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.
The base of a box is a rectangle. The width of the box is half its length. The height of the box is 0.5m. Find the volume of the box if the area of the base is 1.08m² less than the combined area of the sides.
Answer:
Step-by-step explanation:
We assume the box is open-top.
If the width of the box is represented by w, then its length is 2w. The area of the base is then w·2w = 2w².
The combined area of the sides is the product of the perimeter of the base, 2(w+2w) = 6w and the height, 0.5, so is 3w.
Since the base area is 1.08 m² less than the lateral area, we have
... 2w² = 3w -1.08
... 2w² -3w +1.08 = 0 . . . . rearrange to standard form
... w² -1.5w +0.54 = 0 . . . make the leading coefficient 1 (divide by 2)
... (w -0.9)(w -0.6) = 0 . . . factor
The width of the box may be either 0.6 meters or 0.9 meters.
The volume is the product of width, length, and height
V = w·2w·0.5 = w²
V = 0.36 m³ . . . or . . . 0.81 m³. . . . . . (there are two possible answers)
The sum of two numbers is seventy-two. Twice one of them equals ten times the other. What are the numbers?
What is the value of the expression “two less than six times the difference of a number and five” when n = 9?
Answer:
22
Step-by-step explanation:
The value of expression is 22.
Step-by-step explanation:
Given the statement “two less than six times the difference of a number and five” when n = 9. we have to find the value of expression formed by the above statement.
Difference of a number n and 5 gives (n-5)
Now, we have to write two less than 6 times the difference, we get the expression 6(n-5)-2
Here, the number n is 9
∴Value of expression is 6(9-5)-2=6(4)-2=24-2=22
Hence, the value of expression is 22.
What is the perimeter of a polygon with vertices at (-6,-1) (-3,-4) (6,5) and (3,8) ?
Triangle RST has vertices R(2, 0), S(4, 0), and T(–3, –1). The image of triangle RST after a rotation has vertices
R'(0, –2), S'(0, –4), and T'(–3, –1). Which rule describes the transformation?
R0, 90°
R0, 180°
R0, 270°
R0, 360°
Answer:
It should be C aka 270°
Step-by-step explanation:
Answer:
3 option is correct.
Step-by-step explanation:
Given Triangle RST has vertices R(2, 0), S(4, 0), and T(–3, –1). The image of triangle RST after a rotation has vertices R'(0, –2), S'(0, –4), and T'(–3, –1).
We have to tell the rule describes the transformation.
A rotation is transformation that turns a figure about a fixed point. An object and its rotation are the same shape, but the figures may turned or rotate in different directions.
Here, the coordinates shift after rotation according to the rule
(2,0) → (0,-2) i.e (x, y) → (y, -x)
As, Rotation of 270º on coordinate axes.
(x, y) → (y, -x)
which match to the given rule.
hence, 3 option is correct.
Please help not really sure what to do here.
Use the following graph to determine which function is best modeled on the graph.
Define the function g(x) in terms of f(x)
A high-speed bullet train travel 900 feet in 5 seconds at this rate how far would it travel in 1 minute
Which of the following shows the proper steps to construct a perpendicular bisector of a segment through any point?
A computer company can sell 130 boxes of printer paper each week at a price of $9 per box. For each $1 increase in the price, it will sell 10 fewer boxes per week. What price per box will provide the maximum revenue for the computer company?
$9
$10
$11
$12
The maximum revenue for the computer company is achieved at the price of $11 per box which is calculated based on the decrease in quantity sold with every $1 increase in price.
Explanation:To find the price per box that will provide the maximum revenue for the computer company, we need to analyze how changes in price affect the number of boxes sold and the revenue generated. The company sells 130 boxes of printer paper each week at $9 per box. For each $1 increase in price, it will sell 10 fewer boxes.
Let's define the revenue function as R(p) where p is the price per box. The initial revenue is 130 boxes × $9. For each $1 increase, the revenue function becomes (130 - 10(p - 9)) × p. We need to find the value of p that maximizes this revenue function.
Let's calculate:
At $9: R($9) = 130 × $9 = $1170At $10: R($10) = (130 - 10(1)) × $10 = 120 × $10 = $1200At $11: R($11) = (130 - 10(2)) × $11 = 110 × $11 = $1210At $12: R($12) = (130 - 10(3)) × $12 = 100 × $12 = $1200We can see that the revenue is maximum at $11 per box. So, the price per box that will provide the maximum revenue for the computer company is $11.
Mark borrowed $5,500 at 11.5 percent for five years. What is his monthly payment?
