Answers
Answer:
∠ECD = 82°
Step-by-step explanation:
Alternate Interior Angles Theorem : when two parallel lines are cut by a transversal, the alternate interior angles are congruent. Alternate angles form a Z shape and are sometimes called "Z angles".
Therefore,
∠CDF = ∠GBC = 45°
∠CEF = ∠GAC = 53°
The sum of the interior angles of a triangle is 180°
⇒ ∠ECD + ∠CDF + ∠CEF = 180
⇒ ∠ECD + 45 + 53 = 180
⇒ ∠ECD = 180 - 45 - 53 = 82°
In ∆ABC
m<C be x[tex]\\ \tt\longrightarrow x+53+45=180[/tex]
[tex]\\ \tt\longrightarrow x+98=180[/tex]
[tex]\\ \tt\longrightarrow x=180-98[/tex]
[tex]\\ \tt\longrightarrow x=82[/tex]
Now
m<ECD and m<ACB are opposite hence equal
Related Questions
i made a profit of 40 persent of the amount of money i had invested if i had invested 950 how much profit did i make
Answers
Answer:
1330
Step-by-step explanation:
Answer:
380
Step-by-step explanation:
40 percent of the amount invested is 380(Profit)
0.4 * 950 =380
Lucy received a $70 gift card for a coffee store. She used it in buying some coffee that cost $7.49 per pound. After buying the coffee, she had $32.55 left on her card. How many pounds of coffee did she buy?
Answers
She brought 5 pounds of coffee.
Answer:
5 pounds
Step-by-step explanation:
$70 - $32.55 = 37.45
37.45 ÷ 7.49
= 5
hi guys I am from india . can anybody solve this x+2c
Answers
2c + x
ANSWER:⇒ 2c + x
I need an answer to this math problem.
Answers
10k^3 , 6k^3
k^3 ( 10, 6 )
2k^3 (5, 3)
so 2k^3 is the greatest common factor of both the numbers .
Answer:
greatest common factor: 2k³
Step-by-step explanation:
given 10k³ and 6k³
for gcf just simply break them down:
10k³ = 2 * 5 * k * k * k
6k³ = 2 * 3 * k * k * k
-------------------------------------------------------------------------------------------------------------
Analyse both of them and find similarities:
the similarities are: 2 * k * k * k
so the greatest common factor is 2k³
I need help math please math ag2
Answers
Answer: B
Step-by-step explanation:
The volume of a rectangular solid is given by the polynomial 3x^4-3x^3-33x^2+54x. If the length of the solid is 3x and the width of the solid is x-2 Find the height?
Answers
Answer:
[tex]\mathsf{height}=x^2+x-9[/tex]
Step-by-step explanation:
Volume of a cuboid = L x w x h
(where L is the length, w is the width and h is the height)
[tex]\implies \mathsf{height=\frac{volume}{width \times length} }[/tex]
Given:
[tex]\mathsf{volume}=3x^4-3x^3-33x^2+54x[/tex]
[tex]\mathsf{width}=x-2[/tex]
[tex]\mathsf{length}=3x[/tex]
[tex]\implies \mathsf{height}=\frac{3x^4-3x^3-33x^2+54x}{3x(x-2)}[/tex]
Factor expression for volume
Factor out common term [tex]3x[/tex]: [tex]3x(x^3-x^2-11x+18)[/tex]
Factor [tex]x^3-x^2-11x+18[/tex]: [tex]3x(x-2)(x^2+x-9)[/tex]
[tex]\implies \mathsf{height}=\frac{3x(x-2)(x^2+x-9)}{3x(x-2)}[/tex]
Cancel the common factors [tex]3x(x-2)[/tex]:
[tex]\implies \mathsf{height}=x^2+x-9[/tex]
An electrician bought 120 feet of electrical wire and used 105 feet of it. What percent of the wire went unused? 15% 12. 5% 8. 75% 7%.
