A square playground has sides that each measure 120 feet in length.
On a scale drawing, - inch represents 5 feet on the playground.
How long is a side of this playground on the scale drawing?

Answer:  BC = 10

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Work Shown:

The term "collinear" means all points fall on the same straight line.

Point B is on segment AC.

Through the segment addition postulate, we can say

AB+BC = AC

This is the idea where we glue together smaller segments to form a larger segment, and we keep everything to be a straight line.

Apply substitution and solve for x

AB+BC = AC

2x-12+x+2 = 14

3x-10 = 14

3x = 14+10

3x = 24

x = 24/3

x = 8

Then we can find the length of BC

BC = x+2

BC = 8+2

BC = 10

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Note that AB = 2x-12 = 2*8-12 = 16-12 = 4

and how AB+BC = 4+10 = 14 which matches with AC = 14

Therefore we have shown AB+BC = AC is true to confirm the answer.

Collinear points are points on the same line.

The value of BC is 10

Since points A, B and C are on the same line, where B is between points A and C.

So, we have:

[tex]AC = AB + BC[/tex]

Substitute values for AC, AB and BC

[tex]14 = 2x - 12 + x + 2[/tex]

Collect like terms

[tex]2x +x =14 + 12 - 2[/tex]

[tex]3x =24[/tex]

Divide both sides of the equation by 3

[tex]x =8[/tex]

Substitute 8 for x in BC = x + 2

[tex]BC =8 + 2[/tex]

[tex]BC =10[/tex]

Hence, the value of BC is 10

Read more collinear points at:

https://brainly.com/question/15806521

Answer:

Step-by-step explanation:

It is not perfectly linear because the difference between the y values is not constant. However, when you use the regression function on your calculator and enter the L1 values as your x's and the L2 values as your y's and use the LinReg equation, you get an r-squared value of .999900 and an r value of .999950. So it linear, with your answer being "linear, because the r value for the linear model is closest to 1".

In this question, we have two columns, you giving the time and the other the distance. We have to identify it the relationship is linear or exponential.

First, I am going to explain when we have a linear relation and when we have an exponential relation, then we observe the data and solve this question, getting the following correct answer:

linear, because the r value for the linear model is closest to 1

Linear and exponential data:

If the absolute value of the change assume close values, it is linear.

If the rates are, it is exponential.

Data:

t = 1 -> d = 530

t = 2 -> d = 1050

t = 3 -> d = 1600

t = 4 -> d = 2110

t = 5 -> d = 2650

Subtractions:

2650 - 2110 = 540

2110 - 1600 = 510

1600 - 1050 = 550

1050 - 530 = 520

Divisions(rates):

2650/2110 = 1.25

2110/1600 = 1.32

1600/1050 = 1.52

1050/530 = 1.98

The rates change considerably more than the subtractions, so it is linear relationship, and the correct option is:

linear, because the r value for the linear model is closest to 1.

For more on linear/exponential growths, you can check https://brainly.com/question/24282972

Hey there! I'm happy to help!

If we have 6 red marbles and 4 blue marbles, we have 10 total marbles.

First, we have the probability that a marble we draw is red, which is 6/10. This simplifies to 3/5.

If this happens, there are only 5 red marbles left and 9 total ones. So, the probability of drawing a red one again is 5/9.

We multiply these two probabilities together to see the probability of them both happening.

[tex]\frac{3}{5} *\frac {5}{9}= \frac{1}{3}[/tex]

The probability that both marbles are red is 1/3.

Have a wonderful day! :D

Answer:

a is 15, b is 15, c is -15, and d is -15 also

Step-by-step explanation:

The 2 parallel lines that surround the number are called "absolute value signs" everything inside them has an outcome of a positive number and in this case the number is 15. Like I said the number(s) inside the absolute value signs have to have a outcome of a positive number, notice in c and d there is a negative sign outside the absolute value signs. Therefore you multiply the negative seperately so, 15(-1) is -15.

