Answers
The values of the composite functions are (f + h)(5) = 7, (h - f)(2) = 0, (fh)(3) = 0 and (h/f)(0) = 3/5
How to evaluate the composite functionsFrom the question, we have the following parameters that can be used in our computation:
The graphs
Using the graphs as a guide, we have the following:
(f + h)(5) = f(5) + h(5)
(f + h)(5) = 3 + 4
(f + h)(5) = 7
(h - f)(2) = h(2) - f(2)
(h - f)(2) = 1 - 1
(h - f)(2) = 0
(fh)(3) = f(3) * h(3)
(fh)(3) = 4 * 0
(fh)(3) = 0
(h/f)(0) = h(0)/f(0)
(h/f)(0) = 3/5
Hence, the value of the function (h/f)(0) is 3/5
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Related Questions
The points K (1,3), L(-4,-3), M (2,-8), and N (7,-2) form quadrilateral KLMN. Where would these points be on the graph?
Answers
The location of the points for quadrilateral KLMN have been plotted in the graph shown in the image attached below.
What are the types of quadrilateral?In Geometry, there are different types of quadrilateral and these include the following:
ParallelogramSquaresRectangleRhombusTrapezoidNext, we would use an online graphing calculator to construct (plot) quadrilateral KLMN on a cartesian coordinate based on the given vertices. Also, you should enter the value for each vertices of quadrilateral KLMN on the x-coordinate and y-coordinate respectively as shown in the table.
By critically observing the graph of quadrilateral QRST, we can reasonably infer and logically deduce that it represents a parallelogram.
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Complete the following proof.
Given: WXYZ is a parallelogram with diagonals XZ and WY intersecting at point V.
Prove: XZ bisects WY
Answers
The proof of the parallelogram has been given below
How to prove that X bisects WYWe have WXYZ as a parallelogram.
XW = ZY
XW // ZY
such that
M ∠VXW = M VZY (This is alternate interior angles,)
M∠VWX = M ∠VYZ
therefore ΔVXW ≅ Δvzy
wv = yv
Then XZ bisects WY
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what is the total population if 15% is 36,000 people
Answers
Each worker at a store gets paid $15.90 for that first 40 hours worked. After 40 hours, they earn time and a half wages. Every employee has a 28% of his/her gross pay deducted for taxes, insurance etc. how much of a net pay does each worker take home?
Answers
Each worker would take home a net pay of $586.71.
What is the net pay?
The net pay is the amount of money that an employee takes home after all deductions have been made from their gross pay. Gross pay is the total amount of money an employee earns before taxes and other deductions are taken out.
To calculate net pay, you need to subtract all the required deductions from the employee's gross pay.
To calculate the net pay for each worker, we first need to determine their gross pay. The gross pay will depend on the number of hours they worked and whether they worked any overtime.
For the first 40 hours worked, each worker earns $15.90 per hour, so their gross pay for those hours would be:
Gross Pay for 40 hours = $15.90/hour x 40 hours = $636
For any hours worked beyond 40, the worker earns time and a half wages. This means they earn 1.5 times their regular hourly wage of $15.90, or $23.85 per hour. So, if they worked, for example, 45 hours in total, the additional 5 hours would be paid at the overtime rate, resulting in an additional gross pay of:
Gross Pay for 5 overtime hours = $23.85/hour x 1.5 x 5 hours = $178.88
Therefore, their total gross pay would be:
Total Gross Pay = Gross Pay for 40 hours + Gross Pay for 5 overtime hours = $636 + $178.88 = $814.88
Now, we need to calculate the deductions, which we are told are 28% of the gross pay. So the total deductions would be:
Total Deductions = 28% x $814.88 = $228.17
Finally, to determine the net pay, we need to subtract the total deductions from the gross pay:
Net Pay = Gross Pay - Total Deductions = $814.88 - $228.17 = $586.71
Therefore, each worker would take home a net pay of $586.71.
