Answers
The congruency of the right triangles by the Hypotenuse-Leg Congruency Theorem can be made true by the following sides.
1. [tex]\overline{RP}[/tex] ≅ [tex]\overline{MF}[/tex] and [tex]\overline{DP}[/tex] ≅ [tex]\overline{QF}[/tex]
2. [tex]\overline{CI}[/tex] ≅ [tex]\overline{CE}{}[/tex] and [tex]\overline{AI}[/tex] ≅ [tex]\overline{GE}[/tex]
3. [tex]\overline{TR}[/tex] ≅ [tex]\overline{RT}[/tex] and ;[tex]\overline{TQ}[/tex] ≅ [tex]\overline{RS}[/tex]
4. [tex]\overline{DG}[/tex] ≅ [tex]\overline{KN}[/tex] and [tex]\overline{AD}[/tex] ≅ [tex]\overline{HK}[/tex]
What are congruent triangles?Two right triangles are congruent if the hypotenuse side and one leg of one triangle is congruent to the hypotenuse side and one leg of the other triangle.
The hypotenuse leg congruency theorem states that two right triangles are congruent if the hypotenuse and one leg of one triangle are congruent to the hypotenuse and one leg of the other triangle
The hypotenuse side of ΔDPR = [tex]\overline{RP}[/tex]
The hypotenuse side of ΔQMF = [tex]\overline{MF}[/tex]
The corresponding legs of both triangles are;
[tex]\overline{DP}[/tex] corresponds to [tex]\overline{QF}[/tex]
[tex]\overline{DR}[/tex] corresponds to [tex]\overline{MQ}[/tex]
Therefore, ΔDPR is congruent to ΔQFM if [tex]\overline{RP}[/tex] ≅ [tex]\overline{MF}[/tex]
And the leg [tex]\overline{DP}[/tex] ≅ [tex]\overline{QF}[/tex] or [tex]\overline{DR}[/tex] ≅ [tex]\overline{MQ}[/tex]
2. The sides that makes the congruency statement, ΔACI ≅ ΔGCE are found as follows;
The hypotenuse side of ΔACI = [tex]\overline{CI}[/tex]
The hypotenuse side of triangle ΔGCE = [tex]\overline{CE}{}[/tex]
Therefore,
ΔACI ≅ ΔGCE ican be proved when [tex]\overline{CI}[/tex] is congruent to [tex]\overline{CE}{}[/tex], and
[tex]\overline{AI}[/tex] is congruent to [tex]\overline{GE}[/tex] or [tex]\overline{AC}[/tex] is congruent to [tex]\overline{CG}[/tex]
3. In the figure the specified information are;
[tex]\overline{TR}[/tex] is congruent to [tex]\overline{RT}[/tex] by reflexive property
The triangles are congruent if either;[tex]\overline{TQ}[/tex] iis congruent to [tex]\overline{RS}[/tex] or;[tex]\overline{TS}[/tex] iis congruent to [tex]\overline{RQ}[/tex]
4. The appropriate sides that can be used to prove that ΔADG ≅ ΔHKN are the hypotenuse side of both triangles;[tex]\overline{DG}[/tex] and [tex]\overline{KN}[/tex]
and either the legs; [tex]\overline{AD}[/tex] and [tex]\overline{HK}[/tex] or [tex]\overline{AG}[/tex] and [tex]\overline{HN}[/tex]
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Related Questions
The universities budget covers cost for nine months what is Amy’s monthly budget for textbooks in course supplies? What is her monthly budget for rent on utilities and food? What is your monthly budget for a personal and miscellaneous cost? what is her total monthly budget?
Answers
1. Using division operations, Amy's monthly budget for textbooks and course supplies is $100.
2. Amy's monthly budget for rent, utilities, and food is $1,422.
3. Amy's monthly budget for personal and miscellaneous costs is $251.
4. Amy's total monthly budget is $1,825
How is the monthly budget determined?The total monthly budget is the total budget divided by the period (nine months).
We can use division operations to determine the individual monthly budgets for each expense class.
