PLEASE HELP ME. QUAD has coordinates Q(-4, 9), U(2, 3), A(-3, -2), and D(-9, 4). Prove that quadrilateral QUAD is a
rectangle.
Answers
Check the picture below.
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ Q(\stackrel{x_1}{-4}~,~\stackrel{y_1}{9})\qquad U(\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) ~\hfill QU=\sqrt{[ 2- (-4)]^2 + [ 3- 9]^2} \\\\\\ ~\hfill \boxed{QU=\sqrt{72}} \\\\\\ U(\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad A(\stackrel{x_2}{-3}~,~\stackrel{y_2}{-2}) ~\hfill UA=\sqrt{[ -3- 2]^2 + [ -2- 3]^2} \\\\\\ ~\hfill \boxed{UA=\sqrt{50}}[/tex]
[tex]A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{-2})\qquad D(\stackrel{x_2}{-9}~,~\stackrel{y_2}{4}) ~\hfill AD=\sqrt{[ -9- (-3)]^2 + [ 4- (-2)]^2} \\\\\\ ~\hfill \boxed{AD=\sqrt{72}} \\\\\\ D(\stackrel{x_1}{-9}~,~\stackrel{y_1}{4})\qquad Q(\stackrel{x_2}{-4}~,~\stackrel{y_2}{9}) ~\hfill DQ=\sqrt{[ -4- (-9)]^2 + [ 9- 4]^2} \\\\\\ ~\hfill \boxed{DQ=\sqrt{50}}[/tex]
now, let's take a peek at that above, DQ = UA and QU = AD, so opposite sides of the polygon are equal.
Now, let's check the slopes of DQ and QU
[tex]D(\stackrel{x_1}{-9}~,~\stackrel{y_1}{4})\qquad Q(\stackrel{x_2}{-4}~,~\stackrel{y_2}{9}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{9}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{(-9)}}} \implies \cfrac{9 -4}{-4 +9}\implies \cfrac{5}{5}\implies \cfrac{1}{1}\implies 1 \\\\[-0.35em] ~\dotfill[/tex]
[tex]Q(\stackrel{x_1}{-4}~,~\stackrel{y_1}{9})\qquad U(\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{9}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-4)}}} \implies \cfrac{3 -9}{2 +4}\implies \cfrac{-6}{6}\implies \cfrac{-1}{1}\implies -1[/tex]
keeping in mind that perpendicular lines have negative reciprocal slopes, let's notice that the reciprocal of 1/1 is just 1/1 and the negative of that is just -1/1 or -1, so QU has a slope that is really just the negative reciprocal of DQ, those two lines are perpendicular, thus making a 90° angle, and their congruent opposite sides will also make a 90°, that makes QUAD hmmm yeap, you guessed it.
Related Questions
Building A is 875 feet tall and contains 71 stories. Building B contains 109 stories. If the two buildings have the same number of feet per floor, approximate the height of building B rounded to the nearest foot.
Answers
Answer:
Approx. 1343 feet
Step-by-step explanation:
Building A is 71 stories at 875 feet tall. Since the two buildings have the same number of feet per floor, we can divide building A's stories to find the height of 1 story, and then multiply by the stories of building B.
Building A
71 ÷ 71 = 1 story
875 ÷ 71 = 12.32 feet
Each story is approximately 12.32 feet tall
Building B
1 story × 109 = 109 stories
12.32 feet × 109 = 1343.31 feet
Rounded to the nearest foot is 1343 feet.
4. What is the total cost of 400 square feet of land if it sells for
$110 per square foot?
Answers
The total cost of 400 square feet of land if it sells for $110 per square foot is $ 44,000.
what is Area?Area is the quantity that expresses the extent of a region on the plane or on a curved surface.
Here, Total area = 400 sq. units
Cost per square foot = $ 110
Total Cost = Total area X Cost per unit area
TC = 400 X 110
TC = 44,000
Thus, the total cost of 400 square feet of land if it sells for $110 per square foot is $ 44,000.
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What are the sides of (triangle)PQR?
OA. ZP, ZQ, and ZR
OB. None of these
OC. PQ, QR, and PR
OD. P. Q. and A
Answers
A triangle is a three-edged polygon with three vertices. The correct option is C.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
The sides of the triangle PQR are PQ, QR, and PR. Thus, the correct option is C.
