Answer:
Arithmetic sequence
f(n)=30-2(n-1)
Step-by-step explanation:
Chinedu's problem-solving sequence is arithmetic. The explicit formula for the sequence is f(n) = 32 - 2n.
Chinedu's homework problem involves a sequence where he solves 2 problems each minute, starting with 30 problems. To determine the number of problems left at the beginning of the nth minute, we can use an arithmetic sequence since the number of problems decreases by a constant amount (2 problems) each minute.
In an arithmetic sequence, the nth term can be expressed using the formula:
f(n) = a + (n - 1)d
where a is the first term and d is the common difference.
Steps:
Identify the first term (a), which is 30 (the total number of problems initially).Identify the common difference (d), which is -2 (since Chinedu is solving 2 problems each minute).Apply the formula:f(n) = 30 + (n - 1)(-2) = 30 - 2(n - 1) = 32 - 2n
So, the explicit formula for the sequence is f(n) = 32 - 2n.
Tom Johnson had a breakfast consisting of one scrambled egg, one sausage patty, and an 8 oz. glass of orange juice.
How many calories did his meal have?
Answer:342
Step-by-step explanation:100+130+112=342
Final answer:
The breakfast consisting of one scrambled egg, one sausage patty, and an 8 oz. glass of orange juice contains a total of approximately 430 Calories.
Explanation:
The question is about calculating the total calorie content of a breakfast that includes one scrambled egg, one sausage patty, and an 8 oz. glass of orange juice. To answer, we need to know the individual calorie content of each item. Typical values might be around 70 Calories for one large scrambled egg, about 250 Calories for a sausage patty, and approximately 110 Calories for an 8 oz. orange juice.
Add these values together to get the total calorie intake for the meal:
Scrambled egg: 70 CaloriesSausage patty: 250 CaloriesOrange juice (8 oz): 110 CaloriesTotal Calories = 70 + 250 + 110 = 430 Calories.
what is the answer to this problem
Answer:
-5 > -7
-2 < 2
-10 < -3
-9 < 2
5 > -9
Step-by-step explanation:
please give me brainliest
Help 10 points!!!!!!!
Answer:
B.
Step-by-step explanation:
Hope this helps!
Answer:
i think A
Step-by-step explanation:
Rhonda grows and sells pumpkins. The function C = 3n + 25 represents her cost, in dollars, for producing n pumpkins. Her revenue, or the amount she receives for selling n pumpkins, can be represented by the function R = 5n. Which function represents Rhonda’s profit, P, for selling n pumpkins?
Answer:
2n + 25
Step-by-step explanation:
Cost of pumpkin (C) = 3n + 25
Revenue (R) I.e selling price = 5n
Her profit (P) = Selling price (R) - cost price (c)
P = R - C
P = 5n - (3n + 25)
P = 2n - 25
The expression for her profit (p) = 2n - 25
Answer:
P = 2n – 25
Step-by-step explanation:
:)
What is the volume of a sphere with a radius of 1 foot? (Use 3.14 for π.) 37.68 ft 3 12.56 ft 3 4.19 ft 3 50.24 ft 3
If the gradient of a line C is 2/3 what is the gradient of the line which is perpendicular to C
Final answer:
The gradient of the line perpendicular to a line with a gradient of 2/3 is -3/2 since perpendicular slopes are negative reciprocals of each other.
Explanation:
If the gradient of a line C is 2/3, we need to find the gradient of the line which is perpendicular to C. In mathematics, particularly in coordinate geometry, the slopes (or gradients) of two perpendicular lines are negative reciprocals of each other. This means that if the slope of the first line is m, the slope of the line perpendicular to it will be -1/m.
Therefore, the gradient of the line perpendicular to line C, which has a gradient of 2/3, will be the negative reciprocal of 2/3.
perpendicular = -1 / (2/3) = -3/2
So, the gradient of the line perpendicular to C is -3/2.
Which of the following explains why Cosine 60 degrees = sine 30 degrees using the unit circle? E2020?
Answer:
A
Step-by-step explanation:
he side opposite a 30° angle is the same as the side adjacent to a 60° angle in a right triangle. On a unit circle, the y (sin) distance of a 30° angle is the same as the x (cos) distance of a 60° angle.
Explanation of Cosine 60 = Sine 30
Cosine :
The trigonometric function that is equal to the ratio of the side adjacent to an acute angle (in a right-angled triangle) to the hypotenuse.
Sine :
The trigonometric function that is equal to the ratio of the side opposite a given angle (in a right-angled triangle) to the hypotenuse.
So, these are the reasons :
⇒ The side opposite a 30 degree angle is the same as a side adjacent to 60 degree angle in a right triangle.
⇒ On a unit circle, the y (sin) distance of a 30 degree angle is the same as the x (cos) distance of a 60 degree angle.
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6 times a number is 16 less than the square of that number. Find the positive
solution
Answer:
8
Step-by-step explanation:
Janet has $120. If she saves $20 per week, in how many days will she have $500? *
Answer:
19 weeks
Step-by-step explanation:
Make an equation
120+20x=500
Subtract 120 on both sides
20x=380
Divide by 20 on both sides
x=19
Hope this helps!
