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To prove :
ABCD is a parallelogram
For parallelogram, if one pair of opposite sides of a quadrilateral are congruent and parallel then the quadrilateral is a parallelogram.
Thus, in option (2) their is not enought information to prove that ABCD is a parallelogram because AB and CD are given congruent but not given parallel.
Similarly, BC and DA are given congruent but not given parallel.
So, the correct option is (2)
Related Questions
A triangle with side lengths 8, 15, and 17 is a right triangle by theconverse of thePythagorean Theorem. What are the measures of the other 2 angles?Round your answers to the nearest whole number.HINT: Draw a diagram of this problem and label your triangle.The méasure of the smaller acute angle is ____degreesand the larger acute angle measures_______degrees.
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We are given a right-angle triangle with side lengths 8, 15, and 17.
Since it is a right triangle, one angle must be 90°
Let us find the other two angles of this right triangle.
With respect to angle x, the opposite side is 15 and the hypotenuse side is 17.
Recall from the trigonometric ratios,
[tex]\begin{gathered} \sin (x)=\frac{\text{opposite}}{\text{hypotenuse}} \\ \sin (x)=\frac{15}{17} \\ x=\sin ^{-1}(\frac{15}{17}) \\ x=61.9\degree \end{gathered}[/tex]So, the second angle is 61.9°
Recall that the sum of angles inside a triangle must be equal to 180°
So, the third angle can be found as
[tex]\begin{gathered} y+61.9\degree+90\degree=180\degree \\ y=180\degree-90\degree-61.9\degree \\ y=28.1\degree \end{gathered}[/tex]So, the third angle is 28.1°
The measure of the smaller acute angle is 28.1 degrees and the larger acute angle measures 61.9 degrees.
5. Elena wanted to find the slope and y-intercept of the graph of 25x - 20y = 100.She decided to put the equation in slope-intercept form first. Here is her work-25x – 20y = 10020y = 100 – 25x5y = 5 --X-5. Describe Elena's mistake in her work above, and what the correct slopeand y-intercept of the line are.What are the x- and y-intercepts of the equation 4y + 9x = 18?
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Given the equation:
25x - 20y = 100
Let' write the equation in slope-intercept form and find the mistaeke in Elena's worl.
Apply the slope intercept form of a linear equation:
y = mx + b
Rewrite the equation for y:
25x - 20y = 100
• Subtract 25x from both sides:
25x - 25x - 20y = 100 - 25x
-20y = 100 - 25x
• Divide all terms by -20:
[tex]undefined[/tex]a pizza song head offer 6 kinds of meat toppings and 6 vegetable topping and how many different ways could you select a meat topping and in vegetable topping
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Please help me with this ASAP!
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The length of the side AB in triangle ΔABC is 12 centimeters
What is the length of a line or segment?The length of a line or segment is the distance between the endpoints.
The location at which the perpendicular bisector of segment [tex]\overline{AB}[/tex] in ΔABC intersects the side [tex]\overline{BC}[/tex] = Point D
The perimeter of ΔABC = 12 + The perimeter of ΔACD
Please find attached, the possible drawing of the figure in the question;
ΔADE is congruent to ΔBDE by Side-Angle-Side congruency postulate
[tex]\overline{AD}[/tex] is congruent to [tex]\overline{DB}[/tex] by Corresponding Parts of Congruent Triangles are Congruent.
The perimeter of ΔABC = AB + BC + AC
Perimeter of triangle ΔACD = AC + CD + AD
BC = CD + DB
The perimeter of ΔABC = AB + CD + DB + AC = 12 + AC + CD + AC
The substitution and subtraction property of equality indicates;
AB + CD + DB = 12 + CD + AD = 12 + CD + DB
AB = 12
Therefore, AB = 12
Learn more about the substitution property of equality here:
https://brainly.com/question/14576897
#SPJ1
Use the unit circle to identify the reference angle for 155°.
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SOLUTION
Given the question in the question tab, the following are the solution steps to answer the question.
STEP 1: Define Unit circle
[tex]undefined[/tex]What is the probability that Erika will get to move ahead on this spin.
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total outcomes=8
move ahead outcome=4
probabilty of move ahead =4/8=1/2
Thus the answer is 1/2.
