Lia must work at least 5 hours per week in her family’s restaurant for $8 per hour. She also does yard work for $12 per hour. Lia’s parents allow her to work a maximum of 15 hours per week overall. Lia’s goal is to earn at least $120 per week. Write a system of inequalities to represent this situation. Let r be the number of hours worked at the restaurant, and let y be the number of hours of yard work. Graph the inequalities. What is the maximum number of hours Lia can work at the restaurant and still meet her earnings goal? Explain. What is the maximum amount of money Lia can earn in 1 week? Explain.
Answers
Answer:
(a)
[tex]r\geq 5[/tex]
[tex]r+y\leq 15[/tex]
[tex]8r+12y\geq 120[/tex]
[tex]y\geq 0[/tex]
(c)Maximum number of hours Lia can work at the restaurant and still meet her earnings goal = 15 hours
(d)Maximum Earning = $160
Step-by-step explanation:
Let r be the number of hours worked at the restaurant.
Let y be the number of hours of yard work,
Lia must work at least 5 hours per week in her family’s restaurant for $8 per hour.
[tex]r\geq 5[/tex]
Since she does yard work, [tex]y\geq 0[/tex]
Lia’s parents allow her to work a maximum of 15 hours per week overall.
[tex]r+y\leq 15[/tex]
Lia’s goal is to earn at least $120 per week.
The restaurant, r pays $8 per hour
Yard work, y pays $12 per hour.
Therefore:
[tex]8r+12y\geq 120[/tex]
The system of inequalities that represent this problem is therefore:
[tex]r\geq 5[/tex]
[tex]r+y\leq 15[/tex]
[tex]8r+12y\geq 120[/tex]
[tex]y\geq 0[/tex]
(b)The graph of the inequality is attached below
(c)When the graph is plotted, the vertices of the feasible region are:
(5,10)(5, 6.7)(15,0)Where the first term is for the number of hours worked in the restaurant.
The maximum value of r possible is 15 from the three points.
Therefore, she can work at the restaurant for 15 hours and still meet her earning goal.
(d)Maximum Amount Lia can earn in 1 Week
At (5,10), Earning=(5X8)+(10X12)=40+120=$160At (5, 6.7), Earning=(5X8)+(6.7X12)=40+80.4=$120.4At (15,0) Earning=(15X8)+(0X12)=$120Since she has to work at least 5 hours at the restaurant, the maximum amount possible is $160.
Related Questions
what is the value of k?
Answers
Answer: k = 10
Step-by-step explanation:
mLXYZ = 180 - 115 = 65° (angles in a straight line)
65 + (4k+5) + (6k+10) = 180
65+4k + 5 + 6k + 10 = 180
10k = 180 - 80
k = 100 / 10 = 10
Circumference of circles
Answers
Answer:
The circumference formula is 2πr and we know r = 1 so the answer is 2π.
Answer: 6.28 feet
Step-by-step explanation:
The formula for circumference is C= πd Diameter is radius times two. So use a value of π which is usually 3.14 or 3.1416 for practical purposes. Multiply by the diameter. 3.14×2=6.28.
Important!!!
That is the distance between (-5, 4) and (-1, 4)?
-5 units
-4 units
4 units
5 units
Answers
Answer:
4 units
Step-by-step explanation:
Since the y value is the same, we only have to look at the x value
-1 - -5
-1 +5
4
The distance is 4 units
Answer:
4 units
Step-by-step explanation:
if you graph these 2 points, they'll be on the same line of the graph separated by 4 units
2x + 3y = 13
4x - y = -2
Answers
Answer:
x=1/2. y=4
Step-by-step explanation:
4(2x+3y=13)=8x+12y=52
2(4x-y=-2)=8x-2y=-4
subtract equation one from equation two to get
14y=56 then u will divide bothe sides by 14. for x u substitute y in equation one
Answer:
x = 1/2 y = 4
Step-by-step explanation:
Equation 1
2x + 3y = 13
Equation 2
4x - y = -2
Multiply equation 2 by 3
12x - 3y = -6
Add equation 1 to 3
14x = 7
x = 7/14
x = 1/2
Substitute x into equation 1
2(1/2) + 3y = 13
3y = 13 -1
3y = 12
y= 12/3
y = 4
x =1/2 y = 4
Hope this helps.
What is the value of X in the given right triangle? WILL GIVE BRAINLIEST!
Answers
Answer:
Please mark me brainliest and I hope this helped!
x = 45
Step-by-step explanation:
In this case, we can use the Pythagorean Theorem to figure out the other side of the triangle.
c squared - a squared = b squared
10 squared - 7 squared = b squared
100 - 49 = b squared
51 = b squared
7.14 = b
Now that we know the other side is about 7, we can assume that x is equal to the angle between 10 and 7. So x equals 45.
Which graph shows the line y = 2x + 3?
