Based on the calculations, the equation of the triangle's line of symmetry is equal to: B. y = x - 1.
How to determine the equation of the triangle's line of symmetry?First of all, we would determine the midpoint where the line of symmetry passes through points A and B:
Midpoint at point A = (3 + 7)/2 = 10/2 = 5.
Midpoint at point B = (6 + 2)/2 = 8/2 = 4.
Point D = (5, 4)
Mathematically, the standard equation of a line is given by y = ax + b.
D(5, 4); 4 = 5a + b ....equation 1.
C(4, 3); 3 = 4a + b ....equation 2.
Subtracting eqn. 2 from eqn. 1, we have:
1 = a
Next, we would find the value of b:
4 = 5a + b
4 = 5(1) + b
b = 4 - 5
b = -1.
Therefore, the equation of the triangle's line of symmetry is given by:
y = ax + b
y = x(1) + (-1)
y = x - 1.
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Two random samples were taken to determine how often people in a community listen to the local radio station each month.
The first sample surveyed 15 people as they exited the bank on Main Street. The first sample found that the mean number of hours they listened to the radio each month was 20.
The second sample surveyed every sixth person as they exited the only local grocery store until 100 people were surveyed. The second sample found that the mean number of hours they listened to the radio each month was 12.
Which statements are true? Check all that apply.
The true statements about the sample include:
The second sample is random.The second sample is likely to be more representative of the population.The second sample will give a better representation because is it larger.Community members are more likely to listen to the radio station an average of 12 hours a month than 20 hours a month.What is a sample?
Sampling is the selection of a subset of individuals from within a statistical population to estimate the characteristics of the whole population.
The second sample is random because in the second sample, people were surveyed at random. Every sixth person that exited the grocery store was surveyed and this selection represents an unbiased sampling method of the general population.
The options include:
Which statements are true? Check all that apply.
A) The second sample is random.
B) The second sample is likely to be more representative of the population.
C) The first sample is likely to be more representative of the population.
D) The second sample will give a better representation because is it larger.
E) The first sample will give a better representation because it is smaller.
F) Community members are more likely to listen to the radio station an average of 12 hours a month than 20 hours a month.
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Find the value of y in the solution to the system of equations shown.
3y = 18x + 6
y = 2x + 14
A. y = 3
B. y = 4
C. y = 20
D. y = 26
Divide by 3
y=6x+2--(1)y=2x+14--(2)Equating
6x+2=2x+144x=12x=3Now
y=6(3)+2y=18+2y=20C
Answer:
C. y = 20
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}3y = 18x + 6\\y = 2x + 14\end{cases}[/tex]
Multiply the second equation by 3:
[tex]\implies (3)y=(3)2x+(3)14[/tex]
[tex]\implies 3y=6x+42[/tex]
Subtract this from the first equation to eliminate 3y:
[tex]\begin{array}{r l}3y & = 18x+6\\-\quad3y&=6x+42\\\cline{1-2}0&=12x-36\end{array}[/tex]
Solve the resulting equation for x:
[tex]\implies 12x-36=0[/tex]
[tex]\implies 12x=36[/tex]
[tex]\implies x=3[/tex]
Substitute the found value of x into the original second equation and solve for y:
[tex]\implies y=2(3)+14[/tex]
[tex]\implies y=6+14[/tex]
[tex]\implies y=20[/tex]
Ezra has a square brick patio. he wants to reduce the width by 6 feet and
increase the length by 6 feet.
6 ft
6 ft
6 ft
6 ft
let x represent the length of one side of the square patio. write expressions
for the length and width of the new patio. then find the area of the new patio
if the original patio measures 13 feet by 13 feet.
The area of the new patio if the original patio measures 13 feet by 13 feet is 133 ft².
Ezra has a square brick patio. he wants to reduce the width by 6 feet and
increase the length by 6 feet.
What is the area of the square?The area of the square is the measure of the space occupied by it. It is equal to the product of the measure of its two sides.
We need to write the expression for the new patio and the area of the new patio if the original patio measures 13 feet by 13 feet.
let x be the measure of the side of a square.
The length increased by 6 ft, so the new length=x+6.
The width decreased by 6 ft, so the new width=x-6.
The area is the product of length and width, so the new area is
l×w = (x+6)×(x-6)
Since the original side is 13 ft, the new length is 13+6 = 19 ft, and the new width is 13-6=7 ft.
So, the area is (19 ft)×(7 ft) = 133 ft²
Hence, the area of the new patio if the original patio measures 13 feet by 13 feet is 133 ft².
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Which function has the following characteristics?
