in DEF, DE =29 feet, EF = 26 feet, and DF = 32 feet. Which correctly gives the order of the angle measure from largest to smallest?
Answers
Answer:
Choice A.
Explanation:
The sketch of the triangle is given below
The angle opposite the longest side is the widest.
The longest side is DF; therefore, the angle opposite to it (angle E) is the widest.
The second-longest side is DE; therefore, the angle opposite to it (angle F) is the second widest.
Lastly, the third-longest side is EF; therefore, the angle opposite to it (angle D) is the third widest (or the smallest angle).
Hence, the angle measures when ordered from greatest to smallest are
∠E, ∠F, ∠D
which is given by choice A.
Related Questions
the u.s senate has 100 members. after a certain election, there were 6 more democrats than republicans, with no other parties represented. how many memebrs of each party were there in the senate?
Answers
As per the unitary method, the number of democrats are 53 and the number of republicans are 47.
Unitary method:
Unitary method is the process of finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given,
The U.S senate has 100 members. after a certain election, there were 6 more democrats than republicans, with no other parties represented.
Here we need to find the number of democrats and the number of republicans.
Let us consider the number of Republican's be "x"
And then the number of Democrats is "x+6".
We know that the total number of members in the senate is 100.
So, it can be written as
x + (x + 6) = 100
2x + 6 = 100
2x = 100 - 6
2x = 94
x = 94/2
Then the value of x is,
x = 47
Therefore, there are 47 republicans in the senate then the number of democrats is
x + 6 => 47 + 6 => 53
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iley invested $1,000 in savings bonds. If bonds earn 6.75% interest compounded semi-annually, how much will riley earn in 15 years?
Answers
Answer: Riley will earn 2707 in 15 years
Explanation:
The formula for calculating compound interest is expressed as
A = P(1 + r/n)^nt
where
A is the final amount after t years
A is the principal or initial amount
r is the interest rate
n is the number of compounding periods in a year
t is the time
From the information given,
P = 1000
r = 6.75% = 6.75/100 = 0.0675
t = 15
n = 2 because it was compounded twice in a year
By substituting these values into the formula,
A = 1000(1 + 0.0675/2)^2 * 15
A = 1000(1.03375)^30
A = 2707
Riley will earn 2707 in 15 years
Complete the explanation of how you know whether the triangles are similar. If possible, find the Indicated length. A Р 2.0 1.7 во 1.2 C R. Because two pairs of angles are congruent, the triangles are similar by the select) QR =
Answers
When two triangles have two pairs of angles congruent, it means that the third pair of angles also is congruent.
Then, the trianglers are similar by AA (Angle, angle) similar triangle theorem.When two triangles are similar the ratio between corresponding sides is the same.
Corresponding sides in the given triangles:
CB and QR
AC and PR
AB and PQ
[tex]\frac{QR}{CB}=\frac{PR}{AC}=\frac{PQ}{AB}[/tex]Then, as you know the measure of AC and corresponding side CB you use the next to find the measure of side QR:
[tex]\frac{QR}{CB}=\frac{PR}{AC}[/tex]Use the given measures and find QR:
[tex]\begin{gathered} \frac{QR}{1.2}=\frac{1.7}{2.0} \\ \\ QR=\frac{1.7}{2.0}(1.2) \\ \\ QR=\frac{2.04}{2.0} \\ \\ QR=1.02 \end{gathered}[/tex]QR=1.02find the area of a hexagon with sides 20 mm long. Round your answer to the nearest tenth
Answers
When you know the length of the sides of a hexagon you use the next formula to find its area:
[tex]A=\frac{3\sqrt{3}}{2}s^2[/tex]s is the length of the sides
For the given hexagon:
[tex]\begin{gathered} A=\frac{3\sqrt{3}}{2}(20mm)\placeholder{⬚}^2 \\ \\ A=\frac{3\sqrt{3}}{2}(400mm^2) \\ \\ A=3\sqrt{3}(200mm^2) \\ \\ A=600\sqrt{3}mm^2 \\ \\ A\approx1039.2mm^2 \end{gathered}[/tex]Then, the area of the given hexagon is 1039.2 square millimetersI am trying to place the second point at 12.5. My graph only extend to -10.
