The coordinates of B' after the sequence of transformations are given as follows:
B'(3,-4).
How to obtain the coordinates of B'?The coordinates of B are given as follows:
B(-3,1).
After a reflection over the y-axis, the x-coordinate of B is exchanged, hence:
B'(3, 1).
The rule for a 90º clockwise rotation is that (x,y) becomes (y,-x), hence the coordinates of B' after the 90º clockwise rotation are given as follows:
B'(1, -3).
The translation (x + 2, y - 1) means that 2 is added to the x-coordinate while 1 is subtracted from the y-coordinate, hence the final coordinates of B' are given as follows:
B'(3,-4).
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If triangle ABC has points A(2, -4), B(-3, 1), and C(-2, -6) and you perform the following transformations, B' would be at B' (3, -4).
What is a rotation?In Geometry, the rotation of a point 90° about the center (origin) in a clockwise direction would produce a point that has these coordinates (y, -x).
By applying a reflection over the y-axis to the coordinate of the given point B (-3, 1), we have the following coordinates:
Coordinate B = (-3, 1) → Coordinate B' = (-(-3), 1) = (-3, 1).
Next, we would apply a rotation of 90° clockwise as follows;
(x, y) → (y, -x)
Coordinate B' = (-3, 1) → Coordinate B' = (1, (-3)) = (1, 3)
Finally, we would apply a translation (x + 2, y - 1) as follows:
Coordinate B' = (1, 3) → (1 + 2, 3 - 1) = B' (3, 2).
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During the candy sale, nick sold 100 bars,Olivia sold 94,Brandon sold 53, and Grace sold 75. (Rank from greatest to least
The ranking from greatest to least goes on Nick, Olivia, Grace, and Brandon.
So in this, we have to rank the person who got most of the candy bars first and that is Nick.
After Nick Olivia has 94 candy bars so she is second in order.
Then on the third Grace had 75 candy bars.
And at the least Brandon is there with 53 candy bars.
Nick sold 100 candy bars
Olivia sold 94 candy bars
Grace sold 75 candy bars
Brandon sold 53 candy bars
Therefore, the ranking from greatest to least is Nick, Olivia, Grace, and Brandon.
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Determine the slope of the line through the points (-1, 8) and (-1, -4). Plot the points on the graph.
The slope for the given point through which it passes through the graph is [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex] = infinity .
What about slope?
The slope of a line is a measure of its steepness. It is defined as the ratio of the vertical change (rise) between two points on the line to the horizontal change (run) between the same two points. In other words, it is the rate at which the line rises or falls as we move along it in the horizontal direction.
Define graph:
In mathematics, a graph is a visual representation of a set of data or mathematical relationships between variables. Graphs can be used to display and analyze data in a variety of formats, including line graphs, bar graphs, scatter plots, and pie charts.
According to the given information:
As, we know that the slope = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
⇒ In which the point given are (-1,8) and (-1,-4)
By putting the value of the given point we have that
⇒ [tex]\frac{-4-(8)}{-1-(-1)}[/tex] = infinity.
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999999999999999999999999x696969
Answer:
=6.96969e+29
Step-by-step explanation:
Lyla invests $2,500 into a savings account
which earns 5% per year. In 15 years, how
much will Lyla's investment be worth if interest
is compounded semiannually (twice a year)?
Round to the nearest dollar.
Answer:
The formula for compound interest is given by:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money accumulated after n years
P = the principal (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, P = $2,500, r = 0.05 (since 5% = 0.05), n = 2 (since interest is compounded semiannually), and t = 15. Substituting these values into the formula, we get:
A = 2500(1 + 0.05/2)^(2*15)
A ≈ $5,551.33
Therefore, Lyla's investment will be worth approximately $5,551.33 after 15 years if interest is compounded semiannually.
A box contains four apples, six oranges, and a pear. Preston reaches into the box and selects two of the 11 fruits uniformly at random without replacement. Let m/n be the probability that he selects an apple and an orange, where m and n are relatively prime positive integers. Find m+n.
the answer is m + n = 24 + 55 = 79.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
There are two ways this can happen: either he selects an apple first and then an orange, or he selects an orange first and then an apple. We can compute the probability of each of these events separately and then add them together.
