Answer:
Domain: (- ∞, ∞)
Explanation:
The equation y = 2x² + 1 is a somewhat narrow parabola translate up 1 unit on the y-axis from the origin (0, 0). The domain of a graph indicates which x-values the diagram can potentially reach, or how far it can travels on the x-axis.
Because it is a parabola, it goes infinitely in both directions of the x-axis. Therefore, its domain is (-∞ ,∞)
Final answer:
The domain of the function y = 2x² + 1 is all real numbers, which is expressed as [tex]\( (-\infty, +\infty) \)[/tex]
Explanation:
The domain of a function refers to the set of all possible input values for which the function is defined. In the case of the function [tex]\( y = 2x^2 + 1 \)[/tex], it is a quadratic function, meaning it is defined for all real numbers [tex]\( x \).[/tex]
The function[tex]\( y = 2x^2 + 1 \)[/tex] involves squaring [tex]\( x \)[/tex], which can result in any real number. Since there are no restrictions on the values that[tex]\( x \)[/tex] can take, the domain of this function is all real numbers. Mathematically, we denote this domain as[tex]\( (-\infty, +\infty) \)[/tex].
This implies that for any real number you substitute in for [tex]\( x \)[/tex], the function [tex]\( y = 2x^2 + 1 \)[/tex] will produce a corresponding real number for [tex]\( y \).[/tex] There are no values of [tex]\( x \)[/tex] for which the function becomes undefined or non-existent.
Graphically, this function represents a parabola that opens upwards, covering all real values of [tex]\( x \)[/tex] along the x-axis. Therefore, the domain encompasses the entire real number line without any gaps or exclusions.
A bookstore marks up the cost of a book from $6 to $10. What was the percent increase?
Final answer:
To find the percent increase from $6 to $10, subtract the initial cost from the final cost, divide by the initial cost, and multiply by 100. The percent increase is 66.67%.
Explanation:
To find the percent increase, you need to calculate the difference between the final cost and the initial cost, and then divide that difference by the initial cost. Finally, multiply by 100 to get the percentage.
Given that the initial cost is $6 and the final cost is $10, the difference is $10 - $6 = $4.
To find the percent increase, divide $4 by $6: $4/$6 = 0.6667 (rounded to four decimal places).
Multiply by 100 to get the percentage: 0.6667 * 100 = 66.67% (rounded to two decimal places).
Larry has taken out a loan for college. He started paying off the loan with a first payment of $150. Each month he pays, he wants to pay back 1.3 times as the amount he paid the month before. Explain to Larry how to represent his first 15 payments in sigma notation. Then explain how to find the sum of his first 15 payments, using complete sentences. Explain why this series is convergent or divergent.
Helppp!! I need help with this question. Can anyone help me?
Therefore, the height of the ground floor is 9.2 meters above the ground.
The pattern observed in the data is that the difference in height between consecutive floors remains constant. To find this constant difference, we can subtract the height of one floor from the height of the next floor.
For example:
Height of floor 1 (15th floor) - Height of ground floor (8th floor) = 54 m - 31.6 m = 22.4 m
Height of floor 2 (22nd floor) - Height of floor 1 (15th floor) = 76.4 m - 54 m = 22.4 m
The constant difference is 22.4 meters. This represents the height between each residential floor. To find the height of the ground floor (floor 0), we can subtract this constant difference from the height of the first residential floor.
Ground floor height = Height of floor 1 - Constant difference
Ground floor height = 31.6 m - 22.4 m = 9.2 meters.
square root of 75 plus square root of 3
Text messages cost $.15 each. You can spend no more than $10. How many text messages can you send? Show Working
If each text message costs $.15, and you have $10, you can send a maximum of 66 text messages after rounding down.
Explanation:To figure out how many text messages you can send with $10, given that each text message costs $.15, we need to divide the total amount of money ($10.00) by the cost of each text message ($.15).
It's a simple division problem: $10.00 ÷ $.15 = 66.67.
However, you can't send a fraction of a message, so we need to round down to the nearest whole number. So, you can send a total of 66 text messages for $10.
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He probability of choosing a vowel (a, e, i, o, or u) from a deck of cards containing the 26 letters of the alphabet is shown below. what is the probability of choosing the letters a and e one after the other without replacement?
A runner is participating in a 10.3 mile race. If the runner stopped at a water station that is twice as far from the starting line as from the finish line, how far is the runner from the finish line?
Answer:
6.86
Step-by-step explanation:
Which describes a cost that fluctuates depending on the number of units produced?
Variable cost describes a cost that fluctuates depending on the number of units produced. It is defined as a cost that varies in line with the output produced. It increases or decreases based on the volume of the production of the company; they increase as production rises and decreases as production fall.
Answer: Variable Cost APEX
A fire truck has a ladder that can extend to 60 feet in length. the ladder can be safely raised to a maximum angle of 75o with the horizontal. disregarding the height of the fire truck itself, which is closest to the maximum height that the ladder can safely reach?
