We know that the irrational number is between:
6 < √45 < 7
And a good estimation is √45 = 6.71
How to approximate the irrational number?Here we just need to find a lower and upper bound for the given irrational number.
To do it, we just need to find a square number larger and a square number smaller than the number inside the square root.
The larger one will be:
7*7 = 49
The smaller one will be:
6*6 = 36
Then we can write:
√36 < √45 < √49
6 < √45 < 7
So we now know that our number is between 6 and 7, that is already a good estimation, now you can also try to see if it is closer to 6 or 7, by taking the direct square root you will get:
Now just take the product between numbers of the form:
6.10*6.10 = 37.21
And so on, until we almost reach 45.
We will get:
6.71*6.71 = 45.02
So a good estimation is √45 = 6.71
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1
What is the solution to this equation?
-4(-2q + 8) = -6(q - 8) + 12q
Answer: q=40
Step-by-step explanation:
lets multiply first part of the equation
-4(-2q + 8)=8q-32
second part of the equation
-6(q - 8) + 12q= -6q+48+12q=6q+48
lets equal both
8q-32=6q+48
8q-6q=48+32
2q=80
q=80/2=40
f(x)=(x-1)(x-2)(x-3)(x-4)(x-3)(x-2)(x-2)/[(x-2)(x-4)(x-2)]
Answer:
Step-by-step explanation:
(x-2)(x-2)(x-4)
I need definitions of theses now!!!!!!!!!!!!!!!!!!!!!!!!!!!!
4. Adding and Subtracting Complex Numbers
5. Multiplying Complex Numbers
6. Solving Quadratic Equations with Complex Roots
Answer: Hope this helps!
Adding and subtracting complex numbers. Just as with real numbers, we can perform arithmetic operations on complex numbers. To add or subtract complex numbers, we combine the real parts and combine the imaginary parts.
Multiplying a complex number by a real number
(x + yi) u = xu + yu i. In other words, you just multiply both parts of the complex number by the real number. For example, 2 times 3 + i is just 6 + 2i. Geometrically, when you double a complex number, just double the distance from the origin, 0.
When the roots of a quadratic equation are imaginary, they always occur in conjugate pairs. A root of an equation is a solution of that equation. If a quadratic equation with real-number coefficients has a negative discriminant, then the two solutions to the equation are complex conjugates of each other.
Answer:
5 was right
Step-by-step explanation:
In which year will 67% of babies be born out of wedlock?
Based on the trend of the increase in children born out of wedlock, if this trend keeps increasing, the year with 67% of babies born out of wedlock will be 2055 .
What year will 67% of babies be born to unmarried parents?In 1990, the 28% of children were born out of wedlock and this trend was increasing by 0.6% per year.
If the trend continues, the number of years till 67% of children born out of wedlock will be:
= (67% - 28%) / 0.6%
= 65 years
The year will be:
= 1990 + 65
= 2055
The first part of the question is:
According to the National Center for Health Statistics, in 1990, 28% of babies in the United States were born to parents who were not married. Throughout the 1990s, this percentage increased by approximately 0.6 per year.
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What is an equation of a line that passes through the points (3,4) and (4,6)
To find the equation of the line we must use the next equation
\(y-y_1=m(x-x_1)\)First, we need to replace the two points to find the slope (m) of the line
\(\begin{gathered} 6-4=m(4-3) \\ m=\frac{6-4}{4-3}=\frac{2}{1}=2 \end{gathered}\)Then, we must replace on the points and the slope in the initial equation
\(\begin{gathered} y-6=2(x-4) \\ y-6=2x-8 \\ y-6-2x+8=0 \\ y-2x+2=0 \end{gathered}\)Finally, the equation of the line is
\(y-2x+2=0\)An entrepreneur invests in a new play. The cost includes an overhead of $33,750 plus production costs of $1700 per performance. A sold-out performance brings in $2325 . Assume every performance is sold out, and let x represent the number of sold-out performances.
