Step-by-step explanation:
step 1. The circumference (c) of a circle is the diameter of a circle x pi. c = d(pi) = 14pi.
step 2. The area (A) of a circle is the radius of a circle squared x pi. The radius of a circle is 1/2 x the diameter. A = (14/2)^2(pi) = 49pi.
Over what interval is the graph of f(x) = -(x + 3)? - 1 decreasing?
the interval over which the graph of f(x) = -(x + 3) - 1 is decreasing is (-∞, +∞).
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The given function is:
f(x) = -(x + 3) - 1
To find the interval over which the function is decreasing, we need to find the values of x where the function's derivative is negative.
The derivative of the function is:
f'(x) = -1
The derivative is a constant, which means the function has a constant slope of -1. Since the slope is negative, the function is decreasing over its entire domain.
Therefore, the interval over which the graph of f(x) = -(x + 3) - 1 is decreasing is (-∞, +∞).
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For 6 consecutive days, Alejandro studied for 5 minutes more each day than he did the previous day. Which best represents the change in the amount of time that Alejandro studied on the first day to the amount of time he studied on the last day? –30 minutes –11 minutes 11 minutes 30 minutes
Answer:
it is on ed it is 30
Step-by-step explanation:
Answer:
30 minutes
Step-by-step explanation:
How do you write equations in Point-slope form?
For a line with a slope a and a known point (h, k), the point-slope form is:
y = a*(x - h) + k
How to write an equation in point slope form?A general linear equation can be written in slope-intercept form as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know that a line passes through a point (h, k), then the point-slope form of that line is:
y = a*(x - h) + k
Notice that particularly, the y-intercept can be written as (0, b), then the slope-intercept form is also a point-slope:
y = a*(x - 0) + b
y = a*x + b
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2c + y = 7 solve for y
Answer:
y = 7 - 2c
Step-by-step explanation:
Step 1:
2c + y = 7 Equation
Step 2:
y = 7 - 2c Subtract 2c on both sides
Answer:
y = 7 - 2c
Hope This Helps :)
Answer:
y = 7 - 2c
Step-by-step explanation:
2c + y = 7
=> y = 7 - 2c
Jessie is building a cabinet door, which is pictured below. The center of the cabinet door is 12 inches by 16 inches, and the border of the cabinet door has a width of x inches. The entire cabinet door has an area of exactly 396 square inches.
Clockwise from the top, the picture reads, x, 12 inches, 16 inches, x, Figure not drawn to scale.
Write an equation in standard form that can be used to find x , the width of the border.
Answer:
\(x^2+14x-51=0\)
Step-by-step explanation:
Since the entire cabinet door is a rectangle, its area is given by:
\(A=w\ell\)
The center of the cabinet door measures 12 inches by 16 inches.
And the border of the cabinet door has a width of x inches.
Therefore, the total width of the cabinet door will be (12 + 2x).
Likewise, the total length of the cabinet door will be (16 + 2x).
Thus, the area of the entire cabinet door will be:
\(A=(2x+12)(2x+16)\)
We are given that this entire area is 396 square inches. Thus:
\(396=(2x+12)(2x+16)\)
Simplify. We can factor out a two from both of the factors on the right-hand side:
\(396=2(x+6)(2)(x+8)\)
So:
\(396=4(x+6)(x+8)\)
Dividing both sides by four yields:
\(99=(x+6)(x+8)\)
Distribute the right-hand side:
\(x^2+14x+48=99\)
Therefore, our equation in standard form is:
\(x^2+14x-51=0\)
Edit:
We want to find the width of the board. So, we simply have to solve for x. We previously obtained:
\(x^2+14x-51=0\)
We can factor:
\((x+17)(x-3)=0\)
By the Zero Product Property:
\(x+17=0\text{ or } x-3=0\)
Solve for both cases:
\(x=-17\text{ or } x=3\)
Length/width cannot be negative. So, we can reject the first solution.
Thus, our only solution is:
\(x=3\)
The width of the border of the cabinet door is 3 inches.
This means that the total length of the cabinet is 16 + 2(3) = 22 inches, and the total width of the cabinet is 12 + 2(3) = 18 inches.
a hardware store orders twenty lawnmowers for $300 each, but each can only sell 18. The manufacture charges $20 for each mower returned unsold. if the store charges $360 for each mower sold, what is its profit on the lawnmowers
Which function has the same range as \(f(x)= - 2\sqrt{x} =-3 + 8\\\)
Both g(x) = 5 - x² and h(x) = \(5 - e^(6-^x^)\)have the same range as f(x) = -2√(x) - 3 + 8, which is (-∞, 5].
To determine which function has the same range as f(x) = -2√(x) - 3 + 8, we need to first find the range of f(x).
