Answer:
2x * ( 5x + 2 )
Step-by-step explanation:
10x^2 = 2x * 5x
4x = 2x * 2
10x^2 + 4x = 2x * ( 5x + 2 )
Graph the solution to the following inequality on the number line,(x + 6) (x-3) 20
If you have an equality of the form...
[tex](x+a)\cdot(x-b)\ge0[/tex]The inequality can be writen as...
[tex]a\leq x\leq b[/tex]I'll show you how it looks like on the graph
the graph indicates that x is any value less than or equal to -6 or greater than or equal to 3, which is the red area
[tex]\begin{gathered} x\leq-6 \\ x\ge3 \end{gathered}[/tex]Given A(2,4) and B(5,-4) from problem #1. What is the slope of a line that is parallel to (AB) ⃡?What is the slope of a line that is perpendicular to (AB) ⃡?
Solution
Given that
[tex]\begin{gathered} A(2,4) \\ B(5,-4) \end{gathered}[/tex]To find the slope, m, of the line passing through the given points, the formula is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where
[tex]\begin{gathered} (x_1,y_1)\Rightarrow A(2,4) \\ (x_2,y_2)\Rightarrow B(5,-4) \end{gathered}[/tex]Substitute the coordinates into the formula to find the slope, m, of a line
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-4-4}{5-2}=\frac{-8}{3}=-\frac{8}{3} \\ m=-\frac{8}{3} \end{gathered}[/tex]The slope of the line AB passing through the given points is m = -8/3
A) If two lines are parallel, their slopes are equal.
Hence, the slope, m₁ of the line that is parellel to line AB is
[tex]m_1=-\frac{8}{3}[/tex]Thus, the slope of a line parallel to line AB is m₁ = -8/3
B) If two lines are perpendicular, the formula to find the slope m₂ of the line perpedicular to the slope of a given line
[tex]m_2=-\frac{1}{m_{}}[/tex]Where m = -8/3, the slope, m₂, of a line perpendicular to line AB will be
[tex]\begin{gathered} m_2=-\frac{1}{m_{}} \\ m_2=-\frac{1}{\frac{-8}{3}_{}}=\frac{3}{8} \\ m_2=\frac{3}{8} \end{gathered}[/tex]Thus, the slope of a line perpendicular to line AB is m₂ = 3/8
PLEASE HELP!!
An ice cube is freezing in such a way that the side length s, in inches, is s of t equals one half times t plus 4 comma where t is in hours. The surface area of the ice cube is the function A(s) = 6s2.Part B: Find the surface area as a function of time, using composition, and determine its range. (4 points)
Answer:
A(t) = 3/2t² + 24t + 96
Range = (96, ∞)
Explanation:
The equation for the side length of the cube s is given by
[tex]s(t)=\frac{1}{2}t+4[/tex]Where t is the number of hours. In the same way, the equation for the surface area is:
[tex]A(s)=6s^2[/tex]Then, the surface area as a function of time will be the composite function A(s(t)). So, replacing s by the equation of s(t), we get:
[tex]\begin{gathered} A(s(t))=6s(t)^2 \\ A(s(t))=6(\frac{1}{2}t+4)^2 \\ A(t_{})=6(\frac{1}{4}t^2+2(\frac{1}{2}t)(4)+4^2) \\ A(t)=6(\frac{1}{4}t^2+4t+16) \\ A(t)=6(\frac{1}{4}t^2)+6(4t)+6(16) \\ A(t)=\frac{3}{2}t^2+24t+96 \end{gathered}[/tex]Then, the range is the set of all the possible values that A(t) can take. Since t takes values greater than or equal to 0, the minimum value that A(t) will take is 96 because:
A(0) = 3/2(0)² + 24(0) + 96 = 96
Therefore, the range for the surface area will be (96, ∞)
Maria is using a meter stick to determine the height of a door. If the smallest unit on the meter stick iscentimeters, which measurement could Maria have used to most accurately record the height of thedoor?23 meters2 meters2.309 meters2.31 meters
The most accurate measure of the height in meters is in two decimal places
The most accurate measure for maria to use is 2.31meters
The Forth option is correct
Find the magnitude of u using the dot product. Write the result in radical form or decimal form, rounded to the nearest hundredth.u = (-2,-5)
|u| = √29
Explanations:Since we are only given one vector, we cannot compute its dot product. However, the magnitude of a vector (x, y) is expressed as:
[tex]|u|=\sqrt{x^2+y^2}[/tex]Given the vector u = (-2, -5), the magnitude of u is expressed as:
[tex]\begin{gathered} |u|=\sqrt{(-2)^2+(-5)^2} \\ |u|=\sqrt{4+25} \\ |u|=\sqrt{29} \end{gathered}[/tex]Hence the magnitude of the vector in radical form is √29
Estimating which integers are between square roots- please explain the steps!