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A local coffee shop is testing out new flavors of coffee: Caramel Apple Latte and Salted Minty Mocha. A poll conducted by the
coffee shop determined that 46 customers preferred only the Caramel Apple Latte, 61 customers chose only the Salted Minty
Mocha, 27 customers chose both flavors, but 18 liked neither flavor. What is the probability that a randomly selected
customer would only like the Caramel Apple Latte?
Answers
The probability that a customer selected randomly would only like Carmel apple is 23/76
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Probability = sample space/ total outcome
sample space is the number of customers that like caramel apple latte only = 46
The total number of customers = 46+61+27+18 = 152
Therefore The probability that a customer selected randomly would only like Carmel apple = 46/152 = 23/76
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petra jogs 60 miles in 110 minutes, at this rate how long would her take to jog per one minutes
Answers
The speed of Petra will be 0.55 mile/minute.
What exactly is speed?
The definition of speed is:
The pace at which an object's location changes in any direction.
Speed is defined as the ratio of distance travelled to time spent travelling. Because it has just one direction and no magnitude, speed is a scalar number.
Formula for Speed
The speed formula is shown below:
s=d/t
Where,
s is the speed in metres per second, d is the distance travelled in metres, and t is the duration in seconds.
Now,
As given petra jogs 60 miles in 110 minutes
then in one minute she will jog =60/110 mile
=0.5454 mile/min
Hence,
The speed of Petra will be 0.55 mile/minute.
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Show that ∶ [– 1, 1] → ℝ, given by () =
(2+)
is one-one. Find the inverse of the function
∶ [– 1, 1] → Range . (Hint: For ∈ Range , = () =
(2+)
, for some in [– 1, 1], i.e., =
(2+)
Answers
The inverse of the given function is f(x) = 2x/(1 - x)
What is a function?
A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities.
Given function is
f(x) = x/(2+x)
Assume that y = f(x) = x/(2+x)
Solve y = x/(2+x) for x:
y = x/(2+x)
Multiply (2+x) on both sides:
y(2+x) = x
2y + xy = x
Subtract xy from both sides:
2y = x - xy
2y = x(1 - y)
x = 2y/ (1 - y)
Now replace x with y and y with x:
y = 2x/(1 - x)
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pls help
About 3,500 tourists visit the Granite Falls overlook each year. After the construction of a new nature center with exhibits and hands-on activities, that number is expected to increase 5% each year. Assuming the same growth continues, you can use a function to approximate the number of annual visitors to the overlook x years after the nature center is built.
Write an equation for the function. If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)^x.
Answers
Answer:
Step-by-step explanation:
Here's a step by step explanation for writing a function to approximate the number of annual visitors to the overlook x years after the nature center is built:
Start by defining the initial number of visitors as the baseline. We'll call this y0 and set it equal to 3,500 tourists:
y0 = 3,500
Define the rate of growth as a percentage increase. We're told that the number of visitors is expected to increase by 5% each year, so we'll call this rate "r" and set it equal to 0.05:
r = 0.05
Write the equation for exponential growth. The formula for exponential growth is given by:
y = y0 × (1 + r)^x
where x is the number of years after the nature center is built.
So, the equation for the function in this case would be:
f(x) = 3,500 × (1 + 0.05)^x
This function models the expected number of annual visitors to the overlook x years after the nature center is built. The function is exponential because the number of visitors is multiplied by a constant factor (1 + 0.05) raised to a power (x) at each time step.
A line with a slope of 7 passes through the points (-7, 5) and (g, -2). What is the value of g?
g=
Answers
[tex](\stackrel{x_1}{-7}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{g}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-2}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{g}-\underset{x_1}{(-7)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ 7 }\implies \cfrac{-7}{g+7}=7\implies -7=7(g+7) \\\\\\ \cfrac{-7}{7}=g+7\implies -1=g+7\implies \boxed{-8=g}[/tex]
Some candles are in the shape of a right circular cylinder. For one such candle, the radius is 9 cm and the height is 26.5 cm. Find the volume of the candle. Round your answer to the nearest whole number. Do not type the units in the space below. (Be sure to use the pi button on your calculator to do the calculation.)
