in the diagram of PARALLELOGRAM ABCD, segment BE is perpendicular to segment CED, segment DF is perpendicular to BFC and segment CE is congruent to segment CF.
Prove ABCD is a rhombus.
Answers
Answer:
In parallelogram ABCD
FD is perpendicular to BC
BE is perpendicular to CD
Consider triangle BEC and triangle DFC
FC = EC (Given)
Angle BEC = Angle DFC (=90°)
Angle BCE = Angle DCF (common)
Therefore triangle BEC is congruent to triangle DFC (AAS congruency)
DF = BE (CPCT)
Since the altitudes are equal their bases will also be equal
Therefore BC = DC
Therefore BC = DC = AD = AB
Therefore ABCD is a rhombus
Hope this helps!
Mark me as brainliest
Since [tex]\(ABCD\)[/tex] is a parallelogram with all four sides congruent, [tex]\(ABCD\)[/tex] is a rhombus. Hence, [tex]\(ABCD\)[/tex] is proven to be a rhombus.
To prove that parallelogram [tex]\(ABCD\)[/tex] is a rhombus, we need to show that all sides are congruent.
Given:
1. [tex]\(ABCD\)[/tex] is a parallelogram.
2. [tex]\(BE \perp CED\).[/tex]
3. [tex]\(DF \perp BFC\).[/tex]
4. [tex]\(CE \cong CF\).[/tex]
Proof:
1. Parallelogram Properties:
- In a parallelogram, opposite sides are congruent and parallel.
- Therefore, [tex]\(AB \parallel CD\)[/tex] and [tex]\(AD \parallel BC\)[/tex].
- Also, [tex]\(AB \cong CD\)[/tex] and [tex]\(AD \cong BC\)[/tex].
2. Congruent Segments:
- [tex]\(CE \cong CF\) (given).[/tex]
- Since [tex]\(BE \perp CED\)[/tex] and [tex]\(DF \perp BFC\)[/tex], [tex]\(BE\)[/tex] and [tex]\(DF\)[/tex] are heights from [tex]\(B\)[/tex] and [tex]\(D\)[/tex] respectively to line [tex]\(CED\)[/tex].
3. Triangle Congruence:
- Consider [tex]\(\triangle CEF\)[/tex]. Since [tex]\(CE \cong CF\)[/tex] and [tex]\(BE \perp CED\)[/tex], [tex]\(DF \perp BFC\)[/tex], [tex]\(\triangle CEF\)[/tex] is isosceles with base [tex]\(EF\)[/tex].
4. Diagonals in Parallelogram:
- Diagonals of a parallelogram bisect each other.
- Since [tex]\(\triangle CEF\)[/tex] is isosceles and [tex]\(CE = CF\)[/tex], the diagonals [tex]\(BE\)[/tex] and [tex]\(DF\)[/tex] bisect each other at [tex]\(E\)[/tex] and [tex]\(F\)[/tex].
5. Symmetry and Congruence:
- Since diagonals bisect each other and the height from [tex]\(B\)[/tex] and [tex]\(D\)[/tex] are equal, segments from [tex]\(B\)[/tex] and [tex]\(D\)[/tex] to the diagonals are congruent.
6. Sides of Parallelogram:
- From symmetry and congruence, all sides of the parallelogram are equal.
- Therefore, [tex]\(AB \cong BC \cong CD \cong DA\)[/tex].
Conclusion:
Since [tex]\(ABCD\)[/tex] is a parallelogram with all four sides congruent, [tex]\(ABCD\)[/tex] is a rhombus.
Hence, [tex]\(ABCD\)[/tex] is proven to be a rhombus.
Related Questions
I need help plz show steps
Answers
Answer:
D
Step-by-step explanation:
We will solve the equation by using quadratic formula.
x= (-b ± √(b^2-4ac))/2a
The standard form of quadratic equation is:
ax^2+bx+c=0
So by comparing with the standard form, we get:
a=1
b= -4
c=18
Putting the values in the formula
x= (-(-4)± √((-4)^2-4(1)(18)))/2(1)
x = (4± √(16-72))/2
x = (4± √(-56))/2
The minus sign in square root will introduce the imaginary symbol.
x = (4± √(14*4*(-1)))/2
The minus 1 can be replace by the imaginary i => i^2 = -1
x = (4± √(14*2^2*i^2 ))/2
The terms with squares can be brought out of the square root
So,
x = (4± 2i√14)/2
Taking 2 as common
x = (2(2± i√(14)))/2
x = 2± i√14
Kelsey is hiking from the woods to the lodge. She hikes past tree A (3 Miles) and B (4 Miles) in order to get to the lodge. How much distance should she have saved by going straight to the lodge from tree A ?