Answers
Answer:
12.5%
Step-by-step explanation:
105 is what percent of 120?
you can use this proportion:
if/of = %/100
in this problem:
is = 105
of = 120
'what percent' = p/100
105/120 = p/100
cross-multiply to get:
120p = 10500
p = 10500/120
p = 87.5
So the electrician used 87.5%, out of 100%, meaning 12.5% went unused
Answer:
The percent of the wire that went unused was 15%.
Step-by-step explanation:
You can set up these equations:
Turn 15% into 0.15
12.5% into 0.125
8.75% into 0.0875
7% into 0.70
Now, the number of wire unused is 15. Since 120 - 105 = 15. So, we can set up these equations to see which percentage it was that got unused:
0.15 x 120 = 18
0.125 x 120 = 15
0.0875 x 120 = 10.5
0.70 x 120 = 84
So, the answer is 15%.
Evaluate the function
Answers
Answer:
[tex]f(1) = 4[/tex]
Step-by-step explanation:
Solve:
[tex]f(x) = -2x^2 + 2x + 4[/tex][tex]f(1) = -2(1)^2 + 2(1) + 4[/tex][tex]f(1) = -2 + 2 + 4[/tex][tex]f(1) = 4[/tex]-Chetan K
2. Finance Planners recommend no more than 30% of your income should be your rent.
1. How much should Hagatha spend on rent if she brings home $2,000 per month?
2. If the average rent for a one-bedroom in Portland is $1,743, how much does Hagatha need to earn per month to have her rent total 30% of his income?
Answers
She needs to make $5810 a month to have her 1743$ rent be 30% of her income because 30/100 = 1743/x
x= 5810
do i add up the exponents or subtract? i don't quite understand my homework. if you are going to respond, please send a step by step too please.
(n^2-3n+1)(2n+3)
Multiplying binomials by polynomials btw
Answers
Answer:
2n³ - 3n² - 7n + 3
Step-by-step explanation:
Hi there! Don't worry, polynomials seem hard but you will get them with practice.
I am going to show you 2 methods of multiplying polynomials. These methods are universal, or they work with any polynomial multiplication problem:
Method 1: Distributive PropertyThis is perhaps the most common method. You distribute 1 value to another or multiply each and every single term.
Let's solve it!
(n² - 3n + 1)(2n + 3)n²(2n + 3) - 3n(2n + 3) + 1(2n + 3) n²(2n) + n²(3) - 3n(2n) - 3n(3) + 2n + 3 See how I distributed the values?2n³ + 3n² - 6n² - 9n + 2n + 3Now, we add up like terms. Like terms should have the same coefficient and should be raised to the same power.
2n³ + 3n² - 6n² - 9n + 2n + 3 2n³ - 3n² - 7n + 3There you have it! This is how you solve with The distributive Property Method.
Method 2: Area ModelThis is the next universal method, Area modeling.
Area models can be set up by the number of terms we have. In the first polynomial we have three terms:
n²-3n+1Just for this method, keeping the positive signs helps.
For the binomial, we have two terms (hence, binomial)
2n+3We set up our are model like this, with the terms laid out as side lengths of a rectangle. (Attachment "A")
Next, we find the area of each individual tile. (Attachment "B")
Now, we add like terms. Something nice about area models is that most of the time, the like terms are matched up in a diagonal. (Attachment "C")
2n³ + 3n² - 6n² - 9n + 2n + 3 2n³ - 3n² - 7n + 3We end up with the same answer as before.
-Chetan K
Which is true about the functional relationship shown in the graph? Cost of Apples 110 100 90 60 70 180 Cost ($) 50 40 30 20 10 0 1 2 3 4 5 Weight (pounds) O A. The cost of the apples is a function of the type of apples. B. The weight of the apples is a function of their cost. O C. The cost of the apples is a function of their weight. O D. The weight of the apples is a function of the number of apples. a
Answers
Answer:
MY ANSWER IS THIS. IS. A. QUIZ.
Step-by-step explanation:
The cost of the apples is a function of their weight is true about the functional relationship shown in the graph. Correct option is c.
In the graph, the horizontal axis represents the weight (in pounds) of the apples, and the vertical axis represents the cost (in dollars) of the apples. As the weight of the apples increases, the cost also increases. This relationship shows that the cost of the apples is dependent on their weight, making it a functional relationship of "cost as a function of weight."
