Answer:
a. The four sides of the quadrilateral ABCD are equal, therefore, ABCD is a rhombus
b. The equation of the diagonal line AC is y = 5 - x
The equation of the diagonal line BD is y = 5 - x
c. The diagonal lines AC and BD of the quadrilateral ABCD are perpendicular to each other
Step-by-step explanation:
The vertices of the given quadrilateral are;
A(1, 4), B(6, 6), C(4, 1) and D(-1, -1)
a. The length, l, of the sides of the given quadrilateral are given as follows;
[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
The length of side AB, with A = (1, 4) and B = (6, 6) gives;
[tex]l_{AB} = \sqrt{\left (6-4 \right )^{2}+\left (6-1 \right )^{2}} = \sqrt{29}[/tex]
The length of side BC, with B = (6, 6) and C = (4, 1) gives;
[tex]l_{BC} = \sqrt{\left (1-6 \right )^{2}+\left (4-6 \right )^{2}} = \sqrt{29}[/tex]
The length of side CD, with C = (4, 1) and D = (-1, -1) gives;
[tex]l_{CD} = \sqrt{\left (-1-1 \right )^{2}+\left (-1-4 \right )^{2}} = \sqrt{29}[/tex]
The length of side DA, with D = (-1, -1) and A = (1,4) gives;
[tex]l_{DA} = \sqrt{\left (4-(-1) \right )^{2}+\left (1-(-1) \right )^{2}} = \sqrt{29}[/tex]
Therefore, each of the lengths of the sides of the quadrilateral ABCD are equal to √(29), and the quadrilateral ABCD is a rhombus
b. The diagonals are AC and BD
The slope, m, of AC is given by the formula for the slope of a straight line as follows;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Therefore;
[tex]Slope, \, m_{AC} =\dfrac{1-4}{4-1} = -1[/tex]
The equation of the diagonal AC in point and slope form is given as follows;
y - 4 = -1×(x - 1)
y = -x + 1 + 4
The equation of the diagonal AC is y = 5 - x
[tex]Slope, \, m_{BD} =\dfrac{-1-6}{-1-6} = 1[/tex]
The equation of the diagonal BD in point and slope form is given as follows;
y - 6 = 1×(x - 6)
y = x - 6 + 6 = x
The equation of the diagonal BD is y = x
c. Comparing the lines AC and BD with equations, y = 5 - x and y = x, which are straight line equations of the form y = m·x + c, where m = the slope and c = the x intercept, we have;
The slope m for the diagonal AC = -1 and the slope m for the diagonal BD = 1, therefore, the slopes are opposite signs
The point of intersection of the two diagonals is given as follows;
5 - x = x
∴ x = 5/2 = 2.5
y = x = 2.5
The lines intersect at (2.5, 2.5), given that the slopes, m₁ = -1 and m₂ = 1 of the diagonals lines satisfy the condition for perpendicular lines m₁ = -1/m₂, therefore, the diagonals are perpendicular.
Mrs. Arnold took a survey of the types of pants her students were wearing. She collected the data below. What percent of her students were wearing shorts? Jeans: 14 Shorts: 9 Capris: 2
Answer:
36%
Step-by-step explanation:
Jeans: 14
Shorts: 9
Capris: 2
Total number of students = Number of Jeans + Number of Shorts + Number of Capris
Total number of students = 14 + 9 + 2 = 25
% of students wearing shorts = Number of shorts / Total number of students * 100
% of students wearing shorts = 9 / 25 * 100 = 0.36 * 100 = 36%
solve 16y² = 36 using the square root property
Answer:
2/3-3/2
Step-by-step explanation:
Find two positive numbers such that the sum of the first and twice the second is equal to 124 and whose product is a maximum. For your answer, type in the larger of the two numbers.
Answer:
Answer is in photo
Step-by-step explanation:
solve the inequality for n 14
Answer:
14n
Step-by-step explanation:
just rearrange the number with the variable
Inequ
What is the solution to the inequality -3.x + 7 > 1?
Х
DONE
Answer: x < 2
-3x + 7 > 1
<=> -3x > - 6
<=> x < -6/-3
<=> x < 2
Step-by-step explanation:
A rectangular prism is 12 cm long, 6 cm wideand 5 cm high. What is the volume of the rectangular prism?
Ariana has a dimes and y nickels. She has at most 12 coins worth a minimum of
$0.85 combined. Solve this system of inequalities graphically and determine one
possible solution.
