Read the following statement: Line segment CD is congruent to line segment XY.
Which of the following is an equivalent statement?
-CD overbar is similar to XY overbar
- CD overbar is congruent to XY overbar
-CD overbar equals XY overbar
-CD overbar is an element of XY overbar
SOMEONE PLEASE HELP I HAVE A TEST IN 5 MIN!!
The statement which is equivalent to line segment CD is congruent to line segment XY is CD overbar is congruent to XY overbar.
What is a line?A line is made up of an infinite no. of points it can extend in both directions indefinitely.
We know a line has two subsets they are a ray and a line segment.
A ray is a type of line that has one initial point and the other end can extend indefinitely and a line segment is a type of line which has two endpoints.
Given a line, segment CD is congruent to line segment XY.
∴ [tex]\overline{CD}[/tex] ≅ [tex]\overline{XY}[/tex].
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Determine the inverse of f(x) = x^3 - x^2 - 2x show steps
Switch the x and y values to find the inverse.
y=x−3x+2
The inverse is given by
x=y−3y+2
Solve for y now:
x(y+2)=y−3
xy+2x=y−3
2x+3=y−xy
2x+3=y(1−x)
2x+31−x=y
The inverse, f−1(x), is given by f−1(x)=2x+31−x.
The function can be graphed using knowledge of asymptotes, invariant points, and intercepts. Prepare a table of values for f(x). Recall that f−1(x) is simply a transformation of(x) over the line y=x, so f−1(x) has a table of values where X and y are inverted relative to f(x).
For example, if the point (2,3) belongs on the graph of f(x), the point (3,2) belongs on f−1(x).
You toss a coin a randomly selecte a number from 0 to 9. What is the probability of getting tails and selecting a 9?
A.0.05
B.0.95
C.0.25
D.0
An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 3427 feet and Plane B is at an altitude of 5000 feet. Plane A is gaining altitude at 65.75 feet per second and Plane B is gaining altitude at 35.5 feet per second.
How many seconds will pass before the planes are at the same altitude?
What will their altitude be when they're at the same altitude.
The school cafeteria is baking cookies for lunch. each student gets 3 cookies with their lunch. if there are 231 children buying lunch, how many cookies do they have to make?
Find the saving plan balance after 4 years with an apr of 7% and monthly payments of 100
A store sells toaster ovenstoaster ovens for $4646 each, retail price. The wholesale cost to stock the ovensovens is $ 28$28 each. The fixed cost associated with acquiring the ovensovens, storing them in inventory, using shelf space, and advertising the ovensovens for sale is $25002500. a. Write a function for the total cost of stocking the ovensovens for sale. b. Write a function for the total revenue received from selling the ovensovens. c. Write a system of equations and determine the number of ovensovens that must be sold to break even.
The student body of a large university consists of 60% female students. a random sample of 8 students is selected. what is the probability that among the students in the sample at least 7 are female?
The probability of selecting at least 7 female students from the sample of 8 students is 0.2797.
To solve this problem, we'll use the binomial probability formula, which calculates the probability of a certain number of successes (in this case, selecting female students) in a fixed number of trials (the sample size).
Given:
Probability of selecting a female student (success), ( p = 0.60 )
Probability of selecting a male student (failure), ( q = 1 - p = 0.40 )
Sample size, ( n = 8 )
We need to calculate the probability of selecting at least 7 female students from the sample.
Calculate the probability of selecting exactly 7 female students:
[tex]\[ P(X = 7) = \binom{8}{7} \times (0.60)^7 \times (0.40)^{8-7} \][/tex]
[tex]\[ = \frac{8!}{7!(8-7)!} \times (0.60)^7 \times (0.40)^{1} \][/tex]
[tex]\[ = 8 \times 0.60^7 \times 0.40 \][/tex]
[tex]\[ = 8 \times 0.0279936 \times 0.40 \][/tex]
[tex]\[ = 0.1119744 \][/tex]
Calculate the probability of selecting exactly 8 female students:
[tex]\[ P(X = 8) = \binom{8}{8} \times (0.60)^8 \times (0.40)^{8-8} \][/tex]
[tex]\[ = (0.60)^8 \][/tex]
[tex]\[ = 0.60^8 \][/tex]
[tex]\[ = 0.16777216 \][/tex]
Add the probabilities from Step 1 and Step 2 to get the final probability:
[tex]\[ P(X \geq 7) = P(X = 7) + P(X = 8) \][/tex]
[tex]\[ = 0.1119744 + 0.16777216 \][/tex]
[tex]\[ = 0.27974656 \][/tex]
So, the probability of selecting at least 7 female students from the sample of 8 students is 0.2797.
Which of the following terms, when added to the given polynomial, will change the end behavior?
y = –2x7 + 5x6 – 24
a)–x8
b)–3x5
c)5x7
d)1,000
e)–300
Answer:
1.A
2.C
Step-by-step explanation:
The end behaviour of the polynomial function y = -2x⁷ + 56x⁶ - 24 will change for a) - x⁸ and c) 5x⁷.