Answers
We have to graph the line y = -2/5*x-5.
To do that, we need two points that belong to the line.
We can give two arbitrary values to x and calculate y using the equation of the line.
For example, for x=0, we get:
[tex]x=0\Rightarrow y(0)=-\frac{2}{5}\cdot0-5=-5[/tex]Then, the point is (0,-5).
Now, if we make x = 5, we can calculate y as:
[tex]x=5\Rightarrow y(5)=-\frac{2}{5}\cdot5-5=-2-5=-7[/tex]Then, we get the point (5, -7).
Using this two points we can graph the line as:
NOTE: In the case that the graph is limited to certain intervals in x or y, we have to try with different values of x until we find two points within the range shown by the graph.
In this case, (0,-5) and (5,-7) will be located within the range shown.
Find the constant of proportionality when x = 2 and y = 1.5.Record your answer and fill in the bubbles on your answer document. Be sure to usethe correct place value.
Answers
If y is proportional to x, we have this equation:
[tex]y=kx[/tex]If x = 2 and y = 1.5, then the constant is:
[tex]k=\frac{y}{x}=\frac{1.5}{2}=0.75[/tex]The constant of proportionality is k = 0.75
A survey claims that the percent of a city's residents that favor building a new football stadium is likely between 52.3% and 61.7%. What was the sample proportion (what percent of the people in the sample survey said that they wanted to build a new stadium )?
Answers
The confidence interval for the sample proportion is calculated using the following formula:
[tex]\lbrack p\lbrack\text{hat\rbrack}\pm Z_{1-\frac{\alpha}{2}}\cdot\sqrt[]{\frac{p\lbrack hat\rbrack(1-p\lbrack hat\rbrack)}{n}}\rbrack[/tex]Where p[hat] represents the sample proportion. As you see you add/subtract the margin of error to the sample proportion to determine both bonds of the interval, which means that the sample proportion is in the middle of the interval.
The percent of residents in favor of building a new football stadium is between 52.3% and 61.7% → the sample proportion used to determine this interval is in the middle of both bonds. To calculate the said value you have to find the average of both values:
[tex]52.3\%The sample proportion used to estimate the interval was p[hat]=0.57
Which equation models the total profit,y,based on the number of tickets sold,x?
Answers
Answer
D. y - 300 = 4(x - 100)
Step-by-step explanation
Variables
• x: tickets sold
,• y: profit
Equation of a line in point-slope form
[tex]y-y_1=m(x-x_1)[/tex]where m is the slope and (x₁, y₁) is a point on the line.
The slope of the line that passes through the points (x₁, y₁) and (x₂, y₂) is calculated as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]This line passes through the points (100, 300), that is, when 100 tickets are sold, the club had $300 in profit, and the point (200, 700). Then, its slope is:
[tex]\begin{gathered} m=\frac{700-300}{200-100} \\ m=\frac{400}{100} \\ m=4 \end{gathered}[/tex]Substituting into the general equation with m = 4 and the point (100, 300), we get the next equation of the line:
[tex]y-300=4(x-100)[/tex]Question 9 of 10If bis an explanatory variable and cis the corresponding response variable,which of these would be represented by the vertical axis on a scatterplot?O A. b БB. Neither b nor cOC. Both band cD. CSUBMIT
Answers
The response variable is dependent variable , and depends on the explanatory variable. The explanatory variable is independant variable and always represented on the horizontal axis.
The dependent variable (or response varaible) is represented on the vertical axis. So C is represented on the vertical axis of scatter plot.