The entrepreneur's revenue is $2325x, entrepreneur's cost is $33,750 + $1700x and entrepreneur's profit from x sold-out performances is $625x - $33,750
The entrepreneur's revenue from x sold-out performances is given by the formula:
Revenue = (Price per Performance) x (Number of Performances)
Revenue = $2325 x x
Revenue = $2325x
The entrepreneur's cost from x sold-out performances is given by the formula:
Cost = Overhead + (Production Cost per Performance) x (Number of Performances)
Cost = $33,750 + $1700x
The entrepreneur's profit from x sold-out performances is the revenue minus the cost:
Profit = Revenue - Cost
Profit = $2325x - ($33,750 + $1700x)
Profit = $625x - $33,750
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What is the solution to the equation below? Round your answer to two decimal places. In x=0.3
Step-by-step explanation:
Since you are given the values there is no need to try another method then replacing x by the values
We can eliminate the negative values since you'll face math errors We have two remaining values 2 and 1.35㏑(2)= 0.69
㏑(1.35) = 0.3
so the right answer is D
a grocery store sells packages for fresh tortillas . the table shows the relationship between the number of packages and the number of packages and the number of tortillas . how many are in 2 packages
The Tortillas in 2 Packages from Given Data is 14
Calculating Tortillas in 2 Packages from Given DataTo determine how many tortillas are in 2 packages, we can use the given data to find the relationship between the number of packages and the number of tortillas.
From the table, we can see that there is a linear relationship between the two variables, with each package containing 7 tortillas.
Therefore, we can calculate the number of tortillas in 2 packages by multiplying 2 by 7,
So, we have
Packages = 2 * 7
Packages = 14
The answer of 14 tortillas in 2 packages.
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Complete question
A grocery store sells packages of fresh tortillas. The table shows the relationship between the number of packages and the number of tortillas. How many tortillas are in 2 packages?
Number of Packages Number of Tortillas
5 35
7 49
15 105
Indigo went shopping for a new pair of sneakers. Sales tax where she lives is 3.75%. The price of the pair of sneakers is $20. Find the total price including tax. Round to the nearest cent.
Step-by-step explanation:
price=$20tax rate=$3.75multiply the price with rate and you will get tax the add it to the real pricetotal price incl. tax= 20+(20*3.75/100)=20.75there is your answer...The total price of sneakers including tax will be equal to $20.75.
What is the Percentage?The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.
As per the given information in the question,
Price of sneakers = $20
Tax on sneakers = 3.75%
Then, the amount of tax will be,
(20 × 3.75)/100
= 75/100
= $0.75
Then, the total price of the sneakers will be,
$20 + $0.75
= $20.75
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i'll mark brainliest, thanks in advance!
Which equation is equivalent to 45-4+2?
O sotto
Answer:
C. S= t+2/4
Step-by-step explanation:
4s = t+2
All you have to do is divide the four which will go to the bottom of t+2. Hopefully this helps :)
for a special fully discrete 20-year term insurance on (30): the death benefit is 1,000 during the first ten years and 2,000 during the next ten years.
The cost of the 20-year term insurance will be based on age, health, smoking, and other factors to determine the premium.
The cost of a special fully discrete 20-year term insurance on a 30-year-old would depend on a range of factors, including the insured's age, health, smoking status, and lifestyle. These factors would be used to calculate the risk of death during the 20-year term. The death benefit of 1,000 during the first ten years and 2,000 during the next ten years would also be taken into account when calculating the cost of the policy. Depending on the risk of death and the death benefits, the premium could vary significantly. For example, a 30-year-old in good health with no smoking history could pay less for the policy than a 30-year-old with a pre-existing condition and a smoking history. The premium could also be higher for individuals with riskier lifestyles. Ultimately, the cost of the 20-year term insurance will depend on the risk of death and the death benefit offered by the policy.
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help please please please
Answer: the answer is x=30
Step-by-step explanation:
Help help help help help
Answer:
vertex is (-4,-3)
and
axis of symmetry is x = -4
An iPhone costs £850 in London, €800 in Paris and $1,000 in New York.
Using £1 = €1.18 and £1 = $1.43, state the lowest price of the iPhone in £.
Lowest price of an iPhone in Paris is €800 because they stated that one euro is equal to one dollar; when multiplied, the result is 944; this indicates that the iPhone is priced lower in Paris.
What is lowest value of iphone ?It is possible to compare the conversion rates of sterling into the euro and the dollar using the same amount of pounds.
Sterling to Euro : \($750 \times 1.14=6855$\)
Pounds to dollars : \($750 \times 1.39=\$ 1042.5$\)
One phone may be purchased with one pound. The dollar is insufficient to purchase a cell phone, but the euro has enough money to do so. Paris has the lowest pricing for the iPhone from this perspective.
The iPhone SE (2020), which costs Rs 40,000, costs more over a lakh rupees according to the most recent Apple price list for India. Everywhere in the globe, the USA market offers the cheapest prices for iPhones.
