John makes $8 per hour walking dogs and $16 per hour as a math tutor. This weekend, he wants to work no more than 10 hours. He also wants to earn at least $96. Create a system of inequalities to model this
John must work 8 hours walking the dog and 2 hours as a Maths tutor in order to earn at least $96.
Let us assume that m represents the number of hours he walks the dogs
and n represents the number of hours he works as a maths tutor
John wants to work no more than 10 hours.
As we know the statement 'No more' is represented by the inequality '≤'
So, we get an inequality
m + n ≤ 10 ...........(1)
Also, he also wants to earn at least $96.
As we know the statement 'at least' is represented by the inequality '≥'
So, we get an inequality
8m + n ≥ 96 ...........(2)
So, we get a system of inequalities:
m + n ≤ 10
8m + n ≥ 96
Now, we solve this system of inequalities.
Consider m + n = 10 .........(3)
and 8m + n = 96 .........(4)
Substitute m = 10 - n for x in Equation 4
8(10 - n) + 16n = 96
80 - 8n + 16n = 96
8n = 96 - 80
n = 2
Substitute above value of n in equation m = 10 - n
m = 10 - 2
m = 8
Thus, John must work 8 hours walking the dog and 2 hours as a Maths tutor.
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The complete question is:
John makes $8 per hour walking dogs and $16 per hour as a math tutor. This weekend, he wants to work no more than 10 hours. He also wants to earn at least $96. Create a system of inequalities to model this and solve.
Which descriptions and equations could be the function rule? Select all that apply. The table in attached image shows some of the input and output values for a function rule.
For the given table of values the equation that could be the function rule is option 4: y = 3x - 2.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The table of input and output values are given for the function.
The slope-intercept form of an equation/function is - y = mx + b
To find the slope m use the formula -
(y2 - y1)/(x2 - x1)
Substituting the values in the equation -
[-2 - (-11)]/[0 - (-3)]
(-2 + 11)/(0 + 3)
9/3
3
So, the slope point is obtained as m = 3.
The equation becomes - y =3x + b
To find the value of b substitute the values of x and y in the equation -
-11 = 3(-3) + b
-11 = -9 + b
b = -11 + 9
b = -2
So, the value for b is -2.
Now, the equation becomes -
y = 3x - 2
The graph is plotted for the function.
Therefore, the equation is y = y = 3x - 2.
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Which term is missing in this problem?
2x3 + 5x2 + 9
x + 3
After performing the division , the missing term in the problem is (2x³ + 5x² + 9)/(x + 3) = (2x² -x +3) .
The problem is (2x³ + 5x² + 9)/(x + 3) ;
that means , we have to divide , the expression "2x³ + 5x² + 9" by "x + 3" ;
first we multiply (x+3) by 2x² ;
the expression becomes : 2x³ + 5x² + 9
-2x³ - 6x²
-x² + 9
next we multiply by -x : -x² - 3x
3x + 9
next we multiply by 3 : -3x - 9
0 .
So , dividing the "2x³ + 5x² + 9" by "x + 3" , we get the remainder is 0 and the quotient is 2x² - x + 3 .
Therefore , the missing term is 2x² - x + 3 .
The given question is incomplete , the complete question is
Which is the missing term in this problem ?
(2x³ + 5x² + 9)/(x + 3) = ______ ;
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Does anyone know the answer?
Answer:
b or c
Step-by-step explanation:
126+6x=180
180-126=54
54/6=9
x= 9
Move a number to each box to create an equation to solve 8/100+9/10 =
The solution of the given fraction can be gotten through filling the boxes with the following values respectively;
8/100 + 9/10 = 98/100
What is a fraction?A fraction is defined as the representation of a part of a whole value in the form of a numerator and denominator.
The given fraction;
8/100 + 9/10 = ?
Find the lowest common multiple of the denominator = 100.
= 8/100 + 9/10
= 8 + 90/100
= 98/100
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Sylvan solved the division problem below. He made a mistake in his method. 1.6 divided by 0.4 with quotient 0.4. Subtract 1.6 from 1.6. Zero left over. A. What is the mistake that Sylvan made solving the problem?
