Given:
[tex]1993^0[/tex]To Determine: The coterminal angle of the given angle
Solution
Coterminal angles are angles in standard position (angles with the initial side on the positive x -axis) that have a common terminal side. For example 30° , −330° and 390° are all coterminal
[tex]\begin{gathered} 1993^0-360^0=1633^0 \\ 1633^0-360^0=1273^0 \\ 1273^0-360^0=913^0 \\ 913^0-360^0=553^0 \\ 553^0-360^0=193^0 \end{gathered}[/tex]Hence, the angle that coterminal with 1993 degrees is 193⁰
How to solve Use completing the square to find the vertex of the following parabolas
To use completing the square to find the vertex of the given parabola, we proceed as follows:
[tex]g(x)=x^2-5x+14[/tex]- we divide the coefficient of x by 2 and add and subtract the square of the result, as follows:
[tex]g(x)=x^2-5x+(\frac{5}{2})^2-(\frac{5}{2})^2+14[/tex]- simplify the expression as follows:
[tex]\begin{gathered} g(x)=(x^2-5x+(\frac{5}{2})^2)-(\frac{5}{2})^2+14 \\ \end{gathered}[/tex][tex]g(x)=(x^{}-\frac{5}{2})^2-(\frac{5}{2})^2+14[/tex][tex]g(x)=(x^{}-\frac{5}{2})^2-\frac{25}{4}^{}+14[/tex][tex]g(x)=(x^{}-\frac{5}{2})^2-\frac{25}{4}^{}+\frac{56}{4}[/tex][tex]g(x)=(x^{}-\frac{5}{2})^2+\frac{-25+56}{4}^{}[/tex][tex]g(x)=(x^{}-\frac{5}{2})^2+\frac{31}{4}^{}[/tex]From the general vertex equation, given as:
[tex]g(x)=a(x-h)^2+k[/tex]The coordinate of the vertex is taken as: (h, k)
Therefore, given:
[tex]g(x)=(x^{}-\frac{5}{2})^2+\frac{31}{4}^{}[/tex]We have the vertex to be:
[tex](\frac{5}{2},\frac{31}{4})\text{ or (2.5, 7.75)}[/tex]A junk drawer at home contains eight pens four of which work what is the probability that a randomly grab three pens from the drawer and don’t end up with a pen that works express your answer as a fraction in lowest terms or decimal rounded to the nearest million
Answer:
1/14
Explanation:
The number of ways or combinations in which we can select x objects from a group of n can be calculated as:
[tex]\text{nCx}=\frac{n!}{x!(n-x)!}[/tex]So, if we are going to select 3 pens from the drawer that contains 8 pens, the number of possibilities is:
[tex]8C3=\frac{8!}{3!(8-3)!}=\frac{8!}{3!\cdot5!^{}}=56[/tex]Then, if we didn't end up with a pen that works is because we select the three pens from the 4 that didn't work. In this case, the number of possibilities is:
[tex]4C3=\frac{4!}{3!(4-3)!}=\frac{4!}{3!\cdot1!}=4[/tex]Therefore, the probability required is equal to the ratio of these quantities:
[tex]P=\frac{4}{56}=\frac{1}{14}[/tex]So, the answer is 1/14
3(x + 10) < 2 (20 – x)
3(x + 10) < 2 (20 – x)
Distributing multiplication over the addition and the subtraction, we get:
3x + 3*10 < 2*20 - 2x
3x + 30 < 40 - 2x
30 is adding on the left, then it will subtract on the right.
2x is subtracting on the right, then it will add on the left.