Hello there. To solve this question, we want to determine how to find the square root of a value using estimations.
Given a number m, we want to determine an estimation for its square root:
[tex]\sqrt{m[/tex]In this case, we have to find the closest integers to m, considering it is not a perfect square and is positive (greater than zero).
Of course, zero is the trivial case, since every square root is bounded below by zero.
For this, consider the function:
[tex]\lfloor m\rfloor[/tex]It is the floor function and it gives us the nearest integer that is less than or equal to m.
We do the same to fi
hello can yoy help with this plane trigonometry question and in the question turn it into radians and thank you for your time for helping me
Answer:
The angle between 0 and 2 pie that is coterminal to the given angle is;
[tex]\frac{6}{7}\pi[/tex]Explanation:
We want to find the angle between 0 and 2 pie that is coterminal to;
[tex]\frac{34}{7}\pi[/tex]Angles that are coterminal with the given angle can be calculated using the formula;
[tex]x+n2\pi=\frac{34}{7}\pi[/tex]Where n=1,2,3...
and x is the coterminal angle.
At n = 1;
[tex]\begin{gathered} x+2\pi=\frac{34}{7}\pi \\ x=\frac{34}{7}\pi-2\pi \\ x=\frac{34}{7}\pi-\frac{14}{7}\pi \\ x=\frac{20}{7}\pi \end{gathered}[/tex]at n=2;
[tex]\begin{gathered} x+2(2\pi)=\frac{34}{7}\pi \\ x+4\pi=\frac{34}{7}\pi \\ x=\frac{34}{7}\pi-4\pi \\ x=\frac{34}{7}\pi-\frac{28}{7}\pi \\ x=\frac{6}{7}\pi \end{gathered}[/tex]At n=2;
The value of x is between 0 and 2pie;
So, the angle between 0 and 2 pie that is coterminal to the given angle is;
[tex]\frac{6}{7}\pi[/tex]cosx-sin^2x-1how do I write the expression in factored form as an algebraic expression of a single trigometric function?
You use the next trigonometric inentities:
[tex]\begin{gathered} \sin ^2x+\cos ^2x=1 \\ \\ \sin ^2x=1-\cos ^2x \end{gathered}[/tex][tex]\begin{gathered} \cos x-\sin ^2x-1 \\ \\ =\cos x-(1-\cos ^2x)-1 \\ =\cos x-1+\cos ^2x-1 \\ =\cos x+\cos ^2x-2 \\ \end{gathered}[/tex]Common factor cosx:
[tex]=\cos x(1+\cos x)-2[/tex]-3v - 14> 3v+16 It’s for my final review and I’m so confused
The given inequality is
-3v - 14 > 3v + 16,
Add 3v on both side of the inequality
-3v -14 +3v > 3v +16 +3v
-3v +3v -14 > 3v + 3v + 16
0 - 14 > 6v + 16
Subtract 16 from both side of the equation,
-14 - 16 > 6v + 16 - 16
-30 > 6v + 0
Now subtract 6v from both side,
-30- 6v > 6v - 6v
-6v -30 > 0
Add 30 on both side,
-6v -30 + 30 > 30
-6v > 30
Divide both side by 6:
-6v/6 > 30/6
-v > 5
Multiply both side by (-1)
(-1) (-v) < (-1) 5
v < -5
Thus, v < -5
Answer : v < -5
Answer:
v < -5
Step-by-step explanation:
Add 14 to each side
[tex]-3v-14+14 > 3v+16+14[/tex]
Next, you need to simplify these additions by adding non-variable integers
[tex]16 + 14 = 30\\= 3v + 30\\= -3v > 3v + 30[/tex]
Now, subtract each side by 3v, the leading term in this equation.
