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
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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Related Questions
1572 divide 0.3 you must show all workings
Answers
Answer:
5240
Step-by-step explanation:
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
ASAP!!! PlEASE !!!!!!!!!
Answers
Answer:
100 yards cubed
Answer: 100
Step-by-step explanation:
multiply them all together
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
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:
Find the value of each variable.
Answers
M1 = 22
M5 = 22
The measure of angle 1 and 5 are congruent
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
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.
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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
Is this a function or no
Answers
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
-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
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
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.
how do i put 5x^2+6+3xy^5-2x in standard form
Answers
Answer:
it's 3xy^5 + 5x^2 -2x +6
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$
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)
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.
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
simplest radical form
-5√243-3√27
Answers
Answer:
-54√3
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! :))))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
===============================================
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.
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?
Is it 1 2 3 or 4? I need to know
Answers
Answer:
I think it is 1
I'm almost positive
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
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:
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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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 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 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