12(x - 4) + 4(x + 7)
Answer:
16x -20
Step-by-step explanation:
12(x - 4) + 4(x + 7)
12x - 48 + 4x +28
16x - 20
Answer:
16x - 20
Step-by-step explanation:
Given
12(x - 4) + 4(x + 7) ← distribute both parenthesis
= 12x - 48 + 4x + 28 ← collect like terms
= 16x - 20
HELP ASAP MARKJNG AS BRAINLIST
Answer:
114°
Step-by-step explanation:
By property of intersecting chords inside a circle.
[tex] \because \angle \: 1 = \frac{1}{2} (x + y) \\ \\ \therefore \: \angle \: 1 = \frac{1}{2} (96 + 132) \\ \\ \therefore \: \angle \: 1 = \frac{1}{2} \times 228\\ \\ \huge \red { \boxed{\therefore \: \angle \: 1 = 114 \degree}}[/tex]
jada earns $7 per hour mowing her neighbors' lawns. andre gets paid $5 per hour for the first hour of babysitting and $8 per hour for any additional hours he babysits. what is the number of hours they both can work so that they get paid the same amount?
jada 2 andre 3 hours
how do you combine,multiply,divide,and compose functions, and how do you find the domain of the resulting function?
The operations of the function are explained below in the solution.
Let f(x) and g(x) be given functions.
We combine those two functions using following rule
(f±g)(x) = f(x) ± g(x)
The domain of f±g is the intersection of the domain off and the domain
of g.
We multiply those two functions using the following rule:
(f·g)(x) = f(x)-g(x)
The domain of f·g is the set of all real numbers for which f and g and new
function are defined.
We divide those two functions using the following rule:
f/g (x) = f(x) / g(x)
The domain of f/g is set of all real numbers for which ƒ and g and new
function are defined.
We combine these two functions using the following rule:
(f ο g) = f(g(x))
We have that the domain of f ο g is the set of all real numbers z, in the
domain of g, such that g(x) is in the domain of f,
We have that the domain of g ο f the set of all real numbers, in the domain of f, such that f(x) is in the domain of g,
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Final answer:
In mathematics, functions can be combined, multiplied, divided, and composed, and discovering their domain is essential. Combining functions adds their outputs, multiplying them multiplies their outputs, and dividing them divides one output by another. Composing functions applies one to the result of another, with the domain determined by permissible inputs, avoiding division by zero or negative square roots.
Explanation:
When working with functions in mathematics, you can perform several operations, including combining, multiplying, dividing, and composing functions. Finding the domain of the resulting function is crucial as it determines the set of all possible inputs for the function.
Combining Functions
To combine functions (also known as function addition), you simply add the outputs of two functions. For example, if f(x) = 2x and g(x) = x + 3, the combined function is (f + g)(x) = f(x) + g(x) = 2x + (x + 3) = 3x + 3.
Multiplying and Dividing Functions
Multiplying functions involves multiplying the outputs of the functions. If f(x) = 2x and g(x) = x + 3, then[tex](f \cdot g)(x) = f(x) \cdot g(x) = 2x \cdot (x + 3)[/tex]. Dividing functions, on the other hand, involves dividing one output by the other, given that the divisor is not zero.
Composition of Functions
Composing functions refers to applying one function to the result of another function. The composition g o f means applying f first and then g. If h(x) = g(f(x)), you're taking an input x, applying the function f, and then applying g to the result of f(x).
Finding the Domain
The domain of a function is the set of all permissible inputs. To find the domain of a resulting function after performing operations, look for any restrictions such as division by zero or taking the square root of a negative number. For instance, if [tex]f(x) = \sqrt{x}[/tex], the domain is x ≥ 0, as you cannot take the square root of a negative number.
Write the equation of a line with slope of -1/4 and contains the point (4,-3)
Answer:
y = -1/4x -2
Step-by-step explanation:
We can use the slope intercept form of a line
y = mx+b where m is the slope and b is the y intercept
y = -1/4x +b
Substitute the point into the equation
-3 = -1/4(4) +b
-3 = -1 +b
Add 1 to each side
-3 +1 = -1 +1 b
-2 =b
y = -1/4x -2
Solve the systems of equations by substitution
3/8x + 1/3y = 17/24
X + 7y = 8
Answer:
If your solving for y...
The answer would be: y = -9/8x + 17/8 I believe.
For the second one... it would be : y = -1/7x + 8/7
Step-by-step explanation:
Which of the following fractions is the largest: 13/16, 3/4, 7/10, or 5/8?
From the given set of fractions, 13/16 is the largest fraction.
The given set of fractions are 13/16, 3/4, 7/10, and 5/8.
We need to check which of the given fractions is the largest.
How to order the fractions?To order fractions from least to greatest, start by finding the lowest common denominator for all of the fractions. Next, convert each of the fractions by dividing the lowest common denominator by the denominator and then multiplying the top and bottom of the fraction by your answer.
Now, the LCM of denominators of the fractions is as follows:
16, 4, 10 an 8 LCM= 2×2×2×2×5=80
Make the denominators equal to LCM.
