Answers
The given expression is,
[tex](2x^2)^3[/tex]According to the law of exponents,
[tex]\begin{gathered} (xy)^m=x^my^m\text{ ---(a)} \\ (x^m)^n=x^{mn}\text{ ---(b)} \end{gathered}[/tex]Applying the law of exponents to the given expression,
[tex]\begin{gathered} (2x^2)^3=2^3(x^2)^3\text{ (using law (a))} \\ =8x^{2\times3}\text{ (using law (b))} \\ =8x^6 \end{gathered}[/tex]Therefore, the correct expression is
[tex](2x^2)^3=8x^6[/tex]
Related Questions
Write the equation of the line that passes through the points (-2,-2) and (8,0)
Answers
Considering the expression of a line, the equation of the line that passes through the points (-2,-2) and (8,0) is y= -1/5x + 8/5.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:
m= (y₂ - y₁)÷ (x₂ -x₁)
Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, the value of the "b" can be obtained.
Equation of the line in this case
Being (x₁, y₁)= (-2, 2) and (x₂, y₂)= (8, 0), the slope m can be calculated as:
m= (0 - 2)÷ (8 -(-2))
m= (0 - 2)÷ (8 +2)
m= (-2)÷ (10)
m= -1/5
Considering point 1 and the slope m, you obtain:
2= (-1/5)×(-2) + b
2= 2/5 +b
2 -2/5= b
8/5= b
Finally, the equation of the line is y= -1/5x + 8/5.
Learn more about the equation of a line having 2 points:
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need help with question 4
need answer in cubic feet
Answers
Answer: 140cubic feet
Step-by-step explanation:
14Cubic feet x 10cubic feet is 140cubic
How many solutions does this equation have? Solve on paper and enter your answer on Zearn.
1/5(25+15x) = 3x+5
No solutions
One solution
Infinitely many solutions
Answers
Answer: Infinity many solutions
Step-by-step explanation:
1/5(25+15x) = 3x+5 (Multiply 1/5 with the parentheses)
5+3x=3x+5
^ Both sides are the same, meaning that any number can be plugged into x.
We can also simplify it by subtracting 3x and 5 from both sides:
5+3x=3x+5
3x-3x=5-5
0=0
what are the coordinates for the location of the center of the merry-go-round?
Answers
Given the coordinates of the following locations
[tex]\begin{gathered} Q(4,-2) \\ R(2,-4) \\ S(0,2) \end{gathered}[/tex]From the question we have that the distance of the point are equal so we will have;
[tex](x-4)^2+(y+2)^2=(x-2)^2+(y+4)^2=(x-0)^2+(y-2)^2[/tex]Solving equation 1 and 3 simultaneously we will have
[tex]\begin{gathered} x^2-8x+16+y^2+4y+4=x^2+y^2-4y+4_{} \\ -8x+8y=-16 \\ \text{Divide through by 8} \\ -x+y=-2 \\ x=y+2 \end{gathered}[/tex]Solving equation 2 and 3 simultaneously we will have
[tex]\begin{gathered} x^2-4x+4+y^2+8y+16=x^2+y^2-4y+4 \\ -4x+12y=-16 \\ \text{Divide through by 4} \\ -x+3y=-4 \\ x=3y+4 \end{gathered}[/tex]Thus , to solve for y we have;
[tex]\begin{gathered} y+2=3y+4 \\ 2-4=3y-y \\ -2=2y \\ y=\frac{-2}{2}=-1 \end{gathered}[/tex]Substitute y to find x
[tex]\begin{gathered} x=y+2 \\ x=-1+2=1 \end{gathered}[/tex]Hence the coordinates of the center of the merry-go-round is ( 1, - 1)
The second option is the correct option
y varies directly as z and inversely as x; write the sentence as an equation
Answers
Given:
(y) varies directly as (z) and inversely as (x):
[tex]\begin{gathered} y\propto z;y\propto\frac{1}{x} \\ \\ so,y\propto\frac{z}{x} \end{gathered}[/tex]so, the equation will be:
[tex]y=\frac{kz}{x}[/tex]Where: k is the proportionality constant
Find the area ofa cirde with a circumference of 50.24 units,
Answers
Step 1
Find radius r , from circumference
circumference = 50.24
[tex]\begin{gathered} \text{Circumference = 2 }\pi\text{ r} \\ \pi\text{ = 3.142} \\ 50.24\text{ = 2 x 3.142r} \\ 50.24\text{ = 6.284r} \\ r\text{ = }\frac{50.24}{6.284} \\ r\text{ = 7.99} \end{gathered}[/tex][tex]\begin{gathered} \text{Area = }\pi r^2 \\ =3.142\text{ x 7.99 x 7.99} \\ =\text{ 200.58} \end{gathered}[/tex]This is super confused im not the best with graphs
Answers
ANSWER
C. The function is negative when x < 0
EXPLANATION
We want to identify the statement that best describes the function graphed.
