The vertex represents the minimum value of the function. The vertex, in this case, is (-4, 7), which is the point where the function reaches its minimum value of 7.
The vertex represents the minimum value of the function because the coefficient of the squared term is positive, which means that the parabola opens upwards, and the vertex is the lowest point on the curve.
To find the vertex of the parabola, we can use the formula x = -b/2a, where a is the coefficient of the squared term, b is the coefficient of the linear term, and c is the constant term. In this case, a = 1, b = 8, and c = 23, so x = -8/2 = -4.
Substituting x = -4 into the function g(x) gives us g(-4) = (0)^2 + 7 = 7. Therefore, the vertex of the parabola is (-4, 7), which is the point where the function reaches its minimum value of 7.
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How do I get the percentage of numbers. Pls give examples
Answer:
divide by hundred
Step-by-step explanation:
example :
convert to percentage 300
300÷ 100= 3%
Aubrey is flying a kite, holding her hands a distance of 2.5 feet above the ground and letting all the kite’s string play out. She measures the angle of elevation from her hand to the kite to be 25
∘
∘
. If the string from the kite to her hand is 150 feet long, how many feet is the kite above the ground? Round your answer to the nearest hundredth of a foot if necessary.
Using trigonometric ratio, the height of kite above the ground is approximately 65.90 feet.
What is trigonometric ratio?
Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios.
Distance of hand above the ground = 2.5 feet
String length form hand = 150 feet
Angle of elevation = 25°
We can use the sine function of trigonometric ratios to solve this problem.
The formula for sine function is -
sin θ = opposite / hypotenuse
Let's call the height of the kite above the ground "h".
Then we have -
sin (25°) = (h - 2.5) /150
0.42261 = (h - 2.5) /150
(h - 2.5) = 63.392
h = 65.892
Rounding to the nearest hundredth of a foot, we get -
h ≈ 65.90 feet
Therefore, the kite is about 65.90 feet above the ground.
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In a group of 15 children, 5 said they are an only child, 3 said they have 1 sibling only, 4 said they have exactly 2 siblings, and 3 said they have exactly 3 siblings.
What is the average number of siblings for this group?
Enter your answer as a decimal, rounded to the nearest tenth, in the blank.
The average number οf siblings fοr this grοup is 1.3.
Tο find the average number οf siblings fοr this grοup, we need tο calculate the tοtal number οf siblings and divide by the tοtal number οf children.
The 5 children whο said they are an οnly child have 0 siblings each, sο they cοntribute 0 tο the tοtal.
The 3 children whο said they have 1 sibling οnly have 1 sibling each, sο they cοntribute 3 tο the tοtal.
The 4 children whο said they have exactly 2 siblings have 2 siblings each, sο they cοntribute 8 tο the tοtal.
The 3 children whο said they have exactly 3 siblings have 3 siblings each, sο they cοntribute 9 tο the tοtal.
Therefοre, the tοtal number οf siblings is 0 + 3 + 8 + 9 = 20.
The tοtal number οf children is 15.
Sο, the average number οf siblings is 20/15, which is apprοximately 1.3 (rοunded tο the nearest tenth).
Therefοre, the average number οf siblings fοr this grοup is 1.3.
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The value of (– 5)2 x (-5)-2 + (-5)2
is:
Answer:50x-12
Step-by-step explanation:
We need to get rid of parentheses in this term.
All the negative factors will change sign.
In our example, we have 2 negative factors.
The sign of the term will not change, since there is an even number of negative factors.
How much of a 8% salt solution must combined with a 20% salt solution to make 4 gallons of a 15% salt solution? Step 1 of 3 : Identify the variable. Let x= number of gallons of salt solution to add. A
In response to the supplied query, we may state that Consequently, to equation create 4 gallons of a 15% salt solution, we must combine 1.67 gallons of the 8% salt solution with 2.33 gallons of the 20% salt solution.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
We know that 0.08x gallons of salt, or 8% of x gallons, is in the 8% salt solution.
Since we are adding x gallons of the 8% salt solution to a total of 4 gallons of the final solution, we know that 20% of (4 - x) gallons is salt, or 0.2(4 - x) gallons of salt, for the 20% salt solution.
0.08x + 0.2(4 - x) = 0.15(4) (4)
We can condense things and find x:
0.08x + 0.8 - 0.2x = 0.6
-0.12x = -0.2
x = 1.67
Consequently, to create 4 gallons of a 15% salt solution, we must combine 1.67 gallons of the 8% salt solution with 2.33 gallons of the 20% salt solution.
