What is the slope of the graph?
slope = -3
slope = -1/3
slope = 1/3
slope = 3
Answers
Answer:
slope = -3
Step-by-step explanation:
To find the slope of the graphed line, we can use the slope formula:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Slope formula}}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\textsf{where:}\\\phantom{w}\bullet\;\;m\; \textsf{is the slope.}\\\phantom{w}\bullet\;\;(x_1,y_1)\;\textsf{and}\;(x_2,y_2)\;\textsf{are two points on the line.}\end{array}}[/tex]
First, identify two points on the line:
(x₁, y₁) = (0, 3)(x₂, y₂) = (1, 0)Substitute the coordinates into the slope formula:
[tex]m=\dfrac{0-3}{1-0}=\dfrac{-3}{1}=-3[/tex]
Therefore, the slope of the graphed line is:
[tex]\Large\boxed{\boxed{\textsf{slope}=-3}}[/tex]
Related Questions
An auditorium is to seat 2,400 people. The building code requires three square feet for each person. How many square meters will that auditorium have?
Answers
______________________________________
Explanation:
______________________________________
Method 1)
2,400 person (3 ft² / person) = __?__ m² .
The units of "person" ; 'cancel out"; since "person/ person" = 1 ; and 1/1 = 1.
and we have: "2,400 * (3 ft²) = 7, 200 ft² .
______________________________________
We are ask to find the value, in units of "m² " ;
______________________________________
→ So; we convert "7, 200 ft² " ; to "m² " ;
______________________________________
→ Note the conversion: 1 m² = 10.7639 ft² ;
______________________________________
→ 7, 200 ft² * [ ( 1m²) / ( 10.7639 ft²) ] ;
= [ (7, 200 ) / (10.7639 )] m² ;
= 668.9025353264151469 m² ;
⇒ Round to 668.903 m² .
______________________________________
Method 2)
______________________________________
2,400 person (3 ft² / person) = __?__ m² .
Since we want the answer is units of: "m² " ;
___________________________________________
Let us convert: "3 ft² " to units of: "m² " ; and then rewrite the problem.
___________________________________________
→ Note the conversion: 1 m² = 10.7639 ft² ;
___________________________________________
= [ (7, 200 ) / (10.7639 )] m²
= 668.9025353264151469 m²
⇒ Round to 668.903 m² .
______________________________________
Method 3)
______________________________________
2,400 person (3 ft² / person) = __?__ m² .
______________________________________
→ Note the conversion: 1 m² = 10.7639 ft² ;
______________________________________
(2,400 person) * (3 ft² / person) * [ ( 1m²) / ( 10.7639 ft²) ] ;
= { [ (2,400) * (3) * (1) ] / [ 10.7639 ] } m² ;
= { [ (2,400) * (3) ] / [ 10.7639 ] } m² ; {Note: The "1" can be ignored.}.
= [ (7,200) / (10.7639) ] m² ;
= 668.9025353264151469 m² ;
⇒ Round to 668.903 m² .
___________________________________________________
What is the slope below
Answers
(3, -2) and (2, -4)
m = (y2 - y1)/(x2 - x1) = (-4 - (-2))/(2 - 3) (-4 + 2)/(-1) = -2/(-1) = 2
For a craft project, two equilateral triangles are taped together to create a quadrilateral. What is the quadrilateral? rhombus rectangle trapezoid square
Answers
Answer:- The quadrilateral must be a rhombus.
Explanation:-
Given :-For a craft project, two equilateral triangles are taped together to create a quadrilateral.
We know that an equilateral triangle is a triangle in which all the sides and angles are equal such that its each interior angle should be 60°.
If we join two equilateral triangle by to create a quadrilateral then the sides of the quadrilateral would be same as it was constructed by equilateral triangle.
Then the interior angle for the sides which are not joint will remain same as 60°.
But the interior angle for the vertex of quadrilateral which has formed by joining two triangles will become 60°+60°=120°.
Thus it is not a square , rectangle (no right angle )or trapezoid(quadrilateral have equal sides).
Therefore, the quadrilateral must be a rhombus.
Find cotθ if θ terminates in Quadrant III and secθ = - 2.