Living On/Off-Campus:Textbooks and Course Supplies = $900 $100
Rent, Utilities, and Food = $12,798 $1,422
Personal & Miscellaneous Expense = $2,259 $251
Transportation = $468 $52
Total non-tuition expenses = $16,425 $1,825 ($16,425/9)
The number of months = 9 months
Monthly expenses = $1,825
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Find missing length when given area of a parallelogram
Answers
The missing height of parallelogram is 6 units
Define Area of Parallelogram
The area of a parallelogram is defined as the region or space covered by a parallelogram in a two-dimensional plane.Rectangle, square, and rhombus are all examples of a parallelogram.Area of parallelogram = Base * heightGiven,
base = 9 units
Area = 54 unit²
Now, the formula for area of parallelogram is
Area = b * h
let, h = height of parallelogram which we need to find
so, now put the values
54 = 9 * h
h = 54 / 9
h = 6 units
Hence, the missing height of parallelogram is 6 units.
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find the value of for 19 degrees of freedom and an area of 0.010 in the right tail of the chi-square distribution curve. enter the exact answer from the chi-square distribution table.
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The right tail of the chi-square distribution curve's value for 19 degrees of freedom and an area of 0.010 is 3.162.
To find the value of chi-square for 19 degrees of freedom and an area of 0.010 in the right tail of the chi-square distribution curve, we need to consult a chi-square distribution table. The table will list the chi-square values corresponding to different degrees of freedom and areas of the right tail of the distribution. In this case, the table should list the chi-square value corresponding to 19 degrees of freedom and an area of 0.010 in the right tail of the distribution. The value of this chi-square is 3.162, which is the exact answer from the chi-square distribution table.
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12-5e^(-x) ) list all critical numbers of . if there are no critical numbers, enter 'none'. critical numbers
Answers
There are no crictical numbers of the given function 12-5e^(-x).
Let's Consider
[tex]f(x) = 12 - 5*e^-x[/tex].
What is critical number of a function.
If a number causes the derivative of an expression to equal 0, it is critical.
As a result, we must set the derivative of the expression to 0.
Local Maxima and Local Minima points are also consider as critical number of a function.
f`(x) = 0 or f`(x) =1/0 by solving both equation we can find all the critical points of a function f(x).
Derivative of given funciton f(x) is f`(x).
f`(x) = [tex]0 - 5*(e^-x)*(-1).[/tex]
f`(x) = [tex]5*(e^-x)[/tex].
f`(x) = 0
[tex]5*e^-x[/tex] = 0
[tex]e^-x[/tex] = 0
[tex]e^-x[/tex] never going to zero because e^-x is an exponential decreasing function.
So there are no crictical numbers of the given function f(x).
So We enter none in this question.
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a triangle is to have sides of lengths a and b. find the angle between these sides that maximizes the area of the triangle
Answers
The angle between the two sides of lengths a and b that maximizes the area of the triangle is θ = π/2.
What is the formula for finding the area of a triangle?The area of a triangle whose sides of lengths a and b with an angle θ between them is
A = 1/2ab sinθ
Calculation:The given triangle has two sides of lengths a and b.
Consider θ is the angle between the a and b sides. Then the area of the triangle is
A = 1/2ab sinθ
For maximizing the area of the triangle, derivating the area we have and equate to zero i.e.,
dA/dθ = 0
⇒ dA/dθ = 1/2 ab cosθ = 0
⇒ cosθ = 0
∴ θ = π/2
And the condition for the maximum area is d²A/dθ² < 0.
I.e., d²A/dθ² = -1/2ab sinθ
⇒ d²A/dθ² = -1/2ab sin(π/2) = -1/2ab < 0
So, the maximum area is
Δ(max) = 1/2 ab sin(π/2) = 1/2ab
Thus, the angle between the two sides of lengths a and b of a triangle is π/2 when its area is maximum.
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image Complete the table for the function y = + 7. Question 19 options: A) –9, –8, –6, –5 B) –5, –6, –8, –9 C) 5, 6, 8, 9 D) 9, 8, 6, 5
Answers
The values are 5, 6, 8, 9 for the given function y=∛x+7.
So, option D is correct.
What is a function?In mathematics, a function from a set X to a set Y assigns each element of X exactly one element of Y.
The earliest known concept of a function was created by two Persian mathematicians, Al-Biruni and Sharaf al-Din al-Tusi. [4] At first, functions were envisioned as the perfect representation of the relationship between two variables. In mathematics, a function from a set X to a set Y assigns each element of X exactly one element of Y. Simply described, a function is an association of inputs where each input is coupled to a single, distinct output. Each function has a codomain or range.
