Hi I need help explaining this question please.You and some neighbors are landscaping a community park. The organizer of the project selects an area for two congruent triangular rock gardens. You agree to be in charge of placing the pieces of wood to outline the gardens. The only tools you have are a saw, a protractor, and two very long pieces of wood. Describe one way to guarantee that the triangular outlines will be congruent. Justify your answer.
Answers
Congruence of Triangles
There are several theorems for triangles congruence. The SSS theorem, for example, guarantees congruence if all the side lengths are equal.
But for this project, we don't have any tool to measure lengths, just angles. So we need to move to another congruence theorem where angles are implied. That's where our protractor would be handy.
There are two logic choices to select from; ASA (Angle Side Angle) or AAS (Angle Angle Side).
I would use any of these because they only need one side length to be common in length.
Recall the ASA theorem states that two triangles that have two congruent angles and the side between them congruent too are congruent.
Similarly, two triangles are congruent (AAS theorem) if two of its angles are congruent and one of the non-included sides are also congruent.
The procedure would be like follows:
* Take the long pieces of wood and cut two pieces of the exact length. We don't need a ruler for that.
* Using the protractor, measure two angles in the reference triangle and place two additional pieces of wood that form the exact angles. If the angles are adjacent to the original piece of wood, you would be using the ASA theorem. If the angles are not adjacent to the original piece (just one of them), then you would be using the AAS theorem.
Related Questions
April buys soil for her flowerpots. she uses 9 kilograms of soil for her violets and 4 kilograms of soil for her tulips. she has 3,000 grams of soil left for some daisies (1 kilogram = 1,000 grams) use the drop down menus to show how much soil she bought
Answers
April bought 16 kilograms of soil in total.
To show how much soil April bought
We need to add the amounts of soil she used for her violets and tulips. Since April used kilograms for violets and tulips, we need to convert the 3,000 grams to kilograms before we can add them up.
April bought:
9 kilograms of soil for violets
4 kilograms of soil for tulips
3 kilograms of soil for daisies (since 3,000 grams is 3 kilograms)
Therefore, April bought 16 kilograms of soil in total.
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Simplify the following expression:
√-36+√-100+ 7
O A. 7+ 16i
OB. 7+√136i
O C. 16
C. 16 - 7i
O D. 23 + 0i
Answers
√-36 + √-100 + 7
To simplify this expression, we need to first remove the negative radicals. We can do this by squaring both sides of the equation:
√-36 = -6
√-100 = -10
Substituting these values back into the expression, we get:
-6 + -10 + 7 = -19 + 7 = -12
So, the simplified expression is:
-12
Since the expression is already in its simplified form, there is no need to factor it further.
Which of the following sets is equal to {1, 2, 3, ...}?
{x | x E R, x ≥ 1}
{x | x E R, x > 1}
{x | x E N, x ≥ 1}
Answers
5/6x=10/3 solve for x
Answers
Answer: x = 1/4
Step-by-step explanation:
5/6x=10/3
Cross multiply:
15=60x
x = 1/4
Answer:
1/4
Step-by-step explanation:
the answer may be 1/4
Si la posición de 5 m por debajo del nivel del mar se expresa con el número - 5, determina el número que expresa la posición de 7 m por encima del nivel del mar. El punto de referencia
Respuesta:
es el nivel del mar.
Answers
If the position of 5 m below sea level is expressed as -5, then the number that expresses the position of 7 m above sea level would be + 7.
How to reference point ?In this particular instance, with the position residing 7 m above sea level, we articulate it as +7. This notation elegantly captures the notion of elevation, affirming the distance above the familiar sea level benchmark.
In the realm of vertical measurements, sea level occupies a crucial position as the reference point, embodying the zero mark on the vertical scale. It is from this fundamental reference point that we navigate the vast spectrum of altitudes.
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Factor the expression using the GCF: -5x + 20
5(x + 4)
5(x-4)
-5(x + 4)
-5(x-4)
Answers
The answer fam is........-5(x-4)
Answer: Choice [D]
Step-by-step explanation:
Hii, do you need to factor the expression "-5x+20"? Let me help you out! (:
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Note that -5x and 20 have a -5 in common. Let's factor it out! (:
To factor it out, we first need to divide -5x and 20 by -5.
⚜ x-4 ⚜is what we obtain
Next we put parentheses around -x+4
(x-4)is what we obtain
Now, we put 5 outside the parentheses
-5(x-4)\(\Large\boldsymbol{\therefore,\qquad\ Choice\:\:\:\:[D]\;is\;correct}\)
--
Hope I helped! Best wishes.