Answers
If you know your sine/cosine values you know that when:
cos(x) = 1/2 , sin(x) = √(3)/2
The fact that theta, or "x" as I've been using... terminates in Quadrant III means both cosine and sine will be negative and then cotangent will be positive.
cot(x) = cos(x) / sin(x)
cot(x) = (-1/2) / (-√(3)/2)
cot(x) = (1/2) * (2/√(3))
cot(x) = 1/√(3)
or rationalized as √(3)/3
25xy4 + 60xy3 5xy 5xy3 + 12xy2 5y2 + 12 5xy + 12y 5y3 + 12y2
Answers
the simplified expression is 25xy^4 + 65xy^3 + 22xy + 12xy^2 + 18y + 12y^2 + 5y^3 + 12
To simplify the given expression, we first need to combine like terms. Like terms are those that have the same variables raised to the same powers. In this case, we have terms with x and y raised to different powers.
The expression is:
25xy^4 + 60xy^3 + 5xy^3 + 5xy + 12xy^2 + 5y^2 + 12 + 5xy + 12y + 5y^3 + 12y^2
Now, let's combine the like terms:
Combine the terms with xy^4: 25xy^4
Combine the terms with xy^3: 60xy^3 + 5xy^3 = 65xy^3
Combine the terms with xy^2: 12xy^2
Combine the terms with xy: 5xy + 5xy + 12xy = 22xy
Combine the terms with y^2: 5y^2 + 12
Combine the terms with y: 12y + 5y + 12y^2 = 18y + 12y^2
Combine the terms with y^3: 5y^3 + 5y^3 = 10y^3
Now, let's put all the combined like terms together:
25xy^4 + 65xy^3 + 22xy + 12xy^2 + 18y + 12y^2 + 5y^3 + 12
This is the simplified expression.
The probable question maybe:
simplify the given expression [tex]\(25xy^4 + 60xy^3 + 5xy + 5xy^3 + 12xy^2 + 5y^2 + 12 + 5xy + 12y + 5y^3 + 12y^2\)[/tex]
What is the height of an equilateral triangle with sides that are 12 cm long? Round to the nearest tenth. (1 point)
Answers
Answer:
10.4 cm
Step-by-step explanation:
Looking at the triangle in the attached pic, we can see that the right, smaller triangle is a right triangle on which we can apply the pythagorean theorem to solve for the height, h.
Pythagorean theorem tells us [tex]c^2=a^2+b^2[/tex] where c is the hypotenuse (12 in our case) and a & b are the two legs (6 and h are the respective lengths).
So let's solve for h:
[tex]c^2=a^2+b^2\\12^2=6^2+h^2\\144=36+h^2\\144-35=h^2\\108=h^2\\h=\sqrt{108} \\h=10.4[/tex]
If a box measures 1.2m by 3.4m by 0.50m, what is its volume in liter
Answers
1.2(100cm/1m) = 120 cm
3.4(100cm/1m) = 340 cm
0.5(100cm/1m) = 50 cm
the volume of a box is equal to (length)(width)(height)
that is
V = (120cm)(340cm)(50cm)
V = (6000 cm^2)(340cm)
V = 2040000 cm^3
now 1 cm^3 is equal to one mL and 1000 mL is 1 Liter
V =2040000 mL multiply by (1 Liter/1000 mL)
V = 2040 L
That's 2,040 liters.
Hope this helps :)
1.2m * 3.4m * 0.5m = volume
2.04m^3 = volume
Now we need to convert that in liters
1 cubic meter = 1000 liters
So 2.04 cubic meters = 2040 liters
The number of years that Brad has been on the soccer team is 2 less than five times a number of years Scott has in total the boys have been on the soccer team for about 10 years how long has Brad been on the soccer team
Answers
You and your friend are selling raffle tickets for a new laptop. you sell 14 more then your friend sells. Together you and your friend sell 58 tickets. Write a system of linear equations that represent this situation. How many did each of you sell?
Answers
You sold 36 tickets and your friend sold 22 tickets.
Explanation:Let's represent the number of tickets you sell as x and the number of tickets your friend sells as y.
We know that you sell 14 more tickets than your friend, so we have the equation:
x = y + 14
We also know that together you and your friend sell 58 tickets, so the equation becomes:
x + y = 58
Now we can solve these two equations simultaneously to find the values of x and y.