To do this, we have to study the graph of the function.
The function graphed has both positive and negative values. The positive values of the function are the part of the function that is above the horizontal red line while part of the negative values of the function is the part of the function that is below the horizontal red line.
We notice that the part of the function that is below the horizontal red line occurs when x is less than 0 (the part of the graph to the left of the vertical red line).
Hence, we can conclude that the correct statement that describes the function is:
The function is negative when x < 0. The answer is option C.
2. 2. How many rectangles similar to this one 1 Is possible from the figure below? Ans = A.) 24 B) 25 C) 20
Answers
Similar triangles are triangles with corresponding angles and corresponding sides. They don't necessarily mean triangles of the same size(congruent).
From the diagram attached
Anna rolls a die and then flips a coin. Identify the tree diagram which displays the outcomes correctly.
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Let:
1 = Get a 1
2 = Get a 2
3 = Get a 3
4 = Get a 4
5 = Get a 5
6 = Get a 6
H = Get heads
T = Get tails
The set of all possible outcomes of the experiment is:
[tex]\begin{gathered} S=\mleft\lbrace(1,H\mright),(1,T),(2,H),(2,T),(3,H),(3,T),(4,H),(4,T),\ldots \\ \ldots(5,H),(5,T),(6,H),(6,T)\} \end{gathered}[/tex]Therefore, the only tree diagram which displays the outcomes correctly is the one in the option A.
Question 2: Construct a perpendicular to
AB at A and at B (Hint: Extend AB)
Answers
Answer:
Explanation:
Here, we want to construct a perpendicular line at the points
The steps are as follows:
a) We extend the line through A and B
b) Place the compass at Point A, and draw a small semi-circle. Now, divide this semi-circle into 2. The line drawn will be perpendicular to AB and it will pass through A
c) Repeat the same process for B
We have the sketch as follows:
Help me out with details
Answers
Answer:
The numbers are proportional with each other. If you were to divide the length on the table by the corresponding width, you'd get the same answer each time(0.6)
Barney and Robin went shopping at H&M. The store was having a sale on all shirts and pants. Barney spent $70 on 3 shirts and 2 pairs of pants and Robin bought 1 shirt and 4 pairs of pants for $90. d) Use a graphing calculator, to graph your equations in parts a and b. What is the coordinate point where these two lines intersect? How does this compare to your response in part c?
Answers
Barney spent $70 on 3 shirts and 2 pairs of pants
Robin bought 1 shirt and 4 pairs of pants for $90
Let x be the cost for each shirt
Let y be the cost for each pair of pants
3x+2y=70 (1)
x+4y=90 (2)
Having this system of equations, we can graph on the graph calculator:
The solution of two linear equations corresponds to the intersection of the two lines because the coordinate pair naming every point on a graph is a solution to its corresponding equation:
In this case the solution is: (10, 20) and corresponds to the cost of the shirt and pant.
Shirt: $10
Pant:$20
Given the explicit formula below, which is the appropriate list of the first 4 numbers:An = 3(2)n-1A2, 6, 18, 54, .B3, 6, 9, 12,..С3, 6, 12, 24, ...D1, 3, 5, 7, ...
