Solve the equation 2x^3 – 5x² + x + 2 = 0 given that 2 is a zero of f (x) = 2x^3 – 5x^2 + x +2.
Answers
Hence, 2 is a zero of f(x). That is x - 2 is a factor of f(x).
So we can find
[tex]\frac{2x^3-5x^2+x+2}{x-2}[/tex][tex]\Rightarrow\frac{2x^3-5x^2+x+2}{x-2}=2x^2-x-1[/tex][tex]\text{Next we solve }2x^2-x-1=0[/tex][tex]\begin{gathered} \Rightarrow2x^2-x-1=0 \\ 2x^2+x-2x-1=0 \\ x(2x+1)-1(2x+1)=0 \\ \Rightarrow(x-1)(2x+1)=0 \\ \Rightarrow x-1=0\text{ or 2x+1=0} \\ \Rightarrow x=1\text{ or 2x=-1} \\ x=1\text{ or x =-}\frac{1}{2} \end{gathered}[/tex]Hence,
[tex]x=2,1,\text{ or -}\frac{1}{2}[/tex]
Related Questions
Given the functions, f(x) = 6x+ 2 and g(x)=x-7, perform the indicated operation. When applicable, state the domain
restriction.
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The domain restriction for (f/g)(x) is x=7
What are the functions in mathematics?a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable.
What does a domain math example mean?The collection of all potential inputs for a function is its domain. For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.
Given,
f(x) = 6x+2
g(x) = x-7
So,
(f/g)(x) = 6x+2/x-7
Remember that the denominator can not be equal to zero
Find the domain restriction
x-7=0
x=7
Therefore, the domain is all real numbers except the number 7
(-∞,7)∪(7,∞)
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Kara categorized her spending for this month into four categories: Rent, Food, Fun, and Other. Theamounts she spent in each category are pictured here.Food$333Rent$417Other$500Fun$250What percent of her total spending did she spend on Fun? Answer to the nearest whole percent.
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In this problem we have to calculate the total spences so we add all the costs so:
[tex]\begin{gathered} T=333+417+500+250 \\ T=1500 \end{gathered}[/tex]So 1500 is the 100% so now we can calculate which percentage correspount to 250 so:
[tex]\begin{gathered} 1500\to100 \\ 250\to x \end{gathered}[/tex]so the equation is:
[tex]\begin{gathered} x=\frac{250\cdot100}{1500} \\ x=16.66 \end{gathered}[/tex]So she spend 16.66% in fun
5. Graph the system of inequalities. Then, identify a coordinate point in the solution set.2x -y > -3 4x + y < 5
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We have the next inequalities
[tex]\begin{gathered} 2x-y>-3 \\ 4x+y<5 \end{gathered}[/tex]as we can see if we graph these inequalities we will obtain the next graph
where the red area is the first inequality and the blue area is the second inequality
and the area in purple is the solution set of the two inequalities
one coordinate point in the solution set could be (0,0)
Consider the graph below.(3,1) (4,2) (6,3) (4,4) (8,5) Which correlation coefficient and interpretation best represent the given points?1.) 0.625, no correlation 2.) 0.791. no correlation 3.) 0.625, positive correlation4.) 0.791. positive correlation
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Given the information on the problem,we have that the correlation coefficient of the data given is:
[tex]r=\frac{\sum^{}_{}(x-\bar{y})(y-\bar{x})}{\sqrt[]{SS_x\cdot SSy}}=\frac{10}{\sqrt[]{16\cdot10}}=0.79[/tex]therefore, the value of the correlation coeficient is 0.79, which shows a strong positive correlation
An insurance company offers flood insurance to customers in a certain area. Suppose they charge $500 fora given plan. Based on historical data, there is a 1% probability that a customer with this plan suffers aflood, and in those cases, the average payout from the insurance company to the customer was $10,000.Here is a table that summarizes the possible outcomes from the company's perspective:EventFloodPayout Net gain (X)$10,000 -$9,500$0$500No floodLet X represent the company's net gain from one of these plans.Calculate the expected net gain E(X).E(X) =dollars
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The given is a discrete random variable.
