what do mathematicians call a number less than zero
Answers
A number less than zero is called Negative Number.
In mathematics, negative numbers represent opposite numbers. In the system of real numbers, negative numbers are numbers less than zero. Negative numbers are often used to indicate the size of a loss or deficit. The debt owed can be considered as negative equity. If a quantity, such as the charge of an electron, can have one of two opposite directions, one can choose to distinguish these (possibly arbitrary) directions as positive and negative.
Negative numbers are used to describe scale values less than zero, such as degrees Celsius and Fahrenheit for temperature. The laws of arithmetic with negative numbers ensure that the common sense idea of opposite numbers is represented in arithmetic. For example -(-3) = 3 because the opposite of the opposite is the original value.
Negative numbers usually start with a minus sign. For example, -3 is pronounced "minus three" or "minus three" for a negative number of magnitude three.
To help distinguish subtraction operations from negative numbers, the minus sign is sometimes placed slightly above the minus sign (as a superscript). Conversely, numbers greater than zero are called positive numbers; zero is usually (but not always) considered to be neither positive nor negative. The positivity of numbers can be emphasized by placing a plus sign in front of the number, such as G.+3. In general, the sign of a number is called its sign.
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Related Questions
Find the 16th term of the arithmetic sequence whose common difference is d=9 and whose first term is a, = 1.
Answers
Answer: 136
Step-by-step explanation:
a + ( 16 - 1 ) da + 15 d( 1 )
a = 1
d = 9
1 + 15 ( 9 )
1 + 135
136
Answer:
a₁₆ = 136
Step-by-step explanation:
the nth term of an arithmetic sequence is
\(a_{n}\) = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 1 and d = 9 , then
a₁₆ = 1 + (15 × 9) = 1 + 135 = 136
please help me with this
Answers
The function y=(x-2)²-1 has vertex (2, -1), focus (2, -3/4) and axis of symmetry is x=2.
1) y=-x²+4x+3
From the given graph,
Direction: Opens Down
Vertex: (2,7)
Focus: (2,27/4)
Axis of Symmetry: x=2
Directrix: y=29/4
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
x-intercept(s): (2+√7,0),(2−√7,0)
y-intercept(s): (0,3)
Find the domain by finding where the equation is defined. The range is the set of values that correspond with the domain.
Domain: (−∞,∞),{x|x∈R}
Range: (−∞,7],{y|y≤7}
3) y=(x-2)²-1
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: (2,−1)
Focus: (2,−3/4)
Axis of Symmetry: x=2
Directrix: y=−5/4
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
x-intercept(s): (3,0),(1,0)
y-intercept(s): (0,3)
Find the domain by finding where the equation is defined. The range is the set of values that correspond with the domain.
Domain: (−∞,∞),{x|x∈R}
Range: [−1,∞),{y|y≥−1}
Therefore, the function y=(x-2)²-1 has vertex (2, -1), focus (2, -3/4) and axis of symmetry is x=2.
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After observing both the graphs the required fields are described below.
In the given graph of the equation,
y = -x² + 4x + 3
From the graph of the this curve
We can see that,
X - intercept of this graph is at (-0.646 , 0) and (4.646, 0)
Y - intercept of this graph is at (0, 3)
Vertex of this graph is at (2, 7)
Domain is whole real line,
Range is (-∞, 7]
Axis of symmetry is x axis.
Increasing in the interval : (-∞, 2]
Decreasing in the interval : [7, ∞)
In the given graph of the equation,
y = (x-2)² - 1
From the graph of the this curve
We can see that,
X - intercept of this graph is at (1 , 0) and (3, 0)
Y - intercept of this graph is at (0, 3)
Vertex of this graph is at (2, -1)
Domain is real number,
Range is [-1, ∞)
Axis of symmetry is x axis.
Increasing in the interval : (-∞, 1]U[3,∞)
Decreasing in the interval : (1, 3)
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The lexington group has the following unadjusted trial balance as of may 31, 20y6: the lexington group unadjusted trial balance may 31, 20y6 account debit balances credit balances cash 20,350 accounts receivable 37,000 supplies 1,100 prepaid insurance 200 equipment 171,175 notes payable 36,000 accounts payable 26,000 common stock 50,000 retained earnings 94,150 dividends 15,000 fees earned 429,850 wages expense 270,000 rent expense 63,000 advertising expense 25,200 miscellaneous expense 5,100 total 608,125 636,000 the debit and credit totals are not equal as a result of the following errors: the cash entered on the trial balance was overstated by $7,000. a cash receipt of $8,200 was posted as a debit to cash of $2,800. a debit of $16,500 to accounts receivable was not posted. a return of $125 of defective supplies was erroneously posted as a $1,250 credit to supplies. an insurance policy acquired at a cost of $3,600 was posted as a credit to prepaid insurance. the balance of notes payable was understated by $9,000. a credit of $10,000 in accounts payable was overlooked when determining the balance of the account. a debit of $5,000 for dividends was posted as a credit to retained earnings. the balance of $60,300 in rent expense was entered as $63,000 in the trial balance. gas, electricity, and water expense, with a balance of $16,350, was omitted from the trial b
Answers
The unadjusted trial balance of The Lexington Group as of May 31, 20Y6, contains errors resulting in an unequal debit and credit balance of $27,875.