A. $131.50
B. $173.50
C. $120.95
D. $150.22
Answer:
C option is correct
Step-by-step explanation:
Given: payment borrowed (P)= $5,500
rate (r)=11.5 or 0.115
Time(t)= 5 years
Compound monthly(k)=12
To find : Monthly payment (M)
Formula used : [tex]M= P/(\frac{1-(1+\frac{r}{k})^{-kn}}{\frac{r}{k}})[/tex]
Solution : [tex]M= 5500/(\frac{1-(1+\frac{0.115}{12})^{-60}}{\frac{0.115}{12}})[/tex]
by solving we get, M =$120.95
therefore, option C is correct
Triangle LMN is positioned inside rectangle LKPN as shown in the diagram. Which is the area of △LMN△LMN?
Answer:
Step-by-step explanation:
The area of the triangle inside the rectangle is calculated by using the formula for the area of a triangle, 1/2 * base* height. Given the base is the length of the rectangle and the height is the breadth of the rectangle, we substitute these measurements into the formula to determine the area. Area of triangle LMN is 15.6 square cm.
Explanation:To determine the area of the triangle inside the rectangle, we first need to understand the relationship between these two shapes. Given the base of the triangle, LN, is the same as the length of the rectangle, 6.5 cm, and the triangle is between the parallel lines of the rectangle, we can infer that the height of the triangle is the same as the breadth of the rectangle, which is 4.8 cm.
Now, the area of a triangle is given by the formula 1/2 * base * height.
Substituting the given measurements into this formula, we get
= 1/2 * 6.5 cm (base) * 4.8 cm (height)
= 0.5 * 6.5 cm (base) * 4.8 cm (height)
= 15.6 square cm
This will give us the area of the triangle LMN.
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The complete question is given below:
Triangle LMN is positioned inside rectangle LKPN as shown in the diagram. Which is the area of △LMN?
The length of rectangle and triangle are same, 6.5 cm. The breadth of rectangle is 4.8 cm. The triangle lies between the parallel lines of rectangle with base LN.
what are the roots of x in -10x^2 + 12x - 9=0
Answer:
k=-11
Step-by-step explanation:
Correct for plato
Two lines intersect to form a linear pair with equal measures. One angle had the measure 2x and the other angle had the measure (2y-10) find the value of x and y
Final answer:
To find the values of x and y, set up an equation by equating the two angles and solve for x and y using the given measures.
Explanation:
To find the values of x and y, we need to equate the two angles and solve for x and y.
According to the given information, the measure of one angle is 2x, while the measure of the other angle is 2y - 10.
Since the two angles are equal, we can set up the equation: 2x = 2y - 10.
Now, we can solve for x and y.
2x = 2y - 10
x = y - 5
So, the value of x is y - 5.
The values for x and y are found by solving the system of equations that arise from setting up the condition that two angles forming a linear pair add up to 180 degrees and are equal. The solution is x = 45 and y = 50.
Explanation:The student's question involves finding the values of x and y when two lines intersect to form a linear pair with equal measures. Since the angles form a linear pair, they add up to 180 degrees. Therefore, we must set up an equation 2x + (2y - 10) = 180 to find the values of x and y. Because the question tells us the angles are equal, we also know that 2x = 2y - 10. Solving this system of equations will provide the values for x and y.
To solve for x, we can use the second equation directly, 2x = 2y - 10. Since the angles are equal, we substitute the first angle's measure for the second, meaning x = y - 5. Then, we can substitute x into the first equation: 2(y - 5) + 2y - 10 = 180, simplifying it to 2y - 10 + 2y - 10 = 180, which further simplifies to 4y - 20 = 180. Finally, adding 20 to both sides and then dividing by 4 gives us y = 50. With the value of y, we can then find x: x = y - 5, so x = 50 - 5, meaning x = 45.
Which equation represents the value of x?
remember Pythagorean theorem
if we have a right triangle with legs a and b and hytponuse c then
[tex]a^2+b^2=c^2[/tex]
we are given a right triangle with legs x and y and hypotohuse 10
so therfor
[tex]x^2+y^2=10^2[/tex]
[tex]x^2+y^2=100
solve for x
minus y² from both sides
[tex]x^2=100-y^2[/tex]
sqare root both sides
[tex]x=\sqrt{100-y^2}[/tex]
the answer is the 4th option
An equation represents the value of x is x=√100-y².Therefore, option D is the correct answer.
What is the Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
From the given triangle ABC, AB=x units, BC=y units and AC=10 units
By using Pythagoras's theorem, we get
10²=x²+y²
x²=100-y²
x=√100-y²
Therefore, option D is the correct answer.
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Jordan bought 9 pounds of fruit. He paid $2.39 a pound for 5 pounds. He paid $1.99 a pound for the rest. How much did Jordan spend on fruit? (please let me know how you did it)
HELP ME!!!!!!!!!!!!!!!1 translate each sentence into an equation
1- 7 berries are 5 less than twice the number of berries Mickey had for lunch.
2- Negative 4 times the difference of a number 7 is 12
Bill takes the commuter train to work every day. during the morning commute, a train arrives every 25 min. if bill arrives at the station at a random time for the morning commute, what is the probability that he will have to wait at least 5 min for a train?