⚜Reach far. Aim high. Dream big. ⚜
_________________________________\(\underbrace\)
A gym membership is $28 to join and $10 paid monthly.
Create a table to represent this scenario, then create an equation.
Enter your answers in the boxes.
Months Purchased Total Cost ($)
0 28
1
38
2
48
3
58
4
68
The equation to represent this scenario is y =
x +
.
Answers
Answer:
sorry needed points so sorry
Step-by-step explanation:
50 Points, Answer for brainlist and show work.
Use substitution to determine which ordered pairs lie on the graph of the exponential function.
f(x) = 3(4)^2x
(0, 3)
(1, 48)
(1/2, 12)
(.25, 8)
Answers
Substituting the values shows that the point that lies on the exponential function are
(0, 3)(1, 48)(1/2, 12)How to determine which ordered pairs lie on the graphWe can use substitution to determine which ordered pairs lie on the graph of the exponential function f(x) = 3(4)^2x.
For the first ordered pair (0, 3),
f(0) = 3(4)^2(0) = 3(1) = 3
(0, 3) lies on the graph of the exponential function.
For the second ordered pair (1, 48)
f(1) = 3(4)^2(1) = 3(16) = 48
(1, 48) lies on the graph of the exponential function.
For the third ordered pair (1/2, 12),
f(1/2) = 3(4)^2(1/2) = 3(4) = 12
(1/2, 12) lies on the graph of the exponential function.
For the fourth ordered pair (.25, 8), :
f(0.25) = 3(4)^2(0.25) = 6
say that (0.25, 8) does not lie on the graph of the exponential function.
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In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Isabella sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
105 visitors purchased no costume.
41 visitors purchased exactly one costume.
8 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase one or more costumes as a decimal to the nearest hundredth.
Answers
The probability that the next person will purchase one or more costumes can be found by dividing the number of visitors who purchased one or more costumes by the total number of visitors.
The total number of visitors is 105 + 41 + 8 = 154.
The number of visitors who purchased one or more costumes is 41 + 8 = 49.
So the probability that the next person will purchase one or more costumes is 49/154, which is approximately 0.32 to the nearest hundredth.
determine the number of ways to choose five numbers from the first eighteen positive integers such that any two chosen numbers differ by at least 2
Answers
The number of ways to choose five numbers from the first eighteen positive integers such that any two chosen numbers differ by at least 2 is 5,774 ways.
To solve this problem, we can use the principle of inclusion-exclusion. First, let's count the total number of ways to choose five numbers from 1 to 18, which is simply 18 choose 5 or \(${18\choose 5}\)= 8,568.
Next, we need to subtract the number of ways that violate the condition that any two chosen numbers differ by at least 2. We can do this by considering the complement, which is the number of ways to choose five numbers such that at least two chosen numbers differ by less than 2.
To count this, let's first choose one number from the 18 possible choices. Then, we can choose two numbers from the 3 possible adjacent numbers (i.e., the numbers that differ from the first chosen number by 1) and two numbers from the remaining 14 non-adjacent numbers, for a total of \(${18\choose 1}{3\choose 2}{14\choose 2}= 1,764$\)
However, this count includes cases where we choose three adjacent numbers, so we need to add back the number of ways to choose five numbers such that at least three chosen numbers are adjacent. We can do this by choosing one of the 16 possible sets of three adjacent numbers and two additional non-adjacent numbers, for a total of \(${16\choose 1}{15\choose 2}= 840$\)
Therefore, the number of ways to choose five numbers from the first eighteen positive integers such that any two chosen numbers differ by at least 2 is\(${{18\choose 5}} - {{18\choose 1}{3\choose 2}{14\choose 2}} + {{16\choose 1}{15\choose 2}} = 5,774$.\)
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d = 7 mm
Calculate the radius of the circle.
Answers
Answer:
r= d/2
7/2
3.5
3.5 is the answer
Step-by-step explanation:
9x^2-12x-4=0 quadratic graphing
Answers
The solutions of the quadratic equation:
9x² -12x - 4 = 0
are x = 12.944 and x = -0.278
How to solve the quadratic equation?Here we want to solve the quadratic equation:
9x² -12x - 4 = 0
To solve it we can use the quadratic formula, we will get:
\(x = \frac{12 \pm \sqrt{(-12)^2 - 4*9*(-4)} }{2*9} \\\\x = \frac{12 \pm 17}{18}\)
Then the two solutions are:
x = (12 + 17)/18 = 12.944
x = (12- 17)/18 = -0.278
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A cherry pie recipe requires 3/4 cups of sugar for the filling and 1/2 cup of sugar for the topping. Natalya has 71/2 cups of sugar. How many pies can she make? Write an equation with a variable and solve
Answers
Answer:
28
Step-by-step explanation:
Each pie requires 3/4 + 1/2 = 3/4 + 2/4 = 5/4 cups of sugar.