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How do you find the length of an unknown leg in a right triange
Answers
By using the pythagoras theorum you can find an unknown leg of right angled triangle.
Hypotenuse side is in the front of the 90 degree angle and other two sides can be taken as base and perpendicular, so formula goes as :-
(Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2
H^2 = B^2 + P^2
Step-by-step explanation:
Hope it helps you!!
The volume of a cylinder is given by the formula y = ²h, where r is the radius of the cylinder and h is the height.
Suppose a cylindrical can has radius (x + 8) and height (2x + 3). Which expression represents the volume of the can?
Ozx³ +19x²+112x+192
O 27x³ +35mx² +80*x+48
O 27x³ +35x² +1767x+1927
O 47x³+447x² +105x+72
Answers
The expression represents the volume of the can is 2x³ + 35x² + 176x + 192.
What is Volume?Volume is a mathematical term that describes how much three-dimensional space an object or closed surface occupies. The measurement for volume is in cubic units, such m3.
Expression: (Math Operator, Number/Variable, Math Operator)
We have,
radius = (x + 8) and, height = (2x + 3)
So, Volume of can
= πr²h
= π(x+8)² (2x+3)
= π (x² + 16x + 64) (2x+3)
= π (2x³ + 3x² + 32x² + 48x + 128x + 192)
= π (2x³ + 35x² + 176x + 192)
So, the Expression for volume is 2x³ + 35x² + 176x + 192.
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A certain species of animal can has varying fur color. The probability that the animal will have orange fur is 0.7, the probability of brown fur is 0.11 and the probability of grey fur is 0.19. The animal also occasionally will have stripes. If the animal is orange the probability of stripes is 0.16, if the animal is brown the probability of stripes is 0.3, and if the animal is grey the probability of stripes is 0.4.
What is the probability an animal has stripes?
(Round answer to three decimal places)
What is the probability an animal is orange given it does NOT have stripes?
(Round answer to three decimal places)
Answers
The probability that an animal has stripes will be 0.86.
How to calculate the probability?The probability that an animal has stripes will be:
= Orange stripes + Brown stripes + Grey stripes
= 0.16 + 0.3 + 0.4
= 0.86
The probability that an animal doesn't have stripes will be:
= 1 - 0.86
= 0.14
Therefore, the probability that an animal doesn't have stripes is 0.14.
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F(x)=x^2 + 4x + 12 what is the vertex form of f(x)? What is the minimum value of f(x)?
Answers
the equation of f(x) which is "x" terms is the equation of a vertical parabola that is opening upwards like a bowl, the minimum will be at its vertex
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+4}x\stackrel{\stackrel{c}{\downarrow }}{+12} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 4}{2(1)}~~~~ ,~~~~ 12-\cfrac{ (4)^2}{4(1)}\right) \implies \left( - \cfrac{ 4 }{ 2 }~~,~~12 - \cfrac{ 16 }{ 4 } \right) \\\\\\ (-2~~,~~12-4)\implies \stackrel{minimum}{(-2~~,~~\stackrel{\downarrow }{8})}[/tex]
3 (without using trig table) evaluate
It tan 60 x tan 30 divided by
Tan 60 + tan 30
Answers
Answer:
[tex]1.25332[/tex]
Step-by-step explanation:
[tex] tan(30 times tan(60 ) \div \tan(60 \div + 30) [/tex]
I got this question while practicing MAP, can someone lend a hand?
Answers
Answer:
see the attachment photo!
X÷ 5+1 = 11
X =
What does X =
Answers
Answer:
x = 2
Step-by-step explanation:
x/5 + 1 = 11
x/5 = 10
x = 50
Suppose that a sample is taken from a population whose mean value is 45. As the sample size increases, which value will the sample mean approach?
