Matthew has 170 tiles he can use for this project. Identify the largest patio design that he can make. Show or explain your reasoning.

Answers

Answer 1

Answer:

Design 12

Step-by-step explanation:

See the attached for missing part of the question

As we see each design comprises of entrance and exit - each one tile and:

Design 1 has 1 row and 3 columns,Design 2 has 2 rows and 4 columns,Design 3 has 3 rows and 5 columns.

So design x has x rows and two more columns according the pattern we observe.

The number of tiles of design x is:

x by (x + 2) and 2 more tiles

We can put it as equation to get 170 tiles and solve for x:

x(x+2) + 2 = 170x² + 2x - 168 = 0x² - 12x + 14x - 168 = 0x(x - 12) + 14(x - 12) = 0(x + 14)(x - 12) = 0x = - 14 (discarded as negative root)x = 12 (the solution)

So this is a design 12

It has 12 rows, 14 columns, 1 entrance and 1 exit tiles, the total number is

12*14 + 2 = 170 tiles
Matthew Has 170 Tiles He Can Use For This Project. Identify The Largest Patio Design That He Can Make.

Related Questions

What is the length of the shortest altitude in a triangle, if the lengths of the sides are 24 cm, 25 cm, 7 cm?

Answers

Answer:

The shortest altitude is 6.72 cm

Step-by-step explanation:

Given that the side lengths are

24 cm, 25 cm, 7 cm

The area of a triangle =

[tex]A = \sqrt{s \cdot (s-a)\cdot (s-b)\cdot (s-c)}[/tex]

Where;

s = Half the perimeter = (24 + 25 +  7)/2 = 28

A = √((28×(28 - 24)×(28 - 25)×(28 - 7)) = 84 cm²

We note that 84/7 = 12

Therefore, the triangle is a right triangle with hypotenuse = 25, and legs, 24 and 7, the height of the triangle = 7

To find the shortest altitude, we utilize the formula for the area of the triangle A = 1/2 base × Altitude

Altitude  = A/(1/2 ×base)

Therefore, the altitude is inversely proportional to the base, and to reduce the altitude, we increase the base as follows;

We set the base to 25 cm to get;

Area of the triangle A =  1/2 × base × Altitude

84 = 1/2 × 25 × Altitude

Altitude = 84/(1/2 × 25) = 6.72 cm

The shortest altitude = 6.72 cm.

0.00000007834= blank ×10^2 in scientific notation ​

Answers

Answer:

7.834 × 10^-8

Step-by-step explanation:

= 7.834 × 10^-8

(scientific notation)

= 7.834e-8

(scientific e notation)

= 78.34 × 10^-9

(engineering notation)

(billionth; prefix nano- (n))

= 0.00000007834

(real number)

^ means the number after is exponent.

I really need help Please help me please

Answers

I think the answer is 35.28 square units. Because triangle ABC is 1/2 of triangle XYZ, the height must be halved. So, 3.36/2 is 1.68. Now, you times 42 by 1.68 to get 70.56. Then, divide that by 2 to get 35.28

Haley is at the store buying some supplies for an art project. She decides to buy some colored pencils for $3.95 and a drawing tablet. The total cost of the supplies before sales tax is $6.94. What is the cost of the drawing tablet? $2.99 $1.76 $10.89 $3.01

Answers

Its $2.99 because 6.94-3.95=2.99 so $2.99

Answer:

$2.99

Step-by-step explanation:

To find the value of the drawing tablet, we can use the known total cost and the cost of the pencils.  Let's build an equation, where x represents the cost of the drawing tablet:

x + 3.95 = 6.94

Now let's solve the equation for x to find the cost of the tablet.

x + 3.95 = 6.94

x + 3.95 - 3.95 = 6.94 - 3.95

x = 2.99

So the cost of the drawing tablet is $2.99.

Cheers.

Population data from three towns is displayed in the tables below. Which
town has growth that follows an exponential model?