First, let's consider the probability that Preston selects an apple first and then an orange. The probability of selecting an apple first is 4/11, and then the probability of selecting an orange from the remaining 10 fruits (which includes 3 apples and 6 oranges) is 6/10. So the probability of this event is (4/11) * (6/10) = 24/110.
This can be simplified by dividing the numerator and denominator by 2:
48/110 = 24/55
So the probability that Preston selects an apple and an orange is 24/55. Therefore, the answer is m + n = 24 + 55 = 79.
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Find the least positive value of x such that
89 ≡ (x + 3) (mod 4)
is a multiple of
Answer: To find the least positive value of x that satisfies the given congruence, we can use the trial and error method or algebraic manipulation.
Using the trial and error method, we can start by plugging in values of x and checking if the congruence is satisfied.
For x = 1, (x + 3) = 4, so 89 ≡ 0 (mod 4), which is not a multiple of 3.
For x = 2, (x + 3) = 5, so 89 ≡ 1 (mod 4), which is not a multiple of 3.
For x = 3, (x + 3) = 6, so 89 ≡ 2 (mod 4), which is not a multiple of 3.
For x = 4, (x + 3) = 7, so 89 ≡ 3 (mod 4), which is not a multiple of 3.
For x = 5, (x + 3) = 8, so 89 ≡ 0 (mod 4), which is a multiple of 3.
Therefore, the least positive value of x that satisfies the congruence is x = 5.
Alternatively, we can use algebraic manipulation to solve the congruence. We have:
89 ≡ (x + 3) (mod 4)
=> 89 ≡ x + 3 (mod 4)
=> 86 ≡ x (mod 4) (subtracting 3 from both sides)
Now we need to find the least positive value of x that satisfies this congruence and is a multiple of 3.
The solutions for this congruence are x = 2 (mod 4) and x = 6 (mod 4).
Plugging in x = 2, we get 89 ≡ 5 (mod 4), which is not a multiple of 3.
Plugging in x = 6, we get 89 ≡ 3 (mod 4), which is not a multiple of 3.
Therefore, the least positive value of x that satisfies the congruence and is a multiple of 3 is x = 10 (which is equivalent to x = 2 (mod 4) and x = 6 (mod 4)), but this is not the answer to the original question since x must be positive.
Plugging in x = 14, we get 89 ≡ 1 (mod 4), which is not a multiple of 3.
Plugging in x = 18, we get 89 ≡ 3 (mod 4), which is not a multiple of 3.
Finally, plugging in x = 22, we get 89 ≡ 1 (mod 4), which is not a multiple of 3.
Plugging in x = 26, we get 89 ≡ 3 (mod 4), which is not a multiple of 3.
Since we want x to be positive, we can stop here and conclude that the least positive value of x that satisfies the given congruence is x = 5.
Step-by-step explanation:
Simplify:
X- 10 > 3
please help me on this
Answer:
To simplify the inequality x - 10 > 3, we can isolate x by adding 10 to both sides:
x - 10 + 10 > 3 + 10
Simplifying, we get:
x > 13
Therefore, the simplified inequality is x > 13.
Can a triangle with angle measures of 45-45-90 have the side lengths 30, 30 and 60?
(Geometry/Trig)
Step-by-step explanation:
No, the ratio in a 30-60-90 triangle is
::
[tex]1:1:\sqrt{2} [/tex]
not
1:1:2
compare 9\10 and 3\2 on number line
Comparing the numerator 9 < 15 thus, 9/10 is less than 3/2.
What is common denominator?A multiple of the denominators of two or more fractions can be used as a common denominator to add, subtract, or compare the fractions. As fractions with dissimilar denominators cannot be added together or directly compared, they must be changed into comparable fractions with the same denominator. We must determine the least common multiple (LCM) of the fraction denominators in order to determine a common denominator. The lowest number that is a multiple of both denominators is known as the LCM. Once we have the common denominator, we may multiply the numerator and denominator by the same factor to change each fraction to an equal fraction with the same denominator.
The two values are 9/10 and 3/2.