Answers
Suppose that a sample is taken from a population whose mean value is 45, the sample mean will approach
[tex]\mu=45[/tex]
Which value will the sample mean approaches?Generally, the equation for the standard deviation is mathematically given as
Standard deviation sample mean [tex]\mu = \frac{\sigma}{\sqrt{n}}[/tex]
Therefore, where a population whose mean value is 45 for any sample
size, Hence mean of the sample mean is
[tex]\mu = \=x[/tex]
[tex]\mu=45[/tex]
In conclusion, the value the sample mean approach is
[tex]\mu=45[/tex]
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Part A: Describe the solution(s) to 9x² - 36x + 36 = 0 by just determining the radicand. Show your work. (10 points) Part B: Describe the solution (s) to x²-x + 4 = 0 by just determining the radicand. Show your work. (10) points) Part C: Solve 4x² + 23 – 35 using an - appropriate method. Show the steps of your work and explain why you chose the method used. (15 points) (35 points)
Answers
The solution to the equations are:
9x² - 36x + 36 = 0 has two equal real solutionsx² - x + 4 = 0 has no real solutionsThe factored expression of 4x² + 23 – 35 is 4(x² -3)Part A: Describe the solutionThe equation is given as:
9x² - 36x + 36 = 0
The above equation is a quadratic equation which can be represented as:
ax² + bx + c = 0
The discriminant (d) is calculated as:
d = b² - 4ac
So, we have:
d = (-36)² - 4 * 9 * 36
d = 0
A discriminant of 0 means that the equation has two equal real solutions
Hence, 9x² - 36x + 36 = 0 has two equal real solutions
Part B: Describe the solution
The equation is given as:
x² - x + 4 = 0
The above equation can be represented as:
ax² + bx + c = 0
The discriminant (d) is calculated as:
d = b² - 4ac
So, we have:
d = (-1)² - 4 * 1 * 4
d = -15
A discriminant of -15 means that the equation has no real solutions
Hence, x² - x + 4 = 0 has no real solutions
Part C: The solution to the expression
We have:
4x² + 23 – 35
Evaluate the difference
4x² -12
Factor out 4
4(x² -3)
Hence, the factored expression of 4x² + 23 – 35 is 4(x² -3)
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The first three terms of a sequence are given. Round to the nearest thousandth (if
necessary).
36, 27,
81
4
Find the 10th term.
Answers
Answer:
T10=108
Step-by-step explanation:
TN=bn+c
27,36,81=constant difference is 9
Tn=bn+c
Tn=9n+18
T10=9(10)+18
T10=90+18
T10=108.
hope it helps.
Answer: 2.703
Step-by-step explanation:
Which of the following describes the best method of solving two-step equations? A. Apply the multiplication property of equality first, and then apply the addition property of equality to isolate the variable. B. Apply the addition property of equality first, and then apply the multiplication property of equality to isolate the variable. C. Apply only the multiplication property of equality to isolate the variable. D. Apply only the addition property of equality to isolate the variable.
Answers
The best method of solving two-step equation is "Apply the multiplication property of equality first, and then apply the addition property of equality to isolate the variable"
How to solve two step equationFor instance:
40 = 5(x) - 5
40 = 5x - 5
Add 5 to both sides40 + 5 = 5x
45 = 5x
x = 45/5
x = 9
Therefore, the correct answer is "Apply the multiplication property of equality first, and then apply the addition property of equality to isolate the variable".
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4,5,5,6,10,11,12,13 mode
Answers
Answer: 5 is the mode
Step-by-step explanation: The mode is the number that is appeared most often in the data, so the mode in this case (4, 5, 5, 6, 10, 11, 12, 13) is 5.
I need help please asap?!!!
Answers
Answer:
3660
Step-by-step explanation:
'milli..' in the metric system means 1000 th
there are 1000 milliliters in a liter
3.66 liters * 1000 ml/liter = 3660 ml
Gordon had $200,000 in a CD at Lots
a Loot Bank, which just failed. If the
FDIC insurance limit per depositor,
per bank, is $250,000, how much
will Gordon get back?
Answers
Given the FDIC insurance limit, the amount that Gordon would get back is $200,000.
How much would Gordon get back?
The Federal Deposit Insurance Corporation (FDIC) was established after the great depression with the aim of insuring the deposits of customers in banks.
If the limit on insurance is $250,000, depositors with $250,000 or less would get the full amount of their deposits in case of bank failure. If the deposit is greater than $250,000, they would get $250,000.
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Given that ƒ(x) = 3x, identify the function g(x) shown in the figure.
A)
g(x) = −(1∕3)x
B)
g(x) = 3−x
C)
g(x) = −3−x
D)
g(x) = −3x
Answer: D
Answers
Answer:
the answer is D
hope it will help
Pls help me i need quick responses TwT
Answers
Answer:
56%
Step-by-step explanation:
i think your missing some info.
