Answers
Step-by-step explanation:
To prove that two lines are perpendicular, when all we have are those two lines, we can use the Linear Pair Perpendicular Theorem - If two straight lines intersect at a point and form a linear pair of equal angles, they are perpendicular.
Our diagonals intersect at point O, so we'd need to show the two linear angles formed at that intersection point are equal, and we can do that with triangle congruency.
A rhombus is a parallelogram, so we will use what we already know about parallelograms - that the diagonals bisect each other.
It is then easy to show that the triangles ΔAOD and ΔAOB are congruent using the Side-Side-Side postulate, and from that that ∠AOD ≅ ∠AOB.
And now, since ∠AOD and ∠AOB are a linear pair, we use the Linear Pair Perpendicular Theorem - If two straight lines intersect at a point and form a linear pair of equal angles, they are perpendicular.
PROOF
(1) ABCD is a rhombus //Given
(2) AB=AD //definition of rhombus
(3) AO=AO //Common side, reflexive property of equality
(4) BO=OD // A rhombus is a parallelogram, a parallelogram's diagonals bisect each other
(5) △AOD≅△AOB //Side-Side-Side postulate.
(6) ∠AOD ≅ ∠AOB //Corresponding angles in congruent triangles (CPCTC)
(7) AC⊥DB //Linear Pair Perpendicular Theorem
The converse of this is also true: if a parallelogram's diagonals are perpendicular, it is a rhombus.
Related Questions
y = -[tex]\frac{4}{5}[/tex]x - 2
Which equation best describes the graph?
A. y = -[tex]\frac{4}{5}[/tex]x + 2
B. y = [tex]\frac{4}{5}[/tex]x + 2
C. y = [tex]\frac{5}{4}[/tex]x - 2
D. y = -[tex]\frac{5}{4}[/tex]x + 2
Answers
A meal costs $30 before tax and tip.
There is a 7% sales tax. After the tax, a 20% tip is
added.
What is the total after tax and tip?
Answers
Answer:
$38.1
Step-by-step explanation:
Tax: 30*0.07 = 2.1
Tip: 30*0.2 = 6
Total: 30 + 2.1 + 6 = 38.1
Do you know anything about y=mx+b
Answers
Answer:
yes
Step-by-step explanation:
your m is your slope,your b is the y-intercept, and your y is what you are solving for.
Answer:
Y=mx+b is an equation for a linear equation
M is the slope of the line and B is the y-intercept
The y-intercept of this line is the value of y at the point where the line crosses the y axis.
Every straight line can be represented by an equation: y = mx + b.
Hope this helps :))
Tyrone has 16 model airplanes on his shelf. He has 4 times as many model airplanes as model trains. How many model trains does Tyrone have?
Write multiplication and division equations to model and solve the problem. Use m for the unknown
Answers
Step-by-step explanation:
4m =16
divide both sides by 4
m = 4
he has 4 model trains
7x + 2y = 24
8x + 2y = 30
Answers
Answer:
x=6
so
6x7
42+ = 24/2
12-42
y=-30
Step-by-step explanation:
A heron is perched in a tree 50 feet above sea level. Directly below the heron, a pelican is flying 17 feet above sea level. Directly below the birds is a trout, swimming 23 feet below sea level.
A.What’s the difference in height between the pelican and the heron?
B.What’s the distance in height between the pelican.
C.what’s the difference in height between the pelican and the trout.
D.What’s the distance in height between the pelican and the trout.
Answers
Answer:
Step-by-step explanation:
Your answer
A = 73
B= 33
C = 40
D = 40
Mark it as Brainlist answer. Follow me.
A line has equation 2x + y=20 and a curve has equation y=a+
18/x-3, where a is a constant.
Find the set of values of a for which the line does not intersect the curve
Answers
Answer:
we have two equations:
2*x + y = 20
y = a + 18/x - 3
We want to find the values of a such that the graphs of the equations do not intersect.
The first step is to isolate y in the first equation.
now we get:
y = 20 - 2*x
Then we have the system of equations:
y = 20 - 2*x
y = a + 18/x - 3
If the line intersects the curve at a point (x, y), then at that point both functions have the same value of y, then:
20 - 2*x = y = a + 18/x- 3
We want to find a value of such that this does not happen.
Let's solve that equation and see what we can find.