9514 1404 393
Answer:
see attached (7 dimes, 5 nickels)
Step-by-step explanation:
The inequalities are plotted in the attachment. The solution shown is ...
(x, y) = (7, 5)
7 dimes and 5 nickels are 12 coins worth $0.90. This is the maximum number of coins, worth more than $0.85.
Solve the system by the method of your choice. Write your answer as a coordinate point (x,
y)
-6x + 5y = -27
- 3x + 3y = -115
What is an equation of the line that passes through the points (-6,-3) and (-3,-5)
Answer:
y = - [tex]\frac{2}{3}[/tex] x - 7
Step-by-step explanation:
A( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) , B( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )
m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
~~~~~~~~~~~~~
( - 6, - 3 )
( - 3, - 5 )
m = [tex]\frac{-5+3}{-3+6}[/tex] = - [tex]\frac{2}{3}[/tex]
y + 5 = - [tex]\frac{2}{3}[/tex] ( x + 3)
y + 5 = - [tex]\frac{2}{3}[/tex] x - 2
y = - [tex]\frac{2}{3}[/tex] x - 7
6. 5x + 3x + 38+5x-10 180
Answer:
38
Step-by-step explanation:
Simplifying
6 + -5x + -3x = 38
Combine like terms: -5x + -3x = -8x
6 + -8x = 38
Solving
6 + -8x = 38
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-6' to each side of the equation.
6 + -6 + -8x = 38 + -6
Combine like terms: 6 + -6 = 0
0 + -8x = 38 + -6
-8x = 38 + -6
Combine like terms: 38 + -6 = 32
-8x = 32
Divide each side by '-8'.
x = -4
Simplifying
x = -4
Answer:
I think the answer is 14.5x-132
Step-by-step explanation:
6.5x+3x+5x=14.5x
38+10-180=-132
=14.5x-132
A water tank contains 19 gallons of water. Raymond begins to add water to the tank at a rate of 7 gallons per minute. Which equation can be used to find y, the gallons of water in the tank after x minutes?
A y = 19x + 7
B y = x + 26
C y = 7x + 19
D y = 19x + 7x
Answer:
C y = 7x +19
Step-by-step explanation:
There are 19 gallons in the water tank and 7 gallons are added when you take x amount of minutes, which gives you y.
An example is 1 minute.
Y = 7(1) + 19
y = 7 + 19
y = 26
You have to remember that there are 19 gallons already in the tank and that 1 minute has passed, which means 7 gallons have been added. Thus there are 26 gallons in the water tank.
Hope this helps. :)
Answer:
I think the answer is A hopefully this helps
Diego compro un libro y tres cuadernos,pago por ellos 180 solo recuerda que el libre le costó el doble de lo que le costaron los tres cuadernos juntos
Answer: Cada cuaderno cuesta 20, y el libro 120.
Step-by-step explanation:
Vamos a definir:
L = precio de un libro
C = precio de un cuaderno.
Sabemos que Diego compro un libro y tres cuadernos por 180, entonces tenemos:
1*L + 3*C = 180
También sabemos que el libro costo el doble de lo que costaron los 3 cuadernos juntos, entonces:
L = 2*(3*C) = 6*C
Tenemos un sistema de ecuaciones:
1*L + 3*C = 180
L = 6*C
Para resolverlo, podemos reemplazar la segunda ecuación en la primera, para así obtener:
1*(6*C) + 3*C = 180
6*C + 3*C = 180
9*C = 180
C = 180/9 = 20
Cada cuaderno costo 20.
Y el precio del libro se puede obtener con la ecuación:
L = 6*C = 6*20 = 120
El libro costo 120
TVs are measured by
their diagonals. If a 60
inch TV has a height of
24 inches, how wide is
the screen?
Answer:
Step-by-step explanation:
Diagonal is 60 inches, height is 24 inches so
60^2 = 24^2 + width^2
6.25 inches
Find the value of k, if x + 3 is a factor of 3x² + kx + 6. *
Somebody help!!! Please!!!
Answer:
y = -1 !!!!!!!!!!! :)))))))))))))
Answer:
y=-1
Step-by-step explanation:
symmetry is where it is the same on both sides, so that would be the line between the top and bottom point and because they are up and down it is a y whereas if it were side to side it would be x. it is on the left side which are negatives and it is one over to the left making it y=-1
The air pressure P is inversely proportional to the altitude h. write the related variation equation
Step-by-step explanation:
P * h = k, where k is a real constant.
PLS HELP !!
