In order to solve this exercise, you need to use the following property of Radicals:
\(\sqrt[n]{b^n}=b^{\frac{n}{n}}=b^1=b\)Given:
\(\sqrt[]{48}\)The first step is to descompose the Radicand (in this case it is 48) into its prime factors:
\(48=2\cdot2\cdot2\cdot2\cdot3=2^4\cdot3\)Rewrite the Radicand:
\(undefined\)Would you use SSS or SAS to prove the triangles are congruent? If there is not enough information to prove the triangles are congruent, write not enough information. Explain your answer.
The true statement is (c) SSS; two congruent sides are given and the third side is congruent by the Reflexive Property of Congruence.
What is the congruent triangle?Congruent triangles are those that are exactly the same size and shape. Congruent is represented by the symbol ≅ When the three sides and three angles of one triangle match the dimensions of the three sides and three angles of another triangle, they are said to be congruent.
It is given that:
The sides marked with II are congruent.
The triangles are congruent.
Thus, the true statement is (c) SSS; two congruent sides are given and the third side is congruent by the Reflexive Property of Congruence.
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Please look at the photo for the question. Thank you!
The zeros with each multiplicity are given as follows:
Multiplicity one: x = 6.Multiplicity two: x = 11.Multiplicity three: x = -6 and x = -5.How to obtain the multiplicities?The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.
Considering the linear factors of the function in this problem, the zeros are given as follows:
(x + 6)³ -> zero at x = -6 with multiplicity of 3.(x - 11)² -> zero at x = 11 with multiplicity of 2.x - 6 -> zero at x = 6 with multiplicity of 1.(x + 5)³ -> zero at x = -5 with multiplicity of 3.More can be learned about the Factor Theorem at brainly.com/question/24729294
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Which steps are needed to solve this equation? . b + 6 = 21 Subtract 6 from both sides of the equation. The answer is b = 15. Check the solution by substituting 15 for b. Subtract 6 from the left side and add 6 to the right side of the equation. The answer is b = 27. Check the solution by substituting 27 for b. Add 6 to both sides of the equation. The answer is b = 27. Check the solution by substituting 27 for b. Add 6 to the left side and subtract 6 from the right side of the equation. The answer is b = 15. Check the solution by substituting 15 for b. edge
The solution by substituting 15 for b in the Original equation. The answer is true.
The steps needed to solve the equation b + 6 = 21 are:
Subtract 6 from both sides of the equation: b + 6 - 6 = 21 - 6, which simplifies to b = 15.
Check the solution by substituting 15 for b in the original equation: 15 + 6 = 21, which is true.
Therefore, the correct steps to solve the equation are:
Subtract 6 from both sides of the equation. The answer is b = 15
the solution by substituting 15 for b in the original equation. The answer is true.
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Question 1 of 15 What is the solution to this equation? X-9 = 5 A. x = -4 OB. X= 14 OC. x = 4 O D. x = -14
Answer:
B. x = 14
Step-by-step explanation:
1. Add 9 to both sides of the equation
x - 9+9 = 5+9
x = 14
hope this helps :)
Ingredients 12 slices of bacon 34 of a cup of popcorn kernels stick of butter 3 tablespoons pure maple syrup
Answer:
Is this a question? A recipe? Or a challenge?
Step-by-step explanation:
Simplify the variable expression by evaluating its numerical part, and enter
your answer below.
(48-17) - w
Answer here
SUBMIY
The simplified version of the expression would be 31-w
The numerical part of the expression given is :
48-17Simplifying using Subtraction operation:
48-17 = 31Adding the alphabetical part :
31 - wTherefore, the simplified form of the expression is 31-w.
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A motorist travels 228 kilometers in 6 hours. At that rate, how long will it take him to travel and additional 247 kilometers?
Answer:
The motorist's rate is:
rate = distance / time
where distance is measured in kilometers and time is measured in hours.
We are given that the motorist travels 228 kilometers in 6 hours, so we can use this information to find the rate:
rate = distance / time = 228 km / 6 hours = 38 km/hour
To find how long it will take the motorist to travel an additional 247 kilometers at this rate, we can use the same formula and solve for time:
time = distance / rate = 247 km / 38 km/hour ≈ 6.5 hours
Therefore, it will take the motorist approximately 6.5 hours to travel an additional 247 kilometers at the same rate of 38 km/hour.