20 - 2*x = a + 18/x - 3
20 + 3 = a + 18/x + 2*x
23 = a + 18/x + 2*x
(23 - a) = 18/x + 2*x
if we multiply all values by x, we get:
(23 - a)*x = 18 + 2*x^2
Then we have a quadratic equation, we can write this as:
2*x^2 - (23 - a)*x + 18 = 0
Now, remember that if the determinant of the quadratic function is smaller than zero, then the function does not have any real solution, then we need to find a such that the determinant of this quadratic equation is smaller than zero.
Remember that for a quadratic equation:
a*x^2 + b*x + c = 0 is:
b^2 - 4*a*c
In this case, the determinant is:
(-(23 - a))^2 - 4*2*18
(23 - a)^2 - 144
And this must be smaller than zero, then:
(23 - a)^2 - 144 < 0
23^2 - 2*23*a + a^2 - 144 < 0
529 - 46*a + a^2 - 144 < 0
a^2 - 46*a + 385 < 0
Notice that the function has a positive leading coefficient, then the arms of the function go upwards, then the region of the function that is smaller than zero is the values of a that are between both roots of a.
Then we need to solve:
a^2 - 46*a + 385 = 0
We can use the Bhaskara's equation to find the roots, the roots are given by:
[tex]a = \frac{-(-46) +- \sqrt{(-46)^2 - 4*1*385} }{2*1} = \frac{46 +-24}{2}[/tex]
Then the two roots are:
a₁ = (46 + 24)/2 = 35
a₂ = (46 - 24)/2 = 11
Then for all the values of a suc that:
11 < a < 35
The line does not intersect the curve.
Which equation does the model below represent? pls help !
Answers
Answer:
the answer to this is d
Step-by-step explanation:
x-3=5
I need help, I did 1-2b, but i do not mind someone answering it either way so I can double check, but I am mainly stuck with 2c and if someone can tell me the answer and as to why, it would mean a lot and you can get brainlest if it is the right answer :)
Answers
Answer:
i belive the answer is c because they always try and trick you making you choose the wrong one and all the evidence cites that it could be c!!
Step-by-step explanation:
Please help me with this !!
Answers
Answer:
akismsksksialoalqoq kskw! sola skkss
Step-by-step explanation:
smksmskkwow!skkw
Marie is saving $75 each week so she can buy a new laptop which costs $1200. She has already saved $125. Find the minimum number of weeks she will have to save in order to be able to make this purchase.
Answers
Answer:
Step-by-step explanation:
[tex]125+75w\ge 1200\\ \\ 75w\ge 1075\\ \\ w\ge 14.33\\ \\ \text{So she must save for at least 15 weeks.}[/tex]
Describe y= -3x+4 in words.
Answers
Answer:
y=-3x+4
put x =0
y=-3(0)+4
y=4
putx=1
y=-3(1)+4
y=-3+4
y=1
if Seth used 4 ounces of black beans, how many beans did he use altogether?
Answers
Answer: 4 Ounces.
Step-by-step Explanation: I don't know the full context of the problem, but if Seth used 4 ounces, that means that he used 4 ounces all together.
que es la radicasion
Answers
Answer:
La radicación es la operación inversa a la potenciación. Y consiste en que dados dos números, llamados radicando e índice, hallar un tercero, llamado raíz, tal que, elevado al índice, sea igual al radicando. En la raíz cuadrada el índice es 2, aunque en este caso se omite.
Can someone please help me with this? Right answer gets brainliest!!
Answers
Answer:
Part 1: y= 49
Part 2: y=12
Step-by-step explanation:
Part 1: The y is going up by 7, so if you add 7 to 42, you get 49
Part 2: The y is going up by 4, so if you add 4 to 8, you get 12
Someone please explain how to get the answers
Answers
Answer:
[tex] m\angle A =40\degree [/tex]
[tex] m\angle D =40\degree [/tex]
Step-by-step explanation:
By inscribed angle theorem:
[tex] m\angle A = \frac{1}{2} \times 80\degree [/tex]
[tex] m\angle A =40\degree [/tex]
[tex] m\angle D= \frac{1}{2} \times 80\degree [/tex]
[tex] m\angle D =40\degree [/tex]
El perímetro de un rombo es igual al de un pentagono regular más 9, y la medida del lado del rombo es el doble de lo que mide un lado del pentagono. ¿Cuánto miden los lados de cada figura?