The square root function √(x) takes non-negative values as input and gives non-negative outputs, so the expression -2√(x) will always be non-positive. Therefore, the range of f(x) will be all real numbers less than or equal to -3 + 8, which is 5.
In other words, the range of f(x) is (-∞, 5].
So, we need to find a function whose range is also (-∞, 5]. One possible function is g(x) = 5 - x². We can see that when x is zero, g(x) is at its maximum value of 5, and as we increase or decrease x, g(x) will decrease, eventually approaching negative infinity.
Another possible function is h(x) = 5 - e^(-x). When x is negative infinity, e^(-x) is approaching positive infinity, so h(x) is approaching 0. As we increase x, e^(-x) is approaching zero, so h(x) is approaching 5.
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Find x and y in the following figures
Answer:
x = 15 , y = 21
Step-by-step explanation:
using Pythagoras' identity
in Δ ABD
x² + 8² = 17²
x² + 64 = 289 ( subtract 64 from both sides )
x² = 225 ( take square root of both sides )
x = \(\sqrt{226}\) = 15
in Δ ADC
8² + DC² = 10²
64 + DC² = 100 ( subtract 64 from both sides )
DC² = 36 ( take square root of both sides )
DC = \(\sqrt{36}\) = 6
then
y = x + DC = 15 + 6 = 21
Please tell me fast I am on a time crunch
if you randomly choose a number 1-10 what is the probability of choosing either an odd number or an even number
Answer:
wouldn't it be a 10/10 for probability just my thoughts
Flaherty Company had beginning inventory on May 1 of $12,000. During the month, the company made purchases of $40,000 but
returned $2,000 of goods because they were defective. At the end of the month, the inventory on hand was valued at $15,500.
Calculate cost of goods available for sale and cost of goods sold for the month.
Cost of goods available for sale: $___
Cost of goods sold: $___
The cost of goods available for sale is $50,000, and the cost of goods sold is $34,500.
What are arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
The cost of goods available for sale is the sum of beginning inventory and purchases, minus any purchase returns:
Cost of goods available for sale = Beginning inventory + Purchases - Purchase returns
Cost of goods available for sale = $12,000 + $40,000 - $2,000
Cost of goods available for sale = $50,000
To calculate the cost of goods sold, we need to subtract the ending inventory from the cost of goods available for sale:
Cost of goods sold = Cost of goods available for sale - Ending inventory
Cost of goods sold = $50,000 - $15,500
Cost of goods sold = $34,500
Therefore, the cost of goods available for sale is $50,000, and the cost of goods sold is $34,500.
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Select whether the function is discrete or continuous.
Function: The number of basketballs manufactured per day
Answer:
Continuous
Step-by-step explanation:
1. Adding decimals is very similar to adding___________.
2.Line up the number vertically so that all the decimal points are_______.
3. Add extra______to the right of the number so that each number has the same number of digits to the right of the decimal point.
4. Place the______________of the result in line with the other decimal points.
Answers:
1. Adding decimals is very similar to adding whole numbers.
2. Line up the number vertically so that all the decimal points are aligned.
3. Add extra zeros to the right of he number so that each number has the same number of digits the right of the decimal point.
4. Place the decimal point of the result in line with the other decimal points.
I hope this helped you. If it is please click the thanks button. Thank You, Bye! ;-D
1. Adding decimals is very similar to adding whole numbers.
2. Line up the number vertically so that all the decimal points are aligned.
3. Add extra zeros to the right of the number so that each number has the same number of digits to the right of the decimal point.
4. Place the decimal point of the result in line with the other decimal points.
While adding two decimals.
First, the decimals numbers are written under each other so that decimal points are lined up.The numbers are converted to like decimals by attaching the zeros. The number of zeros attached depends on the number with the maximum digits after the decimal point. The digits of each numbers are lined up so that each column contains digits in the same place. Addition is carried out the normal way by starting from the right to the left. The decimal point is then placed in the place as the numbers above it.Learn more about decimal form here:
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Can you please help me solve this problem. I got A but am unsure.
Given these two series:
\(\begin{gathered} \sum ^{\infty}_{n\mathop=1}\frac{1}{n^{2p}} \\ \sum ^{\infty}_{n\mathop{=}1}(\frac{p}{2})^n \end{gathered}\)The second one is a way to write the geometric series, where r = p/2:
\(\text{Geometric series}\colon\sum ^{\infty}_{n\mathop=1}r^n\)This series converges only if 0 < r < 1, so the condition of convergence of the second series is:
\(\begin{gathered} 0\leq\frac{p}{2}<1 \\ 0\le p<2\ldots(1) \end{gathered}\)Now, for the first one, we know that the series diverges when 2p = 1, leading to the so-called Harmonic Series:
\(\sum ^{\infty}_{n\mathop=1}\frac{1}{n}=\infty\)So, the condition of convergence should be:
\(\begin{gathered} 2p>1 \\ p>\frac{1}{2}\ldots(2) \end{gathered}\)Combining these two conditions, (1) and (2), leads to:
\(\frac{1}{2}om is 5 years younger than his brother. If the sum of their ages is 43 years now, find their age.