Answers

Answer:

Rushmont

Step-by-step explanation:

Trenton can be ruled out due to its constant increase rate of 1.5. Rushmont can be ruled out because it goes from an increase rate of ~1.8 to an increase rate of 1.4 to an increase rate of 1.3 (exponential decay, not growth, so possibly...). Springville has a rate of ~1.9, then 1.475, then 1.3, also exponential decay. However, y\ =\ x\frac{38}{10}-185 goes through all of springville's points (or close to it), so Rushmont must be the answer.

The town that has growth that follows an exponential model is Town B, Rushmont where the population increases or decreases at a consistent rate over time.

In this case, analyze the population data from the three towns to determine which one exhibits exponential growth.

Let's go through each option briefly:

A. Springville:

The population of Springville in 1960 is 42, and in 1990 it is 156.The difference in population over 30 years is 156 - 42 = 114.The average increase per year is 114 / 30 = 3.8.The growth in Springville does not follow a consistent exponential pattern, as the average increase is not constant over time.

B. Rushmont:

The population of Rushmont in 1960 is 38, and in 1990 it is 131.The difference in population over 30 years is 131 - 38 = 93.The average increase per year is 93 / 30 = 3.1.The growth in Rushmont exhibits a consistent increase of approximately 3.1 per year, indicating a possible exponential model.

C. Trenton:

The population of Trenton in 1960 is 32, and in 1990 it is 108.The difference in population over 30 years is 108 - 32 = 76.The average increase per year is 76 / 30 = 2.5.The growth in Trenton does not follow a consistent exponential pattern, as the average increase is not constant over time.

Based on the analysis above, the town that shows growth following an exponential model is Rushmont (B). It exhibits a consistent increase in population over time, suggesting exponential growth.

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Clifton drove for 3 hours at 52 mph. How fast must he drive during the next hour in order to have an average speed of 55 mph?

Answers

Answer:

64 mph

Step-by-step explanation:

Given that:

Speed for the first 3 hours = 52 mph

Average speed for 4 hours = 55 mph

To find:

Speed for the next hour = ?

Solution:

Formula for average speed is given as:

[tex]Average\ Speed = \dfrac{Total\ Distance}{Total \ Time \ Taken}[/tex]

Formula for Distance:

[tex]Distance =Speed \times Time[/tex]

Distance traveled in first 3 hours:

[tex]Distance =52\times 3 = 156\ miles[/tex]

Let the speed for the next hour = u mph

Distance traveled in 1 hour = [tex]u \times 1 = u\ miles[/tex]

Total distance traveled = (156 + u) miles

Total time = 4 hours

Average Speed = 55 mph

Putting the values in formula:

[tex]55 = \dfrac{156+u}{4}\\\Rightarrow 220 = 156+u\\\Rightarrow \bold{u = 64\ mph }[/tex]

So, the answer is: 64 mph

explanation please! thx!​

Answers

Answer:

63°

Step-by-step explanation:

complement means that the two angles add to 90°

90 - 27 = 63°

Answer:

Step-by-step explanation:

complement angles have sum of angles=90°

∠AOC=27

∠BOC=90-27=63°

If A has a 3 letter name, but the name doesn’t contain a vowel what would be A’s name?

Answers

A is vowel.

first condition prevents any vowels, thus there will be no A at all

Find the product of 0.3×0.23.

Answers

Answer:

0.069

Step-by-step explanation:

0.3*0.23=0.069

The winning times (in seconds) in a speed-skating event for men can be represented by the formula T = 46.97 - 0.099x, where x represents the year, with x = 0 corresponding to 1920. (For example in 1992, x would be 1992 - 1920 = 72.) According to the formula, what was the winning time in 1997? Round to the nearest hundredth. * 1 point 40.34 sec 39.35 sec 3609.07 sec 41.33 sec

Answers

Answer:

39.35 sec

Step-by-step explanation:

Given that:

The winning time is represented by the function:

T = 46.97 - 0.099x

Where x = year ; x = 0 corresponding to 1920

According to the formula, what was the winning time in 1997?

first find the value of x;

x = 1997 - 1920 = 77 years

Nowing plugging the value of x in the function :

T = 46.97 - 0.099(77)

T = 46.97 - 7.623

T = 39.347 seconds

T = 39.35 s

ASAP PLZ ANSWER!!! Can you tell me step by step to this question 8,595 ÷ 24?