List the coordinates coordinates of vertices of trapezoid ABCD after it has been rotated 90 Counterclockwise bout the origin and then reflected over the x-axis. A(-5,-3) B(-4,0),c(-2,0),D(O,-3)
Answers
Answer:
The coordinates of the final image is;
[tex]A^{\prime\prime}(3,5),B^{\prime\prime}(0,4),C^{\prime}^{\prime}(0,2),D^{\prime}^{\prime}(3,0)[/tex]Explanation:
From the question, the pre-image was been rotated 90 Counterclockwise bout the origin.
Which has a rule;
[tex](x,y)\rightarrow(-y,x)[/tex]Applying the rule to the given points. we have;
[tex]\begin{gathered} A(-5,-3)\rightarrow A^{\prime}(3,-5) \\ B(-4,0)\rightarrow B^{\prime}(0,-4) \\ C(-2,0)\rightarrow C^{\prime}(0,-2) \\ D(0,-3)\rightarrow D^{\prime}(3,0) \end{gathered}[/tex]Then the produced image was then reflected over the x-axis;
Reflection across the x-axis have the rule;
[tex](x,y)\rightarrow(x,-y)[/tex]Applying the rule to the resulting image;
[tex]\begin{gathered} A^{\prime}(3,-5)\rightarrow A^{\prime^{}}^{\prime}(3,5) \\ B^{\prime}(0,-4)\rightarrow B^{\prime}^{\prime}(0,4) \\ C^{\prime}(0,-2)\rightarrow C^{\prime^{}}^{\prime}(0,2) \\ D^{\prime}(3,0)\rightarrow D^{\prime}^{\prime}(3,0) \end{gathered}[/tex]Therefore, the coordinates of the final image is;
[tex]A^{\prime\prime}(3,5),B^{\prime\prime}(0,4),C^{\prime}^{\prime}(0,2),D^{\prime}^{\prime}(3,0)[/tex]Graph each inequality.Do I have to make the equation say y<??
Answers
x + y =< 2
y =< 2 - x Yes, in the inequality y must be alone
4.-
Yes, you must look at the point of the sign if the y is to the left of the sign (<) you must shade the area below the line. if the y is to the right of the sign(<), you must shade the area abocve the line.
Is it better now?
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Which value of x makes the equation 4x+9=x+6 true?
Answers
Answer:
x=-1
Explanation:
Given the equation:
[tex]4x+9=x+6[/tex]First, we subtract 9 from both sides.
[tex]\begin{gathered} 4x+9-9=x+6-9 \\ 4x=x-3 \end{gathered}[/tex]Next, we subtract x from both sides.
[tex]\begin{gathered} 4x-x=x-x-3 \\ 3x=-3 \end{gathered}[/tex]Finally, we divide both sides by the number beside x which is 3.
[tex]\begin{gathered} \frac{3x}{3}=\frac{-3}{3} \\ x=-1 \end{gathered}[/tex]The value of x that makes the equation true is -1.
Drag the prisms to the table in order from least volume to greatest volume.
Answers
Fourth prism, first prism, second prism and fourth prism is order from least volume to greatest.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The volume of first prism with sides 2, 1.5 and 3.2
Volume=2×1.5×3.2
=9.6 in³
The volume of second prism with sides 1.5, 1.5 and 6
Volume=1.5×1.5×6
=13.5 in³
The volume of third prism with sides 2, 5/2 and 7/2
Volume=2×2.5×3.5
=17.5 in³
The volume of fourth prism with sides 1/2, 1/2 and 1/2
Volume=0.5×0.5×0.5
=0.125 in³
Hence fourth prism, first prism, second prism and fourth prism is order from least volume to greatest.
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4.) Miles has saved about $41. He wants to buy an iPod for $129 in 4 months. How much moneydoes he need to save each month to buy the iPod?
Answers
Miles has saved about $41. He wants to buy an iPod for $129 in 4 months.
