On a coordinate plane, square P Q R S is shown. It has points (0, 4), (4, 4), (0, 0), and (4, 0).
Prove the diagonals of the square with vertices P(0, 4), Q(4, 4), R(0, 0), and S(4, 0) are perpendicular bisectors of each other.
Step 1: Calculate the slope of the diagonals.

The slope of diagonal PS is

.

The slope of diagonal QR is


Step 2: Calculate the midpoint of the diagonals.

The midpoint of PS is


The midpoint of QR is

.

The diagonals of the square are perpendicular bisectors because the diagonals are

Answer:

Step-by-step explanation:

Draw a straight line.

Then draw 2 lines of equal length from the 2 ends of the line at angles of 120 degrees  going up and apart.

Then draw the fourth line joining the ends of these 2 lines.

The 2 angles formed will equal 60 degrees.

The quadrilateral formed is a trapezoid.

Answer:

C = 2(h - 1) + 0.80

Answer:

[tex]x = 0.2[/tex]

Step-by-step explanation:

In the question since the angle we were given was 41°, whereby x was the adjacent and 0.3 was the hypothenus. We have to use cosine to find the value of x.

[tex]recall: \: cosine = \frac{a}{h} \\ \\ a = x \: \: \: h = 0.3 \: \: \: \: angle = 41[/tex]

Therefore:

[tex] \cos(41) = \frac{x}{0.3} \\ \\ 0.75 = \frac{x}{0.3} \\ \\ 0.8(0.3) = x \\ \\ 0.24 = x[/tex]

Since we were asked to round it to the nearest tenth, then the answer would be 0.2.

Answer:

x = 0.2

Step-by-step explanation:

Given: Right angle DEF, angle E = 90°, angle D = 41°, angle DF = 0.3

To find value of x:

Solution: In angle DEF, angle E = 90°.

[tex] cos \: 41° = \frac{adjacent \: side}{hypotenuse} = \frac{DE}{DF} [/tex]

[tex]cos \: 41° \: = \frac{x}{0.3} [/tex]

x = 0.3 × cos 41° = 0.226 ≈ 0.2

Hence x = 0.2

HOPE THIS HELPS AND HAVE A NICE DAY <3

Answer:

B)The doctor needs to assign the first 15 patients to the new medication and 15 to the original medication to even out the variability between patients.

OR

D) The doctor needs to randomly assign the 30 patients to the new medication to even out the variability between the patients and to determine if their cholesterol level is lowered.

Answer: No solutions

Step-by-step explanation:

    There are no solutions to 0 = x² - x + 1.

[Method One]

   We can solve this by rewriting the equation, but it is quicker to graph it when there are no solutions. See attached.

[Method Two]

 I said we can solve this by solving an equation, here it is. We will use the quadratic formula since the equation given is already in the proper form.

[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

[tex]\displaystyle x=\frac{1\pm\sqrt{(-1)^2-4(1)(1)} }{2(1)}[/tex]

[tex]\displaystyle x=\frac{1\pm\sqrt{-3} }{2}[/tex]

   -> Negative numbers don't have real square roots, so there is no solution

The measures for the given angles B and E are 12° .

Triangles are similar when the correspondent angles and the ratio of correspondent sides are equal. Also, it must present the same shape, but it is not mandatory the same dimension.

Like the triangles are similar,  ∠B=∠E. Then,

∠B=∠E

3y=6y-12

3y-6y=-12

-3y=-12

y=4

You can write too:

AC=DF

7a+5=5a+9

7a-5a=9-5

2a=4

a=2

Therefore,

∠B=3y= 3* 4 =12

m∠E=6y-12=6*4-12=21-12=12

AC=7a+5= 7*2+5=14+5=19

DF=5a+9=5*2+9=10+9=19

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Answer:

(6x9) + (9x1)

Step-by-step explanation:

Answer:

The investment rate that you need for a 5000$ invest compounded annually to double in 10 years is 55,000

Step-by-step explanation:

Using the Pythagorean Theorem, it is found that the rate of change of the hypotenuse is of -9.8 in/sec.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

Applying implicit differentiation, the rate of change of the hypotenuse is given by:

[tex]2h\frac{dh}{dt} = 2l_1\frac{dl_1}{dt} + 2l_2\frac{dl_2}{dt}[/tex]

[tex]h\frac{dh}{dt} = l_1\frac{dl_1}{dt} + l_2\frac{dl_2}{dt}[/tex]