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On average, Nathaniel drinks
4/5 of a 10-ounce glass of water in
2 2/5
hours. How many glasses of water does he drink in one hour? Enter your answer as a whole number, proper fraction, or mixed number in simplest form.
Nathaniel drinks 3 glasses of water in one hour.
To find out how many glasses of water Nathaniel drinks in one hour, we need to calculate his drinking rate per hour.
In 2 2/5 hours, Nathaniel drinks 4/5 of a 10-ounce glass of water.
Let's convert the mixed number of hours to an improper fraction:
\(2\frac{2}{5} = \frac{(5 \times2 + 2)}{5}\)
\(=\frac{12}{5}\)
Now, we can set up a proportion to find his drinking rate per hour.
We know that \(\frac{12}{5}\) hours corresponds to \(\frac{4}{5}\) of a glass of water.
Let's assign "x" as the number of glasses he drinks in one hour.
The proportion is then
\(\frac{(\frac{12}{5} hours) }{(x glasses) } =\frac{(\frac{4}{5} glass)}{(1 hour)}\)
Cross-multiplying gives us
\((\frac{12}{5} )\times1=\frac{4}{5}\times(x)\)
Simplifying, we get
\(\frac{12}{5} =\frac{4}{5}\times x\)
Dividing both sides by \(\frac{4}{5}\), we find x:
\(x=\frac{(\frac{12}{5} )}{\frac{4}{5} }\)
\(x=\frac{12}{4}\)
\(x = 3.\)
Therefore, Nathaniel drinks 3 glasses of water in one hour.
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Solve for x. 6x-10≤8 or 1/3x+6>12 PLEASE HELP and show work
The value of x in 1st equation is x ≤ 3 i.e. x ∈ (-infinity,3] and the value of x in 2nd equation is x > 18 i.e. x ∈ (18,infinity)
Given two equations 1)6x-10<8 and 2) \(\frac{x}{3}\)+6 > 12
Solving the above equations
1) 6x-10≤8
⇒6x ≤ 18
⇒X≤ 3
⇒x ≤ 3 i.e. x ∈ (-infinity,3]
2)\(\frac{x}{3}\)+6 > 12
⇒\(\frac{x}{3}\) > 6
⇒x>18
⇒ x > 18 i.e. x ∈ (18,infinity)
Therefore,The value of x in 1st equation is x ≤ 3 i.e. x ∈ (-infinity,3] and the value of x in 2nd equation is x > 18 i.e. x ∈ (18,infinity)
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Convert 85 miles per hour to meters per second. (Use 1.61 km = 1 mile)
show the steps
Answer:
38.0 m/s
Step-by-step explanation:
Units conversion can be done by multiplying by appropriate conversion factors. Each conversion factor has a value of 1: the numerator is equal to the denominator, but the units are different. The units are chosen so that cancelling unwanted units gives the set of units you want.
__
\(\dfrac{85\text{ mi}}{1\text{ h}}\times\dfrac{1.61\text{ km}}{1\text{ mi}}\times\dfrac{1000\text{ m}}{1\text{ km}}\times\dfrac{1\text{ h}}{3600\text{ s}}=\dfrac{85\cdot1.61\cdot1000\text{ m}}{3600\text{ s}}\\\\\approx\boxed{38.0\text{ m/s}}\)
The capacity of a swimming pool is given by C = l × w × , where l is the length, w is the width, d1 is the depth of the shallow end, and d2 is the depth of the deep end of the pool.
Select all the correct statements.
The correct statements about the capacity of swimming pool are (a) and (d)
The capacity of a swimming pool is given by C = l × w × (d₁ + d₂)/2
where l is the length,
w is the width,
d₁ is the depth of the shallow end,
and d₂ is the depth of the deep end of the pool.
If C = 9,216 ft, l = 48 ft, w = 24 ft, and d₂ = 12 ft, then d₁ would be,
9216 = 48 × 24 × (d₁ + 12)/2
d₁ + 12 = (9216 × 2) / (48 × 24)
d₁ + 12 = 16
d₁ = 4 ft
And formula for the depth of the shallow end would be,
d₁ = (2C/lw) - d₂
Therefore, the correct statements are (a) and (d)
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The complete question is:
The capacity of a swimming pool is given by C = l × w × (d1 + d2)/2, where l is the length, w is the width, d 1 is the depth of the shallow end, and d 2 is the depth of the deep end of the pool.
