An open area at a local high school is in the shape of a quadrilateral. two sidewalks crisscross this open area as diagonal of the quadrilateral. If the walkways cross at their midpoints and the walkways are equal in length, what is the shape of the open area?

a rectangle
a rhombus
a parallelogram
a trapezoid

Answers

Answer 1

The quadrilateral must be a rectangle.

Based on the properties of quadrilaterals, if the diagonals are congruent and bisect each other, it is a rectangle.

Related Questions

Find dy/dx by implicit differentiation. 8 cos x sin y = 6

Answers

8sin(x)cos(y) = 6
Take derivative with respect to x. Since y is a function of x, take the derivative for y as well but it is multiplied by dy/dx

chain rule
8cos(x)cos(y) - 8sin(x)sin(y)(dy/dx) = 0

solve for dy/dx

8cos(x)cos(y) = 8sin(x)sin(y)(dy/dx)

[8cos(x)cos(y)]/[8sin(x)sin(y)] = dy/dx
simplify
cot(x)cot(y) = dy/dx

A wet bicycle tire leaves a trace of water on the floor. The tire has a radius of 14 inches, and the bicycle wheel makes 3 full rotations before stopping. How long is the trace of water left on the floor? Give your answer in terms of pi.

Answers

now, the bicycle made 3 rotations, namely 3 revolutions, before stopping, one revolution is a full circle, namely 2π radians angle, so 3 times that is 3 * 2π, or 6π.

[tex]\bf \textit{arc's length}\\\\ s=r\theta \quad \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ ------\\ r=14\\ \theta =6\pi \end{cases}\implies s=14\cdot 6\pi [/tex]

I assume the question is "how long is the track of water left by the tire?" The circumference of the tire is the distance around the tire and is equal to: C = 2·pi·radius C = circumference pi=3.14159 r = radius = 14 inches The track of water left on the floor by one full rotation of the tire equals one circumference in length. If the tire rotates 3 full times, the track of water is 3 circumferences long. Use your calculator to get the answer.

x * 1 + x/1 = _______.

Answers

x*1+x/1
=x+x/1
=x+x
=2x

HOPE IT HELPS UH!!☺☺

X * 1 = x

x/1 = x

x + x = 2x

Your answer is 2x

Hope I helped!

Let me know if you need anything else! I love this kind of math!

~ Zoe

find the volume of this prism

Answers

Hello!

The volume formula for a rectangular prism is length x width x height, so all we need to do is plug in the numbers.

L x W x H = V
12.5 x 4.5 x 4.2 = V
236.25 = V

Don't forget the units! We say cubed because the prism is 3-Dimensional but if it was 2-D we would say squared.

The volume is 236.25 centimeters cubed.

A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1.3 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall? (That is, find the angle's rate of change when the bottom of the ladder is 8 ft from the wall.)

Answers

check the picture below.

so, when r = 10 and x = 8, the vertical distance is 6, namely in pythagorean theorem lingo, b = 6.

let's keep in mind that, the ladder is not growing any longer or shrinking, and therefore is constantly always just 10, that matters, since is just a scalar value and also because the derivative of a constant is 0.

[tex]\bf cos(\theta )=\cfrac{x}{r}\implies cos(\theta )=\cfrac{1}{10}x\implies \stackrel{chain~rule}{-sin(\theta )\cfrac{d\theta }{dt}}=\cfrac{1}{10}\cdot\stackrel{chain~rule}{\cfrac{dx}{dt}\cdot 1}[/tex]

[tex]\bf -sin(\theta )\cfrac{d\theta }{dt}=-\cfrac{1}{10}\cdot \cfrac{dx}{dt}\implies \cfrac{d\theta }{dt}=-\cfrac{1}{-10sin(\theta )}\cdot \cfrac{dx}{dt} \\\\\\ \begin{cases} \frac{dx}{dt}=1.3\\ sin(\theta )=\frac{6}{10} \end{cases}\implies \cfrac{d\theta }{dt}=-\cfrac{1}{10\cdot \frac{6}{10}}\cdot 1.3\implies \cfrac{d\theta }{dt}=-\cfrac{1.3}{6}~radians[/tex]

The angle's rate of change when the bottom of the ladder is 8ft from the wall is

[tex]\dfrac{-1.3}{6} rad/s[/tex]

It is given the Length of Ladder [tex](h)[/tex] is [tex]10ft.[/tex]. and the distance between the bottom of the ladder to the wall [tex](r)[/tex] is [tex]8ft.[/tex] as shown in the below figure.

