Given:
RSTU is a parallelogram and ST is congruent to TU.
To find:
Why RSTU must also be a rhombus?
Solution:
We know that the opposite sides of a parallelogram are parallel and congruent.
RSTU is a parallelogram. So,
[tex]RS\parallel TU[/tex] and [tex]ST\parallel RU[/tex] [Property of parallelogram] ...(i)
[tex]RS\cong TU[/tex] and [tex]ST\cong RU[/tex] [Property of parallelogram] ...(ii)
It is given that,
[tex]ST\cong TU[/tex] ...(iii)
From (ii) and (iii), we get
[tex]RS\cong TU\cong ST\cong RU[/tex] ...(iv)
From (i) and (iv), we get RSTU is a rhombus because all sides are congruent and appositive sides are parallel.
A parallelogram with each side equal is known as rhombus.
As for the given parallelogram all the sides are equal, therefore it should be rhombus.
What is parallelogram is rhombus?Parallelogram is a closed shaped quadrilateral polygon in which opposite sides are equal and parallel and opposite angles are equal.
What is rhombus?Rhombus is a closed shaped quadrilateral polygon in which all the sides are equal and opposites sides are parallel also opposite angles are equal.
Given information-
In the given problem [tex]RSTU[/tex] is a parallelogram.
In the given parallelogram [tex]ST[/tex] is congruent to [tex]TU[/tex].
The image of parallelogram is attached below.
For a parallelogram opposite sides are equal. thus,
[tex]RS=TU\\RU=ST[/tex]
As In the given parallelogram [tex]ST[/tex] is congruent to [tex]TU[/tex]. Thus,
[tex]ST=TU[/tex]
Now the side [tex]ST[/tex] is equal to the side [tex]RU[/tex] and side [tex]RS[/tex] is equal to the side [tex]TU[/tex]. Thus,
[tex]RS=ST=TU=RU[/tex]
All the sides of a rhombus is equal in length. A parallelogram with each side equal is known as rhombus.
As all the sides are equal of the given parallelogram. Thus the given parallelogram is rhombus.
Hence, as for the given parallelogram all the sides are equal, therefore it should be rhombus.
Learn more about the parallelogram and rhombus here;
https://brainly.com/question/20627264
Emma has collected information about the cats and dogs that children in her class have as pets
there are 30 pupils total
find the number of children having both cats and dogs as pets
a.4
b.8
c.12
d.16
Answer:
c. 12
Step-by-step explanation:
the answer is c.12 due to the table
Please solve this and show your work. 9.4 + p = 4.8
Answer:
9.4 + p = 4.8
9.4 + p - 9.4 = 4.8 - 9.4
p = -4.6
Answer: p=-4.6
Step-by-step explanation:
you need to rearrange the terms first.
9.4+p=4.8
p+9.4-9.4=4.8-9.4
p=-4.6 after you subtract
This Question is confusing the heck out of me can someone help me with it.
The probability Bob guesses the winner of a certain baseball game is 4/5. The probability Joe independently guesses the winner of another game is 1/3. What is the probability that exactly one of them selects the winner? (Fraction answer)
SANA ALL SMART HAHAHAHHAAHHAHAAHA
Edward has $20,000 in a savings account that earns 13% interest per year. The interest is not compounded.How much interest will he earn in 1 year?
Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
$
Answer:
22,600
Step-by-step explanation:
which expression represents 2 more than the product 5 and 4.
A. (5+4)×2
B. (5×4)+2
C. 2+(5+4)
D.2×(5×4)
Answer:
i think it's B. (5 x 4) + 2
Step-by-step explanation:
pls give brainly crown
and if i'm wrong i'm sooooo sorry
help plz im confused
Answer:
x = 16
Step-by-step explanation:
Δ ABC and Δ ADE are similar , thus the ratios of corresponding sides are equal, that is
[tex]\frac{AB}{AD}[/tex] = [tex]\frac{BC}{DE}[/tex] , substitute values
[tex]\frac{x}{x+6}[/tex] = [tex]\frac{8}{11}[/tex] ( cross- multiply )
11x = 8(x + 6)
11x = 8x + 48 ( subtract 8x from both sides )
3x = 48 ( divide both sides by 3 )
x = 16
What is the slope-intercept form of this equation?
8x + y = 12
Answers:
Y= 2/3x + 2
Y= 4/3x + 6
Y= -4/3x + 6
Y= -4/3x + 2
Answer:
y = -8x + 12
Step-by-step explanation:
Slope intercept form: y = mx + b
m ---> Slope & b ----> y-intercept
8x + y = 12
Subtract 8x from both sides
y = -8x + 12
plz help fast (worth 15 pts) A prism and two nets are shown below:
Image of a right triangular prism and 2 nets. The triangle bases have base 4, height 3, and diagonal side 5. The length of the prism from the bases is 9.4. Net A has 3 rectangles in a row. The middle one has sides AC and CD. This middle one has triangle ABC on top and identical triangle below. Net B is the same except that the triangle base ABC is on top of the last rectangle which has sides AC and CD. Units are in inches.