Gerald is thinking of a number n, and he wants his sister to guess the number. His first clue is that 7 more than 3 times his
number is at least 10 and at most 28. Write a compound inequality that shows the range of numbers that Isabella might be
thinking of.
Write your answer in interval notation. For example-3
Answer:
(1, 7)
Step-by-step explanation:
The number is n.
7 more than 3 times his
number is at least 10 and at most 28.
Thus;
10 ≤ 3n + 7 ≤ 28
Let's solve individually;
10 ≤ 3n + 7
10 - 7 ≤ 3n
n ≥ 3/3
n ≥ 1
Also,
3n + 7 ≤ 28
3n ≤ 28 - 7
3n ≤ 21
n ≤ 21/3
n ≤ 7
Thus, since n cannot be more than 7 or less than 1, it means in interval Notation, the answer is;
(1, 7)
Jeremy's boss increased his salary from $8 per hour to $12 per hour. By
what percent did his hourly wages increase?
Answer:
1.5 percent
Step-by-step explanation:
Joy borrowed $2,000 from the bank and agreed to pay an annual interest rate of 6%for 24 months. What is the amount Of interest she will pay on this loan?
Answer:
2,240
Step-by-step explanation:
6% of 2,000 is 120 so times that by 2
Answer:
$240.00
Step-by-step explanation:
2000(.06)(2)=240
In a recent year, 29.7% of all registered doctors were female. If there were 42,300 female registered doctors that year, what was the total number of registered doctors?Round your answer to the nearest whole number.
ANSWER
142,424 doctors
EXPLANATION
We have that 29.7% of all registered doctors were female and 42,300 female doctors were registered that year.
Let the total number of registered doctors that year be x.
This means that 29.7% of x is 42,300.
Therefore:
\(\begin{gathered} \frac{29.7}{100}\cdot\text{ x = 42300} \\ \text{Divide both sides by 29.7 and multiply by 100:} \\ x\text{ = }\frac{\text{42300 }\cdot\text{ 100}}{29.7} \\ x\text{ }\cong\text{ 142,424 doctors} \end{gathered}\)A total of 142,424 doctors were registered that year.
Which of the exponential growth functions has a multiplicative rate of change of 4? A 2-column table has 4 rows. The first column is labeled x with entries negative 1, 0, 1, 2. The second column is labeled f (x) with entries one-half, 1, 2, 4. A 2-column table has 4 rows. The first column is labeled x with entries negative 1, 0, 1, 2. The second column is labeled f (x) with entries one-eighth, 1, 8, 64. A 2-column table has 4 rows. The first column is labeled x with entries negative 1, 0, 1, 2. The second column is labeled f (x) with entries one-fourth, 1, 4, 16.
Answer:
3rd graph
Step-by-step explanation:
edge
Answer:
it is c, the third graph
Step-by-step explanation:
Find the decimal number halfway between the following decimal numbers: 0.5 and 0.5.
Answer:
Step-by-step explanation:
it would be 15.16
2. Increasing the minimum wage has not traditionally caused massive unemployment though traditional economists have argued that it should. Why have changes to minimum wage not affected unemployment too much?
3. The US has one of the lowest federal minimum wages compared to other developed nations. Can you think of reasons why this might be?
4. The real minimum wage has fallen over time with the rise of inflation. This represents less purchasing power for minimum wage workers. Are you ok with that? Why or why not? How many people actually earn at or near minimum wage?
Despite traditional economic theory suggesting that an increase in the minimum wage should lead to unemployment, the actual impact on employment has been more nuanced. Empirical evidence suggests that moderate increases in the minimum wage have not led to massive job losses, but rather have resulted in small increases in labor costs that are offset by increased productivity and reduced employee turnover. Additionally, higher wages can increase consumer spending, leading to an increase in demand for goods and services, which can ultimately create more jobs.
There are several reasons why the federal minimum wage in the US is lower than in other developed countries. One reason is the political climate in the US, where there is often resistance to government intervention in the labor market. Additionally, many US states have their own minimum wage laws, which can be higher than the federal minimum wage. Finally, the US has a large low-skilled immigrant workforce, which can put downward pressure on wages.