By using the Pythagoras Theorem

[tex]b=\sqrt{10^{2}-8^{2} }\\=\sqrt{36} \\=6ft.[/tex]

and

[tex]cos(\theta)= r/h\\cos(\theta)=r/10[/tex]

Differentiating both sides with respect to [tex]'t'[/tex] by using the chain rule

[tex]-sin(\theta)\dfrac{\mathrm{d}\theta }{\mathrm{d} t}=\dfrac{1}{10} \dfrac{\mathrm{d}r }{\mathrm{d} t}\\\\\dfrac{\mathrm{d}\theta }{\mathrm{d} t}=\dfrac{1}{10} \dfrac{\mathrm{d}r }{\mathrm{d} t} \dfrac{1}{-sin(\theta)} } ......(eq. 1)[/tex]

given

[tex]\dfrac{\mathrm{d}r }{\mathrm{d} t}=1.3ft./s\\sin(\theta)=\frac{6}{10}[/tex]

putting this in eq.1, we get

[tex]\dfrac{\mathrm{d} \theta}{\mathrm{d} t} = \dfrac{1.3}{10} (\dfrac{1}{-\frac{6}{10} }) \\\dfrac{\mathrm{d} \theta}{\mathrm{d} t} =\dfrac{-1.3}{6} rad/s[/tex]

So the angle's rate of change when the bottom of the ladder is 8ft from the wall is[tex]\dfrac{-1.3}{6} rad/s[/tex].

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The sum of 5 consecutive numbers is 135

Answers

27+27+27+27+27 is 135

Answer:

Step-by-step explanation:

The answer is 25+26+27+28+29=135

Is the correct answer I basically divided 135 by 5 and got 27 then I just worked around that number to get the answer.

I need help with this question

Answers

Solve each inequality by itself.

2x - 6 < -12      and        3x + 5 > -13

Add 6 to both sides                            Subtract 5 from both sides

2x < -6                                 and         3x > -18

Divide both sides by 2                        Divide both sides by 3

x < -3                                   and         x > - 6

You can write the solution as

x > - 6 and x < -3

To graph, draw a number line.
Place an open dot on -6.
Place an open dot on -3.
Draw a wide, dark line from one dot to the other dot.

Jill had an AGI of $25,000. She had $2800 in medical expenses, paid $6000 in rent, and had to buy a new uniform for work, which was not reimbursed by her employer. Which expense(s) can she itemize on her tax return? A.Nonreimbursed work expenses, mortgage interest, and medical expenses B.Mortgage interest and medical expenses C.Mortgage interest only D.Medical expenses and nonreimbursed work expenses.

Answers

D. medical expenses and nonreimbursed work expenses

Answer:

medical expenses and non-reimbursed work expenses

Step-by-step explanation:

Just did test

What is the arc length of an angle of 2π 3 radians formed on the unit circle? A) π 3 B) 2π 3 C) 4π 3 D) 5π 3

Answers

The correct answer is:

2π/3.

Explanation:

An angle formed on the unit circle would be a central angle.

The measure of an intercepted arc is the same as the measure of the central angle; since the angle is 2π/3, the arc length is 2π/3.

The arc length of an angle of 2π/3 radians formed on the unit circle is 2π/3.

To find the arc length of an angle of 2π/3 radians on the unit circle, we can use the formula:

Arc Length = Radius * Angle

Since we are considering the unit circle, the radius is 1. Therefore, the arc length is equal to the measure of the angle.

In this case, the angle is 2π/3 radians. So, the arc length is 2π/3.

The correct option is A) π/3.

