In construction, the precision used to build a structure directly influences the strength of the structure. In the Rocky Mountains, many houses’ roofs are built using trusses, which are strong enough to support the heavy load from snow, but light enough to build in a stockyard and transport to the construction site. Chris works in the stockyard. He has been told he needs to build a series of trusses for a new house using the pattern below. He has also been told the pattern may be inaccurate—so he needs to check and make sure the following features are all parallel, and adjust the pattern before starting.

On this discussion board, post your answers to these questions:

1) What method(s) can Chris use to make sure the segments in the pattern are all parallel and that his new trusses are built precisely and strongly?
2) What method(s) can Chris’s boss use to verify the precision of the trusses Chris builds?
3)Identify any alternate interior angles, corresponding angles, and/or alternate exterior angles.

A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle.The triangles formed due to the diagonal of the rectangle are congruent to one another.

A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.

For the given rectangle ABCD, the length of the diagonals AC and BD can be written as,

AC = √(x² + y²)

BD = √(x² + y²)

Now, the triangles formed due to the diagonals AC and BD are ΔABC and ΔBCD. Also, for ΔABC and ΔBCD we can write,

∠ABC = ∠BCD = 90°

AB = CD = x {Oppsite sides of the rectangle are equal}

BC = AD = y {Oppsite sides of the rectangle are equal}

Hence, the two triangles are equal. Therefore, the triangles formed due to the diagonal of the rectangle are congruent to one another.

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A slope is also known as the gradient of a line. The slope of the given linear table is $250 per car.

A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.

slope = (y₂-y₁)/(x₂-x₁)

The slope of the linear table is,

m = ($4,000 - $2,500)/(12-6) = $250 per cars

Hence, the slope of the given linear table is $250 per car.

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The tangents that exists between the two given circles are not common tangents because they are not of the same size or circumference.

A tangent can be defined as the plane line that touches a curved surface such as a circle but doesn't pass through the circle.

From the diagram given, the two circles are not of the same size, that is, they have different circumstances. This means that the point where the line meets the both circles are not the same.

Therefore, the tangents that exists between the two given circles are not common tangents.

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Answer:

31.77 yd/sec

Step-by-step explanation:

Conversions:

Given:

[tex]\sf 65\:miles\:per\:hour=65\:miles/hour=\dfrac{65\:miles}{hour}[/tex]

Therefore, to convert 65 mph to yards per second:

[tex]\implies \sf \dfrac{65\:miles}{hour}=\dfrac{65 \times 1760\:yards}{3600\:seconds}=31.777...\:yd/s[/tex]

Answer:

c.) 31.77... yd/sec

Explanation:

Given: 1 hours → 65 miles

Conversions:

(i) 1 hour = 60 minutes = 3600 seconds

(ii) 1 miles = 1760 yards

Then,

⇒ distance/speed

⇒ 114400/3600

⇒ 31.77777...

⇒ 31.77 yd/sec

Answer:

$2,649.50

Step-by-step explanation:

s

The additional information that would make it immediately possible to prove that triangles AXB and CXB are congruent using the HL theorem is that BD is perpendicular to AC.

From the information, Triangles A B C and A D C share side A C. Line X is drawn from point B to point B to form 4 triangles.

In this case, the additional information that would make it immediately possible to prove that triangles AXB and CXB are congruent using the HL theorem is that BD is perpendicular to AC.

Also, the additional information would make it immediately possible to prove that triangles AXD and CXD are congruent using the SSS congruence theorem is that AX and CX are congruent.

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Answer:

What additional information would make it immediately possible to prove that triangles AXB and CXB are congruent using the HL theorem?

✔ AC and BD are perpendicular.

What additional information would make it immediately possible to prove that triangles AXD and CXD are congruent using the SSS congruence theorem?

✔ AX and CX are congruent.

Step-by-step explanation:

right on edge

The equation that represents the situation will be 4y = 5x.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The number y of objects a machine produces is proportional to the time x (in minutes) that the machine runs.

The machine produces five objects in four minutes.

Let y be the number of objects and x be the number of the minutes.

Then the equation that represents the situation will be

 y = (5/4)x

4y = 5x

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The weight of each one of the five little girls if taken separately is 242.4 lb.

The weight of each girl can be determined from the average weight of the girls.

Weight of each girl = (Total weight) / number of girls

W = (129 + 125 + 124 + 123 + 122 + 121 + 120 + 118 + 116 + 114)/5

W = 1,212/5

W = 242.4 lb

Thus, the weight of each one of the five little girls if taken separately is 242.4.