3x + 2x < 40 - 30
5x < 10
5 is multiplying x on the left, then it will divide on the right.
x < 10/5
x < 2
1. The diagram below, not drawn to scale, shows a flexible piece of paper in the shape of a sector of a circle with centre 0 and radius 15 cm. 22 Use . B А 126 0 15 cm C (a) Show that the perimeter of the paper is 63 cm. [3] (b) Calculate the area of the paper OABC. 121 (c) The paper is bent and the edges OA and OC are taped together so that the paper forms the curved surface of a cone with a circular base, ABC. (1) Draw a diagram of the cone formed, showing clearly the measurement 15 cm, the perpendicular height, h, and the radius, r, of the base of the cone. [1] (ii) Calculate the radius of the circular base of the cone. 121 (iii) Using Pythagoras' Theorem, or otherwise, determine the perpendicular height of the resulting cone. 121
Given
Circle of radius 15 cm and angle at the centre equal to 126 degree.
Find
(a) Perimeter of the paper is 63cm.
(b) Area of the paper OABC
(c) i) Draw a cone
ii) radius of circular base
iii) determine the height
Explanation
(a)
Perimeter of sector = Arc length ABC + AO + OC
Arc Length of ABC =
[tex]\begin{gathered} \frac{\theta}{360}\times2\Pi r \\ \frac{126}{360}\times2\times\frac{22}{7}\times15 \\ 33 \end{gathered}[/tex]so , perimeter = 33 +15 +15 = 63
Hence we proved that perimeter is 63 cm
(b) Area of sector =
[tex]\begin{gathered} \frac{\theta}{360}\times\Pi r^2 \\ \frac{126}{360}\times\frac{22}{7}\times15\times15 \\ 247.5 \end{gathered}[/tex](c) i)
ii) Circumference of base =
[tex]\begin{gathered} 2\Pi r=\text{33} \\ r=\frac{33\times7}{2\times22} \\ r=\frac{21}{4} \end{gathered}[/tex]iii) l = 15 cm, r= 21/7
By pythagoras theorem,
[tex]\begin{gathered} h^2=l^2-r^2 \\ h^2=15^2-(\frac{21}{4})^2 \\ h=\text{ 14.05} \end{gathered}[/tex]Final Answer
(a) 63
(b) 247.5
Evaluate. Express your answer in scientific notation. 7.94 x 10^-3 6.69 x 10^-4
To solve this question, follow the steps below.
Step 01: Write the numbers to have the same powers.
To do it, choose one number to transform.
Let's choose the number with the greaters power (10⁻³).
To write it with the power -4, multiply 7.94 by 10:
[tex]\begin{gathered} 7.94\times10^{-3}=7.94\operatorname{\times}10*10^{-4} \\ =79.4\operatorname{\times}10^{-4} \end{gathered}[/tex]Step 02: Solve the subtraction.
To solve the subtraction, subtract the decimals.
[tex]\begin{gathered} 79.4\operatorname{\times}10^{-4}-6.69\operatorname{\times}10^{-4} \\ =(79.4-6.69)\operatorname{\times}10^{-4} \\ =72.71\operatorname{\times}10^{-4} \end{gathered}[/tex]Step 03: Rewrite the number in scientific notation.
For a number in scientic notation a x 10ᵇ, 1 ≤ |a| < 10.
Then, divide 72.71 by 10 and multiply the exponent part by 10.
[tex]\begin{gathered} \frac{72.71}{10}\times10^{-4}\times10 \\ 7.271\times10^{-4+1} \\ 7.271\times10^{-3} \end{gathered}[/tex]Answer:
[tex]7.271\cdot10^{-3}[/tex]
cit Formula = 18 + 7(58 - 1) 58 CRIBE EN ORACIONES COMPLETAS
a. As you can see, the sequence starts at -3, and increases by 7 each time, Amanda is wrong because she found the following formula:
an = 18 + 7(n - 1)
For n =1 the result should be -3:
n = 1
a1 = 18 + 7(1 - 1) = 18 + 7(0) = 18 + 0 = 18, she miscalculated the first term, and the whole sequence in general.
b. A possible sequence identification could be:
an = 7n - 10
Let's verify it:
n=1
a1 = 7(1) - 10 = 7 - 10 = -3
n=2
a2 = 7(2) - 10 = 14 - 10 = 4
n=3
a3 = 7(3) - 10 = 21 - 10 = 11
and so on...