For a discrete random variable, the expected value is calculated by summing the product of the value of the random variable and its associated probability, taken over all of the values of the random variable.
It is given that the probability of a flood is 1%=0.01.
It follows that the probability of no flood is (100-1)%=99%.
Hence, the expected net gain is:
[tex]E(X)=0.01(-9500)+0.99(500)=-95+495=400[/tex]Hence, the expected net gain is $400.
The expected net gain is E(X) = $400.
The length of the hypotenuse in a 30°-60°-90° triangle is 6√10yd. What is thelength of the long leg?
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In order to calculate the length of the long leg, we can use the sine relation of the 60° angle.
The sine relation is the length of the opposite side to the angle over the length of the hypotenuse.
So we have:
[tex]\begin{gathered} \sin (60\degree)=\frac{x}{6\sqrt[]{10}} \\ \frac{\sqrt[]{3}}{2}=\frac{x}{6\sqrt[]{10}} \\ 2x=6\sqrt[]{30} \\ x=3\sqrt[]{30} \end{gathered}[/tex]So the length of the long leg is 3√30 yd.
Find equation of a parallel line and the given points. Write the equation in slope-intercept form Line y=3x+4 point (2,5)
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Given the equation:
y = 3x + 4
Given the point:
(x, y ) ==> (2, 5)
Let's find the equation of a line parallel to the given equation and which passes through the point.
Apply the slope-intercept form:
y = mx + b
Where m is the slope and b is the y-intercept.
Hence, the slope of the given equation is:
m = 3
Parallel lines have equal slopes.
Therefore, the slope of the paralle line is = 3
To find the y-intercept of the parallel line, substitute 3 for m, then input the values of the point for x and y.
We have:
y = mx + b
5 = 3(2) + b
5 = 6 + b
Substitute 6 from both sides:
5 - 6 = 6 - 6 + b
-1 = b
b = -1
Therefore, the y-intercept of the parallel line is -1.
Hence, the equation of the parallel line in slope-intercept form is:
y = 3x - 1
ANSWER:
[tex]y=3x-1[/tex]
Determine which is the better investment 3.99% compounded semi annually Lee 3.8% compounded quarterly round your answer 2 decimal places
Answers
Remember that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]In the 3.99% compounded semiannually
we have
r=3.99%=0.0399
n=2
substitute
[tex]\begin{gathered} A=P(1+\frac{0.0399}{2})^{2t} \\ \\ A=P(1.01995)^{2t} \end{gathered}[/tex]and
[tex]\begin{gathered} A=P[(1.01995)^2]^t \\ A=P(1.0403)^t \end{gathered}[/tex]the rate is r=1.0403-1=0.0403=4.03%
In the 3.8% compounded quarterly
we have
r=3.8%=0.038
n=4
substitute
[tex]\begin{gathered} A=P(1+\frac{0.038}{4})^{2t} \\ A=P(1.0095)^{2t} \\ A=P[(1.0095)^2]^t \\ A=P(1.0191)^t \end{gathered}[/tex]the rate is r=1.0191-1=0.0191=1.91%
therefore
the 3.99% compounded semiannually is a better investmentBe specific with your answer thank you thank you thank you bye-bye
Answers
The y-axis on the graph, that shows us the cost, goes from 2 to 2 units.
To find the cost at option one, the red line, we look in the graph where the line is when x = 80.
For x= 80, y= 58
Now, the same for option 2:
For x = 80, y= 44.
58-44 = 14
Answer: The difference is 14.
How do we determine the number of hours each family used the sprinklers?
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Given:
The output rate of Martinez family's sprinkler is 25L per hour and Green family's sprinkler is 35L per hour. The combined usage of sprinkler is 40 hours. The resulting water output is 1250L.
To find:
The number of hours each family used the sprinkler.
Solution:
Let Martinez family used sprinkler for x hours and Green family used sprinkler for y hours.
