Answer:
II. 8
III. 2
Step-by-step explanation:
Solving an inequality
9 ≤ 3x +4
Subtract 4 from each side
9-4 ≤ 3x +4-4
5 ≤ 3x
Divide each side by 3
5/3 ≤ 3x/3
5/3 ≤ x
x must be greater than or equal to 5/3
I. - 7 this is not greater than or equal to 5/3
II. 8 this is greater than or equal to 5/3
III. 2 this is greater than or equal to 5/3
Martin, a carpenter wants to make a spice rack for the kitchen. He cuts a 16.24 feet long plank into 5 pieces of equal length. What is the length of each piece of wood ? Round to the nearest hundredth.
Solution
For this case we can solve the problem with the following operation:
[tex]\frac{16.24ft}{5}=3.248ft[/tex]And rounded the answer we got 3.25 ft
16.24*100 = 1624
5*100 = 500
And we can do this:
1624/500 = 812/250 = 406/125
003
_____
125 / 406
-0
____
-40
-0
____
406
-375
_____
31
Which two county libraries charge the same penalty per week
What is the solution to 4x-5(2x-1) <= 7(2x+3)
Fighting fires is a profession that is really heating up. The average firefighter works 160 hours a month and make $4,090 for the month. If you only work 32 hours in a week, how much will you make?
Working 32 hours a week will fetch you $818
How to calculate the amount you will make?From the question, the given parameters are:
Number of hours = 160
Earnings in a month = $4090
Start by calculating the unit rate
This is calculated using the following unit rate formula
So, we have
Unit rate = Earnings in a month/Number of hours
Substitute the known values in the above equation
So, we have
Unit rate = 4090/160
Evaluate the quotient
Unit rate = 25.5625
For 32 hours, the total earnings is
Total = Unit rate x Number of houts
So, we have
Total = 25.5625 x 32
Evaluate
Total = 818
Hence, you will earn $818 weekly
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For each of the following quadrilaterals, select all the properties that must be true.
Answer:
Rhombus: All sides congruent, two pairs of parallel sides
Parallelogram: Two pairs of parallel lines
Rectangle: 4 right angles, Two pairs of parallel sides
Step-by-step explanation:
Multiply and simplify completely ( 3x - 1 ) (3x + 1)
Answer:
9x^2-1
Step-by-step explanation:
Answer:
Step-by-step explanation:
Multiply (3x - 1) * (3x + 1)
= 9(x)^2 + 3x - 3x -1
= 9(x)^2 - 1
Mr. Stewart wants to cut a board that is 34 inches long into four pieces that are the same length. How long will each
board be after he cuts them?
08.0 inches
8.2 inches
8.4 inches
O 8.5 inches
2x-5y = 16 solve for y
[tex]\frac{2(x-8)}{5}[/tex] = y
To Solve: value of y
Given: 2x-5y=16
Solution: The solution to this problem involves the following steps:
2x-5y-16=0
2x-16=5y
[tex]\frac{2x-16}{5}[/tex] = y
[tex]\frac{2(x-8)}{5}[/tex] = y
Answer: The final answer is : [tex]\frac{2(x-8)}{5}[/tex] = y
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How do you solve -m=9
Hello!
So, we are given the following to solve:
[tex]-m=9[/tex]
To solve this, simply divide both sides by -1.
[tex]\frac{-m}{-1}= \frac{9}{-1}[/tex]
Then, simplify the expression and you have your solution.
[tex]m=-9[/tex]
Hope this helps! If so, please lmk! Thanks and good luck!
Answer:
m= -9
Step-by-step explanation:
Divide both sides by -1
[tex]\frac{-m}{-1} =\frac{9}{-1}[/tex]
Simplify m = - 9
What is the area, in square centimeters, of the shaded part of the rectangle shown below
Answer:100 cm
Step-by-step explanation: first, you would find the area of the whole rectangle.