Answers
Answer: Graph D
Step-by-step explanation:
The slope is 2
x goes after the slope in graph functions
The line goes through 3 on the y-axis so that’s where + 3 comes in.
2x + 3
m 1 = a) 40 b) 130 c) 50
Answers
Answer:
A) 40
Step-by-step explanation:
The angle adjacent 40 is complementary to it, meaning that it must have a measure of 90-40=50 degrees. This angle is a vertical angle with the one inside the triangle, meaning that it also has an angle of 50 degrees. Now that you know two of the angles in the triangle and you know that all of the interior angles of a triangle add up to 180 degrees, you can find angle 1:
[tex]\angle 1=180-90-50=40^{\circ}[/tex]
Hope this helps!
Answer:
<1 = 40
Step-by-step explanation:
Corresponding angles are equal and <1 and 40 are corresponding angles on parallel lines
Anybody know this ? Please help :(
Answers
Answer:
D
Step-by-step explanation:
5.50. 5.50+0.25= 5.75, 5.75+0.25= 6.00, 6.00+0.25= 6.25, 6.25+0.25= 6.50
Option D is the answer:
5.50, 5.75, 6.00, 6.25, 6.50...
HELP ASAP What is the explicit formula for this sequence 5,2,-1,-4
Answers
Answer:
For an nth term U(n) = a + (n - 1)d
n = number of terms
a = first term
d = common difference
a = 5
d = 2 - 5 = - 3
U(n) = 5 + (n -1)-3
= 5 - 3n + 3
= 8 - 3n
The formula for the sequence is 8 - 3n
Hope this helps
problems involving ratio and propotion in real life. tete and tuke share P8900 in the ratio 2:3. how much does each get respective?
Answers
Answer:
Step-by-step explanation:
[tex]Tete : Tuke\\2 : 3\\Total-Amount = P8900\\2+3 = 5\\Tete = \frac{2}{5} * 8900\\Tete = P3560\\\\Tuke = \frac{3}{5} *8900\\Tuke = P5340[/tex]
th
Write an explicit formula for An, the nth
term of the sequence 15, 23, 31, ....
Answers
Answer:
a₁ = 15 and common difference = 8 so the formula is:
aₙ = 15 + (n - 1) * 8
= 8n + 7
An account pays 7%per year simple interest. In 1 year, the amount in the account is 950. How much is in the account in year 6
Answers
Answer:
First year's interest is already given.
There are 5 more payments of interest
= 5 * 0.07 * 950 = 332.5
so amount in the account after 6 years = 950 + 332.5 = 1282.5
Answer:
The answer is 1282.50
Step-by-step explanation:
What is the axis of symmetry of the quadratic function y = 2(x + 3)2 + 5?
x = –5
x = –3
x = 5
x = 3
Answers
Answer:
-3
Step-by-step explanation:
solve the equation (X-1) (2x+5)=0
Answers
Answer:
x = -5/2
x = 1
Step-by-step explanation:
(x-1) (2x+5) = 0
Divide both sides by (x-1)
2x+5 = 0
Subtract 5 on both sides.
2x = -5
Divide 2 into both sides.
x = -5/2
(x-1) (2x+5) = 0
Divide both sides by (2x+5).
x - 1 = 0
Add 1 to both sides.
x = 1
Evaluate the expression: log base3 81
Answers
Answer:
4
Step-by-step explanation:
google it
Answer:
the answer is four
Step-by-step explanation:
calculator
Which symbol would make the statement TRUE?
-3/4
-0.75
A. <
B. >
C. =
D. none of the above
Answers
Answer: C
Step-by-step explanation: -3/4 is equal to -.75 ,
Which of the statements is true please show work
Answers
Answer:
f(4)>g(4)
Step-by-step explanation:
f(x)=3x^5 , f(4)= 3072
g(x)=11*4^x when x=4 then g(4)=2816
What is the domain of g(x)?
Answers
Answer:
-2 ≤x≤5
Step-by-step explanation:
The domain is the inputs
The lowest value of x is -2 and every value of x is valid up to 5
-2 ≤x≤5
Please answer this ASAP ❤️
Answers
Answer:
4
Step-by-step explanation:
just change the x into -6
-(-6)-2 = 6 - 2 = 4
Answer:
f(x)=-x-2
f(-6)=-(-6)-2
f(-6)=4
Step-by-step explanation:
Find the vertex of the function given below.
y = 2x2 + 8x + 1
Answers
Answer:
Vertex: (-2, -7)
Step-by-step explanation:
Easiest and fastest way to do this is to graph the equation and trace to the vertex. When you do so you should be able to calculate the coordinates of the vertex.
