what are the coordinates of vertices of quadrilateral ABCD? use the coordinates to find the length of DA.
Need help ASAP ???
Answers
Answer:
The slope of AB is - 2,
Slope of BC is \frac{1}{2}
2
1
Slope of CD is -\frac{3}{4}−
4
3
Slope of AD is \frac{1}{2}
2
1
,
ABCD is trapezoid because one pair of opposite sides is parallel.
Step-by-step explanation:
Given vertices of quadrilateral ABCD,
A(−1, −1) , B(−3, 3) , C(1, 5) , and D(5, 2),
∵ Slope of a line passes through two points (x_1, y_1)(x
1
,y
1
) and (x_2, y_2)(x
2
,y
2
) is,
m=\frac{y_2-y_1}{xc_2-x_1}m=
xc
2
−x
1
y
2
−y
1
Thus, the slope of AB = \frac{3+1}{-3+1}=\frac{4}{-2}=-2
−3+1
3+1
=
−2
4
=−2
Slope of BC = \frac{5-3}{1+3}=\frac{2}{4}=\frac{1}{2}
1+3
5−3
=
4
2
=
2
1
Slope of CD = \frac{2-5}{5-1}=-\frac{3}{4}
5−1
2−5
=−
4
3
Slope of DA = \frac{-1-2}{-1-5}=\frac{-3}{-6}=\frac{1}{2}
−1−5
−1−2
=
−6
−3
=
2
1
Since, when two line segment having the same slope then they are parallel to each other.
∴ BC ║ DA
A quadrilateral only having two parallel sides is called trapezoid,
Hence, ABCD is a trapezoid.
Given the graph of quadrilateral ABCD, the coordinates of A, B, C and D are (-3,-4), (1,4), (4,0) and (1,-4) respectively. The length of DA using distance formula is 4 units.
The coordinates of the points in the graph is given in the form of (x,y) where x is the abscissa and y is the ordinate.
The distance formula is used to find the length of the line given the endpoints of the line.
Given endpoints as [tex](x_1, y_1) \ and \ (x_2, y_2)[/tex],
[tex]d = \sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
The coordinates of vertices are given by:
A = (-3,-4)
B = (1,4)
C = (4,0)
D = (1,-4)
The length of DA can be found by distance formula :
DA = [tex]\sqrt{(1+3)^2+(-4+4)^2} = \sqrt{(1+3)^2} = \sqrt{4^2} = 4[/tex]
Learn more about distance formula here
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Related Questions
A father's age now is three times the age that his son was 4 years ago. In 12 years, the father will be twice as old as his son. find their ages now.
Answers
Dad’s age = D
4 years ago, the son was (S-4) and dad now is three times that so D=3(S-4)
Expand that to get D=3S-12
In 12 years, the son will be (S + 12)
Dad will also be (D + 12) and he will be two times the sons age at that point so:
D + 12 = 2(S + 12)
Expand the right side:
D +12 = 2S + 24
Subtract 12 from both sides:
D = 2S + 12
So now D = 2S + 12 AND
D = 3S - 12
Since both equations equal “D”, they must then equal each other:
2S + 12 = 3S - 12
Do some algebra and you get S = 24
Plug this back into EITHER “D=“ equations to find D
D=2(24) +12
D=60
Answer:
the dad is 60 im not sure about the son
Step-by-step explanation:
In a competition, four of the participants have completed their performances. Their scores are 9.61, 9.66, 9.64, and 9.60. The highest score wins. Which score will enable the last participant to win the competition?
9.67
9.65
9.62
9.06
Answers
For some reason, the scores your teacher gave you and the answer choices don't match up. I'm not sure why this is. Perhaps some kind of typo. Please double check and get back to me.
if a = 4 - √15, find a^4 +1\a^4
Hey! Please answer this question with steps. I will mark you brainliest.
