Answers
The graph for the inequality y ≥ 2 - 2x is a downward sloping line with a y-intercept of 2. The area above this line, including the line itself, is shaded to denote the solutions for the inequality.
Explanation:The equation y ≥ 2 - 2x is a linear inequality with a slope of -2 and a y-intercept of 2. It is represented graphically as a straight line where y is equal to or larger than 2 - 2x. As the coefficient of x is negative, the line will slope downwards towards the right based on the rule mentioned in Figure 12.4 (c).
In a two-dimensional (x-y) graph, x represents the independent variable while y is the dependent variable. Thus, for every increase of 1 unit on the x-axis (horizontally), the value of y decreases by 2 units (vertically) due to the slope of -2.
Since y is greater than or equal to 2 - 2x, the area above the line (including the line itself as it's a 'greater than or equal to' inequality) will be shaded when the inequality is graphed. This shading means that any point within this area is a solution to the inequality.
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Related Questions
Which equations are related equations to 13 + x = 29?
Select each correct answer.
29 + 13 = x
13=29−x
x=29−13
13−x=29
Answers
13 + x = 29
Subtract 13 from both sides:
x = 16
Now look at each choice and solve for x.
A. 29 + 13 = x
x = 42
B. 13 = 29 - x
-16 = -x
x = 16
C. x = 29 - 13
x = 16
D. 13 - x = 29
-x = 16
x = -16
Choices B and C have the same solution as the given equation, so choices B and C are equivalent to the given equation.
Answer:
[tex]13=29-x[/tex]
[tex]x=29-13[/tex]
Step-by-step explanation:
Given equation is [tex]13 + x = 29[/tex]
Solve the given equation for x, subtract 13 from both sides
[tex]x=16[/tex]
Now we solve each equation given for x
[tex]29 + 13 = x[/tex], x=42
[tex]13=29-x[/tex], subtract 29 from both sides
[tex]-16=-x[/tex] divide both sides by -1
x=16
[tex]x=29-13[/tex], x= 16
[tex]13-x=29[/tex] subtract 13 from both sides
[tex]-x=16[/tex] divide both sides by -1
x=-16
Option B and C gives the same solution x=16
Sasha lives 1,493 miles from her grandmother. One year, Sasha's family made 4 round trips to visit her grandmother. How many miles did they travel in all?
Answers
(( 4 round trips = 8 trips ))
(( 1493 x 8 ))
Hope this helps!
Final answer:
Sasha's family traveled a total of 11,944 miles over the course of the year by making 4 round trips to visit her grandmother, with each round trip being 2,986 miles.
Explanation:
The student is asking a mathematics question related to calculating the total distance traveled during multiple round trips. In this problem, Sasha's family traveled 1,493 miles to visit her grandmother, and they made this trip 4 times in a year. To find out how many miles they traveled in all, we need to calculate the distance of one round trip and then multiply by the number of round trips made.
A round trip consists of going to the grandmother's house and then returning back, so that's 1,493 miles each way. Therefore, one round trip would be:
1,493 miles (to grandmother) + 1,493 miles (back) = 2,986 miles.
Since they made 4 round trips, we calculate:
2,986 miles (for one round trip) x 4 (round trips) = 11,944 miles.
Thus, Sasha's family traveled a total of 11,944 miles to visit her grandmother over the course of the year.
4 2/5+k=−3 2/11 solve the equation
Answers
8.4+k=-2.9
k=-2.9-8.4
=-11.3
To solve for k in the equation 4 2/5 + k = -3 2/11, we convert the mixed numbers to improper fractions, find a common denominator, and perform algebraic operations to isolate k. The solution is k = -417/55.
The student is asking to solve the equation 4 2/5 + k = -3 2/11 for k. To solve this, you would convert the mixed numbers into improper fractions, then isolate the variable k by performing algebraic operations.