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Larry used a pattern of colors to make a cube train he use Red Cube a blue cube a Red Cube and another Red Cube before he started the pattern again he use 15 cubes how many red cubes did Larry use

Answers

To answer this you can create the pattern up to and including the 15th term.

Red, Blue, Red, Red
Red, Blue, Red, Red
Red, Blue, Red, Red
Red, Blue, Red

Gary used 11 red cubes to make his cube train that was 15 cubes long.

What is the solution to the system of equations graphed on the coordinate plane?

Answers

The graph of the linear equation is a number of points in the coordinate plane that all are solutions to the equation. In other words, the points in which the line(s) form to create an intersection are a solution.

(3,4) would be the answer on e2020/edge

Suppose you have 15 days until your field trip and you need to raise $900 there are 10 students going on the field trip they will each help fundraise how much should each student have raised in 1 week?

Answers

I think the answer is $90.

35 less than 7 times a number is 98. what is the number?

Answers

The answer is nineteen (19).Let us use this equation: 7x-35= 98x stands for the missing number.To solve for x, we will transfer the -35 to the side of 98, and it will look like this: 7x= 98+35 (NOTE: Once we transfer a number on the other side, their signs will change too. For example, the -35 became positive 35 when it was transferred to the side of the 98)Then, 7x= 133, divide both sides by 7 so that the x will remain. 133/7= 19.Therefore, x=19

Population y grows according to the equation dy/dt=ky, where k is a constant and t is measured in years. if the population doubles every 10 years, then the value of k is

Answers

k = ln(2^(1/10)) ≈ 0.0693147

Given that the population doubles every ten years, k may be found using the population growth equation dy/dt=ky by computing ln(2)/10, or roughly 0.0693 annually.

We begin by thinking about the solution to the differential equation dy/dt = ky, where the population doubles every ten years, in order to determine the value of k. This differential equation can be solved generally as y(t) = y(0)e^kt, where y(0) is the beginning population.

Since there are ten years between population doubling, we can write: y(10) = 2y(0) = y(0)e^10k.

The result of dividing both sides by y(0) is 2 = e^10k.

We get: ln(2) = 10k by taking the natural logarithm on both sides.

After calculating k, we have k = ln(2)/10 ≈ 0.0693.

Thus, k's value is around 0.0693 per year.

Which expression represents the sum of 2/3m - 1 1/6 and 5/6m - 1 1/3

Answers

the options in the attached figure

we have that

[(2/3)m - 1 1/6]+[(5/6)m - 1 1/3]

step 1
1 1/6--------> (1*6+1)/6-----> 7/6
1 1/3--------> (1*3+1)/3------> 4/3

step 2
[(2/3)m - 1 1/6]-------> [(2/3)m - 7/6]-------> [(2*2m-7)]/6------> [4m-7]/6

[(5/6)m - 1 1/3]------- [(5/6)m - 4/3]-------> [(5m-4*2)]/6--------> [5m-8]/6

step 3

[(2/3)m - 1 1/6]+[(5/6)m - 1 1/3]----------> [4m-7]/6+[5m-8]/6-----> [9m-15]/6

[9m-15]/6-----------> (9m/6)-(15/6)------> 1.5m-2.5-----> (1 1/2)m-2 1/2

the answer is the option
c.) 1 1/2m - 2 1/2

HELP PLZ WILL GIVE BRAINLIEST

For what value of x:

is the square of the binomial x+1 twenty greater than the square of the binomial x–3?

Answers

I find it easier just to graph this sort of question rather than multiply it all out.

x = 3.5

_____
(x^2 +2x +1) -(x^2 -6x +9) = 20
.. 8x -8 = 20
.. x = 28/8 = 3.5

Final answer:

The value of x for which the square of the binomial (x+1) is twenty greater than the square of the binomial (x-3) is 3.5.