Answers
The simpliest way to answer the question is by iteration, substituting n with the numbers 1, 2, 3, 4 to find the first 4 numbers. So we have the formula;
[tex]A_n=3(2)^{n-1}[/tex]When n = 1,
[tex]\begin{gathered} A_n=3(2)^{n-1} \\ A_1=3(2)^{1-1} \\ A_1=3(2)^0 \\ A_1=3 \end{gathered}[/tex]When n = 2,
[tex]\begin{gathered} A_n=3(2)^{n-1} \\ A_2=3(2)^{2-1} \\ A_2=3(2)^1 \\ A_2=6^{} \end{gathered}[/tex]When n = 3,
[tex]\begin{gathered} A_n=3(2)^{n-1} \\ A_3=3(2)^{3-1} \\ A_3=3(2)^2 \\ A_3=12 \end{gathered}[/tex]When n = 4,
[tex]\begin{gathered} A_n=3(2)^{n-1} \\ A_4=3(2)^{4-1} \\ A_4=3(2)^3 \\ A_4=24 \end{gathered}[/tex]Therefore when n = {1, 2, 3, 4}, An = {3, 6, 12, 24}, making 3, 6, 12, 24 the first 4 numbers of our formula.
Therefore the answer is LETTER C.
Points L,M and N are collinear.M is between L and N. You are given LM=13 and LN=20.Find the length of MN
Answers
ANSWER
MN = 7
EXPLANATION
Let's draw a diagram first:
Since all the points are collinear we can use the segment addition postulate:
[tex]LM+MN=LN[/tex]Replacing with the values we know:
[tex]13+MN=20[/tex]And solving for MN:
[tex]MN=20-13=7[/tex]We have that the length of segment MN is 7.
What is money? 1. A store of value2. A medium of exchange3. A measure of valuea. Money simplifies the exchange process because it’s a means of indicating how much something costs.b. To use money to buy the goods and services you want.c. People are willing to hold onto it because they’re confident that it will keep its value over time.it is math even if it doesnt look like it
Answers
Given data:
Money can be defined a medium of exchange.
Thus, money is juat a medium of echnage.
This picture is the paragraph of information to answer the questions. The second picture is the questions
Answers
Question 1
a) It could not represent the scenario because the vertex of the parabola is located at (-5,9), and x=-5 is a region beyond the bank.
b) This function does not fit the scenario because the parabola opens up, as if the fish fell towards the sky.
c) This function does not fit the scenario because the expression is negative for all values of x, which means that the fish always remains under water.
Question 2
The x-value at the center of the boat is 5.
Question 3
The fish jumps 4 feet high.
Question 4
The zeros of the function are x=3 and x=7 and they represent the locations over the x-axis where the fish comes out of the water and re-enters the river.
Question 5
The fish comes out of the water 2 feet away from the center of the boat.
Question 6
The domain is: 0≤x≤50.
The range is: -2021≤y≤4.
Question 7
a) The path of the fish is increasing at the interval [0,5).
b) The path of the fish is decreasing at the interval (5,50]
Question 8
a) The fish swims under water at the intervals [0,3) and (7,50].
b) The fish swims abov the water at the interval (3,7).
Explanation:Question 1:
Write the functions in vertex form.
a)
[tex]\begin{gathered} F\left(x\right)=-x^2-10x-16 \\ =-\left(x+5\right)^2+9 \end{gathered}[/tex]The vertex is located at (-5,9), but the bank is the line x=0 and the region x<0 corresponds to land. The fish cannot swim on the land, so it would be impossible for the fish to reach that point. Additionally, the function is negative for all positive values of x, so in the region that corresponds to the river, the fish never comes out of the water.
b)
[tex]F\left(x\right)=x^2-6x+13[/tex]Since the coefficient of the quadratic term is positive, the parabola opens up. Then, this trajectory corresponds to an object that "falls upwards", which is not possible.
c)
[tex]\begin{gathered} F\left(x\right)=-x^2+6x-13 \\ =-\left(x-3\right)^2-4 \end{gathered}[/tex]Notice that the function is negative for all values of x, which can be interpreted as if the fish never came out of the water, which does not correspond to the described situation.