A computer normally sells for $520. During a sale, the computer is
discounted 15% off. How much will it cost to buy the computer during the
sale? (Sale Price)
Answer:
$442
Step-by-step explanation:
Multiply the sales price by the discount percentage. This is the total discount that was taken off.
$520 x 15% = $78.
Subtract the discount amount from the sales price. This gives you the amount that the computer costs after the discount.
$520 - $78 = $442
The computer costs $442.
What are the answers here?
Answer:
1) =3
2)and 3) y-3x-2
Step-by-step explanation:
Hope that help!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The sum of the firstnith term of series
is given by Sn = n2+ 5 n-6. Find the
general term (tn) and (+20)
Answer:
Tn = 2n+4
T20 = 44
Step-by-step explanation:
Given Sn = n²+ 5 n-6
Tn = Sn - Sn-1
Sn-1 = (n-1)² + 5(n-1) - 6
Tn = n²+ 5n-6 - ((n-1)² + 5(n-1) - 6))
Tn = n²+ 5n-6-(n²-2n+1+5n-5-6)
Tn = n²+ 5n-6-n²+2n-1-5n+5+6
Tn = 2n-7+11
Tn = 2n+4
Get the general term is 2n+4
To get the 20th term;
T20 = 2(20) + 4
T20 = 40+4
T20 = 44
Hence the 20th term of the sequence is 44
Drag the tiles to the correct boxes. Not all tiles will be used.
What are the domain and the range of function f?
By undestanding the theory behind rational functions and functional theory, we conclude that the function have:
Domain: (- ∞, - 3) ∪ (- 3, + ∞)
Range: (- ∞, 0) ∪ (0, + ∞)
How to determine the domain and the range
In this question we have a rational function and we must determine its domain and range, whose elements exist if and only if the denominator evaluated at respective point is distinct of zero. Graphically speaking, the domain of the function represents the set of x-values, whereas the range represents the set of y-values.
By a graphing tool (i.e. Desmos) we construct the rational function and derive the following conclusions:
Domain: (- ∞, - 3) ∪ (- 3, + ∞)
Range: (- ∞, 0) ∪ (0, + ∞)
By undestanding the theory behind rational functions and functional theory, we conclude that the function have:
Domain: (- ∞, - 3) ∪ (- 3, + ∞)
Range: (- ∞, 0) ∪ (0, + ∞)
To learn more on rational functions: https://brainly.com/question/27914791
#SPJ1
Answer:
Range: (negative infinity, 0) U (0, 1/9) U (1/9, infinity)
Domain: (negative infinity, -3) U (-3, 6) U (6, infinity)
Step-by-step explanation:
100% on the test
If an object on earth weighs 42 lbs, what is its weight on the moon?
Answer:
6.93 lbs.
Step-by-step explanation:
The weight on the moon is approximately 16.5% of what you would weigh on Earth. Using this information, we can say that 16.5% of 42 lbs would equal how much the object would weigh on the moon.
I prefer to convert percentages the decimal way, so let's do it that way. 16.5% is 0.165 as a decimal, so now all we have to do is multiply 0.165 by 42 (since we are saying 16.5% of 42 lbs), and we get 6.93 lbs.
Hope this helps! :)
A cylinder has a volume of 360 cubic centimeters. Find the volume of a cone with the same height and diameter as
the cylinder.
Formula for the cylinder = V=πr2h
Formula for the cone = 1/3πr²H
Description:
So if the cone and a cylinder have the same radius and the same height then it will be greater. So plug in these formula.
Formula:
Vcone = 3Vcone
Vcylinder = 360cm³
Vcone = 1/3 360cm³ = 120cm³
Answer: 120cm³
Hope this helps.
Suppose that scores on a particular test are normally distributed with a mean of 140 and a standard deviation of 18. What is the minimum score needed to be in the top 5% of the scores on the test? Carry your intermediate computations to at least four decimal places, and round your answer to one decimal place.
Answer:
153.16
Step-by-step explanation:
We solve using z score formula
z = (x-μ)/σ, where
x is the raw score = ???
μ is the population mean = 140
σ is the population standard deviation = 8
Top 5% means the score is in the 95th percentile
The z score of 95th percentile = 1.645
1.645 = x - 140/8
Cross Multiply
1.645 × 8 = x - 140
13.16 = x - 140
x = 13.16 + 140
x = 153.16
Therefore, the minimum score needed to be in the top 5% of the scores on the test is 153.16
PLZZ HELP ME AND ONCE AGAIN THANK YOU
Answer:
2nd option
Step-by-step explanation:
the domain is from 0 to infinity
we count 0 because
f(0)=1 (just look in the graph)
so
[tex]x \geq 0[/tex]
which is the 2nd option
Plss answer!!