D
A vertical asymptote at x = 3
●
A horizontal asymptote at y = -1/2
Using the asymptote concept, the function with a vertical asymptote at x = 3 and an horizontal asymptote at [tex]y = -\frac{1}{2}[/tex] is given by:
[tex]f(x) = -\frac{x}{2(x - 3)}[/tex]
What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.The vertical asymptote at x = 3 means that x = 3 is a root of the denominator, hence:
[tex]f(x) = \frac{g(x)}{x - 3}[/tex]
The horizontal asymptote at y = -1/2 means that:
[tex]\lim_{x \rightarrow \infty} f(x) = -\frac{1}{2}[/tex]
Which happens if [tex]g(x) = -\frac{x}{2}[/tex], hence the function is:
[tex]f(x) = -\frac{x}{2(x - 3)}[/tex]
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Sean spends 35 minutes revising for his exam. Erica spends 1 hours 15 minutes revising for her exam. Work out the total time, in minutes, spent revising by Sean and Erica. please help ASAP
The total time spent in minutes is 110 minutes
How to determine the total time?The given parameters are:
Erica = 1 hour, 15 minutesSean = 35 minutesThe total time is calculated as:
Total = Erica + Sean
So, we have:
Total = 1 hour, 15 minutes + 35 minutes
1 hour = 60 minutes
So, we have:
Total = 60 minutes + 15 minutes + 35 minutes
Evaluate the sum
Total = 110 minutes
Hence, the total time spent is 110 minutes
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can someone help me with theses answers and a explanation
The arrangement of the numbers in the ascending order will be 11, 13, and 17.
The complete question is given below.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Ali picked a three number from a hat.
The lowest number was 11.
The range was 13.
The median was 17.
The arrangement of the numbers in the ascending order. Then we have,
11, 13, and 17.
The arrangement of the numbers in the ascending order will be 11, 13, and 17.
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5x-7≥8
This is a 2-step inequality: solve for x
your work by listing each step of the
process.
Answer:
x≥3
Step-by-step explanation:
Let's solve your inequality step-by-step. 5x−7≥8
Step 1: Add 7 to both sides.
5x−7+7≥8+7
= 5x≥15
Step 2: Divide both sides by 5.
5x/5≥15/5
= x≥3
Sital says that 2.5cm³ is the same as 25mm³. Is she right?
Answer:
Sital is right
Step-by-step explanation:
This is because there are 10mm in a cm so therefore you would times 2.5cm by 10 to get 25mm
6.75 into a mixed number
Answer:
6 3/4
Step-by-step explanation:
Answer:
6 3/4
Explanation:
0.75 is the result of dividing 3 by 4, which is the previous point but inversed.
What is the equation of the linear function represented by the table?
If triangle ABC has vertices A(1, 2), B(-1, -1), and C(0, -2), which of the following coordinates is B’ of the dilation using the scale factor 4?
Answer: B'(-4, -4)
Given : A(1, 2), B(-1, -1), C(0, -2)
"Focusing on B coordinates"
If the points are dilated with a scale factor of 4
Then new coordinates : (-1, -1) × 4 = B'(-4, -4)
Answer:
B' = (-4, -4)
Step-by-step explanation:
Dilation: A type of transformation that makes the pre-image larger or smaller without changing its shape.
Center of a dilation: a fixed point about which all points are dilated.
Given:
A = (1, 2)B = (-1, -1)C = (0, -2)Scale factor = 4For dilation when the center of dilation is the origin (0, 0), simply multiply the coordinates of the vertices of the pre-image by the given scale factor to find the image under dilation:
Therefore:
A' = (1 x 4, 2 x 4) = (4, 8)
B' = (-1 x 4, -1 x 4) = (-4, -4)
C' = (0 x 4, -2 x 4) = (0, -8)
Mathematics
height=1cm,base=√5cm.what is the area of isosceles triangle?
Step-by-step explanation:
what is the formula for the area of a triangle ? hmm ?
area = baseline × height / 2
in our case (it does not matter for this question, if it is an isoceles triangle or not, the formula applies to all)
area = sqrt(5) × 1 / 2 = sqrt(5)/2 cm² = 1.118033989... cm²
Answer:
[tex]\huge\boxed{\sf Area = 1.12 \ cm^2}[/tex]
Step-by-step explanation:
Given data:Height = h = 1 cm
Base = b = √5 cm
Required:Area = A = ?
Formula:[tex]\displaystyle Area = \frac{1}{2}(b)(h)[/tex]
Solution:[tex]\displaystyle Area = \frac{1}{2} (\sqrt{5} )(1)\\\\Area = \frac{\sqrt{5} }{2} \\\\Area = 1.12 \ cm^2\\\\\rule[225]{225}{2}[/tex]
I need help on this pleas,what is 9 ÷ 1/5
Answer:
45
Step-by-step explanation:
Flip the fraction, 1/5 to 5/1, and reverse the equation to a multiplication problem.