So first, we need to subtract the amount that he has already saved.
[tex]\$129-\$41=\$88[/tex]Now we need to divide this amount by 4 months.
[tex]\frac{\$88}{4}=\$22[/tex]Therefore, Miles needs to save $22 each month to buy the iPod.
4Complete the table of values for the following function: y = VX-8X1006493625y-81
Answers
y= √x - 8
Replace each value of x and solve for y
x= 100
y= √100 - 8 = 10-8 = 2
x= 64
y= √64-8 = 8 - 8 = 0
x= 9
y= √9 - 8 = 3 - 8 = -5
x= 36
y=√36 - 8 = 6-8= -2
x= 25
y= √25- 8 = 5 - 8 = -3
For the last values, replace y and solve for x
y=-8
-8= √x - 8
-8+8 = √x
0= √x
x= 0^2
x=0
y=1
1=√x-8
1+8= √x
9 = √x
9^2 = x
x= 81
Large balloons are sold in packages of 12. Select the expressions that can represent the total number of balloons in p packages of largeballoonsA 12-PB. 12*pC. P+12D. P-12E 12p
Answers
Since each package has 12 balloons if we buy p packages the total number of ballons will be given by tha multiplication of 12 by p, that is:
[tex]12p[/tex]Therefore the answer is B and E.
Need help with number 2 not sure how to solve it all
Answers
B(x) will be given by:
[tex]B(x)=100x-5[/tex]Part 1:
x = 9
[tex]B(9)=100(9)-5=900-5=895[/tex]Part 2:
x = 10.34
[tex]B(10.34)=100(10.34)-5=1034-5=1029[/tex]Part 3:
[tex]B(9)+B(10.34)=895+1029=1924[/tex]12) Determine if the number is rational (R) or irrational (I)
Answers
Given
[tex]number=\sqrt{17}[/tex]Find
Determine if the number is rational or irrational.
Explanation
It cannot be expressed in the form of p/q , where q is not equal to 0.
so , it is irrational number.
Final Answer
Therefore , the number is irrational.
Solve the system of equations using elimination.8x - 5y = 13-16x - 10y = -6Show your work here:Solution:
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Solve the system of equations using elimination.
[tex]\begin{gathered} \text{8 x - 5y = 13 -- equation 1} \\ -16\text{ x - 10y = - 6 -- equation 2} \end{gathered}[/tex]Step 2:
Given,
[tex]\begin{gathered} 8x\text{ - 5y = 13 -- equation 1} \\ \text{equation 1 multiplied by 2, we have that:} \\ 16\text{ x - 10y = 26 -- equation 3} \\ -16\text{ x -10 y = - 6 -- equation 2} \end{gathered}[/tex][tex]\begin{gathered} equation\text{ 3 + equation 2, we have that:} \\ -10y\text{ + -10 y = 26 + (-6)} \\ -20y\text{ = 20} \\ \text{Divide both sides by -20, we have that:} \\ y\text{ = }\frac{20}{-20} \\ y\text{ = -1} \end{gathered}[/tex]Now, since y = -1 , we put the value of y = -1 in equation 1,
[tex]\begin{gathered} 8\text{ x- 5y = 13 --equation 1} \\ 8x\text{ - 5 ( -1 ) = 13} \\ 8x\text{ + 5 = 13} \\ 8x\text{ = 13 - 5} \\ 8\text{ x= 8} \\ \text{Divide both sides by 8 , we have that:} \\ x\text{ = }\frac{8}{8} \\ x\text{ = 1} \end{gathered}[/tex]CONCLUSION:
The final answer =
[tex]\text{ x= 1 , }y\text{ = - 1}[/tex]'
Warren flipped a coin and rolled a 20-sided number cube. What is the probability that his coin landed on tails and his number cube rolled a factor of 20? answer as a simplified fraction.
