The following is an incomplete paragraph proving that the opposite sides of parallelogram ABCD are congruent:

Parallelogram ABCD is shown where segment AB is parallel to segment DC and segment BC is parallel to segment AD.

According to the given information, segment AB is parallel to segment DC and segment BC is parallel to segment AD.. Construct diagonal A C with a straightedge. It is congruent to itself by the Reflexive Property of Equality. Angles BAC and DCA are congruent by the Alternate Interior Angles Theorem. Angles BCA and DAC are congruent by the same theorem. __________. By CPCTC, opposite sides AB and CD, as well as sides BC and DA, are congruent.

Which sentence accurately completes the proof?

Triangles BCA and DAC are congruent according to the Angle-Angle-Side (AAS) Theorem.
Triangles BCA and DAC are congruent according to the Angle-Side-Angle (ASA) Theorem.
Angles ABC and CDA are congruent according to a property of parallelograms (opposite angles congruent).
Angles BAD and ADC, as well as angles DCB and CBA, are supplementary by the Same-Side Interior Angles Theorem.

ANSWER: The length of the entire dash is 700 meters.

EXPLANATION:

Because 20% of the dash equals 140 meters, we can use a variable to figure out the length of the entire dash.

Let x be the length of the entire dash.

[tex].2x = 140\\\\x = 700[/tex]

The length of the entire dash is 700 meters.

Answer:

x = -2, y = 0

Step-by-step explanation:

This is a systems of equations. Using substitution, we solve for a single variable, plug it in to solve for the other, and solve that one back in to solve for the original. Let's solve it.

5x + y = -10

Subtract 5x from both sides.

y = -5x - 10

Now that we have y isolated, we can plug it in to the other equation.

4x - 7(-5x-10) = -8

Distribute.

4x + 35x + 70 = -8

Subtract 70 from both sides and simplify.

39x = -78

Divide both sides by 39.

x = -2

Now that we have x as -2, we plug it in to the original.

5(-2) + y = -10

Simplify.

-10 + y = -10

Add 10 to both sides.

y = 0

x = -2, y = 0

[tex]\left\{\begin{array}{ccc}5x+y=-10&|\text{subtract 5x from both sides}\\4x-7y=-8\end{array}\right\\\left\{\begin{array}{ccc}y=-5x-10&|\text{substitute to the second equation}\\4x-7y=-8\end{array}\right\\\\4x-7(-5x-10)=-8\qquad\text{use distributive property}\\\\4x+(-7)(-5x)+(-7)(-10)=-8\\\\4x+35x+70=-8\qquad\text{subtract 70 from both sides}\\\\39x=-78\qquad\text{divide both sides by 39}\\\\\boxed{x=-2}\\\\\text{Put the value of x to the first equation}\\\\y=-5(-2)-10\\\\y=10-10\\\\\boxed{y=0}[/tex]

[tex]Answer:\ \boxed{x=-2\ and\ y=0}[/tex]

Answer:

15377.34375

Step-by-step explanation:

10800*((224+1)/2)/100*((224+1)/2)/100*((224+1)/2)/100

=108 * (225/2)  * ( 225/200)*(225/200)

=15377.34375

Answer:

125%

Step-by-step explanation:

The old population was 100% of the old population since 100% means a whole amount.

Since the population increased by 25%, the new population is 125% of the old population.

Answer:

30

Step-by-step explanation:

To find the area of a triangle you need to multiply base times height. Which in this case is 6 times 10 equals 60. Then you just need to simplify it and it equals 30.

Answer: -12

Step-by-step explanation: 24 divided by -2 = -12

Answer:

-12

Step-by-step explanation:

Divide. 24÷(−2)

Dividing a positive number with a negative number results to a negative number.

24 is positive and 2 is negative.

24 ÷ 2 = 12

But since 2 is negative;

24 ÷ -2 = -12

24 ÷ (-2)

Answer:

EACH TIE COSTS 7.43

Step-by-step explanation:

If 13.35x13=173.55 then that means the ties total is 189.46 now devide that by 22 it equals 13.35

The cost calculation of a tie can be done by subtracting the total cost of the shirts from the total cost. The remainder is then divided by the number of ties bought, resulting in the price of a tie, about $7.43.

To find the cost of a tie, we'll first determine the total cost of the shirts and then subtract this from the total spent. Firstly, we need to calculate the total cost of the shirts by multiplying the cost of one shirt by the number of shirts purchased. That is 13 shirts * $15.35/shirt = $199.55.

Next, we subtract the total cost of the shirts from the total spent to find out how much was spent on ties: $363.01 (total spent) - $199.55 (total spent on shirts) = $163.46 (total spent on ties).

Now, to find the cost of one tie, we divide the total spent on ties by the number of ties purchased. That is: $163.46/22 ties = $7.43/tie. Therefore, each tie costs approximately $7.43.