[tex]-3v-3v > 3v+30-3v[/tex]
Again, we must simplify to get to the next step. This time we are dealing with a negative minus a negative. There on, things get trickier. In short words, a negative minus a positive is going to have a negative result, because both sides are treated as a negative plus a negative. In an equation, -a - b is the same as -a + -b.
[tex]-3v - 3v = -3v + -3v\\= -6v\\3v + -3v = 3v - 3v\\= 0\\= 0 + 30\\= 30\\= -6v > 30[/tex]
Next, we must multiply both sides by -1. The reason we're multiplying by a negative instead of a positive is because we are reversing the inequality.
[tex]= -6v\times -1 < 30\times 1[/tex]
Notice the change from greater than to less than.
IMPORTANT NOTE: A negative times a negative is a positive, a positive times a positive is also a positive. Lastly, a negative times a positive is a negative.
[tex]-6v\times -1 = 6v\\30\times -1 = -30\\= 6v < -30[/tex]
For the next step, we must divide by 6, because 6 can be divided by 6, and -30 can also be divided by 6 fairly.
[tex]\frac{6v}{6} < \frac{-30}{6}\\\frac{6v}{6} = \frac{6\times v}{6}\\Assume\:v=1!\\= \frac{6\times 1}{6}\\= \frac{6}{6}\\= 1\\= v[/tex]
[tex]\frac{-30}{6}\\\\(-a)/b = (-a/b)\\\\=-\frac{30}{6}\\= -5[/tex]
And therefore, v is less than -5.
If you need anything else, let me know!
Hope this helps!
i need the answer i can’t figure it out and my teacher won’t help
Solution:
From the given question, we have
To solve for the ramp angle from the ground, we use trigonometric ratios.
Thus, we have
[tex]\sin\theta=\frac{opposite}{hypotenuse}[/tex]This gives
[tex]\begin{gathered} \sin\theta=\frac{11.5}{175} \\ \Rightarrow\sin\theta=0.06571 \\ take\text{ the sine inverse of both sides} \\ \sin^{-1}(\sin\theta)=\sin^{-1}(0.06571) \\ \theta=3.77^{\circ\:} \\ \therefore \\ \theta\approx3.8\degree(nearest\text{ tenth\rparen} \end{gathered}[/tex]Hence, to the nearest tenth, the ramp angle is
[tex]3.8\degree[/tex]What is 0.6222... as. a fraction, and how do I solve?
The given number is
[tex]0.6222\ldots[/tex]This number is a repeating decimal number, which is a rational number because it has a pattern that repeats infinitely. That pattern or period is 2.
To transform this decimal number into a fraction, we need to do it as follows
[tex]0.6\bar{2}=\frac{62-6}{90}[/tex]Notice that the difference is form by the complete number without a decimal point (62), and the digits before the repeating decimal (6). The denominator is formed by nines and zeros, in this case, we use one 9 because there's only one repeating digit, we use one 0 because there's only one digit between the decimal points and the repeating digit.
Now, we solve the fraction and simplify
[tex]0.6\bar{2}=\frac{62-6}{90}=\frac{56}{90}=\frac{28}{45}[/tex]Therefore, the fraction 28/45 is the one that represents the repeating decimal 0.6222...Provide the correct reason for the statement in line 4.
We have to prove x = -16/3.
The steps are:
[tex]1)3(x+5)=-1\longrightarrow\text{Reason: Given}[/tex][tex]2)3x+15=-1\longrightarrow\text{Reason: Distributive property}[/tex][tex]3)3x=-16\longrightarrow\text{ Reason: substracting 15 from both sides}[/tex][tex]4)x=-\frac{16}{3}\longrightarrow\text{ Reason: divide both sides of the equation by 3}[/tex]enter each answer as a whole number the ratio of United States gold-medal to Russia gold medal was about _________ to 1 b about _________ %of Australia's total medals were gold.
the ratio of United States gold-medal to Russia gold medal was about 46/24=23/12 to 1
about %of Australia's total medals were gold.
Give the domain of the following rational function using (a) set-builder notation and (b) interval notation.f(y) = y —— y-1 ——————————————————(a) Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A. The domain of the given function is {yly is a real number, y # ____}(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)B. The domain of the given function is {yly is a real number).
