Prove that the following four points will form a rectangle when connected in orderby showing the diagonals are congruent. Show all work.AIO. -3). B(-4.0). C(2. 8). D(6. 5)
Answers
SOLUTION
For the four points to form a rectangle, the length of the diagonals will be equal.
This means that we have to find the distance between the point BD and AC. If
BD = AC, then the four points would form a rectangle.
[tex]\begin{gathered} Dis\tan ce\text{ betw}ee\text{n points B and D, that is BD} \\ \text{Distance betw}ee\text{n two points = }\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ BD=\text{ }\sqrt[]{(6-(-4)^2+(5-0)^2} \\ BD=\sqrt[]{10^2+5^2} \\ BD=\sqrt[]{125} \\ BD=\text{ 5}\sqrt[]{5} \end{gathered}[/tex]Now let's find AC
[tex]\begin{gathered} AC=\text{ }\sqrt[]{(2-0)^2+(8-(-3)^2} \\ AC=\sqrt[]{2^2+11^2} \\ AC=\sqrt[]{4+121} \\ AC=\sqrt[]{125} \\ AC=5\sqrt[]{5} \end{gathered}[/tex]So, since BD = AC, the four points A, B, C and D would form a rectangle.
Related Questions
Without graphing, group the systems based on the number of solutions. y=2x-3 y=-2x+3. So my question is how can I find if it has one solution no solution or infinity solutions
Answers
Step 1:
two system of linear equations has one solution
Step 2:
Let deduce the number of solution in the two linear equations
y = 3x - 3 ...............................equation 1
y = -2x + 3 ..............................equation 2
Step 3:
use substitution method to solve the system o
5,624 ÷ 72 using estimation
Answers
Answer: 5,624 rounded would be 5,600 and 72 rounded would be 70.
5,600/70= 80
Step-by-step explanation:
Determine which set of side measurements could be used to form a triangle.
12, 23, 7
10, 7, 2
8, 3, 11
5, 11, 8
Answers
Answer:
Among the given, the set of side measurements (5, 11, 8) could be used to form a triangle.
Step-by-step explanation:
As we know,
For forming a triangle, "The sum of the length of any two sides of a triangle is greater than the length of the third side."
The side opposite the largest angle of a triangle is the largest side. Any exterior angle of the triangle is equal to the sum of its interior opposite angles.
Now taking the value given in the option:
We have the first set of values: 12, 23, 7
As here, let us assume that, a = 12, b = 23, c = 7
So, for the formation of triangle a + b > c
So, 12 + 7 = 19 < 23
Hence, this set of values can't form a triangle.
We have the second set of values: 10, 7, 2
As here, let us assume that, a = 7, b = 2, c = 10
So, for the formation of triangle a + b > c
So, 7 + 2 = 9 < 10
Hence, this set of values can't form a triangle.
We have the third set of values: 8, 3, 11
As here, let us assume that, a = 8, b = 3, c = 11
So, for the formation of triangle a + b > c
So, 8 + 3 = 11 < 11
Hence, this set of values can't form a triangle.
We have the fourth set of values: 5, 11, 8
As here, let us assume that, a = 5, b = 8, c = 11
So, for the formation of triangle a + b > c
So, 5 + 8 = 13 > 11
Hence, this set of values can form a triangle.
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Write an equation in point slope form and slope intercept form for each line passes through (8,-4). Slope =1/2
Answers
Part 1
The equation in point-slope form is
y-y1=m(x-x1)
we have
point (8,-4)
m=1/2
substitute
[tex]y+4=\frac{1}{2}(x-8)[/tex]Part 2
The equation in slope-intercept form
y=mx+b
we have
y+4=(1/2)(x-8)
isolate the variable y
so
y+4=(1/2)x-(1/2)(8)
y+4=(1/2)x-4
y=(1/2)x-8Two sides of an isosceles triangle have lengths of 3 and 6. What is the length of the third side?A. 6B. 9C. 3D. 5
Answers
It is given that the triangle is isosceles and the sides are 3 and 6.
Since the triangle is isosceles so third side will be either 3 or 6 .
If third side is 3 then we have
[tex]3+3=6[/tex]which is a contradiction to the fact that sum of two sides of a triangle is greater than the third side.
So the third side will be 6.
Hence the correct option is (A).
The jones brother, Carl,Cameron, and Carlos, are painters. Together they can paint a standard sized room in 2 hours. If Carl is alone on the job he can paint the room in 5 hours. If Cameron is alone he can paint the room in 6 hours.a)what equation can be used to determine how long it would take Carlos to paint the room alone? b)How long would it take Carlos to paint the room alone?