Use triangle XYZ to answer questions 3-5.
1) Use special right triangles to help find the length of segment XY. What is the exact height of triangle XYZ?
Click the keyboard button to enter your answer.
2)What is the exact area of triangle XYZ? Leave your answer in radical terms.
Click the keyboard button to enter your answer. Show your work.
3)What is the area of triangle XYZ to the nearest tenth of a square in?
Answers
Answer:
Step-by-step explanation:
Solve for (x): (14.5x − 5(x + 2) ≤ 4 + 4(4 − 1/8x)
Answers
Answer:x ≤ 3
Step-by-step explanation:
(14.5x − 5(x + 2) ≤ 4 + 4(4 − 1/8x)
14.5x - 5x-10 ≤ 4 + 16 - 1/2x Get rid of the parenthesis
9.5x-10 ≤ 20-1/2x Combine like terms
10x - 10 ≤ 20
10x/10 ≤ 30/10
x ≤ 3
A group of people were surveyed, and the data about their age and hemoglobin levels was recorded in a two-way table. Based on the data in the
table, match each probability with its correct value.
Age
Hemoglobin Level
Less than 25 Years 25-35 Years Above 35 Years Total
Less than 9
21
32
76
129
Between 9 and 11
49
52
46
147
Above 11
69
44
40
153
Total
139
128
162 429
the probability that a person older
than 35 years has a hemoglobin
level less than 9
the probability that a person
younger than 25 years has a
hemoglobin level above 11
the probability that a person in the
25-35 age group has a hemoglobin
level less than 9
the probability that a person older
than 35 years has a hemoglobin
level between 9 and 11
0.25
0.47
0.28
0.50
Answers
The probability that a person older than 35 years has a hemoglobin level less than 9 is 0.47.
The probability that a person younger than 25 years has a hemoglobin level above 11 is 0 .50
the probability that a person in the 25-35 age group has a hemoglobin
level less than 9 is 0.25.
The probability that a person older than 35 years has a hemoglobin level between 9 and 11 is 0.28.
What are the probabilities?The probability that a person older than 35 years has a hemoglobin level less than 9 = number of people order than 35 that have a hemoglobin level less than 9 / total number of people over 35
= 76 / 167 = 0.47
The probability that a person younger than 25 years has a haemoglobin level above 11 = people over 25 that have a haemoglobin level above 11 / total number of people above 25
69/139 = 0 .50
The probability that a person in the 25-35 age group has a hemoglobin
level less than 9 = people between 25 - 35 that have a haemoglobin level less than 9 / total number of people between 25 - 35
= 32/128 = 0.25
The probability that a person older than 35 years has a hemoglobin level between 9 and 11= number of people order than 35 that have a hemoglobin level 9 - 11 / total number of people over 35
46 / 162 = 0.28
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What is the probability that student A choses yellow and student b choses yellow from their skittles at the same time
Answers
using the digits 4,5,6,and 7,write the greatest 4 digit number you can without repeating any of the digits.
Answers
Answer:
7,654
Step-by-step explanation:
Arrange the digits in order to create the highest possible number.
7000 + 600 + 50 + 4 = 7654
I need this answer asap (fast)
Of the 12.4 million species of organisms in the world today, 64% (almost two thirds) are insects.
Estimate to the nearest million the number of insect species.
Answers
Answer:
8 million insect species
Step-by-step explanation:
Solving :
⇒ Number of species = Total organisms × % of the species
⇒ Number of species = 12.4 × 64%
⇒ Number of species = 0.124 × 64
⇒ Number of species = 7.936 million ≈ 8 million insect species
HELP I'LL GIVE 50 POINTS IF YOU CAN HELP WITH THIS MATH QUESTION
IMAGE BELOW...
Answers
Answer:
last one is the answer brother
The table shows the change in the price of a stock. At the end of the week, the price is $17.17.
Answers
The price of the stock after the change in price on Thursday is $16.76.
The price of the stock at the beginning of the week is $16.81.
What are the price changes?The price at the end of the week is a function of the total changes in price and the price at the beginning of the week.
$17.17 = beginning price + 0.21 + 0.09 - 0.03 - 0.02 + 0.11
$17.17 = beginning price + 0.36
Beginning price = $17.17 - 0.36 = $16.81
Price on Thursday = $16.81 + 0.21 + 0.09 - 0.03 - 0.02 = $16.76
Here are the questions:
What was the price of the stock after the change in price on Thursday?