Explanation:

The student is asking for a value of x for which the square of the binomial (x+1) is twenty greater than the square of the binomial (x-3). To find this value, we set up an equation based on the given information:

(x + 1)² = (x - 3)² + 20

First, we expand both squares:

x² + 2x + 1 = x² - 6x + 9 + 20

Now, simplify and move all terms to one side to solve for x:

8x = 28

Divide both sides by 8 to find the value of x:

x = 28 / 8

x = 3.5

Therefore, the value of x for which the square of (x+1) is twenty greater than the square of (x-3) is 3.5.

Start with the number n = 54527. Divide n by 5 and round the result up to an integer. Keep repeating the division and rounding step until the resulting number is less than 5. How many divisions are performed? You can use a calculator for this problem, but you should not have to actually perform all of the divisions.

Answers

Without rounding, I make it six. You could do it this way
54527/5^6 comes to a little over 3. That should be close enough. I'm going to check this by doing the divisions. I could let the computer do it, but I'd like to see if there's a pattern. There isn't and the correct answer is

6 <<<< divisions.

The question involves applying the concept of significant figures and rounding numbers during divisions to determine how many times 54527 must be divided by 5 before it becomes less than 5 without manually performing each division.

The question asks for the number of times the number n = 54527 needs to be divided by 5 and rounded up until it is less than 5. This is a problem that can be solved by understanding exponential decay and the concept of significant figures. It is also an exercise in rounding numbers appropriately. To determine the number of divisions without actually performing each division, one can use logarithms.

The concept of significant figures is important in this context, as each division reduces the number of significant figures by approximately one (since we're dividing by a number that has only one significant figure, 5). The rule is that when dividing, the number of significant figures in the result should be the same as the smallest number of significant figures in the input values.

Here's the process:

Apply logarithms to find the exponent x in 5ˣ = n.Recognize that each division by 5 reduces the exponent by 1.Calculate the number of times x must be reduced by 1 until the value is less than 1, which corresponds to the original number being less than 5.

The original calculation without the repetition of divisions would use logarithms to solve for x in 5ˣ = 54527, or log5(54527). However, for the purposes of this example and to avoid calculator work, we can estimate that since 5⁴ = 625 and 5⁵ = 3125, it will take more than 4 but significantly fewer than 10 divisions (as 510 is much greater than 54527) to make the number less than 5.

Consuela earns a salary of $40,000 per year plus a commission of $1,00 for each car she sells. Write and solve an equation that shows the number of cars Consuela must sell in order to make $60,000 in one year.

Answers

60000=40000+100x
20000=100x
x=200

Im thinking her commission should be 1000, not 100, and if so, your equation would be

60000=40000+1000
20000=1000x
x=20

Answer:

y = $1,000/car x + $40,000

20 cars

Step-by-step explanation:

Let

x = number of cars sold

y = total earnings

The relationship between y and x can be expressed through a linear equation.

y = mx + b

where,

m is the slope

b is the y-intercept

The slope is how much she earns per car sold, that is, the commission of $1,000/car (I think you meant this number instead of $1,00).

The y-intercept is what she earns even if she does not sell any car, i.e. a salary of $40,000.

The resulting equation is

y = $1,000/car x + $40,000

If she is to make $60,000 in one year (y = $60,000), the number of cars sold is:

$60,000 = $1,000/car x + $40,000

$20,000 = $1,000/car x

x = 20 car

Which equations represent inverse variation? Check all that apply.
y = 2x
pv = 13
z = (2/x)
4 = (y/x)
h = (9g/5)

Answers

For this case, what you should know is that the equations that represent an inverse variation are those that could not form a straight line, for example.

We have then:
Equation 1:
pv = 13
Rewriting:
p = 13 / v
P and v are represent an inverse variation.
Equation 2:
z = (2 / x)
z and x are represent an inverse variation.
Answer:
equations represented inverse variation are:
pv = 13
z = (2 / x)

Answer:

B and C

Step-by-step explanation:

On eight book shelves there are 44 books per shelf. How many books are there altogether? If 1/4 of these books are novels, how many novels would there be?