Question 2:
Write the expression that describes the trajectory of the fish in vertex form. The x-coordinate of the vertex corresponds to the center of the boat.
[tex]\begin{gathered} F\left(x\right)=-x^2+10x-21 \\ =-\left(x-5\right)^2+4 \end{gathered}[/tex]The vertex of the parabola is (5,4), so the center of the boat is located at x=5.
Question 3:
The maximum height of the fish corresponds to the y-coordinate of the vertex. So, the fish's maximum height is y=4 (4 feet).
Question 4:
Set F(x)=0 and solve for x:
[tex]\begin{gathered} F\left(x\right)=0 \\ \Rightarrow-\left(x-5\right)^2+4=0 \\ \Rightarrow4=\left(x-5\right)^2 \\ \Rightarrow\left(x-5\right)^2=4 \\ \Rightarrow x-5=±\sqrt{4} \\ \Rightarrow x-5=±2 \\ \Rightarrow x=5±2 \\ \therefore x_1=3,x_2=7 \\ \end{gathered}[/tex]Then, the zeros of the function are x=3 and x=7, they represent the horizontal location at which the fish is located at the surface of the river, so they are the points where the fish comes out of the water and re-enters the water.
Question 5:
The points x=3 and x=7 are both 2 units away from x=5. Then, the fih comes out of the water and re-enters the water 2 feet away from the center of the boat.
Question 6:
a)
The domain corresponds to all the values of x that the function can take. Since the river is 50 feet wide and the bank is the y-axis, then, the river covers the region 0≤x≤50, which is the same as the domain.
b)
The range corresponds to all the values over the y-axis that the function can take when evaluated at values from the domain.
To find the range, we have to find the maximum and minimum values of F(x) for 0≤x≤50. Since the maximum value of the function is 4 (the maximum height), just check for the values of F(0) and F(50) to find the possibilities for the minimum:
[tex]\begin{gathered} F\left(0\right)=-\left(0-5\right)^2+4 \\ =-25+4 \\ =-21 \end{gathered}[/tex][tex]\begin{gathered} F\left(50\right)=-\left(50-5\right)^2+4 \\ =-\left(45\right)^2+4 \\ =-2025+4 \\ =-2021 \end{gathered}[/tex]Then, the minimum value of the function F for the values in the domain is -2021. Therefore, the range is: -2021≤y≤4.
Question 7:
The path of the fish increases until it reaches it maximum point at x=5, then it decreases. Then:
a) The path of the fish increases at 0≤x<5.
b) The path of the fish decreases as 5.
Question 8:
The fish is initially under water, it comes out at the first zero of the function x=3, it travels through the air until it re-enters the water at x=7 and it continues under water from that point on. Then:
a) The fish is under water in the interval 0≤x<3 and 7.
b) The fish is above the water in the interval 3.
Use the data set to determine which statements are correct. Check all that apply. 35, 41, 18, 75, 36, 21, 62, 29, 154, 70 The median is 36.The median is 38.5.There is an outlier.The lower quartile is 29. The lower quartile is 18. The upper quartile is 29.The upper quartile is 70. The interquartile range is 41.