Taking the LCM we have:
9/ 10 and 15/10
Now comparing the numerator 9 < 15 thus, 9/10 is less than 3/2.
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On number line we can compare 9/10 and 3/2 as 9/10 < 3/2.
What is number line?
A number line is a visual representation of numbers in order, usually shown horizontally. It is a line with a starting point and an endpoint that represent the smallest and largest numbers, respectively.
To compare 9/10 and 3/2 on a number line, we need to first convert them to the same denominator. The least common multiple of 10 and 2 is 10, so we can convert 3/2 to 15/10:
9/10 = 0.9
3/2 = 15/10 = 1.5
Now, we can plot these two numbers on a number line:
We can see that 9/10 is to the left of 3/2 on the number line.
Therefore we can compare 9/10 and 3/2 as 9/10 < 3/2.
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Express the given fraction as percent 3/4?
Answer:
75%
Step-by-step explanation:
3/4 =75%
If you divide 3 by 4 you get 0.75
1=100%
0.75=75%
Answer:
.75
Step-by-step explanation:
think of 3 quarters
Ruggiero Brothers Oil has an R85 000 liability it must pay four years from today. The company is opening a savings account, so that the entire amount will be available when this debt needs to be paid. The plan is to make an initial deposit today, and then deposit an additional R16 000 each year for the next four years, starting one year from today. The account pays a 6% rate of return. How much does the firm need to deposit today?
Answer:
Step-by-step explanation:
To determine the amount that Buggiero Brothers Oil must deposit today in order to have enough money to pay the R85 000 liability four years from today, we can use the present value formula:
Present Value (PV) = Future Value (FV) / (1 + r)^n
where:
- FV is the future value, which is R85 000
- r is the annual interest rate, which is 6%
- n is the number of years until the liability needs to be paid, which is 4
To calculate the future value of the annual deposits of R16 000, we can use the future value of an annuity formula:
FV = PMT x [(1 + r)^n - 1] / r
where:
- PMT is the annuity payment, which is R16 000
- r is the annual interest rate, which is 6%
- n is the number of years of the annuity, which is 3 (since the first payment is made one year from today)
Plugging in the numbers:
FV = R16 000 x [(1 + 0.06)^3 - 1] / 0.06
FV = R61 719.56
Therefore, the total future value that Buggiero Brothers Oil will have in four years, including the initial deposit and the annual payments, will be:
FV = R85 000 + R61 719.56
FV = R146 719.56
Plugging in the numbers to the present value formula:
PV = R146 719.56 / (1 + 0.06)^4
PV = R116 442.12
Thus, Buggiero Brothers Oil needs to deposit R116 442.12 today to have enough money to pay the R85 000 liability four years from today, assuming a 6% rate of return.
To the nearest foot, what is the height of the pole?
The height of the pole to the nearest foot, given the angle of elevation and the surveyor distance, is C. 135 ft
How to find the height of the pole ?To find the height of the pole, we can use the tangent function from trigonometry. The tangent of the angle of elevation (44°) is equal to the ratio of the height of the pole (h) minus the transit height (4 feet) to the distance between the transit and the pole (140 feet).
So, we have:
tan(44°) = (h - 4) / 140
h - 4 = 140 × tan(44°)
h = 140 × tan(44°) + 4
h = 140 × 0.965 + 4
h = 135.1
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If triangle ABC has points A(2, -4) B(-3, 1) C(-2, -6) and you perform the following transformations, where will B' be?
Reflection over the y-axis, rotation 90° clockwise, and translation (x + 2, y - 1)
If triangle ABC has points A(2, -4) B(-3, 1) C(-2, -6) and you perform the following transformations, B' would be located at B' (3, -4).
What is a translation?In Mathematics, a translation is a type of rigid transformation which is used in moving every point of an object in the same direction, as well as for the same distance.
By applying a reflection over the y-axis to the coordinate of the given point B (-3, 1), we have the following coordinates:
Coordinate B = (-3, 1) → Coordinate B' = (-(-3), 1) = (3, 1).