The unadjusted trial balance is a statement that lists all the accounts and their balances before any adjustments are made. It is used as a starting point to prepare the financial statements. In this case, the unadjusted trial balance of The Lexington Group shows a debit total of $608,125 and a credit total of $636,000, resulting in a difference of $27,875.
The errors mentioned in the question are the reasons for the imbalance. Let's go through each error:
1. The cash entered on the trial balance was overstated by $7,000. This means that the cash balance is higher than it should be by $7,000, resulting in an inflated debit balance.
2. A cash receipt of $8,200 was posted as a debit to cash of $2,800. This error resulted in an understatement of the cash balance by $5,400.
3. A debit of $16,500 to accounts receivable was not posted. As a result, the accounts receivable balance is understated by $16,500.
4. A return of $125 of defective supplies was erroneously posted as a $1,250 credit to supplies. This error caused an overstatement of the supplies balance by $1,125.
5. An insurance policy acquired at a cost of $3,600 was posted as a credit to prepaid insurance. This mistake resulted in an understatement of the prepaid insurance balance by $3,600.
6. The balance of notes payable was understated by $9,000. This means that the liability for notes payable is lower by $9,000 than it should be.
7. A credit of $10,000 in accounts payable was overlooked when determining the balance of the account. This error led to an understatement of the accounts payable balance by $10,000.
8. A debit of $5,000 for dividends was posted as a credit to retained earnings. This mistake caused an understatement of the dividends and an overstatement of the retained earnings by $5,000.
9. The balance of $60,300 in rent expense was entered as $63,000 in the trial balance. This error resulted in an overstatement of the rent expense by $2,700.
10. Gas, electricity, and water expense, with a balance of $16,350, was omitted from the trial balance. This omission caused an understatement of the total expenses by $16,350.
When we analyze the errors, we find that some accounts have been overstated, some have been understated, and some transactions have been completely omitted. These errors have led to an imbalance between the debit and credit sides of the trial balance.
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Page 1:
a. If two points on a line are A(-5, 7) and B(-2, 1), the rise is
so the slope of the line is
b. If two points on a line are A(10, -3) and B(12, 9), the rise is
run is
the run is
so the slope of the line is
c. If two points on a line are A(4, 6) and B(8,-8), the rise is
run is
Page 2:
so the slope of the line is
a. In the point-slope form of a line.
mix
the clon
and the
, and
and the
Answers
a) If two points on a line are A(-5,7) and B(-2,1), the rise -6, the run is of 3, and then the slope is of -2.
b) If two points on a line are A(10,-3) and B(12,9), the rise 12, the run is of 2, and then the slope is of 6.
c) If two points on a line are A(4,6) and B(8,-8), the rise -14, the run is of 4, and then the slope is of -3.5.
How to calculate the slope a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
For which the parameters are given as follows:
m is the slope, representing the rate of change.b is the intercept, representing the value of y when x = 0.As the slope represents the rate of change of the output relative to the input, it is calculated as the change in the output y divided by the change in the input x, that is, the rise divided by the run.
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3х + 4y= 4
12х + 16y = 8
Answers
Answer:
No Solution.
Step-by-step explanation:
3x+4y=4
12x+16y=8
--------------
-4(3x+4y)=-4(4)
12x+16y=8
--------------------
-12x-16y=-16
12x+16y=8
-----------------
0=-8
no solution
an isosceles triangle has two sides of length 40 and a base of length 48. a circle circumscribes the triangle. what is the radius of the circle?
Answers
The radius of the circle circumscribing the given isosceles triangle is 40 unit.
To find the radius of the circle circumscribing an isosceles triangle with two sides of length 40 and a base of length 48, we can use the properties of a circumscribed circle.
In an isosceles triangle, the altitude from the vertex angle (angle opposite the base) bisects the base, creating two congruent right triangles. Let's call the altitude h.