Sylvan made a mistake computing the quotient in the problem.
What is the BODMAS rule?According to the BODMAS rule, the brackets have to be solved first followed by powers or roots (i.e. of), then Division, Multiplication, Addition, and at the end Subtraction. Solving any expression is considered correct only if the BODMAS rule or the PEMDAS rule is followed to solve it.
Given here: 1.6 divided by 0.4
We know 1.6 can be expressed as 1.6=0.4×4
x ÷ y = z.
1.6÷0.4=4
Division method is nothing but the inverse of multiplication.
Divide 1.6 by number 0.4.
Solution:1.6÷0.4=1.6/0.4 with remainder zero
=4
Thus the quotient should have been 4
But according to Sylvan 1.6/0.4=0.4 which is not correct.
Hence, Sylvan computed the wrong quotient.
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X+3y=14 and 2x-3y=-8
To solve this system of equations, we can use the method of elimination. The goal is to eliminate one of the variables, such as x or y, by adding or subtracting the equations.
First we can eliminate the y variable by adding the two equations together:
X + 3y = 14
2x - 3y = -8
3x = 6
Dividing both sides by 3:
x = 2
Now we have the value of x, we can substitute it back into one of the original equations:
X+3y=14
2 + 3y = 14
Subtracting 2 from both sides:
3y = 12
Dividing both sides by 3:
y = 4
So the solution of the system of equations is (x,y) = (2,4)
To check the solution, we can substitute the values back into the original equations:
x + 3y = 14
2 + 3(4) = 14
2 + 12 = 14
14 = 14
and
2x - 3y = -8
2(2) - 3(4) = -8
4 - 12 = -8
-8 = -8
As the equation holds true, the solution (2,4) is correct.
The play area in a local park ha the dimenion hown at the right. What i the area of the park? 25 m 24 m 30 m What i the bae of the triangle? What i the height of the triangle? PLEASE HELP
The area of parks is 360 m² , base and height are respectively 30m and 24 m.
Given a triangle shaped park with sides 25m, 24m and 30 m.
The total area that is bounded by a triangle’s three sides is referred to as the triangle’s area.
We know that area of triangle = ½ * base * height
Clearly show that base is 30m and height is 24 m.
So, area of triangle = ½ * 30 * 24 = 720/2 = 360 m²
Therefore, area of triangle shaped park is 360m².
Base and height are respectively 30m and 24m.
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the cover charge for entering mandi's dance hall is $5. drinks are then $6 each. what equation, in point-slope form, will give the total cost for the cover charge and drinks?
The equation of the total cost for the cover charge and drinks in point-slope form is y = 6x + 5.
The point-slope form of a linear equation is given by -
[tex]y - y_1 = m(x- x_1)[/tex]
where m is the slope and [tex](x_1, y_1)[/tex] is a point on the line.
Here, the total cost for the cover charge and drinks can be represented by the equation y = mx + b, where y is the total cost, x is the number of drinks, m is the cost per drink, and b is the cost of the cover charge.
We know that the cover charge is $5 and drinks are $6 each, so, we can find the slope (m) of the equation by using the cost per drink which is m = 6.
We can also find the point [tex](x_1, y_1)[/tex] by using the cover charge cost which is (0,5).
Therefore, the equation in point-slope form of the total cost for the cover charge and drinks will be -
y - 5 = 6(x-0)
y - 5 = 6x
y = 6x + 5
Where x is the number of drinks and y is the total cost i.e. cover charge + drinks.
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USE the figure to complete the statement if not similar choose not similar
Only one angle of the triangles ΔABC and ΔDEF is congruent. Then the triangles ΔABC and ΔDEF are not similar to each other.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
In triangle ΔABC, angle ∠B = 86° and ∠C = 55°, then angle ∠A is given as,
∠A + ∠B + ∠C = 180°
∠A + 86° + 55° = 180°
∠A = 39°
In triangle ΔDEF, angle ∠D = 55° and ∠F = 40°, then angle ∠E is given as,
∠E + ∠F + ∠D = 180°
∠A + 40° + 55° = 180°
∠A = 85°
Only one angle of the triangles ΔABC and ΔDEF is congruent. Then the triangles ΔABC and ΔDEF are not similar to each other.