What was the price of the stock at the beginning of the week?
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Someone please help
Answers
Answer:
Part (a)Given:
[tex]\displaystyle \int\limits_{1}^{3} x^2 \:dx[/tex]
Trapezium Rule
[tex]\displaystyle \int\limits_{a}^{b} y \:dx \approx \dfrac{1}{2}h\left[(y_0+y_n)+2(y_1+y_2+...+y_{n-1})\right] \quad \textsf{where }h=\dfrac{b-a}{n}[/tex]
Calculate the width of each strip (h).
Given:
a = 1b = 3n = 5[tex]\implies h=\dfrac{3-1}{5}=0.4[/tex]
Create a table with the x and y values:
[tex]\large\begin{array}{| c | c | c | c | c | c | c |}\cline{1-7} x & 1 & 1.4 & 1.8 & 2.2 & 2.6 & 3\\\cline{1-7} y & 1 & 1.96 & 3.24 & 4.84 & 6.76 & 9\\\cline{1-7}\end{array}[/tex]
Put all the values into the formula:
[tex]\begin{aligned}\displaystyle \int\limits_{1}^{3} x^2 \:dx & \approx \dfrac{1}{2}(0.4)\left[(1+9)+2(1.96+3.24+4.84+6.76)\right]\\& = 0.2\left[10+2(16.8)\right]\\\\& = 0.2\left[10+33.6\right]\\\\& = 0.2\left[43.6\right]\\\\& = 8.72 \end{aligned}[/tex]
Part (b)[tex]\begin{aligned}\displaystyle \int\limits_{1}^{3} x^2 \:dx &=\left[\dfrac{1}{3}x^3\right]^3_1\\& = \dfrac{1}{3}(3)^3-\dfrac{1}{3}(1)^3\\& = 9-\dfrac{1}{3}\\& = \dfrac{26}{3}\end{aligned}[/tex]
The exact area as a decimal is [tex]\sf 8.\dot{6}[/tex]. Therefore, the estimated answer of 8.72 is an overestimate.
Part (c)Answer to (a) = 8.72
To find the maximum possible error:
Identify the last non-zero digit to the right of the decimal point → 2The precision of the number is the place value: 0.01Divide the precision by 2Therefore, the maximum possible error for 8.72 is 0.005.
Part (d)Trapezoid Error formula
[tex]|E| \leq \dfrac{(b-a)^3}{12n^2}\left[\textsf{max}|f''(x)|\right],\quad a \leq x \leq b[/tex]
Calculate the second derivative:
[tex]f(x)=x^2[/tex]
[tex]f'(x)=2x[/tex]
[tex]f''(x)=2[/tex]
Input the values into the formula:
[tex]\implies |E| \leq \dfrac{(3-1)^3}{12n^2}(2) < 0.001[/tex]
[tex]\implies 16 \leq 0.012n^2[/tex]
[tex]\implies 36.5148...\leq n[/tex]
[tex]\implies 37\leq n[/tex]
Using only the markings given in the diagram, which triangle congruence criterion can be used to prove that PQR and STU are congruent?
Answers
Answer: HL
Step-by-step explanation:
If the hypotenuse and one leg of the two triangles are congruent, then the triangles are congruent. The correct option is D, HL.
What is the HL theorem?According to the HL theorem, If the hypotenuse and one leg of the two triangles are congruent, then the triangles are congruent. therefore, the hypotenuse will be congruent to each other, and the corresponding sides will be congruent to each other.
In the two of the given triangle, ΔPQR and ΔSTU, the following things can be seen,
PR ≅ SU (Leg of the triangle)
RQ ≅ TU (Hypotenuse)
Also, since the two of the triangles are right angle triangle, and the length of the one leg of the two triangles is equal, also, the hypotenuse of the two triangle is equal. Therefore, Using the HL postulate. The two triangles can be said to be congruent.
Hence, the triangle congruence criterion can be used to prove that PQR and STU are congruent is HL Congruency.
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Eugene and three of his friends went out to eat. They decided to split the bill evenly. Each person paid $11. What was the total bill?
Answers
Answer:
Step-by-step explanation:
Je calcule la facture totale
11x4=44
La facture totale d'Eugène et ses trois amis était de 11$