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you flip a coin 16 times and get heads 7 times. based on this experiment, what is the probability of flipping a coin and getting tails? select the correct answer below:
The probability of flipping a coin and getting tails is 50%.
This is because in a fair coin toss, there is an equal chance of getting heads or tails. This means that the probability of each outcome is 50%.
To prove this experimentally, you flipped the coin 16 times and got heads 7 times. This means that out of the 16 times, you got heads 7 times and tails 9 times. Therefore, the probability of getting tails is 9/16, which is the same as 50%.
In general, the probability of flipping a coin and getting tails is always 50%, no matter how many times the coin is flipped or what the result of previous flips were. This is because each flip of the coin is an independent event and has the same probability of being heads or tails.
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quesrion is 6q-12 =84 and the way
Answer:
16
Step-by-step explanation:
6q-12=84
6q=96
q=16
Answer:
q = 16
Step-by-step explanation:
First Step: Add 12 to both sides. giving you 96.
Second Step: Divide both sides by 6 giving you 16.
Solution: q = 16.
Pls answerrrrr
with simple working
Question: Is -451 in the sequence bellow?
15, 7, -1, -9, -17, ...
-451 not in the sequence
Numerical sequenceThis question involves the concepts of arithmetic progression.
Which consists of adding the previous term to a certain ratio (r), which will be found the next term.
Let's seeData to calculate
r = 7-15=-8
an = -451
a1= 15
n=?
[tex]\begin{array}{l}\sf a_{n} = a_{1} + ( n-1 )r\\\sf -451 = 15 + ( n-1 )\times(-8)\\\sf -451=15-8x+8\\\sf -451 = 23-8n\\\sf 8n=23+451\\\sf 8n=474\\\sf n=\dfrac{474}{8}\\\sf n=59{,}25\end{array}[/tex]
The result is not an integer, so -451 is not part of the sequence
what is the value of x
Answer:
D. x = 20
Step-by-step explanation:
All angles equal 180°
x + 5 + 7x -5 + x = 180
Combine like terms
9x = 180
Divide both sides by 9
x =20
Please help find values of c and b.
Answer:
c = 21b = -12Step-by-step explanation:
You want the coefficients of the quadratic with roots (3±2i√3)/2 and a leading coefficient of 4.
CoefficientsThe value b/a is the opposite of the sum of the roots.
b/a = -((3+2i√3)/2 +(3-2i√3)/2) = -(3/2 +3/2) = -3
b = -3a = -3(4)
b = -12
The value c/a is the product of the roots. This will be the difference of squares:
c/a = (3+2i√3)/2 × (3-2i√3)/2 = (3² -(2i√3)²)/4 = (9 +12)/4 = 21/4
c = a(21/4) = (4)(21/4)
c = 21
I need help with payroll accounting. Its in an excel format for multiple months
By following the steps outlined below, you can create a payroll payslip that provides all of the necessary information and helps ensure that your employees are paid accurately and on time.
Open Excel and create a new workbook. In the first row, create headings for the different columns you will need, such as "Employee Name," "Employee ID," "Pay Period," "Gross Pay," "Deductions," "Net Pay," and so on.
Enter the employee's name, ID, and pay period in the appropriate cells.
Calculate the employee's gross pay. Gross pay is the total amount of money the employee earned before any deductions are taken out.
Calculate the employee's deductions. Deductions are the amounts that are taken out of the employee's pay, such as taxes, social security, health insurance, and so on.
Calculate the employee's net pay. Net pay is the amount of money the employee receives after all deductions are taken out. To calculate this, subtract the total amount of deductions from the gross pay.
Once you have calculated all of the necessary amounts, enter them into the appropriate cells on the payslip.
Finally, you can customize the payslip by adding your company logo, address, and other relevant information. You can also format the cells to make the payslip look more professional.
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Complete Question:
How do I create a payroll payslip in Excel?
SOMEONE HELP PLS IF YOU GET ALL OF THE BLANKS RIGHT I'LL GIVE BRAINLIEST AND FIVE STAR
Two trains simultaneously left points M and N and headed toward each other. The distance between point M and N is 380mi. The speed of the train, which started, from point N was 5 mph faster than the speed of the other train. In two hours after the departure the distance between the trains was 30 mi. What is the speed of each train?
Answer: the speed of the train that started from point M is 92.5 mph, and the speed of the train that started from point N is 97.5 mph (92.5 + 5).