Answer:
Brother's age =24
Om's age =19
Step-by-step explanation:
Let bro's age be x
Let om's age be x-5
x+x-5=43
2 x -5=43
2 x = 43+5
2 x = 48
x = 24
Is 27, 333 divisible by 3? Write the number 27,333 as the product of 3 and another factor.
Yes, 3 divides 27,333. We have
27,333 = 27,000 + 333
… = 27•1,000 + 333
… = 3•9•1,000 + 3•111
… = 3•(9•1,000 + 111)
… = 3•(9,000 + 111)
… = 3•9,111
floor of a classroom is 38 feet in length and 34 feet in width. A scale drawing of the floor has a length of 19 inches.
Answer:
38 i think i hope this helps
Answer of question 3 pls
The highest point for the quadratic function for the height of the object, h(t) = -16·t² + 224·t + 816, indicates that the interval over which the height of the object is increasing is; (-∞, 7]
What is the shape of the graph of a quadratic function?The shape of the graph of a quadratic function is a parabola.
The function for the height of the object in question 3 is; h(t) = -16·t² + 224·t + 816
Where;
t = The time in seconds
The height of the object is increasing in the interval to the left of the highest point, which can be found as follows;
The x-coordinate of the highest point of the quadratic function, f(x) = a·x² + b·x + c is; x = -b/(2·a)
Therefore, the x-coordinates of the highest point of the object is; -224/(2 × (-16)) = 7
Therefore, the height of the object is increasing in the interval; -∞ < t ≤ 7
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Find the area of the rectangle shown
7 1/2 ft
5 1/4ft
Answer:
39 3/8 ft ^2
Step-by-step explanation:
To find the area of a rectangle, multiply the length times the width.
A = l*w
= 7 1/2 * 5 1/4
Change the mixed numbers to improper fractions.
A = 15/2 * 21/4
=315/8
Change back to a mixed number.
8 goes into 315 39 times with 3 left over.
= 39 3/8
Answer:
Area = 39.375 ft²
(you can round to 39.4)
Step-by-step explanation:
Find the area of the rectangle shown
7 1/2 ft
5 1/4ft
7 1/2 = 7.5 ft
5 1/4 = 5.25 ft
Area = L x W
Area = 7.5 x 5.25
Area = 39.375
$668 at 9.25% for 15 months
cut a 60 cm ribbon into such that one part is one third of the other half
Answer:
15cm and 45cm
Step-by-step explanation:
If one part is one third of the other, then the long one is three times as long as the short one.
If the short one has length x
x + 3x = 60cm
4x = 60cm
x = 15cm
So short one is 15cm and the long one is 3*15cm = 45cm
someone please help me answer this!!
What's the answer to 8.546 rounded to the nearest ones place
Answer:
8.5
Step-by-step explanation:
because the hundredths place is not above 5
Solve e–5x = 7.4 for x correct to four decimal places. –0.40030.40030.8692–0.8692
Question:
\(e^{-5x}=7.4\)Step 1: Apply the exponent rule but taking ln of both sides
\(\begin{gathered} e^{-5x}=7.4 \\ -5x=\ln 7.4 \end{gathered}\)Step 2:Divide both sides by -5
\(\begin{gathered} -5x=\ln 7.4 \\ \frac{-5x}{-5}=\frac{\ln 7.4}{-5} \\ x=\frac{\ln7.4}{-5} \end{gathered}\)Hence,
The value of x is
\(\begin{gathered} x=\frac{\ln7.4}{-5} \\ x=-4.003 \end{gathered}\)Hence,
The final answer is = -0.4003
Find the probability that there are no T when a fair coin is flipped three times.
The probability that no Tails is achieved on flipping a fair coin for three consecutive times is \((\frac{1}{8})\).
As per the question statement, we are to flip or toss a fair coin thrice consecutively.
We are required to calculate the probability that no Tails is achieved during the above mentioned event.
To solve this question, first let us calculate all the possible outcomes of flipping a fair coin thrice consecutively. [We will denote a Heads outcome as "H" and a Tails outcome as "T"]
The total number of outcomes can be given by the formula \((2^{n})\), where "n" is the number of times, the coin is tossed.
Here, (n = 3), therefore, total number of outcomes in our case \(=(2^{3})=8\).
These 8 outcomes can be listed as \([{(H, H, H), (H, H, T), (H, T, H), (H, T, T), (T, H, H), (T, H, T), (T, T, H), (T, T, T)}]\)
And among the above listed 8, our favorable outcome is (H, H, H), i.e., 1 favorable outcome of 8.