Next, we would apply a rotation of 90° clockwise as follows;
(x, y) → (y, -x)
Coordinate B' = (3, 1) → Coordinate B' = (1, (-3)) = (1, -3)
Lastly, we would apply a translation (x + 2, y - 1) as follows:
Coordinate B' = (1, -3) → (1 + 2, -3 - 1) = B' (3, -4).
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Your firm is considering adding a product line. The accounting department has determined that the cost
function for this new product will be C(x) = 55x + 3500 and the revenue function will be R(x) = 80x,
where x is the number of units sold. Additionally, the sales department has determined that you reasonably
can expect to sell around 164 units. You must decide whether to go ahead with the new product line.
Find the break-even quantity:
Find the profit function: P(x) =
Make your decision:
O Proceed with the product line: the products are profitable and we can reasonably expect to meet
our break-even quantity.
Cancel the product line: the quantity needed to break even is more than our firm can reasonably
expect to sell.
O Cancel the product line: producing these products is not profitable.
Submit Question
the profit function is positive, producing 164 units of the new product line would yield a profit of $600.
We should proceed with the product line since it is profitable and we can reasonably expect to meet our break-even quantity.
To find the break-even quantity, we need to set the cost function equal to the revenue function and solve for x:
C(x) = R(x)
55x + 3500 = 80x
25x = 3500
x = 140
Therefore, the break-even quantity is 140 units.
To find the profit function, we subtract the cost function from the revenue function:
P(x) = R(x) - C(x)
P(x) = 80x - (55x + 3500)
P(x) = 25x - 3500
Now we can evaluate the profit function at different values of x to see if producing these products is profitable or not.
If we plug in x = 164, the expected sales quantity, we get:
P(164) = 25(164) - 3500
P(164) = 4100 - 3500
P(164) = 600
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How to convert 23.01 into a fraction?
Answer:
2301 / 100
Step-by-step explanation:
We take
23.01 time 100 which makes 2301/100 fraction.
A father and son are buying hot dogs and lemonade for a family picnic. They have only a $20 bill to spend. Lemonade costs $3.50 per bottle and they must buy one bottle. Hot dogs cost $2.50 per package. What is the maximum number of packages of hot dogs they can buy?
Answer:
Step-by-step explanation:
subtract 20-3.50 you will get 16.50
Multiply 2.50x6 you will get 15
Subtract 16.50-15.00 you will get 1.50
If x^2-x-6=0 then x is
, then x is
Question 1 options:
-2 or 3
-1 or 6
1 or 6
2 or -3
Answer:
-2 and 3 is the required answer
Answer: The answer is: -2 or 3
Step-by-step explanation:
x^2 -x -6 = 0
x^2 -3x +2x -6 = 0
x(x-3) + 2(x-3) = 0
(x-3)(x+2) = 0
So x-3 = 0 :: x = 3
or x+2 = 0 :: x=-2
It take 4 minites to fill a 2/5 how many minutes per meter
The unit rate in minutes per meter is 10 minutes/meter.
What is unit conversion?
Unit conversion is the method of converting a quantity from one unit of measurement to another. In many cases, it is necessary to convert units of measurement to make them more meaningful, or to enable comparisons between different units.
We can start by finding the total time it would take to fill the aquarium to a depth of 1 meter.
If it takes 4 minutes to fill the aquarium to a depth of 2/5 meters, then we can find how long it would take to fill the aquarium to a depth of 1 meter by setting up the following proportion:
2/5 meters / 4 minutes = 1 meter / x minutes
To solve for x, we can cross-multiply and simplify:
(2/5) * x = 4 * 1
2x = 20
x = 10
Therefore, it would take 10 minutes to fill the aquarium to a depth of 1 meter.
The unit rate in minutes per meter is the time it takes to fill 1 meter of the aquarium, which we just calculated to be 10 minutes.
So, the unit rate in minutes per meter is 10 minutes/meter.
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Complete question : it takes 4 minutes to fill an empty aquarium to a depth of 2/5 meters. what is the unit rate in minutes per meter?
Provide a trigonometric equation. Considering only the space between = 0 and 2π the equation must only have solutions at x = 1 and x = 2. Explain your thought process and the work you did to create the equation. You may round decimal values to 3 places.