Since the combined usage of sprinklers is 40 hours. So,
[tex]x+y=40...\left(i\right)[/tex]The output rate of Martinez family's sprinkler is 25L per hour and Green family's sprinkler is 35L per hour. The resulting water output is 1250L. So,
[tex]\begin{gathered} 25x+35y=1250 \\ 5x+7y=250...\left(ii\right) \end{gathered}[/tex]Multiply (i) by 7 and subtract from (ii), to get:
[tex]\begin{gathered} 5x+7y-7\left(x+y\right)=250-7\left(40\right) \\ 5x+7y-7x-7y=250-280 \\ -2x=-30 \\ x=\frac{-30}{-2} \\ x=15 \end{gathered}[/tex]Now, we get x = 15, Put x = 15 in the equation (i):
[tex]\begin{gathered} 15+y=40 \\ y=40-15 \\ y=25 \end{gathered}[/tex]Thus, x = 15, y = 25.
find a slope of the line that passes through (8,8) and (1,9)
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The slope formula is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]we can use this formula by introducing the values of the given points. In our case
[tex]\begin{gathered} (x_1,y_1)=(8,8) \\ (x_2,y_2)=(1,9) \end{gathered}[/tex]Hence, we have
[tex]m=\frac{9-8}{1-8}[/tex]It yields,
[tex]m=\frac{1}{-7}[/tex]hence, the answer is
[tex]m=-\frac{1}{7}[/tex]I need help creating a tree diagram for this probability scenario
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We need to draw a tree diagram for the information given
The total is 400
120 in finance course
220 in a speech course
55 in both courses
Then we start for a tree for the given number
Then to make the tree for probability we will divide each number by a total 400
Then the probability of finance only is 65/400
The probability of speech only is 165/400
The probability of both is 55/400
The probability of neither is 5/400
The probability of finance or speech is 285/400
Translate to an equation and solve W divided by 6 is equal to 36 w=
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Answer:
[tex]w\text{ = 216}[/tex]Explanation:
Here, we want to translate it into an equation and solve
W divided by 6 equal to 36:
[tex]\begin{gathered} \frac{w}{6}\text{ = 36} \\ \\ w\text{ = 6}\times36 \\ w\text{ = 216} \end{gathered}[/tex]Which of the following is the result of using the remainder theorem to find F(-2) for the polynomial function F(x) = -2x³ + x² + 4x-3?
Answers
Solution
We have the polynomial
[tex]f(x)=-2x^3+x^2+4x-3[/tex]Usin the remainder theorem, we find f(-2) by substituting x = -2
So we have
[tex]\begin{gathered} f(x)=-2x^{3}+x^{2}+4x-3 \\ \\ f(-2)=-2(-2)^3+(-2)^2+4(-2)-3 \\ \\ f(-2)=-2(-8)+4-8-3 \\ \\ f(-2)=16+4-8-3 \\ \\ f(-2)=20-11 \\ \\ f(-2)=9 \end{gathered}[/tex]Therefore, the remainder is
[tex]9[/tex]A coin is tossed an eight sided die numbered 1 through 8 is rolled find the probability of tossing a head and then rolling a number greater than 6. Round to three decimal places if needed
Answers
We are given that a coin is tossed and a die numbered from 1 through 8 is rolled. To determine the probability of tossing head and then rolling a number greater than 6 is given by the following formula:
[tex]P(\text{head and n>6)=p(head)}\cdot p(n>6)[/tex]This is because we are trying to determine the probability of two independent events. The probability of getting heads is given by:
[tex]P(\text{heads})=\frac{1}{2}[/tex]This is because there are two possible outcomes, heads or tails and we are interested in one of the outcomes.
Now we determine the probability of getting a number greater than 6 when rolling the dice. For this, there are 8 possible outcomes and we are interested in two of them, these are the numbers greater than 6 on the die (7, 8). Therefore, the probability is:
[tex]P(n>6)=\frac{2}{8}=\frac{1}{4}[/tex]Now we determine the product of both probabilities:
[tex]P(\text{head and n>6)=}\frac{1}{2}\times\frac{1}{4}=\frac{1}{8}[/tex]Now we rewrite the answer as a decimal:
[tex]P(\text{head and n>6)=}0.125[/tex]Therefore, the probability is 0.125.