Answer:

5x^2 +24x +1

Step-by-step explanation:

First you'll want to find the area of the larger rectangle, and then you'll subtract the area of the smaller rectangle (which is not shaded) to get your answer.

Larger Rectangle:

A = length * width

A = (2x + 3)(4x - 5) = (8x^2 - 10x + 12x - 15) = 8x^2 + 2x - 15

Smaller Rectangle:

A = length * width

A = (x - 8)(3x + 2) = (3x^2 + 2x - 24x - 16) = 3x^2 - 22x - 16

Larger Rectangle minus Smaller Rectangle:

(8x^2 + 2x - 15) - (3x^2 - 22x - 16)

5x^2 +24x +1

Answer:

63/125

Step-by-step explanation:

Turn the decimal .504

=> 504/1000

=> 504/1000 = 252/500

=> 252/500 = 126/250

=> 126/250 = 63/125

=> 63/125 cannot be simplified anymore.

So, 63/125 is the simplified fraction of .504

Answer:

5 hours

Step-by-step explanation:

55/5 is 11 (he worked 11 hours total). 11-6 is 5

Answer:

5 hours on Saturday

Step-by-step explanation:

x = hours

5x + 6(5) = 55

5x + 30 = 55

5x = 25

x = 5

Answer:

[tex]1035[/tex]

Step-by-step explanation:

(63756×60)/(70×5280)

=1035

Answer:

C) 1

Step-by-step explanation:

First half:

Invert and multiply

x²/y²*y³/x²=x²y³/y²x³=y/x

Second half:

Invert and multiply

1/y*x/1=x/y

Combine

y/x*x/y=xy/xy=1

Answer:

216.

Step-by-step explanation:

These numbers are perfect cubes starting with 2^3.

2^3, 3^3,  4^3,  5^3 so the next one is 6^3, which is 216.

Step-by-step explanation:

theanswer is 64 degrees

Answer:

18 square centimeters

Step-by-step explanation:

Notice that if e is the midpoint of the side CB, and angle [tex]\angle x = 45^o[/tex], then this rectangle is in fact two squares of side 3 cm put together. therefore, side CD has a length of 6 cm, and as a result, the area of the figure is given by the product base times height = 6 x 3 = 18 [tex]cm^2[/tex]

Answer:

(B)  18

Step-by-step explanation:

The angle x is 45 degrees.  Since it is bisecting a 90 degree angle, the angle on the other side is 45 degrees.

90 - 45 = 45

Since AB is 3, DC is 3.  Since the right triangle DC is 45-90-45, the other side, CE, will also be 3.  Since CE is half of the side of the rectangle, multiply it by 2 to get 6.  The sides of the rectangle are 3 and 6.  Use the formula for area of a rectangle to solve.

A = lw

A = (6)(3)

A = 18

The answer is B.

Answer:

Ok, our function is:

f(x) = 3*(x - 1)^2 + 2.

First, domain:

We should assume that the domain is all the set of real numbers, and then we see if for some value we have a problem.

In this case we do not see any problem (we can not have a zero in the denominator, and there is no function that has problems with some values of x)

Then the domain is the set of all real numers.

Vertex:

Let's expand our function:

f(x) = 3*x^2 - 3*2*x + 1 + 2

f(x) = 3*x^2 -6*x + 2

The vertex of a quadratic function:

a*x^2 + b*x + c is at:

x = -b/2a

here we have:

a = 3 and b = -6

x = 6/2*3 = 6/6 = 1.

And the value of y at that point is:

f(1) = 3*(1 - 1)^2 + 2 = 2

Then the vertex is at: (1, 2)

Range:

The range is the set of all the possible values of y.

Ok, we can see that the leading coefficient is positive, this means that the arms of our quadratic function will go up.

Then the minimal value of our quadratic function is the value at the vertex, y = 2.

This means that the range can be written as:

R = y ≥ 2

So the range is the set of all real numbers that are larger or equal than 2.