L x W = A
10x14=140
Next, find the area of the unshaded part. To do this, you would subtract 6 from 14
14-6=8
After that, times 8 by 10, then divide by 2
10x8=80
80÷2=40
Take 40 and subtract it from the area of the whole rectangle
140-40=100
The rectangular waiting area for a popular amusement park ride is covered by a large sun canopy. The total area of the canopy, in square feet, is 100 square feet more than twice the area where guests wait.
Which equation could you use to find the area of the place where guests wait for the ride if the area of the canopy is 7,600 square feet?
The equation which can be used to find the area of the place where guests wait for the ride if the area of the canopy is 7600 square feet is:
2a+100=7600.
Given, The rectangular waiting area for a popular amusement park ride is covered by a large sun canopy.
The total area of the canopy, in square feet, is 100 square feet more than twice the area where guests wait.
let the area of the place where guests wait be represented by 'a'.
the canopy covers the area = 2a + 100
total area of the canopy = 7600
equation used to find the area of the place where guests wait for the ride if the area of the canopy is 7,600 square feet = ?
⇒ 2a + 100 = 7600
arrange the like terms.
⇒ 2a = 7600 - 100
calculate the difference.
⇒ 2a = 7500
⇒ a = 7500/2
⇒ a = 3750
Hence the area of the place where guests wait is 3750 square feet.
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Hi, can you help me to solve this problem, please !!!
Remember that
The y-intercept is the value of y when the value of x=0
In this problem
we have the equation
y=7x^2+4
For x=0
substitute
y=7(0)^2+4
y=4
the y-intercept is (0,4)Identifying Variables and Writing Functions Practice . A function describes how a dependent variable changes with respect to one or more independent variables. When there are only two variables, they are often summarized as an ordered pair with the independent variable first: (independent variable, dependent variable) The dependent variable is a function of the independent variable. If x is the independent variable and y is the dependent variable, write the function as y = f(x) Related Quantities. Write a short statement that expresses a possible relationship between the variables. Example: (age, shoe size) Solution: As a child ages, shoe size increases. Once the child is full-grown, shoe size remains constant. 1. (volume of a gas tank, cost to fill the tank) 2. (time, price of a Ford sedan), where time represents years from 1975 to 2017
Let's begin with what we know:
For an ordered pair, we have (independent variable, dependent variable)
For example, when x is the independent variable & y is the dependent variable, we have (x, y)
y = f(x)
We are to write a short statement that expresses a possible relationship between the variables below:
1. (volume of a gas tank, cost to fill the tank)
Volume of gas is the independent variable & Cost to fill the tank is the independent variable. That means that:
As the volume of the gas tank increases. the cost of filling it increases. Once the volume of the gas tank is filled, the cost to fill the tank is at its maximum
2. (time, price of a Ford sedan), where time represents years from 1975 to 2017
Time is the independent variable & price of a Ford sedan is the independent variable. That means that:
As the time lapses from 1975 to 2017, the price of the Ford sedan depreciates/reduces.
due in an hour pls help!!
If the point M (4,3) is translated using the rules (x, y) ⇒ (x, y-2), then the coordinates of the M' = (4,1)
The point is M(4,3)
The translation rules is
(x, y) ⇒ (x, y-2)
The translation states that the movement of the graph either horizontally or vertically. When we translate the graph, the shape and size will not change, only the coordinates of the graph changes.
We know the values of
x = 4
y = 3
Substitute the values in the equation
The coordinates of the M' = (x, y-2)
= (4, 3-2)
= (4,1)
Hence, if the point M (4,3) is translated using the rules (x, y) ⇒ (x, y-2), then the coordinates of the M' = (4,1)
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6. Create a systems of inequalities to represent the graph below
System of inequalities
We are given the graph where two lines represent the solution of a system of inequalities.
The solution is the double-shaded region of the graph.
We need to find the equation of the blue line and the red line and then convert them to inequalities.