hello I'm stuck on this question and need help thank you
Answers
Explanation
[tex]\begin{gathered} -2x+3y\ge9 \\ x\ge-5 \\ y<6 \end{gathered}[/tex]Step 1
graph the inequality (1)
a) isolate y
[tex]\begin{gathered} -2x+3y\geqslant9 \\ add\text{ 2x in both sides} \\ -2x+3y+2x\geqslant9+2x \\ 3y\ge9+2x \\ divide\text{ both sides by 3} \\ \frac{3y}{3}\geqslant\frac{9}{3}+\frac{2x}{3} \\ y\ge\frac{2}{3}x+3 \end{gathered}[/tex]b) now, change the symbol to make an equality and find 2 points from the line
[tex]\begin{gathered} y=\frac{2}{3}x+3 \\ i)\text{ for x=0} \\ y=\frac{2}{3}(0)+3 \\ \text{sp P1\lparen0,3\rparen} \\ \text{ii\rparen for x=3} \\ y=\frac{2}{3}(3)+3=5 \\ so\text{ P2\lparen3,5\rparen} \end{gathered}[/tex]now, draw a solid line that passes troguth those point
(0,3) and (3,5)
[tex]y\geqslant\frac{2}{3}x+3\Rightarrow y=\frac{2}{3}x+3\text{\lparen solid line\rparen}[/tex]as we need the values greater or equatl thatn the function, we need to shade the area over the line
Step 2
graph the inequality (2)
[tex]x\ge-5[/tex]this inequality represents the numbers greater or equal than -5 ( for x), so to graph the inequality:
a) draw an vertical line at x=-5, and due to we are looking for the values greater or equal than -5 we need to use a solid line and shade the area to the rigth of the line
Step 3
finally, the inequality 3
[tex]y<6[/tex]this inequality represents all the y values smaller than 6, so we need to draw a horizontal line at y=6 and shade the area below the line
Step 4
finally, the solution is the intersection of the areas
I hope this helps you
What are all of the x-intercepts of the continuousfunction in the table?Х-4-20246f(x)02820-20 (0,8)O (4,0)O (4,0), (4,0)O (4,0), (0, 8), (4,0)
Answers
The x-intercepts of any function f(x) occur when f(x)=0.
As a reminder, f(x) corresponds to the y coordinate for any given x.
So, we need to focus on the parts of the table where f(x)=0 and look at the x value, that will give us the coordinates of the x-intercepts.
We can see the first entry in the table has f(x)=0 and x= -4.
The only other entry in the table where f(x)=0 has x=4.
As such, the x-intercepts of the given function are (-4,0) and (4,0), which are the coordinates presented in the third option.
4 5 3 7 89 65Each time, you pick one card randomly and then put it back.What is the probability that the number on the card you pickfirst time is odd and the number on the second card you take isa multiple of 2? Keep your answers in simplified improperfraction form.Enter the answer
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We have a total of 8 cards, where 3 of them are a multiple of 2, and 5 is an odd number. Consider that event A represents the probability of picking an odd number and event B is picking a multiple of 2. We know that the events are independent (because we put the cards back), therefore the probability of A and B can be expressed as
[tex]P(A\text{ and }B)=P(A)\cdot P(B)[/tex]Where
[tex]\begin{gathered} P(A)=\frac{5}{8} \\ \\ P(B)=\frac{3}{8} \end{gathered}[/tex]Therefore
[tex]P(A\text{ and }B)=\frac{5}{8}\cdot\frac{3}{8}=\frac{15}{64}[/tex]The final answer is
[tex]P(A\text{ and }B)=\frac{15}{64}[/tex]suppose that z varies jointly with x and y. When x=2, y=2, z=7 write the equation that models the relationship
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quadrilateral WXYZ is reflected across the line y=x to create quadrilateral W’X’Y’Z'. What are the coordinates of quadrilateral W’X’Y’Z'.
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Explanation
We are required to determine the coordinates of W’X’Y’Z' when WXYZ is reflected across the line y = x.