Now for n=58
a58 = 7(58) - 10 = 396
-------------------------------------------------------------------------
32 = 2 + 3(n - 1)
Solving for n:
Use distributive property on the right hand side:
32 = 2 + 3n - 3
32 = 3n - 1
Add 1 to both sides:
32 +1 = 3n - 1 + 1
33 = 3n
Divide both sides by 3:
33/3 = 3n/3
11 = n
n = 11
the question i have says “which statement correctly compares the rates of change of the two functions” and i dont understand how to solve it
The rate of change of function A is 4
The rate of change of function B is 3 (option D)
Explanation:We are looking for the rate of change of two functions.
m is also known as the rate of change
[tex]\begin{gathered} \text{Function A is given as:} \\ y\text{ = 4x + 6} \end{gathered}[/tex]comparing the equation above to a linear function:
y = mx + b
m = slope , b = y -intercept
For function A:
m = slope = 4, b = 6
To get the rate of change of function B, we need to find the slope of any two points on the table.
For linear function, the slope is constant irrespective of the two points used in calculating it.
Formula for slope:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]using points; (1, 3) and (3, 9)
[tex]\begin{gathered} x_1=1,y_1=3,x_2=3,y_2\text{ = 9} \\ \text{slope = }\frac{9-3}{3-1} \\ \text{slope = }\frac{6}{2} \\ \text{slope = 3} \\ \text{Slope for function B is 3} \end{gathered}[/tex]The rate of change of function A is 4
The rate of change of function B is 3 (option D)
A dilation from the origin with scale factor of 3 will map the point (5,4) to (8,7) explain why or why not this statement is correct
This statement is false because if the factor of dilatation is 3, the new coordinates should be 3 times the original ones. So the new point shoud be (15,12)
Graph the parabola.y=-4x² +5Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-function button
This is the basic parabola shifted 5 units up.
So, the vertex is at::
(0, 5)
Now, to get 2 points to the left, we take x = -1 and x = -2 and find corresponding y value.
To get 2 points to the right, we take x = 1 and x = 2 and find corresponding y values.
Thus,
When x = -1,
y = -4(-1)^2 + 5
y = 1
When x = -2,
y = -4(-2)^2 + 5
y = -11
When x = 1,
y = -4(1)^2 + 5
y = 1
When x = 2,
y = -4(2)^2 + 5
y = -11
Plotting these 5 points, we connect a smooth curve.
Shown below:
The units of the subway map below are in miles. Suppose the routes between stations are straight. Find the approximate distance a passenger would travel between stations J and K.
Point J has coordinates (2,6)
Point K has coordinates (-1,-3)
The distance between 2 point is given by
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]where
[tex]\begin{gathered} (x_1,y_1)=\mleft(2,6\mright) \\ (x_2,y_2)=(-1,-3) \end{gathered}[/tex]By substituying these values, we have
[tex]\begin{gathered} d=\sqrt[]{(-1_{}-2)^2+(-3-6)^2} \\ d=\sqrt[]{(-3)^2+(-9)^2} \\ d=\sqrt[]{9+81} \\ d=\sqrt[]{90} \end{gathered}[/tex]hence,
[tex]d=9.49[/tex]Find the area of the region enclosed by y = 7x and y = 8x^2.
Solution
Hence the area under the region is
[tex]A=\int_0^{0.875}7x-8x^2=\frac{343}{384}unit^2[/tex]In a poll, 50 residents in Greenville and Fairfield were asked whether they prefer swimming or jogging for exercise. This table shows the relative frequencies from the survey.The graph is in the pictureBased on the data in the table, which statements are true? Select all that apply.
Looking at the relative frequencies of the data in the table, these statements are true - "Greenville residents prefer jogging over swimming", "Fairfield residents prefer swimming over jogging", "People who prefer swimming are more likely to be from Fairfield", "People who prefer jogging are more likely to be from Greenville", "There is an association between the town a person lives in and their exercise preference".