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The above question is a mathematical proof of the relationship between Lines and angles related to a Rhombus. See the proof below.

A Rhombus is a parallelogram with four sides (that is a quadrilateral). It's sides however are all of equal length.

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Congruent triangles are two or more triangles with the same length of sides and measure of internal angles. Thus the required proof is as shown below:

From the given diagram, it can be observed that:

AB = AC (similar property of two lines)

AC = AE (similar property of two lines)

Also,

m<A is a common angle to ΔABC and ΔADE

So that it can be concluded that;

ΔABC ≅ ΔADE (Side-Angle-Side property)

Thus since ΔABC ≅ ΔADE are congruent, then;

BC = DE (corresponding sides of congruent triangles)

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See below for the proof that sides BC and DE are congruent

The given parameters are:

AC = AE

AB = AD

∠BAD = ∠EAC

By the definition of congruence, side lengths marked with I are congruent and side lengths marked with II are congruent

From the attached figure, we have the following marks:

In triangle ABC,

AB = I and AC = II

In triangle ADE,

AD = I and AE = II

This means that two corresponding sides of ABC and ADE are congruent.

Since both triangles have a congruent angle, then the last corresponding sides are also congruent

i.e. BC = DE

Hence, sides BC and DE are congruent

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Answer:

-56√3x

Step-by-step explanation:

√147 = 7√3

-8(7√3x)

-56√3x

Answer:

she has 23 points

Step-by-step explanation:

hope this helps and mark brainliest please

Yes, the population of Town C increased by at least 100 percent from the year 2000 to the year 2010

Statement 1: The population of Town C in 2000 was 2/3 of the population in 2005

This tells us the population change from 2000 to 2005 since we need to know the population change from 2000 to 2010, this statement is not sufficient.

Statement 2: The population of Town C increased by a greater number of people from 2005 to 2010 than it did from 2000 to 2005.

Since statement 2 provides no information about the population change from 2000 to 2005, there is no to answer this question with certainty. thus, statement 2 is not sufficient

Statement 1 and Statement 2 combined:

Let X= the population in 2000

Let Y= the population in 2005

Let Z= the population in 2010

From statement 1, we can write: X=[tex]\frac{2}{3}[/tex]Y

Multiply both sides by 3 to get [tex]3X=2Y[/tex]

Divide both sides by 2 to get [tex]\frac{3}{2}X=Y[/tex]

=>[tex]Y=1.5X[/tex]

As per statement 2, let's first determine the increase in the number of people from 2000 to 2005

If [tex]Y=1.5X[/tex], we know

X= the population in 2000

1.5X= the population in 2005

[tex]1.5X-X=0.5X[/tex]

So, the population increased  [tex]0.5X[/tex] from 2000 to 2005

So,  from 2005 to 2010, the population increased at least 0.5X

1.5X= the population in 2005

[tex]1.5X+0.5X=2.0X[/tex]

So, the population in 2010 was at least 2.0X

In other words, the population at least doubled from 2000 to 2010

So, the answer to the target question is yes, the population of Town C increased by at least 100 percent from the year 2000 to the year 2010

Did the population of Town C increase by at least 100 percent from the year 2000 to the year 2010?

(1) The population of Town C in 2000 was 2/3 of the population in 2005.

(2) The population of Town C increased by a greater number of people from 2005 to 2010 than it did from 2000 to 2005.

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The function in slope-intercept form is mathematically given as

f(x)=14x+154

Parameters

f(2)=-11,

f(4)=-25

Generally, the equation for the slope is  mathematically given as

[tex]m=\frac{-25+11}{2-}[/tex]

m=7

In conclusion, the line equation

y-2=7(x-+11)

y as subject

y=14x+154

f(x)=14x+154

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Answer:

 The triangle is not acute because 2² + 4² < 5².

Step-by-step explanation:

Answer:

The triangle is not acute because 2² + 4² < 5²

Step-by-step explanation:

got it correct on my quiz

AnsTHE OTHER GUY GOT IT RIGHT SORRY I DID THE MATH WRONG :( Step-by-step explanation:

Answer:

5.2 miles

Step-by-step explanation:

Distance left to ride = 26.8miles - 6 miles = 20.8 miles

There are 4 days left, so on average,

Hassan has to ride:

[tex] \frac{20.8}{4} \\ = 5.2mi[/tex]

Answer:

BC || AD and AB || CD (given)

∠BCA ≅ ∠DAC 2. As alt.interior angles with parallel lines

∠BAC ≅ ∠DCA 3. As alt.interior angles with parallel lines

AC ≅ AC (identity)

△ABC ≅ △CDA (ASA)

AB = CD (CPCT C)

The area of triangle BMN is 124.7 square centimeter.