Answers
Answer:
1 mile
Step-by-step explanation:
The following expression represents the density of an object that has a mass of m and a volume of V.
M/V
If a laptop has a volume of 2,850 cubic centimeters and a mass of 2,300 grams, what is the density of the laptop in G/cm3
A. 1 5/23
B.15/19
C. 1 11/46
D. 46/57
Answers
Final answer:
The density of the laptop is calculated by dividing the mass (2,300 grams) by the volume (2,850 cubic centimeters), resulting in a density of 0.807 g/cm³, which is approximately 46/57.
Explanation:
To find the density of the laptop in grams per cubic centimeter (g/cm³), we use the formula density = mass/volume. The mass of the laptop is given as 2,300 grams and the volume is given as 2,850 cubic centimeters. By substituting into the formula:
Density = Mass / Volume = 2,300g / 2,850cm³ = 0.807 g/cm³.
When expressed as a fraction in simplest form, this is approximately 46/57 (since 0.807 ≈ 46/57). Hence, the answer is D. 46/57.
Fill in the blank so that the ordered pair is a solution of y=8x+3.
Answers
Answer:
11
Step-by-step explanation:
8 plus 3 i dunno know if it is forsure but yeah.
What’s the standard form of the following polynomial?
(3x-2)(x-1)+2(x-5)^2-25
Answers
Answer
x^2 + 4x - 49
Step-by-step explanation:
you have to do PEMDAS first then add all the like-terms
hope this helps
p.s. you're pretty
PERFORM THE MULTIPLICATION
(x–3)^2(x+3)^2
SOMEONE PLZZZ HELP
Answers
Answer:
81 is the answer
Step-by-step explanation:
Answer:
Hold up im solving it
Step-by-step explanation:
what does trace of matrix mean explain with examples
Answers
Trace of a matrix is defined only for a square matrix . It is the sum of the elements on the main diagonal, from the upper left to the lower right, of the matrix
The manager of a store that specializes in selling tea decides to experiment with a new blend.She will mix some Earl Grey tea that sells for $6 per pound with some Orange Pekoe tea that sells for $4 per pound to get 600 pounds of the new blend. the selling price of the new blend is $4.50 per pound and there was something to be no difference in revenue from selling the new blend versus selling the other types. how many pounds of the Earl Grey tea and orange Pekoe tea are required?
Answers
Answer:
Earl Grey: 150 poundsOrange Pekoe: 450 poundsStep-by-step explanation:
Let "e" represent the number of pounds of Earl Grey tea required for the mix. Then (600-e) is the number of pounds of Orange Pekoe tea required. The total cost of the mix is ...
6·e + 4·(600 -e) = 4.50·600
2e = 600·(4.50 -4.00) . . . . . simplify, subtract 4·600
e = 300/2 = 150 . . . . . . . . . . divide by the coefficient of x
Required are 150 pounds of Earl Grey and 450 pounds of Orange Pekoe.
The amount of Earl Grey and Pekoe tea required for the new blend is :
150 pounds of Earl450 pounds of PekoePrice of new blend per pound = $4.50
Price per pound of Earl tea = $6
Price per pound of Pekoe tea = $4
Let :
Pound of Earl tea = a
Pound of Pekoe tea = b
Converting the information to Mathematical expressions :
a + b = 600 - - - (1)6a + 4b = 600(4.50)6a + 4b = 2700 - - - (2)From (1):
a = 600 - b
Put a = 600 in (2)
6(600 - b) + 4b = 2700
3600 - 6b + 4b = 2700
Collect like terms :
-6b + 4b = 2700 - 3600
-2b = -900
b = 900 ÷ 2
b = 450
Recall :
a = 600 - b
a = 600 - 450
a = 150
Therefore,
Pound of Earl tea required = 150Pound of Pekoe tea required = 450Learn more : https://brainly.com/question/11335251
Is this answer ok, please help?