So, letting N = the number of pies that Natalya can make, we have that
N = [ (71/2) / (5/4) ] = [ 28.4 ] = 28, where [ . ] is the greatest integer function.
What is the surface area of the box formed by the pattern below?
Answers
Answer:
h
Step-by-step explanation:
The diameter of the steering wheel of the actual car is 15 inches. What is the diameter of a toy car's steering wheel if the toy is a 1:40 scale model of the real car?
Answers
Answer:
Step-by-step explanation 43 453 645
Mr. Heritage starts a new business, and to get it started he borrows $2 500 from a bank. If the loan is for two years, and the amount of interest for those two years is $175, what SIMPLE interest rate was he charged? (SIMPLE INTEREST: the principle and interest calculations dont change- they stay the same for the entire two year period!) BONUS- if he pays off the whole loan in the two years, what would his monthly bill be, (DON'T FORGET TO INCLUDE THE INTEREST CHARGE FOR HIS MONTHLY BILLS!!! YOU CAN ROUND YOUR CALCULATION TO THE NEAREST HUNDRETH- THAT IS, TO TWO DECIMAL PLACES...)
Answers
The rate of interest is given by the equation R = 3.5 %
What is Simple Interest?Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.
Simple Interest = ( Principal Amount x Rate x Time Period ) / 100
Given data ,
Let the rate of interest be represented as R
Now , the simple interest I = $ 175
The principal amount invested P = $ 2,500
The time period T = 2 years
Simple Interest = ( Principal Amount x Rate x Time Period ) / 100
Rate of Interest = (Simple Interest x 100 ) / Principal Amount x Time Period )
Substituting the values in the equation , we get
Rate of Interest R = ( 175 x 100 ) / ( 2500 x 2 )
Rate of Interest R = 17500 / 5000
Rate of Interest R = 3.5 %
Hence , the interest rate is 3.5 %
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Aaron filled the bird bath with 58 ounces of water. A group of blue jays came by and drank 3.18 ounces. Then a vulture swooped in and drank fourteen and two fifths ounces of the water. How much water is left in the bird bath?
75.58 ounces
72.40 ounces
69.22 ounces
40.42 ounces
Answers
Answer:
40.42 ounces.
Step-by-step explanation:
Initial volume of water: 58 ounces
"A group of blue jays came by and drank 3.18 ounces", it means that they substracted 3.18 ounces, therefore we do the following:
58 ounces - 3.18 ounces= 54.82 ounces.
After that, "...a vulture swooped in and drank fourteen and two fifths ounces of the water", this means that 14 ounces + 2/5 ounces were substracted from the bath.
As for right now, there are 54.82 ounces, let's calculate how much there was after the vulture passed by:
54.82 ounces - 14 ounces= 40.82 ounces.
40.82 ounces - 2/5 ounces, let's convert the fraction to a decimal and substract:
40.82 ounces - 0.4 ounces= 40.42 ounces.
Therefore, the final volume of water remaining in the bath is 40.42 ounces.
--------------------------------------------------------------------------------------------
This problem could be solved by adding up all the substractions and substracting the total amount from the initial volume of water in the bath. This would be the operation:
58 - (3.18 + 14 + 2/5)=
58 - (3.18 + 14 + 0.4)=
58 - (17.58)=
40.42 ounces.
Use the drawing tool(s) to form the correct answer on the provided graph.
Graph the following step function.
Answers
They have different y-intercepts but the same end behavior. Thus, option A is correct.
What is Step functiοn?A step functiοn is mathematical functiοn that takes οn finite number οf cοnstant values οver intervals οf its dοmain. It is alsο knοwn as staircase functiοn οr piecewise cοnstant functiοn. The cοnstant values that functiοn takes οn are οften referred tο as "steps" οf the functiοn.
Tο graph the step functiοn, yοu wοuld start by drawing a cοοrdinate plane with the hοrizοntal axis ranging frοm -5 tο 5 and the vertical axis ranging frοm -2 tο 2. Then, yοu wοuld plοt the pοints (-5,-1), (-4,-1), (-3,0), (-2,1), (-1,1), (0,0), (1,1), (2,-1), (3,-1), (4,0), and (5,1) οn the graph.