To know more about functional relationship:
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A dilation with a scale factor of 1/2 is applied to the three sides of Triangle ABC to create Triangle A'B'C'. The side lengths of Triangle ABC are: A = 4ft, B = 3ft, C = 5ft. What are the lengths of the sides on the new Triangle A'B'C'? Question 8 options:
A. A' = 8ft, B' = 6ft, C' = 10ft
B. A' = 2ft, B' = 1.5ft, C' = 2.5ft
C. A' = 3.5ft, B' = 2.5ft, C' = 4.5ft
D. A' = 4.5ft, B' = 3.5ft, C' = 5.5ft
Please Help...Thank uu
Answers
Answer:
its B.
Step-by-step explanation: just take half off the numbers, and then you have your answer. simple.
Evaluate this expression
A) 20
B) 14
C) 32
D) 5
Answers
Answer:
A) 20
Step-by-step explanation:
[tex] |(12 + 8) \div 2| \times 2 \\ |20 \div 2| \times 2 \\ 10 \times 2 \\ 20[/tex]
If a,b,c,d are in GP, the. (a² + b² + c²)(b² + c² + d²) is equal to
Answers
[tex] \text{Given a,b,c and d are in GP}[/tex]
[tex] \therefore \frac{b}{a} = \frac{ c}{b} = \frac{d}{c} = r \\ \\ \implies b = ar ,c = br,d = cr \implies \: b = ar,c = (ar)r,d = (br)r \\ \\ \implies b = ar,c = a {r}^{2} ,d = {br}^{2} \implies b = ar,c = {ar}^{2} ,d = (ar)r {}^{2} = a {r}^{3} ...(i)[/tex]
[tex] \text{Now, Consider}[/tex]
[tex]( {a}^{2} + {b}^{2} + {c}^{2} )( {b}^{2} + {c}^{2} + {d}^{2} ) = ( {a}^{2} + {a}^{2} {r}^{2} + ( {a}^{2} {r}^{4} )( {a}^{2} {r}^{2} + {a}^{2} r {}^{2} + {a}^{2} {r}^{4} + {a}^{2} {r}^{6} )[/tex]
[tex] = {a}^{2} (1 + {r}^{2} + {r}^{4} ) {a}^{2} {r}^{2} (1 + {r}^{2} + {r}^{4} ) = a {}^{4} {r}^{2} (1 + {r}^{2} + {r}^{4} ) {}^{2} = [a {}^{2}r(1 + {r}^{2} + {r}^{4}) ] {}^{2} [/tex]
[tex] = ( {a}^{2} r + {a}^{2} {r}^{3} + {a}^{2} r {}^{5} ) {}^{2} = (a. \: ar + ar. \: a {r}^{2} + a {r}^{2} .a {r}^{3} ) {}^{2} [/tex]
[tex] = (ab + bc + cd) {}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \text{[From Equation (i)]}[/tex]
Hope This Helps!!! :)
The given polynomial can be rewritten as factors of the common ratio of
the geometric progression.