Answers
Answer:
Step-by-step explanation:
Unfortunately not...
The shape is a triangle, and the area formula is A=[tex]\frac{1}{2}[/tex]bh.
b = 5 ft.
h = 4 ft.
Therefore:
A = [tex]\frac{1}{2}[/tex](5)(4)=10ft
Ellie read 30 pages of her social studies book in 1.5 hours at a constant rate. She then switched to reading a novel and read 150 pages in 2 hours at a constant rate. Wh at percent of Ellie’s social studies reading rate is her Novel reading rate?
Answers
Social Studies rate, S = 30/ 1.5 = 20pages/hr
Novel rate, N = 150/2 = 75pages/hr
Novel rate as a % of Social Studies rate...
N/S × 100% = 75/20 × 100% = 375%
percent of Ellie’s social studies reading rate is her Novel reading rate is 375%.
What are mathematics operations?
A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value. The number of operands determines the operation's arity. Most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive and multiplicative inverses.
• Zero-arity operations, or nullary operations, are constants, and mixed products are arity three operations, or ternary operations.
Here, it is given that :
Ellie read 30 pages of her social studies book in 1.5 hours at a constant rate, let first find Ellie's social studies reading rate :
rate = 30 pages/1.5 hours = 20 pages/ hr.
Now, to find out the unit rate, divide the total number of pages reading novel by the total time spent.
rate = 150 pages/ 2 hours = 75 pages/ hr.
To find out the percentage divide Ellie's novel reading rate by Ellie's social studies reading rate and multiply by 100
percent of Ellie’s social studies reading rate is her Novel reading rate = 75/20 x 100 = 375%.
Therefore, percent of Ellie’s social studies reading rate is her Novel reading rate is 375%.
Read more about mathematics operations at:
https://brainly.com/question/17869111
#SPJ2
find the height, round to the nearest hundredth
Area is 72units squared
Answers
Answer:
[tex]\large\boxed{h=10\dfrac{2}{7}}[/tex]
Step-by-step explanation:
The formula of an area of a triangle:
[tex]A=\dfrac{bh}{2}[/tex]
We ahve b = 14 and A = 72. Substitute:
[tex]72=\dfrac{14h}{2}[/tex] multiply both sides by 2
[tex]144=14h[/tex] divide both sides by 14
[tex]h=\dfrac{144}{14}\\\\h=\dfrac{144:2}{14:2}\\\\h=\dfrac{72}{7}\\\\h=10\dfrac{2}{7}[/tex]
What is the slope of the line?
Answers
The slope is
[tex] - \frac{1}{3} [/tex]
Point W(5, -6) is reflected across the line y = -x. Which of the following is the location of its image, W’.
(-5, -6)
(5, 6)
(-6, 5)
(6, -5)
Answers
(6, -5)
Key Concepts for Reflections:if (a, b) is reflected on the x-axis, the image is the point (a, -b)if (a, b) is reflected on the y-axis, the image is the point (-a, b)if (a, b) is reflected on the line y = x, the image is the point (b, a)if (a, b) is reflected on the line y = -x, the image is the point (-b, -a)(5, -6) --> (-5, 6)
Hope this helps!!
I'd right the key concepts for future reference!
:D
Answer:
(6,-5)
Step-by-step explanation:
The form he builds is 40 1/2 in. long, 10 in. deep, and 8 in. high. How much cement is needed to fill the form
Answers
This question clearly states that it is a 'find the volume' question.
Given dimensions of the object are :
Length of the object = [tex]40\frac{1}{2}[/tex] inches or 40.5 inches
Depth of the object = 10 inches
Height of the object is = 8 inches
So, the volume becomes = [tex]40.5\times10\times8[/tex] = 3240 cubic inch
Hence, the amount of cement needed is 3240 cubic inches.
To fill the form, you use the formula for the volume of a rectangular prism (length x width x height) to find that 3240 cubic inches of cement is needed.
The student is asking about the volume of cement needed to fill a form with specified dimensions. To calculate the volume, we need to use the formula for the volume of a rectangular prism, which is length x width x height. In this case, we need to convert the mixed number into an improper fraction before multiplying, or we could convert it to a decimal.
