Theorems related to equilateral traingle :
Theorem 1: The sum of measures of all 3 interior angles of a triangle is [tex]180^0[/tex].
Theorem 2: The angles opposite to equal sides are also equal in measure.
Theorem 3: The sum of the related internal angles is the measure of the exterior angle of a triangle.
Theorem 4:If a line splits any two triangle sides in the same proportion, it is parallel to the third side of the triangle.
Theorem 5: Each angle of an equilateral traingle have equal measure of [tex]60^0[/tex].
Theorem 6: Any two triangle sides can add up to a length that is longer than the third side.
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i need an answer to this with workings
pls type it if ur answering..cos file links aren't working
Expand (a-b)^7
Answer:
[tex]a^7-7a^6b+21a^5b^2-35a^4b^3+35a^3b^4-21a^2b^5+7ab^6-b^7[/tex]
Step-by-step explanation:
There are multiple ways of expanding a polynomial expression to a high degree. One way of doing it is to write out the problem in the multiplication form, multiply (a - b) by itself (7) times.
[tex](a-b)^7[/tex]
[tex]=(a-b)(a-b)(a-b)(a-b)(a-b)(a-b)(a-b)[/tex]
Now simplify, multiply two terms together,
[tex]=(a^2-2ab+b^2)(a^2-2ab+b^2)(a^2-2ab+b^2)(a-b)[/tex]
Repeat this process,
[tex]=(a^4-4a^3b+6a^2b^2-4ab^3+b^4)(a^3-3a^2b+3ab^2-b^3)[/tex]
Repeat this process one final time,
[tex]a^7-7a^6b+21a^5b^2-35a^4b^3+35a^3b^4-21a^2b^5+7ab^6-b^7[/tex]
simplify the expressing by combining like terms
1 + 3x - 8x + 7
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{1 + 3x - 8x + 7}[/tex]
[tex]\large\text{COMBINE the LIKE TERMS }[/tex]
[tex]\large\textsf{ (3x - 8x) + (1 + 7)}[/tex]
[tex]\large\textsf{3x - 8x = \bf -5x}[/tex]
[tex]\large\textsf{1 + 7 = \bf 8}[/tex]
[tex]\large\textsf{= -5x + 8}[/tex]
[tex]\boxed{\boxed{\large\text{Answer: \huge \bf -5x + 8}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Write an expression, in its simplest form, for the volume of this cuboid
Answer:
[tex]V=10x^2+35x+15[/tex]
Step-by-step explanation:
Given that,
Length = (2x+1)
Width = (x+3)
Height = 5
We need to find an expression for the volume of this cuboid . The formula for the volume of cuboid is given by :
[tex]V=lbh[/tex]
So,
[tex]V=(2x+1)\times (x+3)\times 5\\\\=(2x+1)\times (5x+15)\\\\=10x^2+30x+5x+15\\\\=10x^2+35x+15[/tex]
So, the volume of this cuboid is equal to [tex]10x^2+35x+15[/tex].
Aiden got a loan for $600 that has a 5% simple interest for
2 years.
Answer:
The simple interest is $60 for 2 years
Step-by-step explanation:
1. 600*0.05=30
2. 30*2=60
Solve for x. Show all your steps/work.
216x = 6x + 1
What is the following product ?
Answer:
6 (square root) 200
Step-by-step explanation:
Answer:
the second choice 6/200
Step-by-step explanation:
If out of a sample of 180 drivers prefer a standard transmission over automatic , about a standard transmission in a population of 900
A:700
B:22
C:360
D:200
Answer:
This is a matter of ratio and proportion, let us represent the unknown value as x. Since the two ratios are related,
40 : 180 :::: x : 900
40 / 180 = x / 900
x = (40/180)(900)
x = 200q
Find the factor pairs for 12.
1 and 12
2 and 6
3 and 4
The factors of 12 are 1, 2, 3, 4, 6, and 12.
Answer:
the factor pairs of 12 are 1 and 12 , 2 and 6 , 3 and 4
Step-by-step explanation:
The computation of the factor pairs is shown below:
The factor pairs means the two numbers which are multiplied to get the number 12
So it is
1 and 12
2 and 6
3 and 4
Hence, the factor pairs of 12 are 1 and 12 , 2 and 6 , 3 and 4
The same would be relevant
An 18-ounce bottle of juice costs $4.86. What is the unit rate for the juice
Answer:
3.7
Step-by-step explanation:
Answer:
The Unit Rate would be 0.27:1
Step-by-step explanation:
Divide 4.86 by 18 to get 0.27
Hope this helps! Pls make brainliest
Solve for x in the picture below
Answer:
x=19
Step-by-step explanation:
90+7x+3+128+5x+8+111+9x-19=(6-2)180 (angle sum of polygon)
x=19
Suppose the total area is represented by the equation x^2+14x+24. If the area 1 is x^2 square units and area IV is 24 units, what must be true about area II and area III.