Answers

Answer:

358 and remainder of 3

Step-by-step explanation:

1. Divide it like any other problem

24 goes into 85, 3 times with 13 left overBring down the 9 and 24 goes into 139, 5 times with 19 left overThen bring down the 5 and 24 goes inside 195, 8 times with 3 left overSo your remainder would be 3

Hope this helps

A parabola has an x-intercept of -1, a y-Intercept of -3, and a minimum of -4 at x = 1.
Which graph matches this description?

Answers

Answer:

A

Step-by-step explanation:

Looking for the graph which

crosses the x- axis at x = - 1 ( x- intercept )

crosses the y- axis at y = - 3 ( y- intercept )

has a minimum value of - 4 at x = 1, that is vertex = (1, - 4) and minimum U

The required graph is A

The graph A should match the description.

Graph:Here we look the graph which crosses the x- axis at x = - 1 ( x- intercept )And, crosses the y- axis at y = - 3 ( y- intercept )Now we considered those that contain a minimum value of - 4 at x = 1, that is vertex = (1, - 4) and minimum U

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1+cos(8x)= A.4cos(2x) B.2cos^2(4x) C.4sin(2x) D.2sin^2(4x)

Answers

Answer:

bro please send in a picture format so that it could be more easier

Which of the following is the solution of 5x – 6 = 44?
O x=-10
38
X=--
5
38
X = 10

Answers

Answer:

x = 10

Step-by-step explanation:

5x - 6 = 44

Add 6 on both sides of the equation.

5x = 50

Divide by 5 on both sides of the equation.

x = 10

So, the value of x is equal to 10

Answer:

x=10

Step-by-step explanation:

5x-6=44

grouping constants and numbers with coefficient of x we get

5x=44+6

5x=50

5x/5=50/5

x=10

if jane has 3 apple then buys 4 times as much as that how much does she have

Answers

Answer:

12 apples

Step-by-step explanation:

3*4=12

X
5x – 3y = -20
4x + 5y = -2

Answers

Answer:

x=-106/37

y=70/37

Step-by-step explanation:

I chose to set up the problem as a matrix to solve here.

(Another way to do this would be to isolate one variable in one of the equations, substitute it into the other equation, solve for that, and then plug it back in to get the final variable.)

My work is in the attachment. Lmk if you have any questions.

Answer:

[tex]\huge\boxed{\left\{\begin{array}{ccc}x=-\dfrac{106}{37}\\y=\dfrac{70}{37}\end{array}\right}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}5x-3y=-20&\text{multiply both sides by 5}\\4x+5y=-2&\text{multiply both sides by 3}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}25x-15y=-100\\12x+15y=-6\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad37x=-106\qquad\text{divide both sides by 37}\\.\qquad\boxed{x=-\dfrac{106}{37}}[/tex]

[tex]\text{Substitute it to the first equation}\\\\5\left(-\dfrac{106}{37}\right)-3y=-20\\\\-\dfrac{530}{37}-3y=-20\qquad\text{multiply both sides by (-37)}\\\\(-37\!\!\!\!\!\diagup)\left(-\dfrac{530}{37\!\!\!\!\!\diagup}\right)-(-37)(3y)=(-37)(-20)\\\\530+111y=740\qquad\text{subtract 530 from both sides}\\\\111y=210\qquad\text{divide both sides by 111}\\\\y=\dfrac{210}{111}\\\\y=\dfrac{210:3}{111:3}\\\\\boxed{y=\dfrac{70}{37}}[/tex]