Answers
The workdone by the three(3) is equal to the painting of 1 room in 2 hours.
Time taken by
Carl alone = 5 hours
Cameron alone = 6 hours
Let time taken by Carlos alone = x hours
In One(1) hour, the size of the that will be covered by each of them is:
[tex]\begin{gathered} \text{Carl alone = }\frac{1}{5}\text{ of the room} \\ \text{Cameron alone=}\frac{1}{6}\text{ of the room} \\ \text{Carlos alone= }\frac{1}{x}\text{ of the room} \end{gathered}[/tex]a) Hence, the equation that can be used to determine how long it would take Carlos to paint the room alone is:
[tex]\frac{1}{5}\text{ + }\frac{1}{6}\text{ + }\frac{1}{x}=\frac{1}{2}[/tex]b) We will solve for the value of x in the equation above
[tex]\begin{gathered} \frac{1}{5}\text{ + }\frac{1}{6}\text{ + }\frac{1}{x}=\text{ }\frac{1}{2} \\ \\ \frac{1}{x}=\frac{1}{2}\text{ - }\frac{1}{5}\text{ - }\frac{1}{6} \\ \\ \frac{1}{x}=\frac{15-6-5}{30} \\ \\ \frac{1}{x}=\frac{4}{30} \\ \\ x=\frac{30}{4} \\ x=\frac{15}{2} \\ x=7.5\text{ hours} \end{gathered}[/tex]Hence, it will take Carlos 7.5 hours to paint the room alone
Question ID: 97725The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.A semi-circle sits on top of a rectangle to form the figure below. Find its area and perimeter. Use 3.14 for Te.3 in4 inA = 37.12 square inches, Pz 16.28 inchesA = 18.28 square inches, P 22.56 inchesA = 37.12 square inches, P = 22.56 inchesA ~ 18.28 square inches, P 16.28 inches
Answers
Solution
For this case we can find the area as the sum of the rectangle and the semicircle so we have this:
A1= 3in * 4in= 12 in^2
A2 = (pi/2) *(2in)^2 = 6.28 in^2
then the total area is:
A= A1+ A2= 12+ 6.28 in^2 = 18.28 in^2
And then the perimeter similarly we have:
P= 2*4 in + 2*3in + 2pi*(4in/2) = 8+ 6+ 12.56 in= 26.56in
Then the final answer is:
Area ~18.28 in^2 and Perimeter ~26.56 in
Help me finish show ur steps pls 1/8+3/14 simplify
Answers
Answer:
Step-by-step explanation:
1/8+3/14
=14/112+24/112
=38/112
=19/56
Given: C is midpoint of BD, BD perpendicular to DE, AB perpendicular to BD.
Prove: triangle ABC is congruent to triangle EDC.
(1.)statement = the given above. (1.)reason=given.
Answers
△ABC is congruent to △EDC (△ABC ≅ △EDC) under the SAS congruency condition.
What do we mean by the congruency of triangles?Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles have the same size.These triangles can be moved, turned, flipped, and rotated to produce the same appearance.When moved, they are parallel to one another.Three important theorems establish the connection between equality and congruence.Two angles are only referred to as being congruent if and only if their measures are equal.Two segments are congruent if and only if there are equal amounts of each in them.Two triangles are said to be congruent if and only if all of the corresponding angles and sides are in agreement.So, △ABC ≅ △EDC:
BC = CD (C is the midpoint of BD: Given)CBA = CDE = 90° (BD ⊥ BA and DE: GIven)AC = CE (Angles in front of them are the same, then lines in front of angles will also be similar)Then, △ABC ≅ △EDC under SAS congruency condition.
Therefore, △ABC is congruent to △EDC (△ABC ≅ △EDC) under the SAS congruency condition.
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A paralegal bills a law firm for 19.5 hours of work at a rate of £240 per hour. How much money has the paralegal earned from this job? Include units in your answer.
Answers
The money that the paralegal has earned for this work = £4680
What is the unitary approach for problem solving?
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. This technique essentially involves determining the value of a unit from the value of a multiple.
Given, cost of work per hour = £ 240
Duration of work of a law firm = 19.5 hours
Money earned by paralegal for the work = (240*19.5) = £ 4680
Thus, the money that the paralegal has earned for this work = £4680
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At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 17 knots and ship B is sailing north at 17 knots. How fast (in knots) is the distance between the ships changing at 5 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)
______ knots
Answers
The distance is changing at 153 nots at 5 P.M.