Random answers like 'sdfgh' or wrong answers will be reported
Answers
Answer:
[tex](\frac{-3+\sqrt{15} }{4-\sqrt{15} })^{2} -4\\[/tex]
Step-by-step explanation:
[tex]a=4-\sqrt{15}[/tex]
[tex]a^{4} +\frac{1}{a^{4} }\\=a^{2^{2} } +\frac{1}{a^{2^{2} } }\\\\=(x^{2} +\frac{1}{a^{2} } )^{2} -2a^{2} \frac{1}{a^{2} } \\=(a +\frac{1}{a } )^{2} -2a \frac{1}{a}-2\\=(4-\sqrt{15} +\frac{1}{4-\sqrt{15} }) ^{2} -4\\\=(\frac{16-15-4+\sqrt{15} }{4-\sqrt{15} })^{2} -4\\=(\frac{-3+\sqrt{15} }{4-\sqrt{15} })^{2} -4\\[/tex]
Solve for x. 3:12 = x:16
Answers
48/12 = x (simply left side)
4 = x
Answer:
[tex]x = 4[/tex]
Step-by-step explanation:
We can represent each ratio as a fraction, then use the cross products property to find the value of x.
[tex]\frac{3}{12} = \frac{x}{16} \\\\\\16\cdot3=48\\\\48\div12=4[/tex]
Hope this helped!
ZA and ZB are vertical angles. If m_A = (7x– 20)° and m_B = (6x – 1)º,
then find the measure of ZA.
Answers
[tex]\\ \sf\longmapsto 7x-20=6x-1[/tex]
[tex]\\ \sf\longmapsto 7x-6x=-1+20[/tex]
[tex]\\ \sf\longmapsto x=-19[/tex]
Now
[tex]\\ \sf\longmapsto m<A=7x-20=7(-19)-20=133-20=113[/tex]
How many points are needed to define a plane?
Answers
Answer:
3
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
5
If two of the ordered pairs was removed which two data points will cause the correlation to decrease the most? Select Two points
1) Data point A
2) Data point B
3) Data point C
4) Data point D
Answers
Answer:
1. Data point A
4. Data point D
Step-by-step explanation:
In a scatter plot, the closer the clustered data points are close to the best line of fit, the greater the correlation that would exist between the two variables.
If we are to draw a best line of fit in the scatter plot that is shown above, the closest data points amongst data points A, B, C, D, and E, that would be close to the best line of fit are data points A and D.
Therefore, removing data point A and point D would cause the correlation to decrease the most.
Just need to calculate the area of the shaded region, thanks
Answers
Answer:
Area of the shaded region= 82.2 cm²
Step-by-step explanation:
Please see attached picture for full solution.
how to solve this equation
x2-5x=0
Answers
Answer:
x = 5
Step-by-step explanation:
x² - 5x = 0
(x² - 5x) /x = 0/x
x²/x - 5x/x = 0
x - 5 = 0
x = 5
Check:
x² - 5x = 0
5² - 5*5 = 0
25 - 25 = 0
The solution to the equation is:
x = 0 or x = 5
How to solve the equation?A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.
We have:
x²-5x = 0
We can solve the equation as follow:
x²-5x = 0
Factorize:
x(x - 5) = 0
x = 0 or (x -5) = 0
x = 0 or x = 5
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6. Find the focus for the parabola.