ANSWER:
(a)
A. The domain of the given function is {yly is a real number, y ≠ 1}
(b)
[tex]\begin{equation*} D=\left(-\infty\:,\:1\right)\cup\left(1,\:\infty\:\right) \end{equation*}[/tex]STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]f(y)=\frac{y}{y-1}[/tex]The domain of a function, are the input values of the function, in this case, it corresponds to the values that y can take.
Since it is a rational function and it cannot take values that make the denominator zero, so we set the denominator equal to zero, like this:
[tex]\begin{gathered} y-1=0 \\ \\ y\ne1 \end{gathered}[/tex](a)
That means that y can take the value of all reals except 1.
So the correct answer is:
A. The domain of the given function is {yly is a real number, y ≠ 1}
(b)
In its interval form it would be:
[tex]D=\left(-\infty\:,\:1\right)\cup\left(1,\:\infty\:\right)[/tex]I need help with multi step equations if anybody that would be great
We have the following equation:
[tex]28=-k+16-2k-9[/tex]They ask us to solve this equation, in this case, we must solve for "k"
Now, we clear k
[tex]\begin{gathered} 28=-k+16-2k-9 \\ 28=-3k+7 \\ 3k=-28+7 \\ 3k=-21 \\ k=-\frac{21}{3} \\ k=-7 \end{gathered}[/tex]Compared with your solution, this is also correct, let's see the last step in which you are
[tex]\begin{gathered} -3k=21 \\ k=\frac{21}{-3} \\ k=-7 \end{gathered}[/tex]Your solution to this equation is correct in each step you did, you just need to move on to divide the (-3) to the other side
In conclusion, the answer si k = -7
if the point (-1,4)and (2,13)are on the graph of the quadratic function [tex]y = 7x {}^{2} + bx + c[/tex]what are the values of b and c
The Solution:
Given:
[tex]y=7x^2+bx+c[/tex]Given that the points: (-1,4) and (2,13) are on the graph of the given equation,
We are required to find the values of a and b.
Substitute (x= -1, y = 4) in the equation, we get:
[tex]\begin{gathered} 4=7(-1)^2+b(-1)+c \\ 4=7-b+c \\ -3=-b+c...eqn(1) \end{gathered}[/tex]Substitute (x= 2, y = 13) in the equation, we get:
[tex]\begin{gathered} 13=7(2)^2+b(2)+c \\ 13=28+2b+c \\ -15=2b+c...eqn(2) \end{gathered}[/tex]Solving eqn(1) and eqn(2) simultaneously by the elimination method:
Subtract eqn(1) from eqn(2):
[tex]\begin{gathered} -15--3=2b--b+c-c \\ -12=3b \end{gathered}[/tex]Divide both sides by 3.
[tex]b=\frac{-12}{3}=-4[/tex]Substitute -6 for b in eqn(1).
[tex]\begin{gathered} -3=-b+c \\ -3=-(-4)+c \\ \\ -3=4+c \\ -3-4=c \\ -7=c \\ c=-7 \end{gathered}[/tex]Therefore, the correct answers are:
b = -4
c = -7
Stats To quality for a police academy, applicants are given a lest of physical Itness. Ihe scores are normallyDistributed with a mean of 64 and a standard deviation of 9. If only the top 20% of the applicants are selected,Find the cutoff score.
Since we want just the top 20% applicants and the data is normally distributed, we can use a z-score table to check the z-score that gives this percentage.
The z-score table usually shows the percentage for the values below a certain z-score, but since the whole distribution accounts to 100%, we can do the following.
We want a z* such that:
[tex]P(z>z^*)=0.20[/tex]But, to use a value that is in a z-score table, we do the following:
[tex]\begin{gathered} P(zz^*)=1 \\ P(zz^*)=1-0.20=0.80 \end{gathered}[/tex]So, we want a z-score that give a percentage of 80% for the value below it.
Using the z-score table or a z-score calculator, we can see that:
[tex]\begin{gathered} P(zNow that we have the z-score cutoff, we can convert it to the score cutoff by using:[tex]z=\frac{x-\mu}{\sigma}\Longrightarrow x=z\sigma+\mu[/tex]Where z is the z-score we have, μ is the mean and σ is the standard deviation, so:
[tex]\begin{gathered} x=0.8416\cdot9+64 \\ x=7.5744.64 \\ x=71.5744\cong72 \end{gathered}[/tex]so, the cutoff score is approximately 72.