According to the Pythagoras Theorem, the square of the hypotenuse of a right angle triangle is equal to the sum of squares of the other two sides of the triangle. A derivative is suppose x and y are two variables, then the rate of change of x with respect to y is called a derivative. Differentiation is a process of finding the derivative of a function.
According to the question,
At noon, ship A is 50 nautical miles due west of ship B. (given)
Ship A is sailing west at 17 knots (given)
ship B is sailing north at 17 knots (given)
using the Pythagorean Theorem,
c^2 = a^2+b^2
Here, c is the distance between them at any point
a is the distance of ship A from initial point
b is the distance of ship B from initial point
Now,
initially ship A is due by 50 nautical miles (given)
and in 5 hours it travels 35*17 miles (given)
So, a = 50+5*17 = 50+85 = 135 nautical miles
Similarly b = 5*17 = 85 nautical miles
c^2 = 135^2+85^2 = 18225+7225
= 25450
c = √25450
c = 159.53 nautical miles
But we need to find how fast (in knots) is the distance between the ships changing
that is we need dC/dt (differentiation)
c^2 = a^2+b^2
Differentiating we get,
2cdc/dt = 2a*da/dt + 2b* db/dt
(the power comes on front during differentiating)
We now have da/dt = 17
db/dt = 17
So, dc/dt = (135*17+85*17)/(159.53) = 153 approx. knots
Therefore, we can conclude that the distance is changing at 153 nots at 5 P.M.
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Find the inverse of the following function
h(x) = 2x+16/5
A)h¯¹ (x) = 52 - 16
B)h ¹(x) = 16x+2/5
C)h 1 (z) = 5x-16/2
D)h¹(x) = 2x+ 16
Answers
Answer:
C
Step-by-step explanation:
x-8=29Write which property of equality you used
Answers
The given expression is
[tex]x-8=29[/tex]We have to use the addition property of equality, which means we are going to sum 8 on each side.
[tex]\begin{gathered} x-8+8=29+8 \\ x=37 \end{gathered}[/tex]Hence, the property is "the addition property of equality".When evaluated for y =8the expression y-3/y^2+14
Answers
Given expression is
[tex]\frac{y-3}{y^2+14}[/tex]It is given that y = 8.
Hence the value of the expression is
[tex]\frac{8-3}{8^2+14}=\frac{5}{78}[/tex]Hence the answer is 3. 5/78
7. Brittany and Hanna can paddle 12 mi upstream in the same
time it takes to paddle 28 mi downstream. Determine their
paddling rate in still water if the stream flows at 2 mi/hr.
Answers
Answer and Step-by-step explanation: Paddling 12 miles upstream will take you 12 mi / (vp - 2 mi/hr) = 12 / (vp-2) hr. (If you're having trouble figuring out how to calculate time from speed and distance, just look at the units. Time (hr) is required as a result. We have two units: miles and miles per hour. Divided by mi/hr, mi is equal to mi * hr/mi, which equals hr. 28 / (vp + 2) is the time it takes to paddle 28 miles downstream. Also, these ought to be equal: 12 / (vp-2) = 28 / (vp+2) (cross multiplication) (cross-multiplication) 28 * (vp-2) = 12 * (vp+2) 28 vp - 56 = 12 vp + 24 (collect vp terms on one the left side and constants on the right side) (collect vp terms on one the left side and constants on the right side) (28-12) vp = 24 + 56\svp = 80/16
A certain solution has hydrogen ion concentration of 0.0000653 miles per liter write this number in scientific notation.
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Solution:
Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. In this case, we have that:
[tex]0.0000653=653x10^{-5}[/tex]so that, the correct answer is:
[tex]653x10^{-5}[/tex] En el supermercado puedes llenar tu propio contenedor de osos
de miel. Un cliente compra 12 oz de
miel por $5.40.
1a) ¿Cuánto cuesta la miel por onza? (comunicar dinero usando un $ al principio, *
sin espacios y sin palabras)
Answers
If I got a 92% and there were 40 questions how many did I get wrong?
Answers
Answer: 3.2 were wrong
92% of 40 is 36.8 so you got 3.2 wrong
I hope this helps / Is correct
Complete the proof of the transitive property of parallel lines Theorem
Answers
The most appropriate choice for parallel line has been given by
Transitive property of parallel lines Theorem has been proved.
What are parallel lines?
Parallel lines
Two lines are said to be parallel if on extending them indefinitely, they will never intersect
Transversal
Transversal is a line that intersects two or more parallel lines
Here,
The diagram has been attached
line l ║ line m and line m ║ line n.
To prove line l║ line n
line l ║ line m
∠ABC = ∠ADE [Corrosponding angles are equal]
line m ║ line n.