The coordinates of the vertices of quadrilateral RSTU are R(−4, 1) , S(4, −1) , T(3, −6) , and U(−5, −4) . Which statement correctly describes whether quadrilateral RSTU is a rectangle?
Answer:
For k12- the answer is Quadrilateral RSTU is not a rectangle because it has no right angles.
Step-by-step explanation:
Solution: A quadrilateral RSTU whose vertices are R(−4, 1) , S(4, −1) , T(3, −6) , and U(−5, −4).
RS = [tex]\sqrt{(4+4)^{2}+(-1-1)^{2}} =\sqrt{64+4}= \sqrt{68}[/tex]
ST= [tex]\sqrt{(4-3)^{2}+(-1+6)^{2}}= \sqrt{1+25} =\sqrt{26}[/tex]
TU=[tex]\sqrt{(3+5)^{2}+(-6+4)^{2}}= \sqrt{64+4}= \sqrt{68}[/tex]
UR =[tex]\sqrt{(-5+4)^{2}+(-4-1)^{2}}= \sqrt{1+25} =\sqrt{26}[/tex]
→RS=TU, and ST=UR⇒ Opposite sides are equal.
Slope of RS = [tex]\frac{-1-1}{4+4} = \frac{-2}{8}= \frac{-1}{4}[/tex]
Slope of TS= [tex]\frac{-6+1}{3-4} =\frac{-5}{-1}=5[/tex]
Slope of RS × Slope of TS = -1/4 × 5 = -5/4 ≠ -1, So lines are not perpendicular.
∴ quadrilateral RSTU is not a rectangle.
Point P is the incenter of triangle ABC, PZ = 7 units, and PA = 12 units.
The radius of the incircle centered at point P is ? units.
Answer:
The answer is 7 units
Step-by-step explanation:
I don't know but I got it right
I think you dont need to calculate anything they gave us the answer when they said PZ=7
Martha is cycling at a speed of 20 kilometers per hour. how long will it take her to cover a distance of 60 kilometers?
If 2(m-10) +2=24, then m= ?
Identify the variables, the constant, the coefficients, and the exponents in the algebraic expression: 5x + 3y^{2} + 4. (The 2 is supposed to be little on top of the "y")
The algebraic expression 5x + 3y² + 4 has variables x and y, the constants 5, 3, and 4, the coefficients are 5 and 3 and the exponents are 1 and 2.
What is an algebraic expression?An algebraic equation consists of terms separated by the operation of addition and subtraction.
We know in an algebraic expression a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+aⁿ,
x's are variables a's are constants and n's are exponents.
∴ In the algebraic expression 5x + 3y² + 4,
Constants are the numerical values which are 5, 3, and 4.
The variables are x and y and the exponents are the powers of the variables 2 for y and 1 for x and the coefficients are 5 and 3.
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Given the function f(x)=-5x^2-x+20 find f(3)
f(3) = -5*3^2 - 3 + 20 = -5*9 - 3 + 20 = -45 - 3 + 20 = -28;
Answer: - 28
Step-by-step explanation:
f(x) = -5x^2 - x + 20
To find f(3), we simply put x = 3 and then simplify
f(3) = - 5(3)^2 - 3 + 20
= -5(9) - 3 + 20
= -45 - 3 + 20
= -48 +20
= -28
f(3) = -28
Divide 30 by 1/2 and add 10 what is the answer?
A student solved the problem below by first dividing 20 by 10. What mistake did the student make?
A baseball team has won 20 games and lost 10 games. What percent of the games did the team win?
Answer:
Sample Response: The student divided the number of wins by the number of losses, instead of dividing the number of wins by the total number of games. The student should have divided 20 by 30.
What happens when you multiply a positive number by a positive number less than 1?
The sum of two positive numbers is 42. What is the smalles possible value of the sum of their squares?
A data set contains an independent and dependent variable. Which must be true of the data set if a linear function can be used to represent the data?
The set must have a constant additive rate of change.
The set must have a constant multiplicative rate of change.
The values in the set must be positive.
The values in the set must be increasing.
Answer:- The set must have a constant additive rate of change.
Explanation:-
Let X be a data set contains an independent and dependent variable.
The standard linear function is given by
[tex]y=mx+c[/tex] , where x is a independent variable and y is a dependent variable and m,c are the constants.
for m =1, y=x+c
for m=2, y=2x+c=x+x+c
for m=3, y=3x+c=x+x+x+c
1.Thus ,the set must have a constant additive rate of change.
2.The set must not have a constant multiplicative rate of change as the function will become exponential function given by [tex]y=Ab^X[/tex] which is not linear .
3.The values in the set can be positive or negative as the domain for linear function is the set of real numbers.
4.The values in the set must be increasing it is not necessary.