Using the Pythagorean theorem, we can determine the height:
h² + (24)² = (40)²
h² + 576 = 1600
h² = 1024
h = 32
Now, we have a right triangle with one side measuring 32 and the hypotenuse (radius of the circumscribed circle) as the sum of half the base (24) and the height (32). Let's call the radius r.
r = sqrt((24)² + (32)^2)
r = sqrt(576 + 1024)
r = sqrt(1600)
r = 40
Therefore, the radius of the circle circumscribing the given isosceles triangle is 40 unit.
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Factor by first factoring out the greatest common 1actor 15x 35x-30 15x-35x-30
Answers
Answer:
5(3x+2)(x−3)
Step-by-step explanation:
Answer:
5(3x²-7x-2)
Step-by-step explanation:
15x²-35x-30
5(3x²-7x-2)
when the decimal point of a certain positive decimal number is moved four places to the right, the new number is four times the reciprocal of the original number. what is the original number?
Answers
The original number from the given decimal number is 0.02.
Define the term reciprocal of the number?A multiplicative inverse of such a number is referred to as the reciprocal. In other words, 1 divided by a number is the definition of the reciprocal. Any given number multiplied by its reciprocal would always yield the value 1. By swapping the values of a numerator and denominator, one can find exact reciprocal of a fraction.For the given question;
Moving a decimal point 4 places towards the right corresponds to multiplying the given integer by 10,000 if it is x.
This results in:
10000x = 4.(1/x)
Simplifying.
x² = 4/10000
x > 0.
Taking square root of the number.
x = 2/100
x = 0.02
Thus, the original number from the given decimal number is 0.02.
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What is the surface area of the prism
A. 812
B. 1,190
C. 2,352
D. 132
Answers
Answer:
B. 1,190 square cm
Step-by-step explanation:
For given prism:
l = 16 cm, w = 7 cm, h = 21 cm
Surface area of of the prism
\(= 2 (lw + wh + hl) \\ = 2(16 \times 7 + 7 \times 21 + 21 \times 16) \\ = 2(112 + 147 + 336) \\ = 2 \times 595 \\ = 1190 \: {cm}^{2} \\ \)
The number of minutes m you spend in line is 5 times the number of people p in line. Identify the independent and dependent variables. Then write and graph a function that describes the relationship between p and m.
Answers
Answer:The number of minutes m you spend in line is 5 times the number of people p in line. Identify the independent and dependent variables. Then write and graph a function that describes the relationship between p and m.
Step-by-step explanation:
Part A Are squares also rectangles? Explain.
Answers
Answer:
down below
Step-by-step explanation:
no squares and rectangles are not the same because a square has all 4 sides of the square are the same length while for rectangles have do not have same length for all four sides so therfore squares are not also rectangles
Consider the hypotheses shown below. Given that x
ˉ
=105,σ=26,n=45,α=0.10, complete parts a and b. H 0
:μ=113
H 1
:μ
=113
a. What conclusion should be drawn? b. Determine the p-value for this test. a. The z-test statistic is (Round to two decimal places as needed.)
Answers
The p-value for this test is approximately 0.0515. Since the p-value (0.0515) is greater than the significance level (α = 0.10), we reject the null hypothesis at the α = 0.10 level.
To determine the conclusion and calculate the p-value for the given hypotheses, we can perform a one-sample z-test using the provided information.a. The z-test statistic is calculated as: z = (Xbar - μ) / (σ / √n) = (105 - 113) / (26 / √45) = -8 / (26 / 6.7082) ≈ -1.6346. Since the z-test statistic falls within the critical region for a one-tail test with α = 0.10, we reject the null hypothesis (H0: μ = 113) and conclude that there is evidence to suggest that the population mean is not equal to 113. b. To determine the p-value for this test, we need to find the area under the standard normal distribution curve to the left of the calculated z-test statistic (-1.6346).
Looking up this value in the cumulative probabilities for the standard normal distribution table, we find the corresponding area to be approximately 0.0515. Therefore, the p-value for this test is approximately 0.0515. Since the p-value (0.0515) is greater than the significance level (α = 0.10), we reject the null hypothesis at the α = 0.10 level.
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If a student gets an 89% on a test, this would be what type of score? a. true score b. observed score c. false score d. error score.
Answers
If a student gets an 89% on a test, this would be considered an observed score.
In the context of test scoring, different types of scores are used to evaluate a student's performance.
- True score: The true score represents the student's actual or underlying ability on the test. It is the hypothetical score that would be obtained if all measurement errors were eliminated. However, the true score is typically unknown and cannot be directly measured.