Toss a coin three times. what is the probability of getting a head on the first toss
During a dig, an archaeological team starts at an elevation of −512 feet. At a rate of 234 feet per hour, the team digs deeper into the surface for 312 hours. For the next 412 hours, the team digs at a rate of 1512 feet per hour. Then the team quits for the day.How many feet did the archaeological team dig after 312 hours? feetWhat was the team's elevation at the end of the day?
Paul, Colin and Brian are waiters.
One night the restaurant earns tips totalling £77.40.
They share the tips in the ratio 1:3:5.
How much more does Brian get over Paul?
Two parallel lines are intersected by a transversal. Two parallel lines are intersected by a transversal. One of the angles formed measures 88°
Two parallel lines intersected by a transversal create angles that are congruent or supplementary. The given 88° angle determines the measures of all other angles, which can either be 88° or supplementary to it, totaling 180°.
Explanation:When two parallel lines are intersected by a transversal, several angles are formed. These angles have special relationships with each other. Since one of the angles is given as 88°, we can determine the measures of all other angles formed by using the properties of parallel lines and a transversal.
There are corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles (also known as same-side interior angles). Corresponding angles and alternate angles are equal, while consecutive interior angles are supplementary, meaning they add up to 180°.
Given that one of the angles measures 88°, its corresponding angle also measures 88°. The alternate exterior and alternate interior angles relative to the 88° angle would also measure 88°. The consecutive interior angles to the given angle would measure 92° (180° - 88° = 92°).
In a situation where mirrors are placed at an angle relative to each other, the same principle of angle measurement applies. For example, if two mirrors are inclined at an angle of 60°, the reflections would follow geometry consistent with angle relationships.
Please help please please
\Omega=\{1;\ 2;\ 3;\ 4;\ 5;\ 6;\ 7;\ 8;\ 9;\ 10\}\\\\|\Omega|=10\\\\A=\{1;\ 3;\ 6;\ 7\};\ B=\{2;\ 3\}\\\\A\ \cup\ B=\{1;\ 2;\ 3;\ 6;\ 7\}\\\\|A\ \cup\ B|=5\\\\P(A\ \cup\ B)=\dfrac{|A\ \cup\ B|}{|\Omega|}\to P(A\ \cup\ B)=\dfrac{5}{10}=\dfrac{1}{2}=0.5=0.50
select the values of r, below, that represent a low or no correlation
0.8
0.3
0.1
-0.2
-0.5
1
-0.001
Which situation is represented by the equation? 9x + 90 = 6x + 120
A) Jake has $90 and Mike has $120. Jake saves $6 per week and Mike saves $9 per week. How long will it be before Jake has more money than Mike?
B) Jake has $90 and Mike has $120. Jake saves $9 per week and Mike saves $6 per week. How long will it be before Jake has more money than Mike?
C) Jake has $90 and Mike has $120. Jake saves $9 per week and Mike saves $6 per week. How long will it be before Mike has more money than Jake?
D) Jake has $90 and Mike has $120. Jake saves $9 per week and Mike saves $6 per week. How long will it be before Jake and Mike have the same amount of money?
Answer:
D) Jake has $90 and Mike has $120. Jake saves $9 per week and Mike saves $6 per week. How long will it be before Jake and Mike have the same amount of money?
Step-by-step explanation:
The answer is D, because it make them equal
What is the surface area of a cone, to the nearest whole number?
a.221 cm^2
b.240 cm^2
c.304 cm^2
d.620cm^2
The surface area of a cone is b. 240 cm^2.
What is surface area of a cone?The surface area of a cone is equal to the curved surface area plus the area of the base: π r^2 + π L r .
where r denotes the radius of the base of the cone, and L denotes the slant height of the cone.
Here, we have,
from the given figure,
we get,
L= 12.5 cm
r=9/2
=4.5cm
by using the formula, we get,
the surface area of a cone is = 240.33 cm^2
Hence, the surface area of a cone is b. 240 cm^2.
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the fish aquarium holds 150 liters of water. How many milliliters dose the aquarium holds?
Two forest fire stations, P and Q, are 20.0 km apart. A
ranger at station Q sees a fire 15.0 km away. If the angle
between the line PQ and the line from P to the fire is
how far, to the nearest tenth of a kilometre, is
station P from the fire?
Station P is approximately 15.0 km away from the fire.
Given that:
A right triangle with sides PQ: 20.0 km
And QF: 15.0 km
Where F is the location of the fire.
To find how far station P is from the fire, use trigonometry.
Let's call the distance from station P to the fire x km.
The angle between PQ and PF is given.
Using the trigonometric tangent function:
tan(angle) = opposite/adjacent
In this case, the opposite side is QF , and the adjacent side is PQ.
tan(angle) = 15.0 km / 20.0 km
Now, let's find the value of the angle:
angle = arctan(15.0 km / 20.0 km)
Using a calculator to get,
angle ≈ 36.87 degrees
Now, use trigonometry again to find x:
tan(36.87 degrees) = x / 20.0 km
x ≈ 20.0 km * tan(36.87 degrees)
x ≈ 20.0 km * 0.75
x ≈ 15.0 km
So, station P is approximately 15.0 km away from the fire.