Therefore , the solution of the given problem of equation comes out to be f(x) = sin(/2 x) (when x = 1 or 2).
What is an equation?Variable words are commonly used in complex algorithms to show consistency between two statements that are not compatible. Academic expressions called equations are used to show the equality of various academic numbers. In this case, normalization yields b + 7 as opposed to a single formula the fact that split 12 into two parts, which can be used with data collected from y + 7.
Here,
The goal is to construct a trigonometric equation with only answers at
x = 1 and x = 2.
f(x) = A sin(Bx+C+D)
=> B + C + D + A = 0 (equation 1)
=> Equation 2: A sin(2B + C + D) = 0
=> B + C sin A = 0 (equation 3)
=> Sin(2B+C) = A = 0 (equation 4)
Since sin(x) = 0 when x is a multiple of, formulae 3 and 4 can be rewritten as follows:
=> B + C = nπ (equation 5)
=> 2B + C = mπ (equation 6)
with numbers n and m. When we simultaneously solve equations 5 and 6 for B and C, we obtain:
=> B = (m - n)π/2 (equation 7)
=> C = nπ - B (equation 8)
=> When x = 1, C = /2 - /2 = 0.
=> When x = 2, C = − /2 = 3/2.
Thus, the result is as follows:
when f(x) = sin(/2 x) (when x = 1 or 2)
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area of compound shapes
Answer:
Compound shapes can also be called composite shapes. To find the area of compound shapes we must divide the compound shape into basic shapes and find the area of each of the basic shapes and add them together.
Write 4/8 in lowest terms
Answer:
4/8 in lowest terms is 1/2.
Step-by-step explanation:
Answer: 1/2
4/8 is equivalent to 1/2
Match each metric measurement on the left with an equivalent unit of measurement on the right.
According to the information, the values that coincide are: 2.2 meters with 2200 millimeters, 14 decimeters with 0.014 hectometers, 0.14 meters with 0.014 decameters, 0.022 decameters with 22 centimeters.
How to find the numbers that match?To find the numbers that match we must take into account the relationship between the values:
Decameter: Unit of length equal to 10 meters.Centimeter: Unit of length equal to one hundredth of a meter.Decimeter: Unit of length equal to one tenth of a meter.Millimeter: Unit of length equal to one thousandth of a meter.Hectometer: Unit of length equal to 100 meters.According to the above, we can infer that the values that match are:
2.2 meters with 2200 millimeters.14 decimeters with 0.014 hectometers.0.14 meters with 0.014 decameters,0.022 decameters with 22 centimeters.Learn more about measurements at: https://brainly.com/question/4725561
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Please I need help
The area of the shaded region is
The area of the shaded region under normal distribution is: 3.51
What is the area under the normal distribution?The standard normal distribution is defined as the normal distribution with a mean of 0 and a standard deviation of 1.
The z-table or the standard normal table is one that provides the area under the standard normal curve to the left of a specified value, or "z-value". The value for the area is also the probability that the variable is less than the specified z-value.
To the right of -2.25 and to the left of -0.35
From standard normal table, we have the p-values as:
Area to the left of -0.35 = 0.3632
Area to the left of -2.25 = 0.0122
Area of the shaded region = 0.3632 - 0.0122 = 0.351
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Martin Pincher purchased a snow shovel for $28.61, a winter coat for $23.27, and some rock salt for $7.96. He must pay the state tax of 5 percent, the county tax of 0.5 percent and the city tax of 2.5 percent. What is the total purchase price?
To calculate the total purchase price for Martin Pincher, we need to calculate the total amount of taxes he must pay and then add the purchase price of the items.
Let's start by calculating the taxes.
State Tax:
State Tax = 0.05 x (28.61+23.27+7.96)
State Tax = 0.05 x 59.84
State Tax = 2.99
County Tax:
County Tax = 0.005 x (28.61+23.27+7.96)
County Tax = 0.005 x 59.84
County Tax = 0.30
City Tax:
City Tax = 0.025 x (28.61+23.27+7.96)
City Tax = 0.025 x 59.84
City Tax = 1.50
Total taxes = 2.99 + 0.30 + 1.50
Total taxes = 4.79
Now let's calculate the total purchase price.
