Fiinding and interpreting the zero of a rational function involves solving for x when the function equals zero and understanding its significance within the context.
Hello! I understand you want to find and interpret the zero of a rational function, and I'd be happy to help.
The zero of a rational function occurs when the function's value is equal to zero. In other words, a zero is a value of x that makes the function f(x) = 0. To find the zero, you must set the numerator of the rational function equal to zero and solve for x.
It's important to note that the denominator should never equal zero, as this would make the function undefined.
Interpreting the zero helps us understand the behavior of the function and can be useful in various applications.
For instance, the zero might represent a break-even point in a business context or an equilibrium in a physical system. Whether the result makes sense within the context of a specific problem depends on the given scenario and the mathematical relationship between the variables.
To summarize, Always ensure the denominator is never zero to maintain the function's validity.
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find the length of ab
Answer:
[tex]AB \approx 5.6 \text{ cm}[/tex]
Step-by-step explanation:
We can find the length of side AB using the trigonometric ratio cosine.
[tex]\cos(\theta) = \dfrac{\text{adjacent}}{\text{hypotenuse}}[/tex]
↓ plugging in the given values
[tex]\cos(62\°) = \dfrac{AB}{12}[/tex]
↓ multiplying both sides by 12
[tex]12 \cdot \cos(62\°) = AB[/tex]
↓ plugging into a calculator
[tex]\boxed{AB \approx 5.6 \text{ cm}}[/tex]
What is the measure of angle P?
Enter your answer as a decimal in the box.
Round only your final answer to the nearest hundredth.
P = ___
Therefore, the measure of angle P is approximately 22.62 degrees (rounded to the nearest hundredth).
So, the final answer is P ≈ 22.62.
What is triangle?A triangle is a closed geometric shape that has three sides, three angles, and three vertices (or corners). It is one of the most basic and important shapes in geometry. The sum of the angles in a triangle is always 180 degrees, and the length of each side can be calculated using the Pythagorean theorem or other geometric formulas. Triangles can be classified into different types based on the length of their sides and the size of their angles, such as equilateral, isosceles, scalene, acute, obtuse, and right triangles. Triangles are used extensively in mathematics, science, engineering, and many other fields.
To find the measure of angle P, we can use the Pythagorean theorem and trigonometric functions. Here's the step-by-step solution:
From the given information, we know that one angle of the triangle is 90 degrees, and the lengths of the adjacent sides are 5 and 13.
Using the Pythagorean theorem, we can find the length of the hypotenuse:
c^2 = a^2 + b^2
c^2 = 5^2 + 13^2
c^2 = 194
c = sqrt(194)
c ≈ 13.93
So the length of the hypotenuse is approximately 13.93 units.
Now, we can use the trigonometric function sine to find the measure of angle P:
[tex]sin(P) = opposite / hypotenuse[/tex]
[tex]sin(P) = 5 / 13.93[/tex]
[tex]P = sin^{-1(5/13.93)}[/tex]
P ≈ 22.62 degrees
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The circle below is centred at O.
AB is a tangent to this circle.
Work out the size of angle X.
Justify your answer.
52°
Step-by-step explanation:
It's 180-(90+38)= 52°
Answer:
52∘
Step-by-step explanation:
Since AB is tangent to the circle and OA is a radius, that means, ∠OAB = 90∘
A triangle has 180∘, so:
180∘ - 90∘ - 38∘ = 52∘
A sample of maximum pressure from 12 trials with a stamping machine yielded a mean of 7.2 thousand psi and a standard deviation of 1.2 thousand psi. The histogram of the sample data is approximately normal. Calculate a 90% confidence interval.
The 90% confidence interval for the mean pressure is calculated equivalent to (6.39, 7.99).
What is t-distribution table?A t-distribution table is a statistical table that lists critical values of the t-distribution for various levels of significance and degrees of freedom. The t-distribution is a probability distribution that is used when the sample size is small or when the population standard deviation is unknown.