Find the sum of 5 even positive integers
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sum of 5 even positive integers
[tex]n+(n+2)+(n+4)+(n+6)+(n+8)[/tex]here, n is the first even number,
let's simplify this,
[tex]\begin{gathered} =n+n+2+n+4+n+6+n+8 \\ =5n+20 \end{gathered}[/tex]Thus the expression to find the sum of 5 consecutive even positive integers is, 5*n + 20 , where n is the 1st even positive integer.
let's use it when n = 2 or to sum 2, 4, 6, 8 and 10
[tex]5*2+20=10+20=30[/tex]which is the same as,
[tex]2+4+6+8+10=30[/tex]What definition would justify the following statement?If T is the midpoint of segment RS then, Segment RT is congruent to segment TS.Options:Definition of Angle BisectorDefinition of CongruenceDefinition of MidpointDefinition of Segment Bisector
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ANSWER
Definition of Segment Bisector
EXPLANATION
The statement given is:
If T is the midpoint of segment RS then, Segment RT is congruent to segment TS.
The very first portion of that statement gives us the context of this statement.
We see two key words there:
- Midpoint
- Segment
The statement is talking about a segment and so it cannot be about an Angle Bisector.
Also, we see T acting as a means of bisecting the segment RS into equal parts.
How do we know? We have that Segment RTis congruent (or equal/identical) to segment TS.
This tells us that T acts as a bisector for that segment RS.
We can therefore say that the statement justifies the Definition of a Segment Bisector.
Find the slope of the line that passes through the points (15,-2) and (5,-4).Write answer as an integer or a reduced fraction
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1) To find the slope of the line that passes through those points, we'll need to use the Slope Formula
[tex]\begin{gathered} m=\frac{y_2-y_1_{}}{x_2-x_1} \\ m=\frac{-4-(-2)}{5-15}=\frac{-4+2}{-10}=\frac{-2}{-10}=\frac{-1}{-5}=\frac{1}{5} \end{gathered}[/tex]Note that the slope is the measure of how steep is the line between those points.
2) That is the answer.
What is the volume of this sphere?Use3.14 and round your answer to the nearest hundredth.4 mcubic metersHELPP!!!
Answers
Answer:
Explanation:
The formula for the area of a sphere is:
[tex]V=\frac{4}{3}\pi r^3[/tex]Where r is the radius of the circle.
In this case, the diameter of the circle is 6in, then;
[tex]r=\frac{6in}{2}=3in[/tex]The volume is:
[tex]undefined[/tex]The Homecoming committee wants to raise between $1500 and $2000 at the dance.They have already saved $800 to put towards the dance. If tickets are $20 each, howmany tickets must they sell? Variable Represents:Inequality:Solve:Sentence:
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Answer:
35≤t≤60
Explanation:
Let the variable t represents the number of tickets they must sell.
Cost of a ticket =$20
• Cost of t tickets =$20t
Since they have already saved $800
Total balance = 800+20t
The committee wants to raise between $1500 and $2000 at the dance.
Therefore, the inequality representing this situation is:
[tex]1500\leqslant800+20t\leqslant2000[/tex]We solve for t.
[tex]\begin{gathered} 1500\leqslant800+20t\leqslant2000\text{ (Subtract 800 from all sides)} \\ 1500-800\leqslant800-800+20t\leqslant2000-800 \\ 700\leqslant20t\leqslant1200\text{ (Divide all through by 20)} \\ \frac{700}{20}\leqslant\frac{20t}{20}\leqslant\frac{1200}{20} \\ 35\leqslant t\leqslant60 \end{gathered}[/tex]The homecoming committee must sell between 35 and 60 tickets to meet their goal.
solve the following equation, write the answer in reduced fraction form, if necessary. (x+5)(x-5)=0Separate multiple entries with commas.
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im completely lost on my review it says find the missing angle from these 2 congruent triangles.
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We will reason to find the values of angles 1 through 6. To do so, we will use a key fact of triangles which is:
the sum of the angles of a triangle is 180°.
So, we will start by finding the value of angle 1. Note that angle 1 is in the triangle XYZ, whose other angles are 58° and 65°. Then, we have the following equation
[tex]\text{Angle 1 + 58\degree+65\degree=180\degree}[/tex]Since 58+65 = 123 then we have
[tex]\text{Angle 1 + 123 =180}[/tex]By subtracting 123 on both sides, we get that
[tex]\text{Angle 1 =180-123 = 57\degree}[/tex]So angle 1 measures 57°.