Steps to Solve for k:
Convert mixed numbers to improper fractions: 4 2/5 becomes 22/5 and -3 2/11 becomes -35/11.Write the equation with improper fractions: 22/5 + k = -35/11.Find a common denominator: In this case, the common denominator for 5 and 11 is 55.Write both fractions with the common denominator: 22/5 becomes 242/55, and -35/11 becomes -175/55.Rewrite the equation: 242/55 + k = -175/55.Subtract 242/55 from both sides to isolate k: k = -175/55 - 242/55.Combine the fractions: k = (-175 - 242) / 55.Calculate k: k = -417/55, which can be simplified if necessary.By following these steps, we can find that the value of k is -417/55. We have used algebraic operations, improper fractions, and common denominators to solve the equation.
On the first play of the game, the Wildcats gained 8 yd. What integer represents a gain of 8 yd?
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A positive number would mean you gained more numbers than lost numbers.
A negative number would mean you lost more numbers than gained numbers.
Therefore, positive is a gain.
So a gain of 8 yards would be positive 8, or just 8.
Hope this helps! :)
What is the square root of 0.81
Answers
What is the distance between point A (−1, 3) and point B (−7, 3) ?
1 units
3 units
6 units
8 units
Answers
Answer:
The distance between point A and the point B is:
6 Units.
Step-by-step explanation:
The Cartesian plane is known as 2 perpendicular number lines between them, one horizontal and one vertical, which are cut at a point called the origin.
And the coordinates are given by the values of X and Y (x, y)
Where X are horizontal values and Y are vertical values.
By placing the point (−1, 3) and the point (−7, 3) we realize that two values of Y are exactly the same on the line.
But the values of X are different from each other, so the units of the distance between them are counted.
-7U - (- 1U) = -6U
But since the distance units cannot be negative then the answer is 6 units of distance.
Add. Write your answer as a fraction in simplest form.
−4 5/9 + 8/9=
SHOW YOUR WORK
Answers
The legs of a right triangle are 3 units and 8 units. What is the length of the hypotenuse? Round your answer to the nearest hundredth. A.8.54 B.9.54 C.11.00 D.24.00
Answers
[tex]a^2+b^2=c^2[/tex]
Here we have a=3, b=8:
[tex]3^2+8^2=c^2[/tex]
[tex]c^2=73[/tex]
[tex]c=8.54[/tex]
Answer:
8.54
Step-by-step explanation:
i took the test
Describe at least 3 different ways to express the rate of change when given a situation.
Answers
Determining the starting point.
Measuring the distance to the end point.
I need help I don’t get the question
Answers
a carp can travel at a speed of 3 7/10 miles per hour . At this rate , how far can a carp travel in 2 ½ hours?
Answers
given a right cone with radius r and slant height s, what does the formula pi rs represent
Answers
The formula πrs represent the lateral surface area of the cone.
Step-by-step explanation:Lateral surface area--
The lateral surface area of a solid ( i.e. a three dimensional object) is the area of all the sides of the solid excluding the area of the base as well as top of the solid.
If r is the radius of the cone and s is the slant height of the cone then the lateral surface area of the cone is given by the formula:
[tex]Lateral\ surface\ area=\pi rs[/tex]
A local hamburger shop sold a combined total of 605 hamburgers and cheeseburgers on Friday. There were 55 more cheeseburgers sold than hamburgers. How many hamburgers were sold on Friday?
Answers
c = h + 55
h + h + 55 = 605
2h + 55 = 605
2h = 605 - 55
2h = 550
h = 550/2
h = 275 <== there were 275 hamburgers sold on Friday
c = h + 55
c = 275 + 55
C = 330...there were 330 cheeseburgers sold on Friday
The local hamburger shop sold 275 hamburgers on Friday, which was determined by setting up a system of equations to find the individual sales of hamburgers and cheeseburgers based on the given total sales and difference in numbers.
The question asks us to determine how many hamburgers were sold on a specific day, given the total number of hamburgers and cheeseburgers and the difference in their individual sales numbers. Let's denote the number of hamburgers sold as H and the number of cheeseburgers as C. We are told that the total number of burgers sold is 605, so we can write the equation H + C = 605. We also know there were 55 more cheeseburgers sold than hamburgers, giving us the equation C = H + 55. To find the number of hamburgers sold, we need to solve these two equations simultaneously.