The table is organized by degrees of freedom (df), which is calculated as n-1, where n is the sample size. It also lists different levels of significance, usually ranging from 0.01 to 0.5 or more. The critical values are listed in the table corresponding to the degrees of freedom and the significance level. To use a t-distribution table, you need to know the degrees of freedom and the level of significance.
To calculate the 90% confidence interval for the mean pressure, we can use the formula:
CI = X' ± Z*(σ/√n)
Where X' is the sample mean, σ is the sample standard deviation, n is the sample size, and Z is the critical value for a 90% confidence interval.
Since the sample size is 12, we need to use a t-distribution with 11 degrees of freedom to find the critical value, because we are estimating the population standard deviation from the sample. Using a t-distribution table or calculator, we can find that the critical value for a 90% confidence interval with 11 degrees of freedom is approximately 1.796.
Substituting the values into the formula, we get:
CI = 7.2 ± 1.796*(1.2/√12)
= 7.2 ± 0.81
Therefore, the 90% confidence interval for the mean pressure is:
(7.2 - 0.81, 7.2 + 0.81) or (6.39, 7.99)
So, we can say with 90% confidence that the true mean pressure of the machine lies between 6.39 thousand psi and 7.99 thousand psi.
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Why am I not getting correct anwsers on my geometry questions
Maybe you're bad at math.
But I don't think that's true.
Try reading the questions more carefully and properly reading/understanding the material.
If you have any future questions, please ask me! I would be glad to help with your geometry work.
click (with your mouse) on the image that best represents a 0.02 correlation
Answer:
Step-by-step explanation:
it would be the third one
Rita has coins worth $3.00. If the coins are all dimes, how many dimes does she have?
Answer:
300 dimes I believe because 3.00 is 100 dimes?
Step-by-step explanation:
Question
Jim's music store bought a guitar at the wholesale price of $1,200. Jim marked up the price 50%. Find the list price.
Answer: $1,800
Step-by-step explanation:
There were 15 kids at the park. When it began to rain, k of them went home. Write an expression that shows the number of kids left at the park.
The calcualted expression for the number of kids left at the park would be 15 - k
Calculating the expression of the kids that leftGiven that
Number of kids = 15
Kids that wet home = k
If there were originally 15 kids at the park and k of them went home due to rain, then the expression for the number of kids left at the park would be:
15 - k
This is because the total number of kids at the park (15) is reduced by the number of kids who left due to the rain (k).
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2 Al gives food pellets to the animals on the farm.
• Rabbits: 0.3 kilogram
• Chickens: 1,300 grams
• Ducks: 0.7 kilogram
How many more grams of pellets does Al give
the chickens than he gives the rabbits and
ducks combined?
A 1,000 g
B 2,300 g
C 3,000 g
D 300 g
By answering the presented question, we may conclude that As a result, inequality the correct answer is D) 300 g.
What is inequality?In mathematics, an inequality is a statement that compares two values or expressions and shows the relationship between them, usually using the symbols > (greater than), < (less than), ≥ (greater than or equal to), or ≤ (less than or equal to).
For example, "3 > 2" is an inequality that states that 3 is greater than 2. Similarly, "x ≤ 5" is an inequality that states that the value of x is less than or equal to 5.
Inequalities are used to represent ranges of possible values and are commonly used in algebra, calculus, and other branches of mathematics. They are often used to describe constraints in optimization problems, such as finding the maximum or minimum of a function subject to certain conditions.
To begin, we must convert the weights to the same units. We can convert rabbit weight to grammes as follows:
300 grammes = 0.3 kilos
We can also convert duck weight to grammes:
700 grammes = 0.7 kilos
We can now multiply the weights of rabbits and ducks:
300 grammes plus 700 grammes equals 1000 grammes
300 grammes plus 1300 grammes plus 700 grammes equals 2300 grammes.
To calculate how many more grammes of pellets Al feeds the chickens than the rabbits and ducks combined, subtract the total weight of pellets fed to the rabbits and ducks from the weight of pellets fed to the chickens:
1300 grammes minus 1000 grammes equals 300 grammes
As a result, the correct answer is D) 300 g.