We can see that angles 1 and 2 are supplementary. That is, their measures add up to 180°. So, we have the following equation
[tex]\text{Angle 1 + Angle 2 =180}[/tex]Since angle 1 = 77° we have that
[tex]77\text{ + Angle 2 = 180}[/tex]which implies that angle 2 measures 123°. Using the same principle we can find the value of angle 5, since we have
[tex]\text{Angle 2 + Angle 5 = 180}[/tex]since angle 2 measures 123, we have that
[tex]123+\text{ Angle 5 = 180}[/tex]which implies that angle 5 measures 57°. Now, we see that angle 6 is in triangle VXW, so we can find the value of angle 6 as follows
[tex]\text{Angle 6 + Angle 5 + 67 = 180}[/tex]Then, since angle 5 measures 57° we have
[tex]\text{Angle 6 + 57\degree+67\degree=180\degree}[/tex]Since 57+67=124. Then , we have
[tex]\text{Angle 6 + 124 = 180 }[/tex]Subtracting 124 on both sides, we get
[tex]\text{Angle 6 = 180-124 = 56}[/tex]Now, we are missing to find the values of angles 3 and 4. To do so, first notice that
[tex]\text{Angle 2 + Angle 3 +Angle 4=180}[/tex]since these are the angles of triangle WXZ. We already know the measure of the angle 2 (123), so we have
[tex]\text{Angle 3 + Angle 4 =}180\text{ -123 = 57}[/tex]Unfortunately, the question doesn't give any more details on the triangles, so there are multiple solutions of values of angles 3 and 4 such that the equation holds
wgat us 5he image of (0,-1) after a translation of left 5 units and down 1 unit
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EXPLANATION
Given the point (0,-1), after a translation of left 5 units and down 1 unit the image would be:
Image: (-5,-2)
The data for the control group has a a. first common differenceb. second common difference c. common ratioTherefore the data is being generated by a a. linear functionb. quadratic function c. exponential functionThe data for the original formula has aa. first common difference b. second common differencec. common ratioTherefore the data is being generated by a a. linear functionb. quadratic functionc. exponential function The data for the improved formula has a a. first common difference b. second common difference c. common ratio Therefore the data is being generated by a a. linear functionb. quadratic functionc. exponential function
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Answer:
The data for the control group has a first common difference, therefore the data is being generated by a linear function
The data for the original group has a second common difference, therefore the data is being generated by a quadratic function
The data for the Improved group has a common ratio, therefore the data is being generated by an exponential function
Explanation:
Given the table in the attached image.
The data for the control group has a common difference, that is the difference between consecutive values are the same.
[tex]d=13-6=20-13=27-20=34-27=41-34=7[/tex]Since the values have a common difference then it is a linear function.
The original formula has a second common difference, therefore the data is being generated by a quadratic function.
The improved formula has a common ratio;
[tex]r=\frac{18}{9}=\frac{36}{18}=\frac{72}{36}=\frac{144}{72}=\frac{288}{144}=2[/tex]Therefore, the data is being generated by an exponential function.
J(7, -2), K(-4, 9), L(-3,-1)
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What is the image (11,-5) after the Rx=0 • T(11,-5)(-22,-10)(0,-10)(22,10)(0,10)
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The original point has coordinates (11,-5)
The transformation applied to this point are Rx=0 * T(11,-5)
First, you have to do the translation T(11,-5), this means that you have to make a horizontal translation 11 units to the right, and a vertical translation 5 units down, following the rule:
[tex](x,y)\to(x+11,y-5)[/tex]So, add 11 units to the x-coordinate and subtract 5 units to the y-coordinate of (11,-5)
[tex](11,-5)\to(11+11,-5-5)=(22,-10)[/tex]Once you've made the translation, you have to reflect the point (22,-10) over the vertical line x=0, this vertical line is the y-axis. This means that you have to reflect the point over the y-axis.
To do this reflection you have to invert the sign of the x-coordinate of the point and leave the y-coordinate the same:
[tex]R_{y-\text{axis}}=(x,y)\to(-x,y)[/tex][tex](22,-10)\to(-22,-10)[/tex]The coordinates of the point after the translation and reflection are (-22,-10), option 1
A laboratory tested 82 chicken eggs and found that the mean amount of cholesterol was 228 milligrams with sigma equals 19.0 milligrams. Construct a 95% confidence interval for the true mean cholesterol content u of all such eggs.
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ANSWER
[tex]223.88,232.11[/tex]EXPLANATION
Given;
[tex]\begin{gathered} n=82 \\ \bar{x}=228 \\ \sigma=19.0 \\ \end{gathered}[/tex]At 95% confidence level;
[tex]\begin{gathered} \propto=1-95\% \\ =1-0.95 \\ =0.05 \\ \frac{\propto}{2}=0.025 \\ Z_{\frac{\operatorname{\propto}}{2}}=Z_{0.025}=1.96 \\ \end{gathered}[/tex]At 95% confidence interval for true mean;
[tex]\begin{gathered} \bar{x}\pm Z_{\frac{\operatorname{\propto}}{2}}\frac{\sigma}{\sqrt{n}} \\ =228\operatorname{\pm}1.96\times\frac{19}{\sqrt{82}} \\ =228+1.96\times\frac{19}{\sqrt{82}}<228-1.96\times\frac{19}{\sqrt{82}} \\ =228-4.1124<228+4.1124 \\ =223.88<\mu<232.11 \end{gathered}[/tex]Therefore, 95% confidence interval for the true mean cholesterol content
(223.88,232.11)
hi thank you for helping me . is this just multiplication?