Let's start with the blue line. We need to find two clear points through which it passes. These are (0,6) and (2,0). Now we write the equation of the line when knowing two points (the point-point form):
[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex][tex]\begin{gathered} \displaystyle y-6=\frac{0-6}{2-0}(x-0)=-3x \\ \text{Adding 6:} \\ y=-3x+6 \end{gathered}[/tex]For the red line, the points are (0,0) and (2,2):
[tex]\begin{gathered} y-0=\frac{2-0}{2-0}(x-0)=x \\ y=x \end{gathered}[/tex]Now we have the equations of the lines, we must convert the equation to inequality by inserting one of these symbols instead of the equal sign:
> ≥ < ≤
For the blue line, the equation of the line is:
y = -3x + 6
Testing the origin (0,0):
0 = 0 + 6
0 = 6
To convert this to a true inequality we must replace the = for < or ≤
Since the blue line is solid, the points on the line belong to the solution, thus the first inequality is:
y ≤ -3x + 6
Now for the red line. The equation is
y = x. Let's test the point (2,1)
1 = 2
We must use the sign ≤ to make the expression true, thus the second inequality is:
y ≤ x
Thus, the system of inequalities is:
y ≤ -3x + 6
y ≤ x
Complete the table and use the results to find the indicated limit.
Given the function:
[tex]k(x)=\frac{x^3-x-6}{x-2}[/tex]when x = 1.9
[tex]k(x)=\frac{1.9^3-1.9-6}{1.9-2}=\frac{-1.041}{-0.1}=10.41[/tex]when x = 1.999
[tex]k(x)=\frac{1.999^3-1.999-6}{1.999-2}=\frac{-0.0109944}{-0.001}=10.994001[/tex]When x = 2.001
[tex]k(x)=\frac{2.001^3-2.001-6}{2.001-2}=\frac{0.011006}{0.001}=11.006[/tex]When x = 2.1
[tex]k(x)=\frac{2.1^3-2.1-6}{2.1-2}=\frac{1.161}{0.1}=11.61[/tex]so, the limit of the function k(x) = 11
The answer is option A. 11
Julia just let a new candle and then let it burn all the way down to nothing. The candle
burned at a rate of 0.75 inches per hour and its initial length was 9 inches. Write an
equation for L, in terms of t, representing the length of the candle remaining
unburned, in inches, t hours after the candle was lit.
L=
Answer: L= 9-.75x
Step-by-step explanation: since it starts at 9 inches tall and is melting at .75 inches per hour, it's going to be the initial length, 9, minus the rate, .75, times the time/hours past, so x
Solve the compound inequality. 2x-4 > 8 or 3x-1 < -10
-3 < x < 6
x > 6 or x < -3
x > 2 or x < -3
x < 6 or x < -3
The solution to the compound inequality is x > 6 or x < -3
How to solve compound inequality?An inequality is a mathematical expression that has <, >, ≤ and ≥.
A compound inequality is an inequality that combines two simple inequalities.
Therefore, let's solve the compound inequality as follows:
2x - 4 > 8 or 3x - 1 < - 10
2x - 4 > 8
add 4 to both sides of the inequality
2x - 4 + 4 > 8 + 4
2x > 12
divide both sides by 2
x > 12 / 2
x > 6
3x - 1 < - 10
add 1 to both sides of the inequality
3x - 1 + 1 < - 10 + 1
3x < - 9
divide both sides by 3
x < -9 / 3
x < -3
Therefore, x > 6 or x < -3
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The solution to the compound inequality will be; x > 6 or x < -3
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two functions in an problem.
A compound inequality is defined as an inequality that combines two simple inequalities.
