The number that should be added to the polynomial 2x³ - 3x² - 8x is 12x
When a polynomial is divided by a linear factor, the remainder is equal to the constant term of the polynomial multiplied by the reciprocal of the linear factor.
In this case, the polynomial is 2x³ - 3x² - 8x, and the linear factor is 2x-1.
To find the remainder when this polynomial is divided by 2x-1, we need to multiply the constant term of the polynomial, which is -8, by the reciprocal of 2x-1, which is 1/(2x-1).
So the remainder should be -8*(1/(2x-1)) = -8/(2x-1) = -4/(x-0.5)
To make the remainder 12, we will add 12x to the polynomial so that the new constant term is 12.
The polynomial 2x³ - 3x² - 8x + 12x will have a remainder of 12 when divided by 2x-1.
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. The length of one line segment is 9cm and the length of a parallel line segment is 3cm. What scale factor would you need to use to map the first line segment onto the second line
semgment?
O 9/3=3
O 9x3=27
O 3/9=0.33
O 9/9=1
Scale factor required to map the first line segment onto second line segment is 3/9=0.33
What is scale factor?The scale factor is the ratio of the length of the image to the length of the pre-image.
In this case, we're looking for the that would map the first line segment (length 9cm) onto the second line segment (length 3cm).
To find the scale factor, we can divide the length of the image by the length of the pre-image:
scale factor = length of image / length of pre-image
In this case:
[tex]ScaleFactor=\frac{Length Of Image}{Length Of Pre-image}[/tex]
[tex]scale factor = 3cm / 9cm = 1/3=0.033[/tex]
So the scale factor to map the first line segment onto the second line segment is 1/3.
It means the 1st line is 3 times longer than the second one.
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Be so kind and help me please!
Answer:
2A/h - b2= b1
Step-by-step explanation:
Given f(x) = −x² – 8x, find ƒ(−3)
Answer:
15
Step-by-step explanation:
To find f(-3), substitute x with (-3)
f(x) = -x² - 8x
f(-3) = - (-3)² - 8*(-3)
= - (9) + 24
= - 9 + 24
= 15
Answer:
15
Step-by-step explanation:
f ( x ) = - x² - 8x
Accordingly, to find the value of f ( -3 ) you have to replace x with ( - 3 ).
f ( -3 ) = - (-3)² - 8 × -3
f ( -3 ) = - 9 + 24
f ( -3 ) = 15
A horizontal curve is being designed around a pond with a tangent length of 1200 ft and a central angle of 29.86 degrees. If the PI is at station 105 00, determine the station of PT
The station of PT is 12305.58 ft
The station of PT can be determined using the formula:
PT = PI + R * (central angle in radians)
To use this formula, we first need to convert the central angle from degrees to radians. We can do this by multiplying the central angle by (π/180)
Next, we need to determine the radius (R) of the curve. We can use the formula:
R = L / (central angle in radians)
Where L is the tangent length.
Finally, we can substitute the values into the formula for PT:
PT = 105 00 + (1200 / (29.86 * (π/180)))
PT = 105 00 + (1200 / (0.5236))
PT = 105 00 + 2295.58
PT = 12305.58
It's important to note that this calculation assumes that the degree of curvature is a circular curve and that the PI is at the tangent point of the curve.
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A calculator cost 32.00 if the sales tax is 6% what is the price ?
Answer:
Step-by-step explanation:
Here is how to solve the given problem above.
Given that the calculator costs $32 and has a tax of 6%, what we are going to do is to find how much is 6% of 32. So 32 times 0.06 is 1.92. So, we add this amount to 32 dollars, and the total price would be 33.92 dollars. Hope this answer helps.
Answer:
33.92
Step-by-step explanation:
32 times 6 divided by 100 gives you 1.92, the sales tax,
add it to 32 and then you get 33.92
i need help ive been stuck on it for ages
Answer:
Don't join the points with lines
Make the numbers on the vertical axis larger
Label the axes
Step-by-step explanation:
Make all the points different colours → I don't think that would be useful. Unless the teacher asked you to in class, it's probably not a good answer.
Put the title on the bottom → Same. Unless the teacher asked you to in class, it's not really useful and probably not a good answer.
Don't join the points with lines → Teachers ask indeed not to do this, so I think it's a good answer. Most of the time they prefer students to use curves (hope it's the good translation).
Make the numbers on the vertical axis larger → Since both axes represent notes, it would be easier to compare with the same scale. If that's what the teacher meant, then I think it's correct.
Label the axes → This one is interesting, because right now we don't what they represent at all.
