The members of the gardening group plan to build a walkway through the garden as formed by the hypotenuse of each of the four triangles in the drawing. That way, the gardeners will be able to access all sections of the garden. Calculate the length of the entire walkway to the nearest hundredth of a yard. Show your work

Answers

Answer 1

Pythagoras' theorem is a basic relationship between the three sides of a right triangle. The length of the entire walkway to the nearest hundredth of a yard is 50.24 yds.

What is Pythagoras theorem?

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.

In order to calculate the length of the walkway, we need to calculate the value of b first. Therefore,  the value of b using the Pythagoras theorem can be written as,

[tex]D^2=12^2+b^2\\15^2=12^2+b^2\\225=144+b^2\\b^2= 81\\b=9[/tex]

As we  got the value of b, now the value of each of the four hypotenuses can be written as,

[tex]A = \sqrt{12^2+8^2} = \sqrt{208}=14.422\\\\B=\sqrt{6^2+8^2}=\sqrt{100} = 10\\\\C =\sqrt{6^2+9^2}=\sqrt{117} = 10.82\\\\D = 15[/tex]

Adding the value of all the hypotenuse to get the length of the walkway, therefore, the length will be,

[tex]Sum = A+B+C+D = 14.422+10+10.82+15 = 50.24[/tex]

Hence, the length of the entire walkway to the nearest hundredth of a yard is 50.24 yds.

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The Members Of The Gardening Group Plan To Build A Walkway Through The Garden As Formed By The Hypotenuse

Related Questions

ASAP!!! PlEASE !!!!!!!!!

Answers

Answer:

100 yards cubed

Answer: 100

Step-by-step explanation:

multiply them all together

simplest radical form
-5√243-3√27​

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Answer:

-54√3

Step-by-step explanation:

Is it 1 2 3 or 4? I need to know

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Answer:

I think it is 1

I'm almost positive

Non of those answers seem right bc 5(1/3) = 1.66666 and 3(2/5)=1.2 and 3(3/7)=1.2857 so I guess they aren’t proportional.

a fair coin is tossed 14 times, what is the probability of exactly 6 heads

Answers

Answer:

42.85% or 6/14

Step-by-step explanation:

6 / 14 = 0.428571428571

0.428571428571 * 100 ~ 42.85%                

Can I get Brainliest?                    

Janice determined there were 10 possible outcomes when tossing two coins and spinning a spinner numbered 1 through 6. What is the correct number? What might have been Janice's error? 3; There are only 3 events. 6; There is only 1 possible outcome for the coins. 24; She added the number of possibilities instead of multiplying. 36; The spinner was spun twice.

Answers

Answer:

c: 24

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Franco begins to save for a new Lego set that costs $65. His parents gave him $35 towards the cost and he plans to save $5 per week.
Write an equation modeling the total amount he has saved

Answers

Answer:

T = 35 + 5s

Step-by-step explanation:

Here, we want to write an equation for the the total amount that has been saved.

Let the number of weeks he has saved for be s

Then his total savings will be 5 * s = 5s

Now let’s add the $35 from his parents

This will give 35 + 5s

let T be the total

amount that hass beeem saved

So;

T = 35 + 5s

where a represents the number of weeks for which he has saved and T represent the total money that has been saved

In a triangle, the measure of the middle angle
is triple the measure of the smallest angle, and
the measure of the largest angle is 55° greater
than the measure of the smallest angle. Find
the measures of the
angles.

Answers

Let the smallest angle in a triangle be = x

Largest angle in a triangle = 55 + x

The middle angle in a triangle = 3x ( triple the measure of the smallest angle )

Their sum = 180° ( according to the angle sum property all the angles of a triangle sum up to 180° )

This can be written as :

= x + 55 + × + 3x = 180

Let us find each angle by solving the equation .