MERRY Christmas!!!
Critical Question. AAAAA
Answer:
Step-by-step explanation:
abc = 1
We have to prove that,
[tex]\frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}=1[/tex]
We take left hand side of the given equation and solve it,
[tex]\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+\frac{1}{c}}+\frac{1}{1+c+\frac{1}{a}}[/tex]
Since, abc = 1,
[tex]\frac{1}{c}=ab[/tex] and c = [tex]\frac{1}{ab}[/tex]
By substituting these values in the expression,
[tex]\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+\frac{1}{c}}+\frac{1}{1+c+\frac{1}{a}}=\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+ab}+\frac{1}{1+\frac{1}{ab}+\frac{1}{a}}[/tex]
[tex]=\frac{b}{b+ab+1}+\frac{1}{1+b+ab}+\frac{ab}{ab+1+b}[/tex]
[tex]=\frac{1+b+ab}{1+b+ab}[/tex]
[tex]=1[/tex]
Which equal to the right hand side of the equation.
Hence, [tex]\frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}=1[/tex]
In △ABC, AB = 13.2m, BC = 6.9m and ∠ACB = 90°. H lies on AC such that ∠BHC = 46°. Find (i) ∠ABH (ii) The length of AH
Answer:
(i) ∠ABH = 14.46⁰
(ii) The length of AH = 4.6 m
Step-by-step explanation:
From the image uploaded;
Consider △ABC;
the length of b is calculated by applying Pythagoras theorem as follows;
b² = c² - a²
b² = (13.2)² - (6.9)²
b² = 126.63
b = √126.63
b = 11.25 m
Also, ∠ABC is calculated as;
[tex]Cos \ B = \frac{a^2+c^2-b^2}{2ac} \\\\Cos \ B = \frac{(6.9)^2+(13.2)^2-(11.25)^2}{2(6.9 \times13.2)}\\\\ Cos \ B = \frac{95.288}{182.16} \\\\ Cos \ B = 0.5219 \\\\B = Cos ^{-1} (0.5231)\\\\B = 58.46 ^o[/tex]
Consider △CBH, ∠CBH is calculated as;
∠CBH = 90⁰ - 46⁰ = 44⁰
(i) ∠ABH will be calculated as;
∠ABH = θ
θ + 44⁰ = ∠ABC
θ + 44⁰ = 58.46⁰
θ = 58.46⁰ - 44⁰
θ = 14.46⁰
Thus, ∠ABH = 14.46⁰
(ii) The length of AH
length HC is calculated as;
[tex]tan \ 46^o =\frac{6.9}{HC} \\\\HC = \frac{6.9}{tan \ 46^o } \\\\HC = 6.66 \ m[/tex]
length of AH = CA - HC
x = b - HC
x = 11.25 - 6.66
x = 4.6 m
length of AH = 4.6 m
You had $24 to spend on eight
raffle tickets. After buying them
you had $8. How much did each
raffle ticket cost?
Answer:
$2 each ticket is 2 dollars
Sorry for the blurry picture I'm in a rush if anyone could help me that would be amazing
Answer:
y=1/2x
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form y/x=k or kx
The value of the constant k is equal to the value of the slope m
In this problem we have the point (8,4)
Find the value of k
y/x=k------> substitute the value of x and y
4/8=k
k=1/2
The equation is equal to
y=1/2x
Find the coefficient of correlation between and X and Y if covariance between X and Y is 15 and the variance of X and Y are respectively 10 and 25
Answer:
0.95
Step-by-step explanation:
[tex]Correlation \ coefficient \ (r) = \dfrac{covaraince \ between \ X \ and \ Y }{SD_X \times SD_Y }[/tex]
[tex]Correlation \ coefficient \ (r) = \dfrac{15 }{10^{1/2} \times 25^{1/2} }[/tex]
[tex]Correlation \ coefficient \ (r) = \dfrac{15 }{3.162 \times 5 }[/tex]
[tex]Correlation \ coefficient \ (r) = \dfrac{15 }{15.81 }[/tex]
[tex]Correlation \ coefficient \ (r) \simeq 0.95[/tex]
Simplify the expression.
. [tex]$8x-5+2x$[/tex]
Answer:
[tex]10x - 5[/tex]
Step-by-step explanation:
Combine like terms