2x=(y+3)^2+14
Focus: (x,y) =
Answers
Answer: Focus = (7.5, -3)
Step-by-step explanation:
The Vertex form of a horizontal parabola is: x = a(y - k)² + h where
a is the vertical stretch; [tex]a=\frac{1}{4p}[/tex]p is the distance from the vertex to the focus(h, k) is the vertexRewrite the equation in Vertex form to identify a, h, & k:
2x = (y + 3)² + 14
[tex]x=\dfrac{(y+3)^2+14}{2}\\\\x=\dfrac{1}{2}(y+4)^2+7[/tex]
Vertex: (h, k) = (7, -3)
[tex]a=\dfrac{1}{2}[/tex]
Find p and then find the focus: Focus = (h + p, k)
[tex]a=\dfrac{1}{4p}\quad \rightarrow \quad \dfrac{1}{2}=\dfrac{1}{4p}\quad \rightarrow \quad 4p=2\quad \rightarrow \quad p=\dfrac{2}{4}\quad \rightarrow p=\dfrac{1}{2}\\[/tex]
Focus: (7 + [tex]\frac{1}{2}[/tex] , -3) = (7.5, -3)
Out of a class of 150 one third opted for Germany two fifth for Italian and rest for French. find how many opted for French
Answers
Answer:
40
Step-by-step explanation:
Total is 150
Germany=1/3 *150 = 50
Italian= 2/5 * 150 = 60
Total - Germany- Italian= French
150 - 50 -60= 40
Find f(g(4)).
f(g(4)) =
Answers
Answer:
4fg
Step-by-step explanation:
regrouping terms leaves 4 f variables along with the 4 g variables, since f is also multiplied by g, that would leave the answer to be 4fg. (socratic)
(4g)
Step One: Remove/ Alter the equation= f(gx4)
Step Two: Do the equation= f(gx4); f (4)
I hope I've helped! If you need anything, ask away!
What is the center of the circle with the equation (x+4)2 + (y - 2)2 = 16?
Answers
Answer:
The center of the circle is
( - 4 , 2)Step-by-step explanation:
Equation of a circle is given by
(x - h)² + ( y - k)² = r²where r is the radius
(h, k) is the center of the circle
The center of a circle is given by
( - h , - k)
From the question equation of the circle is
( x + 4)² + ( y - 2)² = 16
Comparing with the general equation above
( h , k) = ( 4 , - 2)
The center of the circle is
( - h , - k) = ( - 4 , -(-2))
We have the final answer as
( - 4 , 2)Hope this helps you
Which expression is equivalent to 18 – 20?
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\boxed{\mathsf{18 - 20}}\\\huge\boxed{=\mathsf{18 + (-20)}}\\\huge\boxed{\mathsf{= -2}}\\\huge\boxed{\textsf{Answer: 18 + (-20)}}\huge\checkmark\\\\\huge\text{Good luck on your assignment \& enjoy your day!}\\\\\huge\boxed{\frak{Amphitrite1040:)}}[/tex]
X+a=3/4
How do I solve for x first then a
Answers
Answer:
[tex]x + a = \frac{3}{4} \\ x = \frac{3}{4} - a[/tex]
for a:
[tex]a = \frac{3}{4} - x[/tex]
[tex]\\ \sf \longmapsto x+a=\dfrac{3}{4}[/tex]
[tex]\\ \sf \longmapsto x=\dfrac{3}{4}-a[/tex]
[tex]\\ \sf \longmapsto x=\dfrac{3-4a}{4}[/tex]
And
[tex]\\ \sf \longmapsto a=\dfrac{3}{4}-x[/tex]
[tex]\\ \sf \longmapsto a=\dfrac{3-4x}{4}[/tex]
What number must be added to the expression for it to equal zero? (–6.89 + 14.52) + (–14.52)
Answers
Answer:
The number to be added is 6.89
Step-by-step explanation:
Here, we want to know what number must be added to the expression to make it equal to zero.
Let the number be x
Thus;
-6.89 + 14.52 -14.52 + x = 0
-6.89 + x = 0
x = 6.89
19 más que dos veces los ahorros de Chrissy
Utilizar la variable c para representar los ahorros de Chrissy.
Answers
- 19 mas (+) 2 veces los ahorros (c).
I need helps will give you a good rating.
Answers
Answer: x = 3
Step-by-step explanation:
Sqrt(x+7) - 1 = x
Sqrt(x+7) = x + 1
x+7 = x^2 + 1
x = x^2 - 6
x=3
!helppppppppp meeeeeeee emmmmmm!