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Mr. Apo Man borrowed K 2 000 from a bank to finance an extension to his home. He agrees to pay back the loan in 8 yearly payments at 14% p.a. compound interest. a) What is the amount of each yearly payment? (2 marks)
If he agrees to pay back the loan in 8 yearly payments at 14% p.a. compound interest. The amount of each yearly payment is K 368.51.
How to find the yearly payment?To calculate the amount of each yearly payment, we can use the formula for the present value of an annuity:
PV = A * [(1 - (1 + r)^-n) / r]
where:
PV = present value of the loan
A = annual payment
r = interest rate per year
n = number of years of the annuity
In this case, Mr. Apo Man borrowed K 2 000 from the bank at an interest rate of 14% p.a. compound interest, and agreed to pay back the loan in 8 yearly payments.
So, we have:
r = 14% = 0.14
n = 8
PV = K 2 000
We can solve for A by rearranging the formula:
A = PV * r / [(1 - (1 + r)^-n)]
Substituting the values, we get:
A = K 2 000 * 0.14 / [(1 - (1 + 0.14)^-8)]
A = K 2 000 * 0.14 / 0.7598
A = K 368.51
Therefore, the amount of each yearly payment that Mr. Apo Man needs to make to repay the loan in 8 years at 14% p.a. compound interest is K 368.51.
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Write the prime factorization of 25 use exponents when appreciate, and order the factors from least to greatest
Answer:5^2
Step-by-step explanation:
25
/ \
5 5
Since both 5 and 5 are prime, it can't be simplified more so the answer is 5^2.
Camila saved 4/5% of her allowance. What is this percent expressed as a fraction and as a decimal
4/5% would easily be represented as 80%. In decimal form, this could be represented as 0.80 or 0.8 if you needed to simplify.
Answer:
Decimal: 0.8
Fraction:4/5
Percent: 80%
8-21. Inspect each data set below and the statement made about it. Each statement is false. Without making any calculations, determine how you can explain or justify that the statement is false. a. "The set of 24, 25, 26, and 28 has a mean of 30." b. "15 is the median of this data set: 12, 14, 15, 13, and 16."
The first statement about mean is false.
The second statement about median is false.
What is mean and median?
The "mean" is the "average" of any data set. Sum of all the data and dividing that by the number of data will give the mean.
The "median" is the "middle" value in the given list of data.
At the first statement the values are 24,25,26,28.
Now the smallest value is 24 and the greatest value is 28. so the average or mean must be in between 24 and 28. It cant exceeds the value 28.
Here given that mean is 30 which is obviously greater than 28. So it cant be the mean of the given data set.
At the second statement the data are 12,14,15,13,16.
The listed values are not in ascending order Without making the values in ascending order we cant find the median. Now if we arrange the values in ascending order the list will be 12,13,14,15,16.
As there are 5 terms so there are odd number of terms. For that the median must be the middle value which is 14.
But here median is 15.
So it cant be the median of the data.
Hence both the statements are false.
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P=$4655, R= 13.83% per year, T=42 months
Answer:
6,908.25$
Step-by-step explanation:
First, convert R to a decimal.
So R=0.1383
Next, 42 months = 3.5 years
A=4655(1+(0.1383 * 3.5)) = 6,908.25275
FIND THE SIZE OF XYZ
The angle of XYZ is approximately 87.6 degrees.
To find the angle of XYZ, you need to use the Law of Cosines, which states that c² = a² + b² - 2ab cos(C), where c is the side opposite the angle C. Given the side lengths of the triangle XYZ, you can find the measure of angle XYZ as follows:
First, use the Pythagorean Theorem to find the length of side XY: XY² = 5² + 12² = 169, so XY = √169 = 13.
Next, use the Law of Cosines to find the measure of angle YXZ: 13² = 7² + 8² - 2(7)(8)cos(YXZ), which simplifies to 169 = 113 - 112cos(YXZ). Solving for cos(YXZ), you get cos(YXZ) = (113 - 169) / (278) = -0.125.