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]Total = x^2 + 14x + 24[/tex]
[tex]Area\ I = x^2[/tex]
[tex]Area\ IV = 24[/tex]
Required
True about area II and III
The question is incomplete; so, I will answer using general knowledge.
If the total area is:
[tex]Total = x^2 + 14x + 24[/tex]
And there are 4 areas, then;
[tex]Total = Area\ I + Area\ II + Area\ III + Area\ IV[/tex]
Rewrite as:
[tex]Total = Area\ I + Area\ IV+ Area\ II + Area\ III[/tex]
This gives:
[tex]x^2 + 14x + 24 = x^2 + 24+ Area\ II + Area\ III[/tex]
Collect like terms
[tex]x^2 -x^2 + 14x + 24 -24= Area\ II + Area\ III[/tex]
[tex]14x = Area\ II + Area\ III[/tex]
Rewrite as:
[tex]Area\ II + Area\ III = 14x[/tex]
So, the sum of areas III and IV must be 14x
If you apply the changes below to the linear parent function ,f(x)=|x| over the x-axis what is the equation to the new function
Answer:
Answer: A. G(x)= ax=y= - f(x) is flip over x-axis. Therefore, f(x) =14x would become f(x) =-14x. Therefore, final transformed function f(x)=-14x is vertically stretch by a factor of 14 and flip over the x-axis.
Step-by-step explanation:
Find the value of ‘N’ in each of the following:
a. 2n = ¼
b. 10⁶÷10n = 10²
[tex] \purple{ \huge{ \tt{ \: ✨ Answer ✨ \: }}}[/tex]
[tex]a. \: \: n \: = \: \red{ \boxed{ \tt{{ \: \frac{1}{8} \: }}}} \\ \\ \: \: \: \: \: \: b. \: \: n \: = \: \red{ \boxed{ \tt{ \: 10 {}^{ - 3} \: }}}[/tex]Answer:
a. n=1/8
b. n=10^-3
please mark as brainliest
Ill give brainiest - please help ASAP with WORK FOR IT please and thank you!! :)
3 pages, with work pleasee
Step-by-step explanation:
isosceles trapezoidtrapezoidrhombussquarerectangleparallelogramquadrilateral10x+18+62=180 co interior angle10x=180-80
x=100/10=10
:.x=10
9.
8x+2=7x+14 corresponding angle of parallelogram are equal
8x-7x=14-2
x=12
10.
4x+4=5x+1 corresponding sides of parallelogram are equal
4-1=5x-4x
x=3
11.
4+3x=19corresponding sides of parallelogram are equal
3x=19-4
x=15/3
x=5
Find what x =
4
9
16
In a polling station, there were 900 registered voters. During an election 10% of the registered voters did not cast their votes. The rest cast their votes to Ahmed, Babu and Chambuko in the ratio 3:2:1.If 30 votes were spoilt,how many votes did Ahmed get?
Answer:
Ahmed got 390 votes
Step-by-step explanation:
Here, we want to know the number of votes obtained by Ahmed
from the question, there were 900 registered voters
10% did not cast their votes
The number that didn’t cast their votes will be;
10% of 900
= 10/100 * 900 = 90
So the rest 90% casted and this value will be 900-90 = 810
810 people casted their votes
30 votes were spoilt;
The number of valid votes is thus;
810 - 30 = 780
Ahmed got a ratio of 3 in 3:2:1
The total value here is 3 + 2 + 1 = 6
So what Ahmed got will be;
3/6 * 780
= 780/2 = 390
Plz help ASAP I will add branliest to the first answer, I need to solve for the letter
Answer:
6. r=2
8.x=3
Step-by-step explanation:
6. 4r-3=5
4r-3=5 add 3 to both sides
4r=8 divide 4 by both sides
r=2
8. 5x-6=9
5x-6=9 add 6 to both sides
5x=15 divide 5 by both sides
x=3
How many solutions does the following equation have?
5x + 8 - 7x = -4x + 1
Which of the rectangular boxes shown has the greater volume?
A. The green box.
B. The purple box.
C. They have equal volumes.
D. There is not enough information to tell.
Answer:
C
Step-by-step explanation:
volumes are width x height x length
4 x 2 x 2 = 16
8 x 2 x 1 = 16
5/7 x 9/10
please show your work and the answer has to be a simplified fraction . thanks :)
Answer:
Step-by-step explanation:
5/7 x 9/10
=5/7 9/5 X 2
=1/7 X 9/2
=1 X 9/ 7 X 2
=9/ 7 X 2
=9/14
The expression 5/7 x 9/10, is equivalent to 9/14.
What is a expression? What is a mathematical equation?Linear function is a function whose degree is one. It is of the form -f(x) = ax + bA mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions.Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have the following expression -
5/7 x 9/10
Given is -
5/7 x 9/10
1/7 x 9/2
9/14
Therefore, the expression 5/7 x 9/10, is equivalent to 9/14.
