Functions can be represented verbally, algebraically, graphically, and numerically. A relationship is a function when for every input, there is exactly one output which is described by the vertical line test. Graphs for different types of functions vary in shape.
Explanation:Functions can be represented in four various ways: verbally, algebraically, graphically, and numerically. For instance, verbal representation uses words to describe the function. Algebraically, we express the function via an equation. Graphically, we visually represent the function through graphs. Numerically, we represent the function using a table.
A relationship is a function if for every input, there is exactly one output. In a graph, this corresponds to an instance where a vertical line drawn anywhere on the graph would intersect it at only one point. This is also known as the vertical line test.
Examples of different types of functions graphically could include (a) a linear graph, showing a straight line, (b) a quadratic graph, parabolic in shape, (c) an inverse graph, where y decreases as x increases, and (d) an exponential graph, where the rate of growth is proportional to the function's current value.
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Find the indicated real nth root(s) of a.
n=2, a=100
You want to buy a new TV. The diagonal measure of the screen is 42 inches, and the screen width is 36.6 inches. What is the screen height? Round your answer to the nearest hundredth.
a baby elephant weighs 250 lb.
What is the elephants weight in TONS AND KILOGRAMS
(1kg=2.2lb)? round to the nearest thousandths place
Answer:
250 lb⋅1 ton2000 lb=2502000 tons = 18 ton = 0.125 tons
250 lb⋅1 kg2.2 lb≈2502.2 kg ≈ 113.636 kg
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The table shows a linear function. Write an equation that represents the function using function notation.
50 pts.
Solve this algebraic equation.
-6x + 5 + 12x -6
In folding to make a 6-sided snowflake, what shape do you have after completing the first 5 steps?
a.
right triangle
c.
rectangle
b.
square
d.
circle
1. ∠E and ∠F are vertical angles with m∠E=9x+12 and m∠F=3x+24
What is the value of x?
2. What is m∠KNL?
How do you simplify -3.3+5.5
According to a survey, 75% of adults in the united states think the u. s. government system is broken. of these 75%, about 7 out of 10 think that the government can be fixed.
a.find the probability that a randomly selected adult thinks the u. s. government system is broken and thinks the government can be fixed.
b.given that a randomly selected adult thinks the u. s. government system is broken, find the probability that he or she thinks the government cannot be fixed.
1. Probability that a randomly selected adult thinks the U.S. government system is broken and can be fixed:
P (A and B) = P (A) * P (B|A) = .75 * .7 = 0.525
2. Probability that given that a randomly selected adult thinks the U.S. government system, he or she thinks the government cannot be fixed.
P (B|A) = (1 – P (B|A) = 3/10 = 0.3
To calculate the probability that an adult thinks the U.S. government is broken and can be fixed, multiply 75% by 70%, resulting in 52.5%. The probability that an adult thinks the government is broken but can't be fixed is found by subtracting 70% from 100%, yielding 30%.
The subject in question pertains to probability and statistics, which involves calculating the likelihood of certain outcomes based on given data and constructing confidence intervals to understand the population parameters.
Part A:
To find the probability that a randomly selected adult thinks the U.S. government system is broken and thinks the government can be fixed, we multiply the two given probabilities: 75% of adults think the system is broken and, of these, 70% think it can be fixed. Therefore:
0.75 (probability of thinking the system is broken) × 0.70 (probability of thinking it can be fixed given the system is broken) = 0.525 or 52.5%.
Part B:
Given that an adult thinks the government system is broken, to find the probability that they think it cannot be fixed, we subtract the probability that they think it can be fixed from 1:
1 - 0.70 = 0.30 or 30%.
The number 0.4 can written as 4/10, so it is a rational number
A line has a slope of 2 and passes through the point (4,0)
What are the coordinates of another point that is on the line?
A. (0,2)
B.(2,0)
C.(4,6)
D.(6,4)
If the number 659983 is rounded to the nearest hundred how many zeros does the rounded number have
Given ONL=MLN, O and M are right angles prove LM=NO
Using the properties of Isosceles triangles and right-angled triangles, it can be deduced that LM = NO given that angles ONL = MLN and O and M are right angles.
Explanation:The given question is about proving equivalency of lines in a geometric figure. Given the figure has the angles ONL and MLN that are equal and O and M are right angles. Given these conditions, using the properties of triangles especially the Isosceles Triangle (where two sides are equal), we can conclude that LM = NO.
To prove this assumption, we incorporate the following facts: In an isosceles triangle, the angles opposite to equal sides are equal. Hence, if ONL = MLN, it implies that NO = LM. Additionally, if angles O and M are right angles, it signifies that the triangles formed are right angled triangles. Therefore, using the property of isosceles right angled triangles, the sides opposite to equal angles are equal.
Based on these facts and the properties of geometric concepts [Isosceles Triangle, Pythagorean theorem and right angled triangles], we can confidently conclude that LM = NO. This proves that given the conditions in the problem, the lines LM and NO are equal in length.
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Given that ONL=MLN and O and M are right angles, we can say that triangles ONL and MLN are congruent right-angled triangles. Therefore, according to the property of congruent triangles, the sides opposite the equal angles in these triangles (i.e., LM and NO) should also be equal to each other.
Explanation:The question involves proving the equivalence of two lines in a geometric configuration, LM and NO, where two angles, ONL and MLN, are given as equal and O and M are right angles. This is quite a typical problem in Geometric Proof, an important topic in High School Mathematics.