Total purchase price = 28.61+23.27+7.96 + 4.79
Total purchase price = 64.63
Answer:
$64.63
Step-by-step explanation:
You want to know the total with tax of purchases of $28.61, 23.27, and 7.96 when they are subject to taxes of 5%, 0.5% and 2.5%.
Total saleThe sum of the individual prices is subject to tax that is the sum of the individual tax rates. The tax rate sum is ...
5% +0.5% +2.5% = 8%
Then the multiplier of the price is ...
total = subtotal × (1 +8%) = 1.08×subtotal
A calculator can do all the computations at once, so we don't actually need to know the subtotals in order to find the total sale amount.
(28.61 +23.27 +7.96) × 1.08 = 64.6272
The tax is generally rounded to the nearest cent, so ...
the total purchase price is $64.63.
__
Additional comment
In the days before smart cash registers, the amount of sales tax was found by looking in a table supplied by the tax authority. It was always the same for any given purchase amount.
These days, the tax may be computed on the fly in such a way that the total tax collected is as near as possible to the total tax that needs to be collected.
That means a hundred instances of this purchase might have a total price of $64.63 for 72 of them, and $64.62 for the remaining 28 of them. That way, the total of the 100 sales would be $6462.72 and exactly the right amount of tax will have been collected. (At least one pizza chain collects tax this way.)
Nine friends share 4 sandwiches equally what fraction of a sandwich does each friend get
Answer:
4/9
Step-by-step explanation:
4 sandwiches in between 9 friends
4 sandwiches must be divided in between 9 people
- > [tex]\frac{4 sandwiches}{9 people}[/tex] = [tex]\frac{4}{9}[/tex]
Answer:
Step-by-step explanation:
2/3
A researcher is studying life Expectancy in different parts of the world. Using birth and death records, she randomly select a sample of 20 people from town A and a sample of 20 people from town B and record their lifespan in years.
The researcher wants to test the claim that there is a significant difference in life span for people in the two towns. What are the Noel and alternative hypotheses that should be used to test this claim?
Please see photo below for the options of answer , thank you!
Answer:
Null Hypothesis (H0): There is no significant difference in life span for people in the two towns.
Alternative Hypothesis (H1): There is a significant difference in life span for people in the two towns.
Answer:
The null and alternative hypotheses that should be used to test this claim are:
Null hypothesis: There is no significant difference in lifespan for people in the two towns. Symbolically, this can be represented as H0: μ1 = μ2, where μ1 and μ2 are the population mean lifespans of Town A and Town B, respectively.
Alternative hypothesis: There is a significant difference in lifespan for people in the two towns. Symbolically, this can be represented as Ha: μ1 ≠ μ2.
To test this claim, the researcher can conduct a two-sample t-test using the data collected from the two towns. The test statistic can be calculated as:
t = (x1 - x2) / (s1^2/n1 + s2^2/n2)^0.5
where x1 and x2 are the sample mean lifespans of Town A and Town B, respectively, s1 and s2 are the sample standard deviations of Town A and Town B, respectively, and n1 and n2 are the sample sizes of Town A and Town B, respectively.
Using the given data, the test statistic can be calculated as:
t = (78.5 - 74.4) / (11.2^2/20 + 12.3^2/20)^0.5 = 1.02
At a significance level of 0.05 with 38 degrees of freedom (df = n1 + n2 - 2), the critical value for a two-tailed test is ±2.024. Since the calculated t-value (1.02) falls within the acceptance region (-2.024 < t < 2.024), the null hypothesis cannot be rejected. Therefore, we do not have enough evidence to conclude that there is a significant difference in lifespan for people in the two towns.
Step-by-step explanation:
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Which of the following choices lists the values of the side lengths of a triangle with 45-45-90 degree angles and a leg = 5?
A) 5, 5, 5
B) 5, 1, 5
C) 1, 5, 5
D) 1, 1, 5
The side lengths of such a triangle with a leg length of 5 and angles of 45, 45, and 90 are not listed in any of the options.