Part A: Which is the correct net for the prism? Explain your answer. (2 points)
Part B: Write the measurements of Sides AB, BC, and CD of the correct net. (4 points)
Part C: What is the surface area of the prism? Show your work. (4 points)
Answer:
This is worth more than 15
Step-by-step explanation:
Image of a right triangular prism and 2 nets. The triangle bases have base 4, height 3, and diagonal side 5. The length of the prism from the bases is 8.6. Net A has 3 rectangles in a row. The middle one has sides AC and CD. This middle one has triangle ABC on top and identical triangle below. Net B is the same except that the triangle base ABC is on top of the last rectangle which has sides AC and CD. Units are in inches.
Step-by-step explanation:
Use the distributive property to rewrite the expression -1 (x -2)
Answer:
Step-by-step explanation:
Distributive property: a*(b + c) =(a*b) + (a*c)
Multiply x by (-1) and (-2) by (-1)
-1(x - 2 ) = (-1)*x - 2 *(-1)
= -x + 2
If f(x) = x3 + 4, then what is the remainder when f(x) is divided by x + 6?
Pls help
What is 4 1/2 + -17 1/4 it doesn’t have to be simplify xo
Answer:
-14 3/4
Step-by-step explanation:
i am not super sure about this. the fraction is right though. i hope
please help i will give brainliest, thanks
Answer:
2x-2 -2 is the y intercept and the 2x is the rate of change its easy lol
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
PLZ HELP RN ILL MARK YOU BRAINLIST IF ITS RIGHT PLZZZ IM DESPERATE
Answer:
x = 24
Step-by-step explanation:
What I would do is use inverse operation. First do -8 x -3 = 24. Then check your work by doing 24 divided by -3 = -8. So x = 24. I am 100% sure this is correct
Pls mark me brainliest
Find the circumference of a circle rounded to the nearest tenth with a
diameter of 4 inches
Answer:
12.6
Step-by-step explanation:
Circumference is πd. So...
(3.14*4)
12.56
12.6
Hope this helps and have a nice day ~(^_^)~
suppose you have a bag of 25 marbles and 3 of the marbles are white.If you choose one without looking, what is the probability you choose a white marble? Write this probability as a percent . Use a word or phrase to describe this probability.
Answer:
3/25
THERE IS AN 11% CHANCE
can i get brainliest
Step-by-step explanation:
Answer:
12%
Step-by-step explanation:
3 is 12% of 25. So you would have a 12 percent chance of getting a white marble.
3 ÷ 25 = 0.12 = 12%
Percent formula
P × V1 = V2
HI THIS IS MY SECOND QUESTION PART 2 TO MY FIRST COULD I PLEASE GET HELP?????>3
Answer:
6. A
7. C
8. C
9. B
10. D
osjshwjwowi
What is the equation of the line –3x–2y=30 in slope-intercept form?
change the equation to : y = mx + b
Enter your answer in the box.
Answer:
y=-3/2x-15
Step-by-step explanation:
slope of (0.2,-0.9) (0.5,-0.9) how do i solve this and get the answer
Step-by-step explanation:
THE SLOPE IS 0
HOPE THIS HELPS
Dante is mailing a box with a length of nine 1/2 inches a width of 8 inches and a height of 6 inches what is the volume of the box
Answer:
456 in³
Step-by-step explanation:
To find the volume of the box, use the volume formula, V = lwh
Plug in the length, width, and height:
V = lwh
V = (9.5)(8)(6)
V = 456
So, the volume of the box is 456 in³
what is 5.52×0.25 explain
Answer: 1.38
Step-by-step explanation:
552
x 25
02760
11040
02760+11040=13800.
then you put your decimal over 4 spots and you take the 2 zeros off the end and get your answer of
1.38somebody please help me ??
Answer: d pretty sure :)
Step-by-step explanation:
A cheese pizza costs $5, each additional topping is $ 1.25. If x
represents toppings, which equation represents the total cost
of the pizza?
Question 1
What is the distance between the points (-3, 4) and (5, 4)?
8 units
9 units
7 units
1 unit
If Mr. Phillips bought 1 3/4 pounds of raspberries, who bought more fruit, Ms. Winn or Mr. Phillips?
Answer:
i think mr phillip bought more fruit
Step-by-step explanation:
Thirty-two is the product of nine and a number decreased by four
Answer:
28
Step-by-step explanation:
32 - 9 = 23,
24 + 4 = 28
Answer:
28, If you need any more help lmk
Step-by-step explanation:
What is the common ratio for geometric sequence: 5,15,45,135 ?
Answer:
the common ratio is 3
Step-by-step explanation:
to solve for the common ratio, I like to take the second term and divide it by the first term
15/5 = 3
then I will check the rest of the terms
15*3 = 45
45*3 = 135
It looks like the common ratio is correct!
How do you graph a quadratic function?
Answer:
Step-by-step explanation:
Compare the equation with the standard form, y=ax2+bx+c . Since the value of a is positive, the parabola opens up.
So, y=0 implies, by the zero product property, x+4=0 or x−2=0 .
Substitute x=−1 in the equation y=−x2−2x+8 to find the y -coordinate of the vertex.
Select all the expressions that are equivalent to
1/2(2).
Z+Z
Z/2
Z/Z
1/4 (z)+1/4 (z)
2(z)
Answer:
Step-by-step explanation:
An ellipse is defined as the locus of all points,the sum of whose from two given points is constant. Here z is a complex number whose distance from (1,0) and (−1,0) is constant. Hence the locus of z is an ellipse in the complex plane. Hence z will be all those points which lies on the ellipse with focus (−1,0) and (1,0).
5x^3-2x^2+14x+7x^2+3x-11