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X 3 6 9 12 y 1 5 10 12 What is the r.o.c? Is this linear?
The rate of change is given a 5 / 6. The values we have here are not linear
How to solve for the rate of changeThe rate of change (r.o.c) is the change in y (or the dependent variable) for every unit change in x (or the independent variable). In this case, the r.o.c is
(10-5) / (12-6) = 5/6.
This is not linear because linear is a relationship between a variable and a constant, here the relationship between y and x is not linear because the change in y is not constant with respect to the change in x.
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Solve and classify the given system of linear equations. p=5(q+2) p=q-3
Answer:
q= -3.25 and p= -6.25
Step-by-step explanation:
p=5q+10. p=q-3
p-5q=10. p-q=-3 subtract the two equations
-4q=13 q= -3.25 and p= -6.25
In 2010 an item costs $9.00. The price increases by 1.5% each year. How much will it be in 2020?
The term is actually forming an AP.
On 2010 = $9 = a
[tex] \frac{1.5}{100} \times 9 \\ = \frac{13.5}{100} \\ = 0.135[/tex]
d = $0.135
now on 2020, that's 10 years after 2010.
n = 10
[tex]an = a + (n - 1)d \\ = 9 + (10 - 1)0.135 \\ 9 + 9(0.135) \\ = 9 + 1.215 \\ = 10.215[/tex]
THE FINAL ANSWER - $10.125Please don't forget to mark braini if u are satisfied with answerthere might be another ways to solve this problem, but the simplest way is AP.Ani bought a bag to hold her dive weights. the bags manufacturer claims that it can hold 53 pounds without breaking. ani has placed 29 pounds in the bag. how many more pounds can she place in the bag before it breaks? What is the inequality to represent the situation. Solve the inequality and graph your solution.
The bag can hold a maximum of 53 pounds before breaking, and Ani has already placed 29 pounds in the bag. To find out how many more pounds she can place in the bag, we can subtract the weight already in the bag from the maximum weight the bag can hold:
53 - 29 = 24
So Ani can place 24 more pounds in the bag before it breaks.
The inequality to represent this situation is:
weight in bag + x <= 53 (x represents the amount of weight Ani can put in the bag before it breaks)
To find the solution, we can substitute the value of weight in bag and get
29 + x <= 53
Now we can solve the inequality for x
x <= 24
The solution is x <= 24, which means Ani can place 24 more pounds or less in the bag before it breaks.
To graph the solution, we can start with the number line, and plot the point 24 to the right of the origin, and shade the region to the left of the point. This represents the solution set of x <= 24, which means Ani can place 24 more pounds or less in the bag before it breaks.
Interest is compounded semianually. Find the amount in the account after the given time. Principal Rate of Interest Time $2000 6% 3 years The amount in the account is $? (Round to the nearest cent)
Answer:
$2837.04
Step-by-step explanation:
semi-annually = every 6 month
p=2000
i=6%
t=3 years = 6 periods
compound 6 times in 3years = (1+6%)^6 =1.418519
multiply principal of $2000 = 2837.04
10)
2(34 + 12) > 50
This inequality contains a variable, b. Choose ALL numbers that make this inequality true.
A)
16
B)
18
0
19
ELIM
D)
20
E)
22
11)
Which factorization is equivalent to this expression?
For the inequality "2(34 + 12) > 5b" that contain a variable "b" , then the numbers that make this inequality true are (a) 16 , (b) 18 .
The inequality containing the variable "b" is ⇒ 2(34 + 12) > 5b ;
simplifying the inequality ,
we have ;
⇒ 2×(46) > 5b ;
⇒ 92 > 5b ;
(a) Substituting value of b = 16 ,
we get ; 92 > 5×16
⇒ 92 > 80 , TRUE .