Answers
Answer & Step-by-step explanation:
Take the last expression:
[tex](3*3)*(4*4)[/tex]
This can be simplified using exponents. [tex]x*x=x^2[/tex] :
[tex]3^2*4^2[/tex]
So, take the two numbers within the parentheses from the first expression and write separately, including the exponent with each. Do this with the next problem:
[tex](5*6)^3=5^3*6^3[/tex]
:Done
Need help, only provide the answer
Answers
Answer:
<R = 30 degrees
LM = 6 sqrt(3)
Step-by-step explanation:
RST = LMN
We know that angle R equals angle L
<L = 30 degrees so <R = 30 degrees
Side RS = side LM
RS = 6 sqrt(3) so LM = 6 sqrt(3)
Answer ASAP, Will give brainliest!!
Answers
Answer:
First. 115°
Second. 65°
Third. 65°
Fourth. 7
Fifth. 425.25
First
angle DAB = angle ADC (since this is an isosceles trapezoid)
Second
In a trapezoid adjacent angle are supplmentary (that is their sum is 180°)
180-115 is 65°
Third
(Same reason as second)
Fourth
The side 3x+4 is same as the opposite side
So 3x + 4 = 25
on solving you get x = 7 in
Fifth
[tex]area \: = \frac{1}{2} \times length \: of \: the \: perpendicular \: (b1 + b2)[/tex]
area = 1/2 × 13.5 (20+43)
area = 1/2 × 13.5 × 63
Thus area is 425.25
Answer:
Step-by-step explanation:
1)As ABCD is isosceles trapezium,
∠ADC= ∠DAB
∠ADC = 115°
2) AD //BC
∠ADC + ∠DCB = 180° {co interior angles}
115 + ∠DCB = 180
∠DCB = 180 - 115
∠DCB = 65°
3) As ABCD is isosceles trapezium,
∠CBA = ∠DCB
∠CBA = 65°
4) As ABCD is isosceles trapezium, non parallel sides are congruent.
AB = DC
3x + 4 = 25 in
3x = 25 - 4
3x = 21
x = 21/3
x = 7 in
5) height = 13.5 in
a= 43 in
b= 20 in
Area of trapezium = [tex]\frac{(a+b)*h}{2}\\[/tex]
[tex]= \frac{(43 +20)*13.5}{2}\\\\=\frac{63*13.5}{2}\\\\\\= 425.25 in^{2}[/tex]
Answer ASAP please!
…
Answers
Answer:
"A" seems to be incorrect....
Step-by-step explanation:
"A" seems to be incorrect....
[tex]\frac{\left(\sin \left(60^{\circ \:}\right)\cdot \:300\right)}{\sin \left(90^{\circ \:}\right)}=150\sqrt{3}\quad \begin{pmatrix}\mathrm{Decimal:}&259.80762\dots \end{pmatrix}[/tex]
A table costs Rs 720 to make. He sells it for Rs 920. What percentage of profit did he earn?
Answers
Answer:
27 7/9%
Step-by-step explanation:
Take the selling price and subtract the cost
920 -720 = 200
Divide it by the cost
200/720
.27777777
Change to percent form
27.777777%
27 7/9%
Answer:
profit percentage = 27.8 %Step-by-step explanation:
To find the percentage of profit we use the formula
[tex] \frac{profit}{cost \: \: price \: } \times 100[/tex]
Subtract the cost price from the selling price to obtain the profit
Cost price = Rs 720
Selling price = Rs 920
Profit = Rs 920 - Rs 720 = Rs 200
So the profit percentage is
[tex] \frac{200}{720} \times 100[/tex]
We have the final answer as
profit percentage = 27.8 %Hope this helps you
The test to detect the presence of respiratory syncytial virus is 97% accurate for a person who has the virus and 99% accurate for a person who does not have the virus. In a given population, 0.55% of the people are infected.
The probability that a randomly chosen person gets an incorrect result is
.