On a local sports team, 20% of 50 players are left-handed. How many left-handed are on the team?There is/are ____ left-handed player(s) on the team. (Type a whole number.)
Answer:
10 left-handed players
Explanation:
The total number of players on the team = 50
We are told that 20% of 50 players are left-handed.
Therefore, the number of left-handed players will be:
[tex]\begin{gathered} =20\%\text{ of 50} \\ =\frac{20}{100}\times50 \\ =\frac{20}{2} \\ =10\text{ players} \end{gathered}[/tex]There are 10 left-handed players on the team.
What is the equation of the line graphed below?A. y = -2xB. y = 2xC. y - xD. y = -x(1,2)
Answer:
B) y = 2x
Explanation:
We were given the following details:
The straight line passes through the origin; it passes through the point (0, 0)
The straight line passes through the point (1, 2)
[tex]\begin{gathered} (x_1,y_1)=(0,0) \\ (x_2,y_2)=(1,2) \end{gathered}[/tex]The general equation of a straight line is given by:
[tex]\begin{gathered} y=mx+b \\ where: \\ m=slope \\ b=y-intercept \end{gathered}[/tex]We will obtain the equation of the straight line as shown below:
I. Obtain the slope of the straight line
[tex]\begin{gathered} \begin{equation*} slope,m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \end{equation*} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{2-0}{1-0} \\ m=\frac{2}{1}=2 \\ m=2 \\ \\ \therefore slope,m=2 \end{gathered}[/tex]The slope of the straight line is 2
II. Obtain the y-intercept
Method 1:
The y-intercept refers to the point where the straight line crosses the y-axis.
In this case, the straight line crosses the y-axis at the origin (0, 0). This implies that:
[tex]\begin{gathered} b=0 \\ Remember:y=mx+b \\ \Rightarrow y=2x+0 \\ y=2x \end{gathered}[/tex]Method 2:
Using the point-slope equation:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-0=2(x-0) \\ y-0=2x-0 \\ y=2x \\ \\ \therefore y=2x \end{gathered}[/tex]Therefore, the answer is B (y = 2x)
The U.S. Weather Bureau has a station on Mauna Loa in Hawaii that has measured carbon dioxidelevels since 1959. At that time, there were 326 parts per million of carbon dioxide in theatmosphere. In 2005, the figure was 366 parts per million. Find the increase in carbon dioxide levelsand the percent of increase, to two decimal places.Increase carbon dioxide levels:parts per millionPercent increase:%
Answer:
12.27 % increase
Carbon dioxide increased by 40 ppm
Explanation:
We know that carbon diox
what is 7.950•100? and how to do it?
This problem uses the symbol •, which is another symbol to denote multiplication. Also, we are multiplying a decimal to 100. When multiplying such number, we move the decimal place to the right by two since we are multiplying the decimal by 100.
For this problem, we have
[tex]7.950\cdot100[/tex]We are multiplying 7.950 by 100. This means that we move the decimal point two times to the right. Hence, 7.950 multiplied by 100 will yield
[tex]7.950\cdot100=795.0[/tex]Answer: 795.0
6. What is the equation in standard form of the line that passes through the point 2 ? (10,-3) and has a slope of 5
The standard form of equation of line is :
[tex]y=m(x-x_1)+y_1[/tex]In the given question, we have coordinates : (10,-3) and slope m = 2/5
[tex]\begin{gathered} y=m(x-x_1)+y_1 \\ y=\frac{2}{5}(x-10)+(-3) \\ y=\frac{2}{5}x-\frac{2}{5}(-10)+(-3) \\ y=\frac{2}{5}x-2(-2)+(-3) \\ y=\frac{2}{5}x-4-3 \\ y=\frac{2}{5}x-7 \\ y+7=\frac{2}{5}x \\ 5y+35=2x \\ 2x\text{ -5y =35} \end{gathered}[/tex]The equation of line is 2x - 5y = 35
Anwer : C) 2x - 5y = 35
35,876 rounded to nearest 100 and 1000
EXPLANATION:
To round a figure we must look specifically at what place value is the number immediately after the comma.
for example:
35,876 rounded round to the nearest thousand:
ANSWER:
As the figure that follows after the comma approaches 9, immediately add one unit to 5, transforming the number into an approximate value of 36,000
Now rounded to nearest 100:
35,900
to round to 100 we only look at the three-unit figures that correspond to the hundred, that is, the place value of the figure after the comma.