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ANSWER:
25.84
STEP-BY-STEP EXPLANATION:
To multiply two decimal numbers:
1. They are multiplied as if they were whole numbers.
2. The final result is a decimal number whose number of decimal places is equal to the sum of the number of decimal places of the two factors.
Therefore:
A real estate agent works on a 11 % commission. What is her commission on a house that she sold for $597,000?Follow the problem-solving process and round your answer to the nearest cent, if necessary.
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Given:
11% commission.
House sold is $597, 000
To find the commission on a house she sold for $597 000, simply find 11 % of that amount.
That is;
Her commision = 11% of $597,000
[tex]=\frac{11}{100}\times597000[/tex][tex]=\text{ 6567000/100}[/tex][tex]=\text{ \$65670}[/tex]Hence, her commision is $65670
please answer the question and please explain in simple way
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The x intercepts are determide when you calculated the equation when y=0
To find the x-coordinate of the vertex you have to apply the next formula:
[tex]x=-\frac{b}{2a}[/tex]Where you follow the form of the equation:
[tex]y=ax^2+bx+c[/tex]X-intercep:
1. In this case if we have the equation in the form: x( x - 2) we can know that y=0 when one of the terms is 0:
y=0 when:
x=0x-2=0
x= - 22. y=0 when:
x-4=0
x=4x+5=0
x=-53. y=0 when:
x-1=0
x=1x-5=0
x=5x-coordinate of the vertex:To identify the coeficeints a and b we express the equation in a different form, we have to multiply. Then we can apply the formula to find the x coordinate of the vertex, as follow:
[tex]x=-\frac{b}{2a}[/tex]1.
[tex]y=x(x-2)=x^2-2x[/tex][tex]x=-\frac{(-2)}{2(1)}=\frac{2}{2}=1[/tex]2.
[tex]y=(x-4)(x+5)=x^2+5x-4x-20=x^2-x-20[/tex][tex]x=-\frac{(-1)}{2(1)}=\frac{1}{2}[/tex]3.
[tex]y=(x-1)(x-5)=x^2-5x-x+5=x^2-6x+5[/tex][tex]x=-\frac{(-6)}{2(1)}=\frac{6}{2}=3[/tex]The missing side length in the right triangle is __ cm.
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364
1) Assuming this is a right triangle, the side whose length is 365 is the hypotenuse, so we can write out the Pythagorean Theorem:
365² = 27² +c²
133225 =729+ c²
133225 -729 = c²
132496= c² Take the square root on both sides
√132496 = √c²
c = 364
2) Hence, the missing leg is 364 cm
M O GEOMETRY Identifying parallelograms, rectangles, and squares Answer the questions about the figures below. 3 m Figure A Explanation 3 m 3 m (a) Which figures are squares? Mark all that apply. Figure A (b) Which figures are parallelograms? Mark all that apply. O Figure A O Figure B (c) Which figures are rectangles? Mark all that apply. O Figure A 3 m O Figure B O Figure C Figure B Check O Figure C O Figure C Figure B 2 m 5 m 4 m O None of the figures O None of the figures O None of the figures 3 m L X Figure C 5 m 5 m ☐ L ? 3 m 0/5 O2022 McGraw Hill LLC. All Rights Reserved. Terms of Use Privacy Center Nikid Ac
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Given the dimensions of each figure:
• Figure A:
Length of each side = 3m
All sides have equal lengths.
• Figure B:
Length of top base = 2 m
Length of bottom base = 5m
Length of each leg = 4m
• Figure C.
Length = 5 m
Width = 3m
Since the length of all sides in figure A are equal and they meet at right angles, we can say figure A is a square.
Also, figure A has 2 pairs of parallel sides.
Since it has 2 pairs of parallel sides, we can say it is also a parallelogram.
Figure B has two parallel bases, while the opposite legs are equal.
Figure B has just one pair of parallel side.
Thus, we can figure B is a trapezoid.
Figure C has two pairs of parallel sides and the opposite sides have equal lengths.
Thus, we can say Figure B is rectangle and also a parallelogram.