Step-by-step explanation:
Let's use the following variables:
x = speed of the train that started from point M
x + 5 = speed of the train that started from point N
We know that:
The total distance between the trains is 380 miles.
In 2 hours, the distance between the trains decreased by 30 miles.
Using the formula: distance = rate x time, we can write two equations:
Equation 1: 2x + 2(x + 5) = 380 (the sum of the distances traveled by the two trains equals the total distance between them)
Equation 2: 2x - 2(x + 5 - 30/2) = 30 (the difference in distances traveled by the two trains in 2 hours equals the decrease in distance between them)
Simplifying Equation 1:
4x + 10 = 380
4x = 370
x = 92.5
Therefore, the speed of the train that started from point M is 92.5 mph, and the speed of the train that started from point N is 97.5 mph (92.5 + 5).
To check, let's substitute these values into Equation 2:
2(92.5) - 2(97.5 - 30/2) = 30
185 - 155 = 30
30 = 30
This confirms that our solution is correct.
In a given city, the probability it doesn’t rain is 0.75 and we find that 40 percent of people carry and umbrella when it’s not raining. What is the probability that a person is carrying an umbrella given that it’s not raining? Round your answer to at least 4 decimal places.
Given that it is not raining, there is a [tex]10.67[/tex]% probability that a man is holding an umbrella, or around [tex]0.1067[/tex].
Is probability simple or complex?As probabilistic arguments sometimes produce outcomes that appear contradictory or counterintuitive, probability is usually regarded as one of the most challenging topics of mathematics.
How do you teach students about probability?Probability is the likelihood that something will occur or the probability that something will happen. Probability is the measure of how probable it is that a coin will land heads up after being tossed into the air.
To find [tex]P(B|A)[/tex],
[tex]P(B|A) = P(A and B) / P(A)[/tex]
[tex]P(B|A) = P(A|B) * P(B) / P(A)[/tex]
Putting it all together,
[tex]P(A|B) = P(B|A) * P(A) / P(B)[/tex]
[tex]= [P(A|B) * P(B)] / P(A)[/tex]
[tex]= [P(A and B) / P(B)] * P(A) / P(A)[/tex]
[tex]= P(A and B) / P(B)[/tex]
Therefore,
[tex]P(B|A) = P(A and B) / P(A)[/tex]
[tex]= P(A) * P(B|A) / P(B)[/tex]
[tex]= 0.4 * (1 - 0.75) / 0.75[/tex]
[tex]= 0.1067[/tex]
So the probability that a person is carrying an umbrella given that it's not raining is approximately [tex]0.1067[/tex], or about [tex]10.67[/tex]%.
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Two shops, Waitroze and Budgins sell the same brand of cans of soup but with different offers. Calculate the price for one tin at each shop. Round your answer to the nearest penny. Write which shop is better value for money in the comment box.
Answer:
Step-by-step explanation:where are you ???
If you start a bank account with 15000 and your bank compound the interest monthly at an interest rate of 9% p. A. How much money do you have at the year's end assume that you do not add or withdraw any money to/from the account
At the end of 1 year, the amount in the account will be 16443.4. To sum up, compound interest is a type of interest calculated on the initial principal and the accumulated interest of the previous periods.
The formula for calculating compound interest is [tex]A = P (1 + r/n)^nt,[/tex]where A is the future value of the account, P is the principal amount, r is the interest rate, n is the number of times the interest is compounded per year and t is the number of years.In the given case, the principal amount is 15000, the interest rate is 9% per annum and the number of times the interest is compounded is 12. Therefore, the future value of the account at the end of 1 year will be[tex]A = 15000 (1 + (9/100)/12)^12x1 A = 15000 (1 + 0.0075)^12A = 15000 (1.0075)^12 A = 15000 x 1.0956A = 16443.4[/tex]Therefore, at the end of 1 year, the amount in the account will be 16443.4. . In the given case, the future value of the account at the end of 1 year will be 16443.4.Step 1:Calculate the monthly interest rate:Interest rate per month = [tex]9% / 12 = 0.75%[/tex],Step 2:Calculate the total amount at the end of the year:Total amount =[tex]15000 x (1 + 0.75%) ^ 12[/tex] Total amount = 15000 x 1.0975, Total amount =[tex]$16,462.50[/tex]
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On a school trip the ratio of staff to students is 1:10. All of the students are either from year 7 or 8. The ratio of y8 to y7 is 3:2. What fraction are y7?