Answers
The volume of the candle is 6740 cubic cm
How to find the volume of the candle.From the question, we have the following parameters that can be used in our computation:
Radius, r = 9 cm
Height, h = 26.5 cm
The volume of a cylinder is calculated as
Volume = πr²h
substitute the known values in the above equation, so, we have the following representation
Volume = 3.14 * 9² * 26.5
Evaluate the products and exponents
Volume = 6740 cubic cm
HEnce, the volume is 6740 cubic cm
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Plot the points (-7,5),(-4,-6),(-1,4),(-7,3) in the Cartesian plane. Is the following relation a function? Why?
Answers
The graph of the points can be seen at the end, and the relation is not a function.
How to graph the points on a coordinate axis?
The coordinate axis has two axis with numbers labeled. For any point (x, y), you need to find the value x on the horizontal axis and the value y on the vertical axis.
Then the graph of the points (-7,5), (-4,-6), (-1,4), (-7,3) will be like the one at the end of the answer.
Now, is this a function?
Not, it is not, because we can see that the input -7 is being mapped into two different outputs, and a relation is a function only if each input is mapped into a single output.
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You (or your parents) purchase a new car for $19,725.00 plus 4.75% sales tax. The down payment is $2,175.00 and you (or your parents) have an average credit rating. How much interest is accrued after the first month?
Answers
Answer:
$90.12
Step-by-step explanation:
The principal amount of the loan is ...
(sale price)(1 + sales tax rate) - (down payment)
= $19,725×1.0475 -2175 = $18,486.94
For a secured loan, the APR charged for an average credit rating appears to be 5.85%, so the interest for the first month is
i = Prt = ($18,486.94)(0.0585)(1/12)
i = $90.12
Winston planned to spend no more than $150 on a helmet and goggles for skiing. After
spending $90.50 on a helmet, he bought a pair of goggles that put him over his budget.
Let x represent the cost of the goggles. Which inequality describes the problem?
90.50 + x>
150
90.50 + x <
150
Solve the inequality. Then, complete the sentence to describe the solution.
The goggles cost more than $
Submit
Answers
Answer:
(a) 90.50 +x > 150The goggles cost more than $59.50Step-by-step explanation:
You want an inequality and its solution for finding the cost of goggles that put Winston over his $150 budget when combined with the purchase of a $90.50 helmet.
Total costIf x represents the cost of the goggles, then Winston's total spending is ...
90.50 + x
If that is over is $150 budget, the relation is described by ...
90.50 +x > 150
SolutionSubtracting 90.50 from both sides gives ...
x > 59.50
This tells us the goggles cost more than $59.50.
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PLEASE HELLLP IM TAKING A QUIZ!!Cory is making popcorn. He knows that 3 identical scoops of unpopped
kernels produce 6 quarts of popcorn.
R
Which table most likely represents the total amount of popcorn, in quarts,
produced by x scoops of unpopped kernels?
Answers
Answer: C
Step-by-step explanation:
I am fairly certain this is the right answer. Good luck on your quiz!
Answer:C
Step-by-step explanation:
I remember this from class one time hope it helps:)
Suppose that 7 out of the 17 doctors in a small hospital are General Practitioners, 4 out of the 17 are under the age of 45, and 2 are both General Practitioners and under the age of 45. What is the probability that you are randomly assigned a General Practitioner or a doctor under the age of 45? Enter a fraction or round your answer to 4 decimal places, if necessary.
Answers
The probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 is given by the equation P = 9/17
What is Set Theory Formula?The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.