This is achieved thus:
From the image, we can deduce the following:
[tex]\begin{gathered} W(-7,3) \\ X(-5,6) \\ Y(-3,7) \\ Z(-2,3) \end{gathered}[/tex]We know that the following reflection rules exist:
Therefore, we have:
[tex]\begin{gathered} (x,y)\to(y,x) \\ W(-7,3)\to W^{\prime}(3,-7) \\ X(-5,6)\to X^{\prime}(6,-5) \\ Y(-3,7)\to Y^{\prime}(7,-3) \\ Z(-2,3)\to Z^{\prime}(3,-2) \end{gathered}[/tex]Hence, the answers are:
[tex]\begin{gathered} \begin{equation*} W^{\prime}(3,-7) \end{equation*} \\ \begin{equation*} X^{\prime}(6,-5) \end{equation*} \\ \begin{equation*} Y^{\prime}(7,-3) \end{equation*} \\ \begin{equation*} Z^{\prime}(3,-2) \end{equation*} \end{gathered}[/tex]This is shown in the graph bwlow for further undertanding:
How much of the wall does the mirror cover? Use the π button in your calculations and round your answer to the nearest hundredths. Include units.
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Since the diameter of the mirror is given, calculate the area of the mirror using the formula
[tex]A=\frac{1}{4}\pi\cdot(D)^2[/tex]replace with the information given
[tex]\begin{gathered} A=\frac{1}{4}\pi\cdot24^2 \\ A=144\pi\approx452.39in^2 \end{gathered}[/tex]The mirror covers 452.39 square inches.
Sparkles the Clown makes balloon animals for children at birthday parties. At Bridget's party, she made 5 balloon poodles and 1 balloon giraffe, which used a total of 15 balloons. For Eduardo's party, she used 7 balloons to make 1 balloon poodle and 1 balloon giraffe. How many balloons does each animal require?
Answers
Let p be the number of balloons required to make one balloon poodle and g the number of balloons required to make one balloon giraffe.
Then we have:
I) 5p + g = 15
II) p + g = 7
Subtracting equation II from equation I, we have:
5p - p + g - g = 15 - 7
4p = 8
p = 8/4
p = 2
Replacing p with 2 in equation II we have:
2 + g = 7
g = 7 - 2
g = 5
Answer: Each poodle requires 2 balloons and each giraffe requires 5 balloons.
"Solve for x. Enter as a decimal not as a fraction. Round to the nearest hundredth if necessary."
Answers
Answer:
x =
5
Explanation
From the given diagram, it can be infered that WY = 2QR
From the diagram
WY = x+9
QR = 2x-3
substitute into the expression
x+9 = 2(2x-3)
x+9 = 4x - 6
Collect the like terms
x-4x = -6-9
-3x = -15
x = -15/-3
x = 5
Hence the value of x is 5
cos(alpha + beta) = cos^2 alpha - sin^2 beta
Answers
The trigonometric identity cos(α + β)cos(α - β) = cos²(α) - sin²(β) is verified in this answer.
Verifying the trigonometric identityThe identity is defined as follows:
cos(α + β)cos(α - β) = cos²(α) - sin²(β)
The cosine of the sum and the cosine of the subtraction identities are given as follows:
cos(α + β) = cos(α)cos(β) - sin(α)sin(β).cos(α - β) = cos(α)cos(β) + sin(α)sin(β).Hence, the multiplication of these measures is given as follows:
cos(α + β)cos(α - β) = (cos(α)cos(β) - sin(α)sin(β))(cos(α)cos(β) + sin(α)sin(β))
Applying the subtraction of perfect squares, it is found that:
(cos(α)cos(β) - sin(α)sin(β))(cos(α)cos(β) + sin(α)sin(β)) = cos²(α)cos²(β) - sin²(α)sin²(β)
Then another identity is applied, as follows:
sin²(β) + cos²(β) = 1 -> cos²(β) = 1 - sin²(β).sin²(α) + cos²(α) = 1 -> sin²(α) = 1 - cos²(a).Then the expression is:
cos²(α)cos²(β) - sin²(α)sin²(β) = cos²(α)(1 - sin²(β)) - (1 - cos²(a))sin²(β)
Applying the distributive property, the simplified expression is:
cos²(α) - sin²(β)
Which proves the identity.