The fraction of Year 7 students can be found by dividing y7 by the total number of students, which is 11 times the number of staff members; using the ratio of y8 to y7, we get y7/(11S) = 5/8.
Let's denote the number of staff members as S and the number of students as T. Since the ratio of staff to students is 1:10, we have:
S:T = 1:10
We can rewrite this as S = (1/11)T and T = 11S, where S is the number of staff members and T is the total number of students.
Let's denote the number of Year 7 students as y7 and the number of Year 8 students as y8. Since all students are either in Year 7 or Year 8, we have:
[tex]y7 + y8 = T[/tex]
Substituting T = 11S, we get:
[tex]y7 + y8 = 11S[/tex]
The ratio of y8 to y7 is 3:2, which means that:
[tex]y8:y7 = 3:2[/tex]
We can rewrite this as y8 = (3/5)y7. Substituting this expression into the equation y7 + y8 = 11S, we get:
[tex]y7 + (3/5)y7 = 11S[/tex]
Simplifying, we get:
[tex](8/5)y7 = 11S[/tex]
Dividing both sides by 11S, we get:
[tex]y7/(11S) = 5/8[/tex]
Therefore, the fraction of Year 7 students is 5/8.
The ratio of staff to students is 1:10, so S:T = 1:10, which can be rewritten as S = (1/11)T and T = 11S.
Let y7 and y8 be the number of Year 7 and Year 8 students, respectively. Then y7 + y8 = 11S.
The ratio of y8 to y7 is 3:2, so [tex]y8 = (3/5)y7[/tex].
Substituting [tex]y8 = (3/5)y7[/tex] into [tex]y7 + y8 = 11S[/tex], we get [tex](8/5)y7 = 11S[/tex].
Dividing both sides by 11S, we get [tex]y7/(11S) = 5/8[/tex].
Therefore, the fraction of Year 7 students is 5/8.
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Jennifer bought 14. 75 gallons of gasoline for her car at a cost of $2. 95 a gallon. Which is closest to the amount she paid for the gasoline? HELPPP
The amount Jennifer paid for the gasoline is closest to $43.51.
This is because we can multiply the number of gallons by the cost per gallon to get the total cost, which in this case is 14.75 x 2.95 = 43.5125. Rounding this to two decimal places, we get $43.51, which is the closest answer option.
In general, when calculating the total cost of gasoline, we need to know the number of gallons purchased and the cost per gallon. These two values can be multiplied together to find the total cost of the gasoline. So here the answer is $43.51.
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How does the value of a in the function effect is graph when compared to the graph of the quadratic parent function G parenthesis experience disease equals 22X squared 2
Changing the value of 'a' changes the shape, position, and concavity of the graph of the function.
What is function?In mathematics, a function is a rule that assigns to each element in a set (called the domain) a unique element in another set (called the range or codomain).
Stretching or compressing the graph: If 'a' is greater than 1, the graph of the function will be stretched vertically, making it thinner and taller. If 'a' is between 0 and 1, the graph will be compressed vertically, making it wider and shorter. If 'a' is negative, the graph will be upside down.
Shifting the graph: If 'a' is positive, the graph will be shifted up or down depending on the value of 'a'. If 'a' is negative, the graph will be shifted down or up.
Changing the concavity of the graph: The graph of the parent function G(x) is an upward-facing parabola, which means it has a positive concavity. If 'a' is positive, the graph of the function will also have a positive concavity. If 'a' is negative, the graph of the function will have a negative concavity, which means it will be a downward-facing parabola.
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A park ranger counted the number of squirrels he saw while giving tours in three sections of a national park that have different areas.
Determine the unit rate in terms of the number of squirrels per square mile in the park, and complete the sentences below. Assume the relationship of squirrels to square miles shown in the table can be extended to the entire park.
Fill in the Blank.
The park ranger counted ___ squirrels for every mile in the park.
For every 128 square miles in the park, the park ranger would count ___ squirrels.
For every ___ square miles in the park, the park ranger would count 324 squirrels.
Area is a measure of the size of a two-dimensional surface or region. It is typically measured in square units, such as square meters or square feet. The area of a shape is found by multiplying the length and width of the shape in most cases, although the formula for finding the area may vary depending on the shape.
In the given question,
To find the unit rate in terms of the number of squirrels per square mile, we need to divide the total number of squirrels by the total area of the park.
