64 is 8, 18+8 is 26
Answer:
26
Step-by-step explanation:
2(square root of 81)+square root of 64
2(9)+8=
18+8=
26
8. What is the result of (11x + 18i)(117 - 18i)?
Answers
Ryan and two of his friends contribute $8.33 each, to buy a baseball bat from a sports shop. Find
the price of the baseball bat.
Answers
Answer:
24.99
Step-by-step explanation:
Evaluate the expression when c=5 and d=6.
7c+d.
Answers
Answer:
41
Step-by-step explanation:
Step 1:
7c + d Equation
Step 2:
7 ( 5 ) + 6 Input c and d
Step 3:
35 + 6 Multiply
Answer:
41 Add
Hope This Helps :)
C=5 & D=6
so u would when they ask 7C+D u have to add parentheses for the numbers that are getting plugged in
7(5) + (6) = 41
Riley buys a swim pass for the pool in January. The first month costs $30. Each month after that, the cost is $20 per month.
Write the equation for finding the total cost of
a one-year swim pass.
Answers
Answer:
you pay 240 dollars a year
Step-by-step explanation:
y=20x
x is 12
20*12=
240
Answer: $250
Step-by-step explanation:
$3,000 is invested in an account paying 4% interest and twice that amount is invested at 6%.
Which of the following expressions represents the amount of interest earned on the money invested at 6%?
a. 2(3,000)
b. 0.06(6,000)
c. 0.06(3,000)
Answers
Answer:
B
Step-by-step explanation:
can you guys please help
Answers
Answer:
I cant read all of that. Im sure others ant either.
Step-by-step explanation:
Answer:
i cant read it for some reason, can you type it?
Step-by-step explanation:
Write the word sentence as an equation. Then solve.
The difference between a number pand 6 is -14
Equation
Solution p=
25
Answers
Answer:
p - 6 = -14
p = -8
Step-by-step explanation:
The difference between a number p and 6 is -14
Let the number = p;
Equation:
difference between the numbers:
p - 6
equality;
p - 6 = -14
Equation; p - 6 = -14
Solution:
p - 6 = -14
add (+6) to both sides of the expression;
p - 6 + (+6) = -14 +(+6)
p = -8