Response:
If a, b, c, d are in GP, (a² + b² + c²) × (b² + c² + d²) = [tex]\underline{(a\cdot b + b \cdot c + c\cdot d)^2}[/tex]
Which method can be used to analyze the given polynomial relation?The assumed parameters are;
a, b, c, and d for a geometric sequence
Therefore;
[tex]\mathbf{\dfrac{b}{a}} = \dfrac{c}{b} = \dfrac{d}{c} = r[/tex]
Which gives;
b = a·r
c = b·r
d = c·r
Therefore;
c = b·r = a·r²
d = c·r = a·r³
(a² + b² + c²) × (b² + c² + d²) = (a² + (a·r)² + (a·r²)²) × ((a·r)² + (a·r²)² + (a·r³)²)
(a² + a²·r² + a²·r⁴) × ((a²·r²) + (a²·r⁴) + a²·r⁶) = a⁴·r²·(r⁸ + 2·r⁶ + 3·r⁴ + 2·r² + 1)
Which gives;
a⁴·r²·(r⁸ + 2·r⁶ + 3·r⁴ + 2·r² + 1) = a²·r·(r⁴ + r² + 1) × a²·r·(r⁴ + r² + 1)
a²·r·(r⁴ + r² + 1) × a²·r·(r⁴ + r² + 1) = (a²·r·(r⁴ + r² + 1))²
a²·r·(r⁴ + r² + 1) = a²·r⁵ + a²·r³ + a²·r
a²·r = a·b
a²·r³ = b·c
a²·r⁵ = c·d
Therefore;
a²·r⁵ + a²·r³ + a²·r = a·b + b·c + c·d
(a² + b² + c²) × (b² + c² + d²) = (a²·r·(r⁴ + r² + 1))² = [tex]\underline{(a\cdot b + b \cdot c + c\cdot d)^2}[/tex]
Learn more about geometric progression (GP.) here:
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Find the product of (2x − 3)(2x2 7x − 1). 4x3 − 6x2 − 9x 3 4x3 8x2 − 23x 3 4x3 20x2 − 9x 3 4x3 − 6x2 − 23x 3.
Answers
Product of polynomials can be done by distribution of multiplication over addition. The product of [tex](2x - 3)(2x^2 + 7x - 1)[/tex] is [tex]4x^3 + 8x^2 -23x + 3[/tex]
What is distributive property of multiplication over addition?Suppose a, b and c are three numbers. Then we have:
[tex]a(b + c) = a\times b + a\times c[/tex]
(a(b+c) means a multiplied to (b+c). The sign of multiplication is usually hidden when using symbols and both quantities which are in multiplication are written together without space)
The product result of the given expression is
[tex](2x - 3)(2x^2 + 7x - 1) = 2x(2x^2 + 7x - 1) -3(2x^2 + 7x - 1) \\(2x - 3)(2x^2 + 7x - 1) = 4x^{1+2} + 14x^2 -2x - 6x^2 - 21x + 3\\(2x - 3)(2x^2 + 7x - 1) = 4x^3 + (14 -6)x^2 + (-2 -21)x + 3\\(2x - 3)(2x^2 + 7x - 1) = 4x^3 + 8x^2 -23x + 3[/tex]
It is because when bases are same and there is multiplication, then powers add up, so we have: [tex]a^b \times a^c = a^{b+c}[/tex]
Also, we've
[tex](-ve \times (+ve) = -ve\\(-ve) \times (-ve) = +ve\\(+ve) \times (+ve) = +ve\\(+ve) \times (-ve) = -ve[/tex]
where -ve, +ve are sign of operands and result.
That's why [tex]2 \times -1 = -2[/tex]
Thus,
The product of [tex](2x - 3)(2x^2 + 7x - 1)[/tex] is [tex]4x^3 + 8x^2 -23x + 3[/tex]
Learn more about product of polynomials here:
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find area of circle given radius of (3x^9 y^11)
Answers
Given radius: [tex]3x^9 y^{11}[/tex]
Formula for area: πr²
Area of circle:
( [tex]\pi 3x^9 y^{11}[/tex] )²
[tex]\pi 3^2x^{9*2 }y^{11*2}[/tex]
[tex]9\pi x^{18}y^{22}[/tex]
Answer: [tex]9\pi x^{18}y^{22}[/tex]
Formula for area: [tex]\pi {r}^{2} [/tex]
Area of circle:
[tex](\pi3 {x}^{9} {y}^{11} {)}^{2} [/tex]
[tex]\pi {3}^{2} {x}^{9}{ \times }^{2} {y}^{11} { \times }^{2} [/tex]
[tex]9\pi {x}^{18} {y}^{22} [/tex]
what is the equation of 44 = t/11 *
Answers
Answer:
[tex]\large\boxed{\textsf{ t = 484.}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to solve for the value of t. We should first begin with a review of}[/tex]
[tex]\textsf{what the \underline{Properties of Equality} are.}[/tex]
[tex]\large\underline{\textsf{What are Properties of Equality?}}[/tex]
[tex]\textsf{Properties of Equality are properties that allows us to manipulate an equation}[/tex]
