All categories

3 years ago

Which biconditional statement is true?

Mathematics

2 answers:

tatyana61 [14]3 years ago

6 0

Answer: A shape is a rectangle if and only if the shape has exactly four sides and four right angles.

Step-by-step explanation:

If both a conditional statement and its converse statement is true then we write a combine form of both the statements known as a bi-conditional statement. It is written in the if and only if form.

From the given options only option one is correct because it is true from both ways.

It can be written as If a shape has exactly four sides and four right angles then the shape is a rectangle.

A shape is a trapezoid if and only if the shape has a pair of parallel sides.

It is not true because a if the shape has a pair of parallel sides then it can be a parallelogram.

A shape is a triangle if and only if the shape has three sides and three acute angles.

It is not true because a if the shape has three sides and three acute angles then it is only a acute triangle.

A shape is a square if and only if the shape has exactly four congruent sides.

It is not true because if the shape has exactly four congruent sides then it can also be rhombus.

So the only true bi-conditional statement is "A shape is a rectangle if and only if the shape has exactly four sides and four right angles. "

Oksana_A [137]3 years ago

4 0

Answer:

The first one: A shape is a rectangle if and only if the shape has exactly four sides and four right angles.

Step-by-step explanation:

The true statement is the first one:

A shape is a rectangle if and only if the shape has exactly four sides and four right angles.

You might be interested in

Show that if u+v and u-v are orthognal, then the vectors u and v must have the same length.

pashok25 [27]

Answer with Step-by-step explanation:

We are given that

u+ v and u-v are orthogonal

We have to prove that u and v must have the same length.

When two vector a and b are orthogonal then

$a\cdot b=0$

By using the property

$(u+v)\cdot (u-v)=0$

We know that

$(a+b)\cdot (a-b)=\mid a\mid^2-\mid b\mid^2$

$\mid u\mid ^2-\mid v\mid^2=0$

$\mid u\mid^2=\mid v\mid^2$

Magnitude is always positive

When power of base on both sides are equal then base will be equal

Therefore,

$\mid u\mid=\mid v\mid$

Hence, the length of vectors u and v must have the same length.

5 0

3 years ago

2% of the ducks in a pond have a fluffy tail. If 4 ducks have a fluffy tail, how many ducks are in the pond. Please answer best

GuDViN [60]

Answer:

200 ducks total in the pond

Step-by-step explanation:

2% of x equals 4

0.02x = 4

x = 200

6 0

3 years ago

Solve the equation on the interval [0,2π]

WARRIOR [948]

$\bf 16sin^5(x)+2sin(x)=12sin^3(x)
\\\\\\
16sin^5(x)+2sin(x)-12sin^3(x)=0
\\\\\\
\stackrel{common~factor}{2sin(x)}[8sin^4(x)+1-6sin^2(x)]=0\\\\
-------------------------------\\\\
2sin(x)=0\implies sin(x)=0\implies \measuredangle x=sin^{-1}(0)\implies \measuredangle x=
\begin{cases}
0\\
\pi \\
2\pi 
\end{cases}\\\\
-------------------------------$

$\bf 8sin^4(x)+1-6sin^2(x)=0\implies 8sin^4(x)-6sin^2(x)+1=0$

now, this is a quadratic equation, but the roots do not come out as integers, however it does have them, the discriminant, b² - 4ac, is positive, so it has 2 roots, so we'll plug it in the quadratic formula,

$\bf 8sin^4(x)-6sin^2(x)+1=0\implies 8[~[sin(x)]^2~]^2-6[sin(x)]^2+1=0
\\\\\\
~~~~~~~~~~~~\textit{quadratic formula}
\\\\
\begin{array}{lcccl}
& 8 sin^4& -6 sin^2(x)& +1\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array} 
\qquad \qquad 
sin(x)= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}
\\\\\\
sin(x)=\cfrac{-(-6)\pm\sqrt{(-6)^2-4(8)(1)}}{2(8)}\implies sin(x)=\cfrac{6\pm\sqrt{4}}{16}
\\\\\\
sin(x)=\cfrac{6\pm 2}{16}\implies sin(x)=
\begin{cases}
\frac{1}{2}\\\\
\frac{1}{4}
\end{cases}$

$\bf \measuredangle x=
\begin{cases}
sin^{-1}\left( \frac{1}{2} \right)
sin^{-1}\left( \frac{1}{4} \right)
\end{cases}\implies \measuredangle x=
\begin{cases}
\frac{\pi }{6}~,~\frac{5\pi }{6}\\
----------\\
\approx~0.252680~radians\\
\qquad or\\
\approx~14.47751~de grees\\
----------\\
\pi -0.252680\\
\approx 2.88891~radians\\
\qquad or\\
180-14.47751\\
\approx 165.52249~de grees
\end{cases}$

3 0

3 years ago

If 5 bulbs are $24.95 how much money is 1 bulb?

Elden [556K]

Answer:

4.99

Step-by-step explanation:

If you divide:

$24.95/5bulbs

you get

4.99/1 bulb

5 0

3 years ago

Looking at the Vertex Form of the quadratic function f(x) = a (x - h)2 + k, how does the ( h ) affect the parabola?

Kaylis [27]

Answer:

H affects horizontal shift (shift to the right or left) means moves graph right or left

Step-by-step explanation:

4 0

2 years ago