Answers
Answer:
1) ΔABC ≅ ΔDBC by Side-Angle-Side (SAS)
2) ΔABC ≅ ΔCDB by Side-Side-Side (SSS)
3) ΔABC ≅ ΔDBE by Angle-Angle-Side (AAS)
4) m∠Y = 53°
5) y = 3
6) ΔABC ≅ ΔEDC by Side-Angle-Side (SAS)
7) ΔABC ≅ ΔADC by Angle-Angle-Side (AAS)
8) ΔABC ≅ ΔADC by Side-Angle-Side (SSS)
Step-by-step explanation:
1) Side AC ≅ Side BD [tex]{}[/tex] given
Side BC ≅ Side BC [tex]{}[/tex] reflexive property
∠DBC ≅ ∠ACB [tex]{}[/tex] given
Therefore ΔABC ≅ ΔDBC by Side-Angle-Side (SAS)
2) Side AC ≅ Side BD [tex]{}[/tex] given
Side DC ≅ Side BA [tex]{}[/tex] given
Side BC ≅ Side BC [tex]{}[/tex] reflexive property
Therefore, ΔABC ≅ ΔCDB by Side-Side-Side (SSS)
3) ∠BAC ≅ ∠DEB [tex]{}[/tex] given
Side BC ≅ Side BD [tex]{}[/tex] given
∠ABC ≅ ∠DBE [tex]{}[/tex] vertically opposite angles
Therefore, ΔABC ≅ ΔDBE by Angle-Angle-Side (AAS)
4) ΔXYZ ≅ ΔABC [tex]{}[/tex] given
m∠A = 44°, and m∠C = 83°
m∠B = 180 - (44 + 83) = 53° [tex]{}[/tex] Sum of angles in a triangle
m∠Y = m∠B = 53° [tex]{}[/tex] Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
5) Given that Triangle GHK is congruent to Triangle TZK
GH ≅ XT, KG ≅ KT, and HK ≅ ZK by the definition of congruency
Therefore, GH = 4 = XT = 3y - 2
4 = 3y - 2
3y - 2 = 4
3y = 4 + 2 = 6
y = 6/2 = 3
y = 3
6) Side BC ≅ Side EC [tex]{}[/tex] given
Side AC ≅ Side DC [tex]{}[/tex] given
∠ACB ≅ ∠DCE [tex]{}[/tex] vertically opposite angles
Therefore, ΔABC ≅ ΔEDC by Side-Angle-Side (SAS)
7) ∠BAC ≅ ∠DAC [tex]{}[/tex] given
∠ADC ≅ ∠ABC [tex]{}[/tex] given
Side AC ≅ Side AC [tex]{}[/tex] reflexive property
Therefore, ΔABC ≅ ΔADC by Angle-Angle-Side (AAS)
8) Side AD ≅ Side BC [tex]{}[/tex] given
Side AC ≅ Side AC [tex]{}[/tex] reflexive property
Side AB ≅ Side DC [tex]{}[/tex] given that the included angle between the two legs side AD and side AC and side AC and side BC are both acute, the third sides side AB and side DC are equal
Therefore, ΔABC ≅ ΔADC by Side-Angle-Side (SSS)
Related Questions
An object was dropped off the top of a building. The function f(x)=-16x^2+144f(x)=−16x 2 +144 represents the height of the object above the ground, in feet, xx seconds after being dropped. Find and interpret the given function values and determine an appropriate domain for the function.
Answers
Answer:
Step-by-step explanation:
Given the height at which an ogject dropped modelled by the function f(x)=-16x^2+144
The height of the body on the ground occurs at when f(x) = 0
0 =-16x^2+144
16x^2 = 144
x^2 = 144/16
x^2 = 9
x = 3
The ball reached the ground after 3 secs
The domain of a function is the input function that will make the function exist. Based on the function given, the function can exist on all given input value of x. Hence the domain of the function will be;
Domain =(-\infty, infty)
The domain of the function is required.
The domain of the function is the set of real numbers
[tex]x\in(-\infty,\infty)[/tex]
The function is
[tex]f(x)=-16x^2+144[/tex]
The y intercept of the function is
[tex]y=-16\times 0+144\\\Rightarrow y=144[/tex]
[tex](0,144)[/tex]
The y intercept is the maximum height here.
The x intercepts are the points where the object is on the ground.
They are
[tex]0=-16x^2+144\\\Rightarrow 16x^2=144\\\Rightarrow x=\pm\sqrt{\dfrac{144}{16}}\\\Rightarrow x=\pm3[/tex]
[tex](3,0),(-3,0)[/tex]
The domain of the function is the set of real numbers
[tex]x\in(-\infty,\infty)[/tex]
The graph of the figure is attached.