Substitute the value of x from the first equation into the second equation:(y + 14) + y = 58
Combine like terms:2y + 14 = 58
Subtract 14 from both sides to isolate the variable:2y = 44
Divide both sides by 2 to solve for y:y = 22
Now substitute the value of y back into one of the original equations to solve for x:x = 22 + 14
Simplify:x = 36
Therefore, you sold 36 tickets and your friend sold 22 tickets.
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The system of equations representing the problem is y = x + 14 and x + y = 58. Solving this system we get x = 22 (friend's sold tickets) and y = 36 (your sold tickets).
Explanation:We'll use a system of linear equations to model this situation. Let's define x as the number of tickets your friend sells, and y as the number of tickets you sell. From the problem, we know two things:
1. You sell 14 more tickets than your friend: y = x + 14.
2. Together, you and your friend sell 58 tickets: x + y = 58.
To solve this system, we can substitute y in the second equation with x + 14 from the first equation. This gives us:
x + (x + 14) = 58.
Solving this we get x = 22 and substituting x into the first equation gives: y = 22 + 14 = 36.
So, your friend sold 22 tickets, and you sold 36 tickets.
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Which canadian island has a population density that ranges from under 2 people to as many as 250 people per square mile?
Answers
Prince Edward Island in Canada has a population density that can range from less than 2 people to as many as 250 people per square mile. This is due to various factors including climate, farmland, and job opportunities.
Explanation:The Canadian island with a population density that ranges from under 2 people to as many as 250 people per square mile is Prince Edward Island. This island is one of the three Maritime Provinces in Canada and is the smallest in both land area and population. But, when it comes to population density, it has a higher range than many other islands in Canada. This is due to its favorable climate, good farmland, and the job opportunities, mainly in farming and tourism, which attract a decent population.
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I need help with my essay questions!! Can someone please help me!! It would mean so much to me!!
24. You use a line of best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is -0.015. How confident can you be that your predicted value will be reasonably close to the actual value ?
I get 2 points for this essay. Please help me someone! I really don't know how to answer this!! :[
Answers
so -.015 is very close to 0, you would be not confident at all. This means your prediction is no better than a random guessing.
Arithmetic sequence find the next next term in the sequence 44, 51, 58, 65
Answers
Hii!
_________________________________________________________
[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]
72
[tex]\rightsquigarrow\circ\boldsymbol{Explanation.}\circ\leftharpoonup[/tex]
To find the next term in the arithmetic sequence, we should first find the common difference.
The common difference is the amount we add or subtract to obtain the next term. In the given sequence we add 7.
So, let's find the next term.
[tex]\twoheadrightarrow\sf65+7[/tex]
[tex]\bullet[/tex] Add 7
[tex]\twoheadrightarrow\sf72[/tex]
[tex]\bullet[/tex] Great job! We found the next term
--
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]
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explain using complete sentences whether or not this is the most appropriate format for representing data and why if it is not the best format explain which format should have been used instead
Answers
The most appropriate format for representing data depends on the intended audience, data type, and presentation purpose. Adherence to professional formatting guidelines is critical, and while figures can make data accessible, they should not duplicate table data. The effectiveness of formats such as complete sentences, tweets, Prezi, and visual figures varies based on the context.
When choosing the most appropriate format for representing data, several factors need to be considered such as the intended audience, the type of data, and the purpose of the data presentation. Complete sentences, Prezi presentations, 140 character tweets, and drawn pictures each have their own strengths in conveying information effectively and engagingly depending on these factors.
For professional or academic reports, complete sentences and structured paragraphs provide in-depth analysis and explanation. However, for social media platforms, 140 character tweets can quickly capture attention and convey key points. A Prezi can be highly engaging and visually appealing for presentations, making complex information accessible. Conversely, when displaying detailed findings, sometimes a well-illustrated figure or a clear table can speak volumes more efficiently.
Nonetheless, adhering to formatting guidelines is crucial in a professional context, as non-compliance could lead to the rejection of the report. It's also important to note that while figures are useful for making data accessible, they should not duplicate data presented in tables. When using figures, they must be clearly titled, referenced in the text, and situated conveniently in the report. If the figures are too dense, they can be relegated to an appendix.