I am not okay with the real minimum wage falling over time with the rise of inflation. Inflation erodes the purchasing power of workers, making it difficult for them to make ends meet. This can lead to increased financial hardship, which can have negative effects on individuals and families. Furthermore, the minimum wage was originally designed to ensure that workers earn a living wage, which is a basic necessity for a decent standard of living. As such, it is important that the minimum wage keep pace with inflation.
According to the Bureau of Labor Statistics, in 2021, about 1.9 million workers in the US earned at or below the federal minimum wage of $7.25 per hour. However, many more workers earn slightly above the minimum wage, and an increase in the minimum wage could potentially raise wages for those workers as well. Additionally, many states have higher minimum wage rates than the federal minimum wage, which means that the number of workers affected by changes to the minimum wage will vary depending on the state.
~~~Harsha~~~
3 Mallie purchases a $12,000 car by taking out a loan. She will pay an 8% sales tax on the price of the car. She has also agreed to pay the loan plus tax back within 36 months at a simple Interest rate of 5%. Find each value listed in the table below, as well as the minimum monthly payment Mallie should make in order to repay the loan within the allotted time. Use the space provided to show your process.
PLEASE PLEASE HELP!! A ferris wheel with a radius of 38 feet rotates at a rate of 8 revolutions per minute. The height above the ground of the carriage labeled C below is a function of time, t, in minutes
) Emily baked a cake in 42.5 minutes. She finished making dinner 9 1/10 minutes sooner than the cake. How long did it take her to make dinner? Hint: Change the 9 1/10 to a decimal
It took Emily 33.4 minutes to make dinner.
Define a mixed number?A mixed number is a kind of fraction that also has a proper fraction and a whole number. The number of whole units is represented by the whole number, and the fraction of a unit is represented by the proper fraction.
To solve the problem, we have to convert the mixed number \(9 \frac{1}{10}\) to a decimal number:
⇒ \(9 \frac{1}{10} = 9 +\frac{1}{10} = \frac{(9*10)+1}{10}\)
⇒ \(\frac{91}{10}\) = 9.1
This means that Emily finished making dinner 9.1 minutes sooner than the cake.
To find out how long it took Emily to make dinner, we can subtract 9.1 from the cake baking time:
⇒ 42.5 - 9.1 = 33.4 minutes
Therefore, it took Emily 33.4 minutes to make dinner.
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Arrange the integers 1,4,8,12,17,32 so that all consecutive integers add to a perfect square. Enter your answer with numbers separated by commas.
One possible answer is: 1, 8, 17, 32, 4, 12
I don't know if there's a methodical way to get this answer. I used trial and error. I started with 1 and looked through the list to see what adds to 1 to get a perfect square. That would be 8 since 1+8 = 9 = 3^2
The process is repeated but this time for 8. After a bit of guess and checking, we see that 8+17 = 25 = 5^2.
Then after 17 is 32 because 17+32 = 49 = 7^2.
Keep doing this until all of the values are used up. If you get stuck, then try backtracking to a previous branch/path where everything worked and try another fork in the road. If that doesn't work, then try starting the sequence with a completely different value (instead of 1).
Other answers may be possible. I haven't checked all possible permutations.
The sum of two consecutive odd integers in 680
Consecutive numbers are numbers next to one another.
The odd numbers are 339 and 341
Let the smaller number be x.
So, the next number will be x + 2
The sum of the two numbers is:
\(\mathbf{x + x + 2 = 680}\)
\(\mathbf{2x + 2 = 680}\)
Subtract 2 from both sides
\(\mathbf{2x= 678}\)
Divide both sides by 2
\(\mathbf{x= 339}\)
So, the numbers are 339 and 341
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What is the value of the underlined digit: 498,217 *
Answer:
B.) 90.000
Step-by-step explanation:
Your pre-selected answer choice is correct. The 9 is in the Ten Thousands place.
You have several numbers in a data set: 5, 7, 9, 11, 13, 15, 17. What is the z Score for the number 15? (the SD is 4.32)
The value of the z-score for the number 15 in a data set is 0.93.
Define z-score.
A data point's z-score, also known as a standard score, indicates how far it deviates from the mean. In practical terms, however, it's a measurement of how many standard deviations a raw number is from or above the population mean.