[tex]1/5 \rightarrow 5/1\\9 \cdot 5/1 = 45[/tex]
Let me know if you have questions or concerns.
Apply the 45º-45º-90º Triangle Theorem to find the length of the hypotenuse of the triangle.
Answer:
The sine of the angle = the length of the opposite side. the length of the hypotenuse.
The cosine of the angle = the length of the adjacent side. the length of the hypotenuse.
The tangent of the angle = the length of the opposite side. the length of the adjacent side.
Step-by-step explanation:
Answer:
c = a√2
Step-by-step explanation:
Apply the 45º-45º-90º Triangle Theorem to find the length of the hypotenuse of the triangle.
since there is no measure, I will write you the formula:
c (hypotenuse) = a√2
help me please these dot plots show hourly earnings for a sample of workers in two different
careers
career a
0
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
career b
0
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
hourly eamings (5)
what are the differences between the centers and spreads of these earning
distributions?
select two choices: one for the centers and one for the spreads
a. spreads: the hourly earnings for career b are more spread out
b. spreads: the hourly earnings for career a are more spread out.
c. centers career bhas greater median hourly earnings than career
d. centers: career a has greater median hourly earnings than career
The hourly earnings for career a are more spread out.
Career a has greater median hourly earnings than career.
What is the spread and median of the data plots?Median is the number at the center of the dataset that is arranged either in ascending order or descending order.
The median of career A is 60.
The median of career b is 40
Spread refers to the range of the dataset. Career A has a greater range than career B.
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100 points and brainlyest !!! ONLY ANSWER IF U KNOW THE ANSWER !!!
Answer:
Step-by-step explanation:
A” (-2,2)
B” (-1,-2)
C” (-4,-4)
Answer:
A''(-1,5)
B''(0,1)
C''(-3,7)
a) At what percent rate of compound interest per annum will the compound interest on Rs 1,25,000 be Rs 91,000 in 3 years?
The rate of compounding on the investment is 20%.
What is the rate of compounding?
When an amount compounds annually, it means that both the amount invested and the interest accrued increases in value once a year.
The formula that can be used to determine the rate of compounding is: (FV / PV)^(1 /n)
Where:
FV = future value = 125,000 + 91,000 = 216,000PV = present value = 125000n = number of years - 3(216,000 / 125000)^ (1 / 3) - 1 = 20%
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f(x)=x^2+2x-5
g(x)=2x+4
what is (f•g)(x)
The product of the functions is 2x³ + 8x² - 2x - 20. Then the correct option is C.
What is a function?A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.
The functions are given below.
f(x) = x² + 2x - 5
g(x) = 2x + 4
Then the product of the functions will be given as
(f•g)(x) = f(x) × g(x)
(f•g)(x) = (x² + 2x - 5) × (2x + 4)
(f•g)(x) = 2x³ + 8x² - 2x - 20
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I need help asap please? and this is for math? what is the missing angle of the triangle? the 2 angles are 55 and 90!!
Answer:
the missing angle of the triangle is 35
Step-by-step explanation:
180-90= 90-55= 35
Answer:
i agree with losesight57
Step-by-step explanation:
A summer job as a life guard at lincoln pool pays 9.50 per hour how much willl you earn for working 6 hours
57
Step-by-step explanation:
$ 9.50 -> 1 hr
? -> 6 hrs
9.50(6) = $ 57
The first graph represent a=450-20t, which describes the relationship between gallons of water in tank and time in minutes. a. Where on the graph can we see 450? Where can we see the -20? b. What do these numbers mean in this situation?
Answer:450 is the intercept. We see it when t=0 (where the line cross the y axis). -20 is the slope
Step-by-step explanation: y = 20 is a thing no one would ever solve for but to do it, 20=450-20t -> y =20 when t=(20-450)/20. I don’t know why anyone would ever need to find this value
The only thang i need help is area and for question 7. 8. and 9. no bots ONLY THE AREA
The area of the triangle based on the information given is 16.67 inches ²
How to calculate the triangle?It should be noted that the area of a triangle is given by the formula:
= 1/2 × base × height
In this second figure, the height will be:
= 5.9² - (3.4/2)²
= 5.9² - 1.7²
= 34.81 - 2.89
= 5.65
The area will be:
= 1/2 × base × height
= 1/2 × 5.65 × 5.9
= 16.67 inches ²
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Which value of y forms the solution of the systems defined by y=11x+1 and 11x+12y=12
A. 1
B. 1/13
C. 11
D. 11/13
Answer:
b because it can't be full number
I'm not good at time questions can someone help me?
Randy should begin his homework by 07:10 in order to sleep by 10:00
How to determine the time to start the homework?The given parameters are:
Social studies = 45 minutesScience = 40 minutesMath = 1 hour and 15 minutesBed preparation = 10 minutesIf the above activities are done, the time spent would be:
Time = 45 minutes + 40 minutes + 1 hour and 15 minutes + 10 minutes
Add the time
Time = 2 hour and 50 minutes
He wants to go to bed by 10:00.