In summary, there is no one-size-fits-all format for data presentation. Preference may vary depending on personal comfort with certain formats or the requirements of a specific assignment. Reflecting on the exercise of presenting information in various formats can elucidate which is most effective for your specific needs and audience.
given f(x)=x^2-x; find f(-5)
Answers
f(- 5) = (- 5)^2 - ( - 5).
(- 5)( - 5) = 25 so now we have 25 - (- 5). Because there are two negatives back to back, the number becomes a positive so the equation becomes 25 + 5 = 30.
f(- 5) = 30.
What's the probability of getting an even number and a head when rolling a die and then tossing a coin?
Answers
Answer: 1/4
Step-by-step explanation:
Describe in a couple of sentences what key features you can identify from the graph of a quadratic equation?
Answers
The roots. These are the points where the graph crosses the x-axis, and is the solution of the quadratic equation when y=0. Usually, there are either two or zero.
The coefficient of the leading term. In the quadratic equation y= ax^2 + bx + c,
the parabola points upward if a is positive, and downward if a is negative.
The vertex. You can find the vertex, or where the two sides of the parabola meet, by looking at the graph.
Can someone please help me with number 37?
Answers
Answer:
x = 10Step-by-step explanation:
[tex]4-(3x-5)=6-(2x+7)\\\\/-(a+b)=-1(a+b)=(-1)(a)+(-1)(b)-\text{distributive property}/\\\\4-3x-(-5)=6-2x-7\\\\4-3x+5=6-2x-7\qquad\text{combine like terms}\\\\-3x+(4+5)=-2x+(6-7)\\\\-3x+9=-2x-1\qquad\text{subtract 9 from both sides}\\\\-3x+9-9=-2x-1-9\\\\-3x=-2x-10\qquad\text{sdd}\ 2x\ \text{to both sides}\\\\-3x+2x=-2x+2x-10\\\\-x=-10\qquad\text{change the signs}\\\\\boxed{x=10}[/tex]
Answer: [tex]x=10[/tex]
Simplify both sides of the equation
[tex]4-(3x-5)=6-(2x+7)[/tex]
[tex]4+-1(3x-5)=6+-1(2x+7)[/tex] (Distribute the Negative Sign)
[tex]4+-1(3x)+(-1)(-5)=6+-1(2x)+(-1)(7)[/tex]
[tex]4+-3x+5=6+-2x+-7[/tex]
[tex](-3x)+(4+5)=(-2x)+(6+-7)[/tex] (Combine Like Terms)
[tex]-3x+9=-2x+-1[/tex]
Add 2x to both sides
[tex]-3x+9+2x=-2x-1+2x\\-x+9=-1[/tex]
Subtract 9 from both sides
[tex]-x+9-9=-1-9\\-x=-10[/tex]
Divide both sides by -1
[tex]-x/-1=-10/-1\\x=10[/tex]
I Reaally Need Help If You Wamt Ill Eve Go Over 100 Points
Answers
(b) (1,5), (3,3); y = 3x + 3 5 = m1 + b, 3 = m3 + b
(c) coincident i believe, because it is not independent or inconsistent
(d) 2x + 3 = 3x + 3
(-2x)(-3) (-2x)(- 3)
0 = -2x
x = 0
hope this helps
side walk 1
slope = (7-3)/(2-0) = 4/2 = 2
b = 3
slope intercept form
y = 2x + 3
b)
sidewalk 2
slope = (3-5)/(3-1) = -2/2 = -1
point slope form equation
y - 5 = -1(x - 1)
slope intercept form
y - 5 = -1(x - 1)
y - 5 = -x + 1
y = -x + 4 ....slope intercept form
c)
sidewalk1 : y = 2x + 3
sidewalk2: y = -x + 4
2x + 3 = -x + 4
3x = 1
x = 1/3
y = 2(1/3) + 3
y = 2/3 + 3
y = 3 2/3
solution x = 1/3 and y = 3 2/3
A system of two linear equations can have one solution so it's consistent and exactly 1 solution so it is independent
d) you can use this from c)
x = 1/3 and y = 3 2/3
By definition a simple random sample of size n is any sample
Answers
An airplane traveling 245 m/s east experiences turbulence, so the pilot slows down to 230 m/s. It takes the pilot 7 seconds to slow down to this speed. What is the acceleration of the plane? Round your answer to the nearest hundredth.