What is the end behavior of a polynomial?A polynomial function's final behavior is how its graph behaves as x gets closer to positive or negative infinity.
The graph's final behavior is determined by a polynomial function's degree and leading coefficient.
Given, a polynomial function y = -2x⁷ + 56x⁶ - 24.
So, the given polynomial function has a degree of 7 and its end behavior will be changed by adding or subtracting terms that are of degree 7 and higher.
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Solve the Pythagorean Theorem for the variable a.
c²=a²+b²
Mr. Small, the store manager for Jay's Appliance, is having a difficult time placing a selling price on a refrigerator that cost $410. Mr. Small knows his boss would like to have a 45% markup based on cost. The selling price should be
Answer:
$594.50
Step-by-step explanation:
1. Divide markup into decimal form
45/100 = .45
2. multiply by cost of Refrigerator
.45 x 410 = $184.50
3. Add markup cost to original Refrigerator cost.
184.50 + 410 = $594.50
Melanie connected a brown garden hose, a green garden hose, and a black garden hose to make one long hose. The brown hose is 10.75 feet long, the green hose is 16.4 feet long, and the black hose is 8.5 feet long. What is the farthest distance the one long hose can reach?
Answer:
35.65 feet.
Step-by-step explanation:
We have been given that the brown hose is 10.75 feet long, the green hose is 16.4 feet long, and the black hose is 8.5 feet long. We are asked to find the distance that one long hose can reach.
The length of one long hose will be equal to sum of distances of each hose.
[tex]\text{The length of one long hose}=10.75\text{ ft}+16.4\text{ ft}+8.5\text{ ft}[/tex]
[tex]\text{The length of one long hose}=35.65\text{ ft}[/tex]
Therefore, the one long hose can reach 35.65 feet.
A customer has six (6) $1 bills, three (3) $5 bills, four (4) $10 bills, seven (7) quarters, ten (10) dimes, seven (7) nickels, and nine (9) pennies. The customer buys a pair of shoes for $49.86. Based on the combination of bills and coins the customer has, what are the least number of bills and coins the customer can give the cashier in order to buy the shoes for the exact amount and not require any change back?
Suzanne bought 50 apples at the apple orchard she bought four times as many red apples has green apples how many more red apples and green apples that Suzanne buy
if R and S are two points in a plane, the perpendicular bisector of line RS is the set of all points equidistant from R and S. True or false?
Answer: True
Step-by-step explanation:
What is the average rate of change of f(x), represented by the graph, over the interval [0,2]?
A: 2
B: 1
C: 0.5
D: -0.5
Value of the expression
The formula for any arithmetic sequence is a n = a 1 + d(n - 1), where a n represents the value of the nth term, a 1 represents the value of the first term, d represents the common difference, and n represents the term number. What is the formula for the arithmetic sequence -7, -3, 1, 5, ...?
Plz help
What is the justification for each step in solving the inequality?
−2(x+1)≥3x+8−2(x+1)≥3x+8
Select from the drop-down menus to correctly justify each step.
2nd picture is the dropdown box answers
For the function f(x) = −2(x + 3)2 − 1, identify the vertex, domain, and range.
The vertex is (3, −1), the domain is all real numbers, and the range is y ≥ −1.
The vertex is (3, −1), the domain is all real numbers, and the range is y ≤ −1.
The vertex is (−3, −1), the domain is all real numbers, and the range is y ≤ −1.
The vertex is (−3, −1), the domain is all real numbers, and the range is y ≥ −1.
Answer:
C. The vertex is [tex](-3,-1)[/tex], the domain is all real numbers, and the range is [tex]y\leq -1[/tex].
Step-by-step explanation:
We have been given a function [tex]f(x)=-2(x+3)^2-1[/tex]. We are asked to identify the vertex, domain and range of the given function.
We can see that our given parabola is in vertex form [tex]y=a(x-h)^2+k[/tex], where [tex](h,k)[/tex] represents vertex of parabola.
We can rewrite our given equation as:
[tex]f(x)=-2(x-(-3))^2-1[/tex]
Therefore, the vertex of our given parabola would be [tex](-3,-1)[/tex].
We know that parabola is a quadratic function and the domain of a quadratic function is all real numbers.
We know that range of a quadratic function in form [tex]f(x)=a(x-h)^2+k[/tex] is:
[tex]f(x)\leq k[/tex], when [tex]a<0[/tex] and,
[tex]f(x)\geq k[/tex], when [tex]a>0[/tex]
Upon looking at our given function, we can see that [tex]a=-2[/tex], which is less than 0, therefore, the range of our given function would be [tex]y\leq -1[/tex].