First, convert the length from 40 1/2 inches to 40.5 inches. Then, use the formula:
Volume = length x width x height
Volume = 40.5 in x 10 in x 8 in
Volume = 405 in x 8 in
Volume = 3240 cubic inches
Therefore, to fill the form, 3240 cubic inches of cement is needed.
recognizing the no-solution case algebraically
need geometry help!!
Answers
Answer:
"The values for y are square roots of negative numbers"
Step-by-step explanation:
The steps shown are correct. But at the end we can see that we have to "take the negative square roots".
This means we have to take the square root of -1. In the real number system, we CANNOT take the square root of any negative number. Hence, there is NO SOLUTION to the system.
2nd answer choice, "The values for y are square roots of negative numbers", is right.
I NEED HELP REALLY BAD!
Answers
The area is 168 yd²
Step-by-step explanation:The area of Trapezoid is given by
A= (a+b)/2 * h
Putting the values
A = (5+23)/2 * 12
A = 168 yd²
Answer:
A = 168 Square Yards
How to solve for x in math
Answers
Answer:
x = 15; m<(3x) = 45; m<(2x + 15) = 45
Step-by-step explanation:
The measures of the angles measuring 3x and 2x + 15 add up to 90 degrees.
3x + 2x + 15 = 90
5x + 15 = 90
5x = 75
x = 15
m<(3x) = 3 * 15 = 45
m<(2x + 15) = 2 * 15 + 15 = 30 + 15 = 45
Is 6(4x-5) equivalent to 3+22x-33-2x?
YES or NO?????
Show your work!
6(4x-5) 3+22x-33-2x
Answers
Answer:
NO
Step-by-step explanation:
To find if they are equivalent, we need to simplify them first.
Using the distributive property we get:
6(4x-5) = 24x - 30
In this case we need to combine like terms.
3 + 22x - 33 - 2x = 20x - 30
So now we can compare.
24x - 30 ≠ 20x - 30
So we can conclude that the two expressions are not equal because 24x - 30 and 20x - 30 are obviously not equal.
Answer:
Not equivalent
Step-by-step explanation:
We are given an expression [tex] 6 ( 4 x - 5 ) [/tex] and we are to check if it is equal to [tex] 3 + 22 x - 33 - 2 x [/tex] or not.
Evaluation the given expression first:
[tex] 6 ( 4 x - 5 ) = 24 x - 30 [/tex]
While adding the terms in [tex] 3 + 22 x - 33 - 2 x [/tex], we get:
[tex] 22 x - 2 x - 33 + 3 = 20 x - 30 [/tex]
[tex] 24 x - 30 \neq 20 x - 30 [/tex]
Therefore, [tex] 6 ( 4 x - 5 ) [/tex] is not equivalent to [tex] 3 + 22 x - 33 - 2 x [/tex].
Y=f(x) = -1x find f(x) when x= 0
Answers
f(0) equals 0. When x is 0 in the given function, the result of f(x) is also 0.
To find the value of f(x) when x=0 for the function f(x) = -1x, substitute 0 for x:
f(0) = -1(0) = 0.
Therefore, f(0) equals 0. When x is 0 in the given function, the result of f(x) is also 0.
Gina has 400 records. If Johnny were to double the number of records that he now owns, he would still have fewer than Gina has.
Answers
Johnny currently owns fewer than 200 records.
Let's denote:
- \( x \) as the number of records Johnny currently owns.
Given:
- Gina has 400 records.
- Johnny would still have fewer than Gina has if he were to double the number of records he owns.
We can set up the following inequality:
[tex]\[ 2x < 400 \][/tex]
To find the maximum value of \( x \), we solve for it:
[tex]\[ x < \frac{400}{2} \]\[ x < 200 \][/tex]
So, Johnny currently owns fewer than 200 records.
Add -5+2/8 PLEASE HELP MEEE
Answers
[tex]\bold{Hey\ there!} \\ \bold{-5+\frac{2}{8}} \\ \bold{-5=-\frac{5}{1}}\\ \bold{Problem\ becomes\rightarrow -\frac{5}{1}+\frac{2}{8}} \\ \bold{\frac{2\div2}{8\div2}=\frac{1}{4}}\\ \bold{-\frac{5}{1}+\frac{1}{4}} \\ \bold{-5\times4=-20}\\ \bold{1\times4=4} \\ \bold{Problem\ becomes:\frac{-20+1}{4}} \\ \bold{-20+1=-19} \\ \bold{4=4} \\ \boxed{\boxed{\bold{Answer:\frac{-19}{4}}}}\checkmark[/tex]
[tex]\bold{Good\ luck\ on\ your\ assignment\ \& \ enjoy\ your\ day!} \\ \\ \\ \frak{LoveYourselfFirst:)}[/tex]
What is the value of x and y in degrees? Please show steps!
