Answers
The answer of EG is 30. We can find it by Triangle Proportionality Theorem and Angle Bisector Theorem.
What is Triangle Proportionality Theorem?According to Triangle Proportionality Theorem, A triangle's other two sides are proportionately divided by a line that runs parallel to one of its sides.
So here, [tex]\frac{DN}{NG} = \frac{DM}{ME}[/tex] (Triangle Proportionality Theorem)
⇒ [tex]\frac{30}{24} = \frac{y}{12}[/tex]
⇒ 24 * y = 30 * 12
⇒ y = 15
So, we get [tex]DE = y + 12 = 15 + 12 = 27[/tex]
The angle bisector theorem states that a triangle's opposing side is divided into two halves by an angle bisector that is proportionate to the triangle's other two sides.
Now, we can find EG by Angle Bisector Theorem,
⇒ [tex]\frac{DG}{FG} = \frac{DE}{FE}[/tex]
⇒ [tex]\frac{54}{x+10} = \frac{27}{x}[/tex]
⇒ [tex]54x= 27 x + 270[/tex]
⇒ [tex]54x-27x = 270[/tex]
⇒ [tex]27x = 270[/tex]
⇒ [tex]x = 10.[/tex]
So, [tex]EG = x + x + 10 = 2x + 10 = 20 + 10 = 30[/tex].
So, finally we get EG = 30.
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Related Questions
(3xy²)³ × (- 4x²y) =
Answers
Answer:
− 108 x 5 y 7
Step-by-step explanation:
My computer wont allow it but the 5 and the 7 are exponents
Answer:
[tex]-108x^{5}y^{7}[/tex]
Step-by-step explanation:
Simplify using the laws of exponents (there are more rules than listed, these given rules are just the ones that come into play here);
- when there is a term in parenthesis with an exponent outside, the term's exponent gets multiplied by the exponent outside
- when multiplying two exponents, one can only combine terms with the same base, and one must add the exponents
[tex](3xy^{2})^{3}*(-4x^{3}y)\\\\=(3^{3}*x^{3}*y^{2{^{3}}}) *(-4x^{2}y)\\\\=(27x^{3}y^{6})(-4x^{2}y)\\\\=-108x^{5}y^{7}[/tex]
Write 3/15 3/7 3/21 3/8 3/11 in ascending order
Answers
Answer:
The sorted inputs in order from least to greatest is:
3/21 < 3/15 < 3/11 < 3/8 < 3/7
Step-by-step explanation:
Using the given inputs:
3/15 3/7 3/21 3/8 3/11
As the least common denominator (LCD) is: 9240
Rewriting as equivalent fractions with the LCD:
3/15 3/7 3/21 3/8 3/11
1848/9240 3960/9240 1320/9240 3465/9240 2520/9240
Sorting this table by the numerators of the equivalent fractions in order from least to greatest:
3/21 3/15 3/11 3/8 3/7
1320/9240 < 1848/9240 < 2520/9240 < 3465/9240 < 3960/9240
Therefore, the sorted inputs in order from least to greatest is:
3/21 < 3/15 < 3/11 < 3/8 < 3/7
Which expression represents the sentence "five times a number, n"?
Answers
Answer:
5n
Step-by-step explanation:
:)
Answer:5n
Step-by-step explanation:
Joe got all three of his sons braces for their teeth altogether he paid $3750 write an equation that could be used to find how much the braces were for each son individually.
Answers
Answer:1,250
Step-by-step explanation:
You have to do 3750 Divided by 3 and you get 1,250
Okay i have to do a whole test and i need help!!
The picture is up there!
Answers
Answer:
a is triangular prism :)
Answer:
Before you take a proctored exam, make sure have approved ID verification photos ... Photo verification may take up to 5 days to process, so please make sure to ... approval above, you would also need to complete onboarding exam 5 days
Step-by-step explanation:
3.2h+4=23.2 please help me
Answers
Answer:
h = 6
Step-by-step explanation:
Express 432 as a product of powers of its prime factors.
Answers
We can see easily this is an even number, so let's first divide by 2.
432=2*216
We can see the remaining 216 is still even so we continue.
432=2*2*108
And continue
432=2*2*2*54
and continue
432=2*2*2*2*27
Now we can see that 27 is a multiple of 3 in fact its 3^3.