Graphing Linear Equations

Answers

Answer:

Kyra=15 points

Liam=20 points

30 points=y=4/3x+5

Step-by-step explanation:

I graphed each equation and point on the graph given

HOPE THIS HELPS!!! :)

PLEASE CORRECT ME IF IM WRONG

Helpp me pleaseeeeee

Answers

Answer:

On-time Buses: 75%

Running late Buses: 13.46%

Step-by-step explanation:

Part 1: Solve for the probability of Jerry owning an "on-time" bus

Of the 48 buses that run on time, Jerry owns 36 of them. Therefore, the probability of a bus running on time being owned by Jerry will be solved with the ratio of 36 buses to 48 buses.

This is represented by the fraction 36/48. Simplifying this fraction will give us 3/4. Convert to a decimal and then multiply by 100 to get a percentage - 75%.

Part 2: Solve for the probability of Jerry owning a "running late" bus

Of the 52 buses that run late, Jerry owns 7 of them. Therefore, the probability of a bus running late & being owned by Jerry will be solved with the ratio of 7 buses to 52 buses.

This is represented by the fraction 7/52.Simplifying this fraction will give us 7/52 (cannot be simplified).Convert to a decimal and then multiply by 100 to get a percentage - 13.46%.

Is the function f(x) increasing or decreasing over the interval -2 < x <-1?

Answers

Answer:

increasing

Step-by-step explanation:

a function is increasing when y increases as x increases

Since the graph goes up as x increases, the function f(x) is increases between -2 and -1

The probability that a civil servant own a car is 1/6,if two civil servants are selected at random.Find the probability that a.Each own a carb.Only one owns a car​

Answers

Answer:

Step-by-step explanation: Given that a civil servant own a car is 1/6.

A) The Pr. that each own a car = Pr of each multiplied by the other.

Pr = 1/6 ×1/6

P = 1/36

B) Pr that only one owns a car

= 1/6 × (1-1/6) + 1/6 × (1-1/6)

= 1/6 × 5/6 + 5/6 × 1/6

= 5/36 + 5/36

= 10/36

= 5/18

Aaron and his 2 friends found some money and split it even. Each received $5.00. How much did they find? a. $1000 b. $100 c. $15 d. $1500

Answers

Answer:

15

Step-by-step explanation:

Aaron and his 2 friends = 3 people

Each received $5.00 = 3 people*5 each = 15 total

Please answer quickly, what is the measure of c

Answers

Answer: B. 140

===================================================

Explanation:

The only given number here is the 20 degree angle. So we'll start with that. This is an inscribed angle, which doubles to 2*20 = 40, and this is the measure of the arc the inscribed angle cuts off (inscribed angle theorem). Consequently, it means that central angle b is also 40 degrees.

With b = 40, we can see that c = 180-b = 180-40 = 140. This is because b+c = 180 as the two angles are supplementary.

Answer:

140 degrees

Step-by-step explanation:

If the given angle is 20 degrees then the other unknown angle would also be 20 degrees because this triangle is an isosceles triangle. 20+20+20=180 proving the triangle sum theorem.

Write an expression for 267 multiplied by x

Answers

Answer:

267x

Step-by-step explanation:

Multiplication  means times

267 * x

267x

Answer:

267x

when you multiply a number by a variable, you can combine the terms if there is no coefficient for the variable.

What is the answer??

c — 10 ≥ 15

Answers

Answer:

Step-by-step explanation:

c - 10  ≥  15 =

c  ≥ = 15 + 10

c  ≥ = 25

c  = 26 ( or numbers above 26)

Find the value of cotA x sinA x secA.

Answers

Answer:

The value = 1

Step-by-step explanation:

Here in this question, we are interested in calculating the product of the trigonometric identities given.