Hence, probability that no Tails is achieved on flipping a fair coin thrice consecutively = \(\frac{1}{8}\).
Probability: In Mathematics, probability is the chance to of the occurrence of a specific event among the occurrence of all possible events, and is measured by the ratio of the favorable cases to the whole number of cases possible.To learn more about Probability, click on the link below.
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Isabel went to the grocery store. She spent $15.91 on vegetables and $11.22 on fruit. She also bought some bread. If she paid with 3 ten dollar bills and got 45 cents back in change, how much did she spend on bread?
Based on an equation, the amount that Isabel spent on bread was $2.42.
How the equation was solved?To solve the equation for the amount spent on bread, we determined the total amount Isabel spent by subtracting the change from the total bills she had.
An equation is a mathematical statement of the equality or equivalence of two or more mathematical expressions.
The amount Isabel spent on vegetables = $15.91
The amount she spent on fruits = $11.22
Let the amount she spent on bread = x
The total amount she went with = $30 (3 x $10)
The change she got after giving the cashier $30 = $0.45
The total amount Isabel spent for vegetables, fruits, and bread = $29.55 ($30.00 - $0.45)
x = $2.42 ($29.55 - $15.91 - $11.22)
Check:
Vegetables = $15.91
Fruits = $11.22
Bread = $2.42
Total expenses = $29.55
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I need help guys thanks
The approximate measurements of the Great Pyramid of Khufu are shown below. A square pyramid. The base is 230 meters by 230 meters. The triangular sides have a base of 230 meters and height of 187 meters. The pyramid has a height of 147 meters. What is the surface area of the pyramid? 86,020 meters squared 138,920 meters squared 224,940 meters squared 2,592,100 meters squared
Answer:
138,920 m²
Step-by-step explanation:
A square pyramid has 1 square base and 4 lateral triangular faces.
Area of square pyramid is given as BASE Area (BA) + ½*Perimeter of Base (P) × Slant height
Area of pyramid = \( b^2 + \frac{1}{2}*4(b)*l \)
Where,
b = base length = 230 m
l = slant height = 187 m (height of the triangular sides)
Surface area = \( 230^2 + \frac{1}{2}*4(230)*187 \)
\( = 52900 + 2(230)*187 \)
\( = 52900 + 86020 \)
\( = 138920 \)
Surface area of the pyramid = 138,920 m²
Answer:
hope i helped thank you
Step-by-step explanation:
2x² + 5x, what will it a Perfect Square? make
Answer:
2x² + 5x + c = 0
For this quadratic equation to have one double root, the discriminant must equal 0.
5² - 4(2)(c) = 0
25 - 8c = 0
c = 25/8
2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.
Explanation:2x² + 5x is not a perfect square.
A perfect square is an expression that can be factored into the square of a binomial. To determine if an expression is a perfect square, we can look at the coefficient of x². In this case, the coefficient is 2, which is not a perfect square.Learn more about Perfect Square here:https://brainly.com/question/34063927
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Determine whether the following statement makes sense or does not make sense, and explain your reasoning. I found the expected value for the number of boys for a family with five children to be 2.5. I must have made an error because a family with 2.5 boys cannot occur. Question content area bottom Part 1 The statement ▼ does not make sense makes sense because the expected value of 2.5 represents the ▼ average number total number of boys for all the families with five children. In a five-child family, ▼ all the children half the children are expected to be boys, so the expected value of 2.5 is ▼ inconsistent. consistent.
This is due to the fact that the anticipated value is determined by multiplying the likelihood of each potential occurrence by its value, then adding the results.
what is probability ?Probability is a metric for determining the possibility of an event happening in mathematics and statistics. It is a number between 0 and 1, where 0 denotes that the action is impossible and 1 denotes that it is guaranteed to occur. Usually, the likelihood of a particular occurrence is calculated through dividing the number of possible outcomes by the number of alternative ways the event could happen. As an illustration, the likelihood of rolling a six on a regular die is 1/6 since there is just one method for scoring a six and a total of six options. Many practical applications of probability can be found in the fields of insurance, banking, and gaming. Also, it aids in risk management and assessment throughout scientific research and decision-making processes.
given
The assertion "I discovered that there should be 2.5 more boys in a household of five than was anticipated. A family of 2.5 boys cannot exist, thus I must have made a mistake "contradicts itself.
A family cannot have 2.5 males just because the number of boys in a household of five is supposed to be 2.5. Instead, it suggests that a family with five children may typically anticipate to have 2.5 boys.
This is due to the fact that the anticipated value is determined by multiplying the likelihood of each potential occurrence by its value, then adding the results.
It is indeed impossible to have 2.5 males in a family of five.
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