Answers
Q1 = 35.75
Q2 = 40
Q3= 45.5
IQR = 9.75
Lower Outlier =15
Upper Outlier=55
1) Let's calculate the quartiles, by using a formula for that and considering that the Distributions is:
2) But we need to orderly write this distribution, so:
15 29 29 35 35 36 36 37 38 40 40 42 44 45 45 47 51 52 52 55
The first Quartile is given by the formula, below where n is the number of observations in this case, since we have a decimal let's find the average between the 5th and the 6th number:
[tex]\begin{gathered} Q_1=\frac{1}{4}(n+1)^{th} \\ Q_1=\frac{1}{4}(20+1)^{th} \\ Q_1=\frac{1}{4}(21)^{th} \\ Q_1=5.25 \\ Q_{,1}=\frac{35+36}{2}=35.75 \end{gathered}[/tex]Then The upper Quartile:
[tex]\begin{gathered} Q_3=\frac{3}{4}(n+1)^{th} \\ Q_3=\frac{3}{4}(21)^{th} \\ Q_3=\text{ 15.75 position} \\ Q_3=\frac{45+47}{2}=45.5 \end{gathered}[/tex]3) And the Second Quartile is going to be the median
[tex]Q_2=\text{ Median =}\frac{40+40}{2}=40[/tex]The interquartile range is going to be the difference, between the first quartile and the third one
IQR = 45.5 -35.75 =9. 75
The outliers in the distribution
15 29 29 35 35 36 36 37 38 40 40 42 44 45 45 47 51 52 52 55
They can be found by a formula:
[tex]\begin{gathered} Lower\colon Q_1-(1.5\text{ }\times IQR) \\ \text{Lower: 35.75-(1.5}\times9.75) \\ L=35.75-(14.625) \\ L=21.125\approx21 \\ \\ \text{Upper: Q}_3+(1.5\times IQR) \\ \text{Upper: }45.5+(1.5\times9.75) \\ \text{Upper: }60.125\approx60 \end{gathered}[/tex]The lower outlier is below 21.125, and the upper one 60.125 so in our distribution, Lowe Outlier is 15, and the Upper one, is closer to 60.125 in this case, 55.
The answers are:
Q1 = 35.75
Q2 = 40
Q3= 45.5
IQR = 9.75
To solve the rational equation2. 3-x+65X+25how can the expressionX+2be rewritten usingthe least common denominator?
Answers
The expression given is:
[tex]\frac{2}{x}+\frac{3-x}{6}[/tex]The Least Common Denominator (L.C.D) of the expression is the product of the denominator:
[tex]6\times x=6x[/tex]Since
[tex]\frac{2}{x}+\frac{3-x}{6}=\frac{5}{x+2}[/tex]Then, we can multiply both the numerator and denominator with the L.C.D of 6x:
[tex]\begin{gathered} \frac{5}{x+2} \\ \\ \frac{5}{x+2}\times\frac{6x}{6x} \\ \\ \frac{30x}{6x(x+2)} \end{gathered}[/tex]Therefore, the final answer is: Option B
ABOUT HOW MANY NO RESPONCES COULD YOU EXPECT FROM A POPULATION OF 500 WITH 15 OUT OF 60 YES RESPONSES FROM A SAMPLE. A. 15B. 45C. 125D.375 NOT A TEST.
Answers
Total population = 500
15 out of 60 gives a YES response
This implies
Probability of getting a YES response is
[tex]\frac{15}{60}[/tex]Out of the 500 population
The number of YES responses will be
[tex]500\times\frac{15}{60}[/tex]Simplifying this gives
[tex]\begin{gathered} 500\times\frac{15}{60} \\ =500\times\frac{1}{4} \\ =125 \end{gathered}[/tex]Hence out of 500 population 125 responses will be YES
Therefore, the number of NO responses is
[tex]500-125=375[/tex]Therefore, the number of NO responses is 375
2xy^2-x^2Evaluate where x=2 and y=5is that first step correct and what would be the order of operations from there
Answers
To evaluate this , replace the terms with the numbers as
2 xy^2 - x^2
[tex]2xy^2-x^2[/tex][tex]2\cdot2\cdot5^2-2^2[/tex][tex]4\cdot5^2-4[/tex][tex]4\cdot25\text{ - 4}[/tex][tex]100-4=96[/tex]he spent $54integer:
Answers
Since the person is spending it means that the money they have is decreasing.
when anything is decreasing we use the negative sign
[tex]He\text{ spent \$54}\rightarrow-54[/tex]The point enter your response here is also on the graph of the equation.