Hope it helps, good luck for your exercices :)
Please help!! ;(((( I’m struggling
On solving the provided question, we can say that - the function value will be [tex]g(x) = -3 + 12x + 15[/tex] and
what is function?The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.
Here,
[tex]y =a(x-x1)(x-x2),[/tex] y equals a(x-5)(x+1)
g(x) = -3(x-5)(x+1)
[tex]g(x) = -3(x-5)(x+1)[/tex]
g(x) = -3 + 12x + 15
y-intercept of g(x) is (0,15)
Therefore , the solution to the given problem of the equation comes out be y-intercept of g(x) is (0,15).
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Evaluate the expression x2+y210 when x = 6 and y = 8.
A:100
B: 1 2/5
C: 2 4/5
D: 10
A group of friends wants to go to the amusement park. They have no more than $90 to spend on parking and admission. Parking is $16.50, and tickets cost $10.50 per person, including tax. Use the drop-down menu below to write an inequality representing pp, the number of people who can go to the amusement park.
The inequality representing p, the number of people who can go to the amusement park, is given as follows:
10.5p + 16.5 ≤ 90.
How to build the inequality?The inequality for this problem is build considering the linear cost function, defined in slope-intercept format as follows:
C(p) = mp + b.
In which the parameters are given as follows:
m is the slope, representing the cost of the ticket per person.b is the intercept, representing the cost of parking.Parking is $16.50, and tickets cost $10.50 per person, hence the numeric values of the slope and the intercept are given as follows:
m = 10.50, b = 16.50.
Thus the cost function is given as follows:
C(p) = 10.5p + 16.5.
They have no more than $90 to spend on parking and admission, hence the inequality is defined as follows:
C(p) ≤ 90.
10.5p + 16.5 ≤ 90.
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When a calcium atom forms an ion, it loses two electrons. what is the electrical charge of the calcium ion? responses −2 negative 2 −1 negative 1 1 1 2
When a calcium atom forms an ion, it loses two electrons. The electrical charge of the calcium ion is +2
What do you meant by electrical charge of a calcium ion?Calcium ions are net positive two charges. In calcium, when it has assumed its most stable state, the relationship between the quantity of protons (20) and the quantity of electrons (18) is represented by the +2 charge.
In the event that calcium (Z = 20) picks up two electrons, the resultant ion will have 18 electrons and 20 protons, giving it a charge of +2. (two more positive protons than negative electrons). It's a cation, this ion. Using the Ca2+ symbol, we can identify a calcium ion.
Atoms that lose electrons acquire a positive charge as there are fewer electrons left with negative charges to balance the positive charges of the protons in the nucleus. Positively charged ions are known as cations.
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Could someone pls help me solve this ive been struggling for the past hour.no calculator allowed but im allowed a trigonometric circle.thx
The numeric value for each trigonometric expression is given as follows:
3. [tex]\sin{\left(-\frac{5\pi}{6}\right)}\cos{\left(\frac{2\pi}{3}\right)} - \cos{(-\pi)} = \frac{5}{4}[/tex]
4. [tex]\frac{\sin{\left(\frac{\pi}{4}\right)}}{\cos^2{\left(\frac{\pi}{3}\right)}} = 2\sqrt{2}[/tex]
How to obtain the numeric value for the trigonometric expressions?The first trigonometric expression for this problem is defined as follows:
[tex]\sin{\left(-\frac{5\pi}{6}\right)}\cos{\left(\frac{2\pi}{3}\right)} - \cos{(-\pi)}[/tex]
The numeric value of each term of the expression is given as follows, using equivalent angles on the trigonometric circle:
[tex]\sin{\left(-\frac{5\pi}{6}\right)} = \sin{\left(2\pi - \frac{5\pi}{6}\right)} = \sin{\left(\frac{7\pi}{6}\right)} = -\sin{\left(\frac{\pi}{6}\right)} = -\frac{1}{2}[/tex] (negative to positive, then find equivalent of the third quadrant angle on the first).[tex]\cos{\left(\frac{2\pi}{3}\right)} = -\cos{\left(\pi - \frac{2\pi}{3}\right)} = -\cos{\left(\frac{\pi}{3}\right)} = -\frac{1}{2}[/tex] (cosine on the second quadrant is negative).[tex]\cos{(-\pi)} = \cos{(\pi)} = -1[/tex] (cosine is an even function).Hence:
[tex]\sin{\left(-\frac{5\pi}{6}\right)}\cos{\left(\frac{2\pi}{3}\right)} - \cos{(-\pi)} = \left(-\frac{1}{2}\right)^2 + 1 = \frac{1}[4} + 1 = \frac{5}{4}[/tex]
For item 4, the angles are on the first quadrant, hence:
[tex]\sin{\left(\frac{\pi}{4}\right)} = \frac{\sqrt{2}}{2}[/tex][tex]\cos{\left(\frac{\pi}{3}\right) = \frac{1}{2}[/tex]Hence the numeric value of the expression is given as follows:
[tex]\frac{\frac{\sqrt{2}}{2}}{\left(\frac{1}{2}\right)^2} = 4 \times \frac{\sqrt{2}}{2} = 2\sqrt{2}[/tex]
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What is == and === in Python?
