The value of x using the F.O.I.L method can be determined by the expression: [tex]54x^2-129x-23[/tex]
What is FOIL Method?
FOIL is a mnemonic for the standard method of multiplying two binomials, hence the method may be referred to as the FOIL method. The word FOIL is an acronym for the four terms of the product:
First (“first” terms of each binomial are multiplied together)
Outer (“outside” terms are multiplied—that is, the first term of the first binomial and the second term of the second)
Inner (“inside” terms are multiplied—the second term of the first binomial and the first term of the second)
Last (“last” terms of each binomial are multiplied)
In the question, It is given:
(6x + 1)°
(9x - 23)°
Now Apply the F.O.I.L Method, to find the value of x;
⇒(6x + 1) (9x-23)
Remove parenthesis and multiply;
⇒6x×9x+6x×(-23)+1×9x+1×(-23)
⇒6x x 9x+6 x 23x + 1 x 9x + 1 x 23
Now, we have to simplify the terms,
⇒6x x 9x + 6 x 23x + 1 x 9x + 1 x 23
So after simplification, we get:
[tex]54x^2-129x-23[/tex]
Hence,
The value of x can be determined by the expression: [tex]54x^2-129x-23[/tex]
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50 percent of 25 percent of the number is 96. What is the number?
Answer: 48
Step-by-step explanation:
first you divide 25/2 and you get 12.5 and that is irrelevant but what is relevant is that you divide 96 by 2 and you get 48 thus giving you the answer to that question. :)
In Ms. Q's deck of cards, every card is one of four colors (red, green, blue, and yellow), and is labeled with one of seven numbers (1, 2, 3, 4, 5, 6, and 7). Among all the cards of each color, there is exactly one card labeled with each number. The cards in Ms. Q's deck are shown below.
Yunseol draws 5 cards from Ms. Q's deck. What is the probability that three cards have the same number?
The probability that three cards have the same number, using the hypergeometric distribution, is of:
0.0448 = 4.48%.
What is the hypergeometric distribution formula?The probability mass function for the hypergeometric distribution is defined as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters of the function are listed below:
x is the number of successes in the sample.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes in the population.In the context of this problem, the values of these parameters are given as follows:
N = 28, k = 4, n = 5, x = 3.
Hence for one color, the probability that three cards have the same number is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 3) = h(3,28,5,4) = \frac{C_{4,3}C_{24,2}}{C_{28,5}} = 0.0112[/tex]
There are four colors, hence the probability is:
p = 4 x 0.0112 = 0.0448 = 4.48%.
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Madison wanted to go to the mall, but first she attended her brother Zane's basketball
game. The basketball game lasted 135 minutes, or 15 minutes longer than double the
time Madison spent at the mall. How long was Madison at the mall?
Answer: 60 minutes
Step-by-step explanation:
x=time Madison spent at the mall
2x + 15 = 135
2x = 135-15
x = 120/2 = 60
En la pecera de Simón hay 6 veces la cantidad de peces de colores que peces guppy. Hay un total de 21 peces en la pecera. ¿Cuántos peces de colores más que peces guppy hay?
Answer:god is good
Step-by-step explanation:if u put this 1 stars u hate god
if u give 5 stars u love god
The Wilson family had 8 children. Assuming that the probability of a child being born a girl is 0.5, find the probability that the Wilson family had: at least 3 girls
how do I do this problem
The probability that the family had at least 3 girls is 0.6367
How to determine the probability that the family had at least 3 girls?
This is a binomial probability experiment. We are going to use the binomial distribution formula for determining the probability of x successes:
P(x = r) = nCr . p^r . q^n-r
Given: n= 8, probabibility of sucess (p) = 0.5, x≥3 (at least 3 girls)
The failures can be calculated using q = 1 - p = 1 - 0.5 = 0.5
P(x≥3) = 1 - P(x≤3) = 1 - ( P(x= 0) + P(x= 1) + P(x= 2) + P(x= 3) )
Using the formula:
P(x≥3) = 1 - ( (8C0 x 0.5⁰ x 0.5⁸⁻⁰) +(8C1 x 0.5¹ x 0.5⁸⁻¹) + (8C2 x 0.5² x 0.5⁸⁻²) + (8C3 x 0.5³ x 0.5⁸⁻³) )
= 1 - ( (1/256) + (1/32) + (7/64) + (7/32) )
= 0.6367
Therefore, the probability that the Wilson family had at least 3 girls is 0.6367
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1x(3x6)=18 create a equivalent multiplication sentence that illustrates the associative property of multiplication
The equivalent multiplication sentence that shows associative property is 3x(1×6)
What is associative property?Associative property is defined as, when more than two numbers are added or multiplied, the result remains the same, irrespective of how they are grouped.
