Answer:
since ABC and ADE are similar,they have equal areas.
(AC)^2/(AE)^2=area ABC/ADE
areaABC=ACE=1
so substitute it in the afformentioned equation
u will get,AC=AE
The length of side CA in triangle ABC is c * (a² + ab + ac) / (a * (a + b + c)).
To find the length of side CA in triangle ABC, we need to use the concept of similarity and corresponding sides. Let's denote the lengths of sides in each triangle:
Triangle ABC:
Length of side AB: a
Length of side BC: b
Length of side CA: c
Triangle ADE:
Length of side AD: x (corresponding to side AB in ABC)
Length of side DE: y (corresponding to side BC in ABC)
Length of side EA: z (corresponding to side CA in ABC)
Since triangles ABC and ADE are similar, their corresponding sides are in proportion:
AD/AB = DE/BC = EA/CA
We know that AD corresponds to AB, and DE corresponds to BC, so we can set up the following proportions:
x/a = y/b
Solving for y, we get:
y = (b * x) / a
Next, we can set up the proportion for EA/CA:
z/c = x/a
Solving for z, we get:
z = (c * x) / a
Now, we have expressions for y and z in terms of x, a, and b. Since the sum of the lengths of the sides of a triangle is always constant, we can write the equation:
x + y + z = a + b + c
Substituting the expressions for y and z:
x + (b * x) / a + (c * x) / a = a + b + c
To find the value of x, we can multiply the entire equation by a to eliminate the denominator:
a * x + b * x + c * x = a² + ab + ac
Combining the x terms:
x * (a + b + c) = a² + ab + ac
Dividing both sides by (a + b + c):
x = (a² + ab + ac) / (a + b + c)
Now that we have found the value of x, we can substitute it back into the expression for z:
z = (c * x) / a
z = (c * (a² + ab + ac) / (a + b + c)) / a
Simplifying:
z = c * (a² + ab + ac) / (a * (a + b + c))
Thus, we have found the length of side CA in triangle ABC:
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Based on the given segment lengths, determine whether the segments can form a triangle.
11.5,10.5, 6.1
9.5, 3.5, 4.5
8, 6.7, 1
8, 6.7, 9.8
5, 6, 8
9.5, 7.5, 8.5
For 3 sides to form a triangle two sides added together need to be greater then the 3rd side. You need to check all 3 combinations:
1. 11.5 + 10.5 = 22, 22> 6.1
11.5 + 6.1 = 17.6 17.6 > 10.5
10.5 + 6.1 = 16.6, 16.6 > 11.5
This one can make a triangle.
2. 9.5 + 3.5 > 4.5
9.5 + 4.5 > 3.5
4.5 + 3.5 < 9.5
Cannot make a triangle.
3. 8 + 6.7 > 1
6.7 + 1 < 8
Cannot make a triangle.
4. Can make a triangle
5. Can
6. Can
Can form triangle : 11.5,10.5, 6.1 & 8, 6.7, 9.8 & 5, 6, 8 & 9.5, 7.5, 8.5
Can not form triangle : 9.5, 3.5, 4.5 & 8, 6.7, 1
What is triangle inequality theorem ?
If sum of any two line segments is greater than the third line segment, then we can say that, they can make a triangle.
How to know which sets form triangle ?1st problem,
The given line segments are 11.5, 10.5, 6.1
Now, 11.5+10.5 = 22 > 6.1
10.5+6.1 = 16.6 > 11.5
11.5+6.1 = 17.6 > 10.5
So, this three segments can form triangle.
2nd problem,
The given line segments are 9.5, 3.5, 4.5
Now, 9.5+3.5 = 13 > 4.5
9.5+4.5 = 14 > 3.5
4.5+3.5 = 8 < 9.5
Here triangle inequality rule isn't applicable.
So, it can not form triangle.
3rd problem,
The given line segments are 8, 6.7, 1
Now, 8+6.7 = 14.7 > 1
8+1 = 9 > 6.7
6.7+1 =7.7 < 8
Here triangle inequality rule isn't applicable.
So, it can not form triangle.
4th problem,
The given line segments are 8, 6.7, 9.8
Now, 8+6.7 = 14.7 > 9.8
8+9.8 = 17.8 > 6.7
6.7+9.8 = 16.5 > 8
So, this three segments can form triangle.
5th problem,
The given line segments are 5, 6, 8
Now, 5+6 = 11>8
5+8 = 13 > 6
6+8 = 14 > 5
So, this three segments can form triangle.