Answer:

x = 11.5 hours

Step-by-step explanation:

Set up a proportion:

[tex]\frac{460}{8}[/tex] = [tex]\frac{661.25}{x}[/tex]

661.25/460 = 1.4375

Multiply 8 by 1.4375 to find x:

8(1.4375) = 11.5

x = 11.5 hours

Answer: $10

Step-by-step explanation:

let x = the price of green fabric, then x+2 = blue fabric price

8x+5(x+2)=62

8x+5x+10=62

    13x+10=62

          13x=52

              x=4

price of green fabric=$4

price of blue fabric=$6

4+6=$10

Answer:

The two inequalities that show the solution to these equations are n ≥ 55 and y ≥ 6

Step-by-step explanation:

We are given two inequalities that we have to solve. We can solve these inequalities as if we are solving for the variable.

n/5 ≥ 11

Multiply by 5 on both sides.

n ≥ 55

Now, let's do the second one.

-3y ≤ -18

Divide by -3 on both sides. When we divide by a negative in inequalities, then the sign is going to flip to its other side. So, this sign (≤) becomes this sign (≥)

y ≥ 6

Answer:

[tex]243.2cm^{2}[/tex]

Step-by-step explanation:

Step 1: Understand what this shape is constructed out of

2 Congruent Trapezoid

2 Congruent Rectangles

1 Small Rectangle

1 Large Rectangle

Step 2: Find the surface area of the shapes

Area of 2 Trapezoids =[tex](\frac{a+b}{2}h)2=(\frac{4+6}{2}2.8)2=(\frac{10}{2}2.8)2=((5)}(2.8))2= (11.6)(2)=23.2cm^{2}[/tex]

Area of 2 Rectangles = [tex](3)(10)(2)=(60)(2)=120cm^{2}[/tex]

Area of Smaller Rectangle = [tex](4)(10)=40cm^{2}[/tex]

Area of Larger Rectangle = [tex](6)(10)=60cm^{2}[/tex]

Step 3: Add the surface areas up

[tex]23.2cm^{2} +120cm^{2} +40cm^{2} +60^{2} =243.2cm^{2}[/tex]

Therefore the surface area of the Trapezoidal Prism is [tex]243.2cm^{2}[/tex]

you are correct. all angles (except central) are not equal (iff TU and CB are not parallel)

the triangles are not similar

Answer:

it's A

They don't give you enough information to determine if they are similar or not

Answer:

9.1 hours

Step-by-step explanation:

Given

Sally

Speed = 66mph

Keith

Speed = 75mph

Time = 8 hours

Required

Determine how long Sally has traveled

To solve this, we make use of Speed formula.

Speed = Distance/Time

Make Distance the subject of formula

Distance = Speed * Time

For Sally:[Substitute 66mph for speed]

Distance = 66 * Time ------ Equation 1

For Keith [Substitute 75mph for speed and 8 hours for Time]

Distance = 75 * 8

Distance = 600m----- Equation 2

From the question, we understand that Keith caught up; this implies that they've both traveled the same distance.

Hence;

Equation 1 = Equation 2

66 * Time = 600

Time = 600/66

Time = 9.1 hours

Hence, Sally has traveled 9.1 hours

Answer:

'y', "addition", '9'.

Step-by-step explanation:

The variable is an unknown value in an algebraic equation or expression. It is represented by a letter.

'y' would be the variable in the given equation.

The operation in the expression is addition. The '+' sign represents addition, which means 9 and 'y' would be added together to get the sum.

Constants are terms in a expression or equation that contains no variables. This means that constants are only numbers.

'9' would be the given constant in the expression.

Hope this helps.

Answer:

y

+

9

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

5^2

This is 5 multiplied by itself 2 times

5*5

25

Answer:

D: 4x² - 4x + 1

Step-by-step explanation:

(2x - 1) ( 2x - 1)

4x² - 2x - 2x + 1

4x² - 4x + 1

The correct answer is d) 4x2 - 4x + 1.