To adequately calculate this correctly, we shall need to express the trigonometric identities in their normal division form which is as follows ;

Mathematically;

cotA = 1/tanA

let’s leave sin A

sec A = 1/cos A

So inputing the values of the following, we have ;

1/tan A * sin A * 1/cos A

This can be written as;

1/tan A * sin A/cos A

Mathematically; sinA/cos A = tan A

making that substitution, we have;

1/tan A * tan A

= tan A/tan A = 1

round off 3867 in nearest 100​

Answers

Answer:

3900

Step-by-step explanation:

since its to the nearest 100th we use the common rule that if the number is greater than half way then we round up otherwise if it is less then we round down. In the number 3867, 867 is greater than 850 so we round up. It becomes 3900 then.

what expression is equivalent to this Expression?
(-5cd-4)(2cd2)2​

Answers

Answer:

[tex]-40c^{2} d^{2} -32cd[/tex]

Step-by-step explanation:

-20c³ is the expression which is equivalent to (-5cd⁻⁴)(2cd²)².

To simplify the given expression, (-5cd⁻⁴)(2cd²)², we can apply the power of a product rule, which states that (ab)² is equal to a²b².

Let's break down the expression step by step:

(-5cd⁻⁴)(2cd²)²

First, let's square the expression (2cd²)²:

(2cd²)² = (2)²(c)²(d²)² = 4c²d⁴

Now, we substitute this result back into the original expression:

(-5cd⁻⁴)(4c²d⁴)

To simplify further, we can multiply the coefficients and combine the variables:

(-5)(4) = -20

(c)(c²) = c³

(d⁻⁴)(d⁴) = 1

Putting it all together, the expression (-5cd⁻⁴)(2cd²)² simplifies to -20c³.

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Beth is planning a playground and has decided to place the swings in such a way that they are the same distance from the jungle gym and the monkey bars. If Beth places the swings at point D, how could she prove that point D is equidistant from the jungle gym and monkey bars?

Answers

Answer:

Following are the answer to this question:

Step-by-step explanation:

Some of the information is missing which is defined in the attached file, and the solution to this question can be defined as follows:    

When the point AC ≅ BC point is in the equal distance from point A and Point B then Point A is perpendicular and the bisector point is in equally distant from the endpoints of that intersects points.

please find the attachment of the full question:

Answer:

If segment AC ≅ segment BC, then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.

Step-by-step explanation:

Find the length of the base and the height and calculate the area

Answers

Answer:

44

Step-by-step explanation:

base = 3- -5 = 8

height = 8 - -3 = 11

1/2 bh

1/2(8)(11) = 44

Drag each tile to the correct box.
Arrange the functions in increasing order of their periods.
y=-3tan(x+2pi)
y = 2/3csc(x/4)+6
y=-1/2cos(5x/6+pi)
y=5sec(3x) +6
y =-1/3sin(x/3)
y=-10cot(x/2-2pi)

Answers

Answer:

y=5sec(3x) +6

y=-3tan(x+2pi)

y=-10cot(x/2-2pi)

y=-1/2cos(5x/6+pi)

y =-1/3sin(x/3)

y = 2/3csc(x/4)+6

The functions in increasing order of their periods are given below.

y=5sec(3x) +6

y=-3tan(x+2pi)

y=-10cot(x/2-2pi)

y=-1/2cos(5x/6+pi)

y =-1/3sin(x/3)

y = 2/3csc(x/4)+6

As y = 2/3csc(x/4)+6 gives a high value than the other, it is considered the highest.

What are increasing order and decreasing order?

Ascending order way going up from small value to excessive cost and textual content from A to Z. Descending order manner arranging the numbers from largest to smallest and textual content from Z to A. while the names are arranged for a list, then it is usually arranged in A to Z order, alphabetically.

Steps to find the Period of a Function

If a function repeats over a constant period we say that is a periodic function.It is represented like f(x) = f(x + p), p is the real number and this is the period of the function.Period means the time interval between the two occurrences of the wave.

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