Answers

281.6.................................if my calculations are right wich the are. all the time

Find the general solution of the given second-order differential equation. y'' − y' − 30y = 0 webassign

Answers

y''-y'-30y=0;
1) the characteristic equation is:
a²-a-30=0, where a²⇒y'', a⇒y' and 1⇒y.
[tex] \left[\begin{array}{ccc}a=6 \\a=-5\end{array}[/tex]
2) y=C₁*e⁶ˣ+C₂*e⁻⁵ˣ

The general solution of the given second-order differential equation

y'' - y' - 30y = 0 is,

⇒ y = C₁ e⁶ˣ + C₂ e⁻⁵ˣ

What is mean by Function?

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The second-order differential equation is,

⇒ y'' − y' − 30y = 0

Now, We can simplify as;

⇒ y'' − y' − 30y = 0

This gives the general form as;

⇒ m² - m - 30y= 0

⇒ m² - 6m + 5m - 30 = 0

⇒ m (m - 6) + 5 (m - 6) = 0

⇒ (m + 5) (m - 6) = 0

⇒ m = - 5 or m = 6

Hence, The general solution of the given second-order differential equation y'' - y' - 30y = 0 is,

⇒ y = C₁ e⁶ˣ + C₂ e⁻⁵ˣ

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I don't understand this at all

Answers

Try this option:
if to re-write and simplify the given expression, then answers:
the coeffic. for a²= -2;
the coeffic. for ab= -2+6=4;
the coeffic. for b=6-8= -2.

PLEASE HELP PLEASE WILL GIVE BRAINLIEST !!!!! Freya is training for a track race. She starts by sprinting 200 yards. She gradually increases her distance

Answers

Answer:

A. [tex]a_n=200+(n-1)5[/tex]

Step-by-step explanation:

Given,

The initial sprinting of Freya = 200 yards,

Also, She gradually increases her distance by 5 yards per day,

So, in second day her sprinting = 200 + 5 = 205 yards,

In third day = 205 + 5 = 210 yards,

In fourth day = 210 + 5 = 215 yards,

...................., so on,.....

Hence, the sequence that shows the given situation,

200, 205, 210, 215, .........

Which is an A.P.

That having first term, a = 200,

Common difference, d = 5,

Thus, the explicit formula for the given situation is,

[tex]a_n=a+(n-1)d[/tex]

[tex]\implies a_n=200+(n-1)5[/tex]

Option A is correct.

Answer:

Option A.

Step-by-step explanation:

The explicit formula of an AP is

[tex]a_n=a+(n-1)d[/tex] .... (1)

where,

a is the first of the AP,

d is common difference.

It is given that Freya starts by sprinting 200 yards and she gradually increases her distance, adding 5 yards a day.

200, 205, 210,..., 305

Here,

First terms = 200

Common difference = 5

Substitute a=200 and d=5 in equation (1), to find the required explicit model

[tex]a_n=200+(n-1)5[/tex]

Therefore, the correct option is A.

Is the number of total molecules on the left side of a balanced equation always equal to the number of total molecules on the right side of the equation? explain your answer.3. is the number of total molecules on the left side of a balanced equation always equal to the number of total molecules on the right side of the equation? explain your answer?

Answers

Since no reaction creates or destroys atoms, every balanced chemical equation must have equal numbers of atoms of each element on each side of the equation. However, the number of molecules does not necessarily have to be the same.

The answer is

No, the total number of molecules can be equal or not

Answer:

No, the number of total molecules on the left side of a balanced equation is not equal to the number of total molecules on the right side of the equation. A molecule is the smallest number of atoms bonded together for a chemical reaction. The total number of atoms must be the same, but not molecules. The reactants and products will bond together in different ways leading to different numbers of reactants and products

Step-by-step explanation:

this is for pennfoster

Steven, a tailor, got an order to make a blazer. The customer specifically asked him to save 5/6 of a foot of the given cloth to make a pocket square. However, Steven accidentally saved 5/12 of a foot. What is the difference between the requested cloth and the saved cloth? A. 0.1466' B. 0.4166' C. 0.4265' D. 04066'

Answers

The answer to your question is B. The 6 is forever repeated fyi...