The area of a square is found by squaring the side length:

(2x-1)? = (2x-1)(2x-1) = 2x*2x - 2x*1 - 2x*1 - = 1(-1) = 4 x 2 - 2x - 2x + 1 = 4x2-4x+1

Answer:

4.10526315789

Step-by-step explanation:

Answer: 4.10526315789

Step-by-step explanation:

Answer:

Problem 1)  frequency:  160 heartbeats per minute, period= 0.00625 minutes (or 0.375 seconds)

Problem 2) Runner B has the smallest period

Problem 3) The sound propagates faster via a solid than via air, then the sound of the train will arrive faster via the rails.

Step-by-step explanation:

The frequency of the football player is 160 heartbeats per minute.

The period is (using the equation you showed above):

[tex]Period = \frac{1}{frequency} = \frac{1}{160} \,minutes= 0.00625\,\,minutes = 0.375\,\,seconds[/tex]

second problem:

Runner A does 200 loops in 60 minutes so his frequency is:

[tex]\frac{200}{60} = \frac{10}{3} \approx 3.33[/tex]   loops per minute

then the period is: 0.3 minutes (does one loop in 0.3 minutes)

the other runner does 200 loops in 65 minutes, so his frequency is:

[tex]\frac{200}{65} = \frac{40}{13} \approx 3.08[/tex]   loops per minute

then the period is:

[tex]\frac{13}{40} =0.325\,\,\,minutes[/tex]

Therefore runner B has the smaller period

Answer:

Its usual speed is 25 kilometre/hour

Step-by-step explanation:

Let the usual  time duration for a journey of 300 km. = t

Let the usual speed = v

The parameters given are;

The time duration for the 300 km. journey at increased speed = t - 2

The increased speed of the passenger train = v + 5

Distance, d = Speed, v × Time, t

Therefore, we have;

v × t = 300

∴ t = 300/v

Also (v + 5)×(t - 2) = 300

Substituting the value of t = 300/v, we have;

(v + 5)×(300/v - 2) = 300

[tex]- \dfrac{2 \cdot v^2 - 290 \cdot v - 1500}{v} = 300[/tex]

Which gives;

2·v² + 10·v - 1500 = 0

Which is equivalent to v² + 5·v - 750 = 0

Therefore we have;

(v + 30)·(v - 25) = 0  whereby v = -35 or 25 km/h

v = Natural number = 25 km/hour

Therefore its usual speed is 25 kilometre/hour.

Answer:

mean is adding up all the numbers.

range means the difference between the Lowest and highest value.

Step-by-step explanation:

when we add the answer is 240.6.

divide it to 12..do the final answer is 20.05

range is 25.4_16.3

9.1

Answer:

Mean: 20.05

Range: 9.1

Step-by-step explanation:

To find the mean in this problem, first you add all the following numbers together then subtract by the quantity.

20.1 + 19.6 + 18.0 + 17.8 + 25.2 + 18.7 + 21.9 + 16.3 + 25.4 + 20.5 +17.8 + 19.3

= 240.6

Now, divide by the quantity which is 12 since there's 12 numbers.

240.6 divided by 12 = 20.05.

The mean is 20.05.

To find the range in the problem, you must subtract the smallest value from the largest value.

In this case, 16.3 is the smallest value and 25.4 is the largest.

25.4 - 16.3 = 9.1

9.1 is the range.

Hope this helps you!

Answer:

Step-by-step explanation:

a) area of rhombus = 1/2 × d1 × d2 = 90cm^2

here d1 and d2 are the diagonals

d1 = 18 cm

1/2 × 18 × d2 = 90

9 × d2 = 90

d2 = 90/9

d2 = 10 cm

∴The length of other diagonal is 10 cm

b) d1 = 28 cm

d2 = 24 cm

area = 1/2 × d1 × d2

= 1/2 × 28 × 24

= 336 cm^2

∴ The are of the rhombus = 336 cm^2

Hope this helps

plz mark as brainliest!!!!!