Therefore, solve the compound inequality that will be;
2x - 4 > 8 or 3x - 1 < - 10
2x - 4 > 8
Then add 4 to both sides of the inequality so,
2x - 4 + 4 > 8 + 4
2x > 12
Now, divide both sides by 2
x > 12 / 2
x > 6
3x - 1 < - 10
Again, add 1 to both sides;
3x - 1 + 1 < - 10 + 1
3x < - 9
Then divide both sides by 3;
x < -9 / 3
x < -3
Therefore, solution to the compound inequality is; x > 6 or x < -3
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(10, 10) А (2, 4) Find point C so that that the ratio of length Ad to the length of CB is 3:1
ANSWER
[tex](8,8.5)[/tex]EXPLANATION
When a line segment is divided by ratio m:n, the coordinates of the point of division are given as:
[tex](\frac{mx_2+nx_1}{m+n},\frac{my_2+my_1}{m+n})[/tex]where (x₁, y₁) and (x₂, y₂) are the coordinates of the ends of the line.
Therefore, we have that:
[tex]\begin{gathered} m=3;n=1 \\ (x_1,y_1)=(2,4) \\ (x_2,y_2)=(10,10) \end{gathered}[/tex]Therefore, the coordinates of point C are:
[tex]\begin{gathered} (\frac{3\cdot10+1\cdot2}{3+1},\frac{3\cdot10+1\cdot4}{3+1}) \\ (\frac{30+2}{4},\frac{30+4}{4}) \\ (\frac{32}{4},\frac{34}{4}) \\ (8,8.5) \end{gathered}[/tex]Those are the coordinates of C.
An economy size car can travel 32 miles for each gallon of gasoline. The function d(g) = 32g represents the distance traveled in miles, d(g), that the car can travel with g gallons of gasoline. Find d(30).
*Type in your answer.
d(30) = miles
The number of miles to drive for 30 gallons is 960 miles
How to determine the function value?From the question, the function definition is given as
d(g) = 32g
Where g represents the number of gallons and d represents the distance
The function value to calculate is given as
d(30)
This means that we calculate the number of miles to drive for 30 gallons
So, we have
d(30) = 32(30)
This gives
d(30) = 32 x 30
Evaluate the product
d(30) = 960
Hence, the function value is d(30) = 960
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XYZ has coordinates X(2, 3), Y(1, 4), and Z(8, 9). A translation maps X to X′(4, 8). What are the coordinates for Z′? *
Answer:
Z'(10, 14)
Explanation:
Taking into accoun that the vertex point X(2, 3) is mapped to X'(4, 8), we can say that the translation rule is:
(a, b) ----> (a + 2, b + 5)
Because
X(2, 3) ----> (2 + 2, 3 + 5)
----> X'(4, 8)
So, using this rule, we can find the coordinates for Z' as:
Z(8, 9) ----> (8 + 2, 9 + 5)
----> Z'(10, 14)
Therefore, the answer is Z'(10, 14)
Identify at least two pairs of congruent angles in the figure and explain how you know they are congruet
you didn't attach the figure....
Pls help solve all 3 questions
Thank you :)
Answer:
Q18: x = 21, y = 15
Q19: x = 16, y = 10
Q20: x = 24, y = 19
Step-by-step explanation:
Q18:
(3x - 16) + (6x + 7) = 180 (corresponding angles, sum of angles on a straight line=180°)
9x - 9 = 180
9x = 189
x = 21
11y - 32 = 6x + 7 (vertically opposite angles)
11y - 32 = 6(21) + 7
11y - 32 = 133
11y = 165
y = 15
Q19:
8x - 14 = 5x + 34 (corresponding angles, vertically opposite angles)
3x = 48
x = 16
(8x - 14) + (5y + 16) = 180 (sum of angles on a straight line=180°)
8(16)-14 + (5y + 16) = 180
114 + 5y + 16 = 180
5y + 130 = 180
5y = 50
y = 10
Q20:
47 + 3x + (2x + 13) = 180 (corresponding angles, sum of angles on a straight line=180°)
5x + 60 = 180
5x = 120
x = 24
5y - 23 = 3x (corresponding angles)
5y - 23 = 3(24)
5y - 23 = 72
5y = 95
y = 19
What is the value of the expression below when z=3?