To solve this, we need to apply the properties of triangles and the concept of congruent triangles. Since ONL and MLN are given as equal angles and O and M are right angles, we know that triangle ONL and MLN are right-angled triangles. In a right-angled triangle, if one angle is equal, then the other angles will be equal because the summing of angles in a triangle is 180 degrees.
Because we have now two right-angled triangles with their respective angles equal (ONL = MLN and NOM = LNM), they must be congruent triangles by the Angle-Angle (AA) criterion for congruency. This implies that the sides opposite the equal angles in these two triangles should also be equal. So, LM = NO in these triangles.
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Drag a statement or reason to each box to complete this proof.
If 3x−4=14, then x=6.
1. 3x−4=14 >>>> Given
2. 3x−4+4=14+4 >>>>?
3. Simplifying >>>>?
4. 3x3=183 >>>>?
5. >>>?
A. Simplifying
B. Division property of equality
C. Addition property of equality
D. x=6
E. 3x=18
Final answer:
In this proof, we use the Addition and Simplifying properties of equality to show that if 3x-4 equals 14, then x equals 6.
Explanation:
Given: 3x-4=14
3x-4=14 >> Given
3x-4+4=14+4 >> Addition property of equality
Simplifying >> Simplifying
3x=18 >> x=6
Answer: x=6
CAN SOMEONE HELP ASAP!! Please!
A cold front moved in last weekend. In 8 hours overnight the temperature outside dropped 24 degrees. What was the average temperature change for each hour?
What is the point-slope form of the equation of a line that passes through the point (6, −8) and has a slope of −2? y+8=2(x-6) openstudy?
Find the height of the pole if the shadow of a boy 6 ft. tall is 3 ft. and the shadow of the pole is 2 1/3 yards. 1 yards 4 feet 14 feet
Answer:
14 feet
Step-by-step explanation:
CAN YOU PLEASE SOLVE THESE PROBLEMS!!! THANKS!!!!!
1) -3/4x=5
2) 0.6x= 0.48
3) -30=1.25x
4) -12 2/3= -1 1/9x
5) 12-3/5x = 27.
6) -17= 6x-5
7) 13= x/3 +4
8) -2/3x -4=10
9) 9x-14=2x
10) 2.5x -15=4x
11) 2x-31=-9x+24
Use the given property to complete the statement. Transitive Property of Congruence If Angle X Y Z is congruent to angle A O B and Angle A O B is congruent to angle W Y T, then A. Angle W Y T is congruent to angle A O B B. Angle A O B is congruent to angle A O B C. Angle X Y Z is congruent to angle W Y T D. Angle A O B is congruent to angle X Y Z
When two straight lines or rays intersect at a shared endpoint, an angle is generated. The correct option is C, ∠XYZ ≅ ∠WYT.
What is an angle?When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."
Given that Angle XYZ is congruent to angle AOB, therefore, we can write,
∠XYZ ≅ ∠AOB
Also, it is mentioned that Angle AOB is congruent to angle WYT, Therefore, we can write,
∠AOB ≅ ∠WYT
Now, we can write the two congruency together as,
∠XYZ ≅ ∠AOB ≅ ∠WYT
∠XYZ ≅ ∠WYT
Hence, the correct option is C, ∠XYZ ≅ ∠WYT.
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he equation for the line of best fit is y = 0.39x + 15.89. Which of the following statements is true for the above graph?
How do i do this problem?
(13z^9+6v)-11z^9
The hypotenuse of a right triangle is 6 inches and one of the legs is √ 6 inches, the exact value of the other leg is _______ inches.
A. 30
B. √ 15
C. 15
D. √ 30
What is the capacity of the cube in liters? Cube with length, width, and height labeled as 9 centimeters. 0.81 L 0.729 L 81 L 729 L
The product of two prime numbers is one less than 12 squared. What are they two prime numbers?
CAN ANYONE HELP ME WITH THIS QUESTION!!!!!??? The length of a string in yards is a function f(n) of the length n in inches. Write a function rule for this situation.
A. f(n)=36n
B. f(n)=1/36 n
C. f(n)=12n
D. f(n)=n/12
Answer+explanation plz and thank you! :) these are quadratic equations.
What are the x-intercepts of the graph of the function f(x)=x2-16x+64
To find the x-intercepts of the function f(x) = x^2 - 16x + 64, we set f(x) to zero and solve for x. The quadratic factors to (x - 8)^2 = 0, revealing that the graph has a single x-intercept at x = 8.
Explanation:To determine the x-intercepts of the graph of the function f(x) = x^2 - 16x + 64, we need to find the values of x for which f(x) equals zero. This involves solving the quadratic equation, x^2 - 16x + 64 = 0.
One approach is to factor this equation if possible. Another approach is to use the quadratic formula.
The given quadratic equation can be factored as (x - 8)^2 = 0.
Therefore, the only solution to this equation is x = 8, which means the graph of the function touches the x-axis at this point and has a vertex at (8, 0), making the x-intercept of the graph equal to 8.
The factored form indicates that the function has a double root at x = 8, which means the parabola touches and then bounces off the x-axis at this point.
Thus, rather than crossing the x-axis at two distinct points, the parabola has a single x-intercept at x = 8. This is often referred to as a repeated or double root because the solution appears twice when the quadratic is factored.
Huilan is 15 years older than thomas. the sum of their ages is 55 . what is thomas's age?
C write function distance that calculates the distance between two points (x1, y1) and (x2, y2). all numbers and return values should be of type double.