Answers
An equation that has a graph that is symmetric to the origin, has a reflection of each point through the origin, reflects across the x-axis and y-axis.
Therefore, if one point of the graph is (-4,1).
Reflected to both axis, we can find that another is is (-x,-y) = (-(-4), -1) = (4, -1)
So, the answer is the point (4, -1)
In the first episode of a reality show, contestants had to spin two wheels of fate. Spinning the first wheel determined the remote location where contestants would reside for the duration of the season. Spinning the second wheel determined which "bonus survival tool" they would be allowed to bring, along with a few other necessary items. A tent Matches Desert 4 1 Rainforest 3 1 Mountain peak 1 1 What is the probability that a randomly selected participant spun the second wheel and landed on a tent given that the participant spun the first wheel and landed on mountain peak? Simplify any fractions.
Answers
Answer:
1/2
Explanation:
Taking into account the table, we know that 2 participants spun the first wheel and it landed on a mountain peak and 1 of those participants spun the second wheel and landed on a tent. So, we can calculate the probability as:
[tex]P=\frac{1}{2}[/tex]Because there are 2 people on a mountain peak and for one of them landed on a tent.
Therefore, the answer is 1/2
It is known that the events ANB are mutually exclusive that p(a)=0.60 and p(b)=0.16
Answers
The probability of two mutually exclusive events to happen simultaniously can be described as below:
[tex]P(A\text{ and }B)=P(A)\cdot P(B)[/tex]We can replace the terms above with the probabilities to determine the answer for this problem.
[tex]P(A\text{ and }B)=0.6\cdot0.16=0.096[/tex]The probability of both events happening simultaneously is 0.096.
Simplify the following expression.(3x – 5)(4 – 9x) + (2x + 1)(6x2 + 5)O12.3 – 21.12 - 671 - 15O12 x3 – 21–2 + 671 - 1512r 3 + 21,2 – 675 + 15O12 x3 + 21x2 + 67x + 15Submit
Answers
The Solution:
Given the expression below:
[tex]\mleft(3x-5\mright)\mleft(4-9x\mright)+\mleft(2x+1\mright)\mleft(6x^2+5\mright)[/tex]We are required to simplify the above expression.
[tex]\begin{gathered} \mleft(3x-5\mright)\mleft(4-9x\mright)+\mleft(2x+1\mright)\mleft(6x^2+5\mright) \\ 3x(4-9x)-5(4-9x)+2x(6x^2+5)+1(6x^2+5) \end{gathered}[/tex]Clearing the brackets, we get
[tex]\begin{gathered} 12x-27x^2-20+45x+12x^3+10x+6x^2+5 \\ 12x^3+6x^2-27x^2+12x+45x+10x-20+5 \end{gathered}[/tex][tex]12x^3-21x^2+67x-15[/tex]Therefore, the correct answer is
[tex]12x^3-21x^2+67x-15[/tex]Someone explain I know the answer Reflect the figure at the right across the y-axis. Then rotate theimage 180° around the origin. Draw the image after eachtransformation. What single transformation could you performon the figure to get the same final image?
Answers
The single transformation one could per form on the figure to get the final image is a rotation of 270 degrees counterclockwise around the origin.
The original figure cordinates (x,y)
A Reflection of the figure at the right across the y-axis, gives a coordinate(-x, y)
The y axis will remain the same. While the x axis will change sign.
A rotation of 180 degrees around the origin around the origin will have the coordinates (-x, -y)
The x and y axis changes signs.
When we carry out both transformation, the coordinates we get represent a transformation of 270 degrees counterclockwise around the ori
Find the x-and y-intercepts of the graph of x - 2y = 32. State each answer as an integer or an improper fraction in simplest form.
Answers
The x- intercepts of the function is (32,0) and y- intercepts of the function is (0, -16).
Given,
In the question:
The equation is :
x - 2y = 32
To find the x-and y-intercepts of the graph.