Learn more:
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At a football stadium, 4% of the fans in attendance were teenagers. If there were 120 teenagers at the football stadium, what was the total number of people at the stadium?
Answers
Answer:
3000 people
Step-by-step explanation:
4% teenagers --> 120 teenagers were there
120/4 means 1% so 30 is 1%
1% times 100 is 100% so 30 times 100 equals 100% so 3000 is 100% of the people at the stadium
120/1= 120*25= 3000
.04*3000= 120
3000 people in total
2) If x+y=6 and xy=5 find x-y?
Answers
Answer:
x - y = ± 4Step-by-step explanation:
Given
x + y = 6 and xy = 5To find
x - ySolution
(x - y)² = (x + y)² - 4xy = 6² - 4*5 = 36 - 20 = 16 = 4²(x - y)² = 4²x - y = ± 4an initial amount of $55,000 is invested in an account with interest compounded continuously the interest rate is 10% find the value of the account after 14 years
Answers
P = $55,000 r= 0.10 t= 14 years
A = 55,000(1+(0.10)(14) = 55,000(2.4)
A = $132,000 after 14 years
Somebody help please
Answers
Answer:
[tex]\sqrt{2000}\phantom{a}yards[/tex]
Step-by-step explanation:
For a right triangle, [tex]a^{2} =b^{2} +c^{2}[/tex], if a is the hypotenuse. So, [tex]60^{2} =40^{2} +c^{2}[/tex], and c is the the distance we are trying to find:
[tex]60^{2} =40^{2} +c^{2}[/tex]
[tex]3600=1600+c^{2}[/tex]
[tex]c^{2} =2000[/tex]
[tex]c=\sqrt{2000}\phantom{a} yards[/tex]
Find the sum.. -3/2 + 8/5
Answers
Answer: 0.1 or 1/10
Step-by-step explanation:
danny tosses a ball into the air. it's height, as a function of time , is modeled by y=-16x2+9x+4
which statement best describes the function ?
((this is for a text so please don’t guess))
Answers
Answer:
The function is non linear.
Step-by-step explanation:
Answer:
The function is nonlinear
Step-by-step explanation:
I got it wrong when i guessed something else
HELP
1.75^-0.5
(3/2)^2.4
Answers
Answer:
first off i just want to say i hate aleks but ill still give the answer
Step-by-step explanation:
1.75^-0.5 = 0.75592894
3/2^2.4 = 2.6461778
The table shows a relationship between x-and y- values which statement describes the pattern created by the values ?
Answers
Answer:
3rd one
Step-by-step explanation:
The correct pattern created by the values is,
⇒ Each value of y is determined by adding 4 to each x - values, so the pattern is additive.
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
We have to given that;
The table shows a relationship between x-and y- values.
Now, We have;
x = 2, 4, 6, 8
y = 6, 8, 10, 12
⇒ 2 + 4 = 6
⇒ 4 + 4 = 8
⇒ 6 + 4 = 10
⇒ 8 + 4 = 12
Clearly, Each value of y is determined by adding 4 to each x - values.
Hence, The pattern is additive.
Learn more about the addition visit:
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Answer PLEASE ASAP
question on the image.
Answers
Answer:
The answer is DF
Step-by-step explanation:
The opposite side is 4 or EF, so the ADJACENT side would be 3 or DF according to SOH CAH TOA.
this is one thing in math I can't figure out.
Answers
Answer:
12/9 and 4/3... Hit it in the calculator
what is 4y³ - 3z⁴ when y=3 and z=2 =
Answers
Answer:
60Step-by-step explanation:
4(y)3 - 3(z)4
Sub:- 4(3)raise to three - 3(2)raise to four
4(27)-3(16)
4*27-3*16
108-48
=60.
I need help with this question.
Answers
Answer:
[tex]\displaystyle S_{27}=675[/tex]
Step-by-step explanation:
The sum of N consecutive natural numbers is given by:
[tex]\displaystyle S_N=\frac{N}{2}(F+L)[/tex]
We need to find the sum of the natural numbers between 12 to 38.
To calculate the required sum we have F=12, L=38, but we don't have the value of N.
From 12 to 38 there are 38 - 12 + 1 = 27 natural consecutive numbers, thus N=27.
Substituting in the formula:
[tex]\displaystyle S_{27}=\frac{27}{2}(12+38)[/tex]
[tex]\displaystyle S_{27}=\frac{27}{2}(50)[/tex]
[tex]\displaystyle S_{27}=27*25[/tex]
[tex]\mathbf{\displaystyle S_{27}=675}[/tex]
Given the following information, write the linear equation in slope-intercept form.