This means that if a,b,c are real numbers then a×(b×c)=b×(a×c)
using the associative property,1×(3×6)= 3×(1×6)
To verify the statement,let's find out
solving the parentheses first
1×(3×6)=1×18= 18
3×(1×6)= 3×6= 18
this means that 1×(3×6) and 3×(1×6) are associative
therefore 1×(3×6)=3×(1×6)
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A Mrs. Sharpe’s Starbucks card has a balance of $37.45 remaining. If each visit she spends$5.35, which equation represents the number of visits, v, she may make using the card?
Answer:
the equation is 37.45-5.35v=0
Step-by-step explanation:
37.45-5.35v=0
minus 37.45 to both sides
-5.35v=-37.45
divide -5.35 from both sides
v=7
after 7 days she will finish the card
what is -3/4x - 1/3 + 7/8x - 1/2 written in siplest form?
help me pls
Answer: 1/8x - 5/6
Step-by-step explanation:
Let's move the similar terms of the problem together.
So first we have:
-3/4x + 7/8x
And then we have:
-1/3 - 1/2
So to add/subtract fractions, the denominators have to be equal. We can change the -3/4 into -6/8 by just multiplying by 2/2 which is just 1. (Anything multiplied by 1 is just itself). So then we have:
-6/8x + 7/8x ---> 1/8x
Next, the second part.
Since neither denominators (3 or 2) can turn into one another by multiplying them with a number, we'll just multiply them with the opposite denominator.
So then we have:
-1/3 * (2/2) = -2/6
-1/2 * (3/3) = -3/6
-2/6 - 3/6 = -5/6
So finally we have:
1/8x - 5/6
The answer please this is geometry, we’ve been trying to identify triangles by angles & sides
The measure of the required angle ∠VUT = 80 degrees
Given : A triangle with angle measures as :
∠RTU = 50°
exterior angle ∠UVR = 120°
To find : ∠VUT
In the given triangle we can use the exterior angle sum property
which states that the angle opposite to the inside of the triangle and the angle outside the triangle
The angle outside the triangle is 120 degrees
120 = ∠VUT + 50
thus on subtracting 50 both sides we will get
∠VUT = 120 - 50
∠VUT = 80 degrees
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(7/4x - 5) - (2y - 3.5) - (-1/4x + 5)
The value of the expression given as (7/4x - 5) - (2y - 3.5) - (-1/4x + 5) is 2x - 2y - 6.5
How to determine the solution of the expression?In this question, the representation of the expression is given as
(7/4x - 5) - (2y - 3.5) - (-1/4x + 5)
Start by removing the brackets in the expression
So, we have
7/4x - 5 - 2y + 3.5 + 1/4x - 5
Evaluate the fractions in the expression
The expression becomes
1.75x - 5 - 2y + 3.5 + 0.25x - 5
Collect the like terms
1.75x + 0.25x - 2y - 5 + 3.5 - 5
Evaluate the like terms
2x - 2y - 6.5
Hence, the solution is 2x - 2y - 6.5
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NO LINKS!! Please help me with these sequences Part 2x
Answer:
4. 121,800
5. 591 3/32
6. 1/4
Step-by-step explanation:
4. Sum of arithmetic sequenceYou want the sum of the first 200 terms of the arithmetic sequence starting 12, 18, 24, ....
The sum of the first n terms of an arithmetic sequence is given by the formula ...
Sn = (2·a1 +d(n -1))(n/2)
where a1 is the first term and d is the common difference. Your sequence has first term 12 and common difference 18-12 = 6. The desired sum is ...
S200 = (2·12 +6(200 -1))/(200/2) = (24 +1194)(100) = 121,800
5. Sum of geometric sequenceYou want the sum of the first 8 terms of the geometric sequence starting 12, 18, 27, ....
The sum of the first n terms of a geometric sequence is given by the formula ...