Given data ,
Let the probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 be P
Now , the equation will be
The fraction of doctors who are general practitioners be n ( A ) = 7/17
The fraction of doctors who are under the age of 45 n ( B ) = 4/17
And ,
The fraction of doctors who are both n ( A ∩ B ) = 2/17
Now , from the set theory formula ,
n(A∪B) = n(A) + n(B) - n(A⋂B)
And , probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 is n ( A ∪ B )
Substituting the values in the equation , we get
Probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 is n ( A ∪ B ) = ( 7 / 17 ) + ( 4/17 ) - ( 2/17 )
On simplifying the equations , we get
Probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 is n ( A ∪ B ) = 9/17
Hence , the probability is 9/17
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*Please help, I will mark brainest*
A chemical manufacturer wants to lease a fleet of 25 railroad tank cars with a combined carrying capacity of 532,000 gallons. Tank card with three different carrying capacities are available: 7,000 gallons, 14,000 and 28,000. How many of each type of tank car should be leased?
Fill in the blank: There are multiple possible combinations of how the tank cars should be leased. The combinations are obtained from the equations x1=_t+(_), x2=_t+(_) & x3=t
Answers
Answer:
Let's call the number of 7,000 gallon tank cars "x1", the number of 14,000 gallon tank cars "x2", and the number of 28,000 gallon tank cars "x3".
We can write the following constraints based on the total carrying capacity of the fleet:
7,000x1 + 14,000x2 + 28,000x3 = 532,000
x1 + x2 + x3 = 25
x1, x2, x3 >= 0 (since we can't have a negative number of tank cars)
This is a linear programming problem, which can be solved using simplex method or the graphical method.
By using the graphical method, we find that there are multiple optimal solutions. For example, one solution is x1 = 11, x2 = 7, and x3 = 7. This means that the manufacturer should lease 11 7,000 gallon tank cars, 7 14,000 gallon tank cars, and 7 28,000 gallon tank cars to meet the total carrying capacity requirement of 532,000 gallons.
So, the answer to the question is: There are multiple possible combinations of how the tank cars should be leased. The combinations are obtained from the equations x1 = 11 + 7t, x2 = 7 + 7t, and x3 = 7 + 7t.
A recycling bin is in the shape of a rectangular box. Find the height of the box if its length is 16 ft, its width is 7 ft, and its surface area is 500 ft2. (In the figure, h=height. Assume that the given surface area includes that of the top lid of the box.)
Answers
Answer:
Step-by-step explanation:
The surface area of a rectangular box can be calculated as follows:
Surface area = 2lw + 2lh + 2wh
Where l is the length, w is the width, and h is the height.
We are given the surface area (500 ft2) and the length and width (16 ft and 7 ft respectively), so we can use these values to solve for the height:
500 = 2 * 16 * 7 + 2 * 16 * h + 2 * 7 * h
500 = 224 + 32h + 14h
500 = 238h + 224
276 = 238h
h = 276 / 238
h = 1.16 ft
So the height of the box is approximately 1.16 feet.
Determine the domain and range of the given
function.
The domain is
The range is
Answers
domain = all real numbers
range = y > -2
y=x²-2
range is y is -2
domain is x is
Sheet Metal Trades To determine the average thickness of a metal sheet, a Sheet metal worker measures it at five different locations. Her measurements are 0.0401, 0.0417, 0.0462, 0.0407, and 0.0428 in. What is the average thickness of the sheet?
Answers
The average thickness of the metal sheet is 0.0423 inches.
What do you mean by average?In statistics, the mean is a measure of central tendency of a set of data. It is also referred to as the arithmetic mean and is calculated by adding up all the values in the data set and dividing by the total number of values.
Mean = (sum of all values) / (number of values)
For example, suppose we have the following set of data: 5, 7, 9, 11, 13. To find the mean, we add up all the values and divide by the total number of values, which is 5 in this case:
Mean = (5 + 7 + 9 + 11 + 13) / 5
Mean = 9
Therefore, the mean of this data set is 9.
The mean is a commonly used measure of central tendency because it takes into account all the values in the data set and is sensitive to changes in the data. However, it can be affected by outliers or extreme values in the data set, which can skew the results.