So, the time to begin his homework is:
Begin = 10:00 - 2 hour and 50 minutes
Evaluate the difference
Begin = 07:10
Hence, Randy should begin his homework by 07:10
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To sell 300 notebooks and 120 pens quickly, a store decided to create two types of gift sets. one set is to include 2 notebooks and 1 pen, and the other will consist of 1 pen and 3 notebooks. the first set will be sold for $8, while the second will be sold for $11.50. it is unprofitable to sell more than 20 of any gift set. how many gift sets of each type must the store sell to obtain the biggest possible income?
The store must sell 60 of each set each to obtain the biggest possible income
How to determine the number of each gift set?The given parameters can be represented using the following table:
Set 1 Set 2 Available
Notebook 2 3 300
Pen 1 1 120
Selling price 8 11.5
Using the above data values, we have:
Objective function: Max P = 8x + 11.5y
Subject to:
2x + 3y ≤ 300
x + y ≤ 120
Next, we plot the graph of the above inequalities (see attachment)
From the attached graph, we have:
(x,y) = (60,60)
Hence, the store must sell 60 of each set each to obtain the biggest possible income
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The domain of a function f(x) is x > 1, and the range is y< 2. what are the
domain and range of its inverse function, f '(a)?
o a. domain: * > - 2
range: y si
o
b. domain: x < -2
range: y > 1
c. domain: x > 1
range: y < -2
o d. domain: x = 1
range: y > -2
submit
Answer: Domain: x<-2 Range: y>1
Step-by-step explanation:
I don't know for sure but I am taking the test and that was the outcome of the answer.
A timer is started and a few moments later a model airplane is launched from the ground. Its height (in feet) as a function of time (in seconds after the timer was started) is given by the equation h(t)=−(t−10)2+95. Which of the following statements is true?
The airplane reaches its maximum height of 10 feet in 95 seconds.
The airplane reaches its maximum height of 95 feet in 10 seconds.
The airplane reaches its minimum height of 95 feet in 10 seconds.
The airplane reaches its minimum height of 10 feet in 95 seconds.
Considering the given quadratic function, the correct statement is given by:
The airplane reaches its maximum height of 95 feet in 10 seconds.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient. If a > 0, the vertex is a minimum point, and if a < 0 it is a maximum point.
In this problem, the function is:
h(t) = -(t - 10)² + 95.
Hence the vertex is (10, 95), and since a < 0, the correct statement is given by:
The airplane reaches its maximum height of 95 feet in 10 seconds.
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Write an equation for the function whose graph is the shape of f(x) = x2, but shifted three units to the lef
9₁(x) =
Write an equation for the function whose graph is in the shape of g₁(x), but shifted five units up.
9₂(x) =
Write an equation for the function whose graph is in the shape of g₂(x), but reflected in the x-axis.
93(x)
The equation for the functions g₁(x), g₂(x), and g₃(x) are (x + 3)², (x + 3)² + 5, and -[(x + 3)² + 5] respectively.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
f(x) = x²
We have:
g₁(x) which is a transformed function of f(x)
f(x) shifted three units to the left.
Plug x → (x + 3)
g₁(x) = (x + 3)²
Similarly,
Equation for the function whose graph is in the shape of g₁(x), but shifted five units up.
g₂(x) = (x + 3)² + 5
Equation for the function whose graph is in the shape of g₂(x), but reflected in the x-axis.
g₃(x) = -[(x + 3)² + 5]
Thus, the equation for the functions g₁(x), g₂(x), and g₃(x) are (x + 3)², (x + 3)² + 5, and -[(x + 3)² + 5] respectively.
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A right triangle has a hypotenuse of 14 inches and another side that is 12 inches. What is the length of the missing side of the triangle?
Answer:
7.2111
Step-by-step explanation:
14 squared times 12 squared= squareroot ofmissing angle
Find the coordinates of P so that P partitions segment AB in the part-to-whole ratio of 1 to 5 with A(-9, 3) and B(1, 8). Explain.
Find point Z that partitions the directed line segment XY in the ratio of 2:1 where X(1, 2) and Y(7, 5). Explain.
For both problems, we can use the section formula.
1) [tex]P=\left(\frac{(1)(1)+(5)(-9)}{6}, \frac{(1)(8)+(5)(3)}{6} \right)=\boxed{\left(-\frac{22}{3}, \frac{23}{6} \right)}[/tex]
2) [tex]Z=\left(\frac{(2)(7)+(1)(1)}{3}, \frac{((2)(5)+(1)(2)}{3} \right)=\boxed{(5, 4)}[/tex]