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The distance from station P to the fire is approximately 21.23 km.
Explanation:To find the distance from station P to the fire, we can use trigonometry. Since the ranger at station Q sees the fire at an angle between the line PQ and the line from P to the fire, we can consider the triangle created by station P, station Q, and the fire.
Using the tangent function, we can determine this distance:
tan(angle) = opposite / adjacent
Let x be the distance from station P to the fire:
tan(angle) = x / 15
Solving for x, we get:
x = 15 * tan(angle)
Now, we need to find the angle between the lines PQ and the line from P to the fire. Since the triangle created by station P, station Q, and the fire is a right triangle, we can use the inverse tangent function to find the angle:
angle = arctan(opposite / adjacent) = arctan(20 / 15)
Using a calculator, we find that the angle is approximately 53.13 degrees.
Substituting this angle into the equation for x, we have:
x = 15 * tan(53.13)
Solving for x, we get:
x ≈ 21.23 km
How do I factorise
28x-4
On a island, the population of flamingos is currently 400, and this population doubles every 3 years. Which of the following functions will correctly model this situation? Assume t is measured in years.
F f(t)= 2 x 400^3t
G f(t)= 400 x 3^t/2
H f(t)= 400 x 2^t/3
J f(t)= 400 x 2^3t
Find the sum of this problem
Options:
52
26
13
32
A set of weights includes a 4 lb barbell and 6 pairs of weight plates. Each pair of plates weighs
20 lb. If x pairs of plates are added to the barbell, the total weight of the barbell and plates in
pounds can be represented by f x( ) = 20x + 4.
What is the range of the function for this situation?
Please explain.
The range of the function is the distance from the maximum of the function to the minimum of the function. The minimum amount of pairs of plates that you can add to the bar (x) is 0, meaning you add no plates. The maximum amount of plates that you can add to the bar is 6, because this is how many plates come in one weight set. The range of the function is y values, and 0 and 6 are x values, so we must plug these values into the function to find the range values.
f(x) = 20x + 4 = 20(0) + 4 = 0 + 4 = 4
f(x) = 20x + 4 = 20(6) + 4 = 120 + 4 = 124
Therefore, the range of the function is 120 pounds, or from [4, 124].
Hope this helps!
The range of a function is the possible output values of the function. The range of [tex]f(x) =20x + 4[/tex] is [4,124]
Given that:
[tex]f(x) =20x + 4[/tex]
To determine the range of the function, we simply determine the value of f(x) using the input values
When no pair is added (this means x = 0).
So, we have:
[tex]f(0) =20 \times 0 + 4[/tex]
[tex]f(0) = 0 + 4[/tex]
[tex]f(0) = 4[/tex]
When 4 pairs are added (this means x = 4).
So, we have:
[tex]f(4) = 20 \times 4 + 4[/tex]
[tex]f(4) = 84[/tex]
When 6 pairs are added (this means x = 6).
So, we have:
[tex]f(6) = 20 \times 6 + 4[/tex]
[tex]f(6) = 124[/tex]
f(6) is greater than f(4).
i.e. [tex]124 > 84[/tex]
So, the range of the function is: [0,124] or [tex]4 \le x \le 124[/tex]
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Given the following functions f(x) and g(x), solve fraction f over g ( 3) and select the correct answer below. f(x) = 2x2 – 8 g(x) = x – 5
4/10= heeeeeeellllllppppppppppppp
What is the area of the figure? The diagram is not drawn to scale.
A. 1,190 in^2
B. 595 in^^2
C. 1,435 in^2
D. 1,394 in^2
How many numbers between 50 and 250 (inclusive) are not perfect squares?
Choose the correct answer. two cars leave phoenix and travel along roads 90 degrees apart. if car 1 leaves 30 minutes earlier than car 2 and averages 42 mph and if car 2 averages 50 mph, how far apart will they be after car 1 has traveled 3.5 hours? miles.
The answer is 210 miles.
What is the sum of this geometric series?5 + 25 + 125 + 625 + 3,125 + 15,625?
The sum of the given geometric series (5 + 25 + 125 + 625 + 3,125 + 15,625) is -78120.
Explanation:The question is asking for the sum of a geometric series. In a geometric series, each term is multiplied by a common ratio to get the next term. In this case, the first term (a) is 5 and the common ratio (r) is 5 (since we get each term by multiplying the previous one by 5).
The sum (S) of the first n terms of a geometric series can be calculated using the formula S = a * (1 - r^n) / (1 - r). In this case, there are n=6 terms in the series, so we will plug these values into the formula.
Therefore, S = 5 * (1 - 5^6) / (1 - 5). So, the sum of this geometric series is -78120.
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The reciprocal of two more than a number is three times the reciprocal of the number. find the number