In this problem, we have that the parameters are given as follows:

[tex]l_1 = 21, \frac{dl_1}{dt} = -7, l_2 = 28, \frac{dl_2}{dt} = -7[/tex]

[tex]h = \sqrt{l_1^2 + l_2^2} = \sqrt{21^2 + 28^2} = 35[/tex]

Hence, the rate of change of the hypotenuse, in inches per second, is given by:

[tex]h\frac{dh}{dt} = l_1\frac{dl_1}{dt} + l_2\frac{dl_2}{dt}[/tex]

[tex]35\frac{dh}{dt} = 21(-7) + 28(-7)[/tex]

[tex]\frac{dh}{dt} = \frac{21(-7) + 28(-7)}{35}[/tex]

[tex]\frac{dh}{dt} = -9.8[/tex]

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And XZ=1/2XY

XZ be x

Now

XZ=21.4units

Answer:

XZ = 21.4 units

Step-by-step explanation:

If  ΔXYZ  is an isosceles triangle then XY = ZY

(the dashes on the line segments indicate they are of equal measure)

If XZ = ¹/₂XY then

⇒ 2XZ = XY = ZY

If the perimeter is 107 units:

⇒ Perimeter of ΔXYZ = XY + ZY + XZ

⇒ 107 = 2XZ + 2XZ + XZ

⇒ 107 = 5XZ

⇒ XZ = 107 ÷ 5

⇒ XZ = 21.4 units

[tex]v = \frac{4}{3} \pi {r}^{3} [/tex]

[tex]v = \frac{4}{3} \times \pi \times {2}^{3} [/tex]

[tex]v = 33.51 \: {m}^{3} [/tex]

[tex]v = \pi {r}^{2} h[/tex]

[tex]v = \pi \times {2}^{2} \times 6[/tex]

[tex]v = 75.40 \: {m}^{3} [/tex]

[tex]v = 75.40 + 33.51[/tex]

[tex]v = 108.91 \: {m}^{3} [/tex]

Hence, the volume of the given compound shape is 108.91 cubic meters.

sphere:

= 33.51 m^3

cylinder:

= 75.40 m^3

all together:

= 108.91 m^3

Answer:

16

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

Follow the PEMDAS order of operations

3 x (6 + 2) - 3 + 4 ÷ 2

Parenthesis (P):

(6 + 2) = (8)

Exponents (E):

none

Multiply/Divided (MD) left to right:

Multiply: 3 x 8 = 24

           = 24 - 3 + 4 ÷ 2

Divided: 4 ÷ 2 = 2

           = 24 - 3 + 2

Add/Subtract (AS) left to right:

Subtract: 24 - 3 = 21

            = 21 + 2

Add: 21 + 2 = 23

Answer:

x = 60

Step-by-step explanation:

Discussion

You have 3600 boxes and 60 trucks

The formula you want is

Total Boxes = Number of trucks * number of boxes per truck.

Givens

Total boxes = 3600

Total trucks = 60

Solution

3600 = 60 * x                    Divide by 60

3600/60 = 60x/60

x = 60

Answer: 16 cups per second.

Step-by-step 5.5 minutes into seconds 320.

620 gallons into cups 9920.

9920 divided by 320 seconds.

16 cups per second

answer is: Notice that if the population doubles every 12 years, it quadruples (4 times) in 24, multiplies by 8 in 36, and multiplies by 16 in 48 years.

The graph represents the function (D) because the graph of the function  is not defined at x = 1 and x = 2 option (D) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a graph of a function:

If we take the function:

[tex]\rm f(x) = \dfrac{1}{\left(x-1\right)\left(x-2\right)}[/tex]

At x = 1 and x = 2 the function will be not defined, so this region would be hollow and as we can see in the graph of a function.

The function is not defined at x = 1 and x = 2.

Thus, the graph represents the function (D) because the graph of the function is not defined at x = 1 and x = 2.

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[tex]5 \frac{3}{5} \% \: of \: 750[/tex]

[tex]5 \frac{3}{5} = 5.6[/tex]

[tex] \frac{5.6\%}{100} \times \frac{x}{750} [/tex]

[tex] = 42%[/tex]

Answer:

Getting sum 6 when rolling two dice

Answer:  1 1/8 or 9/8

Step-by-step explanation:

5 1/2-4 3/8= 1/ 1/8

Answer:

1. -3*-4+3= 15Y=152.-3*-2+3=9Y=93. -3*0+3=3Y=34. -3*2+3= -3Y= -3

by-step explanation:

Answer:

The statement is correct about the radionuclide the atomic number is 31, the mass number is 67, and its symbol is superscript 67 subscript 31 baseline upper g a.