[tex]\textsf{stating whenever a constant is added, removed, squared, square rooted... then}[/tex]
[tex]\textsf{both expressions will still show equality to each other.}[/tex]
[tex]\underline{\textsf{Example;}}[/tex]
[tex]\textsf{The Addition Property of Equality. This Property states that whenever a constant,}[/tex]
[tex]\textsf{or the same term is added to both sides of an equation, the equation remains}[/tex]
[tex]\textsf{equal. Say we were given this equation;}[/tex]
[tex]\tt a - 7 = 9[/tex]
[tex]\textsf{We would use the Addition Property of Equality to isolate a.}[/tex]
[tex]\textsf{This is done by adding 7 to both sides of the equation.}[/tex]
[tex]\tt a \ -\not{7} + \not{7} = 9 + 7[/tex]
[tex]\boxed{\tt a=16.}[/tex]
[tex]\large\underline{\textsf{For Our Problem;}}[/tex]
[tex]\textsf{We should use the Multiplication Property of Equality, which states that whenever}[/tex]
[tex]\textsf{both sides of the equation are multiplied by a constant, then they are still equal.}[/tex]
[tex]\textsf{Let's use the Multiplication Property of Equality to multiply both sides of the}[/tex]
[tex]\textsf{equation by 11 in order to remove the fraction.}[/tex]
[tex]\tt \frac{\not{11} \times t}{\not{11}} = 44 \times 11[/tex]
[tex]\underline{\textsf{We are left with our final answer;}}[/tex]
[tex]\large\boxed{\textsf{ t = 484.}}[/tex]
Answer:
t = 484
Step-by-step explanation:
[tex]\frac{44}{1} = \frac{t}{11}[/tex]
[tex]44*11 = 484[/tex]
Hence, t = 484
[RevyBreeze]
Please help!
Look at the pic
Answers
Answer:
it is 5 I belive
Step-by-step explanation:
The measure of c is .
Answers
[tex]\text{By the Pythagorean Theorem}\\c^2=6^2+8^2\\c^2=36+64\\c^2=100\\c=\sqrt{100} \\c=10[/tex]
Fran is going to transfer her credit card balance over to a new card. She has an existing balance of $752. 69. Her current card charges her a transfer fee of 12. 5%, added to her balance, for transferring her debt. The new card has an opening fee of $50, which is also added to her balance. She will also have to make an immediate minimum payment, which is 3. 35% of her total balance. How much will her balance be after she makes this payment, assuming that she pays the minimum amount? Round all dollar values to the nearest cent. A. $866. 74 b. $868. 40 c. $818. 41 d. $926. 82 Please select the best answer from the choices provided A B C D.
Answers
Answer:
$752.69 + 12.5%=$753+$50=$803+ 3.35%=803.0335=
answer: c. $818.
Step-by-step explanation:
Answer:
✅ C. $818⬇️ i got 100% on the test
Find the value of x. (PLEASE HELP ME)
Answers
Answer:
x ≈ 34.9
Step-by-step explanation:
x is the hypotenuse of the triangle, for which one leg is given. Either the sine or the cosine relation can be used. We choose to use the cosine relation:
Cos = Adjacent/Hypotenuse
cos(53°) = 21/x
x = 21/cos(53°) ≈ 34.9
I need question b answered please
Answers
Is Triangle M'S'V' a reduction or an enlargement of the original Triangle MSV?
Answers
Answer:
Reduction
Step-by-step explanation:
In this problem, there are 2 triangles: the solid lines represent the preimage and the dotted lines represent the image. All of the vertices of the dotted lines are inside the solid line. This means that the preimage is larger than the image. If the preimage is larger, then a reduction has occurred.
There are 2 ways to tell that this is a reduction. The simplest is to just say that the image is inside the preimage and therefore smaller. More mathematically, you could also see that all of the coordinate pairs are closer to the origin by a scale factor of 2/3. Thus, the triangle must be smaller and reduced.