The == operator determines if two operands are equivalent in terms of value. The === operator determines if two operands are equivalent in terms of value and datatype.
The assignment operator = is straightforward. The left side operand receives values from the right side operands.
On the other hand, == determines whether or not the values of two operands are equal.
The Python is operator determines if two variables point to the same memory item as opposed to the == operator, which compares the value or equality of two objects. This implies that you should almost always employ the equality operators == and != Difference between == and = in Python.
A single equal sign is used to assign a value to a variable in Python and many other programming languages, whereas two successive equal signs are used to determine if two expressions provide the same result.
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a) What is the size of angle ABC? b) Use your answer to part a) to work out the size of reflex angle CBD. Give your answers to the nearest degree.
Answer:
a) 110
b) 250
Step-by-step explanation:
Read the top row of numbers for a. We are starting at zero and going to 110
Reflex is when two angles add up to 360
360 - 110 = 250
O. Test Practice Alaska has the longest coastline in the United States. Traveling at 62 miles per hour, how many hours would it take to travel along the Pacific Coast? A 17 hours B 89 hours 90 hours D 100 hours Alaska Coastline Coast Pacific Arctic Miles 5,580 1,060
Answer:
17
Step-by-step explanation:
What is the domain of the logarithmic function f/x )= LOGB X?
The domain of the given function would be x > 0.
What is a function?
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
The given function is f(x) = logb(x)
The domain of the logarithmic function [tex]f(x) = log_b(x)[/tex] is the set of all positive real numbers x such that x > 0. This is because the logarithm of a non-positive number is undefined.
Hence, the domain of the given function would be x > 0.
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The domain of the given function would be x > 0.
What is a function?
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
The given function is f(x) = logb(x)
The domain of the logarithmic function [tex]f(x)=log_b(x)[/tex] is the set of all positive real numbers x such that x > 0. This is because the logarithm of a non-positive number is undefined.
Hence, the domain of the given function would be x > 0.
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choose sss, sas, or neither to compare these two triangles
Answer:
SSS
Step-by-step explanation:
We have three pairs of corresponding, congruent sides. Therefore, the SSS Postulate can be used to prove the two triangles congruent.
What ordered pairs are the solutions of the system of equations shown in the graph below?
Therefore ,the ordered pairs which are the solutions of the system of equations shown in the graph below are (1,-4) and (4,-7).
Ordered pair: what is it?The term "ordered pair" refers to a pair of two variable that are shown in a way that they convey a specific order.
In an order pair, the first term denotes the x- and second term, the y-coordinates. The ordered pair is written in close brackets as shown in the example below.
Here ,
Is an equation system:
A set of equations is referred to as a system of equations when a limited set of equations is available and a common solution is sought.
The intersection of two lines, for the two equations drawn on a graph, represents the system's solution.
In the given graph, one linear line and one parabola is shown. In this graph the parabola intersect with the line at point (1,-4) and (4,-7).
Therefore ,the ordered pairs which are the solutions of the system of equations shown in the graph below are (1,-4) and (4,-7).
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The ratio of the number of model cars that jim owns to the number of model cars Terrence owns is 8:6. Terrence owns 36 model cars
Part A
How many model cars does Jim own?
___
Part B
How will the ratio change if Jim and Terrence each sell ten of their model cars?
O The new ratio would stay the same
O The new ratio would be 4:3
O The new ratio would be 23:29
O The new ratio would be 19:13
When Jim's model car ownership is compared to Terrence's model car ownership, the ratio is 8:6, Jim possesses 48 model vehicles.
what is equation ?An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, according to the definition given by the term in its most basic form. When two terms are placed on each side of an equal sign, a simple equation is used to show their relationship. The four mathematical operations of addition, subtraction, multiplication, and division may be used singly or in combination in simple equations.
given
You are aware that Jim and Terrence both own four model automobiles in comparison to three owned by Jim.
Let's assume that Jim owns Jim has the following number of model cars, then you can answer the task as follows:
4/3 = x/36
x = (4* 36)/ 3
x = 48
Therefore, Jims owns 48 model cars.