You can plot a z-score on a normal distribution graph. Z-scores can be anywhere between -3 and +3 standard deviations.
∴ z = (x – μ) / σ
Given:
σ = 4.32
x = 15
Data set: 5, 7, 9, 11, 13, 15, 17
So, mean = 5 + 7 + 9 + 11 + 13 + 15 + 17/7
= 77/7
μ = 11
z = (x – μ) / σ
= (15 - 11)/4.32
= 4/4.32
z = 0.93
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factor step by step:
x^2+1
Answer:
(x + i) (x - i)
Step-by-step explanation:
The expression x^2 + 1 is a sum of squares, which means that it cannot be factored using real numbers. However, it can be factored using complex numbers.
To factor x^2 + 1, we can use the fact that i^2 = -1, where i is the imaginary unit.
We can rewrite x^2 + 1 as:
x^2 + 1 = x^2 - (-1)
Now, we can use the difference of squares formula to factor x^2 - (-1):
x^2 - (-1) = (x + i)(x - i)
Therefore, the factored form of x^2 + 1 is:
(x + i)(x - i)
Write an exponential equation, given initial population of 2500 and doubling time of 2 years
A population of 32,000 with a 5% annual growth rate would be modeled by the equation:
y=32000(1.05)t
with t in years.
8. Triangle JKL with vertices J(-2, 3), K(2, 4),
and L(6, -1): (x, y) → (x - 2, y - 6)
The resulting coordinate of the vertices after the translation is J'(-4, -3), K'(0, -2), and L'(-4, -7)
Given the vertices of a triangle given as J(-2, 3), K(2, 4), and L(6, -1)
If the coordinates are translated using the rule (x, y) → (x - 2, y - 6), the resulting coordinate will be derived by shifting 2 units left and downward by 6 units
J' = (-2-2, 3-6) = (-4, -3)
K' = (2-2, 4-6) = (0, -2)
L' = (2-6, -1-6) = (-4, -7)
Hence the resulting coordinate of the vertices after the translation is J'(-4, -3), K'(0, -2), and L'(-4, -7)
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The sum of two triangles is 136 degrees. How many degrees is the third angle
Answer:
44°
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesGeometry
All angles in a triangle add up to 180°Step-by-step explanation:
Step 1: Set up Equation
136° + x° = 180°
Step 2: Find missing angle
Subtract 136 on both sides: x = 44The measure of an angle is 35.4°. What is the measure of its supplementary angle?
Answer:
144.6°
Step-by-step explanation:
180-35.4
144.6°
Answer:
144.6
Step-by-step explanation:
Supplementary angles add to 180
Let x be the unknown angle
x + 35.4 = 180
Subtract 35.4 from each side
x = 180-35.4
x =144.6
Each can of tennis balls has $x$ balls. Initially, Sam has 14 cans of tennis balls, plus 3 extra balls. Jerri initially has 7 cans of tennis balls, plus 8 extra balls. If Jerri doubles the number of tennis balls she has, how many more balls will she have than Sam has?
NEED ASAP PLS
Answer:
13balls
Step-by-step explanation:
2(7x+8)-14x+3=? distribute
14x+16-14x+3 do like terms
14x-14x cancel
16-3 =13
it may seem confusing in the explanation but i hope that helps.
Mrs. Postler’s dinner costs $36.00. She wants to leave 20% tip. How much money should Mrs. Postler leave to cover her bill and tip?
Answer:
43.2
Step-by-step explanation:
so you would multiply 36 by .20 or .2 and you would get a answer so you add it to your original amount
The sum of two consecutive numbers is
27. Find the two numbers.
Answer: 14 and 14
Step-by-step explanation:
So u would Since 13 and 14 are both consecutive integers and their sum is 27, we have our answer.
Ally picked 25 roses. She gave away 10 roses. What percent of the roses does Ally still have?
Answer:
She still has 60%
Step-by-step explanation:
First you make the 25 a 100 which is basically multiply by 4 which you should do the same for 10
so 40/100 is how much she game away
She gave away 40%
She still has 60%
The percent of the roses does Ally still have is 60%.
Given that,
Ally picked 25 roses. She gave away 10 roses.
Based on the above information, the calculation is as follows:
\(= \frac{25-10}{25}\)
= 60%
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