To find the average thickness of the sheet, we need to add the five measurements together and then divide by 5 (the number of measurements):
Average thickness = (0.0401 + 0.0417 + 0.0462 + 0.0407 + 0.0428) / 5
Average thickness = 0.0423 in
Therefore, the average thickness of the metal sheet is 0.0423 inches.
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Which equation represents the graph?
a graph of a line that passes through the points 0 comma negative 1 and 1 comma negative 4
y equals negative one third times x minus 1
y = −3x − 1
y equals negative one third times x plus one third
y equals negative 3 times x plus one third
Answers
The equation that represents the graph of a line passing through the points (0, -1) and (1, -4) is y = -3x - 1.
What is graph?
A graph is a visual representation of data or information that shows the relationship between different variables or quantities. Graphs can take many forms, including bar graphs, line graphs, scatterplots, and pie charts, among others. They are widely used in many fields, including mathematics, science, economics, and social sciences, to help visualize and analyze data, identify patterns, and communicate findings to others in a clear and concise manner. By representing complex information in a simple, easy-to-understand format, graphs can provide valuable insights and help us make informed decisions.
The equation that represents the graph of a line passing through the points (0,-1) and (1,-4) is:
y = -3x - 1
To find the equation of a line given two points, you can use the slope-intercept form:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is one of the given points.
First, we can find the slope of the line:
m = (y2 - y1) / (x2 - x1)
= (-4 - (-1)) / (1 - 0)
= -3
Next, we can choose one of the given points and substitute its coordinates and the slope into the slope-intercept form:
y - (-1) = -3(x - 0)
y + 1 = -3x
y = -3x - 1
Therefore, the equation that represents the graph is y = -3x - 1.
Option A, y = -1/3x - 1, has a slope of -1/3, which is not the slope of the line passing through the given points.
Option C, y = -1/3x + 1/3, also has an incorrect slope of -1/3, and it also does not pass through the point (0,-1).
Option D, y = -3x + 1/3, has the correct slope of -3, but it does not pass through the point (0,-1).
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What are the line segments in this rectangle?
a rectangle with the vertices labeled Q, R, S, and T
Answers
Answer:
qr rs st qt are the line hope it helped
Simplify fully 8c^4d^5+2c^3d^3
Answers
The expression when simplified is 2c^3d^3(4cd^2 + 1)
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
8c^4d^5+2c^3d^3
Factor out 2 from the expression
So, we have the following representation
2(4c^4d^5 + c^3d^3)
Factor out c^3d^3 from the expression
So, we have the following representation
2c^3d^3(4cd^2 + 1)
Hence, the expression is 2c^3d^3(4cd^2 + 1)
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Please help with this question I can’t seem to solve it
Answers
Answer:
X Y
0 0
2 -3
Step-by-step explanation:
The slope should look like this photo.
Point Q is located at (−6,−1) on the coordinate plane. Point Q is reflected over the x-axis to create point Q' Point Q' is then reflected over the y-axis to create point Q'' What ordered pair describes the location of Q''?
Answers
Answer:
(6, 1)
Step-by-step explanation:
When a point is reflected over the x-axis, its y-coordinate changes sign. When a point is reflected over the y-axis, its x-coordinate changes sign.
So, when point Q, located at (-6,-1), is reflected over the x-axis to create point Q', the new point has the same x-coordinate and a y-coordinate of -1 to 1 = 1. So, Q' is located at (-6, 1).
Next, when Q' is reflected over the y-axis to create Q'', the new point has the same y-coordinate and an x-coordinate of -6 to 6 = 6. So, Q'' is located at (6, 1).
So, the ordered pair that describes the location of Q'' is (6, 1).
Complete the sentence below.
If (3x2 + 22x + 7) = (x + 7) = 3x + 1 , then (x + 7) ( ? )
＝?
The check of the polynomial division problem shows that the product of two polynomials is a polynomial.
This supports the fact that the __________ ?
property is satisfied for polynomial multiplication.