Answers
Check the picture below.
How do I solve? (10y+9)-(4y-8)=
Answers
Answer:
(6y+17)
Step-by-step explanation:
1. Subtract 4y from 10y to get 6y
2. 9 is positive and 8 is negative but to subtract a negative is basically adding so you would add 9 to 8
3. You final equation would be (6y+17)
4. (10y+9)-(4y-8)= (6y+17)
Answer:
(10y + 9) - (4y - 8) = 6y + 17Step-by-step explanation:
[tex](10y+9)-(4y-8)\\\\=10y+9-4y-(-8)\\\\=10y+9-4y+8\qquad\text{combine like terms}\\\\=(10y-4y)+(9+8)\\\\=6y+17[/tex]
Solve for x 34=-2x solve for x
Answers
Answer:
x = -17
Step-by-step explanation:
Divide both sides by two and get:
x = -17
Answer:
x=-17
Step-by-step explanation:
-2x=34
-2x/-2=34/-2
x=-17
how do I simplify 15x+42-8y+20-4x
Answers
Answer:
[tex]\large\boxed{15x+42-8y+20-4x=11x-8y+62}[/tex]
Step-by-step explanation:
[tex]15x+42-8y+20-4x\\\\\text{combine like terms}\\\\=(15x-4x)-8y+(42+20)\\\\=11x-8y+62[/tex]
You add like terms together.
Ex. You would add 15x and(-4x) together, giving you 11x
So to simplify it, you need to do 15x-4x, 42+20, and 8y would be left by itself since there are no like terms for 8y.
So the simplified version would be: 11x+62+8y
Factor the polynomial: x^3+x^2+x+1
Answers
Answer:
(x+1)(x2+1)
Step-by-step explanation:
Factor x3+x2+x+1
x3+x2+x+1
=(x+1)(x2+1)
also a great website for your problems is called mathpapa-algebra calculator
The area is a rectangle is 56 cm. The length is 2 cm more than x and the width is 5 cm less than twice x. Round to the nearest whole number.
Answers
Answer:
The solution is [tex]x=6\ cm[/tex]
Step-by-step explanation:
we know that
The area of rectangle is equal to
[tex]A=LW[/tex]
we have
[tex]A=56\ cm^{2}[/tex]
so
[tex]56=LW[/tex] ------> equation A
[tex]L=x+2[/tex] -----> equation B
[tex]W=2x-5[/tex] -----> equation C
Substitute equation B and equation C in equation A
[tex]56=(x+2)(2x-5)[/tex]
solve for x
[tex]56=(x+2)(2x-5)\\56=2x^{2}-5x+4x-10\\2x^{2}-x-66=0[/tex]
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]2x^{2}-x-66=0[/tex]
so
[tex]a=2\\b=-1\\c=-66[/tex]
substitute in the formula
[tex]x=\frac{1(+/-)\sqrt{-1^{2}-4(2)(-66)}} {2(2)}[/tex]
[tex]x=\frac{1(+/-)\sqrt{529}} {4}[/tex]
[tex]x1=\frac{1(+)23} {4}=6[/tex]
[tex]x2=\frac{1(-)23} {4}=-5.5[/tex]
The solution is [tex]x=6\ cm[/tex]
[tex]L=6+2=8\ cm[/tex]
[tex]W=2(6)-5=7\ cm[/tex]
Please please please please PLEASE answer
Answers
Yea it’s the second one
a fruit drink is made by mixing lemon juice, orange juice and lime juice in the ratio 5:2:3 james makes 400ml of the fruit drink how much lemon juice is used
Answers
Answer:
200ml
Step-by-step explanation:
5+2+3=10
400/10=40
Since lemon's ratio is 5, you multiply 40 by 5 to get 200.
Which word has a horizontal line of symmetry?
A. LIT
B. HAD
C. HIP
D. BED
Answers
D.Bed because if you were to split the word BED in half horizontally you would be able to put them together and it match up.