Select all the correct statements.
a) The depth of the shallow end is given by d1 = 2C/lw - d2.
b) If C = 9,216 ft, l = 48 ft, w = 24 ft, and d2 = 16 ft, then d1 = 4 ft.
c) The depth of the shallow end is given by 2C - d2/lw .
d) If C = 9,216 ft, l = 48 ft, w = 24 ft, and d2 = 12 ft, then d1 = 4 ft.
Can I please get some help I’ve been stuck on this question for a while!
Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes
How many minutes of the ride are spent higher than 28 meters above the ground?The radius of the Ferris wheel is 30 / 2 = 15 meters.
The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.
The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.
The angle between these two positions is 180 degrees.
The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.
Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.
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Review the simple interest rate based on FICO scores to answer the question:
FICO Score Simple Interest Rate
800–850 5.295%
740–799 6.597%
670–739 9.132%
580–669 10.358%
300–579 14.313%
Kamryn plans to borrow $13,250.00 with a simple interest rate loan. Determine the amount of interest Kamryn will save if she is able to raise her credit score from 665 to 680.
Kamryn would save $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.
To determine the amount of interest Kamryn will save by raising her credit score from 665 to 680, we need to compare the interest rates associated with each credit score range.
According to the given information, a credit score of 665 falls within the range of 580-669, where the corresponding simple interest rate is 10.358%.
Let's calculate the interest Kamryn would pay on a loan of $13,250.00 at an interest rate of 10.358%.
Interest = Principal * Rate
= $13,250.00 * 0.10358
≈ $1,370.56
Therefore, if Kamryn were to borrow $13,250.00 with a credit score of 665, she would pay approximately $1,370.56 in interest.
Now, let's consider the scenario where Kamryn raises her credit score to 680. A credit score of 680 falls within the range of 670-739, where the corresponding simple interest rate is 9.132%.
Calculating the interest with a credit score of 680:
Interest = Principal * Rate
= $13,250.00 * 0.09132
≈ $1,210.57
Thus, if Kamryn were able to raise her credit score from 665 to 680, she would save approximately $1,370.56 - $1,210.57 = $159.99 in interest.
Therefore, Kamryn would save approximately $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.
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Which value of x in the equation 18x + 5 - 3 = 65 makes the equation true
Answer:
the value of x that makes the equation true is x = 3.5.
Step-by-step explanation:
To find the value of x that makes the equation 18x + 5 - 3 = 65 true, we need to simplify the equation and solve for x.
Starting with the equation:
18x + 5 - 3 = 65
First, combine like terms:
18x + 2 = 65
Next, isolate the term with x by subtracting 2 from both sides:
18x = 65 - 2
18x = 63
Finally, divide both sides of the equation by 18 to solve for x:
x = 63 / 18
x = 3.5
Therefore, the value of x that makes the equation true is x = 3.5.
The answer is:
x = 7/2 (3.5 in decimal form)Steps & work :
First, I focus only on the left side.
Combine like terms:
\(\sf{18x+5-3=65}\)
\(\sf{18x+2=65}\)
Subtract 2 from each side:
\(\sf{18x=63}\)
Now, divide each side by 18:
\(\sf{x=\dfrac{63}{18}\)
Clearly, this fraction is not in its simplest terms, and we can divide the top and bottom by 9:
\(\sf{x=\dfrac{7}{2}}\)
\(\therefore\:\:\:\:\:\:\stackrel{\bf{answer}}{\boxed{\boxed{\tt{x=\frac{7}{2}}}}}}\)
For what value of Θ is cotΘ undefined?
0°
180°
270°
The value of such that = k * 180, where k is an integer, is the value at which cotangent is undefinable.
Cotangent, or cot, is one of the six standard trigonometric functions. Cotangent of an angle is defined as the ratio of the adjacent side to the opposite side of a right-angled triangle.
The value of cotangent is undefined when the denominator is zero. This implies that cotangent is undefined at angles where the value of sine is zero.
Since the sine function is periodic and has a period of 360 degrees, the values of sine repeat themselves after every 360 degrees.
For this reason, cotangent is undefined at angles such that θ = k * 180, where k is an integer.
That is, cotangent is undefined at 0°, 180°, 360°, and so on. It is also important to note that cotangent is a periodic function, and its values repeat every 180 degrees.
Therefore, cotangent is undefined at 0° + k * 180°, where k is an integer.
To summarize, the value of Θ at which cotangent is undefined is such that θ = k * 180, where k is an integer.