= x + 55 + x + 3x = 180°

= x + x + 3x + 55 = 180°

= 5x + 55 = 180°

= 5x = 180 - 55 ( transposing +55 from LHS to RHS changes +55 to -55 )

= 5x = 125

= x = 125 ÷ 5 (transposing ×5 from LHS to RHS changes ×5 to ÷5 )

= x = 25

Using this let us find the measure of each angle .

Smallest angle = x = 25

Smallest angle = 25°

Middle angle = 3x = 3 × 25 = 75

Middle angle = 75°

The largest angle = x + 55 = 25 + 55 = 80

Largest angle = 80°

Therefore , the measure of the smallest angle = 25° , the measure of the middle angle = 75° and the measure of the largest angle = 80° .

We have that the measures of the  angles are as follows

[tex]\theta_1=80 \textdegree[/tex]

[tex]\theta_2=75 \textdegree[/tex]

[tex]\theta_3=25 \textdegree[/tex]

From the question we are told that:

The measure of the middle angle  is triple the measure of the smallest angle

The measure of the largest angle is 55° greater  than the measure of the smallest angle

Let

[tex]\theta_1=Largest\ angle[/tex]

[tex]\theta_2=Middle\ angle[/tex]

[tex]\theta_3=Smallest\ angle[/tex]

Therefore

[tex]\theta_1=55 \textdegree+\theta_3\\\\\theta_2=3*\theta_3[/tex]

Generally, the equation for the angle of a triangle is mathematically given by

[tex]\theta_1+\theta_2+\theta_3=180[/tex]

Therefore

[tex]55 \textdegree+\theta_3+3*\theta_3+\theta_3=180[/tex]

[tex]\theta_3=25 \textdegree[/tex]

Therefore

Substitute [tex]\theta_3[/tex] into equations of [tex]\theta_1[/tex] and [tex]\theta_2[/tex]

For [tex]\theta_1[/tex]

[tex]\theta_1=55 \textdegree+25 \textdegree\\\\\theta_1=80 \textdegree[/tex]

For [tex]\theta_2[/tex]

[tex]\theta_2=3*\theta_3[/tex]

[tex]\theta_2=3*25 \textdegree[/tex]

[tex]\theta_2=75 \textdegree[/tex]

in conclusion

The measures of the  angles are as follows

[tex]\theta_1=80 \textdegree[/tex]

[tex]\theta_2=75 \textdegree[/tex]

[tex]\theta_3=25 \textdegree[/tex]

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Someone helppppppppppppp

Answers

Answer:

10 and 11

Step-by-step explanation:

10 and 11.

These are the closest whole numbers, because the square root of 100 is 10, and the square root of 121 is 11.

If this helped, please rate and give THANKS!

Find the value of each variable.

Answers

X = 5
M1 = 22
M5 = 22
The measure of angle 1 and 5 are congruent

1572 divide 0.3 you must show all workings

Answers

Answer:

5240

Step-by-step explanation:

Which sequence of transformations will result in a parallelogram with vertices A(−2, 1), B(−4,−3), C(2,−5), D(4,−1) being carried onto the parallelogram A'B'C'D' shown below?

Answers

Answer:

translated  1 unit right and 2 units up followed by a reflection across x axis

Step-by-step explanation:

Parallelogram has vertices A(−2, 1), B(−4,−3), C(2,−5), D(4,−1) while parallelogram A'B'C'D' has vertices A'(-1, -3) B'(-3, 1) C'(3, 3) D'(5, -1)

Transformation is the movement of a point from its initial location to  new location. If an object is transformed then all its points are transformed. Types of transformation are rotation, reflection, dilation and translation.

If a point X(x, y) is translated a units right and b unit up , the new point is X'(x + a, y + b).

If a point X(x, y) is reflected across the x axis, the new point is X'(x, -y)

If parallelogram ABCD is translated  1 unit right and 2 units up (i.e. x + 1, y + 2), the new points is A*(-1, 3), B*(-3, -1), C*(3, -3), D*(5, -1). If a reflection across x axis is then done, the new point is A'(-1, -3) B'(-3, 1) C'(3, 3) D'(5, -1)

Answer:

A translation 1 unit right and 2 units up followed by a reflection across the x-axis.