- Observed score: The observed score is the score that is actually obtained by the student on the test. It is based on the student's performance and reflects their achievement or outcome on the test.
- False score: The term "false score" is not commonly used in the context of test scoring. It does not have a specific meaning related to the interpretation of test scores.
- Error score: The error score refers to the discrepancy between the true score and the observed score. It represents the measurement error or uncertainty associated with the test administration and scoring process. The error score reflects the extent to which the observed score deviates from the true score due to factors such as test administration conditions, scoring errors, or other sources of measurement variability.
In this case, an 89% on a test would be considered an observed score because it represents the actual score obtained by the student based on their performance on the test.
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what is the midpoint of (0,0.55) and (-3,6)
Answers
Answer:
(-1.5, 3.275)
Step-by-step explanation:
midpoint = ( x1+X2/2 , y1+y2/2)
=(0+(-3)/2, 0.55+6/2)
=( -3/2, 6.55/2)
=( -1.5, 3.275)
Can someone help me? What is the angle?
Answers
one of the factors of 6x^3-864x is
Answers
Answer:
(x + 12)
Step-by-step explanation:
It is given that6x3 - 864x
Taking 6x as common = 6x (x2) + 6x (-144)
We can write it as := 6x (x2 - 144)
a2 - b2 = (a + b) (a - b)
= 6x (x + 12) (x - 12)
Therefore, the factors of 6x3 − 864x are 6x (x + 12) (x - 12).
-3t + 9 greater than or equal to-21
Answers
Answer
t = -4
Step-by-step explanation:
First you subtract 9 from both sides. You get 12 on the right. Then you divide both sides by -3. You get -4.
Answer: t<=10
Step-by-step explanation:
-3t+9>=-21
-3t>=-30
3t<=30
t<=10
Gavin was thinking of a number. Gavin adds 9 to it, then doubles it and gets an answer of 83.2. What was the original number?
Answers
Answer: it is 32.6
Step-by-step explanation:
The orginal number that Gavin was thinking of is 32.60.
What is the original number?
Let the orginal number be represented with y
Gavin adds 9 to the original number: 9 + y
The answer is doubled: 2(9 + y)
The answer is 83.2: 2(9+y) = 83.2
In order to determine the value of y, take the following steps:
Divide both sides of the equation by 2
9 + y = 41.60
Subtract 9 from both sides of the equation
y = 41.60 - 9
y = 32.60
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A line passes through point (6, -6) and has a slope of -4/3
Write an equation in Ax+By=C form for this line.
Use integers for A, B, and C.
-
Answers
Answer:
4x + 3y = 6
A = 4
B = 3
C = 6
Step-by-step explanation:
A line have a function:
y = ax + b
Because the line has a slope of - 4/3
=> a = - 4/3
=> y = - 4/3 x + b
Because the line go through point (6; - 6)
=> - 6 = - 4/3 .6 + b
=> b - 8 = - 6
=> b = 2
=> The function of the line
y = - 4/3 x + 6
=> 3y = - 4x + 6
=> 4x + 3y = 6
Calvin hiked 2,384 miles last year. This year, he has hiked 3,763 miles. How many miles has Calvin hiked in the past two years in total?
Answers
Answer:
The answer to this question is 6,147.
Step-by-step explanation:
2,384 + 3,763=6,147
please help me with this. i have trouble finding the slopes in these problems.
Answers
Answer:
Slope = rise over run
So you start where the line hits the corner which is at (4,1) and until it hits a corner again which is at (7,5)
Step-by-step explanation:
The slope is 4/3
We can use points (4, 1) and (7, 5) and plug these values into the slope formula.
Let (x1, y1) = (4, 1)
(x2, y2) = (7, 5)
Use the slope formula:
m = (y2 - y1)/(x2 - x1)
m = (5 - 1)/(7 - 4)
m = 4/3
Therefore, the slope of the line is 4/3.
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5a + 7+ 3(a_+5) = 70 What is the value of a?
Answers
Step-by-step explanation:
5a + 7+ 3(a_+5) = 70 expand left side
5a + 7 + 3a + 15 = 70 gather 'like terms'
(5a+3a) + (7+15) = 70 simplfy ....and subtract 22 from both sides
8a = 48 divide through by 8
a = 6
P(Head, Diamond AND Head, Heart) = ?
Answers
The probability of drawing a head card of diamonds and then a head card of hearts is:
P = 0.003
How to find the probability?
Here we assume that we have a deck of 52 cards, and we want to find:
P(Head, Diamond AND Head, Heart)
This is the probability of drawing a head of diamonds and then a head of hearts.