Sn = a1·(r^n -1)/(r -1)
where a1 is the first term and r is the common ratio. Your sequence has first term 12 and common ratio 18/12 = 3/2. The desired sum is ...
S8 = 12·((3/2)^8 -1)/(3/2 -1) = 24·6305/256 = 591 3/32
6. Sum of geometric sequenceFor this sequence, a1 = 1/12 and r = 2/3. When the sum is infinite and |r| < 1, the sum formula becomes ...
S = a1/(1 -r)
The desired sum is ...
S = (1/12)/(1 -2/3) = (1/12)/(4/12) = 1/4
Answer:
[tex]\textsf{4.} \quad 121,800[/tex]
[tex]\textsf{5.} \quad \dfrac{18915}{32}=591.09375[/tex]
[tex]\textsf{6.} \quad \dfrac{1}{4}[/tex]
Step-by-step explanation:
Question 4[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of an arithmetic series}\\\\$S_n=\dfrac{1}{2}n[2a+(n-1)d]$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $d$ is the common difference.\\ \phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
Given arithmetic sequence:
12, 18, 24, ...The first term of the given sequence is 12.
The common difference can be found by subtracting the first term from the second term:
[tex]\implies d=a_2-a_1=18-12=6[/tex]
Therefore:
a = 12d = 6To find the sum of the first 200 terms, substitute n = 200, a = 12 and d = 6 into the formula:
[tex]\begin{aligned}S_{200}&=\dfrac{1}{2}(200)[2(12)+(200-1)(6)]\\&=100[24+(199)(6)]\\&=100[24+1194]\\&=100[1218]\\&=121800\end{aligned}[/tex]
Question 5[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of a geometric series}\\\\$S_n=\dfrac{a(1-r^n)}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\ \phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
Given geometric sequence:
12, 18, 27, ...The first term of the given sequence is 12.
The common ratio can be found by dividing the second term by the first term:
[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{18}{12}=1.5[/tex]
Therefore:
a = 12r = 1.5To find the sum of the first 8 terms, substitute n = 8, a = 12 and r = 1.5 into the formula:
[tex]\begin{aligned}\implies S_{8}&=\dfrac{12(1-1.5^8)}{1-1.5}\\\\&=\dfrac{12\left(1-\frac{6561}{256}\right)}{-0.5}\\\\&=\dfrac{12\left(-\frac{6305}{256}\right)}{-0.5}\\\\&=\dfrac{-\frac{18915}{64}}{-0.5}\\\\&=\dfrac{18915}{32}\\\\&=591.09375\end{aligned}[/tex]
Question 6[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Sum of an infinite geometric series}\\\\$S_{\infty}=\dfrac{a}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}[/tex]
Given geometric sequence:
[tex]\dfrac{1}{12},\dfrac{1}{18},\dfrac{1}{27},...[/tex]The first term of the given sequence is ¹/₁₂.
The common ratio can be found by dividing the second term by the first term:
[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{\frac{1}{18}}{\frac{1}{12}}=\dfrac{2}{3}[/tex]
Therefore:
a = ¹/₁₂r = ²/₃To find the sum of the infinite geometric sequence, substitute a = ¹/₁₂ and r = ²/₃ into the formula:
[tex]\begin{aligned}\implies S_{\infty}&=\dfrac{\frac{1}{12}}{1-\frac{2}{3}}\\\\&=\dfrac{\frac{1}{12}}{\frac{1}{3}}\\\\&=\dfrac{1}{12} \times \dfrac{3}{1}\\\\&=\dfrac{3}{12}\\\\&=\dfrac{1}{4}\end{aligned}[/tex]
Find x and y. I need it ASAP
Using the proportionality theorem, the values are:
x = 3
y = 2
How to Apply the Proportionality Theorem?The proportional theorem states that if two triangles are similar to each other, then their corresponding side lengths have the same ratios.
The triangles above are similar to each other, therefore, their corresponding sides will have lengths that are proportional or have the same ratios.
Therefore:
3/1.5 = 6/x
Cross multiple
3x = (1.5)(6)
3x = 9
3x/3 = 9/3
x = 3
Find y:
3/1.5 = 4/y
3y = (1.5)(4)
3y = 6
3y/3 = 6/3
y = 2
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Beth makes $10.25/hour and Bartley makes $11.50 an hour. If Beth worked for 23 hours and Bartley worked for 17 hours, what was their difference in the amount of money they each earned?
The difference in the amount of money earned by Beth and Bartley is $40.25.
Given that, Beth makes $10.25/hour and Bartley makes $11.50 an hour.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
If Beth worked for 23 hours
Money earned by Beth is
10.25×23=$235.75
If Bartley worked for 17 hours
Money earned by Bartley is
11.50×17 =$195.5
So, difference of money = 235.75-195.5
= $40.25
Hence, the difference in the amount of money earned by Beth and Bartley is $40.25.
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Graph the equation using the point and the slope.
1
y-4=(x-2)
Use the graphing tool to graph the equation. Use the point contained in the equation when drawing
the line.
Answer:
slope: 1
y-intercept: (0,2)
the second point to plot: (1,3)
Step-by-step explanation:
Points to plot
(0,2),(1,3),(-2,0)
Beth's family is on a road trip. After driving for a while, they stopped for gas, and then traveled 65 1/4 more miles before they decided to stop for lunch. After lunch, they tripled their distance traveled before stopping for the night. Their total distance traveled that day was 372 miles. How many miles had they traveled before their first stop for gas?
Enter your answer as a simplified mixed number in the box.
The distance travelled before their first gas stop is 76.68 miles.
What is a mixed fraction?A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.
Consider that the distance covered before their first stop for gas be 'x'
The Total distance travelled is 372 miles
WE have given that after stopping for gas they travelled 65 1/4 miles and then tripled their distance. The equation is;
x + 261/4 + 3x = 372
4x + 261/4 = 372
16x + 261 = 1488
16x = 1227
x = 76.68 miles
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Select the correct answer from each drop-down menu.
The decimal equivalent of the fraction 2/15 is ____. The number of digits that should be repeating are __.
For the first blank options, 0.13, 0.1313, 0.133133, 0.1333
For the second blank options, 3, 2, 1, 0
Answer: 1. 0.1333 2. 1
Step-by-step explanation:
Step 1: 2/15 is the same as 2 divided by 15 which is 1.33333333333333333333333333333333333333333333333333 and so on.
Step 2: Clearly, the only number that is repeating is the 3.
A concession stand at the Tennis Center sells a hamburger/drink combination dinner for $7. The profit, y (in dollars), can be approximated by
y=-0.001x² +
2+3.2x-400 where x is the number of dinners prepared.
(a) Find the number of dinners that should be prepared to maximize profit.
(h) What is the maximum profit?
The number of dinners that should be prepared to maximize profit is 1200.
The maximum profit is $1040
We know that,
y = ax²+ bx + c
The expression has the greatest value at x = -b/2a
From the question, we have
y=-0.001x² +2.4x-400
x = -b/2a
= -2.4/2*(-0.001)
=1200
substituting the value we get
y=-0.001x² +2.4x-400
y=-0.001*1200² +2.4*1200-400
y=$1040
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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a. {(−5,4), (−4, −1), (−2,1), (0,4), (1,3)
What is the domain and range and it is a function
b. {(−3, −4), (−1,2), (0,0), (−3,5), (2,4)}
Domain:
Range:
Function?
The domain is {-5, -4, -2, 0, 1} and range is {4, -1, 1, 4, 3}
The given relation is {(−5,4), (−4, −1), (−2,1), (0,4), (1,3)
We need to find its domain and range
Domain of the set is {-5, -4, -2, 0, 1}
Range of the set is {4, -1, 1, 4, 3}
If in an relation every input has an single output, it is said to be a function
Here, every element of the domain has a single element in range, so it is a function
The given relation is {(−3, −4), (−1,2), (0,0), (−3,5), (2,4)}
We need to find its domain and range
Domain of the set is {-3, -1, 0, -3, 2}
Range of the set is {-4, 2, 0, 5, 4}
If in an relation every input has an single output, it is said to be a function
Here, every element of the domain has a single element in range, so it is a function
Therefore, the domain is {-5, -4, -2, 0, 1} and range is {4, -1, 1, 4, 3}
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The display on a calculator screen is shown below.
What number does the calculator display represent?
OA. 0.0000012312
B. 0.0000001231
OC. 1,231,151
D. 123,115.1
1.231151 E-6
The number which is as represented on the calculator display is; Choice A; 0.000001231151
What number does the calculator display represent?It follows from the task content that the number which is represented on the calculator display is to be identified.
By checking, The display of the calculator is; 1.231151 E-⁶.
The number above can be represented as follows;
1.231151 × 10-⁶.
Since a negative exponent on the number ten indicates a shift leftwards, it follows that the number represented on the calculator display is;
0.000001231151.
Therefore, the correct number represented on the calculator display is; Choice A; 0.000001231151.
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Please select ONLY ONE of the two questions below to respond to. Choose the one you feel
you can answer the best! This portion of your test will be graded after you submit your exam.
Rubric / Requirements:
1) Make sure your response answers each part of the prompt and is written in at least 3 complete
sentences. (2 points)
2) Proof read your response to ensure you have used proper capitalization and spelling. (1 point)
3) Explain the WHY or HOW behind your ideas! Justify your stances using your knowledge from this unit.
(7 points)
4) Plagiarism in any form is not permitted. You risk a 0% on this section of the exam if you plagiarize.
5) You may use a speech to text tool for your response.
OPTION 1: Political Factions
In his Farewell Address in 1796, George Washington gave the following warnings about the dangers of political
parties:
"[Parties always] distract the public councils and (weaken] the public administration. It agitates the community with ill-
founded jealousies and false alarms, kindles the animosity of one party against another, [encourages) occasionally riot
and insurrection. It opens the door to foreign influence and corruption, which finds access to the government itself
through the channels of party passions..."
QUESTION: Why did George Washington caution against the formation of political parties?
What potential risks do political parties pose towards democracy? Do you think that the
country should have followed his advice?
Answer of the why did George Washington caution against the formation of political parties?
What potential risks do political parties pose towards democracy? Do you think that the country should have followed his advice are as follows :
(a) He believes that the government was undermined by differences between the political parties. Additionally, he argues that "the alternate domination" of one party over another and concurrent attempts to exact revenge on their rivals have resulted in terrible atrocities and "is itself a frightful despotism."
(b)The democratic theory's main tenet is that democracies force administrations to take citizens' preferences into account. Every contemporary democracy is organized by political parties, and some observers contend that parties are what makes democracies responsive. Others, however, contend that parties give extremists a platform and make governments less receptive to the needs of the populace. As newly established democracies around the world grapple with concerns of representation and governability, the discussion of parties and democracy assumes fresh prominence.
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Show that f(x)= 2x-3/2 & g(x)= 2x+3/2 are inverse fractions. Must show fog=x and gof=x. I really don’t understand this and it’s frustrating me. I must show work
Hence its proven that f and g are inverse of one another
What is a Function?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Given,
f(x)= 2x-3/2
g(x)= 2x+3/2
Step 1: show that fog=x
f(g(x))
[2((2x + 3) / 2) - 3]/2
[(2x + 3) - 3] / 2
(2x + 3 - 3) / 2
2x / 2
x , which is equals to x
Now, for Step 2: gof = x
g(f(x))
g((2x - 3)/2)
[2((2x - 3)/2) + 3]/2
[(2x - 3) + 3]/2
(2x - 3 + 3)/2
2x/2
x , which is equals to x
Since, both fog(x) and gof(x) equals to x
Hence, its proven that f and g are inverse of one another
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Select the correct answer. Which inequality can this number line represent? A. 7 − x ≥ 1 or 4x + 9 < 13 B. 3x + 2 < 5 or 2x − 1 ≥ 11 C. 7 − x ≥ 1 and 4x + 9 < 13 D. 3x + 2 < 5 and 2x − 1 ≥ 11
Answer: A
Step-by-step explanation: A
A
Add the rational expressions. Show all work.
5/(x+3)(x-4) + 7/(x+2)(x-4)
The given rational expression when added gives
[tex] \frac{12x + 31}{(x + 3)(x - 4)(x + 2)} [/tex]
How to add rational expression?Given:
[tex] \frac{5}{(x + 3)(x - 4)} + \frac{7}{(x + 2)(x - 4)} [/tex]
Find the lowest common multiple (LCM)=
[tex] \frac{5(x + 2) + 7(x + 3)}{(x + 3)(x - 4)(x + 2)} [/tex]
Open parenthesis=
[tex] \frac{5x + 10 + 7x + 21}{(x + 3)(x - 4)(x + 2)} [/tex]
Collect and add like terms=
[tex] \frac{12x + 31}{(x + 3)(x - 4)(x + 2)} [/tex]
So therefore, the addition of the rational expression is
[tex] \frac{12x + 31}{(x + 3)(x - 4)(x + 2)} [/tex]
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What is the graphing form of y = x2 - 12x + 7
The vertex of the equation y=x^2-12x+7 is (6,-29) and the graph is given below.
In the given question we have to find the graphing form of y=x^2-12x+7.
The given equation is y=x^2-12x+7.
To graph the given equation we firstly express that equation in the standard form of parabola.
y=a(x-h)^2+k
Add and subtract 36 in the given equation;
y=x^2-12x+36-36+7
y=x^2-2×6×x+(6)^2-29
y=(x-6)^2-29
The vertex of the given equation is (6,-29).
The graph of the given equation is given below:
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ne
Problem 14:
From this diagram, select the
pair of lines that must be
parallel if 45 47. If there
is no pair of lines, select
"none."
Playback
2
7
4
3
(first taught in
lesson 24)
9
8
6
After you pick your answer press GO.
A. l || n
B. oll q
C. l | m
D. pllq
E. None
10
7
GO
l
Contro
Lecture
& Problem
Scratchpa
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From the given pair of parallel lines , the lines which satisfies the condition of two angles to be congruent that is ∠5 ≅ ∠7 are l || m .
As given in the question,
Given pair of lines,
Condition given that two angles are congruent ,
∠5 ≅ ∠7
Angle 5 is congruent to vertical opposite angle and to make a pair of parallel line Opposite angle should be congruent to angle 7.
Opposite angle and Angle 7 are pair of corresponding angles.
Line l should be parallel to the line m to satisfied the condition of
∠5 ≅ ∠7.
Therefore, from the given pair of parallel lines , the lines which satisfies the condition of two angles to be congruent that is ∠5 ≅ ∠7 are l || m .
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help please! Trig question on homework this is the only one I can’t really figure out!
The measure of central angle is 45°
Here, arc length S = 5π/4
radius r = 5
We need to find central angle θ
Using the formula of arc length,
S = r * θ
5π/4 = 5 * θ
θ = π/4
θ = 45°
Therefore, the measure of central angle is 45°
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NO LINKS! Please help me with this problem #4l
Answer:
equation: (x -1)²/64 -(y -4)²/80 = 1foci: (-11, 4), (13, 4)Step-by-step explanation:
You want the steps to finding the equation of the hyperbola with center (1, 4), vertices (-7, 4) and (9, 4) and that includes the point (-11, -6).
Equation of a hyperbolaThe standard-form equation of a hyperbola with center (h, k) and semi-axes 'a' and 'b' is ...
[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]
The "linear eccentricity" 'c' is the distance from the center to a focus, and satisfies the equation ...
c² = a² +b²
The vertices are (h±a, k) and the foci are (h±c, k).
ApplicationThe center of the hyperbola is given as (1, 4). The distance from the right vertex to the center is ...
a = 9-1 = 8
The equation thus far is ...
(x -1)/8² -(y -4)/b² = 1
The value of 'b' can be determined from the given point:
(-11 -1)²/8² -(-6 -4)²/b² = 1
9/4 -100/b² = 1
5/4 = 100/b²
b² = 100/(5/4) = 80
The linear eccentricity is ...
c² = a² +b²
c² = 64 +80 = 144
c = √144 = 12
The foci are (1±12, 4) = (-11, 4) and (13, 4).
The equation is ...
(x -1)²/64 -(y -4)²/80 = 1
Step summaryThe given information was used to find semi-major axis 'a'. Together with the given center value (h, k), and the given point, the equation was written and solved for b².The value of 'c' was found from a² and b², and used to find the locations of the foci.
Answer:
[tex]\dfrac{(x-1)^2}{64}-\dfrac{(y-4)^2}{80}=1[/tex]
Center = (1, 4)Vertices = (-7, 4) and (9, 4)Foci = (-11, 4) and (13, 4)Step-by-step explanation:
Standard equation of a horizontal hyperbola (opening left and right):
[tex]\boxed{\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1}[/tex]
where:
Center = (h, k)Vertices = (h±a, k)Co-vertices = (h, k±b)Foci = (h±c, k) where c² = a² + b²Given:
Center = (1, 4)Vertices = (-7, 4) and (9, 4)Point on the hyperbola = (-11, -6)Therefore:
h = 1k = 4Find the value of a using the x-values of the vertices:
[tex]\begin{aligned}\implies h-a &= -7\\1-a &= -7\\a &= 8\end{aligned}[/tex]
[tex]\begin{aligned}\implies h+a &= 9\\1+a &= 9\\a &= 8\end{aligned}[/tex]
Therefore, a = 8.
Substitute the values of h, k and a into the formula:
[tex]\implies \dfrac{(x-1)^2}{8^2}-\dfrac{(y-4)^2}{b^2}=1[/tex]
[tex]\implies \dfrac{(x-1)^2}{64}-\dfrac{(y-4)^2}{b^2}=1[/tex]
Substitute the given point on the hyperbola (-11, -6) into the equation and solve for b²:
[tex]\implies \dfrac{(-11-1)^2}{64}-\dfrac{(-6-4)^2}{b^2}=1[/tex]
[tex]\implies \dfrac{(-12)^2}{64}-\dfrac{(-10)^2}{b^2}=1[/tex]
[tex]\implies \dfrac{144}{64}-\dfrac{100}{b^2}=1[/tex]
[tex]\implies \dfrac{144}{64}-1=\dfrac{100}{b^2}[/tex]
[tex]\implies \dfrac{144}{64}-\dfrac{64}{64}=\dfrac{100}{b^2}[/tex]
[tex]\implies \dfrac{80}{64}=\dfrac{100}{b^2}[/tex]
[tex]\implies \dfrac{5}{4}=\dfrac{100}{b^2}[/tex]
[tex]\implies b^2=\dfrac{4 \cdot 100}{5}[/tex]
[tex]\implies b^2=\dfrac{400}{5}[/tex]
[tex]\implies b^2=80[/tex]
Therefore, the equation of the hyperbola is:
[tex]\boxed{\dfrac{(x-1)^2}{64}-\dfrac{(y-4)^2}{80}=1}[/tex]
To find the foci, first find c where c² = a² + b²:
[tex]\implies c=\sqrt{a^2+b^2}[/tex]
[tex]\implies c=\sqrt{64+80}[/tex]
[tex]\implies c=\sqrt{144}[/tex]
[tex]\implies c=12[/tex]
Substitute the found value of c, along with the values of h and k into the foci formula:
[tex]\implies (h+c, k)=(1+12, 4)=(13,4)[/tex]
[tex]\implies (h-c,k)=(1-12,4)=(-11,4)[/tex]
Therefore, the foci are (-11, 4) and (13, 4).
Draw the image of AABC under the translation (x, y) → (x, y + 3).
PLEASE HELPP! ORDER THE NUMBERS FROM LEAST TO GREATEST
Answer:
least
- 1/4 ft
- 14 3/4 ft
- 15 1/2 ft
- 20 3/5 ft
greatest
Answer:
- 20 3/5 ft
- 15 1/2 ft
- 14 3/4 ft
- 1/4 ft
I the number is larger looking but have a negative symbol, then it is smaller.
For example, -1 is greater than -6. Also -1/4 is greater than -20 3/5.
Trust me, I am a year ahead in school, so trust me.
I hope this helped.
The vertices of a rectangle are located at the coordinates (1, 4), (1, 5), (6, 5), and (6, 4). Find the length of the sides of the rectangle and its perimeter.
Answer: This is a 1 by 5 rectangle
perimeter = 12 units
========================================================
Work Shown:
Label the vertices A,B,C,D
A = (1, 4)
B = (1, 5)
C = (6, 5)
D = (6, 4)
The x coordinates of points A and B are the same (x = 1). The difference in y values of these points is 5-4 = 1 unit. This is the height of the rectangle. In other words, it's the length of segment AB.
Points B and C have the same y coordinate (y = 5). The difference in x value is 6-1 = 5 which is the horizontal length of the rectangle. This is the length of segment BC.
In short, this is a 1 by 5 rectangle. It's one unit tall and five units across.
--------
Perimeter = 2*(length+width)
Perimeter = 2*(5+1)
Perimeter = 2*6
Perimeter = 12 units
Or you can add up the four sides (1,5,1 and 5) to get the same result.