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a) A train travels from City A to City B. The table below shows the distance and
the amount of time it takes on the train.
Distance (km)
Time (in minutes)
9
3
15 21
5 7
OThe train does not always go the same distance each minute.
OThe train appears to go the same distance each minute.
Predicted distance traveled in 8 minutes: km
Answer:
Step-by-step explanation:
from the figure we kown the speed is 9/3=15/5=21/7=3 km per minute
the distance in 8 minute is 3 ×8=24 km
What is the relationship between the ratios of sin x° and cos y°?
The ratios are both identical (three fifths and three fifths).
b
The ratios are opposites (negative three fifths and three fifths).
c
The ratios are reciprocals (three fifths and five thirds).
d
The ratios are both negative (negative five thirds and negative three fifths).
Answer:
A. The ratios are both identical (three fifths and three fifths).
Step-by-step explanation:
ratio means fraction
ratio also means division
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"SOHCAHTOA"
sine equals opposite over hypotenuse cosine equals adjacent over hypotenuse tangent equals opposite over adjacent
mathworldwolframcom
sine equals opposite over hypotenuse
sine X equals 3 over 5
cosine equals adjacent over hypotenuse
cosine Y equals adjacent over hypotenuse
cosine Y equals 3 over 5
side thats 3 is adjacent for y but
side thats 3 is also opposite for x
both identical, aka C on their question is right
its the 1st option for flvs
What is adjacent angle Class 7?
In class 7, adjacent angles are defined as two angles that share a common vertex and a common side but do not have any common interior points. They are angles that are next to each other.
Adjacent angles are often used in geometry to describe the angles formed by intersecting lines or figures. The adjacent angles can be classified into two types, namely:
Interior adjacent angles: They are formed by two lines that intersect inside a closed figure, such as in a parallelogram.
Exterior adjacent angles: They are formed by two lines that intersect outside a closed figure, such as in a straight line.
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The rectangular floor of a classroom is 30 feet in length and 36 feet in width. A scale drawing of the floor has a length of 5 inches. What is the area, in square inches, of the floor in the scale drawing?
HURRYYYYYYYYYYYYYY
Answer:
30 in.²
Step-by-step explanation:
Real:
length 30 ft
width 36 ft
Scale:
length 5 in.
width ?
30/36 = 5/x
30x = 5 × 36
x = 6
The scale width is 6 inches.
Scale area:
area = length × width
area = 5 in. × 6 in.
area = 30 in.²
The area, of the floor in the scale drawing is 30 in.²
What is the unitary method?The area is the total amount of space that an object's shape or a flat (2-D) surface occupies.
Given that rectangular floor of a classroom is 30 feet in length and 36 feet in width. A scale drawing of the floor has a length of 5 inches.
length 30 ft
width 36 ft
Scale: length 5 in.
Then we have
30/36 = 5/x
30x = 5 × 36
x = 6
The scale width is 6 inches.
Scale area:
The area = length × width
area = 5 in. × 6 in.
area = 30 in.²
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Lia bought 4 3/5 pound of trail mix. She gave 3/5 of it to her iter. How much did give away?
Lia gave away 3/5 of the trail mix, which is equal to 2 2/5 pounds.
Lia bought 4 3/5 pounds of trail mix. She gave 3/5 of it to her iter.Since Lia bought 4 3/5 pounds of trail mix, we can express this as 4 + 3/5 pounds, or 9/5 pounds.
To find out how much trail mix Lia gave away, we can multiply 9/5 by 3/5.
3. 3/5 multiplied by 9/5 is equal to 27/25.
To simplify this fraction, we can divide both the numerator and denominator by 3.
27/25 can be simplified to 9/5 or 2 2/5 pounds.
Therefore, Lia gave away 2 2/5 pounds of the trail mix.
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Hey I need help with this problem here in the picture, would rlly appreciate some quick help
Using the Pythagoras Theorem the value of c=11.40 and the number that goes beneath the radical is 130.
What is Pythagoras Theorem?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.
The rectangle is divided into two triangles which have exactly same sides.
So take any one triangle.
Apply the Pythagoras theorem since it is a right-angled triangle with base = 9 and perpendicular = 7.
So, according to Pythagoras theorem -
(Hypotenuse)^2=(Base)^2+(Perpendicular)^2
Plugging in the values in the equation -
c^2=(9)^2+(7)^2
c^2=81+49
c^2=130
c=[tex]\sqrt{130}[/tex]
c=11.40
Therefore, the value of c is obtained as 11.40.