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Answer: k = -12

The mixed number -1 & 1/3 converts to the improper fraction -4/3

Let r be the common ratio. To go from one term to the next, we multiply by this common ratio. So,

second term = (first term)*(common ratio)

4 = (-4/3)*r

3*4 = 3*(-4/3)*r

12 = -4r

-4r = 12

r = -3

We multiply each term by -3 to get the next term. The third term is therefore,

third term = (second term)*(common ratio)

third term = 4*r

third term = 4*(-3)

third term = -12

and if we keep going...

fourth term = (third term)*(common ratio)

fourth term = -12*(-3)

fourth term = 36

So it matches up

If a, b, c are the geometric sequence, then

[tex]ac=b^2[/tex]

We have a = 4, b = k, c = 36. Substitute:

[tex](4)(36)=k^2\\\\k^2=144\to k=\pm\sqrt{144}\to k=-12\ \vee\ k=12[/tex]

First term is negative, therefore it's the alternating sequence. Therefore your answer is

The answer is George Washington.

Answer:

The first president was George Washington. Hope this helps you out.

Step-by-step explanation:

Answer:

1) Increased by 2 times then 16 hours

2) Increased by 4 times then 8 hours

Step-by-step explanation:

Given :-

==> 4 construction crew members need 32 hours to pour concrete foundations.

==> All the members work at a same pace.

1) If the numbers of workers are increased by 2 time i.e., 4 workers × 2 = 8 workers. It would take half of the time that is taken now i.e., 32 hours ÷ 2 = 16 hours.

2) If the numbers of workers are increased by 4 time i.e., 4 workers × 4 = 16 workers. It would take 1/4th of the time that is taken now i.e., 32 hours ÷ 4 = 8 hours.

Answer:

10 is 5,650

9 is 18.5

11 is 71.24

Step-by-step explanation:

11 .2.74  x25

3*x*x*5*x

If x=3 then:

3*3*3*5*3

=27*15

= 405

Hope this helps! <3

Answer:

120

Step-by-step explanation:

Answer:

A=m-n-p

Step-by-step explanation:

So solve for a, we have to isolate it on one side, so -a=n+p-m. So a=m-n-p

Answer:

a = m - n - p

Step-by-step explanation:

isolate the term in a by subtracting m from both sides

- a = n + p - m ( multiply through by - 1 )

a = - n - p + m = m - n - p

Answer:

$13.72

Step-by-step explanation:

To get the answer, we need to find out how much one bag costs. We can divide 5.88 by 3 and get 1.96. One bag is $1.96. To find out how much seven bags cost, we can multiply 1.96 x 7 to get 13.72. It costs $13.72 for 7 bags of popcorn.

Find the volume of the bath tub by multiplying all the dimensions together:

18 inches = 1.5 feet:

5 ft x 3 feet x 1.5 feet = 22.5 cubic feet.

The tub is 3/4 full so multiply the volume by 3/4 to find the amount of water in the tub:

22.5 x 3/4 = 16.875 cubic feet of water.

The tub drains at 1 cubic foot per minute, so it would take about 17 minutes to drain.    (16.875 rounded to the nearest whole minute).

Answer:

speed = 67/6 miles per hour

Step-by-step explanation:

To find the average speed, we divide the distance by the time

d/t = 134 miles/ 12 hours

speed = 134/12 miles per hour

We can simplify this fraction  by dividing the top and bottom by 2

speed = 67/6 miles per hour

Answer:

11.16 mph

Step-by-step explanation:

You divide Distance by Time to get the speed.

134/12= 11.1667

Answer:

let x be the Robert piece

y Maria's piece

x+y=10

0,5*x ( half of Robert piece)= 2/3 y( 2 thirds)

2 equations then

x+y= 10 then x= 10-y

0,5x= 0,67 y  then we replace x by 10-y on the second equation and it gives

0,5(10-y)= 5-0,5y=0,67y

5= 1,17 y so y= 4,27    and then x= 10-y= 5,73

the question asks how much Robert wire is longer than Maria's wire

so we get x-y= 1,46

Robert's wire is longer [tex]\frac{4}{3}[/tex] times than Maria's wire and also   it [tex]\frac{10}{7}[/tex] longer than Maria's wire

A wire is a single, usually cylindrical, flexible strand or rod of metal. It are used to bear mechanical loads or electricity and telecommunications signals.  