siplifier
cos(π/7)+cos(2π/7)+cos(3π/7)+cos(4π/7)

Answers

we know that
cos a+cos b=cos[(a+b)/2]*cos[(a-b)/2]
we have
cos(π/7)+cos(2π/7)+cos(3π/7)+cos(4π/7)-------------> equation 1

cos(4π/7)+cos(2π/7)=cos[(4π/7+2π/7)/2]*cos[(4π/7-2π/7)/2]
=cos(3π/7)*cos(π/7)
then
cos(4π/7)+cos(2π/7)=cos(3π/7)*cos(π/7)--------------> equation 2

[cos(3π/7)+cos(π/7)]=cos[(3π/7+π/7)/2]*cos[(3π/7-π/7)/2]
=cos(2π/7)*cos(π/7)
then
[cos(3π/7)+cos(π/7)]=cos(2π/7)*cos(π/7)-----------> equation 3

I substitute 2 and 3 in 1
[cos(3π/7)+cos(π/7)]+[cos(4π/7)+cos(2π/7)]
{cos(2π/7)*cos(π/7}+{cos(3π/7)*cos(π/7)}
=cos(π/7)*[cos(2π/7)+cos(3π/7)]

the answer is
cos(π/7)+cos(2π/7)+cos(3π/7)+cos(4π/7)=cos(π/7)*[cos(2π/7)+cos(3π/7)]

1. A paper cup designed to hold popcorn is in the shape of a cone. The diameter of the cup is 12 centimeters and the height is 16 centimeters. What is the volume of popcorn the cup could hold? Use 3.14 for pi. Enter your answer, as a decimal, in the box.

Answers

Answer, as a decimal, in the box. 602.88

Answer:

Volume of popcorn cup = 602.88 cm^3

Step-by-step explanation:

Volume of a cone = 1/3 πr^2 h

Given: π = 3.14, r = 12/2 = 6 cm, h = 16 cm

Now plug in these values in the above formula, we get

Volume of popcorn cup = 1/3 * 3.14*6^2*16

= 1/3*3.14 *36*16

= 3.14 *12*16

Volume of popcorn cup = 602.88 cm^3

Hope this will helpful.

Thank you.

write a polynomial (x+6)(x-2)(x-1)

Answers

Write a polynomial (x+6)(x-2)(x-1)
x3+3x2−16x+12I Hope this help

(x + 6) (x-2) (x-1)
Let's rewrite the expression step by step.
We have:
We multiply the first two parentheses:
(x ^ 2-2x + 6x-12) (x-1)
We rewrite:
(x ^ 2 + 4x-12) (x-1)
Now we multiply the remaining parentheses:
(x ^ 3 + 4x ^ 2-12x-x ^ 2-4x + 12)
We rewrite
(x ^ 3 + 3x ^ 2-16x + 12)
Answer:
The polynomial is:
(x ^ 3 + 3x ^ 2-16x + 12)

In a survey of 1756 adults 37% responded yes to the Severy question how many adults answer yes?

Answers

About 650 adults answered yes

Hey there! :D

Turn 37% to a decimal.

37%=.37

1756*.37= 649.72

Round that to 650.

650 adults said yes to the survey question.

I hope this helps!
~kaikers

A scientist finds that on one side of a mountain 35 cacti have purple flowers and 16 have white flowers. If he goes to the other side of the mountain, what is the experimental probability that the first cactus he comes across has white flowers?

Answers

The experimental probability it 16/51

Answer: The experimental probability that the first cactus he comes across has white flowers is 16/51.

Step-by-step explanation:

Since,

[tex]\text{Experimental probability} = \frac{\text{Number of event occurrence}}{\text{Number of trials}}[/tex]

Let W represents the event of occurrence of white flower and P represents the occurrence of purple flower,

Then, According to the question,

n(P) = 35 and n(W) = 16

Also, the total number of trials, n(S) = 35 + 16 = 51

Thus, the probability of occurring white flower is,

[tex]P(W)=\frac{n(W)}{n(S)}=\frac{16}{51}[/tex]

Other Questions

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