Total number of squirrels = 20 + 32 + 128 = 180
Total area of the park = 5 + 8 + 32 = 45
Unit rate of squirrels per square mile = 180/45 = 4 squirrels per square mileFor every 128 square miles in the park, the park ranger would count 512 squirrels. (4 squirrels per square mile x 128 square miles = 512 squirrels)For every 40 square miles in the park, the park ranger would count 324 squirrels. (4 squirrels per square mile x 40 square miles = 160 squirrels)Note: The last blank can be filled with 40, as shown above.
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Answer:
1. 4
2. 512
3. 81
Step-by-step explanation:
Explore the categorical predictors (excluding the first four)by computing the average fare in each category and using boxplots. Which categorical predictor seems best for predicting fare?
The 'Pclass' predictor seems to be the best predictor of fare, as it was seen that the average fare increases as the passenger class increases.
The average fare in each category can be calculated by calculating the average fare for each category of the categorical predictors (excluding the first four). For example, for the 'Sibsp' predictor, the average fare can be calculated by taking the sum of all fares for each category and dividing it by the total number of passengers in that category.
The boxplots can then be used to visualize the average fares for each category of the categorical predictors. From the boxplots, it can be seen that the 'Pclass' predictor seems to be the best predictor of fare, as the average fare increases as the passenger class increases. Specifically, the average fare for passenger class 1 is much higher than that for passenger class 2 and 3, confirming that 'Pclass' is the best predictor of fare.
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Complete question:
Which categorical predictor is most effective for predicting the fare of an airline ticket?
Let A and B be events with P(A)=0.6, P(B)=0.4, and P(B|A)=0.4. Find P(A and B)
The value of P(A and B) is 0.24.
What is Conditional probability?
Conditional probability is a type of probability that describes the likelihood of an event occurring given that another event has already occurred. It is calculated by dividing the probability of the joint occurrence of both events by the probability of the occurrence of the event that has already occurred.
More formally, if we have two events A and B, the conditional probability of event A given event B is denoted by P(A|B) and is defined as:
P(A|B) = P(A and B) / P(B)
We are given :
P(A)=0.6, P(B)=0.4, and P(B|A)=0.4
We can use the formula for conditional probability to solve :
P(B|A) = P(A and B) / P(A)
We can write it as :
P(A and B) = P(B|A) * P(A)
Now, Substituting in the given values, we get:
P(A and B) = 0.4 * 0.6 = 0.24
Therefore, the probability of both events A and B occurring is 0.24.
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True or false: f(x) represents a function.
f(x)
• A. False
• B. True
Answer:
• B. True
Step-by-step explanation:
Answer each for 100 points
Step-by-step explanation:
1. 36g+9-5g=31g+9
2. 12x-4g+4x=16x-4g
3. 15h-6g
4. 2h-6g
5. 60g-20f
Answer:
31g+9, 16x-4g,15h-6g, 2h-6g, 20(3g-f)
Step-by-step explanation:
Q.1 9(4g+1)-5g=36g+9-5g
=31g+9
Q.2 4(3x-g)+4g=12x-4g+4x
=16x-4g
or 4(4x-g)
Q.3 3(5h-2g)=15h-6g
Q.4 2(h-3g)=2h-6g
Q.5 5(12g-4f)=60g-20f
or =20(3g-f)
find area of compound shape
Answer:
110
Step-by-step explanation:
Basically, in area, we do length x width.
So, All we had to do is do 11 (length) x 10 (width)
And the answer is 110!
(I think this is right?)
HELP ASAP is the relationship between the amount of dry dog food and the amount of wet dog food proportional the numbers are for dry god food (cups) (Y) there 4.5 6 9
for wet dog food (oz) (x) SHOW WORK THX
Yes, there is direct relatiοn in amοunt οf dry dοg fοοd and the amοunt οf wet dοg fοοd.
If amοunt οf dry dοg fοοd is x and the amοunt οf wet dοg fοοd is y then the relatiοn is given as: x = 3y
Hοw tο find the prοpοrtiοnality?Tο determine whether the relatiοnship between the amοunt οf dry dοg fοοd and the amοunt οf wet dοg fοοd is prοpοrtiοnal, we need tο check whether the ratiο οf the twο quantities remains cοnstant.
A) yes, there is direct relatiοn in amοunt οf dry dοg fοοd and the amοunt οf wet dοg fοοd. as amοunt οf dry dοg fοοd increases there alsο increase in amοunt οf wet gοοd.
if amοunt οf dry dοg fοοd is x and the amοunt οf wet dοg fοοd is y then the relatiοn is given as:
x = 3y
fοr example lets take values frοm first rοw
4.5 = 3 × 1.5
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Complete question:
Find the exact value of x
The exact value of x is ±8√2. However, since x represents a length, the positive square root is the appropriate solution. Thus, x = 8√2.
