ΔABC is an equilateral triangle with AD perpendicular to BC. Prove that ΔADB ≅ ΔADC.
Answers
Step-by-step explanation:
An equilateral triangle means all sides are congruent.
AB≅BC≅AC
All angles are also congruent.
∠ABC≅∠BCA≅∠CAB
AD being perpendicular makes it a bisector of both BC and ∠CAB.
BD≅CD
∠BAD≅∠CAD
Now, there are multiple ways to prove that ΔADB≅ΔADC. All 3 sides and all 3 angles of both triangles are congruent, so you could do it however you want.
1) ASA (one of the possible ASA combinations)
∠ABD ≅ ∠ACD because this is an equilateral triangleBD ≅ CD because AD bisects BC∠BDA ≅ ∠CDA because AD is perpendicular to BC, both 90°2) HL (again, one of the multiple possible HL combinations)
AD is perpendicular to BC, creating 2 right trianglesAB ≅ AC because ΔABC is equilateralAD ≅ DA by the reflexive property, it is congruent to itselfThere are many more but I won't write them all out.
Related Questions
Help me please!! :) :)
Answers
Please help and no links!!!!
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Answer: 18
Step-by-step explanation:
someone please help me
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Answer:
∡3 & ∡6 are same side interior angle.
∡4 & ∡6 are alternate interior angles.
∡2 & ∡8 are vertical angles.
∡1 & ∡5 are corresponding angles (because they are in the same spot).
∡1 & ∡3 are vertical angles (because they are the opposite angle of each other).
∡1 & ∡2 are supplementary angles (because they add up to 180°).
i don’t understand can I have help please
Answers
Answer:
(y + 1)³
Step-by-step explanation:
Answer:
y^3+3y^2+3y+1
Step-by-step explanation:
Factor the numerator and denominator to cancel the common factors.
(Whenever ^ is in the answer, it means that the number to the right of it is the exponent)
Someone plz help me :(
Answers
Answer:
A
Step-by-step explanation:
the ratio shows that for every two songs beth's mom has, beth has one more.
*3 is larger than 2 by 1
meaning, if her mom has 6 songs, then she will have 7
if Beth has 12 songs, her mom would have one less, 11
Divide $80 among three people so that the second will have twice as much as
the first, and the third will have $5 less than the second. Using an algebraic
equation, find the amount that each will get.
Answers
Answer: 19,38, and 33.
Step-by-step explanation:
80=2x+x+2x-5=5x=95=x=19
A submarine is cruising at an elevation of
-250/3 meters below sea level, then
descends another 120% meters into the
sea. What is the new location of the
submarine?……NO LINKS
Answers
Answer:
Step-by-step explanation:
these are two different questions .
first i solve first
position of submarine= -250/3 meters below see level
height descended=120 % of 250/3=120/100 ×(250/3)=300,00/300=100 m
new location=-250/3+(-100)=-650/3 below see level.
2nd question
position of submarine=-250 2/3=-752/3 m below see level
height descended=120 5/8=965/8 m =-965/8 m below see level
new positin=-752/3+(-965/8)=-(6016+2895)/24=-8911/24=-371 7/24m below sesa level.
pls help asap! i will mark brainliest!
Answers
Answer:
3
Step-by-step explanation:
2 x 7= 14 - 17= 3
Which ordered pair is a solution to
the equation
3x + 9y = 27 ?
Answers
Answer:
x=9-3y
Step-by-step explanation:
- Move the variable to the right & change its sign
3x + 9y = 27
- Divide both sides by 3
3x = 27 - 9y
- Write the solution x in parametric form
x=9-3y
- Solution:
x= 9-3y
13- pls help with this pre-algebra problem is urgent
Answers
Answer:
What else is in the equation?
Step-by-step explanation:
Also, i think the - should be right here>-13 instead of it being here 13-<
A piece of fabric for a quilt design is in the shape of a parallelogram. The base is 5 in
and the height is 4.3 in. What is the total area of the 23 parallelogram pieces needed for
the quilt?