∠ADE = ∠AFG [Corrosponding angles are equal]
So, ∠ABC = ∠AFG
So corrosponding angles of line l and line n are equal. So,
line l ║line n
Transitive property of parallel lines Theorem has been proved.
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find the probability that a family with 12 children will have at least one boy 
Answers
The probability that a family with 12 children will have at least one boy is 99.97%.
What is probability?The study of random events is the focus of the mathematical field known as probability theory. A random event's outcome can take any of a number of possible forms; it cannot be predicted before it happens. The outcome as it occurs is thought to have been determined by chance.
In everyday language, the word "probability" can mean a number of things. In order to develop and apply the mathematical theory of probability, two of these are particularly crucial. One is the interpretation of probabilities as relative frequencies; simple games involving coins, cards, dice, and roulette wheels serve as examples for this.
Assuming that the outcome of child born as a bopy or girl is 50% then each boy has a probability of 1/2
The odds of having all girls is = 1/2¹² = 1/4096 ≈ 0.000244
The odds of have at least 1 boy = 1 - 1/4096
= 0.999756
Converting to percentage = 99.97%
Thus, the probability that a family with 12 children will have at least one boy is 99.97%.
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Question 4Given AGEO 2 AFUMZE = (42.)in/N = 40mZU = 80ånd m_G = 60find the value of a(The problem is sort of messed up because of canvas)
Answers
It is stated in the problem that ΔGEO is congruent with ΔFUN. On the first triangle, the measurement of angle E and angle G is given but the measurement of angle O is not given. Using the congruence relation of the two triangles, it is true that
[tex]m\angle O\cong m\angle N[/tex]The measurement of angle N is provided in the problem, which is equal to 40 degrees. Hence, we can say that angle O has also an angle measurement of 40 degrees base on the statement above.
The sum of the interior angles of the triangle is equal to 180 degrees. This means that if we add up the interior angles of the triangle GEO, we have the following equation
[tex]m\angle G+m\angle E+m\angle O=180[/tex]Substitute the measurement of each angle on the equation above and compute, we get
[tex]\begin{gathered} 60+4x+40=180 \\ 4x+100=180 \\ 4x=180-100 \\ \frac{4x}{4}=\frac{80}{4} \\ x=20 \end{gathered}[/tex]Therefore, the value of x is equal to 20 degrees.
Find a polynomial with integer coefficients that satisfies the given conditions.
Q has degree 3 and zeros
−4
and 1 + i.
Answers
An arithmetic polynomial that meets the requirements.
Q has zeros of degree 3 is -4 and 1+i is Q(x)=x³+4x²-10x+12..
Given that,
We have to find an arithmetic polynomial that meets the requirements.
Q has zeros of degree 3 is -4 and 1+i.
There is a complex number is i.
When working with complex numbers, the following relationship is the most crucial:
i²=-1
A function's zeros:
This polynomial, given by f(x), has roots of x₁, x₂, x₃..... in which an is the leading coefficient and can be represented as a(x-x₁)(x-x₂)(x-x₃).....
Degree 3 and zeros -4 and i+1 make up Q.
Given that complex roots are always complex-conjugate, 1 - i is also a root if 1 + i is a root.
The leading coefficient, as we will mention, is 1.
Q(x)=(x-(-4))(x-(1-i))(x-(1+i))
Q(x)=x³+4x²-10x+12
Therefore, the polynomial we get is Q(x)=x³+4x²-10x+12.
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Determine if the triangle with the given sides is acute, obtuse, or right.80, 84, 116
Answers
Given: The sides of a triangle below
[tex]\begin{gathered} side1=80 \\ side2=84 \\ side3=116 \end{gathered}[/tex]To Determine: If the triangle is acute, obtuse or right
Solution
If it is right triangle, then the Pythagoras theorem would hold
[tex]\begin{gathered} Pythagoras-Theorem \\ Hypothenuse^2=Opposite^2+Adjacent^2| \\ Hypothenuse=Longest-side \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} 116^2=80^2+84^2 \\ 13456=6400+7056 \\ 13456=13456 \end{gathered}[/tex]From the above calculation, we can conclude that the triangle is
RIGHT TRIANGLE
i need to round to tge narest tenth
Answers
Answer:
[tex]\lbrace8.4,0.6\rbrace[/tex]Step by step explanation:
Solve for x:
[tex]x^2-11x+5=-2x[/tex]As a first step, solve using inverse operations to solve equations:
[tex]\begin{gathered} x^2-11+2x+5=0 \\ x^2-9x+5=0 \end{gathered}[/tex]Now, to solve this quadratic function we need to use the quadratic formula:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{where,} \\ ax^2+bx+c=0\text{ is the form of the function} \end{gathered}[/tex]Then, the solutions for the equation:
[tex]\begin{gathered} x_1=\frac{9+\sqrt[]{(-9)^2-4(1)(5)}}{2(1)}=8.4 \\ x_2=\frac{9-\sqrt[]{(-9)^2-4(1)(5)}}{2(1)}=0.6 \end{gathered}[/tex]Find the remainder when f(x) = x³ - 4x² - 6x-3 is divided by x + 1.