2.14 m/s2
–2.14 m/s2
67.86 m/s2
–67.86 m/s2
Answers
Answer:
Acceleration, [tex]a=-2.14\ m/s^2[/tex]
Step-by-step explanation:
Initial speed of the airplane, u = 245 m/s
Final speed of the airplane, v = 230 m/s
The pilot takes 7 seconds to slow down to this speed. Let a is the acceleration of the plane. The change in velocity per unit time is called the acceleration of an object. It can be calculated as :
[tex]a=\dfrac{v-u}{t}[/tex]
[tex]a=\dfrac{230\ m/s-245\ m/s}{7\ s}[/tex]
[tex]a=-2.14\ m/s^2[/tex]
So, the acceleration of the plane is [tex]-2.14\ m/s^2[/tex]. Hence, the correct option is (b).
NEED HELP FAST PLEASE!!!
What is the equation of this line?
y = -3/2x
y = 2/3x
y = -2/3x
y = 3/2x
Answers
The slope is rise/run = 2/3 meaning we go up 2 and over to the right 3. For instance, moving from (0,0) to (3,2) has us move up 2 and over to the right 3.
Alternatively you can use the slope formula m = (y2-y1)/(x2-x1) to get the same result of 2/3.
so slope = (2 + 2)/(3+3) = 4/6 = 2/3
y = mx + b
b = y - mx
b = -2 - (2/3)(-3)
b = -2 + 2
b = 0
equation
y = 2/3x
answer
B. y = 2/3x
If 8 times a number is decreased by 20,the result is the same as 3 times the number increased by 80
Answers
Final answer:
The algebraic expression for the problem is '8n - 20 = 3n + 80', which simplifies to 'n = 20'. Therefore, the number in question is 20.
Explanation:
The question presents a classic algebra problem where we have to find the value of a variable that satisfies a given condition. Specifically, this problem states:
"If 8 times a number is decreased by 20, the result is the same as 3 times the number increased by 80."
To solve this, we'll convert the words into an algebraic equation and solve for the number. Let's use 'n' to represent the number:
8n - 20 = 3n + 80This equation tells us that when you multiply the number by 8 and subtract 20, it's equal to the result of multiplying the number by 3 and adding 80. To find 'n', we combine like terms and solve:
8n - 3n = 80 + 205n = 100n = 100 / 5n = 20Thus, the number we're looking for is 20.
The perimeter of a rectangle is 525 inches and the ratio of the length to the with is 7:3 find the length of the with
Answers
Width: 15 centimeters
The sum of the digits of a two-digit number is 7. the new number obtained when the digits are reversed is 27 less than the original number. find the original number
Answers
0 + 7 = 7 (07)
1 + 6 = 7 (16)
2 + 5 = 7 (25)
3 + 4 = 7 (34)
4 + 3 = 7 (43)
5 + 2 = 7 (52)
6 + 1 = 7 (61)
7 + 0 = 7 (70)
Obviously 70 can't be our number, as it would be a one digit number,
Since we're going down in value ( 27 less ) our original number will be a larger number.
52 reversed is 25 which is 27 less than 52.
Our original number is 52 here.
Ten times the square of a non zero number is equal to eighty times the number
What is the number?
Answers
The Number in the statement is 4/5.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Ten times the square of a non zero number is equal to eighty times the number.
let the number be x.
So, 10x² = 8x
10x² - 8x= 0
2(5)(x)(x) - 2 (2)(2)(x) = 0
2x( 5x - 4)= 0
Now, 2x= 0 or 5x-4=0
x= 0 or x= 4/5
Hence, the number is 4/5.
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A wedge is cut out of a circular cylinder of radius 10 by two planes. one plane is perpendicular to the axis of the cylinder. the other intersects the first at an angle of 30° along a diameter of the cylinder. find the volume v of the wedge, taking rectangular cross-sections to be parallel to the line of intersection of the two planes, which is the x-axis. (let r = 10.)