Answer: the answer is (-2,-7)
Step-by-step explanation: APPEX
Convert 14 ft to yd
a.4 2/3 b. 1 1/7 c. 42 d. 168
Answers
Answer:
4 2/3
Step-by-step explanation:
14 ÷ 3 = 4 2/3
3 × 4 = 12
14- 12= 2
choose all functions below that have a vertex of (4.5,-8)
Answers
Answer: Answer: A
Explanation:
Just plug in numbers since you know the unknown values,
x + r = 4 + 5
4 + 5 = 9
Step-by-step explanation:
Andros has an oil fired heating system. In a 30-day period he used a full tank of oil at a constant rate per day. At a different time of the year the amount of oil Andros uses per day is 1 3 of the rate used in the 30-day period. (a) How many days should a full tank of oil?
Answers
Step-by-step explanation:
30 days period multiply by 7 days
=210 therefore our answer is =210
PLZ HLP ME I BEG!!! 13 POINTS 1. During a trip, Amy had to take two different trains. Her first train traveled for 3hrs and the second train traveled for 4hrs Combined, the trains traveled 625 miles If the equation 3m + 4n = 625 represents this situation, which statements are true regarding this equation? select two that apply a. The variable m in the equation represents the speed of the second train. b. The variable n in the equation represents the speed of the first train. c. The variable m in the equation represents the speed of the first train. d. The variable n in the equation represents the number of hours Amy traveled on the second train. e. The variable m in the equation represents the number of hours Amy traveled on the first train. f. The variable n in the equation represents the speed of the second train. 2. What is the point-slope form of the equation for the line with a slope of −2 that passes through the point (4,−6)? a. y+6=−2(x−4) b. y−4=−2(x+6) c. y=−2x−6 d. y−6=−2(x+4) 3. Examine the following table that represents some points on a line. x | -6, -4, 6 y | -10, -9, -4 Which equations in point-slope form represent this line? Select all that apply. a. y+9=1/2(x+4) b. y+4=1/2(x−6) c. y+10=1/2(x+6) d. y+10=2(x+6) e. y+4=2(x−6) f. y−9=2(x−4)
Answers
The diagonal of a rectangle is 58" the site is 40" and the base is 42" what is the ratio of the diagonal to the base of the rectangle
Answers
Answer:
29:21
Step-by-step explanation:
The ratio of the diagonal to the base of the rectangle is 58:42
The ratio can be simplified further.
The simplified ratio is 29:21.
pls hurry; 10 pts The first equation in the following system gives a company's income, in dollars, for selling x baseball caps. The second equation gives the cost of making x baseball caps. y = 8x y = -0.01 x2 + 4x + 3,200 The solution of the system is (400, 3,200). How would you interpret this solution?
Answers
Answer: The cost to make 400 baseball caps is $3,200
Step-by-step explanation:
The answer they gave you is a set of coords, x and y coords to be exact. That means that x value is inputed into the equation and that y value is the asnwer.
You put in 400, you get 3200.
They also gave us that x equals the number of baseball caps. Then y equals the cost of making those baseball caps
Answer:
The cost to produce 400 caps is the same as the income made from selling 400 caps.
The company will break even when it sells 400 caps; it will not make a profit.
Step-by-step explanation:
EDGE 2021
Evaluate xy - y if x=6 and y=-5
Answers
Answer:
-25
Step-by-step explanation:
xy - y
Replace 'x' with 6, and 'y' with -5:
[tex]6(-5)-(-5)\\\\-30+5\\\\\boxed{-25}[/tex]
What is the area of the composite figure? -70 cm2 -100 cm2 -105 cm2 -130 cm2
Answers
Make two shapes out of it.
The bottom is a rectangle 14 x 5 = 70 square cm
The top is a triangle 1/2 x 12 x 5 = 30 square cm
Total area = 70 + 30 = 100 square cm
Answer:
100 cm²
Step-by-step explanation:
The composite shape can be cut into two shapes. One triangle and one rectangle. The sum of their areas is the area of the whole composite shape.
The area of the triangle:
b × h × 1/2
(14 - 2) × 5 × 1/2
60 × 1/2
= 30 cm²
The area of the rectangle:
l × w
14 × 5
= 70 cm²
Add the areas of the two shapes.
30 cm² + 70 cm²
= 100 cm²
The area of the composite shape is 100 cm².
expand the following 5( 2x -4 )
Answers
Answer:
10x-20
Step-by-step explanation:
5(2x-4)
5x2=10
5x4=20
can i have help thanks
Answers
Answer:
∠ BOC = 42°
Step-by-step explanation:
Since OA and OC are perpendicular , that is at 90° to each other, then
∠ AOB + ∠ BOC = 90 , substitute values
5x + 8 + 6x - 6 = 90
11x + 2 = 90 ( subtract 2 from both sides )
11x = 88 ( divide both sides by 11 )
x = 8
Thus
∠ BOC = 6x - 6 = 6(8) - 6 = 48 - 6 = 42°