That is, 65/80, 60/80, 56/80, and 50/80
Here, 65/80 is the largest, since the numerator is the greatest number.
Therefore, from the given set of fractions 13/16 is the largest fraction.
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There are three boys and three girls at a party. In how many ways can they be seated if they can sit down four at a time?
Answer:
6 Ways. (I could be wrong. If I am, I will come back and edit)
Step-by-step explanation:
BBBG
BBGB
BGBB
BGBG
BGGG
BGGB
The number of the ways of sitting of the three girls and three boys will be 4.
What are permutation and combination?Combination and permutation are two alternative strategies in mathematics to divide up a collection of components into subsets. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order.
Given that there are three boys and three girls at the party. The number of the ways will be calculated as,
N = ⁴C₃
N = (4!) / (3)!(4-1)!
N = 4
Therefore, the number of the ways of sitting of the three girls and three boys will be 4.
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-5 < x - 4 greater than it equal 1
We have expression [tex]-5 < x - 4 \geq 1[/tex] that renders the system of inequalities,
[tex]
\begin{cases}
-5 < x - 4 \\
x - 4 \geq 1
\end{cases}
[/tex]
Which can be simplified to,
[tex]
\begin{cases}
x > -1 \\
x \geq 5
\end{cases}
[/tex]
So what we get is something greater than -1 and at the same time greater or equal to 5, so the solution is,
[tex]x\in(\infty,-1)\cap(\infty, 5]=\boxed{(\infty,5]}[/tex].
Hope this helps.
A right pyramid with a square base has a base length
of x inches, and the height is two inches longer than
the length of the base. Which expression represents
the volume in terms of x?
x
(x
+ 2)
cubic inches
X(X
+ 2)
03
cubic inches
cubic inches
x+2
cubic inches
Answer:
x = 20
Step-by-step explanation:
-10x=-200
x = -200/ -10
x = 20
Answer:
A. x^2 (x+2) / 3
Step-by-step explanation:
A video rental store charges $4 per day to rent a movie and $3 per day to rent a video game. During one summer, Tony paid a total of $140 to rent movies and
video games from this store. If he rented twice as many video games as movies, how much did he spend on movie rentals during the summer?
Answer: The answer should be 35
Step-by-step explanation: If you take 140 divide it by 4 it should be the answer
|x−12| =4
please help and show steps I have this due today!
Answer
x=-8
Step-by-step explanation:
so the right answer is 16...
A dog shelter had 20 puppies last month. This month, 31 puppies are at the shelter!
What is the percent of increase?
Answer:11
Step-by-step explanation:
Because I said so
Started at 15 degrees and dropped 4 degrees and dropped 4 degrees each minute
Answer:
15-4 11 -4x
Step-by-step explanation:
Simplify to create an equivalent
1+ 46p - 9)
Choose 1 answer:
Answer:
[tex]8 + 46p[/tex]
Step-by-step explanation:
Step 1: Combine like terms
[tex]1 + 46p - 9[/tex]
[tex](1 - 9) + 46p[/tex]
[tex]8 + 46p[/tex]
Answer: [tex]8 + 46p[/tex]
You can also pull out a two from both
[tex]8 + 46p[/tex]
[tex]2(4 + 23p)[/tex]
a) Work out the value of (square root of 5)^2 x (square root of 3)^2?
Answer:
15
Step-by-step explanation:
Square root of 5=√5
Square of the square root=(√5)^2
=5
Square root of 3=√3
Square of the square root=(√3)^2
=3
So (square root of 5)^2×(square root of 3)^2
5×3
15
Therefore the final answer is 15
_____the number or variable that is raised to a power in an exponential expression
Answer:
Base
Step-by-step explanation:
To give an example, in the expression [tex]10^6[/tex], 10 is our base and 6 is our exponent or power.
help me please :((: thank u
Hey there!
In order for you to find the one that is equivalent to the given expression is to COMBINE YOUR LIKE TERMS then work from there!
12q + q^2 - 8 + q = ?
(q^2) + (12q + q) + (-8)
q^2 = q^2 since it doesn't have any like term(s)
12q + q = 12q + 1q = 13q
-8 = -8 since it doesn't have any like term(s)
Put all the numbers we solved for in An equation and Thats your answer!
If you did it correctly you should have: q^2 + 13q - 8
Answer: q^2 + 13q - 8 ✅
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
Point B has coordinates (4,2). The x-coordinate of point A is negative 1. The distance between point A and point B is 13 units. What are the possible coordinates of point A?
The possible coordinates of point A are
Answer:
5.8 and 7.4
Step-by-step explanation:
What two numbers added equal 40 but when subtracted equal 10?
PLZ!!!!!!!!!!!!!!!!!!!! HELPPPPPPPPPPPPPPPPPPPP
Answer:
25 and 15
You can easily make a system of equations:
x + y = 40
x - y = 10
Solving for x on equation 2 gets x = 10 + y.
Plugging in this into the first equation, you get 10 + y + y = 40
Thus, 10 + 2y = 40
y = 15.
Plugging this back into either equation gets x = 25.
I need help with is math
Answer: 9
Step-by-step explanation: