The conjecture that any real number squared is a nonnegative number is correct. This is because squaring a positive number gives a positive result, squaring a negative number also gives a positive result, and squaring zero equals 0, which is nonnegative.
Explanation:This mathematical conjecture proposes that for any real number, when squared, the result is a nonnegative number. Given n is a real number, the conjecture n^2 is a nonnegative number is indeed true. In mathematics, a real number is considered nonnegative if it is greater than or equal to zero.
To provide more insight, let's look at a few examples: If we take a positive number such as 3, and you square it (3^2), you get 9, which is a positive number. Equally, if you take a negative number like -3 and square it (-3^2), you get 9 again, which is also a positive number. Even if you take the number zero (which is neither positive nor negative) and square it, you get 0, which is still considered nonnegative. Thus, any real number when squared is always a nonnegative number.
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At one point on the trip, the miles are recorded as 15,121 when the gas tank is 75% full. Use a ratio equation to determine the miles per gallon the sedan averages. Round your answer to the nearest whole number.
The most common size of a sedan tank is 18.5 gallons. So if it is 75% full, it contains 13.875 gallons of gas. If it recorded a mileage of 15,121 miles, mileage per gallon, therefore, is 1090 rounded off to the nearest whole number.
Given: Gas full tank of a sedan – 18.5 gallons
75% full = 13.875 gallons
Mileage using 13.875 gallons of fuel = 15,121 miles
The mileage per gallon computation using the ratio equation:
Ratio is 15121:13.875 or
X/1= 15121/13.875
13.875x = 15121
X = 15121/13.875
X =1089.80 or 1090 miles per gallon (rounded off)
Evaluate the expression (ab)2 for a = 4 and b = 3.
a.81
b.36
c.24
d.144
Part A: Amir rented a scooter at $43 for 3 hours. If he rents the same scooter for 8 hours, he has to pay a total rent of $113.
Write an equation in the standard form to represent the total rent (y) that Amir has to pay for renting the scooter for x hours. (4 points)
Part B: Write the equation obtained in Part A using function notation. (2 points)
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)
Answer:
A: r-14x-1=0
B: r(x)=14x+1
C: x= left to right axis
y= up to down axis
domain= x,0
range= r,0
slope= 14
x-intercept= r=0 ==> 0=14x+1 ==>x=(-1/14,0)
r-intercept= x=0 ==> r=14(0)+1= (0,1)
make sure to right it in your own.
angle of elevation and depression worksheet
For which value of k will the roots of the equation 2x^2-5x+k=0 be real and rational numbers
25/8 is the value of k will the roots of the equation 2x^2-5x+k=0 be real and rational numbers
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
We need to find the value of k will the roots of the equation 2x²-5x+k=0 be real and rational numbers.
A quadratic equation has real roots when the discriminant is positive or zero (not negative).
b²-4ac≥0
b=-5, a=2, c=k
(-5)²-4((2.k)≥0
25-8k≥0
25≥8k
Divide both sides by 8
25/8≥k
k≤25/8
Hence, 25/8 is the value of k will the roots of the equation 2x^2-5x+k=0 be real and rational numbers
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What are the coordinates for the x and y intercepts of the function 4y - 2x = 24?
PLEASE HELP!!!!! How does “rationalizing the denominator” use the form of 1?
Stan, a local delivery driver is paid $3.50 per mile driven plus a daily amount of $75. On Monday he is assigned a route that is 30 miles longer. How much is he being paid for that day? Independent and dependent variables?
A sample value that lies very far away from the majority of the other sample values is _____.
Answer:
It would be an outlier
Step-by-step explanation:
What is the meaning of life? What makes this world so great? Is there something to look forward to in the future?
I don't get how to do this please help
the answer is D
the exponent is 8.869 where the 9 is 9/1000, the 6 is 6/100 and the 8 to the right od the decimal point is 8/10
Find the total amount in the compound interest account.
$1740 is compounded daily at a rate of 12% for 5 years. Let 1 yearequals=365 days.
=$
Solve for PQ 4x+19=2x+32
If two angles of a triangle are complementary, then the triangle must be
The seventh grade math classes are going on a field trip. the field trip will cost $7 per student. write an expression to find the cost of the field trip for s students. what is the total cost if 26 students go on the trip?
7s is the expression to find the cost of the field trip for s students and 182 is the total cost if 26 students go on the trip
What is Expression?An expression is combination of variables, numbers and operators.
Given,
The seventh grade math classes are going on a field trip.
the field trip will cost $7 per student.
Given s is number of students.
7s is the expression to find the cost of the field trip for s students.
When number of students are twenty six 26, i.e s=26
Total cost=7×26
seven times of twenty six
182
Hence 7s is the expression to find the cost of the field trip for s students and 182 is the total cost if 26 students go on the trip
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The water level at Lake Penny changed −1 1/10 in. this year. Next year, it is predicted to change another −1 2/5 in. What is the total change that will likely occur in 2 years? Enter your answer as a simplified mixed number in the box. 20 POINTS
add 1 1/10 + 1 2/5
first get both fractions with the same bottom number: 2/5 = 4/10 ( multiply both numbers by 2)
so now you have 1 1/10 + 1 4/10 = 2 5/10
5/10 reduces to 1/2
so answer is 2 1/2 inches, and since the level is going down it would be negative 2 1/2 inches
Answer:
-2 1/2 inches is your answer
A line passes through the point (3,2) and (6,2) a write an equation for the line in point-slope form rewrite the equation in standard form usung integers
The declaration opens with a rational statement of its purpose. in a document with such radical intent, its is not surprising that supporting details often use emotionally laden language.Find at least 5 details in the document that use loaded words to cite factual support . What emotions are revealed in the use of charged language ?
The document uses emotionally loaded language to support its claims. This creates a strong emotional impact on readers and helps persuade them.
Explanation:When analyzing a document, it is important to pay attention to emotionally loaded language used as factual support. Here are five details in the document that use loaded words:
Quoting from interviews with government workers and bystanders who were hiding behind locked doors and had no police protection, appealing to the emotion of fear.Recreating images with vivid descriptions and concrete language of lone officers overwhelmed by crowds of people and beaten, appealing to the emotions of fear and empathy.Using nonaggressive language to address opposing views, showing empathy and attempting to convince others to support the author's position.Adhering to descriptive diction and employing sensory detail, creating a rhetorical effect.Refuting counterclaims and appealing to readers' logic and emotions, demonstrating fairness and advanced skill at persuasion.The use of emotionally charged language reveals the emotions of fear, empathy, conviction, and persuasion in the document.
To support a shelf, the diameter of a bolt can be measured anywhere from 0.2 cm less than 1.5 cm to 0.2 greater than 1.5 cm. Which graph represents the possible measures of the diameter of the bolt
Answer:
The answer is A.
Step-by-step explanation:
We use filled in dots because it can be anything .2 and less or, .2 or more.
Mike bought 4 new baseball trading cards to add to his collection. the next day his dog ate half of his collection. there are now only 42 cards left. how many cards did mike start with
Triangle STU has been reflected over line m to form triangle S'T'U'. what is the value of y
Talia wants to write the equation of the graphed line in point-slope form. These are the steps she plans to use: Step 1: Choose a point on the line, such as (2, 5). Step 2: Choose another point on the line, such as (1, 3). Step 3: Count units to determine the slope ratio. The line runs 1 unit to the right and rises 2 units up, so the slope is . Step 4: Substitute those values into the point-slope form. y – y1 = m(x – x1) y – 3 = (x – 1) Which of Talia’s steps is incorrect? Step 1 is incorrect because it uses a point that is not on the line. Step 2 is incorrect because it uses a point that is not on the line. Step 3 is incorrect because it shows an incorrect ratio for the slope. Step 4 is incorrect because it shows an incorrect substitution of (1, 3) into the point-slope form.
Answer:
Step 3 is incorrect because it shows an incorrect ratio for the slope.
Step-by-step explanation:
what is 4x-9=k solve for the x
please help me
An irregular polygon is shown below:
The area of the irregular polygon is ____ square units.
Answer:
26
Step-by-step explanation:
well we see that it is at its longest is 9, and the tallest is four
we have two missing sides...
so for the top left on long, it is 5
the full length is 9, and we have a 4 on the top, so we have 5 left, the top right line is 5
the one on the left side is two, because the middle line is a 2, and the full items height is 4.
4x2=8
2x2=4
5+9=14
8+4=12
14+12=26
butch, harry, and nicky are playing a game. Harry has half as many points is butch. Nicky has 5 fewer points than Harry. Together, the three players have 31 points. How many points does Harry have?
Find two numbers whose product is 20 and whose sum is 12
The numbers are 10 and 2 if the product is 20 and whose sum is 12 after making the two equations.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The product of two numbers is 20 and whose sum is 12
Let the numbers are x and y
xy = 20
x + y = 12
y = 12 - x
x(12 - x) = 20
x² - 12x + 20 = 0
After solving the above quadratic equation, we get:
x = 10, 2
y = 2, 10
Thus, the numbers are 10 and 2 if the product is 20 and whose sum is 12 after making the two equations.
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The office manager ordered145 packs of printer paper. Based on average daily use, she knows that the paper will last 65 days. What graph represents this situation? How many packs of printer paper should the manager expect to have after 25 days?
What three consecutive integers have a sum of 252?
252/3 = 84
84-1 = 83
84+1=85
83 +84 +85 = 252
the numbers are 83, 84, 85
Help with finding value of x?
A movie theater sells student tickets for $5 and adult tickets for $10. On Saturday night, 2,500 people go to the theater and ticket sales total $18,000. How many adults and children went to the theater on Saturday night? Which solution is reasonable? A) 2000 students and 1000 adults B) 1100 adults and 1400 students C) 3000 students and 0 adults D) 500 students and 1500 adults
The reasonable solution is B) 1100 adults and 1400 students, as it satisfies both attendance and revenue criteria.
Consider a movie theater that sells student tickets for $5 and adult tickets for $10. On a Saturday night, 2,500 people attended the theater, and the total ticket sales amounted to $18,000. The goal is to determine the number of adults and students who attended, with multiple choices provided:
We can set up two equations to represent the information:
The total number of people who attended: S + A = 2500
The total ticket sales amount: 5S + 10A = 18000
Solving this system of equations gives the correct solution:
B) 1100 adults and 1400 students.
This solution satisfies both equations (S + A = 2500 and 5S + 10A = 18000). It is reasonable as it accounts for both students and adults attending, and the total revenue aligns with the given information. The number of students (1400) and adults (1100) adds up to the total attendance of 2500.