Answers
Warren flipped a coin and rolled a 20-sided number cube. What is the probability that his coin landed on tails and his number cube rolled a factor of 20? answer as a simplified fraction.
we have that
the probability that his coin landed on tails is
P=1/2
and
Factors of 20 are ----> 1,2,4,5,10,20
so
The probability that his number cube rolled a factor of 20 is
P=6/20=3/10
therefore
the probability that his coin landed on tails and his number cube rolled a factor of 20 is equal to
P=(1/2)*(3/10)
P=3/20In quadrilateral BADC, AB = AD andBC = DC. The line AC is a line ofsymmetry for this quadrilateral
Answers
Given the quadilateral: BADC
AB = AD
BD = DC
The line AC is a diagonal of the quadilateral.
The given quadilateral is a kite.
Let's answer the following questions using the given information.
Part a:
Diagonal AC and diagonal BD are perpendicular.
The diagonals of a kite are perpendicular, this is because the point of intersection of both diagonals form a right angle (90 degrees).
Therefore, based on the line of symmetry, we can say diagonals AC and BD are perependicular because the quadilateral is symmetric along the diagonals AC and BD of the figure.
• Part b:
Based on the line of symmetry, angle ABC and angle ADC have the same measure because the qudilateral has
EFGH is translate 5 units to the left and 2 units up.A. E(-1,-3)B. E(6,-6)C. E (-1,1)D. E(9,-3)
Answers
To translate the figure 5 units to the left and 2 up, apply the following translation to each coordinate of the figure
[tex]T_{(-5,2)}\colon(x,y)\rightarrow(x-5,y+2)[/tex]So, you have
[tex]\begin{gathered} E(4,-1)\rightarrow E^{\prime}(4-5,-1+2)\rightarrow E^{\prime}(-1,1) \\ F(0,-3)\rightarrow F^{\prime}(0-5,-3+2)\rightarrow F^{\prime}(-5,-1) \\ G(2,-4)\rightarrow G^{\prime}(2-5,-4+2)\rightarrow G^{\prime}(-3,-2) \\ H(6,-2)\rightarrow H^{\prime}(6-5,-2+2)\rightarrow H^{\prime}(1,0) \end{gathered}[/tex]Therefore, the coordinates of E' are (-1,1) and the correct answer is C. E(-1,1).
Its a project for my consumer math class and i have to record all the information on a template
Answers
We are asked to fill up the transactions in the table.
Remember that Payments, fees, and withdrawals are always subtracted from the balance, and deposits are always added to the balance.
The starting balance is $275
1st transaction:
Payment of $85.67 to the electric company on 2nd October.
Since it is a payment, it must be subtracted from the previous balance.
Balance = $275 - $85.67 = $189.33
2nd transaction:
You want to deposit the $20 that your friend gave to you.
Since it is a deposit, it must be added to the previous balance.
Balance = $189.33+$20 = $209.33
One of the two persons P or Q is to solve a technical problem with chances ½ and ¼, respectively. Find the probability that the technical problem is solved.A.1/8B.3/8C.5/8D.7/8
Answers
The probability that the technical problem is solved can be defined as follows:
The probability that P solves the problem or probability that Q solves the problem or probability that both (P and Q) solve the problem
The probability that P solves the problem = 1/2
The probability that Q solves the problem= 1/4
The probability that both solve the problem = (1/2) x (1/4) = 1/8
The probability that the technical problem is solved =
[tex]\begin{gathered} \frac{1}{2}\text{ + }\frac{1}{4}\text{ -}\frac{1}{8} \\ =\frac{4+2-1}{8} \\ \frac{5}{8} \end{gathered}[/tex]The correct option is C
Solve for X. Write down what type of solution the equation has. 3) [tex] \frac{10}{2x + 1} = \frac{14}{4x - 7} [/tex]
Answers
You have the following equation:
[tex]\frac{10}{2x+1}=\frac{14}{4x-7}[/tex]In order to solve for x the previous equation, multiply both sides by the LCM of the denominators, which is (2x+1)(4x-7):
[tex]\begin{gathered} (2x+1)(4x-7)\frac{10}{2x+1}=(2x+1)(4x-7)\frac{14}{4x-7} \\ (4x-7)10=(2x+1)14 \\ 40x-70=28x+14 \\ 40x-28x=14+70 \\ 12x=84 \\ x=\frac{84}{12} \\ x=7 \end{gathered}[/tex]Hence, the solution to the given equation is x = 7
Is this relation a function?