They have different y-intercepts but the same end behavior.
They have different y-intercepts because function f(x) is 4, while the y-intercept on graph is 6
But they have the same end behavior at 2.
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Complete question:
Function g is represented by the equation.
\(\rm g(x) = 4 (\frac14)^x + 2\)
Which statement correctly compares the two functions?
A. they have different Y-intercepts but the same end behavior
B. they have the same Y-intercept and the same end behavior
C. they have the same Y-intercept but different end behavior
D. they have different Y-intercepts and different end behavior
Sphenathi stated that the distance from Bloemfontein to upington is 16.3 show all calculations whether his claim is correct
Answers
The distance between Bloemfontein and Upington is a distance of 582 kilometers. The distance between two cities may vary depending on the route taken, traffic, and other factors. The distance between these two cities is measured in a straight line, which may not be the actual road distance.
To determine the distance between Bloemfontein and Upington, we used the Haversine formula, which computes the shortest distance between two points on the surface of a sphere. We first begin by finding the latitude and longitude of the two cities.Bloemfontein is located at -29.1211° latitude and 26.2140° longitude.Upington is located at -28.4478° latitude and 21.2561° longitude.Using the Haversine formula, we can determine that the distance between the two cities is about 582 kilometers.Sphenathi's statement that the distance from Bloemfontein to Upington is 16.3 kilometers is incorrect. Perhaps they mistakenly calculated the distance between two points within the cities. They could also have made a typographical mistake while writing their statement. Therefore, the statement is false, and the actual distance between Bloemfontein and Upington is 582 kilometers.For such more question on longitude
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In the expansion of (2+3x)^n, the coefficients of x^3 and x^4 are in the ratio of 8:15. FIn the expansion of (2+3x)^n, the coefficients of x^3 and x^4 are in the ratio of 8:15. Find the value of n.ind the value of n.
Answers
The value of n is 8.
What is Binomial Theorem?Binomial theorem is the method of expanding an expression consisting of two terms raised to any power.
Using the expansion of Binomial theorem, we can write,
(2 + 3x)ⁿ = ⁿC₀ (2)ⁿ (3x)⁰ + ⁿC₁ (2)ⁿ⁻¹ (3x)¹ + ⁿC₂ (2)ⁿ⁻² (3x)² + ⁿC₃ (2)ⁿ⁻³ (3x)³ + ⁿC₄ (2)ⁿ⁻⁴ (3x)⁴ + .............
Coefficient of x³ is ⁿC₃ (2)ⁿ⁻³ (3)³ and the coefficient of x⁴ is ⁿC₄ (2)ⁿ⁻⁴ (3)⁴.
Ratio of these coefficients is 8 : 15.
[ⁿC₃ (2)ⁿ⁻³ (3)³] / [ⁿC₄ (2)ⁿ⁻⁴ (3)⁴] = 8 / 15
Simplifying,
(4 × 2) / [(n - 3) 3] = 8/15
8 / 3n - 9 = 8 /15
Equating, we have,
3n - 9 = 15
3n = 24
n = 8
Hence the value of n is 8.
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Find the value of x
Answers
Answer: The value of x is 49.
Step-by-step explanation:
To find the value of x, you will first need to cross multiply the fractional variables together.
5x - 80 = 3x + 18
Then, move the numerical term 80 to the right side of this equation and add it to 18.
5x - 80 = 3x + 98
Move 3x to the left side of the equation and subtract it this time to the variable 5x.
2x = 98
Finally, you divide both of the equation's sides by 2 and you will get 49.
x = 49
When you actually add x to this problem, you would get 33/55.
49 - 16/49 +6 = 33/55
You can then simplify 33/55 and get the same answer 3/5.
3/5
Therefore, the value of x for this variable equation with the fractions would be equal to x = 49. Hope this helps!
-From 5th Grader Honors Student
The Blue Ridge parkway is 469 miles long. The parkway is a road that runs through 29 Virginia and North Carolina counties. Sam drove 2/5 of the parkway on vacation. How many miles did he drive? Simplify your answer and said it as a mixed number
Answers
187.6miles
Step-by-step explanation:
blue ridge parkway is 469miles
sam drove 2/5 of the parkway
2/5×469
=469×2/5
938/5
187.6miles
Solve for X and Y
1. y = 2x
6x + 3y = 12
2. y = -4x + 2
y = 6x - 8
3. y = x - 4
-4x - 6y = -16
4. x = 3y + 1
2x + 4y = 12
Answers
Answer:
What do you mean?