So we can conclude that 432=[tex]2^4*3^3[/tex]
The sale price of every item in a store is 65% of its usual price. The usual price of a tennis racket is $70, what is its sale price?
Answers
Answer: 24.50$
Step-by-step explanation:
[Help Asap] For each ordered pair, determine whether it is a solution to the system of equations.
Answers
Answer:
(-4,-4)
Step-by-step explanation:
6x - 7y = 4
6(-4) - 7(-4) = 4
-24 + 28 = 4
4 = 4 This is correct to the first equation.
Now let us try the second equation.
-5x + 3y = 8
-5(-4) + 3(-4) = 8
20 - 12 = 8
8 = 8 This is also correct to the second equation.
Hope this helps, thank you !!
Plsss help this is a grade!!!
Answers
add like terms
Answer:
The answer is 11x +8
Step-by-step explanation:
Please markme the brainliest,5 stars, and a thanks!Have a good day!
hi I need help with this question
Answers
Answer:
Use your calculator to find the value of:

Write all the figures on your calculator's display for th
If possible step by step explanation. thank you!
Answers
Answer:
A
Step-by-step explanation:
[tex]\frac{(3x^{2} )^\frac{1}{2} }{3^\frac{1}{2} } =3[/tex]
[tex](3x^2)^\frac{1}{2} = 3^\frac{1}{2} x[/tex]
Remember that [tex]\frac{x^b}{x^c} =[/tex]x^(b-c)
Using that [tex]\frac{3^\frac{1}{2}x }{3^\frac{1}{2} }[/tex]=3^(1/2x-1/2)=3^((x-1)/2)
[tex]3^\frac{x-1}{2} =3^1[/tex]
So we can say: [tex]\frac{x-1}{2} =1[/tex], because the bases are the same
We can multiply both sides of the equation by 2. We get x-1=2, and x=3. Which is A.
i dont know how to do this please help
Answers
8x + 6 – 7x = 6
I need some help
Answers
Answer: x = 0
Step-by-step explanation:
Please help and make it right..
Answers
Answer:
2.67 and 4.67 I think .........
Answer:
first blank is 2.67
second blank is 4.67
Step-by-step explanation:
that should be right, hope this helps!
What is the slope for this table?
Answers
Answer:
7
Step-by-step explanation:
[tex]Slope=\frac{dy}{dx}= \frac{200-172}{28-24}=7[/tex]
ok what is this 2(x +3)
Answers
Multiply the 2 by x and by 3
= 2x + 6
Answer:
2(x+3)=15 x=6
Step-by-step explanation:
Please help!! Needed asap, due soon!!:
Given line m and point O not on line m, the image of line m is constructed through a dilation centered at O with a scale factor of 3. Which of the following best describes the image of line m?
A. a line parallel to line m
B. a line intersecting with line m
C. a line passing through point O
D. a line perpendicular to line m
Answers
Answer:
The correct answer is A
Step-by-step explanation:
A line parallel to M
The difference of two numbers is 3. Their sum is 13. Which pair of equations can be used to determine, X, first number, and y, second number.
i just need the answer!
Answers
Answer:
x = 8; y = 5
Step-by-step explanation:
x + y = 13
x - y = 3
8 + 5 = 13
8 - 5 = 3
Answer: The two numbers are 8 and 5
8is first and 5 is second
Step-by-step explanation:
x-y=3
x+y=13
8-5=3
8+5=13
Find the value of x in the equation 2(x +1)=14
Answers
Answer:
the x=6
Step-by-step explanation:
2(6+1)=14
2(7)=14
14=14
the measure of the hypotenuse is? (side c)
Answers
explanation:
7² + 24² = c²
49 + 576 = c²
625 = c²
c = √625
c= 25
or just know some pythagorean triples
The answer is 25
Sooooo to find the hypotenuse you gotta use this formula: a^2+b^2=c^2.
PLEASE HELP (algebra 1)
A sports store employee needs to decide how many soccer balls to put on display. The store manager wants the number of soccer balls on display to be at least two more than the number of basketballs on display. The
store employee represents this restriction as y2 + x, where x is the number of basketballs, and y is the number of soccer balls on display
Which of the following ordered pairs represent viable solutions in terms of the context? Select all that apply.