Look at the triangle what is the value of sin X ?
a law firm charges $100 per hour plus a $300 origination fee for its services find a function notation
The required function notations for the total law firm charges is expressed as f(t) = 100t + 300
Given the following
Law firm charges = $100 per hour
The amount of charge for "t" hours will be 100t hours
Also, the original fee = $300
In other to get the total charge using function notation;
f(t) = Law firm charges for "t" hours + Original fee
f(t) = 100t + 300
The required function notations for the total law firm charges is expressed as f(t) = 100t + 300
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Two curves are orthogonal if their tangent lines are perpendicular at each point of intersection. are the given families of curves orthogonal trajectories of each other? that is, is every curve in one family orthogonal to every curve in the other family? x2 + y2 = ax x2 + y2 = by
Yes, the given curves are orthogonal. A further explanation is below.
Given equation is:
[tex]x^2+y^2=ax[/tex]By differentiating both sides, we get
→ [tex]2x+2yy'=a[/tex]
→ [tex]y'=\frac{a-2x}{2y} = m_1[/tex]
again,
[tex]x^2+y^2=by[/tex]By differentiating both sides, we get
→ [tex]2x+2yy' =by'[/tex]
→ [tex]y' = \frac{-2x}{2y-b}[/tex]
For both curves are orthogonal, we get
→ [tex]m_1 \ m_2 = -1[/tex]
By substituting the values, we get
→ [tex]\frac{(a-2x)}{2y} \ \frac{(-2x)}{2y-b} = -1[/tex]
→ [tex]-2ax +4x^2=-4y^2+2yb[/tex]
→ [tex]4(x^2+y^2)=2ax+2yb[/tex]
Since,
[tex]ax=x^2+y^2[/tex][tex]by=x^2+y^2[/tex]then,
→ [tex]4(x^2+y^2) =2(x^2+y^2)+2(x^2+y^2)[/tex]
→ [tex]4x^2+4y^2=4x^2+4y^2[/tex] (true)
Thus the above response is appropriate.
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tina wants to save money for school. tina invests 1100 in an account that pays an interest of 7.25%. how many years will it take the account to reach 6600?
It would take approximately 19 years for Tina's investment to grow from $1100 to $6600 with an annual interest rate of 7.25% if the interest is compounded annually.
Explanation:This problem deals with the concept of compound interest. To find out how many years it will take for Tina's investment to grow from $1100 to $6600 with an interest rate of 7.25%, we would use the formula for compound interest: A = P(1 + r/n)_(nt), where A is the final amount, P is the principal amount (initial investment), r is the annual interest rate (in decimal form), n is the number of times interest is compounded per time unit (year), t is the time the money is invested for in years.
In Tina's case, she does not make additional contributions, so we assume the interest is compounded once per year (n=1). Our formula becomes A = P*(1 + r)_t. Arranging for t, we get t = log(A/P) / log(1+r).
Using these values: A=$6600, P=$1100, r=7.25/100=0.0725, we can find t = log(6600/1100) / log(1+0.0725). Calculating this, you would get around 19 years.
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Complete the square
The circumference of circle p is 800 mm, the circumference of circle q is 200 cm, and the circumference of circle r is 4 m. What is the sum of the distance around each circle
Let us use the following conversions:
1 cm = 10 mm
1 meter = 100 cm = 1000 mm
Given:
p = 800 mm
q = 200 cm = 2000 mm
r= 4 m = 4000
X = sum of the distance around each circle
X = p+q+r
X = 800+2000+4000
X = 6800 mm or 680 cm or 6.80 m
A girl is now one-third as old as her mother. In three years, she will be two-fifths as old as her mother will be. What are their present ages?
A girl is 9; mom is 27
B girl is 18; mom is 54
C girl is 25; mom is 75
Option: A is the correct answer.
A girl is 9; mom is 27
Step-by-step explanation:A girl is now one-third as old as her mother.
i.e. if x is the present age of girl.
and y is the present age of her mother.
Then,
[tex]x=\dfrac{1}{3}y[/tex]
i.e.
[tex]y=3x-----------(1)[/tex]
In three years, she will be two-fifths as old as her mother will be.
This means after three years.
The age of girl will be: x+3
and the age of her mother will be: y+3
This means that:
[tex](x+3)=\dfrac{2}{5}\times (y+3)[/tex]
[tex]5(x+3)=2(y+3)\\\\i.e.\\\\5x+15=2y+6[/tex]
i.e.
[tex]5x+15=2\times 3x+6[/tex]
( since on using equation (1) )
i.e.
[tex]5x+15=6x+6\\\\i.e.\\\\6x-5x=15-6\\\\i.e.\\\\x=9[/tex]
and the value of y from equation (1) is:
[tex]y=27[/tex]
The degree of the Boolean function given by f(x,y,z,w) = xy + yz + zw is........
Find the slope of a line that passes through the points (-3,-1) and (0,-5)
Three consecutive integers have a sum of 297 . Find the integers.
297 /3 = 99
99-1 = 98
99 +1 = 100
98 + 99 + 100 = 297
the numbers are 98, 99 , 100