Substituting the second equation into the first, we get:
H + (H + 55) = 6052H + 55 = 6052H = 605 - 552H = 550H = 550 / 2H = 275Therefore, the hamburger shop sold 275 hamburgers on Friday.
the nth term of a sequence is n+7 . what are the first 3 terms of the sequence
Answers
Answer:
First 3 terms of the sequence are:
8,9,10
Step-by-step explanation:
The nth term of a sequence is n+7 .
We have to find the first three terms of the sequence
First term(n=1) = 1+7 =8
Second term(n=2) = 2+7 =9
Third term(n=3) = 3+7 =10
Hence, first 3 terms of the sequence are:
8,9,10
the expression 6xi³(4xi+5) is equivalent to what?
Answers
= 24x^2 i^4 + 30xi³
hope it helps
Francisco makes $12 per hour doing part time work on Saturdays. He spends $4 on transportation to and from work. The equation y=12x-4 gives his earnings y, after transportation costs, for working x hours. Make a table for values for this situation. Please help.
Answers
x=2 y=20
x=3 y=32
x=4 y= 44
The y increases by 12 every hour, so it is a linear equation
In the given linear equations, we can use the equation y=12x-4 to create a table of earnings for different numbers of hours Francisco might work, taking into account his transportation costs. For example, if he does not work he loses $4 (-$4); if he works one hour he earns $8; if he works two hours he earns $20; if he works three hours he earns $32.
Explanation:In the equation y=12x-4, 'x' represents the number of hours Francisco works, and 'y' gives his earnings after transportation costs. Let's start creating a table using different values for 'x (hours)'.
For 0 hours (x=0), we substitute x into the equation to get y = 12*0 - 4 = -$4. Since Francisco can't earn negative money, we can consider this as him simply not going to work.For 1 hour (x=1), y = 12*1 - 4 = $8.For 2 hours (x=2), y = 12*2 - 4 = $20.For 3 hours (x=3), y = 12*3 - 4 = $32.So, the table would look something like this:
(0, -$4)(1, $8)(2, $20)(3, $32)This table provides four possible combinations of hours worked (x) and the corresponding earnings (y), taking into account the cost of transportation.
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While driving from his home to his workplace, Chris has to pass through two traffic lights. The general probability of getting a red signal at the first traffic light (event A) is 36%. The general probability of getting a red signal at the second traffic light (event B) is 25%. The probability of Chris getting a red signal at both traffic lights is 9%. In this scenario, A and B are events.
Answers
The general probabilities of each event to happen separately is 36% for event A and 25% for event B. When considering that Chris passes one before passing the other, indicates that whether he gets the first light open or not will affect if he gets the other one also open or not. This can even be seen by noticing how the probability of Chris getting both red lights is 9%, a much inferior probability then considering both lights separately which means that one event has influence over the other.
Jim drove 153 miles in 3 hours. If he can keep the same pace, how long will it take him to drive 1377 miles?
Answers
Use ratios
153:3
1377:x
x=27
153h=3
h= 51
1377÷51
27
find the product of 2and 3 and then take away 5
Answers
use the five step plan to solve the word problem. Show all five steps in youre response. doug is twice anns age. doug is 34 years old. how old is ann?
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Sydney has piles of 10 stickers sheets. She has 100 sheets in all. How many piles does she have?
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Chan her Bought 3.4 pounds of coffee that cost 6.95 per pound how much did you spend on coffee
Answers
Hope it helps
$23.63
Write 0.000000874 in scientific notation please. (SO CONFUSING :/)
Answers
Using the numbers 1,2,3,4 only once and the operations + or x as many times as you like, write an expression that evaluates to 16. Use this expression and any combination of those symbols as many times as you like to write an expression that evaluates to 816.