Answers
[tex]r^2=x^2+y^2 \\ \\ \Rightarrow y=\sqrt{10^2-x^2}=\sqrt{100-x^2}[/tex]
The wedge makes a shape whose cross-section perpendicular to the x -axis at distance x from the origin is a triangle whose base is is given by: [tex]y=\sqrt{100-x^2}[/tex]
The height of the wedge is given by:
[tex]y\tan30^o= \frac{\sqrt{100-x^2}}{\sqrt{3}} [/tex]
The cross sectional area of the wedge is given by:
[tex]A(x)= \frac{1}{2} bh \\ \\ = \frac{\sqrt{100-x^2}}{2} \cdot\frac{\sqrt{100-x^2}}{\sqrt{3}} \\ \\ = \frac{100-x^2}{2\sqrt{3}} [/tex]
The volume is given by:
[tex]V= \int\limits^{10}_{-10} {A(x)} \, dx \\ \\ = \int\limits^{10}_{-10} {\frac{100-x^2}{2\sqrt{3}}} \, dx =2\int\limits^{10}_{0} {\frac{100-x^2}{2\sqrt{3}}} \, dx \\ \\ =\int\limits^{10}_{0} {\frac{100-x^2}{\sqrt{3}}} \, dx=\frac{1}{\sqrt{3}}\left[100x-\frac{x^3}{3}\right]^{10}_0 \\ \\ =\frac{1}{\sqrt{3}}\left[100(10)-\frac{(10)^3}{3}\right]=\frac{1}{\sqrt{3}}\left[1000-\frac{1000}{3}\right] \\ \\ =\frac{1}{\sqrt{3}}\left[\frac{2000}{3}\right]=\frac{2000}{3\sqrt{3}}[/tex]
The volume of the wedge is 50π/3 - 25√3.
Explanation:To find the volume of the wedge, we need to calculate the volume of the cylindrical segment between the two intersecting planes. The formula for the volume of a cylindrical segment is V = h((R^2θ)/2 - (R^2sinθ)/2), where h is the height of the segment, R is the radius of the cylinder, and θ is the angle of the intersection between the planes. In this case, h is 10 and θ is 30°, so the formula becomes V = 10((10^2 * π/6)/2 - (10^2 * sin(π/6))/2). Simplifying the equation gives V = 50π/3 - 25√3.
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PLZ HELP ASAP!!!
1. Give me an example of irrational number (other than pi).
Be prepared to explain how you know its irrational.
2. How do you simplify x8 / x3?
3. Estimate square root of 39 without a calculator.
Be prepared to explain.
4. Write the following number in scientific notation: 402000.
Answers
An irrational number is something that cant be expressed as a ratio. For ex:the square root of 2. Hope this helps.
If applying 6 newtons of force to an object results in 42 joules of work, what distance (in meters) would the object travel?
Answers
Answer:
The object would travel 7 meters.
Step-by-step explanation:
The distance the object would travel is 7 meters if applying 6 newtons of force to an object results in 42 joules of work.
What is distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.
We have:
If applying 6 newtons of force to an object results in 42 joules of work
We know,
Work = Force x Distance
42 = 6xDistance
Distance = 7 meters
Thus, the distance the object would travel is 7 meters if applying 6 newtons of force to an object results in 42 joules of work.
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Give an example of a rational function that has a horizontal asymptote of y = 2/9.
Answers
Ou work as a cashier for a grocery store and earn $5 per hour. you also mow lawns and earn $10 per hour. you want to earn at least $50 per week, but would like to work no more than 10 hours per week. which system of inequalities, along with y ≥ 0 and x ≥ 0, would you use to solve the real-world problem?
Answers
The problem can be represented by two inequalities: one to ensure earning at least $50 per week (5x + 10y >= 50) and another to restrict working to no more than 10 hours per week (x + y <= 10), alongside x >= 0 and y >= 0 to indicate non-negative hours worked for each job.
To determine the system of inequalities to solve the problem, we need to define variables for the number of hours spent on each job. Let's use x to represent the number of hours working as a cashier at the grocery store, and y to represent the number of hours mowing lawns. The student earns $5 per hour at the grocery store and $10 per hour mowing lawns. They want to earn at least $50 per week and work no more than 10 hours in total.
From this information, we can establish the following inequalities:
5x + 10y >= 50 (To ensure earning at least $50 per week)
x + y = 10 (To ensure working no more than 10 hours per week)
Additionally, we include y >= 0 and x >= 0 to represent that the number of hours worked at either job cannot be negative.