{(1, 3), (2, 3), (3, 4), (4, 5)}
No, because at least one output maps to more than one input.
No, because at least one output maps to more than one input.
Yes, because every input has exactly one output.
Yes, because every input has exactly one output.
No, because at least one input maps to more than one output.
No, because at least one input maps to more than one output.
Answers
The given relation {(1, 3), (2, 3), (3, 4), (4, 5)} is a function. Therefore, the correct statement is "Yes, because every input has exactly one output."
Relation:
A relation is a relationship between the x and y-coordinates. It must maps inputs to outputs.
Given,
Here we have the relation
{(1, 3), (2, 3), (3, 4), (4, 5)}
Now, we have to find whether this relation is a function or not.
We know that, a relation is said to be a relation is a function if the x values map to only one y - value. Simply said that if a relation is one-to-one or many-to-one it is a function.
Based on this rule, here each input has exactly one output. therefore, the given relation is said to be a function.
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#3 What does the slope tell you about the rate of change in elavation during Ryan’s uphill climb? What was the total elevation change?
Answers
Solution
Step 1:
Let find the slope
[tex]\begin{gathered} Slope\text{ = }\frac{Change\text{ in elevation}}{Change\text{ in time}} \\ S\text{lope = }\frac{1500\text{ - 300}}{120\text{ - 0}} \\ Slope\text{ = }\frac{1200}{120} \\ Slope\text{ = 10} \end{gathered}[/tex]His answer and these calculations are correct because he followed all the steps correctly to findtwo points' slope.
Step 2; First we need to determine how many different slopes there are on the given graph. Assume time is represented in minutes and distance is represented in meters. There are three in this graph, one goes from 0 minutes to 120 minutes and the second one is from 120 minutes to 150 minutes. The final one goes from 150 to 180 minutes. To calculate the speed of traveling we convert the distance traveled into a constant period of time i.e. an hour.
Question1
What does the slope tell you about the rate of change in elavation during Ryan’s uphill climb?
The first slope(line) tell us that Ryan travels from 300 meters to 1,500 meters from 0 minutes to 120 minutes.
meaning he traveled 1200 meters in 120 minutes which is equal to 600meters per hour or 0.6km/h.
In the second line, Ryan's travels no distance from 120 minutes to 150 minutes. So he was at rest and did not travel in this period of time.
In the third line (slope) , Ryan travels from 1,500 meters to 300 meters from 150 minutes to 180 minutes. So he traveled 1,200 meters in 30 minutes. This equals 2,400 meters per hour, which is 2.4 kilometers per hour.
Final answer
The slope tell you about the rate of change in the elevation during Ryan's uphill climb that:
Ryan ascends at a speed of 0.6 kilometers per hour for the two hours, takes rest for half an hour and then descends at 2.4 kilometers per hour for the half-hour.
Question 2
What is the total elevation change?
Elevation gain is the total amount you will climb in a day, and elevation loss is the total amount you will descend in a day. For example, if you climb 1000 feet, descend 500 feet, and then climb an additional 300 feet, the elevation gain would be 1300 feet and the elevation loss would be 500 feet.
From the graph?