Explain about property of the right triangles?The right angle is established when 2 straight lines cross at a 90° angle or when they are perpendicular at the intersection. The symbol is used to indicate a right angle.
A triangle's (of all varieties) cumulative sum of angles is 180°.The length of a triangle's two longest sides added together is longer than for third side.Similar to this, the length of a third side of a triangle's third side is shorter than the difference between its two sides.For the given question:
Triangle with degree angles - 45-45-90
It means two legs are of same length 5 units.
Then, hypotenuse H will be:
H² = 5² + 5²
H² = 25 + 25
H² = 50
H = 5√2
Thus, the correct third side of the triangle will be 5√2.
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Find the derivative of f(x) 5/x + 7/x^2
Answer:
[tex] \rm \: f(x) = \dfrac{5}{x} + \dfrac{7}{ {x}^{2} } [/tex]
Differentiating both sides with respect to x
[tex] \rm \dfrac{d}{dx} ( {f}( x) = \dfrac{d}{dx} \bigg( \dfrac{5}{x} + \dfrac{7}{ {x}^{2} } \bigg)[/tex]
Using u + v rule
[tex] \rm \: {f}^{ \prime} x = \dfrac{d}{dx} \bigg( \dfrac{5}{x} \bigg) + \dfrac{d}{dx} \bigg( \dfrac{7}{ {x}^{2} } \bigg)[/tex]
[tex] \rm \: {f}^{ \prime} x = 5. \dfrac{d}{dx} ( {x}^{ - 1} ) + 7. \dfrac{d}{dx} ( {x}^{ - 2} )[/tex]
[tex] \rm \: {f}^{ \prime} x = 5.( - 1. {x})^{ (- 1 - 1)} + 7.( - 2. {x})^{ - 2 - 1} [/tex]
[tex] \rm \: {f}^{ \prime} x = { - 5x}^{ - 2} { - 14x}^{ - 3} [/tex]
[tex] \rm \: {f}^{ \prime} x = - \dfrac{5}{ {x}^{2} } - \dfrac{14}{ {x}^{3} } [/tex]
[tex] \rm \: {f}^{ \prime} x = - \bigg(\dfrac{5}{ {x}^{2} } + \dfrac{14}{ {x}^{3} } \bigg)[/tex]
Hense The required Derivative is answered.
Derivative Formulae:-[tex]\boxed{\begin{array}{c|c} \rm \: \underline{function}& \rm \underline{Derivative} \\ \\ \rm \dfrac{d}{dx} ({x}^{n}) \: \: \: \: \: \: \: \: \: \ & \rm nx^{n-1} \\ \\ \rm \: \dfrac{d}{dx}(constant) &0 \\ \\ \rm \dfrac{d}{dx}( \sin x )\: \: \: \: \: \: & \rm \cos x \\ \\ \rm \dfrac{d}{dx}( \cos x ) \: \: \: & \rm - \sin x \\ \\ \rm \dfrac{d}{dx}( \tan x ) & \rm \: { \sec}^{2}x \\ \\ \rm \dfrac{d}{dx}( \cot x ) & \rm- { \csc }^{2}x \\ \\ \rm \dfrac{d}{dx}( \sec x ) & \rm \sec x. \tan x \\ \\\rm \dfrac{d}{dx}( \csc x ) & \rm \: - \csc x. \cot x\\ \\ \rm \dfrac{d}{dx}(x) \: \: \: \: \: \: \: & 1 \end{array}}[/tex]
Interpret the data in the circle graph. If 560 books were sold at the book fair, find the number of the books that were mystery books.
If 560 books were sold at the book fair,
(Type a whole number.)
of the books were mystery books.
Circle graph
Fantasy 8%
Science
Fiction
12%
Comic 15%
Other 5%
Mystery 20%
-Fictic
Answer:
112
Step-by-step explanation:
According to the circle graph, the mystery books make up 20% of all books sold. So, we can calculate the number of mystery books sold as follows:
Number of mystery books = 20% of 560
= (20/100) x 560
= 112
Therefore, the number of mystery books sold at the book fair was 112.
a) Supplementary angles are congruent.
O Always
O Sometimes
O Never