Answers
Answer:
A =a l × w and then you solve the equation you get the answer
Answer:
494.5 square inches
Step-by-step explanation:
5 times 4.3 is 21.5
21.5 times 23 is 494.5
Urgent! Someone please answer! Will give Brainliest!
4 cm
x cm
The area of rectangle ABCD is 28 cm2
B
B
a) What is the length of side AB in terms of x?
6 cm
length of AB =
(1)
x cm
D
с
b) If the area of rectangle ABCD is 28 cm,
we can show that x2 + ax = b where
a and b are integer values.
Work out the values of a and b.
b
a =
(1)
b=
(1)
Total marks: 3
Answers
Step-by-step explanation:
it is the most easiest answer we get 566474 I think this will help you
Using substitution, which value of x makes this equation true?
3+x = 10
A. 13
B. 7
C. -7
D. -13
Answers
Answer:
The answer is B. 7
Step-by-step explanation:
3 + x = 10
3 + 7 = 10
x=7.
Step by step:
x+3=10.
x=7.
(I subtracted 3 on both sides)
Hope this helped!! :)
some one please help
Answers
Answer:
i can't see the photo
Step-by-step explanation:
pleas send it again
Answer:
Step-by-step explanation:
f(x) = 3-x/5
Explanation:
The inverse of a function completely swaps the x and y values. One way to find the inverse of a function is to switch the "x" and "y" in an equation
y=3x -5
turns into
x = 3y+5
Then solve the equation for y
x=3 y- 5
x+5 = 3y
the divide all by three
1/3x + 5/3 =y
f ( x ) − 1 = 3/1 x + 5/3
?.....helpp lolllll helpppp
Answers
Answer: the answer is F
Step-by-step explanation: the pictures that are used for the yearbook are added to the picture for the paper which results in 450, the 270 is on top because it’s the pictures for the yearbook
What’s the product of 2.6
Answers
Answer:
2×6=12
Step-by-step explanation:
3х — бу - z = 3
4х +4y +z= — 1
X-2y – z = -1
Answers
Answer:
[tex]3x - 6y - x + 3 = =[/tex]
Find the product of (3x + 7y)(3x − 7y)
Answers
Answer:
9x^2 - 49y^2
Step-by-step explanation:
Answer: 9x^2 - 49y^2
Step-by-step explanation:
(3x + 7y)(3x − 7y)
9x^2 -21xy + 21xy - 49y^2
9x^2 - 49y^2
PLS HELP ASAP ITS AN EMERGENCY ITS DUE IN A FEW HOURS THANKS
Answers
Answer: -8
Step-by-step explanation:
-8+22=14
Has to be less than 14 so the value has to be less than -8
Josh, Ben and Rick have 70 marbles altogether. The ratio of the number marbles Josh has to the number of marbles Rick has is 1: 2. However, Ben has 15 marbles fewer than Rick. How many marbles does Ben have?
Answers
Answer:
Ben has 19 marbles
Step-by-step explanation:
First taking that josh and ricks ratio is 1:2, this would set up in an equation as [tex]2j = r[/tex] and with ben having 15 less than rick, his formula would be [tex]r = b + 15[/tex] as well as the total of all the boys marbles together being this [tex]j+r+b=70[/tex]
Now we put all of these equations into a set to answer them.