It is given to us that -
50 residents in Greenville and Fairfield were asked whether they prefer swimming or jogging for exercise
The given table shows the relative frequencies from the survey.
We have to find out all the statements that are true about this survey.
Greenville people that like swimming = 0.18Greenville people that like jogging = 0.38=> Most Greenville residents prefer jogging over swimming
Similarly, we can see that
Fairfield residents prefer swimming over jogging (0.24>0.20)It can also be said true about the statements that -
People who prefer swimming are more likely to be from FairfieldPeople who prefer jogging are more likely to be from GreenvilleSince more people from Greenville prefers jogging to swimming and more people people from Fairfield prefers swimming to jogging, therefore "There is an association between the town a person lives in and their exercise preference"
Thus, according to the relative frequencies these statements are true - "Greenville residents prefer jogging over swimming", "Fairfield residents prefer swimming over jogging", "People who prefer swimming are more likely to be from Fairfield", "People who prefer jogging are more likely to be from Greenville", "There is an association between the town a person lives in and their exercise preference".
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The glass portion of a small window is 12 inches by 24 inches. The framework on each side adds on x inches. Express the area of the entire window as a function of x. 72 + x square inches 36+x square inches x² + 36x + 288 square inches 288 + x² square inches
The area of the entire window expressed as a function of x is x²+36x+288 square inches
How to express the area of the window as a function of x?
Given that: The glass portion of a small window is 12 inches by 24 inches
The framework on each side adds on x inches
That means (x+12) by (x+24) inches. This is the representation of the area of the entire window as a function of x. Thus:
(x+12)(x+24) = x(x+24) + 12(x+24) (Clear the brackets)
= x²+24x+12x+288 (Add like terms)
= x²+36x+288 in²
Therefore, the area of the entire window as a function of x is x²+36x+288 square inches
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Amy and Fraser walk inside a circular lawn. Point O is the center of the lawn, as shown below:
Answer
Amy walks a distance equal to the diameter, and Frasier walks a distance equal to the radius of the lawn
Step-by-step explanation
Segment BC represents the diameter of the circle (a segment that connects two points on the circle and it passes through the center of the circle).
Segment OA represents the radius of the circle (a segment that connects the center of the circle and a point on the circle)
Chapter 3: Linear Functions - HomeworkScore: 65/100 12/18 answeredQuestion 11<>Linear ApplicationThe function E(t) = 3863 77.8t gives the surface elevation (in feet above sea level) of LakePowell t years after 1999.Pr
The given function is:
[tex]E(t)=3863-77.8t[/tex]This function is written in the form:
[tex]y=b+mx[/tex]Where b is the y-intercept, and m is the slope of the function. In this case, b=3863 and m=-77.8
The slope is negative, it means the function is decreasing, and the rate of decreasing is the value of the slope, so:
The surface elevation of Lake Power is decreasing at a rate of 77.8 ft/year
Help Please! Will give brainliest and 45 points!
What is 12/10 as a decimal? What is 132/100 as a decimal? What is 546/100 as a decimal? What is 123/10 as a decimal? What is 872/100 as a decimal?
Answer:
That's literally all there is to it! 12/100 as a decimal is 0.12. I wish I had more to tell you about converting a fraction into a decimal but it really is that simple and there's nothing more to say about it. If you want to practice, grab yourself a pen and a pad and try to calculate some fractions to decimal format yourself.
Step-by-step explanation:
Happy 2 help :)
Answer:
12/10 = 1.2132/100 = 1.32 546/100 = 5.46123/10 = 12.3 872/100 = 8.72Step-by-step explanation:
1) 12/10 as a decimal is?
→ 12/10
→ 6/5 = 1.2
2) 132/100 as a decimal is?
→ 132/100
→ 1.32
3) 546/100 as a decimal is?
→ 546/100
→ 5.46
4) 123/10 as a decimal is?
→ 123/10
→ 12.3
5) 872/100 as a decimal is?