Answers
Answer:
Rombo es 6
Pentágono es 3
Step-by-step explanation:
Formula del perímetro de un rhombus es 4a
Formula del perímetro de un pentágono es 5b
La pregunta dice
4a = 5b + 9
Otra vez, la pregunta dice la medida del lado del rombo es el doble de lo que mide un lado del pentagono. Entonces,
a = 2b
Si
4a = 5b + 9 y
a = 2b, entonces que
4(2b) = 5b + 9
8b = 5b + 9
8b - 5b = 9
3b = 9
b = 9/3
b = 3
si, b = 3, tan
a = 2(3)
a = 6
Entonces, la medida del lado del rombo es 6 y la medida del lado del pentágono es 3
Here is the assignment : You are "selling" the polynomial. You must convince the buyer you have the Best polynomial on the market by describing as many of its specific characteristics.
(Have fun and be creative, but most importantly, be accurate to avoid bad reviews)
Here is your Polynomial: f(x)=x^3-10x^2+28x-24
Answers
Step-by-step explanation:
A polynomial is an expression that can be built from constants and symbols called variables or indeterminates by means of addition, multiplication and exponentiation to a non-negative integer power. Two such expressions that may be transformed, one to the other, by applying the usual properties of commutativity, associativity and distributivity of addition and multiplication, are considered as defining the same polynomial.
A polynomial in a single indeterminate x can always be written (or rewritten) in the form
{\displaystyle a_{n}x^{n}+a_{n-1}x^{n-1}+\dotsb +a_{2}x^{2}+a_{1}x+a_{0},}a_{n}x^{n}+a_{n-1}x^{n-1}+\dotsb +a_{2}x^{2}+a_{1}x+a_{0},
where {\displaystyle a_{0},\ldots ,a_{n}}a_{0},\ldots ,a_{n} are constants and {\displaystyle x}x is the indeterminate.[2][3] The word "indeterminate" means that {\displaystyle x}x represents no particular value, although any value may be substituted for it. The mapping that associates the result of this substitution to the substituted value is a function, called a polynomial function.
This can be expressed more concisely by using summation notation:
{\displaystyle \sum _{k=0}^{n}a_{k}x^{k}}{\displaystyle \sum _{k=0}^{n}a_{k}x^{k}}
That is, a polynomial can either be zero or can be written as the sum of a finite number of non-zero terms. Each term consists of the product of a number – called the coefficient of the term[a] – and a finite number of indeterminates, raised to nonnegative integer
Find the equation of the line that passes through both points (6,-5) (0,3)
Answers
Answer:
y = -4/3x + 3
Step-by-step explanation:
QUESTION: If Z is the incenter of (triangle shape)TUV, find m(triangle shape)ZTV .
x =
m(triangle shape)ZTV = _ degrees
Answers
Solution :
It is given that Z is the incenter
So, we get from the figure
[tex]$5x +1= 8x -14$[/tex]
⇒ [tex]$-3x = -15$[/tex]
⇒ x = 5
So, [tex]$5x+1 = 26 ^\circ \text{ and}\ 8x-14 = 26^\circ$[/tex]
We have to find ∠ ZTU.
In Δ UTV,
∠ TUV + ∠ UTV + ∠ TVU = 180°
⇒ (2 x 21°) + ∠ UTV + (2 x 26°) = 180°
⇒ ∠ UTV = 180° - 52° - 42°
= 86°
So, [tex]$\angle ZTV = \frac{1}{2} \ \angle UTV$[/tex]
[tex]$ = \frac{1}{2} \times 86^\circ$[/tex]
[tex]$=43^\circ$[/tex]
Therefore, m ∠ ZTU = 43°
Ahh- yes—- I need help, again-
Answers
How can the decimal 1.245 repeating be written as a quotient of two integers?
Answers
Answer:
1244/999
Step-by-step explanation:
So we have 1.245245245245.... which we call x.
If we times this by 1000 (because 3 digits repeat) we get
1000x = 1245.245245245....
Subtract x from both sides:
999x = 1245.245245245... - 1.245245... = 1244
This means that x = 1244/999
This fraction cannot be simplified so this is the answer.