6th problem,
The given line segments are 9.5, 7.5, 8.5
Now, 9.5+7.5 = 17 > 8.5
9.5+8.5 = 18 > 7.5
7.5+8.5 = 16 > 9.5
So, this three segments can form triangle.
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If you help me solve b. I will give you brainlst please fill out the blanks :)
Answer:
for the top, it is 120n-150=45n
The bottom is 75
Step-by-step explanation:
Hope this helps!! ;-)
PLS ANSWER ASAP!!!!!!!!! I WILL GIVE EXTRA POINTS AND BRAINLIEST FOR THE CORRECT ANSWER!!!
You need to find a Number with 10 digits.
The first digit is divisible by 1
The second digit is divisible by 2
The third digit is divisible by 3
The fourth digit is divisible by 4
The fifth digit is divisible by 5
The sixth digit is divisible by 6
The seventh digit is divisible by 7
The eigth digit is divisible by 8
The ninth digit is divisible by 9
The full number is divisible by 10
Answer:
3816547290
Step-by-step explanation:
this is from a puzzle called notable numbers
Find the measure of
Answer:
See below.
Step-by-step explanation:
∠D = 180° - 30° = 150°
P = 2(16 + 25) = 2(41) = 82 cm
The correct option is :-
B) ∠D = 150°, P = 82 centimeters, A = 200 square centimeters
explain what the standard deviation is for a set of data.
Answer:
The Standard Deviation is a measure of how spread out numbers are. You might like to read this simpler page on Standard Deviation first. But here we explain the formulas. The symbol for Standard Deviation is σ (the Greek letter sigma)
Answer:
Shows the variation in data(average of all means of the data)
Step-by-step explanation:
Ok,so, if for example, data is grouped close together, then the standard deviation will be small, if the data is more spread out then the deviation will be larger. How to tell?
Well, it all depends on the distance away from the mean. The center is usally where the mean is. How far from the mean is your data?
How to calculate?
-There are multiple equations you can use depending on your data.
If you are analyzing data which represents a larger set, use sample standard deviation, if you collect data from every member of the set, then use population standard deviation.
First, calculate the mean(average) of each set of data.
Then subtract the deviance(subtract mean from each number -/+)
Square each deviation
add up all squared deviations
Divide the number by one less than the number of items in the data. (If it was 5 it would be 4.)
Then calculate the square root of the resting value.
How does the graph below change between point A and point B?
Lena is reading a book. The product of the two page numbers facing each other is 5852. What is the sum of the two pages?
Answer:
first page is 12, and the facing page is 13.
Step-by-step explanation:
The pages are facing each other, so they are consecutive numbers:
Let x = the first page number
y = the second page number
The second page number is just 1 more than the first, because they are consecutive numbers:
x+1 = y
We also know that the products of the numbers is equal to 156:
xy = 5852
Now we will sub y = x+1 into the second equation:
x(x+1) = 5852
x^2 + x = 5852
x^2 + x - 5852 = 0
Factoring (or using the quadratic formula) gives us:
(x+13)(x-12) = 0
x = - 13, or x = 12.
A page number can't be negative, so we will choose x=12.
This means that the second page must be page 13.
Determine if the relationship in the table is proportional X-3,12,5,7,9 Y-12,20,21,36
Answer:
No
Step-by-step explanation:
The numbers skip around here and there. The increase isn't uniform
calculate the loan for $10,000, at an annual percentage rate of 5%, for a term of 5 years. what is the amount of accrued interest?
i dont know how to do this could someone help me?
Answer:
the second one is 2 the third one is 0 the forth one is 5 and the fifth one is 4
Step-by-step explanation:
because there is 1 more white than red in the first one
we need standard units to measure the physical quantity
Answer:
true
Step-by-step explanation:
Is it possible to draw a quadrilateral that is not a rectangle but has at least one right angle?
The answer is yes.
Explanation :
The only requirement for a quadrilateral is that it has four sides. It is not necessary for them to be equal sides. This implies that as long as the angles total up to 360, you may have any angles you desire.
Answer: Triangle or Square
Step-by-step explanation:
Each have one right angle
36 new kittens were brought to the animal shelter in Houston in one day. The shelter did not want all 36 of the new kittens in a pen, and they also wanted more than 2 kittens to be together. How could they group the new kittens? You will select two answer choices.
Answer:
12 kittens in 3 pens
4 kittens in 8 pens
Step-by-step explanation:
12x3=36
4x8=36
4 is more than 2
12 is more than 2
Hope this helps! :)
PLEASE MARK ME AS BRAINLIEST I REALLY WANT TO LEVEL UP
Answer:
An option: Group the kittens by 3, so there will be 12 groups in total.