(b) Substituting value of b = 18 ,
we get ; 92 > 5×18
⇒ 92 > 90 , TRUE .
(c) Substituting value of b = 19 ,
we get ; 92 > 5×19
⇒ 92 > 95 , FALSE .
(d) Substituting value of b = 20 ,
we get ; 92 > 5×20
⇒ 92 > 100 , FALSE .
Therefore , the inequality is TRUE for two values of b that are (a) 16 , (b) 18.
The given question is incomplete , the complete question is
This inequality 2(34 + 12) > 5b ; contains a variable "b". Choose ALL numbers that make this inequality true.
(a) 16
(b) 18
(c) 19
(d) 20
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If triangle NPQ is congruent to triangle RSQ the perimeter of triangle NPQ= 7x+2, and the perimeter of triangle RSQ=10x-4, find the perimeter of triangle NPQ
The perimeter of triangle NPQ is calculated to be 72 when NPQ is given congruent to RSQ.
Perimeter of triangle NPQ = 7x + 2
Triangle perimeter: RSQ = 10x - 4
As triangle NPQ is given congruent to triangle RSQ, we have,
NQ / RQ = PQ / SQ = 24 / 32 = 21 / 28 = 3 / 4
The above ratio can be equated to the ratio of perimeters of the triangles NPQ and RSQ.
Perimeter of triangle NPQ/Perimeter of triangle RSQ = 7x + 2/10x - 4 = 3/4
7x + 2/10x - 4 = 3/4
On cross multiplication and solving, we have, x = 10.
The perimeter of triangle NPQ = 7x + 2 = 70 + 2 = 72
The question is incomplete. The complete question has the picture of two congruent triangles given in the below attachment.
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6. Which measure is equivalent to 660 feet?
7800 inches
mile
330 yards
1980 yards
=> Convert feet into yards.
660 feet = 220 yards.
=> Convert feet into inches.
660 feet = 7920 inches.
Now, According to the question:
=> Convert feet into inches.
660 feet = 7920 inches
Formula: multiply the value in feet by the conversion factor '12'.
So, 660 feet = 660 × 12 = 7920 inches.
=> Convert feet into yards.
660 feet = 220 yards
Formula: divide the value in feet by 3 because 1 yard equals 3 feet.
So, 660 feet = 660/3
660 feet = 220 yards.
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Solve the following linear equations.
1. y + y+1 + y+2 = 90
2. 5(m+4)=-20
3. 3x-8=2x+2
Answer:
1. y=29
2. m= -8
3. x=10
Step-by-step explanation:
1. Add the numbers
y+y+1+y+2=90
y+y+3+y=90
combine like terms
3y+3=90
Subtract 3 from both sides
3y+3-3+90-3
3y=87
Divide both sides by the same factor
3y/3 = 87/3
y=29
2. Distribute
5(m+4)=-20
5m+20=-20
Subtract 20 from both sides
5m+20=-20
5m+20-20+-20-20
Simplify
5m=-40
Divide both sides by the same factor
5m/5 = -40/5
m= -8
3. Add 8 to both sides
3x-8=2x+2
3x-8+8+2x+2+8
Simplify
3x=2x+10
Subtract 2x from both sides
3x=2x+10
3x-2x+2x+10-2x
x=10
A ski resort charges $14 for snowshoe rental, plus an additional dollar per hour. Let h represent the duration of a rental in hours and c represent the total cost of the rental. Complete the equation that represents the relationship between h and c.
c=14+xh is the equation that represents the relationship between h and c.
What is Expression?An expression is combination of variables, numbers and operators.
Given that ski resort charges $14 for snowshoe rental, plus an additional dollar per hour.
Let h represent the duration of a rental in hours and c represent the total cost of the rental.
We have to find the relationship between h and c.
c=14+xh
Here x represents the dollar.
Hence, c=14+xh is the equation that represents the relationship between h and c.