Given,
y=∛x+7
Let x=-8,
y=∛8+7
y=-2+7
y=5
x=-1, y=∛(-1)+7
y=-1+7
y=6
x=1, y=∛1+7
y=1+7
y=8
x=8, y=∛8+7
y=2+7
y=9
Therefore, the values are 5, 6, 8, 9
So, option D is correct
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The complete question is:
"Complete the table for the function y = ∛x+7
OA) -5, -6, -8, -9
OB) -9, -8, -6, -5
Oc9,8. 6. 5
OD) 5,6, 8, 9".
onsider the line =+7x5y−4. Find the equation of the line that is parallel to this line and passes through the point −−4, 5. Find the equation of the line that is perpendicular to this line and passes through the point −−4, 5.
Answers
The equation of the line perpendicular to 7x+5y = 4 is y = 5/7(x) -15/7. The equation of the line parallel to 7x+5y = 4 is y = -7/5(x) -53/5
How to find the equation of the lines parallel and perpendicular to 7x+5y = 4?Given that: the line is perpendicular/parallel to the line 7x+5y = 4 and it passes through (−4,-5)
The slope-intercept form of a straight line is:
y = mx + c
where m is the slope and c is the y-intercept
For perpendicular case:
When the two lines are perpendicular, the product of their slope is -1 i.e.
m₁ x m₂ = -1
where m₁ and m₂ represent the slope of the lines
Let the slope of the given line be m₁ and the slope of the unknown line be m₂
Line1(given):
7x+5y = 4 => y = (-7/5)x + 4/5
Thus, m₁ = -7/5
m₁ x m₂ = -1
-7/5 x m₂ = -1
m₂= 5/7
Line 2(unknown) with the point (−4,-5):
y = mx + c
-5 = 5/7 (-4) + c
-5 = -20/7 + c
c = -15/7
Thus, the equation of the line is y = 5/7(x) -15/7
For parallel case:
When the two lines are parallel, they have equal slope i.e. m₁ = m₂
Line1(given):
7x+5y = 4 => y = (-7/5)x + 4/5
Thus, m₁ = -7/5
m₂= -7/5
Line 2(unknown) with the point (−4,-5):
y = mx + c
-5 = -7/5(-4) + c
-5 = 28/5 + c
c = -53/5
Thus, equation of the line is y = -7/5(x) -53/5
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Prepared building plans for Spangler Construction Company. Sent Spangler an invoice for $900 requesting payment within 30 days. (The appropriate revenue account is entitled Drafting Fees Earned.)
Answers
The appropriate sales journal entry for the building plans prepared for Spangler Construction Company is as follows:
Sales Journal Entry:Debit Accounts Receivable (Spangler Construction Company) $900
Credit Drafting Fees Earned $900
(To record the revenue from drafting fees.)
What are sales journals?Sales or service journals are used to record sales or service revenue transactions.
When the services are performed on credit, the Accounts Receivable account is debited while the Service Revenue account is credited.
Transaction Analysis:Accounts Receivable (Spangler Construction Company) $900 Drafting Fees Earned $900
Thus, the above demonstrates the appropriate recording of the service revenue transaction in the sales/service revenue journal.
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Question Completion:Prepare the appropriate journal entry.
when you graduated from high school you had a choice between coming to jmu and working at walmart where you would earn $37,870 per year. suppose tuition at jmu is $20,000 per year, textbook expenses are $2,699 per year, and room and board expenses are $15,000 per year. assume that when you graduate you will get a job that pays you $75,000 per year.
Answers
Therefore , the best choice is you to join jmu and after that you will able to earn the same amount you spend on the graduation in 2 year.
What is equation ?Equation: A statement that two variable or integer expressions are equal. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.
Here,
Given:
You would earn $37,870 per year at walmart
Tuition at jmu is $20,000 per year, textbook expenses are $2,699 per year, and room and board expenses are $15,000 per year.
and you will get a $75,000 per year after graduation.
So the total expense is = 20,000 + 15000 + 2699 =37,699
Therefore , the total expense at jmu = $37,699
and total 4 year graduation course fees = 37,699 * 4=1,50,796
Thus, total fees you have to pay = $1,50,796
and after this you will get a job of $75,000 per year.
you will able to earn the same amount you spend on the graduation in 2 year.
Therefore , the best choice is you to join jmu and after that you will able to earn the same amount you spend on the graduation in 2 year.
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