Remember that for each suit has 3 head cards, J, Q, and K.
Then for the first card, the probability of getting a head of diamonds is equal to the quotient between the number of cards with these properties (3) and the total number of cards (52).
P = 3/52
Then we need to draw a head of hearts, the probability is computed in the same way, but before we drew a card, so now the total number of cards is 51, so we get:
Q = 3/51
Then the joint probability is:
p = (3/52)*(3/51) = 0.003
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You have one type of candy that sells for $7.10/lb and another type of candy that sells for $9.70/lb. You would like to have 10.4 lbs of a candy mixture that sells for $9.40/lb. How much of each candy will you need to obtain the desired mixture
Answers
You will need 5.2 pounds of candy from each candy. The reason is because you have 2 kinds of candy and 10.4 pounds so divide 10.4 by 2 and you get 5.2
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What is the value of x in the equation 8x – 2y = 48, when y = 4?
6
7
14
48
Answers
Answer:
x=7
Step-by-step explanation:
8x – 2y = 48
Let y = 4
8x - 2(4) = 48
8x - 8 = 48
Add 8 to each side
8x-8+8 = 48+8
8x = 56
Divide each side by 8
8x/8 = 56/8
x=7
Answer:
\(x = 7\)
Step-by-step explanation:
\(8x - 2y = 48 \\ 8x = 48 + 2y \\ x = \frac{48 + 2y}{8} \)
\(y = 4\)
\(x = \frac{48 + 2y}{8} \\ x = \frac{48 + 2 \times 4}{8} \\ x = \frac{48 + 8}{8} \\ x = \frac{56}{8} \\ x = 7\)
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Occupants are ____ times more likely to be killed in a crash when not buckled in.
a)2
b)5
c)10
d)100
Answers
Occupants are 10 times more likely to be killed in a crash when not buckled in. option c.
Wearing a seatbelt is one of the simplest ways to protect oneself while in a vehicle. When properly worn, it decreases the likelihood of being seriously injured or killed in a collision by as much as 50%. When an individual is not wearing a seatbelt, they are putting their lives at risk. Wearing a seatbelt should be a routine habit whenever an individual sits in a vehicle.
Buckling up is the easiest and most effective way to prevent injuries and fatalities on the road. If drivers, passengers, and children buckle up every time they travel in a vehicle, the likelihood of being killed or injured in a collision is greatly reduced. When occupants of a vehicle do not buckle up, they are 10 times more likely to be killed in a crash. This means that the likelihood of being killed is significantly higher when not wearing a seatbelt.
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hello can someone please help me
Answers
Answer: on what?
Step-by-step explanation:
Answer:
The math looks kind of hard
Step-by-step explanation:
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2. The angle of elevation of the top of a vertical
cliff, as seen from a boat 120 m away, is 32°.
The angle of elevation of the top of a flagpole
at the edge of the cliff, as seen from the boat,
is 37º. Find the height of the flagpole.
Answers
Answer: 15.44 m
Step-by-step explanation:
We can think this as two triangle rectangles.
In both cases, the adjacent cathetus is 120m.
When the angle is 32°, the opposite cathetus will be the height of the cliff.
When the angle is 37°, the opposite cathetus will be the heigth of the cliff plus the height of the flagpole.
Then we need to compute both of them and calculate the difference.
We can use the trigonometric relation:
Tan(θ) = (opposite cathetus)/(adjacent cathetus)
in this case we have:
Tan(32°) = (height of the cliff)/(120m)
Tan(32°)*120m = height of the cliff = 74.98m
Now we can use the other angle to compute:
Tan(37°) = (heigth of the cliff + heigth of the flagpole)/120m
Tan(37°)*120m = heigth of the cliff + heigth of the flagpole = 90.42m
Then the height of the flagpole will be:
H = 90.42m - 74.98m = 15.44 m
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Use the ratio table to find the unit rate with the specified units.
feet per year
The unit rate is
feet per year.
Answers
Answer:
0.27(Repeating)
Step-by-step explanation:
If you take 7.2 and divide it by 2, you get 0.27777777777 , exact same thing for every other ratio. Therefore, your answer would be 0.27777777777
The length of a rectangle is five times its width.
If the perimeter of the rectangle is 84 yd, find its length and width.
Answers
First you set your equation to equal 84 since that’s the total for perimeter is 84. Then you would let the length be 5x since the length is five times the width, that would leave your width to be x. Then you would do x+x+5x+5x=84 then combine like terms. So then it would be 12x=84 divide by 12 which equals x=7 then you plug that in for x which would create the answers of 7 and 35.