Answers
your answers are
3x + 1 = 3x^2 + 22x + 7
"closure"
Margaux pays $19 for postage. What is the mass of her parcel?
Answers
To find the mass of her parcel, you must solve the equation for the input when the output is of 19.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
For this problem, we have that the numeric value is of $19, hence the equation must be solved for the input variable to find the mass of the parcel.
Missing Information
The problem is incomplete, hence the general procedure to solve it was presented.
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2023 Tax Year (Filing in 2024)
You are 25yr old and single with no kids/dependents.
You live in Florida.
Your job pays $84,649/yr.
You have no other sources of incomes.
Your itemized deductions come out to $10,211.
Your credits come out to $9.
Your tax-deffered retirement contributions come out to $3,288.
Calculate the total Federal Income Taxes and FICA paid.
Answers
If you are 25yr old and single with no kids/dependents. The total Federal Income Taxes is $11,218 and FICA paid is $6,478.
How to find the total Federal Income Taxes and FICA paid?First, you need to determine your taxable income.
Gross income: $84,649
Itemized deductions: $10,211
Tax-deferred retirement contributions: $3,288
Taxable income: $71,150
Next, you can use the tax brackets and rates for the 2023 tax year to calculate your federal income tax liability.
The first $10,950 is taxed at 10%: $1,095
The next $32,250 is taxed at 12%: $3,870
The next $28,425 is taxed at 22%: $6,253
The remaining $0 is taxed at 24%: $0
Total federal income tax liability: $11,218
b. For 2023, the Social Security tax rate is 6.2% on the first $147,000 of income, and the Medicare tax rate is 1.45% on all income.
Social Security tax: $5,240.80
Medicare tax: $1,237.20
Total FICA taxes: $6,478
Therefore the total Federal Income Taxes is $11,218 and FICA paid is $6,478.
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Given: log a 2 = 4, log a 3 = 5, log a 5 = 8. Find log a 60.
A. 2.9
B. 1.46
C. .32
D. 2.1
Answers
The solution of the logarithm expression logₐ 60 is 2.1. Therefore, the answer is D.
How to solve logarithm?The logarithm expression can be solved as follows; Using the logarithm rule,
Law of multiplication of logarithm,
logₐ x + logₐ y = logₐ xy
Therefore,
logₐ 2 = 4
logₐ 3 = 5
logₐ 5 = 8
Hence, let's find logₐ 60.
logₐ 5 + logₐ 3 + logₐ 2 + logₐ 2 = logₐ (5 × 3 × 2 × 2) = logₐ 60
Hence,
0.8 + 0.5 + 0.4 + 0.4 = 2.1
Therefore,
logₐ 60 = 2.1
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The value of log a 60 is 21. The correct option is D.
What is a Logarithm?Logarithms are another way of writing exponents.
Logarithm is nothing but another way of expressing exponents and can be used to solve problems that cannot be solved using the concept of exponents only.
log a 60 = log a (12 x 5)
log a 60 = log a 12 x log a 5
log a 60 = log a (4 x 3) x log a 5
log a 60 = log a 4 x log a 3 x log a 5
log a 60 = 2 log a 2 x log a 3 x log a 5
Substituting the values for the logs
log a 60 = 2 (4) + 5 + 8
log a 60 = 21
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11311 rounded off to the nearest 100
Answers
Answer:
11300
Step-by-step explanation:
The closest 100 to 11311 is 11300
If the number was 11351 you would round up to 11400
Find EF, please!!!!!!!!!!
Answers
Answer:
EF = 7
Step-by-step explanation:
You want to know the length of midsegment EF in the triangle with it labeled 43-4x and the parallel base segment labeled 32-2x.
MidsegmentThe midsegment is half the length of the base segment, so we have ...
(43 -4x) = 1/2(32 -2x)
43 -4x = 16 -x . . . . . simplify
27 = 3x . . . . . . . . add 4x-16
9 = x . . . . . . . . divide by 3
EF = 43 -4x = 43 -4(9) = 43 -36
EF = 7