Missing informationThe complete identity is:
cos(α + β)cos(α - β) = cos²(α) - sin²(β)
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Anna weighs 132 lb. Determine her mass in kilograms using the conversion 1 kg equal 2.2 lb. Use this mass to answer this question. calculate Anna's weight on Jupiter. (G= 25.9 m/ S2) must include a unit with your answer
Answers
Input data
132 lb
132 lb * 1kg / 2.2lb = 60 kg
Anna's weight on Jupiter
w = 60 kg * 25.9 m/S2
w = 1554 N
A trapezoid has a height of 16 miles. The lengths of the bases are 20 miles and 35miles. What is the area, in square miles, of the trapezoid?
Answers
Given:
A trapezoid has a height of 16 miles.
The lengths of the bases are 20 miles and 35 miles.
To find:
The area of the trapezoid.
Explanation:
Using the area formula of the trapezoid,
[tex]A=\frac{1}{2}(b_1+b_2)h[/tex]On substitution we get,
[tex]\begin{gathered} A=\frac{1}{2}(20+35)\times16 \\ =\frac{1}{2}\times55\times16 \\ =440\text{ square miles} \end{gathered}[/tex]Therefore the area of the trapezoid is 440 square miles.
Final answer:
The area of the trapezoid is 440 square miles.
Imagine you asked students to draw an area model for the expression 5+4x2.
Walking around the room, you see the following three area models.
First, briefly explain the student thinking process you think might be behind each answer.
Answer Describe the thinking process
Which order would you call students A, B and C to present their work to the class and how would you guide the discussion?
Answers
Answer:
area 1
Step-by-step explanation:
please help me please
Answers
F (x) = (-1/20)x + 13.6
Then
Radmanovics car y -intercept is= 13.6 gallons
Mr Chin's car y-intercept is= 13.2
Then , in consecuence
Radmanovics car has a larger tank, than Mr Chin's car.
Answer is OPTION D)
An arctic village maintains a circular cross-country ski trail that has a radius of 2.9 kilometers. A skier started skiing from the position (-1.464, 2.503), measured in kilometers, and skied counter-clockwise for 2.61 kilometers, where he paused for a brief rest. (Consider the circle to be centered at the origin). Determine the ordered pair (in both kilometers and radii) on the coordinate axes that identifies the location where the skier rested. (Hint: Start by drawing a diagram to represent this situation.)(x,y)= ( , ) radii(x,y)= ( , ) kilometers
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The solution to the question is given below.
[tex]\begin{gathered} The\text{ 2.6km is some fraction of the entire Circumference which is: C= 2}\pi r\text{ = 2}\times\text{ }\pi\text{ }\times2.9 \\ \text{ = 5.8}\pi cm \\ \text{ The fraction becomes: }\frac{2.61}{5.8\pi}\text{ = }\frac{0.45}{\pi} \\ \text{The entire circle is: 2 }\pi\text{ radian} \\ \text{ = }\frac{0.45}{\pi}\text{ }\times2\text{ }\times\pi\text{ = 0.9} \\ The\text{ skier has gone 0.9 radian from (-.1.464, 2.503)} \\ \text{The x- cordinate become: =-1.}464\text{ cos}(0.9)\text{ = -1.4625} \\ while\text{ the Y-cordinate becomes: =-1.}464\text{ sin}(0.9)\text{ = -}0.0229 \\ \text{The skier rested at: (-1.4625, -0.0229)} \\ \end{gathered}[/tex]0.75 greater than 1/2
Answers
True
0.75 is greater than 0.5
Explanation
Step 1
remember
[tex]\frac{a}{b}=\text{ a divided by b}[/tex]then
[tex]\frac{1}{2}=\text{ 1 divided by 2 = 0.5}[/tex]Step 2
compare
0.75 and 0.5
[tex]0.75\text{ is greater than 0.5}[/tex]I hope this helps you
FOR GREATER THAN WE ADD THE TERMS.
MATHEMATICALLY THIS MEANS
[tex] = 0.75 + \frac{1}{2} \\ = 0.75 + 0.5 \\ = 1.25[/tex]
1.25 is the answer.