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You work at an oil refinery and are in charge of draining a tank until the
are 635 gallons left inside. The tank starts with 859 gallons, and you can
drain it at a rate of 56 gallons per minute. How many minutes do you
need to drain the tank to the right level?
You need
minutes.
Answer:
To drain the tank to the right level, you need to remove 859 - 635 = <<859-635=224>>224 gallons.
So you need to work for 224 / 56 = <<224/56=4>>4 minutes.
Step-by-step explanation:
What is the first month in which the board will see the cumulative total number of cars shipped to Japan exceeded the cumulative total in Vietnam
The cumulative total in Vietnam j(n) is 23(n-1),cumulative takes into account all data up to the present. In month four, j(n) will be worth more than v(n).
Is the sum the same as the total?The distinction between total and cumulative is that total refers to the entirety of something, whereas cumulative takes into account all data up to the present.
When a new number is added to a series of numbers, the running total is updated by adding the new number's value to the previous running total. Partially sum is another name for it. Running totals serve two distinct objectives.
We take it for granted that you mean that vehicles delivered to Vietnam should be modeled by v(n) = 5 + 11 and those sent to Japan by j(n) = 23(n-1).
In month four, j(n) will be worth more than v(n).
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The graph of a proportional relationship contains the point (-12, 3)
What is the corresponding equation?
Enter your answer as a fraction in simplest form by filling In the boxes.
y= __/__ x
The corresponding equation of the proportional relationship will be;
⇒ y = - 1/4x
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
The graph of a proportional relationship contains the point (-12, 3).
Now,
Let the equation of the proportion is,
⇒ y = kx
Where, 'k' is constant of proportion.
Since, The graph of a proportional relationship contains the point (-12, 3).
Hence, Substitute x = 0 12 and y = 3 in above equation we get;
⇒ 3 = k × - 12
⇒ 3 / (-12) = k
⇒ k = - 1/4
Thus, The equation of the proportion is,
⇒ y = - 1/4x
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In 2010, the population of a city was 237,000. From 2010 to 2015, the population grew by 7.6%. From 2015 to 2020, it fell by 4.7%. To the nearest whole number, by what percent did the city grow from 2010 to 2020?
The population of the city grew from 2010 to 2020 by 13.37%.
What is percentage?A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.
We have to given that;
In 2010, the population of a city was 237,000.
And, From 2010 to 2015, the population grew by 7.6%. From 2015 to 2020, it fell by 4.7%.
We know that;
Where, A = P (1+r)ⁿ
A = final population.
P = Initial population.
r = rate
n = time
Hence, The population in 2015 is, =
A = 237,000(1 + 0.076)⁵
A = 341829.629
And, The population in 2020 =
A = P (1 - r)ⁿ
A = 341829.629 (1 - 0.047)⁵
A = 268704.047
So, Percent grow = (268704.047 - 237,000) / 237,000 × 100
= 31704.047 / 237,000 × 100
= 13.37 %
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1. a room has dimensions 15m by 9m by 12m the dimensions of its
scale model is 5m by
3m by 4m what is the ratio of the dimensions of the actual room to that of the scale
model
2. the ratio of the dimensions of the scale model to that of the
actual object s 1:16 the length and width of the actual object are
2.4m and 1.8m respectively
Answer: To find the ratio of the dimensions of the actual room to that of the scale model, we can divide the dimensions of the actual room by the dimensions of the scale model.
The dimensions of the actual room are 15m by 9m by 12m, and the dimensions of the scale model are 5m by 3m by 4m.
Therefore, the ratio of the dimensions of the actual room to that of the scale model is:
length: 15m / 5m = 3 : 1
width: 9m / 3m = 3 : 1
height: 12m / 4m = 3 : 1
So, the ratio of the dimensions of the actual room to that of the scale model is 3:1 for all dimensions (length, width, and height)
The ratio of the dimensions of the scale model to that of the actual object is 1:16
so to find the length and width of the actual object, you can use this relation
length = scale model length * 16 = 2.416 = 38.4m
width = scale model width * 16 = 1.816 = 28.8m
So the length and width of the actual object are 38.4m and 28.8m respectively.
Step-by-step explanation:
If sin 0<0 and cos0>0, then the terminal point determined by 0 is in :
Answer: The statement "if sin 0 < 0 and cos 0 > 0" is not true, as both the sine and cosine of an angle of 0 degrees are equal to 0. Therefore, the statement is not meaningful and the question cannot be answered.
It is important to note that sine, cosine, and all the trigonometric functions are defined in radians and not degrees and the value of sin(0) and cos(0) is not zero but 1
Please provide more context or specify what you are asking about in order to give a more accurate answer.
Step-by-step explanation: