Answer:
x = 5
Step-by-step explanation:
By the property of intersecting chords inside a circle:
\((x - 2)(x + 7) = 4(2x - 1) \\ \\ {x}^{2} + 7x - 2x - 14 = 8x - 4 \\ \\ {x}^{2} + 5x - 14 - 8x + 4 = 0 \\ \\ {x}^{2} - 3x - 10 = 0 \\ \\ {x}^{2} - 5x + 2x - 10 = 0 \\ \\ x(x - 5) + 2(x - 5) = 0 \\ \\ (x + 2)(x - 5) = 0 \\ \\ x + 2 = 0 \: \: or \: \: x - 5 = 0 \\ \\ x = - 2 \: \: or \: \: x = 5 \\ \\ \because \: length \: can \: not \: be \: - ve \\ \\ \therefore \: x \neq - 2 \\ \\ \implies \: x = 5\)
if the population of an anthill doubles every 10 days and there are currently 20 ants living in the ant hill, what will the ant hill population be in 20 days?
Please help me solve this math. It’s due soon
Answer:
the awnser would be a I'm pretty sure
Step-by-step explanation:
make the other side the same ones so like take the bottom 8 and duplicate it to the top. do the same thing with the 6 but put it on the left side. and then combine 12 + 18 and there you go.
Question
What is the scale factor for the similar figures below?
The value of the scale factor for the similar figures is 1/2
What is the scale factor for the similar figures?From the question, we have the following parameters that can be used in our computation:
The similar figures
The corresponsing sides of the similar figures are
Original = 8
New = 4
Using the above as a guide, we have the following:
Scale factor = New /Original
substitute the known values in the above equation, so, we have the following representation
Scale factor = 4/8
Evaluate
Scale factor = 1/2
Hence, the scale factor for the similar figures is 1/2
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Find the inverse Laplace transform of: 32 points (16 points each) (a) F(s) a) F0=1. 1 1 + S S +3 S? S-3 (b) F(S) = s(s - 1)(s +2)
Taking the inverse Laplace transform of each term using the table of Laplace transforms, we get: f(t) = -1/2 + 2e^t
(a) To find the inverse Laplace transform of F(s) = 1/(s+1)(s+3)(s-3), we can use partial fraction decomposition as follows:
1/(s+1)(s+3)(s-3) = A/(s+1) + B/(s+3) + C/(s-3)
Multiplying both sides by (s+1)(s+3)(s-3), we get:
1 = A(s+3)(s-3) + B(s+1)(s-3) + C(s+1)(s+3)
Expanding and equating coefficients of s^2, s and the constant term, we get:
A = 1/24
B = -1/8
C = 1/24
Therefore, we have:
F(s) = 1/24(s+1) - 1/8(s+3) + 1/24(s-3)
Taking the inverse Laplace transform of each term using the table of Laplace transforms, we get:
f(t) = 1/24(e^(-t) - e^(-3t)) - 1/8e^(-3t) + 1/24e^(3t)
(b) To find the inverse Laplace transform of F(s) = s(s-1)(s+2), we can use partial fraction decomposition as follows:
s(s-1)(s+2) = As^2 + Bs + C
Multiplying both sides by (s-1)(s+2), and setting s=0, 1, and -2, we get:
C = 0
-2A + 2B = -2
2A + B = 1
Solving for A and B, we get:
A = -1/2
B = 2
Therefore, we have:
F(s) = -1/2s + 2/(s-1)
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How many solutions does this equation have? –9h + 9h = 0
Answer:
Infinite
Step-by-step explanation:
Let's assume that h=2
-9(2)+9(2)=0
-18+18=0
And if we assumed that h=9
Then: - 9(9)+9(9)=0
- 81+81=0
Thus, h can be any number
Consider the argument form: p ∧ ∼ q → r p ∨ q q → p Therefore r. Use the truth table below to determine whether this form of argument is valid or invalid. Annotate the table (as appropriate) and include a few words explaining how the truth table supports your answer.
The argument is not valid.
The argument form is: p ∧ ∼ q → r, p ∨ q, q → p, therefore r. We can use the truth table to determine whether this argument is valid or invalid. Here is the annotated truth table:
p
q
∼q
p ∧ ∼q
p ∨ q
p ∧ ∼q → r
q → p
r
T
T
F
F
T
T
T
T
T
F
T
T
T
T
T
T
F
T
F
F
T
T
F
F
F
F
T
F
F
T
T
F
From the truth table, we can see that the conclusion r is not always true, even when all the premises are true. For example, in the third row of the table, all the premises are true, but the conclusion is false. This means that the argument is invalid. The truth table supports this conclusion because it shows that there are cases where the premises are true but the conclusion is false. Therefore, the argument is not valid.
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Given point B is located at
(-2,-4), what are the
coordinates of B' after a
reflection over the line y = x?
Answer: \(\Large\boxed{Point~B'~=~(-4,~-2)}\)
Step-by-step explanation:
Given information
Point B = (-2, -4)
Reflection line: y = x
Concept:
When reflecting over the line y = x, the position of y and x in the original coordinate switches places.
This is because it is " y = x ", assuming that they could interchange
Find the coordinate of Point B'
Original (x, y) = (-2, -4)
Point B' = (x', y') = (y, x) = \(\Large\boxed{(-4,~-2)}\)
Please refer to the attachment below for a graphical understanding
Hope this helps!! :)
Please let me know if you have any questions
The coordinates of B' after the reflection over the line y = x are (-4, -2).
Given that a point B = (-2, -4) has been reflected over the line x = y, we need to find the coordinates of the reflected point B'.
To find the coordinates of point B' after a reflection over the line y = x, we need to understand what a reflection over this line means.
The line y = x is a diagonal line that passes through the points where the x-coordinate and the y-coordinate are equal.
It has a 45-degree angle with both the x-axis and the y-axis. When you reflect a point over this line, you essentially swap its x and y coordinates.
Let's take point B(-2, -4) as an example. To reflect this point over the line y = x, we swap its x and y coordinates:
New x-coordinate of B' = Old y-coordinate of B = -4
New y-coordinate of B' = Old x-coordinate of B = -2
So, the coordinates of B' will be (y, x) = (-4, -2).
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can someone please help me!!!!!
Answer:
5
120
20
Step-by-step explanation:
Given the following coordinates the glide reflection transformation
Answer:
see explanation
Step-by-step explanation:
Under a reflection in the x- axis
a point (x, y ) → (x, - y ) , then
A (4, 2 ) → A' (4, - 2 )
B (7, 0 ) → B' (7, 0 )
C (9, 3 ) → C' (9, - 3 )
A translation of a shift to the left of 3 units is a horizontal shift.
This means subtracting 3 fro the x- coordinate and leaving the y- coordinate
A' (4, - 2 ) → A'' (4 - 3, - 2 ) → A'' (1, - 2 )
B' (7, 0 ) → B'' (7 - 3, 0 ) → B'' (4, 0 )
C' (9, - 3 ) → C'' (9 - 3, - 3 ) → C'' (6, - 3 )
Please I need help QUICKLY
Answer: x = 7 or x = -2
Step-by-step explanation:
x² - 5x - 14 = 0
↓ Split the middle term into 2 terms
x² - 7x + 2x - 14 = 0
↓ Factor the first 2 terms and the last 2 terms separately
x(x - 7) + 2(x - 7) = 0
↓ Factor that out
(x - 7)(x + 2) = 0
↓ You apply the Zero Product Property
x - 7 = 0 or x + 2 = 0
↓ Rearrange the variables to the left side of the equation
x = 7
or ------------------------------------------
x + 2 = 0
↓ Rearrange the variables to the left side of the equation
x = -2
The theater sells two types of tickets: adult tickets for $14 and child tickets for $6.
Last night, the theater sold a total of 438 tickets for a total of $5012. How many adult tickets did the theater sell last night?
Answer:
Number of adult tickets = 298
Number of child tickets = 140
Step-by-step explanation:
Number of adult tickets = a
Number of child tickets = c
a + c = 438 -------------------(I)
14a + 6c = 5012 ----------------(II)
Multiply equation (I) by (-6) and then add, so c will be eliminated.
(I) * (-6) -6a - 6c = -2628
(II) 14a + 6c = 5012 {Add}
8a = 2384
a = 2384/8
a = 298
Plugin a = 298 in equation (I)
298 + c = 438
c = 438 - 298
c = 140
How many inches are in 8 feet?
Answer: 96
Step-by-step explanation:
Answer: 96 inches
Step-by-step explanation:
1 Feet=12 inches
--------------------------------
So.....
8 Feet= 12 × 8 inches
8 Feet= 96 inches
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You want to estimate the number of eighth-grader students in your school who find it relaxing to listen to music. You consider two samples. Fifteen randomly selected members of the band. Every fifth student whose name appears on an alphabetical list of eighth-grade students
Please show work
To estimate the number of eighth-grader students in your school who find it relaxing to listen to music, you consider two samples.Fifteen randomly selected members of the band and every fifth student whose name appears on an alphabetical list of eighth-grade students.
The work for this estimation is as follows:Sample 1: Fifteen randomly selected members of the band.If the band is a representative sample of eighth-grade students, we can use this sample to estimate the proportion of students who find it relaxing to listen to music.
We select fifteen randomly selected members of the band and find that ten of them find it relaxing to listen to music. Therefore, the estimated proportion of eighth-grader students in your school who find it relaxing to listen to music is: 10/15 = 2/3 ≈ 0.67.Sample 2: Every fifth student whose name appears on an alphabetical list of eighth-grade students.Using this sample, we take every fifth student whose name appears on an alphabetical list of eighth-grade students and ask them if they find it relaxing to listen to music.
We continue until we have asked thirty students. If there are N students in the eighth grade, the total number of students whose names appear on an alphabetical list of eighth-grade students is also N. If we select every fifth student, we will ask N/5 students.
we need N/5 ≥ 30, so N ≥ 150. If N = 150, then we will ask thirty students and get an estimate of the proportion of students who find it relaxing to listen to music.To find out how many students we need to select, we have to calculate the interval between every fifth student on an alphabetical list of eighth-grade students,
which is: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150
We select students numbered 5, 10, 15, 20, 25, and 30 and find that three of them find it relaxing to listen to music. Therefore, the estimated proportion of eighth-grader students in your school who find it relaxing to listen to music is: 3/30 = 1/10 = 0.10 or 10%.Thus, we can estimate that the proportion of eighth-grader students in your school who find it relaxing to listen to music is between 10% and 67%.
To estimate the number of eighth-grade students who find it relaxing to listen to music, you can use two sampling methods: sampling from the band members and sampling from an alphabetical list of eighth-grade students.
Sampling from the Band Members:
Selecting fifteen randomly selected members of the band would give you a sample of band members who find it relaxing to listen to music. You can survey these band members and determine the proportion of them who find it relaxing to listen to music. Then, you can use this proportion to estimate the number of band members in the entire eighth-grade population who find it relaxing to listen to music.
Sampling from an Alphabetical List:
Every fifth student whose name appears on an alphabetical list of eighth-grade students can also be sampled. By selecting every fifth student, you can ensure a random selection across the entire population. Surveying these selected students and determining the proportion of those who find it relaxing to listen to music will allow you to estimate the overall proportion of eighth-grade students who find it relaxing to listen to music.
Both sampling methods can provide estimates of the proportion of eighth-grade students who find it relaxing to listen to music. It is recommended to use a combination of these methods to obtain a more comprehensive and accurate estimate.
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Choose the two expressions that are equivalent to 5. 75 ÷ 1. 15
A: 575 ÷115
B: 5,750 ÷ 1,150
C: 5,750 ÷ 115
D: 575 ÷ 1,150
Answer:
A and B, but I’m gonna explain it the best I can too.
Step-by-step explanation:
5.75 divided by 1.15 is the same as answer A, since all you are doing is taking away the periods, making it whole numbers.
Again 5.75 divided by 1.15 is the same as B as well, Since it is the same just without the periods and an added zero at the end of each.
This Is so that they are both all equivalent by being whole numbers, but whatever you do to one numbers in the expression that you think is the answer you have to do to the other numbers in the expression
they have to add up completely the same.
solution set of 2x+4 greater than or equal to -8
Step-by-step explanation:
equal because of the 8+7
Answer:
x \geq -6
Step-by-step explanation:
2x+4 \geq -8
-4 -4
2x \geq -12
/2 /2
x \geq -6
solve the qaudratic equation by using a numeric or a graphic approach
x^2-14x-49=0
Therefore, the solutions to the quadratic equation \(x^2 - 14x - 49 = 0\)are \(x = 7 + 7\sqrt{2}\) and \(x = 7 - 7\sqrt{2}\) .
What is quadratic equation?A quadratic equation is a second-degree polynomial equation in a single variable. In other words, it is an equation of the form \(ax^2 + bx + c = 0\), where x is the variable, and a, b, and c are constants.
The goal of solving a quadratic equation is to find the values of x that make the equation true. There are several methods for solving quadratic equations, including factoring, completing the square, and using the quadratic formula.In the given question,
To solve the quadratic equation x² - 14x - 49 = 0 ,
we can use the quadratic formula:
\(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
where a = 1, b = -14, and c = -49.
Plugging in these values, we get:
\(x = \frac{-(-14) \pm \sqrt{(-14)^2 - 4(1)(-49)}}{2(1)}\)\(x = \frac{14 \pm \sqrt{196 + 196}}{2} = \frac{14 \pm \sqrt{392}}{2} = \frac{14 \pm 14\sqrt{2}}{2} = 7 \pm 7\sqrt{2}\)
Therefore, the solutions to the quadratic equation x²- 14x - 49 = 0 are x = 7 + 7√2 and x = 7 - 7√2.
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Therefore, the solutions to the quadratic equation x²- 14x - 49 = 0 are x = 7 + 7√2 and x = 7 - 7√2.
What is quadratic equation?A quadratic equation is a second-degree polynomial equation in a single variable. In other words, it is an equation of the form , where x is the variable, and a, b, and c are constants.
The goal of solving a quadratic equation is to find the values of x that make the equation true. There are several methods for solving quadratic equations, including factoring, completing the square, and using the quadratic formula.
In the given question,
To solve the quadratic equation x² - 14x - 49 = 0, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.
In this case, a = 1, b = -14, and c = -49. Substituting these values into the quadratic formula, we get:
x = (-(-14) ± √((-14)² - 4(1)(-49))) / 2(1)
x = (14 ± √(196 + 196)) / 2
x = (14 ± √392) / 2
x = (14 ± 14√2) / 2
Simplifying this expression, we get:
x = 7 ± 7√2
Therefore, the solutions to the quadratic equation x² - 14x - 49 = 0 are:
x = 7 + 7√2 or x = 7 - 7√2
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John is going to the store. His house is located 3 miles south and 4 miles east from the store, as shown below. What is the shortest distance from his house to the store? Explain
Answer:
5 miles
Step-by-step explanation:
It is a right triangle, with 3 miles down, and 4 miles to the right
the shortest distance would be and southeast line.
Using the Pythagorean theorem, you get:
3^2 + 4^2 = x^2
9 + 16 = x^2
25 = x^2
x = 5
solve the initial-value problem. t du dt = t² 3u, t > 0, u(3) = 18
The solution to the initial-value problem t du/dt = t^2 * 3u, t > 0, u(3) = 18 is given by the function u(t) = (18/3^3) * t^3.
To solve the initial-value problem, we can separate variables and integrate both sides. Starting with the given equation t du/dt = t^2 * 3u, we can rearrange it as du/u = 3/t dt. Next, we integrate both sides. The integral of du/u is ln|u|, and the integral of 3/t dt is 3 ln|t| + C, where C is the constant of integration.
Therefore, we have ln|u| = 3 ln|t| + C. Exponentiating both sides, we get |u| = e^(3 ln|t| + C). Since e^C is just another constant, we can rewrite the equation as |u| = K * t^3, where K = e^C. Finally, using the initial condition u(3) = 18, we can determine the value of K: |18| = K * 3^3, which gives us K = 2. Plugging in K and removing the absolute value, we obtain u(t) = (18/3^3) * t^3 as the solution to the initial-value problem.
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Find the volume of a cone
Answer:
96π or 301.59 in³
Step-by-step explanation:
V(cone) = 1/3πr²h
= 1/3·π·6²·8
= 96π or 301.59
Answer:
301.58
Step-by-step explanation:
In the coordinate plane, the point A (-2,2) is translated to the point A (2,-3). Under the same translation, the points B (-4,-1) and C (-6,5) are translated to B and C respectively. What are the coordinates of B and C?
Answer: B(0,-6); C(-2,0)
Step-by-step explanation:
A was translated 4 units to the right (x) and 5 units down (y)
Do the same for the other points
B(-4+4, -1-5) C(-6+4, 5-5)
B(0, -6) C(-2, 0)
describe how lady macbeth fulfills a traditional feminine role at the banquet in macbeth
Lady Macbeth exemplifies the traditional role of a woman by showing her hospitality, generosity, graciousness, and support to her guests.
At the banquet in Macbeth, Lady Macbeth fulfills a traditional feminine role in several ways. Firstly, she demonstrates her hospitality and generosity by welcoming the guests and providing them with food and drink. Secondly, she shows her nurturing nature by urging Macbeth to be more hospitable and to provide the guests with more generous servings. Thirdly, she shows her graciousness and hospitality by offering the guests timely compliments. Lastly, she shows her caring and supportive nature by encouraging Macbeth to be more gracious and generous. Altogether, Lady Macbeth exemplifies the traditional role of a woman by showing her hospitality, generosity, graciousness, and support to her guests.
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Find the formula for the nth term of these sequences:
(a) 2, 5, 10, 17, 26, …….
(b) 4, 10, 20, 34, 52, ………
Part of a geometric sequence is given below:
,,,,, -1, ,,,, , ,,,,,, 64, ,,,,,
Where uₙ means the nth term, hence, u₂ = -1, and u₅ = 64.
Second term is -1, and the fifth term is 64. Calculate:
(a) The common ratio (r)
(b) The value of the first term (a) or u₁
(c) The value of the 10th term.
I need it by today!! and please for the people who type to get points please dont do it with me
A child makes a pitcher of fruit punch by completely dissolving fruit- flavoured powder in water. The child drinks a glass and decides the punch needs to be sweeter, so she stirs in more powder. This time the powder does not all dissolve, but settles on the bottom of the pitcher. A) Is the fruit-flavoured powder a pure substance or a mixture? * helpme anyone?
if you pay 6$ for a pound of something how much would it cost to buy 2.6 pounds
Answer:
\(6\cdot2.6=15.6\)$ for \(2.6\) pounds
Step-by-step explanation:
Rate - \(6\) dollars per pound
We have \(2.6\) pounds
Here's our equation
\(6\cdot2.6\)
Solve\(6\cdot2.6=15.6\) for \(2.6\) pounds
Help me solve this problem please
Answer:
8
Step-by-step explanation:
4 + 2³- |-4|
~Take the absolute value of -4
4 + 2³- 4
~Simplify the exponent
4 + 8 - 4
~Add
12 - 4
~Subtract
8
Best of Luck!
Answer:
8
Step-by-step explanation:
Do the cube of 2, which equals 8
Add 8 to 4 and you get 12
Absolute value of -4 is 4
Subtract 4 from 12 and you get 8
What must you assume when you use a rate for a prediction? (Please Help!! I'm in 6th grade and this is math.)
Answer:
For anything to do with force you have to assume an even amount of force is spread out evenly. But for things like growing rate you have all those variables so you can't assume a constant growing rate like acceleration.
Step-by-step explanation:
hope it helps (:
Please help I don't understand!
Answer:
AA similarity postulate.
Explanation:
Here given that one triangle has 70° and 30°, so other angle should be 80°.
For the other triangle same, it has 30°, 80°, so other angle should be 70°
So when two angles are equal of one triangle to another triangle.
Then the triangles are equal by the AA similarity postulate.
plz help i'll mark u brainliest
Answer:
\(h = 34 \times \sin(27) + 5 = 15.43 + 5 = 20.43\)
A woman had less than 1,100 with her when she went to the market.She spent all her money and used a certain number 50.00notes and twice as many as 20.00 notes.Find the maximum number of 50.00 notes she used
Answer:
12
Step-by-step explanation:
Let x = number of 50.00 notes.
They are worth 50x
Then, 2x = number of 20.00 notes.
They are worth 2x * 20 = 40x
50x + 40x < 1100
90x < 1100
9x < 110
x < 12.2
Answer: 12
Check:
x = 12 (number of 50.00 notes)
2x = 24 (number of 20.00 notes)
12 * 50 + 24 * 20 = 1080
If she used one more 50.00 note, she'd go over 1,100, so 12 is correct.
Convert the following equation
into standard form.
y = -x - 3
Answer:
x+y=−3
Step-by-step explanation:
hope this heps:)
Answer:
x+y=-3 (put -3 into the box)
Step-by-step explanation:
add x to both sides, and you get x+y= -3.
You get in an elevator and ride down 5
floors. You realize you forgot something, so you stay on the elevator and ride back up 5
floors. Which expression represents the number of floors you are from your original position?
Answer:
y = x - 5 + 5
Step-by-step explanation:
Let x be the original position and y be a new position.
After rid down, 5 floors, the expression would be y = x - 5.
After rid back up 5 floors, the expression changed to y = x - 5 + 5.
Hence, the required expression is y = x - 5 + 5 = x.