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20 points!!!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!20 points!!!!!!!!!! In an animal shelter, the ratio of dogs to cats is 5 to 3. There are 25 dogs. Write and solve a proportion to find the number c of cats. due in 40 min
help
There are 15 cats in the animal shelter.
What is equation?An equation in which is the highest power of to the variables 1 is knowns as the linear equation. Mathematically: it is an algebraic equations that can be also written in the form of ax + b = 0 or ax + by + c = 0, where a, b and c are definitely real numbers and x and y are variables with the highest power one.
In order to solve this problem, we must set up a proportion. Proportions are an equation that states that two ratios are equal. In this case, we are looking for the number of cats (c) in the animal shelter.
Let's set up the proportion.
5/3 = 25/c
We can then solve for c by multiplying both sides by c.
5c/3 = 25
c = 15
Therefore, there are 15 cats in the animal shelter.
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Find the length of the third side. If necessary, round to the nearest tenth.
Answer:
Adjacent, b = 5.3 units
Step-by-step explanation:
Let the length of sides of the triangle be;
Opposite side = aAdjacent side = bHypotenuse side = cFrom the right-angle triangle, we can deduce the following data;
Hypotenuse, c = 8
Opposite, a = 6
To find the length of the adjacent (third) side, we would have to apply Pythagorean' theorem.
From Pythagorean theorem;
c² = a² + b²
Substituting into the formula, we have;
8² = 6² + b²
64 = 36 + b²
Rearranging the equation (collecting like terms), we have;
b² = 64 - 36
b² = 28
Taking the square root of both sides, we have;
b = √28
Adjacent, b = 5.3 units
the length of a rectangle is three more than double the width. if the perimeter is 126 inches, find the dimensions.
The dimensions of the rectangle are 43inches and 20inches if the perimeter of the rectangle is 126 inches.
Leth the width of the revtangle be x.
According to the given question.
The perimeter of the rectangle is 126 inches.
The length of the rectangle is three more than double the width.
⇒ Length of the rectangle = 3 + 2x
Now, according to the given conditions we can say that
Perimeter of the rectangle = 2( length + width)
⇒ 126 = 2(3 + 2x + x)
⇒ 126 = 2(3 + 3x)
⇒ 63 = 3 + 3x
⇒ 63 - 3 = 3x
⇒ 60 = 3x
⇒ x = 20 inches
Therefore, the length of the rectangle = 3 + 2(20) = 3 + 40 = 43
Hence, the dimensions of the rectangle are 43inches and 20inches if the perimeter of the rectangle is 126 inches.
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Will give brainlst!!
Answer:
2.5, 21/8, ³√25, π, √19
Step-by-step explanation:
The following data were obtained from the question:
³√25, π, 21/8, 2.5, √19
Next, we shall express each data as a decimal number where necessary. This can be obtained as follow:
³√25 = 2.9
π = 3.14
21/8 = 2.6
2.5 = 2.5
√19 = 4.4
Finally, we shall order the expression from least to greatest. This is illustrated below:
2.5, 21/8, ³√25, π, √19
3 6 9 12 15 18 21 24 27 30 is odd or even numbers?
Answer: Half of them are even and half of them are odd.
Step-by-step explanation:
The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.
The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.
Therefore, out of the given numbers, half of them are even and half of them are odd.
________________________________________________________
A professor tells a student that he has a 90% chance of getting an A for the course that he score an 85 or better on the midterm exam. The student thinks he has only a 50% chance of getting 85 better. what is the probability that the student scores an 85 or better and he receive an A in the score?
The probability that the student scores an 85 or better and he receive an A in the score is 0.45.
In the question it is given that the professor tells that the student has 90% chance of getting A, if he gets 85 or better in mid term exam.
The student is 50% sure that he will get 85 or better in the examination.
To get the probability of the student scores an 85 or better and he receives an A grade, we use multiplication rule.
P( student getting A grade and 85 or better)= P(getting A) x P(getting 85 or better)
P(getting A)=0.9
P(getting 85 or better)=0.5
= 0.9x0.5
P( student getting A grade and 85 or better)=0.45
Therefore, probability that the student scores an 85 or better and getting A is 0.45.
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What is the scale factor for triangle P to R
Answer:When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles. In Figure 1 , Δ ABC∼ Δ DEF. Figure 1 Similar triangles whose scale factor is 2 : 1.
Step-by-step explanation:
When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles. In Figure 1 , Δ ABC∼ Δ DEF. Figure 1 Similar triangles whose scale factor is 2 : 1.