Half of Robert's wire = 2 thirds of Maria's wire, so

[tex]\frac{1}{2} *[/tex]  Robert's wire = [tex]\frac{2}{3} * Maria's wire[/tex]

The total length of their wires = 10 feet

10 feet =  Robert's wire + Maria's wire

10 feet =  [tex]\frac{4}{3} * Maria's wire[/tex] + Maria's wire

10 feet =  [tex]\frac{7}{3} * Maria's wire[/tex]

Maria's wire =  [tex]\frac{30}{7}[/tex]  feet

 [tex]\frac{1}{2} *[/tex]   Robert's wire = [tex]\frac{2}{3} * Maria's wire[/tex]

Robert's wire = [tex]\frac{4}{3} * \frac{30}{7} [/tex]

Robert's wire =  [tex]\frac{120}{21} feet[/tex]

Robert's wire = [tex] \frac{40}{7} feet[/tex]

If we draw the piece, we get the information that

7 units = 10 feet

1 unit = [tex]\frac{10}{7}[/tex] feet

Hence the  Robert's wire is [tex]\frac{10}{7}[/tex] longer than Maria's wire because

Robert's wire - Maria's wire =   [tex]\frac{40}{7} - \frac{30}{7} feet = \frac{10}{7} feet[/tex]

Grade:  5

Subject:  math

Chapter:  wire

Keywords:  

wire, feet,  piece of wire, piece, wires

Answer:

$2

Step-by-step explanation:

$40 * 0.02 = 5

Answer:

A) 2(6x + 13)

Step-by-step explanation:

2(5 + 8 + 6x)

= 2(13 + 6x)

= 2(6x + 13)

Answer:

2(6x + 13)

Step-by-step explanation:

x = number of hours after 9 am (eg: x = 1 means 1 hr after 9 am, so 10 am)

f(x) = population count x hours after 9 am

f(1) = population count at 10 am (1 hour later)

f(2) = population count at 11 am (2 hrs after 9 am)

f(2) - f(1) represents the difference in population counts from 10 am to 11 am, or put another way, how much the population increased during that time interval.

f(2)-f(1) represents the change in the population of bacteria from the first to the second hour after 9 a.m., giving us the rate of population growth over that one-hour period.

The expression f(2)-f(1) in the function f(x), where x represents the hours after 9 a.m., illustrates the change in the population of the bacteria between the first and second hour after 9 a.m. Population growth in bacteria usually follows a logarithmic scale where it doubles every given time period, typically every hour. Thus, by calculating the difference between the population at the second hour (f(2)) and the first hour (f(1)), we can get the increase in the population of bacteria over that one-hour period.

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Answer:

y^2 +8y + 16

Step-by-step explanation:

 6y^2 +2y +5  - (5y^2 -6y -11)

I distribute the minus sign

6y^2 +2y +5  - 5y^2 +6y +11

Then I put them vertical.

6y^2 +2y +5  

-5y^2 +6y +11

------------------------

y^2 +8y + 16

This is in standard from since the exponential decreases.

Answer:

15/216 (6.944%)

Tienes suerte, me tomé 5 años de español! Hoep me ayudó!

Answer:

Suceso A= (6;4) (5;5) (4;6)

n(A)= 3

Suceso B= (5;5)

n(B)= 1

P(AnB)= (5;5)= 1

Espacio muestral= 36

P(B/A)= 1/36 / 3/36= 0.33= 33%

Suceso C= (4;6) (6;4)  

n(C)= 2

P(AnC)= (4;6) (6;4)

P(AnC)= 2

P(C/A)=2/36 / 3/36= 2/3= 0.66= 66%

Answer:

If Aaron leaves one city at noon and has to be at another city at 3:00pm traveling at a rate of 65km/h, he will arrive to the second city on time.  

Step-by-step explanation:

Aaron has three hours (from noon to 3:00pm) to travel a distance of 186km.  If he travels at a speed of 65km per hour, then we can multiply 65 km times the number of hours he has available, three, to get a total of 195km.  So, Aaron can travel up to 195 km in the three hour period and since the city is only 186km away, he has time to make it there before the 3:00pm deadline.  

Answer:

Yes, he can.

Step-by-step explanation:

From noon to 3:00 pm, it's 3 hours.

If he drives on the speed limit with 65 km/h, andhas 186 kilometers to drive, he can make it on time.

3(65)=195 km.

195 is greater than 185, so he can make it on time.

Question

6v²+ 4v²  please solve this equation

Answer:

Step-by-step explanation:

6v²+ 4v² =

(6 + 4)v² =

10v²

Answer:

295.16 feet

Step-by-step explanation:

We need to find the length of the diagonal of a right angled triangle with equal length legs.

Length of each leg = √(43560)

Using the Pythagoras theorem:-

x^2 = (√(43560))^2 + (√(43560))^2    (where x = length of the diagonal)

x^2 = 43560 + 43560

x = √(87120) = 295.16 feet

Answer:

distance from corner to corner = 295.16 ft

Step-by-step explanation:

Given the land is square, then its area is computed as:

Area = (length of a side)^2

Replacing with area = 1 acre =  43560 sq. ft.

43560 = (length of a side)^2

length of a side = √43560

length of a side = 208.71 ft

The distance from corner to corner and two sides of the square form a right triangle, where the distance from corner to corner is the hypotenuse and the square sides are the legs. From Pythagorean theorem:

(distance from corner to corner)^2 = 208.71^2 + 208.71^2

distance from corner to corner = √(208.71^2 + 208.71^2)

distance from corner to corner = 295.16 ft

3=x/100*12

x/25*3=3

x=3:3/25

x=25

The answer is 25%. Hope this helps! <3

Answer:

3 is 25% of 12

Step-by-step explanation:

Answer:

Step-by-step explanation:

Factor out 6

I assume you mean 6x^2+30x+36, because that makes far more sense

6(x^2+5x+6) = 6(x^2 + 2x +3x +6)

(To find that it is 2x and 3x: 2 +3 = 5, 2 * 3 = 6)

Factor by grouping:

6* x(x+2) +3(x+2) = 6(x+3)(x+2)

For binomials, it could be either (6x+18) (x+2) or (x+3) (6x+12), depending on where you multiply the 6.

Answer:x+2

Step-by-step explanation:

(a) <TOR=pi/3 radians

To determine <TOR we use the fact that in the right-angled triangle ORT we know two sides:

|OT|=radius=8cm and |OR|=radius/2=4cm

and can use the sine:

[tex]\sin \angle OTR=\frac{r/2}{r}=\frac{1}{2}\implies \angle OTR =\frac{\pi}{6}[/tex]

and since <TRO=pi/2, it must be that

[tex]\angle TOR =\pi-\frac{\pi}{2}-\frac{\pi}{6}=\frac{\pi}{3}[/tex]

(b) The arc length is approximately 7.255 cm

In order to calculate the arc length QT, we need to first determine the length |ST| and the angle <OST.

Towards determining angle <OST:

[tex]\angle SOT = \pi - \angle TOR = \pi - \frac{\pi}{3} = \frac{2}{3}\pi[/tex]

Next, draw a line connecting P and T. Realize that triangle PTS is right-angled with <PTS=pi/2. This follows from the Thales theorem. Since R is a midpoint between P and O, it follows that the triangles ORT and PRT are congruent. So the angles <PTR and <OTR are congruent. Knowing <PTS we can  determine angle <OTS:

[tex]\angle OTR \cong \angle PTR=\frac{\pi}{6}\implies\angle OTS=\angle PTS -\angle PTR -\angle OTR\\\angle OTS = \frac{\pi}{2}-\frac{\pi}{6}-\frac{\pi}{6}=\frac{\pi}{6}[/tex]

and so the angle <OST is

[tex]\angle OST = \pi - \angle TOS - \angle OTS = \pi -\frac{2}{3}\pi - \frac{1}{6}\pi=\frac{\pi}{6}[/tex]

Towards determining |TS|:

Use cosine:

[tex]\cos \angle OST =\frac{|RS|}{|ST|}\implies |ST|=\frac{\frac{3}{2}r}{\cos \frac{\pi}{6}}=\frac{12\cdot 2}{\sqrt{3}}=8\sqrt{3}cm[/tex]

Finally, we can determine the arc length QT:

[tex]QT = {\angle OST}\cdot |ST|=\frac{\pi}{6}\cdot 8 \sqrt{3}=\frac{4\pi}{\sqrt{3}}\approx 7.255cm[/tex]

Answer:

$104.738

Step-by-step explanation:

Let's work out the stock plan first:

$2,000 - 7% in the first year = $1,860

$1,860 + 10% = $2,046 in the second year

Savings account:

$2,000 + 3.7% = $2,074 in the first year

$2,074 + 3.7% = $2,150.738 in the second year

The difference:

$2,150.738 - $2,046 = $104.738

At the end of the second year, the savings account earns $104.74 more than the stock plan.

We are required to calculate the difference in earnings between a stock investment and a savings account after two years. To do this, we need to account for the changes in the stock plan's value and the compound interest from the savings account.

For the stock plan:

Year 1: $2,000.00 - (7% of $2,000.00) = $2,000.00 - $140.00 = $1,860.00

Year 2: $1,860.00 + (10% of $1,860.00) = $1,860.00 + $186.00 = $2,046.00

For the savings account:

Year 1: $2,000.00 + (3.7% of $2,000.00) = $2,000.00 + $74.00 = $2,074.00

Year 2: $2,074.00 + (3.7% of $2,074.00) = $2,074.00 + $76.74 = $2,150.74

The difference in earnings at the end of the second year is the amount in the savings account minus the amount in the stock plan:

$2,150.74 - $2,046.00 = $104.74.