→ 872/100
→ 8.72
Hence, these are the answers.
Given vector v equals open angled bracket negative 11 comma negative 5 close angled bracket comma what are the magnitude and direction of v? Round the magnitude to the thousandths place and the direction to the nearest degree.
We will begin by finding the magnitude of a vector, denoted |v|.
The formula we can use is
[tex]|v|=\sqrt{a^2+b^2}[/tex]where a and b represent the vector components. Since we are given the vector <-11,-5>, we will let a be -11 and b is -5.
Substituting those values, we have
[tex]\begin{gathered} |<-11,-1>|=\sqrt{(-11)^2+(-5)^2} \\ \sqrt{121+25} \\ \sqrt{146} \\ \approx12.083 \end{gathered}[/tex]So far, your answer is either the first option or the second option.
Next, we want to find the direction of the vector. We can use another helpful formula:
[tex]\tan\theta=\frac{b}{a}[/tex]Substituting our original values for a and b, we have:
[tex]\tan\theta=\frac{-5}{-11}[/tex]Be careful here! Since the both the a-value and b-value are negative, we are going to be in the third quadrant. After finding our angle (which will be in quadrant 1), we will need to add 180 degrees.
Take the inverse tangent of both sides to get the angle:
[tex]\begin{gathered} \theta=\tan^{-1}(\frac{-5}{-11}) \\ \theta\approx24^{\circ} \end{gathered}[/tex]We'll add 180 degrees to get our final angle:
[tex]24+180=204[/tex]Since our final angle is 204 degrees, the correct answer is the second option.
Answer:
12.083; 24°
explanation:
Magnitude of v = sqrt((-11)^2 + (-5)^2)
Direction of v = atan(-5 / -11)
Calculating these values:
Magnitude of v = sqrt(121 + 25) ≈ 12.083 (rounded to the thousandths place)
Direction of v = atan(-5 / -11) ≈ 0.435 radians
Converting radians to degrees:
The direction of v ≈ 0.435 * (180 / π) ≈ 24.881° ≈ 24° (rounded to the nearest degree)
Therefore, the correct answer is 12.083; 24°.
What are the solution(s) to the quadratic equation 9x² = 4?O x = and x = -- 90x = ² and x = -1/33O= and x = --X=no real solutionM/NK
Given:
The quadratic equation is:
9x² = 4
Required:
Find the solutions to the given equation.
Explanation:
The given equation is:
[tex]9x²=4[/tex]Divide both sides by 4.
[tex]x^2=\frac{4}{9}[/tex]Take the square root on both sides.
[tex]\begin{gathered} x=\pm\sqrt{\frac{4}{9}} \\ x=\pm\frac{3}{2} \end{gathered}[/tex]the solutions to the equation are
[tex]x=\frac{3}{2}\text{ and x =-}\frac{3}{2}[/tex]Final Answer:
Option third is the correct answer.
Hey can you help me with my homework also can you tell me the points so I can put them into the graphs
Step 1
Find the equation of f(x)
[tex]\begin{gathered} The\text{ absolute value function is;} \\ y=a|x-h|+k \end{gathered}[/tex][tex]From\text{ the graph the vertex \lparen h,k\rparen is 3,3}[/tex][tex]\begin{gathered} h=3,k=3 \\ y=1,x=5 \end{gathered}[/tex][tex]1=a|5-3|+3[/tex][tex]\begin{gathered} 1=2a+3 \\ 2a=1-3 \\ 2a=-2 \\ \frac{2a}{2}=-\frac{2}{2} \\ a=-1 \end{gathered}[/tex]Thus f(x) will be;
[tex]y=-1|x-3|+3[/tex]Step 2
Find the equation of y= -f(x) then plot the graph
[tex]\begin{gathered} y=-(-1|x-3|+3) \\ y=1\left|x-3\right|-3 \end{gathered}[/tex]Thus the graph using the points below will look like;
[tex](-4,4),(0,0),(3,-3),(6,0),(8,2)[/tex]Choose either Yes or No to tell whether there is an angle of the given measure shown in the diagram.