Step-by-step explanation:

Because you slid the shape over.

Hope this helps! Stay safe! :))))

How do I solve this?(tangent segment)

Answers

Answer:

x = 6

Step-by-step explanation:

Given a tangent and a secant from an external point to the circle, then

The square of the tangent is equal to the product of the measures of the external part and the entire secant, that is

x² = 4(4 + 5) = 4 × 9 = 36 ( take the square root of both sides )

x = [tex]\sqrt{36}[/tex] = 6

10points!
will make brainliest for correct answer
-8 1/3 + (- 1/6)

Answers

Answer:

-8 1/2

Step-by-step explanation:

-8 1/3 + (- 1/6)

Get a common denominator

-8 2/6 - 1/6

Combine terms

-8 3/6

Simplify

-8 1/2

Anoushka needs to stain the circular wooden deck in the backyard. The deck has a diameter of 30 feet. A gallon of stain covers approximately 250 square feet. Each gallon is $33.99. How much will Anoushka spend in order to stain the deck? Use 3.14 to approximate .

Answers

Answer:

$101.97

Step-by-step explanation:

Diameter of circular wooden deck = 30 ft

Radius of the deck = ½ of diameter = ½*30 = 15 ft

Area of deck = πr² = 3.14*15² = 706.5 ft²

1 gallon covers 250 ft² (1 gallon = 250 ft²)

Let x be the number of gallons that will cover 706.5 ft² of the deck

Thus:

1 gallon = 250 ft²

x = 706.5 ft²

Cross multiply

1*706.5 = 250*x

706.5/250 = x

2.826 = x

Number of gallons to cover the deck is approximately 3 gallons (approximated to nearest whole number). Since the we can't buy a gallon that is not full, we approximate to give us 3 gallons.

1 gallon cost $33.99 (1 gallon = $33.99)

3 gallons cost: 3*33.99 = $101.97

What are the y vale’s of the equation y = -3x + 4 at x values -1, 0, 1, 2?

Answers

Answer:

(-1, 7)

(0, 4)

(1, 1)

(2, -2)

Step-by-step explanation:

y = -3x + 4

y = -3(-1) + 4 = 3 + 4 = 7

y = -3(0) + 4 = 4

y = -3(1) + 4 = 1

y = -3(2) + 4 = -6 + 4 = -2

7. Given (3, 5) and (-2, 1), find the slope of the line passing through these two points.​

Answers

Answer:

4/5

Step-by-step explanation:

y2-y1/x2-x1 so....... 5-1/3-(-2)

You plug it into the equation for calculating slope:

(Y₂ - Y₁) ÷ (X₂ - X₁)

Let X₂ be 3 and Y₂ be 5.

X₁ = -2 and Y₁ = 1.

(5 - 1) ÷ (3 - (-2))

4 ÷ 5

4/5

The slope is 4/5.

Hope this helps

what is the translation of the expression 5 more than twice x

Answers

Answer:

5+2x

Step-by-step explanation:

Answer:

5 + 2x

Step-by-step explanation:

What is 13 / 143 as a unit fraction

Answers

Answer:1/11

Just got it using some brain cells >:)

Answer:

1/11

Step-by-step explanation:

13/143=1/11

What are the y-intercepts to graph the equation -4x – 3y = 36?

Answers

4x-3y =36

Move the constant to the left by adding its opposite to both sides

4x-3y-36=36-36

The sum of two opposites equals 0

Answer: 4x-3y-36=0

PLEASE MARK ME AS BRAINLIEST

-4x+3=-2 y=x-1 solve for x and y

Answers

Answer:

x=1 1/4 (1.25), y=1/4

Step-by-step explanation:

Since the equation "y=x-1" seems simple enough, we're going to plug that in for our other equation, "-4x+3=-2".