Hence, we have the following:
• Squares ==> Figure A
,• Parallelogram ==> Figure A and Figure C
,• Rectangle ==> Figure C.
• ANSWER:
(a).
(c).
If cosθ=3√2cosθ=32 then which of the following could be true?tan=−3√tangent is equal to negative square root of 3cscθ=12cosecant theta is equal to 1 halfsecθ=−2secant theta is equal to negative 2sinθ=2√2sine theta is equal to the fraction with numerator square root of 2 and denominator 2
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Given that
[tex]\cos\theta=\frac{\sqrt{3}}{2}[/tex]we can determinate the sine of this angle using the following identity
[tex]\sin^2\theta+\cos^2\theta=1[/tex]If we substitute the value of the cosine on this identity, we're going to have:
[tex]\begin{gathered} \sin^2\theta+(\frac{\sqrt{3}}{2})^2=1 \\ \sin^2\theta+\frac{3}{4}=1 \\ \sin^2\theta=\frac{1}{4} \\ \sin\theta=\pm\frac{1}{2} \end{gathered}[/tex]The definitions of secant, tangent, and cosecant in terms of the sine and cosine are given by:
[tex]\begin{gathered} \tan\theta=\frac{\sin\theta}{\cos\theta} \\ \sec\theta=\frac{1}{\cos\theta} \\ \csc\theta=\frac{1}{\sin\theta} \end{gathered}[/tex]Using the known values for the sine and cosine functions on those definitions, we have:
[tex]\begin{gathered} \tan\theta=\frac{\pm\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\pm\frac{1}{\sqrt{3}}=\pm\frac{\sqrt{3}}{3}\ne-\sqrt{3} \\ \\ \csc\theta=\frac{1}{\pm\frac{1}{2}}=\pm2\ne\frac{1}{2} \\ \\ \sec\theta=\frac{1}{\frac{\sqrt{3}}{2}}=\frac{2}{\sqrt{3}}=\frac{2\sqrt{3}}{3}\ne-2 \\ \\ \sin\theta=\pm\frac{1}{2}\ne\frac{\sqrt{2}}{2} \end{gathered}[/tex]All options are false.
enclose the figure that occupies the position of the tens of thousand in each number. then write its value 573901 1926734 103485 2801345
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ANSWER:
STEP-BY-STEP EXPLANATION:
The tens of thousand, would be the values of 10,000 in 10,000, therefore for each value it would be:
[tex]undefined[/tex]What is 4.73 x 3.4?
Please answer
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Answer:
Explanation:
The product of 4.73 and 3.4 is calculated below:
Which of the following represents vector u = −3i + 8j in component form?
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Solution
- The way to write vectors in component form is given below:
[tex]\begin{gathered} u=u_xi+u_yj \\ \text{ In Component form, we have:} \\ u=\langle u_x,u_y\rangle \end{gathered}[/tex]- Thus, we can apply the rule stated above to the question given to us.
- This is done below:
[tex]\begin{gathered} u=-3i+8j \\ \\ \therefore u=\langle-3,8\rangle \end{gathered}[/tex]Final Answer
The answer is
[tex]u=\langle-3,8\rangle\text{ (OPTION 2)}[/tex]A 150 lb individual weighs how many kg? Round to nearest kilogram.
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Take into account that the relation between pounds and kilograms is:
1 kg = 2.204 lb
Then, you can use a conversion factor to determine how many kg are 150 lb, as follow:
[tex]150lb\cdot\frac{1\operatorname{kg}}{2.204lb}\approx68.05\operatorname{kg}[/tex]Hence, 150 lb are approximately 68.05 kg
Find the height of the trapezoid.Base1: 100Base2: 56Leg1: 31Leg2: 31 Please help!!
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To find the area of a trapezoid we can use this equation:
[tex]A=A_r+A_{t1}+A_{t2}[/tex]so we have to find the missing sides so:
So the area is:
[tex]undefined[/tex]Section 1.5: Mortgages and Credit Cards8. A car costs $10,500, and you're offered a loan that requires $800 down and a monthly payment of $187.53 for 60 months, how much will you pay in interest? Round your answer to the nearest dollar.$
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A monthly payment of $187.53 for 60 months will give us:
[tex]187.53\times60=\text{ \$11,251.8}[/tex]The total money paid is:
[tex]\begin{gathered} \text{the down payment of \$800 + \$11,251}.8 \\ \Rightarrow800+11,251.8=12051.8 \end{gathered}[/tex]Hence, the interest paid is:
[tex]\begin{gathered} 12,051.8-10,500 \\ \Rightarrow\text{ \$}1551.8 \end{gathered}[/tex]