The addition of all angles in the diagram is equal to 360 degrees. Let's call angle x to the unknown angle. Then, we have:
[tex]\begin{gathered} m\angle x+160\degree+40\degree+65\degree+25\degree=360\degree \\ m\angle x=360\degree-160\degree-40\degree-65\degree-25\degree \\ m\angle x=70\degree \end{gathered}[/tex]Therefore, there is an angle that measures 70°.
Combining the angles of 160°, 40°, and 65°, we get a new angle, let's call it y, that measures:
[tex]\begin{gathered} m\angle y=160\degree+40\degree+65\degree \\ m\angle y=265\degree \end{gathered}[/tex]Therefore, there is an angle that measures 265°.
Combining the angles of 160°, 70°, 25°, and 65°, we get a new angle, let's call it z, that measures:
[tex]\begin{gathered} m\angle z=160\degree+70\degree+25\degree+65\degree \\ m\angle z=320\degree \end{gathered}[/tex]Therefore, there is an angle that measures 320°.
Combining the angles of 25°, and 65°, we get a new angle, let's call it a, that measures:
[tex]\begin{gathered} m\angle a=25\degree+65\degree \\ m\angle a=90\degree \end{gathered}[/tex]Therefore, there is an angle that measures 90°.
On the other hand, there is no combination of angles that add up to 225°
What is 2902 divided by 3
Answer:
967.333333
Step-by-step explanation:
If you need to round it, it's 967.33
As a fraction, it's 2902/3 or 967 1/3
solve for 18 degreex 29
The given triangle is a right angle triangle. Considering angle 18 as the reference angle,
x = hypotenuse
29 = adjacent side
We would find the hypotenuse, x by applying the cosine trigonometric ratio which is expressed as
Cos# = adjacent side/hypotenuse
Thus, we have
Cos18 = 29/x
29 = xCos18
x = 29/Cos18 = 29/0.95
x = 30.53
what would the length of segment BC have to be in order for line BC to be tangent to circle
Given data:
The first given length is AC=53.
The second given length is AB= 45.
The expression for the Pythagoras theorem is,
[tex]\begin{gathered} AB^2+BC^2=AC^2 \\ (45)^2+BC^2=(53)^2 \\ BC^2=784 \\ BC=28 \end{gathered}[/tex]Here, consider only positive sign of BC length as side cannot negative.
Thus, the BC length is 28.
solve the following equation y^4+7y^2-44=0
Answer:
y = 2, y = -2, y = i √11, y = - i √ 11
Explanation:
To solve the equation for y, we first make the substitution x = y^2. Doing this we write
[tex]x^2+7x-44=0[/tex]The above can be written as
[tex](x-4)(x+11)=0[/tex]Which gives two equations
[tex]\begin{gathered} x-4=0 \\ x+11=0 \end{gathered}[/tex]Substituting back x = y^2 gives
[tex]\begin{gathered} y^2-4=0\rightarrow y=-2,y=2 \\ x^2+11=0\rightarrow y=i\sqrt[]{11},y=-i\sqrt[]{11} \end{gathered}[/tex]Hence, to summarize, the solution to the equation is
[tex]\begin{gathered} y=-2,y=2 \\ y=i\sqrt[]{11},y=-i\sqrt[]{11} \end{gathered}[/tex]A bag contains the following marbles: 12 black marbles, 8 blue marbles, 16 brown marbles and 14 green marbles. what is the ratio of black marbles to blue marbles.
Let:
Nbk = Number of black marbles = 12
Nb = Number of blue marbles = 8
The ratio of black marbles to blue marbles will be given by:
[tex]Nbk\colon Nb=12\colon8=\frac{12}{8}=\frac{3}{2}[/tex]a ladder 15 feet long leans against a house and make a angle of 60 degrees with the ground . find the distance from the house to the foot of the ladder .