Leo wants to buy some shoes. He found the shoes at three different stores for a price of $35. The stores are each having a sale. Store X is offering 15% off the price of the shoes. Store Y is offering $5 off the price of the shoes. Store Z is offering a 15 discount off the price of the shoes. Which statement about the sale price of these shoes is true?.
Answers
Leo should buy the shoes from the store Z, as store Z has the best selling price of $28. Statement 2 is true.
What is percentage ?Percentage of a number is the part of the number expressed in the in every hundred. Percentage of a number is expressed with the symbol '%'.
Leo wants to buy some shoes. He found the shoes at three different stores for a price of $35.
The final price of store X-
As store X is offering 15% off the price of the shoes and the price of shoes is $35. Thus the selling price of store X is,
[tex]P_x=35-35\times\dfrac{15}{100}\\P_x=35-5.25\\P_x=29.75[/tex]
As store Y is offering $5 off the price of the shoes and the price of shoes is $35. Thus the selling price of store Y is,
[tex]P_y=35-35\times\dfrac{5}{100}\\P_y=35-1.75\\P_y=23.25[/tex]
As store Z is offering a 1/5 discount off the price of the shoes and the price of shoes is $35. Thus the selling price of store Z is,
[tex]P_y=35-35\times\dfrac{1}{5}\\P_y=35-7\\P_y=28[/tex]
Thus, Leo should buy the shoes from the store Z, as store Z has the best selling price of $28. Statement 2 is true.
Learn more about the percentage here;
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What is 40% of a circle of radius 225 feet
Answers
Answer:
About 63,617 ft²
Step-by-step explanation:
[] The area of a circle is equal to πr²
π(225)² ≈ 159,043
[] To find 40%, we can multiply our whole by 40%
-> 40% divided by 100, 0.4, becomes a decimal
159,043 * 0.4 = 63,617
-> Don't forget to add on the units once you are done, this problem was done in feet, since it is an area we used feet squared
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.
- Heather
Determine if (3, -1) is a solution to the system.
Answers
Answer:
There are a few ways to solve systems of equations.
There are a few ways to solve systems of equations. substitutionThere are a few ways to solve systems of equations. substitutioneliminationThere are a few ways to solve systems of equations. substitutionelimination GraphicallyIf you are looking at a multiple choice question use the ordered pair to plug into the answer choices and whichever one balances out will be your answer. To assist you further I would need more information from the problem.
Step-by-step explanation:
hope it will help you have a great day bye and Mark brainlist if the answer is correct
[tex]kai6417[/tex]
#carry on learning
What is the simplified form of the complex fraction
Assume no denominator equal zero
Answers
Answer:
[tex] \frac{12 + x}{4(x + 3)} [/tex]
Step-by-step explanation:
hopes this helps
pls mark me brainest
Which statement is sometimes true:
1. A square is a rhombus
2. A trapezoid is a parallelgram
3. A rectangle is a parallelogram
4. A rectangle is a square
Answers
Answer:
4. A rectangle is a square
Step-by-step explanation:
A rectangle can be a square, but not always. A rectangle has 2 pairs of parallel sides, 2 pairs of congruent sides, and 4 right angles. Squares have 2 pairs of parallel sides, 4 congruent sides, and 4 right angles. So, the difference between the two is that adjacent sides are not necessarily congruent in rectangles, but they are in squares. This means that some rectangles can be a square. If a rectangle has all congruent sides, then it is a square. On the other hand, some rectangles do not have all congruent sides, and thus are not squares.
how many different ways can 18 different questions on a true of false test be answered if a student answers every question
Answers
Answer:
2^18
Step-by-step explanation:
Every true or false question can be either answered true / false (2 options)
So, there are 2.2.2.2.2... (2^18) ways to answer if a student answers every question.
Please help!! Ill give brainlist.
Answers
Answer:
sorry for being late, here is the answers :)!
Answer:
2y-6=x >>> Y= 1/2x+3
-x+(1/2)y=3 >>> Y=2x+6
2x+y=3 >>> Y=-2x+3
x-3y=-6 >>> Y=(1/3)x+2
Step-by-step explanation:
Hope this helps! :)