1. Rearrange y=x-1 to fit our other equation, -4x+3=-2.

y=x-1 (add 1 to both sides)

y+1=x x=y+1

2. Plug our newly rearranged equation into -4x+3=-2.

-4(y+1)+3=-2

-4y-4+3=-2 (distributive property)

3. Add/subtract like terms.

-4y-1=-2

4. Get y to be by itself.

-4y=-1 (add 1 to both sides)

y=1/4

1. Now for y=x-1. Plug 1/4 into y.

1/4=x-1

1 1/4=x

PLEASE HELP ME! I am not sure how to answer this question.​

Answers

Answer:

yes

Step-by-step explanation:

the diagnols are congruent meaning that the diagnol lines in the middle are the same length. So theoretically the left and right lengths are the same, and the top and bottom lengths are the same. The triagles named both have the same base and they're hieght is sbviouysly the same so they would be SSS each of the sides on one triangle coresspondes to the other.

Write the equation of a line that passes through the point (3, 4) and has a slope of -1

Answers

Answer:

[tex]Y = -1x + 4[/tex]

Step-by-step explanation:

Hope this helps

how do i put 5x^2+6+3xy^5-2x in standard form

Answers

Answer:

it's 3xy^5 + 5x^2 -2x +6

Is this a function or no

Answers

I believe this is not a function(pleaseee give me a like)
That’s most definitely not a function..

name the sets of numbers to which 7/9 belongs

Answers

Answer:

OK.

the sets are

natural numbers (or counting numbers), this is like 1,2,3,4,5 etc

whole numbers, this is including 0, so 0,1,2,3,4,5,6 etc

integers, this includes the previoius set and negatives, so -3,-2,-1,0,1,2,3,4,5 etc

rational numbers, this is the set of numbers that can be written in form a/b where b≠0, so all integers can be written like this, like example -3=-3/1, so -7/9 belongs here

-7/9 goes in the rational set

Find the x - and y - intercepts of the graph of the linear equation-4x+8y=-16

Answers

Answer:

y-intercept: (0, -2)

x-intercept: (4, 0)

Step-by-step explanation:

The x intercept occurs when y = 0, so you can substitute 0 in for y and solve for x as shown:

-4x+8y=-16

-4x+8(0)=-16

-4x+0=-16

-4x=-16

x=4 ---------- format correctly in (x, y) : (4, 0)

The y intercept occurs when x = 0, so you can substitute 0 in for x and solve for y as shown:

-4x+8y=-16

-4(0)+8y=-16

0+8y=-16

8y=-16

y=-2 ---------- format correctly in (x, y) : (0, -2)

a little boy gets a haircut.the total cost is $24 and the tip should be 10% how much should the barber get as a tip?

Answers

Answer:

2.40$ or 2.4$

Step-by-step explanation:

divide 24 and 10 and you should get the answer of 2.40$ or 2.4$

Please help asap!! I'll give you brainliest!!

What is the slope of the function, represented by the table of values below?

Answers

Answer:

-4

Step-by-step explanation:

To find the slope, you can use the formula y2-y1/x2-x1. Plugin any set of values. Say 13 is y2, and 5 is y1. 13-5=8. We now have 8/x2-x1. You have to use the x-values of the y-values that you already used. -2 is x2 and 0 is x1. -2-0=-2. 8/-2 = -4.

There are approximately 1.2 × 10 8 households in the U.S. If the average household uses 400 gallons of water each day, what is the total number of gallons of water used by households in the U.S. each day?

Answers

Answer:

Que

Step-by-step explanation:

Noah’s dog weighs 15 1⁄3 pounds (lbs). Aiden’s dog weighs three times as much as Noah’s. How many pounds does Aiden’s dog weigh?

Answers

Answer:  46 pounds

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

Work Shown:

N = weight of Noah's dog = 15 & 1/3 pounds

A = weight of Aiden's dog = unknown

A = 3*N

A = 3*(15 & 1/3)

A = 3*(15 + 1/3)

A = 3*15 + 3*(1/3) .... distribute

A = 45 + 1

A = 46

Aiden's dog weighs 46 pounds.

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