To answert the question, we need to know what an atom is.

An atom is the smallest indivisible part of a substance. It is represented by letters.

So, since the atom of this radionuclide contains 31 protons and 36 neutrons.

So, its atomic number is 31. Its mass number is number of protons + number of neutrons = 31 + 36 = 67. Its symbol is superscript 67 and subscript 31.

So, the statement is correct about the radionuclide the atomic number is 31, the mass number is 67, and its symbol is superscript 67 subscript 31 baseline upper g a.

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Answer:

14th term

Step-by-step explanation:

12÷10 = 1.2

14.4÷12 = 1.2

17.28÷14.4 = 1.2

Then it’s a geometric sequence of first term ‘V₀=10’ and common ration ‘q = 1.2’

We call it (Vn)

The general term of the sequence:

Vn = V₀×qⁿ⁻¹ = 10×(1.2)ⁿ⁻¹

To determine the term at which the sequence exceeds 100 we have to solve the equation:

Vn ≥ 100

⇔ 10×(1.2)ⁿ⁻¹ ≥ 100

⇔ (1.2)ⁿ⁻¹ ≥ 100/10

⇔ (1.2)ⁿ⁻¹ ≥ 10

⇔ ln(1.2)ⁿ⁻¹ ≥ ln(10)

⇔ (n-1)×ln(1.2) ≥ ln(10)

[tex]\Longleftrightarrow n-1\geq\frac{ln10}{ln1.2}[/tex]

[tex]\Longleftrightarrow n-1\geq12.6\\\Longleftrightarrow n\geq13.6\\\Longrightarrow n=14[/tex]

Verification:

[tex]V_{14}=10\times \left( 1.2\right)^{14-1} =106.993205379072[/tex]

[tex]\setlength{\unitlength}{1cm}\begin{picture}(6,5)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1)\put(.3,2.5){\large\bf \!\!\!\!Wall}\put(2.8,.3){\large\bf Ground}\put(1.02,1.02){\framebox(0.3,0.3)}\put(.7,4.8){\large\bf A}\put(.8,.3){\large\bf B}\put(5.8,.3){\large\bf C}\qbezier(4.5,1)(4.3,1.25)(4.6,1.7)\put(3.8,1.3){\large\bf$39^{\circ}$ }\end{picture}[/tex]

We need the walls height then ground distance

[tex]\\ \rm\Rrightarrow sin\theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]\\ \rm\Rrightarrow sin39=\dfrac{P}{26}[/tex]

[tex]\\ \rm\Rrightarrow P=26sin39[/tex]

[tex]\\ \rm\Rrightarrow P=16.4in[/tex]

Distance of wall from skateboard touching point on ground:-

[tex]\\ \rm\Rrightarrow cos\theta=\dfrac{Base}{Hypotenuse}[/tex]

[tex]\\ \rm\Rrightarrow cos39=\dfrac{B}{26}[/tex]

[tex]\\ \rm\Rrightarrow B=26cos39[/tex]

[tex]\\ \rm\Rrightarrow B=20.2in[/tex]

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Answer:

One of these movies was an animated movie rated G for general audiences. Do you think it was movie A, B, or C?    

movie B

Which movie has a dot plot with ages that that center at about 30 years?    

movie C

What is a typical age for the people who were at Movie A?    

40

Step-by-step explanation:

I had the same question but I'm pretty sure that is the correct answer for it, sorry if I am wrong.

A parallelogram is a type of quadrilateral(four sides polygon) that has both the pair of opposite sides parallel and equal.

Area of a parallelogram = height× base

from the question,

height= 6cm

base= 5cm

area= 6×5= 30cm^2

Answer:

the answer is 11 because there are so many no. repeating so in this case we count total no of terms and say it n if terms are odd then mode

Step-by-step explanation:

mode = n+1÷2

Answer:

I guess 25%..

Step-by-step explanation:

Solution,

Here,

Amount of decrease= $180 - $135

= $45

Now,

Percent of decreasement = $45/$180 × 100%

= 25%