If you want to include the 1 in the repeating (1.2451245...) do the same but the sequence is 4 digits so times by 10000 instead.
what is the hcm of 18 and 45
Answers
Answer:
90
Step-by-step explanation:
90 Or, we can say that it is a method of breaking down the given integer into its prime factors. Therefore, the HCF of 18 and 45 is 9. Therefore, the HCF of 18 and 45 is 90.
Each unit on the grid represents 5
feet. About how far, in feet, is the
drinking fountain from
the bench?
A. 8.5 feet
B. 37.1 feet
C. 33.5 feet
D. 42.7 feet
Answers
Answer:
There's no grid but I'd say A if you can give me the grid I'll edit my answer
Step-by-step explanation:
Teddy is writing a proof about the figure shown on the coordinate plane below. He wants to show that quadrilateral WXYZ is a parallelogram.
Which statement proves that WXYZ is a parallelogram?
A. Show that segments WX and YZ have equal slopes.
B. Show that segments WX and YZ have equal lengths.
C. Show that the midpoints of segments WY and XZ are the same point.
D. Show that segments WX and XY have slopes that are opposite reciprocals of each other.
Answers
The statements are -
A. Show that segments WX and YZ have equal slopes.
B. Show that segments WX and YZ have equal lengths.
C. Show that the midpoints of segments WY and XZ are the same point.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Teddy is writing a proof about the figure shown on the coordinate plane below. He wants to show that quadrilateral WXYZ is a parallelogram.
The statements that prove WXYZ as a parallelogram are -
A. Show that segments WX and YZ have equal slopes.
B. Show that segments WX and YZ have equal lengths.
C. Show that the midpoints of segments WY and XZ are the same point.
Therefore, the statements are -
A. Show that segments WX and YZ have equal slopes.
B. Show that segments WX and YZ have equal lengths.
C. Show that the midpoints of segments WY and XZ are the same point.
To solve more questions on algebraic expressions, visit the link below-
brainly.com/question/1041084
#SPJ6
Evaluate the expression 30 + 10 -10
Answers
12.92 divided by 3.4 And if you can put how you solved it that also would be great
Answers
Answer:
The answer is 3.8
Step-by-step explanation:
Change the divisor 3.4 to a whole number by moving the decimal point 1 places to the right. Then move the decimal point in the dividend the same, 1 places to the right.
We then have the equations:
129.2 ÷ 34 = 3.800000
and therefore:
12.92 ÷ 3.4 = 3.800000
Both calculated to 6 decimal places.
( In 3.800000, you can take away the zeros, which will be equal to 3.8 )
I hope this was helpful! :)
You are reading a new book. On Monday you read 3 pages. On each day after that, you read 3 times the number of pages you read on the previous day. How many pages do you read on Thursday?
pages plz answer me
Answers
81 pages.
Step-by-step explanation:
Tuesday: 3 x 3 = 9
Wednesday: 9 x 3 = 27
Thursday: 27 x 3 = 81
Answer:
81
Step-by-step explanation:
3x3x3x3
what is the length of side n?
Answers
Answer:
6
Step-by-step explanation:
Does anyone know how to solve this?
Answers
Answer:
A point in polar coordinates is written as (R, θ)
If we want to transform this point to rectangular coordinates, we get:
x = R*cos(θ)
y = R*sin(θ)
Now we can remember that the sine and cosine functions have a period of 2*pi, then:
cos(θ) = cos(θ + 2*pi)
or:
cos(θ) = cos(θ + 2*pi + 2*pi)
and so on.
Then the point (R, θ) is the same as (R, θ + 2*pi) and (R, θ + k*(2*pi))
where k can be any integer number.
Then if we have a point in polar coordinates:
(-4, -5*π/3)
Then another two polar representations of this point are:
(-4, -5*π/3 + 2*π) = (-4, -5*π/3 + 6*π/3) = (-4, π/3)
Now we can not add 2*π (nor subtract) because we would have an angle outside the range [-2*π, 2*π]
For example, if we have:
(-4, π/3 + 2*π) = (-4, 7*π/3)
And we can not change the value of the radius and get the coordinates for the same point.
So another representation could be something like:
(-8/2, π/3)
Where i just wrote -4 in another way.
Now, a really important point.
When working with polar coordinates, we always use R as a positive number (here you can see that R is negative) so this is not the standard notation for the polar representation of a point.