Answers
Final answer:
To obtain 16 using the numbers 1, 2, 3, and 4 with addition and multiplication, the expression is 4 x (3 + 1). To reach 816, place 8 in the hundreds place by calculating 8 x 100 and add the previously obtained 16.
Explanation:
To create an expression that evaluates to 16 using the numbers 1, 2, 3, 4 each only once and the operations + or x as many times as you like, we can use the following expression:
4 x (3 + 1) = 16
To write an expression that evaluates to 816 using our 16, simply prepend the number 8 to 16, which can be done by using multiplication and addition as follows:
8 x 100 + 4 x (3 + 1) = 800 + 16 = 816
This utilizes the concept that numbers can be broken down into sums of multiples of powers of 10 (place value), which is a fundamental principle in mathematics.
0.3•10^4 is it scientific notation why or why not?
Answers
No, this is not scientific notation. Scientific notation has a number multiplied by 10 to the power of something. But, that number has one digit in front of the decimal point. Since, here, there are none, this is not a number in scientific notation.
what is 64.3-3x2 to the third power divide by 2
Answers
To solve the expression 64.3-3x2 to the third power divided by 2, simplify inside the parentheses, raise the result to the third power, and divide by 2.
Explanation:To solve the expression 64.3-3x2 to the third power divided by 2, we need to follow the order of operations, which is parentheses, exponents, multiplication, and division from left to right.
First, let's simplify the expression inside the parentheses: 64.3-3x2 = 64.3-6 = 58.3
Next, we raise the result to the third power: 58.3^3 = 19671.327
Finally, we divide the result by 2: 19671.327 / 2 = 9835.6635
five added to 2 times a number is equal to 7 less than 4 times the number: what is the number?
Answers
Answer:
6
Step-by-step explanation:
Five added to 2 times a number is equal to 7 less than 4 times the number
Five is added to 2 times a number 2x + 5
7 less than 4 times the number 4x - 7
Put them together
2x+5=4x-7
2(6)+5=17
4(6)-7=17
x=6
Identify a temperature colder than -7.2 F. Write an inequality that relates the temperatures. Describe their positions on a horizontal number line. (I'll give most of my points!!!)
Answers
-9 < -7.2
The -9 would be 1.8 units to the left of -7.2 on the number line.
30 POINTS Talia drives a bus. The function P=25h+50 represents her daily pay, in dollars, for working h hours. She picks up 45 passengers per hour. She also receives $0.20 for each passenger she picks up. The function B=45h·(0.20) represents the amount she earns for her bonus. Which function represents Talia's earnings, P, for driving h hours?
A.) P=16h+50
B.) P=34h+50
C.) P=50h+34
D.) P=20h+50
Answers
total earning=25h+50+45h(0.2)=25h+50+9h=34h+50
The function P=34h+50 represents Talia's earnings, P, for driving h hours. The correct option is B.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Talia drives a bus. The function P=25h+50 represents her daily pay, in dollars, for working h hours. She picks up 45 passengers per hour. She also receives $0.20 for each passenger she picks up. The function B=45h·(0.20) represents the amount she earns for her bonus.
The total earnings will be calculated as,
TE = 25h + 50 + 45h.(0.2)
TE = 25h + 50 + 9h
TE = 34h + 50
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what are two`fractions whose product is -3/5
Answers
I hope this helps.
To find two fractions whose product is -3/5, we can choose any two fractions that follow the rules of multiplying fractions. For example, the fractions 1/5 and -3/1 or -4/5 and 3/4 both have a product of -3/5.
Explanation:To find two fractions whose product is -3/5, we need to consider the rules of multiplying fractions. When we multiply two fractions, we multiply their numerators to get the new numerator and multiply their denominators to get the new denominator. In this case, we can choose any two fractions that satisfy these rules and have a product of -3/5.
For example, let's consider the fractions 1/5 and -3/1. When we multiply these fractions, we get (1 × -3) / (5 × 1) = -3/5.
Another example is the fractions -4/5 and 3/4. When we multiply these fractions, we get (-4 × 3) / (5 × 4) = -12/20, which can be simplified to -3/5.