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Школьник поднял гирю весом 16 кг на высоту 2,1 м за 2 с. Определите:
а) Механическую работу, выполненную школьником;
б) Механическую мощность, развитую им;
в) На сколько увеличилась при этом потенциальная энергия си-
стемы „гиря-земля". Считать g = 10 Н/кг.
ОЧЕНБ ОЧЕНЬ СРОЧЬНО НАДО. ПОМОГИТЕ ПОЖАЛУЙСТА ЩЯС.
Answer:
what type of language is this isn't this India?
Are there any supplementary angles ? If so name two pairs if not explain why not
A smoothie recipe calls for 1.2 cups of strawberries for one batch. Michael uses 4.8 cups of strawberries today. How many batches did Michael make today?
Answer:
4 batches
Step-by-step explanation:
4.8/1.2 = 4
8 + 7 + (-4) on a number line
Answer:
11 is the answer
Step-by-step explanation:
8+7-4
15-4
11
on number positive 11 is the answer
its just simple addition and substraction then the result can displayed on number line where 11 comes on number line mark that point
Please help!!! I’ll mark you as brainliest!!!!!
Step-by-step explanation:
PLZS help need by today!
Answer:
15
Step-by-step explanation:
We know that the expression is equal to 110° since it is a vertical angle. So what we do is we ad 10 to both sides of the equation. We are left with 8x=120 so if we divide 120/8 we get 15 which would leave it as x=15. Now plug it in and check it.
Which equation can be used to solve for xxx in the following diagram?
Answer:
A
Step-by-step explanation:
math
We can solve for x in the diagram based on the vertical angles theorem using the equation: A. 60 = (4x - 20)
What is Vertical Angles Theorem?Angles that lie vertically opposite each other when two straight lines intersect are congruent too each other, based on the vertical angle theorem.
Applying the vertical angles theorem, we can solve for x in the given diagram using the equation below:
60 = (4x - 20)
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Can somebody plz help answer these last questions correctly (only if u know how to do this) if u can answer the because ones too I would appreciate it
Thanks :2
WILL MARK BRIANLIEST WHOEVER ANSWERS FIRST :DDD
Answer:
∠e = 105° because ∠e and the 105° angle are vertically opposite angles
∠h = 75° because ∠h and the 105° angle are supplementary angles
∠f = ∠h = 75° because ∠f and ∠h are vertically opposite angles
∠c = 105° because ∠c and the 105° are corresponding angles
∠b = 75° because ∠b and ∠f are corresponding angles
∠a = 105° because ∠a and ∠e are corresponding angles
∠d = 75° because ∠d and ∠h are corresponding angles
Step-by-step explanation:
The given diagram includes two parallel lines having a common transversal that crosses both (parallel) lines
By sing angle properties, we have;
∠e = 105° because ∠e and the 105° angle are vertically opposite angles formed by the same two straight lines and are therefore always equal
∠h = 180° - 105° = 75° because ∠h and the 105° angle are angles that form a straight line and are therefore supplementary angles which are angles that sum up to 180°. Therefore, ∠h + 105° = 180°, therefore ∠h = 75°
∠f = ∠h = 75° because ∠f and ∠h are vertically opposite angles
∠c = 105° because ∠c and the 105° are corresponding angles and corresponding angles are equal
Similarly, we have;
∠b = ∠f = 75° because ∠b and ∠f are corresponding angles
∠a = ∠e = 105° because ∠a and ∠e are corresponding angles
∠d = ∠h = 75° because ∠d and ∠h are corresponding angles
Much of the declaration of independence consist of a list what does it list?
Answer: complaints of the wrongs done to the colonists.
Which set of data has the highest interquartile range? Group of answer choices 8,12,14,14,20 8,12,14,14,22 9,13,14,15,19 all of the above
Given:
The given data set are:
8,12,14,14,20
8,12,14,14,22
9,13,14,15,19
All of the above
To find:
The set of data that has the highest interquartile range(IQR).
Solution:
We know that, the interquartile range(IQR) of a data set is the difference between the third quartile and first quartile.
[tex]IQR=Q_3-Q_1[/tex]
All the given data set has five values in ascending order. So, the first value is the minimum value, second value is the first quartile, third value is the median, the fourth value is the third quartile and the fifth value is the maximum value.
For 8,12,14,14,20,
[tex]IQR=14-12[/tex]
[tex]IQR=2[/tex]
For 8,12,14,14,22,
[tex]IQR=14-12[/tex]
[tex]IQR=2[/tex]
For 9,13,14,15,19,
[tex]IQR=15-13[/tex]
[tex]IQR=2[/tex]
All interquartile ranges are equal. So, all the data sets has t he highest interquartile range.
Therefore, the correct option is D.