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Which tables represent functions? Select all that apply.
Group of answer choices
x y
-2 -2
-1 0
-2 3
2 5
x y
4 -2
1 -1
0 0
4 2
x y
-3 -9
-1 -3
0 0
5 15
x y
0 -2
2 0
3 1
7 5
Answer:
3 and 4
Step-by-step explanation:
numbers don't repeat in the X side
what is the distance between (-6 5) and (-6 -3.5)
The distance between (-6 5) and (-6 -3.5) is 14.71 units
How to find length of the lineThe length of line in an ordered pair is calculated using the formula
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
where
d = distance between the points
x₂ and x₁ = points in x coordinates
y₂ and y₁ = points in y coordinates
distance between points (-6, 5) and (-6, -3.5) is calculated as follows
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
d =√{(-6 - 6)² + (5 - -3.5)²}
d =√{144 + 72.25}
d = √216.25
d = 14.71 units
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Curated Practice Problem Set #9
1.
It takes 2 ounces of paint to completely cover all 6 sides of a rectangular prism box which holds 15
cups of sugar. Double the dimensions of the box. Approximately how much paint would the new
box need? How much sugar would it hold?
As per the given ratio, the amount of paint is 8 ounces needed is and the amount of sugar it will hold 120 ounces.
In math then term ratio is defined as an ordered pair of numbers a and b, written a / b where b does not equal 0
Here we have given that it takes 2 ounces of paint to completely cover all 6 sides of a rectangular prism box which holds 15 cups of sugar.
And then here we have know that they double the dimensions of the box.
Let us consider that the dimension be a.
And as we all know that double the dimensions of the box then dimensions are 2a
Then the ratio of paint and the area of the box remains constant and it can be calculated as,
=> paint / area = 2/x
=> 2/x = 6a² / 6(2a)²
When we simplify this one then we get then x is 8 ounces.
Here we know that the ratio of sugar and the volume of the box remains constant.
Then the sugar volume is calculated as,
=> 15 / X = a³ / (2a)³
When we simplify this then we get the value of x is 120
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Given f (x)=9-14/x, find all c in the interval [2, 7] that satisfy the Mean Value Theorem
The value of c is √14 in the interval [2, 7], which satisfies the Mean Value Theorem.
By definition, the mean value theorem is
f'(c) = [f(b) - f(a)]/b - a
So, in this case, we know that a = 2 and b = 7.
Now, we need to find f(2) and f(7) by replacing those values with the given function
f(x) = 9 - 14/x
f(7) = 9 - 14/7 = 9 - 2 = 7
So, f(b) = f(7) = 7.
f(x) = 9 - 14/x
f(2) = 9 - 14/2 = 9 - 7 = 2
So, f(a) = f(2) = 2
Then, we replace all values,
f'(c) = [f(b) - f(a)]/b - a
= (7 - 2)/(7 - 2)
= 5/5
= 1
Now, calculate the derivative of the function, which has to be equal to 1,
f(x) = = 9 - 14/x
f'(x) = 14/x² = 1
Now, we solve the equation to calculate the value of c,
14/x² = 1
x² = 14
x = √14
Therefore, c = √14 is the value inside the given interval that satisfies the mean value theorem.
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Which of the following statements is true?
C
Step-by-step explanation:
c,c is the answer i think so
you know there are 2 boys and an unknown number of girls in a nursery at a hospital. then a woman gives birth a baby, but you dont know its gender, and it is placed in the nursery. then a nurse comes in a picks up a baby and it is a boy. given that the nurse picks up a boy, what is the probability that the woman gave birth to a boy?
The probability that the woman gave birth to a boy, given that the nurse picked up a boy, is 1/3.
There are 2 boys initially and an unknown number of girls in the nursery, so there were a total of 2 + x babies in the nursery, where x is the number of girls.
Since we know that one of those babies is a boy, there are a total of 2 + x - 1 = 1 + x babies left in the nursery.
So the probability of the nurse picking up a boy, given that the woman gave birth to a boy, is 1/(1+x).