A.-2
B. -14
C. 6
D. -12
Answers
The remainder of the given function [tex]x^{3} -4x^{2} -6x-3[/tex] is -2, founded by using division of polynomial
The correct option is option A).
What is division of polynomial?
Polynomial division is a generalized variant of the well-known arithmetic operation known as division. It is an algorithm for dividing a polynomial by another polynomial of the same or lower degree.
Our given polynomial is [tex]x^{3} -4x^{2} -6x-3[/tex]
We have to divide this polynomial by x+1 .
This can be done by
Therefore the remainder on division of the polynomial is -2
Hence the correct option is A)
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PLEASE ANY ONE IF YOU KNOW THIS ANSWER IT PLEASE DONT NOT I REPEAT DONT ANSWER IF YOU DO NOT KNOW IT OK THANK YOU.
Determine which set of side measurements could be used to form a right triangle.
square root of 2, square root of 3, 5
square root of 2, 3, square root of 11
7, 9, 11
5, 10, 14
Answers
Answer:
Option 2
Step-by-step explanation:
The side lengths satisfy the Pythagorean theorem.
Reduce this fraction to lowest terms.
35/49
Select the correct answer.
5/7
5/6
6/7
4/9
Answers
Answer:
the answer to your problem is 5/7.
AABC and AXYZ are similar triangles. The lengths of two sides of each triangle are shown. Find the lengths of the thiside of each triangle.A6.5X3.6B5.2YZCProvide your answer below:MORE INSTRUCTIONayFEEDBACK4.5SUBMIT
Answers
Since the triangles are similar this means that the ratios between similar sides have to be equal; this means that:
[tex]\begin{gathered} \frac{6.5}{3.6}=\frac{5.2}{y} \\ \frac{6.5}{3.6}=\frac{a}{4.5} \end{gathered}[/tex]Solving the first equation we have:
[tex]\begin{gathered} \frac{6.5}{3.6}=\frac{5.2}{y} \\ y=\frac{5.2}{\frac{6.5}{3.6}} \\ y=2.88 \end{gathered}[/tex]Solving the second equation:
[tex]\begin{gathered} \frac{a}{4.5}=\frac{6.5}{3.6} \\ a=4.5(\frac{6.5}{3.6}) \\ a=8.125 \end{gathered}[/tex]Therefore, a=8.125 and y=2.88
Aaron buys 5 pounds of potatoes. He divides the potatoes into 1/6 pound portions for dinner. How many portions does Aaron have?
Answers
In one pound, there are 6 portions of 1/6 pounds each one of them because
[tex]1\text{pound}=\frac{6}{6}\text{pound}[/tex]Therefore, in five pounds there are 30 portions of 1/6 pounds each one of them because
[tex]5\text{pounds}=\frac{30}{6}\text{pounds}[/tex]How many portions does Aaron have? He has 30 portions.
Suppose that on January 1 you have a balance of $3,100 on a credit card whose APR is 13%, which you want to pay off in 1 year. Assume that you make no additional charges to the card after January 1. a. The monthly payment is?b. When the card is paid off, how much will you have paid since January 1?c. What percentage of your total payment from part (b) is interest?
Answers
The monthly payment M of an initial balancen P, with a APR r during a period of t months is given by:
[tex]M=P\frac{\frac{r}{12}(1+\frac{r}{12})^t}{(1+\frac{r}{12})^{12}-1}[/tex]a) For P = $3,100, r = 13% and t = 12 months, we have:
[tex]M=3100\frac{\frac{0.13}{12}(1+\frac{0.13}{12})^{12}}{(1+\frac{0.13}{12})^{12}-1}\approx\text{ \$}276.88[/tex]b) The total payment after 12 months will be:
[tex]T=12\cdot M=12\cdot276.88=\text{ \$}3322.60[/tex]c) The total interest is given by:
[tex]I=\frac{T}{P}-1=\frac{3322.60}{3100}-1\approx0.072=7.2\%[/tex]