(4. 10)
(15, 18,5)
(14, 12)
(10, 12)
(-1,3)
Answers
Answer:
I think it's 15 18 and 5 or 14,12
The solution are (4, 10) and (10, 12).
What is inequality?The phenomenon of unequal or unequal distribution of resources and opportunities among members of a given society is referred to as inequality. In different contexts and for different people, the concept of inequality may mean different things. In addition, there are distinct but interconnected economic, social, and spatial dimensions to inequality. The disjuncture between the moral ethics of equity and social justice, on the one hand, and the normative concept of "deservingness," on the other, adds complexity to debates about inequality.
Given equation of inequality for basket ball and soccer ball
y ≥ 2 + x
where x is the number of basketballs, and y is the number of soccer balls on display,
situation says the second number must be at least 2 more than the first number. Also, we are dealing with basket ball and soccer ball, so we won't have negative numbers (Choice E is out) or fractions (Choice B is out).
for choice A: x = 4 and y = 10 (10 is 6 more than 4)
for C: x = 14 and y = 12 (12 is 2 lee than 14 it is not correct)
for D: x= 10 and y = 12 (12 is 2 more than 10)
Hence the option A and D is correct representation for solutions.
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(-2) x (-4.5)=? What’s the answer
Answers
Step-by-step explanation:
Given
(-2) * ( - 4.5)
= 9
Hope it will help :)
In 2p
, 2 is known as
Answers
Answer:
the variable
Step-by-step explanation:
A variable is a quantity that may change within the context of a mathematical problem or experiment. for example
coefficient->2p<-variable
Factorising
factorise 8p - 4
Answers
Answer:
4(2p−1)
Step-by-step explanation:
4(2p−1)
-Tay did this oop-
3 left parenthesis x space minus space 8 right parenthesis greater than negative 4 space plus space x
Answers
Answer:
The solution of the given inequality
x > 10
Step-by-step explanation:
Step(i):-
Given inequality
3 ( x-8) > -4 + x
Multiply
3 x - 24 > -4 +x
subtract 'x' on both sides , we get
3 x - 24 - x > - 4 + x - x
⇒ 2 x - 24 > - 4
Step(ii):-
Adding '2'4' on both sides , we get
⇒ 2x - 24 + 24 > -4 +24
⇒ 2 x > 20
Dividing '2' on both sides , we get
[tex]\frac{2x}{2} > \frac{20}{2}[/tex]
x > 10
Final answer:-
The solution of the given inequality
x > 10
The difference between six times a
number and one is seventeen
Answers
Directions:
Using the digits 1 to 6, at most one time each, fill in the
boxes so that top two equations are equal and the
bottom equation has the greatest value.
You can move the numbers around on the graph to
help.
First Attempt:
column 1
column 2
Answers
-2-1=-3
-4-(-5)=1
3.3.3.3.3^2
Write the expression as a single power
Answers
Answer:
I think
Step-by-step explanation:
I think its 3 ^7 but i could be wronf
5(2Y - 3) – 4y = 8 – 2y - 15
Justify this please
Answers
Answer:
y=1
Step-by-step explanation:
Let's solve your equation step-by-step.
5(2y−3)−4y=8−2y−15
Step 1: Simplify both sides of the equation.
5(2y−3)−4y=8−2y−15
(5)(2y)+(5)(−3)+−4y=8+−2y+−15(Distribute)
10y+−15+−4y=8+−2y+−15
(10y+−4y)+(−15)=(−2y)+(8+−15)(Combine Like Terms)
6y+−15=−2y+−7
6y−15=−2y−7
Step 2: Add 2y to both sides.
6y−15+2y=−2y−7+2y
8y−15=−7
Step 3: Add 15 to both sides.
8y−15+15=−7+15
8y=8
Step 4: Divide both sides by 8.
The value of y is 1
Given the equation 5(2Y - 3) – 4y = 8 – 2y - 15
Expand
10Y - 15– 4y = 8 – 2y - 15
6y - 15 = -7 - 2y
Collect the like terms
6y + 2y = -7 + 15
8y = 8
Divide both sides by 8
8y/8 = 8/8
y = 1
Hence the value y of is 1
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