Elevation gain = 1200 feet
Elevation loss = 1200 feet
If v, = (2,4) and v2 = (-1,5), then w,-V is equal to which of the following?O 18O (-2. 20)O 22O (8.-5)
Answers
We are given the following matrix:
[tex]A=\begin{bmatrix}{4} & {-7} & {} \\ {-2} & {1} & {} \\ {} & {} & {}\end{bmatrix}[/tex]We are asked to determine the coefficients of:
[tex]A^{-1}[/tex]Which is the inverse matrix. To do that let's remember that the inverse of a 2 by 2 matrix of the form:
[tex]A=\begin{bmatrix}{a_1} & {a_2} & {} \\ {a_3} & {a_4} & {} \\ {} & {} & {}\end{bmatrix}[/tex]is:
[tex]A^{-1}=\frac{1}{\det A}\begin{bmatrix}{a_4} & {-a_2} & {} \\ {-a_3} & {a_1} & {} \\ {} & {} & {}\end{bmatrix}[/tex]The value of the determinant of A (det A) is given by:
[tex]\det A=a_1a_4-a_2a_3[/tex]Replacing we get:
[tex]A^{-1}=\frac{1}{a_1a_4-a_2a_3}\begin{bmatrix}{a_4} & {-a_2} & {} \\ {-a_3} & {a_1} & {} \\ {} & {} & {}\end{bmatrix}[/tex]Replacing the values:
[tex]A^{-1}=\frac{1}{(4)(1)-(-7)(-2)}\begin{bmatrix}{1_{}} & {7_{}} & {} \\ {2_{}} & {4_{}} & {} \\ {} & {} & {}\end{bmatrix}[/tex]Solving the operations:
[tex]A^{-1}=-\frac{1}{10}\begin{bmatrix}{1_{}} & {7_{}} & {} \\ {2_{}} & {4_{}} & {} \\ {} & {} & {}\end{bmatrix}[/tex]Or:
[tex]A^{-1}=\begin{bmatrix}{-\frac{1}{10}_{}} & {-\frac{7}{10}_{}} & {} \\ -{\frac{1}{5}_{}} & {-\frac{2}{5}_{}} & {} \\ {} & {} & {}\end{bmatrix}[/tex]Therefore, we have:
[tex]\begin{gathered} a=-\frac{1}{10} \\ b=-\frac{7}{10} \\ c=-\frac{1}{5} \\ d=-\frac{2}{5} \end{gathered}[/tex]Which is the image of vertex T after the hexagon is rotated 180 degreesabout the origin?
Answers
Answer:
Image of vertex T: (5,2)
Step-by-step explanation:
It will be rotated 180 degrees about the origin. This means that the x-value of T will stay the same, while the y-value will be the same distance as now, just in a different direction.
Current position: -2
Distance from the origin: |-2 + 0| = 2
New coordenate: 0 + 2 = 2
Current value of x: 5
Image of vertex T: (5,2)
3.Find the values of x and y. Leave your answers in simplest radical form.6022yxX =y =Page
Answers
To calculate the values of x and y we need to apply the trigonometric relations to the right triangle. For this we will use the sine and cosine, their expressions are shown below:
[tex]\begin{gathered} \sin (\alpha)=\frac{\text{ opposite cathetus}}{\text{ hypothenuse}} \\ \cos (\alpha)=\frac{\text{ adjacent cathetus}}{\text{ hypothenuse}} \end{gathered}[/tex]Where alpha is the angle we know, the opposite cathetus is the cathetus that is farther from the angle and the adjacent cathetus is the cathetus that is closer to the angle. With this in mind we can use the data from the problem to calculate x and y.
[tex]\begin{gathered} \sin (60)=\frac{x}{22} \\ 0.866=\frac{x}{22} \\ x=22\cdot0.866=19.052 \end{gathered}[/tex][tex]\begin{gathered} \cos (60)=\frac{y}{22} \\ 0.5=\frac{y}{22} \\ y=0.5\cdot22=11 \end{gathered}[/tex]The value of x is equal to 19.052 and y is equal to 11.