Pretty please help!!!If x= -3, which number line shows the value of |x|?
it is given that
x = -3
now
IxI = I-3I = 3
so
IxI = 3
so the correct answer is option C
write an equation in slope intercept form of the line that is perpendicular to the line Y equals 1/4 x -9 and passes through 1, 1
For perpendicularity
[tex]\begin{gathered} \text{slope of line 1 =}\frac{-1}{slope\text{ of line 2}}_{} \\ \text{slope of line 1 = m}_1 \\ \text{slope of line 2 =m}_2 \end{gathered}[/tex][tex]\begin{gathered} \text{Hence,} \\ m_1=\frac{-1}{m_2} \end{gathered}[/tex][tex]\begin{gathered} \text{From the question} \\ m_1=\text{ }\frac{1}{4} \end{gathered}[/tex][tex]undefined[/tex][tex]3 = \frac{g}{ - 4} - 5[/tex]what does g equals ?
To solve the equation, first, add 5 to both sides
[tex]\begin{gathered} 3=\frac{g}{-4}-5 \\ 3+5=\frac{g}{-4}-5+5 \\ 8=\frac{g}{-4} \end{gathered}[/tex]Now, multiply by -4 from both sides of the equation
[tex]\begin{gathered} 8\cdot-4=\frac{g}{-4}\cdot-4 \\ -32=g \end{gathered}[/tex]Therefore, the value of g is -32.
Suppose you walk 2 miles in 35 minutes.Write a proportion to find how far you would walk in an hour if you were to continue at the same rate.이A.1235CaB.235C.235OD60235
To find the required proportion, you first write down the proportion between the distance you walk and time, just as follow:
proportion = 2/35
In this case numerator is distance and denominator is time in minutes.
Now, if you want to know hof war you would walk in 1 hour (60 mins) with the same rate, you can write:
for 1 hour:
x/60 =
x is the uknown distance, which have to stay in the numerator, and denominator is 60 because 1 hour = 60 mins.
But the two previous expression must be equal because you walk at the same rate both times. Hence, the searched equation is:
2/35 = x/60
find X and Y so that the quadrilateral is a parallelogram 5y 5x 25
x=31
y=5
Explanation
Step 1
if the green angles are equal and the blue angles are equal, then
is is a parallelogram, then
[tex]\begin{gathered} green\text{ angle} \\ 5y=25 \\ \\ y=\frac{25}{5} \\ \\ y=5 \end{gathered}[/tex]Step 2
blue angles
we do not have the value for the last angle, but we know
" the sum of the internal angles of a quadrilateral = 360
replacin
2 green angles +1 blue angle+5x=360
2*5y+5x+5x=360
[tex]\begin{gathered} 10y+10x=360 \\ 10x=360-10y \\ x=36-y \\ \text{replace }y=5 \\ x=36-5 \\ x=31 \end{gathered}[/tex]I hope this helps you
what's the simplest form to represent the area of a rectangular building that's 2y feet and the length to be 9y-4
The area of a rectangle is given by the formula:
[tex]A=lw[/tex]Where
A is area
l is length
w is width
We find the expression for the area by multiplying the two "lengths" given:
[tex]\begin{gathered} A=2y(9y-4) \\ A=18y^2-8y \end{gathered}[/tex]The answer is:
[tex]A=18y^2-8y[/tex]Which of the following is true about a kite?a.All angles are rightb.The diagonals have the same lengthc.All four sides are equald.Adjacent sides are congruent
In a kite, there is always an angle that is not right, otherwise, it would have a rectangular shape.
The diagonals are not of the same length because that would mean it would have a rectangular shape as well.
The sides are not equal, because that would mean it would have a rhomboid shape, to which a square belongs to.
The top edges are congruent with each other, as well as the bottom ones. This is because you can turn one into the other by reflecting them using an isometry, so D is true.