Another option: Group the kittens by 4, so there will be 9 groups in total.
PLEASE GIVE BRAINLIEST!
Which situation most directly illustrates a possible outcome of a fiscal policy?
A. A corporation decides a to expand its operation to several new states.
B. The amount of federal money available to support education decreases.
C. Employees at a company are forced to take a pay cut while executives do not.
D. The value of the dollar goes down relative to a foreign currency's value.
Answer: B. The amount of federal money available to support education decreases.
Step-by-step explanation:
The Fiscal policy of a Government relates to the spending and taxation policies of that Government in an effort to control the direction of the Economy.
Normally there are two types of Fiscal Policy: Expansionary and Contractionary. Expansionary fiscal policy works by the Government increasing spending and/ or cutting taxes so that consumers in the economy have more money.
Contractionary policy is the opposite and involves Government spending reducing and/ or taxes increasing. Reducing the amount of Federal money available for education is a possible product of Contractionary fiscal policy.
Answer:
the amount of federl money B
Step-by-step explanation:
∠A and ∠B are supplementary. The measure of ∠A is 87°.
What is the measure of ∠B?
Enter your answer in the box.
Point theif = ban
Answer: The answer is BCD is 77 degree
Step-by-step explanation:
Answer:
∠B = 93°
Step-by-step explanation:
Supplementary angles are such pairs that sum up to 180°. In this case, we are given that ∠A and ∠B are supplementary. This means that the sum of ∠A and ∠B is 180°.
⇒ ∠A + ∠B = 180°
⇒ 87 + ∠B = 180°
⇒ ∠B = 180 - 87
⇒ ∠B = 93°
Given the costs for several of the same grocery items in two countries find the rate of the total cost for these item in the united kingdom to that of the total cost of items in Canada
Rates are used to compare related quantities such as costs of items in two countries
How to determine the ratioThe question is incomplete;
So, I will give a general explanation on how to calculate the rate.
Assume that the costs are:
United Kingdom = 500
Canada = 750
The ratio would be:
Ratio = United Kingdom : Canada
So, we have:
Ratio = 500 : 750
Simplify
Ratio = 2 : 3
Express as rate
Rate = 2/3
Using the assumed values, the rate of the total cost for items in the United Kingdom to that of the total cost of items in Canada is 2/3
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If Sarah has 20 cookies but 40 friends and 2 are lactose intolerant what should she do to satisfy all of her friends?
Answer: split the cookies in half and throw 1 cookie away
Step-by-step explanation: This question is not too specific so i cannot answer it to my full capacity but if there are 40 and 20 cookies split them and if 2 of those friends cannot eat it you can play a game to see who gets those pieces of cookies or throw them away or eat them yourself.
Find the measure of one interior angle of a regular 23-gon.
A. 164.3
B. 160
C. 165.6
D. 161.1
can someone answer this question plsss I need it now!!!!!
Answer:
First one: 55 minutes
Second one: 50 minutes
Third one: 45 minutes
Fourth one: 1 hour and 5 minutes
Fifth one: 40 minutes
Hope this helps!
Solve for x:
4(3x8-x)=4
Step-by-step explanation:
[tex]4\left(3\cdot \:8-x\right)=4[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}4[/tex]
[tex]\frac{4\left(3\cdot \:8-x\right)}{4}=\frac{4}{4}[/tex]
[tex]Simplify[/tex]
[tex]24-x=1[/tex]
[tex]\mathrm{Subtract\:}24\mathrm{\:from\:both\:sides}[/tex]
[tex]24-x-24=1-24[/tex]
[tex]Simplify[/tex]
[tex]-x=-23[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}-1[/tex]
[tex]\frac{-x}{-1}=\frac{-23}{-1}[/tex]
[tex]Simplify[/tex]
[tex]x=23[/tex]
Answer:
[tex]x=23[/tex]
Step-by-step explanation:
[tex]4(3\cdot8-x)=4[/tex]
Divide both sides by 4:
[tex]\implies 3\cdot8-x=1[/tex]
Add x to both sides:
[tex]\implies 3\cdot8=x+1[/tex]
Multiply 3 × 8:
[tex]\implies 24=x+1[/tex]
Subtract 1 from both sides:
[tex]\implies 23=x[/tex]
• What is the difference in the graph of a less/greater and a less than or = in a Inequalities with Quadratics
Essentially the greater/less than shows the range of the values that are accepted or rejected + not to forget that points that lie on the parabola are rejected solutions, since i want the solutions that are strictly greater than/less than these points
If the equation suggests that it might be also equal, then the points that lie of the the parabola are also accepted solutions, since they belong to our interval [Hence the =]
y = 14x + -10
y = 7x +-3
Answer:
oops i forgot the answer o well ill just play fortnite
Step-by-step explanation:
Which statement about numbers is true?