Step-by-step explanation:
2.1. Provide a general rule to describe the relationship between the dates of spread and number of people infected infected.
Answers
The relationship between the dates of spread and the number of people infected can vary depending on various factors such as the infectiousness of the disease, the effectiveness of containment measures, population density, and individual behaviors.
However, there is a general rule that can describe the relationship:As the dates of spread progress, the number of infected individuals tends to increase initially, reaching a peak, and then gradually decreasing over time.
This pattern is often referred to as the epidemic curve or the epidemiological curve. In the early stages of an outbreak, the number of cases may grow rapidly as the disease spreads through a susceptible population. This rapid increase is often influenced by factors such as the contagiousness of the disease, population density, and social interactions.
As containment measures, such as vaccination campaigns, public health interventions, and behavioral changes, are implemented, the rate of new infections may start to decline. This can lead to a peak in the number of cases, after which the curve gradually decreases as the disease is brought under control and fewer susceptible individuals remain.
It's important to note that the specific shape, duration, and magnitude of the epidemic curve can vary significantly depending on the disease and the effectiveness of the response measures implemented. Additionally, emerging variants, changes in behavior, and other factors can impact the trajectory of the epidemic curve.
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What’s the circumference of a circle with radius of 10 inches? Use 3.14 for pie
Answers
You do 2pi x the radius (10) to get the circumference of a circle
The midpoint of AB is M(1, 4). If the coordinates of A are (8, 7), what are the
coordinates of B?
Answers
\(~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{8}~,~\stackrel{y_1}{7})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +8}{2}~~~ ,~~~ \cfrac{ y +7}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M}}{(1~~,~~4)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +8}{2}=1\implies x+8=2\implies \boxed{x=-6} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +7}{2}=4\implies y+7=8\implies \boxed{y=1}\)
After filling a gas tank the odometer read 27,8295After the next filling it read 28,1760. It took 17.5 gal to fill the tank How many miles per gallon did the driver get?
Answers
Answer:
198 mpg
Step-by-step explanation
28,1760-27,8295 = 3465 miles
3465miles/17.5gal = 198 mpg
What is the equation of the line? y=3/4x−1 y=4/3x+1 y=4/3x−1 y=3/4x+1
Answers
Answer:
y=4/3+1
Step-by-step explanation:
The y-intercept is positive 1,
The slope form is always rise over run,
Therefore rising from 1 takes us to 5 then we run 3 times, so it takes us to (3,5)
Find the volume of the rectangular pyramid below.
Answers
Answer:
315 yd cubed
Step-by-step explanation:
To find the volume of the pyramid, we first need to consult the equation below. Thebase is for the rectangular portion, then after multiplied by the height it is divided by 3 to get the pyramid.
\(\frac{1}{3} (B * H )\)
To get the base, we multiply the length by the width.
21 * 9 = 189
189 * 5 = 945
945 divided by 3 = 315
Answer:
Let's find the base area:
21 x 9 = 189
Now let's multiply the base area by the height:
189 x 5 = 945
Now let's divide by 3( x 1/3 ):
945 divided by 3(x 1/3) = 315 yd^3 is your answer
Step-by-step explanation:
Formula area of a rectangular Pyramid(just like any other pyramid):
BH x 1/3
To find base we multiply length by width just using the basic formula of finding area of a rectangle.
Then we multiply our base area by our height.
One we've done that we now divide by 3(multiplying by 1/3)
The surface area of the rectangular prism is given by formula S=2(ab+bh+ah). Find the value of h when a=6, b=5 and s=214
Answers
The value for the height of the rectangular prism is found as; h = 7.
What is defined as the rectangular prism?A rectangular prism is a three dimensional solid shape with six faces that have rectangles as their bases. Right rectangular prisms as well as non-right (oblique) rectangle prisms are the two types of rectangular prisms. The right rectangle prism does have two parallel end faces and 4 lateral faces, each of which is an rectangle; this same faces are perpendicular to the bases of the prism.The formula for the surface area of rectangular prism is;
S = 2(ab+bh+ah)
Where,
a=6, b=5 and s=214
Substitute the values in the formula.
214 = 2(6×5 + 5h + 6h)
Simplifying;
30 + 11h = 107
11h = 107 - 30
11h = 77
h = 7
Thus, the value for the height of the prism is found as; h = 7.
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