Finally, take the inverse cosine (cos⁻¹) of -0.125 to find the measure of angle YXZ in degrees: YXZ ≈ 102.4°.
Therefore, the measure of angle XYZ is 180° - 90° - 102.4° = 87.6°.
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Calculate the arithmetic mean of these numbers. -12 and 7
Answer:
The arithmetic mean is the simplest and most widely used measure of a mean, or average. It simply involves taking the sum of a group of numbers, then dividing that sum by the count of the numbers used in the series.
Step-by-step explanation:
Therefore, the arithmetic mean of -12 and 7 is -2.5
Where v
is the final velocity (in m/s), u
is the initial velocity (in m/s), a
is the acceleration (in m/s²) and s
is the distance (in meters).
Find v
when u
is 6 m/s, a
is 3 m/s², and s
is 29 meters.
the final velocity is approximately 14.5 meters per second.
Define accelerationThe rate at which an object's velocity alters over time is known as acceleration. It is a vector quantity, which means it has both magnitude (a numerical value) and direction.
Using the formula: v² = u2 + 2as
We can plug in the values given:
u = 6 m/s (initial velocity)
a = 3 m/s² (acceleration)
s = 29 m (distance)
v² = (6 m/s)² + 2(3 m/s²)(29 m)
v² = 36 m²/s² + 174 m²/s²
v²= 210 m²/s²
To solve for v, we need to take the square root of both sides of the equation:
v = √(210 m²/s²)
v ≈ 14.5 m/s (rounded to one decimal place)
Therefore, the final velocity is approximately 14.5 m/s.
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The complete question is:
v²=u²+2as
Where v
is the final velocity (in m/s), u
is the initial velocity (in m/s), a
is the acceleration (in m/s²) and s
is the distance (in meters).
Find v
when u
is 6 m/s, a
is 3 m/s², and s
is 29 meters.
Multiply and simplify the following complex numbers: ( − 4 + 4 � ) ⋅ ( 3 + 2 � ) (−4+4i)⋅(3+2i)
Answer:
Step-by-step explanation:(−4+4i)⋅(3+2i);
= -4(3+2i)+4i(3+2i);
=-12-8i+12i-8;
= -20+4i
5.9 rounded to the nearest tenth
Step-by-step explanation & Answer
5.9 roundest to the nearest ten is:
5.9 .9 is a tenth which can be rounded
But since you said nearest tenth answer is
= 5.9
Look at picture :)
Thus the answer to your problem is, 5.9
Area between curves questions
Answer:
16.739
Step-by-step explanation:
How much will I have by the end of the year if I clean the yards of roughly 6 houses for 25$ every month?
If you clean the yards of 6 houses for $25 every month, you will earn $1,800.
$25/month * 6 houses = $150/month . If you continue earning $150 every month for a year (12 months), then your total earnings for the year will be: $150/month * 12 months = $1,800
Therefore, you will have approximately $1,800 by the end of the year if you clean the yards of roughly 6 houses for $25 every month. However, please note that this assumes that you will be able to consistently clean the yards of all 6 houses every month for the entire year.
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4.) Ayana wants to be a marine biologist when she grows up. Her entire room is
ocean-themed, so she is painting her bed frame blue to match. She estimates
that she will need 800 milliliters of paint, but the hardware store only sells
paint in liters. If Ayana buys 1 liter of paint, how many milliliters will she have
left?
Answer:
200ml
Step-by-step explanation:
1000ml =1l
1000-800=200
A 500g packet of beans costs £1.55
A 125g packet of the same beans costs £0.36
Which packet is better value for money?
The packet is better value for money is a 125 g packet of beans which costs £0.36.
The better value for money of packet of beans can be calculated as follows?The first step we can check on the first packet value for money by calculating the costs of 1 g of beans as follows :
[tex](1/500) \times \£1.55 = \£0,003[/tex]
The second step we can check on the second packet value for money by calculating the costs of 1 g of beans as follows :
[tex](1/125) \times \£0.36 = \£0,0028.[/tex]
Hence, the better value for money between those two packet of beans is the second packet of beans which given by 125 g and costs £0.36.
Answer:
125g
Step-by-step explanation:
Find 1g of beans for both packets
500g /500 = 1
£1.55 / 500 = £0.0031 per gram
125 / 125 = 1
£0.36 / 125 = £0.00288 per gram
0.00288 < 0.0031
125g packet is better value for money
Select the coordinates A′ and B′ after dilation of the line segment AB with a scale factor of 4, centered at the origin where the endpoints are A(−2,−3) and B (−4,−5).(1 point)
Answer: A'(-8,-12); B'(-16,-20)
Step-by-step explanation:
Since the line is scaled about the origin, simply multiplying the points (x,y) by 4 will give you A' and B'.
I need help with this please
The total amount of sugar that was consumed by Kylie in the past nine (9) days is equal to 3 units of sugar.
What is a line plot?In Mathematics and Statistics, a line plot refers a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.
Based on the data and information provided in the line plot shown in the image attached above, we can calculate the total amount of sugar that was consumed by Kylie in the past nine (9) days as follows:
Total sugar consumed = (1/8 + 1/8 + 1/8) + 1/4 + (3/8 + 3/8 + 3/8) + (5/8 + 5/8)
Total sugar consumed = 3(1/8) + 1/4 + 3(3/8) + 2(5/8)
Total sugar consumed = 3/8 + 1/4 + 9/8 + 10/8
Total sugar consumed = 22/8 + 1/4
Total sugar consumed = (22 + 2)/8
Total sugar consumed = 24/8
Total sugar consumed = 3 units of sugar.
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Please help asap, i need it fast
After 13 years, the account will have a balance of $[tex]12,197.97[/tex].
Account balance or bank balance?The final cash amount for just a bank account that appears on the financial statements is known as the bank balance. When a query is made about the bank's records of the cash amount in an account, the bank balance may also be obtained at any time.
Can I utilize the balance on my account?Indeed, as your bank balance balance informs you of the amount of money in your account. That money serves a purpose when you remove or leave in situ, potentially in order to receive interest costs on it.
[tex]A = P (1 + r/n)^{nt}[/tex]
A = final amount
P = initial principal (or investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = time (in years)
Substituting the given values, we have:
[tex]P = 6,759[/tex]
[tex]r = 0.05[/tex]
[tex]n = 2[/tex]
[tex]t = 13[/tex] years
[tex]A = 6,759 (1 + 0.05/2)^{2*13}[/tex]
[tex]A = 6,759 (1.025)^{26}[/tex]
[tex]A = 6,759 (1.80611)[/tex]
[tex]A = 12,197.97[/tex]
Therefore, the account balance after [tex]13[/tex] years will be $[tex]12,197.97[/tex].
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Hi i need help on this question please real answers!
Answer:
0.75
Step-by-step explanation:
0.75
or 3/4
Answer: 3/4
3/8x2= 3/4
Simplify the following
8⁶÷8
Answer: 8^5
Step-by-step explanation:
To simplify this expression, we can use the rules of exponents which state that when we divide two exponential terms with the same base, we can subtract their exponents. So we have:
8⁶ ÷ 8 = 8^(6-1) = 8^5
Therefore, the simplified expression is 8^5.
The table shows the numbers of feet and the equivalent numbers of inches. Lionel painted a wall that is 12 feet long. How many inches long is the wall that Lionel painted?
A. 144
B. 122
C. 156
D. 132
The wall is 144 inches long that Lionel painted
What are unit cοnversiοns?Unit cοnversiοn is the prοcess οf cοnverting οne unit οf measurement tο anοther unit οf measurement that is equivalent tο the οriginal unit.
Given table:
Number οf feet's Number οs inches
3 36
5 60
8 96
10 120
Tο cοnvert feet tο inches, we need tο multiply the number οf feet by 12 since there are 12 inches in οne fοοt.
Fοr 12 feet, we have:
12 feet = 12 x 12 inches = 144 inches
Hence, the answer is A. 144.
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