Describe Triangle?A triangle is a two-dimensional geometric shape that is formed by three straight lines or segments that connect three non-collinear points. These points are called the vertices of the triangle, and the line segments are called its sides. The sides of a triangle may be of different lengths and can form different angles with each other.
Let the side of the triangle be AB, and let the perpendicular from C to AB divide AB into segments of length 4 and 16, with the shorter segment adjacent to A. Let the foot of the perpendicular be D. Then, we have:
AC = 4 + 16 = 20 (by the segment addition postulate)
AD = 4 (given)
CD = 16 (given)
By the Pythagorean theorem, we have:
AC² = AD² + CD²
Simplifying and substituting the values we have:
20² = 4² + 16²
400 = 16 + 256
400 = 272 + x² [where x is the height of the perpendicular]
Subtracting 272 from both sides, we get:
128 = x²
Taking the square root of both sides (since x cannot be negative), we get:
x = ±√128
Simplifying:
x = ±8√2
Therefore, the exact value of x is ±8√2. However, since x represents a length, the positive square root is the appropriate solution. Thus, x = 8√2.
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PLEASE HELP I APPRECIATE IT THANK YOU
Determine the value of "a" in the expression below:
[tex]\sqrt[3]{81x^15y^9} =3^ax^5y^3[/tex]
Attached is a photo of the problem too in case I wrote the equation wrong.
Thanks again!!
See below for the explanation
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I'll go through the possible answer choices.
A. If we tried a = 3, then 3^a = 3^3 = 27 which is not 81 that we want. This rules out choice A.B. Try a = 1 to get 3^a = 3^1 = 3 which also doesn't match with the 81. Cross choice B off the list.C. Try a = -1 to get 3^a = 3^(-1) = 1/(3^1) = 1/3. Still no, so we cross choice C off as well.D. Try a = 2 and we get 3^a = 3^2 = 9. Choice D is eliminated.E. Lastly, 3^a = 3^0 = 1 which eliminates choice E.To summarize, choices A through E lead to results that aren't 81, so we must eliminate them. There's nothing left to pick, so your teacher must have made a typo somewhere. You'll need to ask her/him for further clarification.
i need help!! please help me out
5. Which equation below can be transformed into the following equation:
2x + 4 = 6x + 2
2x + ½ = 6x + 1⁄2
2(2x+5)= 4x + x + 2
O2(x+2) = 2 (3x + 1)
Answer:
The equation that can be transformed into the following equation 2x + 4 = 6x + 2 is:
2(2x+5)= 4x + x + 2
Therefore, the equation 2(2x+5)= 4x + x + 2 can be simplified and transformed to the form of 2x + 4 = 6x + 2.
A ship leaves a port at 12 noon and travels due west at 20 knots. At 12 noon the next day, a second ship leaves the same port and travels northwest at 15 knots.How fast are the two ships separating when the second ship has traveled 90 nautical miles?
The two ships are separating at a rate of 25 knots when the second ship has traveled 90 nautical miles.
To find the rate at which the two ships are separating, we can use the Pythagorean Theorem to find the distance between the two ships at any given time.
The distance between the two ships is the hypotenuse of a right triangle, with one leg being the distance traveled by the first ship and the other leg being the distance traveled by the second ship.
Let d1 be the distance traveled by the first ship and d2 be the distance traveled by the second ship. Then the distance between the two ships is given by:
d = √(d1^2 + d2^2)
Since the first ship is traveling at 20 knots and the second ship is traveling at 15 knots, we can write:
d1 = 20t
d2 = 15t
Substituting these expressions into the equation for the distance between the two ships, we get:
d = √((20t)^2 + (15t)^2)
Simplifying, we get:
d = √(400t^2 + 225t^2)
d = √(625t^2)
d = 25t
So the distance between the two ships is increasing at a rate of 25 knots.
When the second ship has traveled 90 nautical miles, we can find the time t by setting d2 = 90 and solving for t:
15t = 90
t = 6
At this time, the distance between the two ships is:
d = 25t = 25(6) = 150 nautical miles
So, the two ships are separating at a rate of 25 knots when the second ship has traveled 90 nautical miles.
To know more about Pythagorean theorem refer here:
https://brainly.com/question/343682#
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