A. All integers are Natural numbers
B. All rational numbers are Integers
C. All natural numbers are whole numbers
D. All rational number are Natural numbers
Answer:
C, I hope this is correct or this will be embarrassing but everyone have a good day
Step-by-step explanation:
The statement about numbers is true "All natural numbers are whole numbers" which is the correct answer that would be an option (C).
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9. Based on the basic value of its digits, different types of number systems exist.
The natural number now includes all positive integers from 1 to infinity.
Natural numbers include 1, 2, 3, 4, 5, and so on.
Whole numbers now include all positive integers from 0 to infinity.
The whole number is 0, 1, 2, 3, 4, 5, and so on.
As can be seen, every natural number are the whole number
Hence, the statement about numbers is true "All natural numbers are whole numbers"
Therefore, the correct answer would be an option (C).
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Solve for x. Choose the best simplified radical answer where applicable. NO LINKS!!
Answer:
d. x = 10 (the correct answer is marked)
Step-by-step explanation:
The Pythagorean theorem tells you the sum of the squares of the sides of a right triangle is the square of the hypotenuse.
x² +4² = (2√29)²
x² +16 = 116 . . . compute the squares
x² = 100 . . . . subtract 16
x = 10 . . . . take the square root
Answer:
d) [tex]\sf x=10[/tex]
Step-by-step explanation:
Pythagoras' Theorem: [tex]\sf a^2+b^2=c^2[/tex]
(where [tex]\sf a[/tex] and [tex]\sf b[/tex] are the legs, and [tex]\sf c[/tex] is the hypotenuse, of a right triangle)
Given:
[tex]\sf a=4[/tex][tex]\sf b=x[/tex][tex]\sf c=2\sqrt{29}[/tex]Substituting these values into the equation and solving for [tex]\sf x[/tex]:
[tex]\sf \implies 4^2+x^2=(2\sqrt{29})^2[/tex]
[tex]\sf \implies 16+x^2=116[/tex]
[tex]\sf \implies x^2=116-16[/tex]
[tex]\sf \implies x^2=100[/tex]
[tex]\sf \implies x=\pm \sqrt{100}[/tex]
[tex]\sf \implies x=\pm10[/tex]
Since distance is positive, [tex]\sf x=10[/tex] only
Therefore, the answer is d) [tex]\sf x=10[/tex].
Given 4x+10=5(x-4)
Prove x=30
Answer:
Step-by-step explanation:
First, we expand the brackets, so we have
4x + 10 = 5x - 20, then we collect like terms to have
5x - 4x = 10 + 20, then we sum them up
x = 30
There you go
Marques made a mistake when solving this problem. On what line did he make the error?
Line 1
Line 2
Line 3
Line 4
Line 5
Answer:
B) Line 2
i hope this work for you
and sory if im wrang
X - 5<3 OR x – 5 > 8
Answer: the first one is x < 8 and the second one is x > 13
Step-by-step explanation: so is prolly the second one
In a market for pink salmon, other things being equal, the relation between price and quantity demanded can be described by Qd=60-P, while the relation between price and quantity supplied can be described by Qs=20+4P.
A chocolate factory makes 6060 chocolates in an hour .How many chocolates can it make in a day , if the factory is operational for 13 hours?
I want in step by step please ....
Answer:
78,780
Step-by-step explanation:
Given:
6060 chocolates made per hour13 hours in one dayNumber of chocolates made in 1 day = number of chocs/hr × number of hours
= 6060 × 13
= 78,780
HELPP PLEASE!!!!!
PYRAMIDS Hermán is building a pyramid out of
blocks for an engineering class. On the top level,
there is one block. In the second level, there are
5 blocks. In the third, there are 9 blocks. This
pattern continues for the rest of the levels down to
the 18th level at the base of the pyramid. Use this
information to determine how many blocks will be
in the 13th level of the pyramid.
41 blocks
A.
B.
45 blocks
C.
49 blocks
D.
53 blocks
Answer:
I think C 45 blocks are the right answer.
Answer: B 45
Step-by-step explanation: bc 9 x 5 +45