Similar triangles are triangles that their corresponding angles are equal and the ratio of their corresponding lengths are equal. They are often similar When at least Two angles are equal or The ratio of any corresponding lengths are same.

Analysis:

AB = AC = BC = 50cm

AH = AC/2 = 50/2 = 25cm

From Δ ABH, using Pythagoras theorem to find BH.

[tex](BH)^{2}[/tex] = [tex](AB)^{2}[/tex] - [tex](AH)^{2}[/tex]

[tex](BH)^{2}[/tex] = [tex]50^{2}[/tex] - [tex]25^{2}[/tex]

[tex](BH)^{2}[/tex] = 2500 - 625

[tex](BH)^{2}[/tex] = 1875

BH = [tex]\sqrt{1875}[/tex] = 43.3cm

ΔBMN and BHC are similar,

so, BM/BH = MN/HC

BM/43.3 = 12/25

25BM = 12 X 43.3

BM = 519.6/25 = 20.78cm

Area of ΔBMN

= 1/2(MN)(BM) = 1/2 x 12 x 20.78 = 124.7 square centimeter

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Both angles have a measure of 125°.

Assuming the two horizontal lines are parallel, we know that the measure of the two indicated angles must be the same one.

Then:

-1 + 14x = 12x + 17

Now we need to solve this for x:

14x - 12x = 17 + 1

2x = 18

x =18/2 = 9

Now that we know the value of x we can replace it in any of the expressions for the angles:

-1 + 14*9 = 125°

Both angles have a measure of 125°.

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Answer:

Step-by-step explanation:

The domain is the set of x values, and the range is the set of y values.

It will require 2 tablespoons of salt for just 1 tablespoon of sugar for the combination.

Word problems are a systematic approach used in mathematics for solving real-life cases by determining unknown values.

From the given information:

i.e.

11 tablespoon of sugar  + 22 teaspoon of salt = 1 recipe

Then it will require 2 tablespoons of salt for just 1 tablespoon of sugar.

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Total time for whole journey would be 3 hours.

The total trip is divided into three intervals :-

Hence to find the total time of the trip we need time taken in each interval and just add them up.

The final expression would be :-

Total time taken = Time taken by bus + Time taken by train +

                                Time taken to change between them

Given:-

Thus Total time for whole journey would be 3 hours.

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Step-by-step explanation:

all real numbers not equal to 0

all real numbers

Step-by-step explanation:

[tex]What \ is\ the \ range \ of \ y = log_8x?\\x > 0 \ or\ x\in(0;\infty).\\Answer: \ all \ real \ numbers \ greater\ than \ 0.[/tex]

1) [tex]4x+5=-6x+5[/tex] (given)

2) [tex]4x=-6x[/tex] (subtraction property of equality)

3) [tex]10x=0[/tex] (addition property of equality)

4) [tex]x=0[/tex] (division property of equality)

The total cost or amount that Tiger Biscuits will pay will be Rs 16000.

From the information given, the factory is planing to produce 10,000 units and the standard time per 200 units is 8 hours.

The time taken to produce 10000 units will be:

= (10000/200) × 8

= 400 hours.

The amount that the company will pay will be:

= 400 × Rs 40

= Rs 16000

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The solution of the system of linear equation are (1, 7)

3a + 6b = 45

2a - 2b = -12

multiply equation(ii) by 3

Therefore,

3a + 6b = 45

6a - 6b = -36

9a  = 9

a = 1

Hence,

2(1) - 2b = -12

2 - 2b = -12

-2b = -12 - 2

- 2b = - 14

b = -14 / -2

b = 7

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The solution to the equation below to the nearest fourth of a unit is 0.75

Given the linear equation below expressed as:

2-5x=2x - 3

Collect the like terms

-5x - 2x = -3- 2

-7x = -5

Divide both sides by -7 to have:

-7x/-7 = -5/-7
x = 5/7

x = 0.75

Hence the solution to the equation below to the nearest fourth of a unit is 0.75

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Answer:

The answer is 32

Step-by-step explanation:

Answer:

15¢

Step-by-step explanation:

$12.75 - 6 × $2.10 = $12.75 - $12.60 = $0.15

Answer: 15 cents