3. slope = 1/3; y-intercept = -1
4. slope = 2/5; y-intercept = 0
5. slope = -1; y-intercept = 4
Answers
Answer:
3) y = 1/3x - 1
4) y = 2/5x + 0 or just y = 2/5x
5) y = -1x +4
Step-by-step explanation:
because i aint never seen two pretty best friends, its always one of em gotta be ugly
what is 22.680 rounded
Answers
Answer:
22.68 or 22.7
Step-by-step explanation:
hope this helps
Answer:
23
My logic:
Well i just rounded up to the nearist one because you didn't specify how to round.
A recipe states that 5 servings of peanuts have 1,250 calories. How many servings is 375 calories of peanuts? *
Answers
375/250 = 1.5 servings
Answer:
500 calories
Step-by-step explanation:
divide the 1250 calories by the initial five servings and you get 250 then multiply that by the 2 servings they are asking for and you get 500 calories
What is the slope-intercept form of the line with the point (0, 3) and a slope = -2?
O A. y = 2x + 3
O C. y = -2x + 3
D. y = -2x - 3
B. y = 2x - 3
Answers
Answer:
2nd choice OC.y=-2x+3
Step-by-step explanation:
The equation for the slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept. With these two numbers both given to us, we can just plug them in and get y=-2x+3.
Hope this helps you
please help me please please
Answers
Answer:
I think it is the second one, flown by women
Step-by-step explanation:
A woman goes to macy's and wants to purchase the following items: A sweater for $19.99, a belt for $29.99 and a pair of earrings for $79.99. How much is her total bill? (assume no tax )
Answers
Answer:
129.97
Step-by-step explanation:
19.99+29.99+79.99=129.97
Find the distance between the points (3, 9) and (-9, -7).
Answers
Answer:
20
I hope this helps!
Which one represents a proportional relationship?
Answers
Hope this helps you
Find the total surface area of this cuboid,
5 cm
4 cm
6 cm
Answers
please help , picture above!
Answers
Answer:
The Slope of the hypotenuse of triangle ABC is equal to the slope of the hypotenuse of triangle CDE
Step-by-step explanation:
AE is a continuous line with consistent slope.
AC is a segment of this line and is the hypotenuse of triangle ABC.
CE is also a segment of AE and is the hypotenuse of triangle CDE.
Hope this helps.
The revenue earned from a sporting event can be determined by the ticket price, $125 each.
Answers
Answer:
all whole numbers
all whole-number multiples of 125
Step-by-step explanation:
The domain and the range of a function is the set of input and output values of the function.
The domain is the set of all whole numbersThe range is the set of all whole numbersLet the number of tickets be x, and the revenue be y.
So, the revenue function will be:
[tex]\mathbf{y = 125x}[/tex]
The number of tickets cannot be less than 0.
So, the domain of the revenue function is:
[tex]\mathbf{Domain = [0,\infty)}[/tex]
The above means that, the domain is the set of all whole numbers
Similarly, the revenue cannot be less than 0.
So, the range of the revenue function is:
[tex]\mathbf{Range = [0,\infty)}[/tex]
The above means that, the range is also the set of all whole numbers (in multiples of 125)
Read more about domain and range at:
https://brainly.com/question/1632425
2x+5y=-62x+5y=−6 Determine the intercepts of the line
Answers
Answer:
(0,-6/5)
(X,Y)
Step-by-step explanation: MARK BRAINLIEST
Answer:
(-3,0) (0,-1.2)
Step-by-step explanation:
when this polynomial is divided by (m+1), the remainder is 0. What is the value of the polynomial’s constant term?
Answers
Answer: it would be -4
Step-by-step explanation:
I got it right one the mastery test
Answer: -4
Step-by-step explanation:
which value is equivalent to 3^2+5x2-8
Answers
9+5x2-8
9+10-8
19-8
Answer: 11
The movie theater makes $750 in a hour period, how many hours will it take for the theater to make $2575?
Answers
Answer:
3.43 hrs
or
3 13/30
orrrr
103/30
Step-by-step explanation:
Which of these is a consumable good?
O Clothing
O Cell phone
O Automobile
O Food
Answers
Answer:
Food
Step-by-step explanation:
Answer:
food
Step-by-step explanation:
Which number is closest to 22 ?
Answers
Answer:
21 or 23
Step-by-step explanation:
Cuz 22 is in the middle of both.
.-.
Answer:
21 or 23
Step-by-step explanation:
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