10z^2 +7z+4
The value of the expression [tex]10z^2[/tex]+7z+4 when z = 3 is 115
The expression is
[tex]10z^2[/tex]+7z+4
The expression is defined as the statements that have a minimum of two terms containing numbers or variables , connected by an operator in between. The operator maybe addition, subtraction, division, multiplication etc..
The expression is
[tex]10z^2[/tex]+7z+4
The value of z = 3
Substitute the value of z in the given expression
= [tex]10(3)^2[/tex]+ 7×3 + 4
= 10×9 + 21 + 4
Multiply the terms first
= 90 + 21 + 4
Add them together
= 115
Hence, the value of the expression [tex]10z^2[/tex]+7z+4 when z = 3 is 115
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What is the answer? Pls
Answer:
70
Step-by-step explanation:
f(1)=6, f(n)=f(n-1)+4
n = 1 → a1 = 6 ← given value
n = 2 → a2 = 6+4 = 10
n = 3 → a3 = 6+4+4 = 14
n = 4 → a4 = 6+4+4+4 = 18
n = 17 → a4 = 6+(4 * 16) =
(its 4 times 16 because 16 is 17 - 1 or n - 1)
n = 17 → a4 = 6+(64) = 70
socraticorg
Tony B
What number is five times the first number. The third number is 100 more than the first number. Of the sound of three numbers is 490, find the numbers
Answer:
The three numbers are:
4.62,
23.1, and
462.2
Step-by-step explanation:
Let X be the "first number."
B = What number is five times the first number: 5X
C = third number is 100 more than the first number: 100X
The sum of all three is 490: X + B + C = 490
----
X + B + C = 490
X + 5X + 100X = 490
106X = 490
X = 4.622
Check:
X = 4.622
B = 5X = 23.11
C = 100X = 462.2
Check:
Sum (4.622 + 23.11 + 462.2) = 490
A car rental company charges an initial fee plus an additional fee for each mile driven. The charge depends on the type of careconomy luxury The charge E dollars) to rent an economy car is given by the function E = 15.95 + 0.60M where M is the number of miles drivenThe charge (dollars) to rent a luxury car is given by the function L = 18.20 + 1.25M be how much more it costs to rent a luxury car than an economy car (in dollars)an equation relating C to Simplify your answer as much as possible
C=34.15+0.65M
ExplanationGiven
[tex]\begin{gathered} E=15.95+0.60M \\ L=18.20+1.25\text{ M} \\ where \\ E\text{ is the cost to rental an Economy car} \\ Lis\text{ the total cost to rental an Luxury car} \\ M\text{ is the number of miles traveled} \end{gathered}[/tex]so
to Know C, how much more it costs to rent a Luxuy can than an economc, we need to do a subtraction, hence
[tex]\begin{gathered} C(M)=L(M)-E(M) \\ \end{gathered}[/tex]so, replace and simplify
[tex]\begin{gathered} C(M)=L(M)-E(M) \\ C=18.20+1.25M-(15.95+0.60M) \\ C=18.20+1.25M-15.95-0.60M \\ C=34.15+0.65M \end{gathered}[/tex]therefore, the answer is
C=34.15+0.65M
I hope this helps you
C=34.15+0.65M
ExplanationGiven
[tex]\begin{gathered} E=15.95+0.60M \\ L=18.20+1.25\text{ M} \\ where \\ E\text{ is the cost to rental an Economy car} \\ Lis\text{ the total cost to rental an Luxury car} \\ M\text{ is the number of miles traveled} \end{gathered}[/tex]so
to Know C, how much more it costs to rent a Luxuy can than an economc, we need to do a subtraction, hence
[tex]\begin{gathered} C(M)=L(M)-E(M) \\ \end{gathered}[/tex]so, replace and simplify
[tex]\begin{gathered} C(M)=L(M)-E(M) \\ C=18.20+1.25M-(15.95+0.60M) \\ C=18.20+1.25M-15.95-0.60M \\ C=34.15+0.65M \end{gathered}[/tex]therefore, the answer is
C=34.15+0.65M
I hope this helps you
The sum of three palm tree heights range from 32 to 42 feet. The height of two of the trees are 8 feet and 16 feet. If the height of the third tree is x feet, write and solve a compound inequality to show the possible heights of the third tree.