Now, According to the question;
Equation is :
x - 2y = 32
Find x - intercepts
Isolate the dependent variable:
y = x/2 - 16
Find the x - intercept of the function
x = 32
Equation is :
x - 2y = 32
Find y - intercepts
Isolate the dependent variable:
y = x/2 - 16
Find the y - intercept of the function
y = -16
Hence, The x- intercepts of the function is (32,0) and y- intercepts of the function is (0, -16).
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Lucy earns $326.87 each week. The federal government withholds 18% ofthat for federal income tax. How much is withheld from her pay annuallyfor federal income tax?a. $58.84b. $2,967.05c. $13,937.74d. $3,059.50
Answers
ANSWER:
d. $3,059.50
STEP-BY-STEP EXPLANATION:
The first thing is to calculate the annual salary, knowing that a year has a total of 52 weeks, therefore:
[tex]\begin{gathered} a=326.87\cdot52 \\ a=16997.24 \end{gathered}[/tex]The annual price is $ 16,997.24, we calculate 18% of this value, as follows:
[tex]\begin{gathered} tax=16,997.24\cdot\frac{18}{100} \\ tax=3059.50 \end{gathered}[/tex]Which means that federal income tax is $ 3,059.50
can you help me on this one?I need to determine whether the figure is a parallelogram using the distance formula.
Answers
If we graph the given points, we have:
One property of the parallelograms is that their opposite sides are equal.
Then, we have to verify if the segments QT and RS are equal.
[tex]QT=RS[/tex]To find the measure of segments QT and RS, we can use the distance formula.
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}\Rightarrow\text{ Distance formula} \\ \text{ Where} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are the coordinates of the points} \end{gathered}[/tex]• Measure of segment QT
[tex]\begin{gathered} (x_1,y_1)=Q(-10,-2) \\ (x_2,y_2)=T(-11,-8) \\ d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt[]{(-11-(-10))^2+(-8-(-2))^2} \\ d=\sqrt[]{(-11+10)^2+(-8+2)^2} \\ d=\sqrt[]{(-1)^2+(-6)^2}\rbrack \\ d=\sqrt[]{1+36} \\ d=\sqrt[]{37} \\ d\approx6.08\Rightarrow\text{ The symbol }\approx\text{ is read 'approximately'} \end{gathered}[/tex]• Measure of segment RS
[tex]\begin{gathered} (x_1,y_1)=R(1,-1) \\ (x_2,y_2)=S(1,-7) \\ d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt[]{(1-1)^2+(-7-(-1))^2} \\ d=\sqrt[]{(0)^2+(-7+1)^2} \\ d=\sqrt[]{0+(-6)^2} \\ d=\sqrt[]{(-6)^2} \\ d=\sqrt[]{36} \\ d=6 \end{gathered}[/tex]As we can see, the segments QT and RS are different.
[tex]\begin{gathered} QT\ne RS \\ 6.08\ne6 \end{gathered}[/tex]Then, the figure does not satisfy the mentioned property of parallelograms.
Therefore, the figure is not a parallelogram.
[tex]2x {}^{2} + 2x - 4 = 0[/tex]Find zeros/roots by completing the sqaures
Answers
Answer:
x = 1 and -2
Explanation
Given the expression
2x^2 + 2x - 4 = 0
We are to find the zero of the equation using the completing the square method
Step 1: Divide through by 2
2x^2/2 + 2x/2 - 4/2 = 0/2
x^2 + x - 2 = 0
Step 2: Add 2 to both sides of the equation
x^2 + x - 2 + 2 = 0+2
x^2 + x = 2
Step 3: Complete the square by adding the square of half of coefficient of x to both sides as shown
Coefficient of x is 1
Half of 1 = 1/2
Square of 1/2 = (1/2)^2 = 1/4
Add 1/4 to both sides
x^2 + x + (1/2)^2= 2 + 1/4
(x+1/2)^2 = 9/4
Sqare root both sides
x + 1/2 = \sqrt[9/4]
x + 1/2 = 3/2
x = 3/2 - 1/2 and -3/2 - 1/2
x = 2/2 and -4/2
x = 1 and -2