Answers
Answer:
The probability that a randomly selected person gets incorrect result is 2.2 × 10⁻⁴
Step-by-step explanation:
The parameters given are;
The accuracy of the test for a person who has the respiratory synctial virus = 97%
The accuracy of the test for a person who does not have the respiratory synctial virus = 99%
We have;
a = TP =
b = FP
c = FN
d = TN
a/(a + c) = 0.97
d/(d + b) = 0.99
a/(a + b) = 0.97*0.0055/(0.97*0.0055 + (1 - 0.99)*(1-0.0055))
PPV = 0.349 = 34.9%
Therefore, we have;
a/(a + c) = 0.97 and
a/(a + b) = 0.349
0.97(a + c) =0.349(a + b)
(0.97 - 0.349)a = 0.349·b - 0.97·c
a = (0.349·b - 0.97·c)0.621
b × (1 - 0.0055) = (1 - 0.97)×(1 - 0.0055)
b = 1 - 0.97 = 0.03
Similarly,
c = 1 - 0.99 = 0.01
The proportion of the population that have false positive and false negative = 0.03 + 0.01 = 0.04 = 4%
The probability that a randomly selected person gets incorrect result = 0.04×0.0055 = 0.00022.
Answer:
0.01011
Step-by-step explanation:
Which of the following is an irrational number
o 18
o 2.6
o π
o -16/3
Answers
Answer:
pi
Step-by-step explanation:
A rational number can be written as a fraction
18/1 is a fraction
2.6666666 can be written as 2 2/3 = 8/3
-16/3 is a fraction
pi is a non repeating non termination decimal which is irrational
Answer:
The answer is π
Step-by-step explanation:
An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio.
The triangle shown below has an area of 4 units
Find the missing side.
Answers
Answer:
[tex]\boxed{4 units}[/tex]
Step-by-step explanation:
Hey there!
Well if the base is 4 and we use the formula,
b*h / 2
4*4 = 16
16/2 = 8
So x is 4.
Hope this helps :)
Answer:
x = 2 unitsStep-by-step explanation:
Area of a triangle is given by
base × height
[tex] A = \frac{1}{2} base × height[/tex]
From the question
Area = 4 units²
height = 4 units
let x represent the base
We have
[tex]4 = \frac{1}{2} \times x \times 4[/tex]
4 = 2x
Divide both sides by 2
x = 2 unitsHope this helps you
What is the factored form of the expression x^2-7x-18
Answers
Answer:
(x-9)(x+2)
Step-by-step explanation:
x^2-7x-18
What 2 numbers multiply to -18 and add to -7
-9*2 = -18
-9+2 = -7
(x-9)(x+2)
Answer:
Below.
Step-by-step explanation:
x^2 - 7x - 18
-9 * 2 = -18 and -9 +2 = -7 so the factors are:
(x - 9)(x + 2)
please help :) Geography doesn’t simply begin and end with maps showing the location of all the countries of the world. In fact, such maps don’t necessarily tell us much. No—geography poses fascinating questions about who we are and how we got to be that way, and then provides clues to the answers. ~Kenneth Davis The speaker in the passage above is stating that a. maps are not helpful to historians. b. human geography is more important than physical geography. c. historians want to know where people settled. d. physical features and locations tell historians about the ways people lived.
Answers
Answer:
d. physical features and locations tell historians about the ways people lived.
Step-by-step explanation:
I believe this is the correct answer
Please help!! Graph a line with a slope of 1/4 that contains the point (6,3).
Silly comments will the reported!!! Please explain if possible!!
Answers
To get a before point, start at the given point (6,3). Move along the x axis backwards four, and down 1. (2,2)
WORKED EXAMPLES
Try Vertical Angle Problems
ZC and Dare vertical angles.
m_C=° and mZD=(-3x +80)°
What is mZC
Enter your answer in the box.
Answers
Answer:
M<C = 20°
Step-by-step explanation:
Because they’re vertical angles, that means they’re equal to each other so:
m<C = m<D
x = -3x + 80
x + 3x = 80
4x = 80
x = 20
Since m<C equals x, that means m<C is 20°