P(boy | picked up boy) = P(picked up boy | boy) * P(boy) / P(picked up boy)
= (1/(1+x)) * 1/2 / (1/(1+x) * 1/2 + x/(1+x) * 1/2)
= 1/3
So the probability that the woman gave birth to a boy, given that the nurse picked up a boy, is 1/3.
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When filled to the brim, a swimming pool can hold 9.745 cubic yards of water. Calculate the width of the swimming pool if it has a length of 3 yards and a height of 2 yards.
The width of the swimming pool is 1.624yards.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
Here, we have,
a swimming pool can hold 9.745 cubic yards of water.
i.e. V = 9.745
it has a length of 3 yards and a height of 2 yards.
i.e. l= 3
h=2
so, width = w = V/(l*h)
i.e. w = 1.624
Hence, the width of the swimming pool is 1.624yards.
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how many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3, and 4? repetition of digits is allowed.
The integers greater than 999 but not greater than 4000 is 375.
Integers are the collection of whole numbers and negative numbers. Similar to whole numbers, integers also does not include the fractional part. Thus, we can say, integers are numbers that can be positive, negative or zero, but cannot be a fraction. We can perform all the arithmetic operations, like addition, subtraction, multiplication and division, on integers. The examples of integers are, 1, 2, 5,8, -9, -12, etc. The symbol of integers is “Z“.
The smallest number in the series is 1000, a4-digit number.
The largest number in the series is 4000, a4-digit number
The left most digits (thousands place) of each of the 4 digit numbers other than 4000 can take one of the 3 values 1 or 2 or 3.
The next 3 digits (hundreds, tens and units place) can take any of the 5 values 0 or 1 or 2 or 3 or 4.
Hence, there are 3×5×5×5 or 375 numbers from 1000 to 3999.
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12.) Solve the right triangle. Round answers to the nearest tenth. To receive full credit you must show all work. M 8 40° K L 2 Solve the right triangle Bound answers to the nearest tonth KL = ML = mZK =
Answer: KL = 6.1, MK = 5.2 and the angle mZK = 40.
Step-by-step explanation: In this problem, to solve for the remaining sides and angles of the triangle, we can use trigonometry.
First, let's use the sine function to find the value of KL:
sin(40) = KL/ML
KL = (sin(40))(ML)
KL = (sin(40))(8)
Next, let's use the cosine function to find the value of MK:
cos(40) = MK/ML
MK = (cos(40))(ML)
MK = (cos(40))(8)
Finally, let's use the tangent function to find the value of mZK:
tan(40) = KL/MK
mZK = tan(40)
To round the answers to the nearest tenth, we can use the function Math.round(x * 10) / 10 in Javascript.
sin(40) = 0.766
cos(40) = 0.644
tan(40) = 1.193
KL = (0.766)(8) = 6.128 ≈ 6.1
MK = (0.644)(8) = 5.152 ≈ 5.2
mZK = 1.193
So the triangle KL = 6.1, MK = 5.2 and the angle mZK = 40.
Answer:
To solve the right triangle, we can use the trigonometric ratios sine, cosine, and tangent.
Given:
angle K = 40°
ML = 8
KL = 2
We can use the sine function to find the value of angle M:
sin(M) = KL / ML
sin(M) = 2 / 8
sin(M) = 0.25
So M = arcsin(0.25) = 14.04 (approximately)
Next, we can use the cosine function to find the value of MK:
cos(M) = ML / KL
cos(M) = 8 / 2
cos(M) = 4
So MK = 4
Lastly, we can use the tangent function to find the value of angle L:
tan(L) = KL / MK
tan(L) = 2 / 4
tan(L) = 0.5
So L = arctan(0.5) = 26.57 (approximately)
So the triangle is ML = 8, KL = 2, and angles M = 14.04° and L = 26.57° rounded to the nearest tenth.
x-y = -8 7x + 5y = 16
Which one is correct?
(8,16) or (-2,6)
Please explain how you got the answer.
Answer:
I think it is (8,16).