The inequality to show the possible heights of the third tree is 8 ≤ x ≤ 18.
How to calculate the value?Inequalities are created through the connection of two expressions. It should be noted that two expressions in an inequality aren't always equal. They are denoted by the symbols ≥ < > ≤
Let the height of the third tree be x.
By the given condition, this will be:
8 + 16 + x ≥ 32 and 8 + 16 + x ≤ 42
The first relation will give x ≥ 32 - 24 = x ≥ 8
The second relation will give:
8 + 16 + x ≤ 42
24 + x ≤ 42
x ≤ 42 - 24
x ≤ 18
The inequality is 8 ≤ x ≤ 18.
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If sum of three palm tree heights range from 32 to 42 feet. The height of two of the trees are 8 feet and 16 feet. If the height of the third tree is x feet. Then compound inequality is 8 ≤ x ≤ 18.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
Let height of the third tree be x.
By the given condition
The sum of three palm tree heights range from 32 to 42 feet
8 + 16 + x ≥ 32 and 8 + 16 + x ≤ 42
Solve these inequalities
8 + 16 + x ≥ 32
24+x ≥ 32
x≥ 32-24
x≥ 8
and 8 + 16 + x ≤ 42
24+ x ≤ 42
x≤ 42-24
x ≤ 18
Hence the inequality is 8 ≤ x ≤ 18.
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A glacier is moving at a rate of 0.3 inches every hour. The table below represents this relationship.
Glacial Movement
Distance Moved (inches)
Time
(hours)
0.3
1
0.6
2
0.9
3
x
4
What value of x completes the table?
1.2
1.5
3.6
13.3
Answer:
1.2
Step-by-step explanation:
7
1
-5
35
-4 24
-3 15
-2 8
-1 3
0 0
1 -1
Match the average rates of change of f(x) to the corresponding intervals.
-7
-4
300
[-5, -1]
(-4,-1]
[-3, 1]
-2,1]
The rates of changes of the given function for the corresponding intervals are: [-5, -1] = -8, [-4, -1] = -7, [-3, -1] = -6, [-2, -1] = -5.
What is function?
A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.
This means that a function f will map an object x to exactly one object f(x) in the set of potential outputs if the object x is in the set of inputs (referred to as the domain) (called the codomain).
The rate of change of a function can be calculate using the formula:
[tex]R = \frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
Putting the value from the question:
given [x₁, x₂] = [-5, -1]
f(-5) = 35 , f(-1) = 3
Putting these value in formula:
[tex]R = \frac{3-35}{-1 -(-5)}[/tex]
R = -32/4
R = -8
given [x₁, x₂] = [-4, -1]
f(-4) = 24, f(-1) = 3
Putting these value in formula:
[tex]R = \frac{3-24}{-1 -(-4)}[/tex]
R = -21/3
R = -7
given [x₁, x₂] = [-3, -1]
f(-3) = 15, f(-1) = 3
Putting these value in formula:
[tex]R = \frac{3-15}{-1 -(-3)}[/tex]
R = -12/2
R = -6
given [x₁, x₂] = [-2, -1]
f(-2) = 8, f(-1) = 3
Putting these value in formula:
[tex]R = \frac{3-8}{-1 -(-2)}[/tex]
R = -5/1
R = -5
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