We can use the next diagram in order to solve the question
we need to find x, x is the distance from the house to the foot of the ladder, we will use a trigonometric function in order to find x in this case we will use the cosine
[tex]\cos (\theta)=\frac{AS}{H}[/tex]where
θ= 60°
AS=x
H=15 ft
we substitute the values
[tex]\cos (60)=\frac{x}{15}[/tex]we need to isolate the x
[tex]x=\cos (60)(15)=7.5ft[/tex]the distance from the house to the foot of the ladder is 7.5 ft
F(x)=15x+25 find f(1/5)
Given the function:
[tex]f(x)=15x+25[/tex]You need to substitute the following value of "x" into the function:
[tex]x=\frac{1}{5}[/tex]And then evaluate, in order to find:
[tex]f(\frac{1}{5})[/tex]Therefore, you get:
[tex]f(\frac{1}{5})=15(\frac{1}{5})+25[/tex][tex]f(\frac{1}{5})=\frac{15}{5}+25[/tex][tex]\begin{gathered} f(\frac{1}{5})=3+25 \\ \\ f(\frac{1}{5})=28 \end{gathered}[/tex]Hence, the answer is:
[tex]f(\frac{1}{5})=28[/tex]If _____________, then the graph of the polynomial function is symmetric about the origin.f(x) = -f(-x)f(x) = -f(x)f(x) = f(-x)f(x) = f(x + 1)
ANSWER:
1st option: f(x) = -f(-x)
STEP-BY-STEP EXPLANATION:
The polynomial function is symmetric about the origin in the odds functions, where the following is true:
[tex]\begin{gathered} f(-x)=-f(x) \\ \\ \text{ Therefore:} \\ \\ f(x)=-f(-x) \end{gathered}[/tex]Then it would be:
If f(x) = -f(-x), then the graph of the polynomial function is symmetric about the origin.
The correct answer is the 1st option: f(x) = -f(-x)
give some examples in mathematics for a 4th grader.
• Equivalent Fractions
Two or more fractions are called equivalent fractions if they keep the same proportion. For example:
[tex]\begin{gathered} \frac{1}{2}=\frac{2}{4}=\frac{3}{6}=\frac{4}{8}=\frac{5}{10} \\ \frac{3}{9}=\frac{6}{18}=\frac{9}{27}=\frac{12}{36} \end{gathered}[/tex]Notice that we multiplied the numerator and the denominator by the same number to produce those equivalent fractions. We did by two on the first line, and by 3 on the 2nd line.
These fractions are equivalent since we can simplify all of them and reduce them to 1/2. Dividing both numerator and denominator by the same number.
• Mixed Fractions and Improper fractions
Whenever we divide the numerator by the denominator and it is greater than or equal to 1. We can use Mixed Numbers.
For example:
[tex]\begin{gathered} \frac{9}{8}\longrightarrow\text{ 9}\colon8=1.125 \\ \frac{9}{8}=\text{ 1 +}\frac{1}{8}=1\text{ }\frac{1}{8} \\ \frac{12}{10}=1.2\text{ = 1 + }\frac{1}{5}\text{ =1}\frac{1}{5} \end{gathered}[/tex]We use mixed numbers for recipes (in daily life), and to better understand fractions.
When we need to operate them we must turn those Mixed Numbers into improper fractions (fractions whose denominator is lesser than its denominator (bottom number).
A straight line passes through points (1, 15) and(5, 3) What isthe equation of the line?Select one:A) y = - 3x + 18B) y = – 7x + 18C) y = 2x + 18D) y = 3x + 18
Points (1,15) and (5,3)
Find the slope (m)
[tex]m=\frac{y2-y1}{x2-x1}[/tex]where:
(x1,y1) = (1,15)
(x2,y2) = (5,3)
Replacing:
[tex]m=\frac{3-15}{5-1}=\frac{-12}{4}=-3[/tex]the function has a slope m= -3
slope intercept form:
y=mx+b
Where
m= slope
so, the correct function is
y=-3x+18 (A)