[tex]2j = r\\ r = b + 15\\j+r+b=70[/tex]
First we solve for j
[tex]2j = r\\ j=\frac{1}{2} r[/tex]
Then substitute j
[tex]j+r+b=70\\ \frac{1}{2}r+r+b=70\\ 2b+3r=140[/tex]
Then simplify and multiply by 2 to even out
[tex]r = b + 15\\ -b+r=15\\2b+3r=140[/tex]
Now eliminate the b variable and combine equations
[tex]2b+3r=140\\-2b+2r=30[/tex]
[tex]5r=170[/tex]
Now divide and solve for r
[tex]5r=170\\r=34[/tex]
Now we know Rick has 34 marbles of the 70 marbles, so we can substitute his number back into the original equation
[tex]-b+34=15\\b=19[/tex]
Now we know Ben has 19 marbles of the remaining 36, and can substitute his number as well
[tex]j=\frac{1}{2}(34)\\j=17[/tex]
And now we know how much everyone has, to check we rewrite all the equations with their respective numbers
[tex]11+34+19=70\\2(17)=34\\34=19+15[/tex]
[tex]70=70\\34=34\\34=34[/tex]
Which means the ordered pairing of (b, j, r) is (19, 17, 34)
what is 2+3-4+6+22=
not that hard
Answers
Answer:
29
Step-by-step explanation:
Simplify 2+3 to 55-4+6+22
Simplify 5-4 to 1.1+6+22
Simplify 1+6 to 7.7+22
Simplify.29
pls help!!!!
Sandra uses 6.39 ounces of beans in a recipe. If she triples the recipe, how many ounces of beans will Sandra need?
Answers
Answer:
19.17 ounces
Step-by-step explanation:
If she uses 6.39 ounces for 1 recipe and she wants to "triple" the recipe we then know that triple also means 3 times.
Due to that fact we now know what our equation is:
6.39 x 3 which equals 19.17
I hope this helps have great day :)
Answer: 19.17
Step-by-step explanation: 6.39 x 3 = 19.17
100 POINTS IF U GET THIS RIGHT!
Answers
Answer:
The y-intercept is 4.
Step-by-step explanation:
Our equation: y = mx + b
m = slope
b = y-intercept
=> Now, let's compare:
=> y = mx + b = y = -7x + 4
We can tell that b = 4
Hoped this helped.
[tex]y =-7x +4 \\\\\text{ The above equation is in a form of y=mx+b, where b is the y-intercept}\\\\\\\text{Hence the y-intercept of the given equation is}~ 4.[/tex]
Why is math hard????
Answers
Answer:
It doesnt have to be, you are making it. It's really just addition multiplication divison and subtraction in different ways
Step-by-step explanation:
Answer:
BECAUES IT IS
Step-by-step explanation:
I don´t know
Describe the steps you used to solve the equation and find the amount of Carrie’s allowance.
Linear equation:
1/4a+ 1/3 a + 8 = 22
Answers
1/4 x 3/3 = 3/12
1/3 x 4/4 = 4/12
New Equation:
3/12a + 4/12a + 8 = 22
now add up similar terms
7/12a + 8 = 22
subtract 8
7/12a = 14
multiply each side by your denominator
12(7/12)a=12(14)
7a=168
divide by 7
a = 24
PLZ HELP ME WITH THIS ASAP
Answers
Answer: y= 9
Step-by-step explanation: x, y= 9
Sophie liked 35 of the 50 different flavors of Jelly Beans. Enter the percent of the Jelly Bean flavors she did not like.
Answers
simplify.
remove all perfect squares from inside the square roots. assume x and y are positive.
√8x^3y^2
Answers
Answer:
[tex]2xy\sqrt{2x}[/tex]
Step-by-step explanation:
Because this is a whole term in itself (no addition or subtraction), you can just directly find squares and factor them out. First, when looking at 8, you can factor out 4, to get 2 on the outside. Then, while looking at x cubed, you can factor out x squared, to get x on the outside, and when looking at y squared, you can just pull that outside itself, to get y. Now, we have one 2 and one x remaining, for a total of [tex]2xy\sqrt{2x}[/tex]
а Ava and her children went into a movie theater and she bought $48 worth of drinks and candies. Each drink costs $4 and each candy costs $3. She bought 2 more candies than drinks. Graphically solve a system of equations in order to determine the number of drinks, x, and the number of candies, y, that Ava bought.
Answers
Answer:
x = 6
y = 8
Explanation and graph is given in picture
I hope it helps.
The Stock Market Nadia is a stockbroker. She earns 13% commission each week. Last week, she sold $5,300 worth of stocks. How much did she make last week in commission? If she averages that same amount each week, how much did she make in commission in 2011?
Answers
Answer:
34
Step-by-step explanation: