- Tan²θ is the left side expression as the difference of two squares in trigonometric ratios.
What do trigonometric ratios represent?
As specified by the definition of a right-angled triangle's side ratio, trigonometric ratios are the values of all trigonometric functions. Trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.Review the sine, cosine, tangent, cotangent, secant, and cosecant trigonometric ratios.When calculating unknown distances from known or measured angles in geometric figures, trigonometric functions are used.(sec θ+1)(sec θ-1)= tan² θ
use ( a+ b ) ( a - b) = a² - b²
= 1² - sec²θ { we know that 1 + tan²θ = sec²θ}
= 1 - sec²θ
= - tan²θ
LHS = RHS
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50 points again!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
f(x)=|5x|
f(2)= |5(2)| Substitute 2 for x
f(2)= 10 Answer
Answer:
f(2) = | 5 • 2 | = | 10 | = 10
Step-by-step explanation:
Replace x with 2 then solve with the absolute value
A hiker on the Appalachian Trail planned to increase the distance covered by 10% each day. After 7 days, the total distance traveled is 75.897 miles.Part A: How many miles did the hiker travel on the first day? Round your answer to the nearest mile and show all necessary math work. (4 points)Part B: What is the equation for Sn? Show all necessary math work. (3 points)Part C: If this pattern continues, what is the total number of miles the hiker will travel in 10 days? Round your answer to the hundredths place and show all necessary math work. (3 points)
Answer with explanation: A hiker has increased his distanced covered by 10% each day since the start, the total distance covered at the end of the 7th day is 75.897mile:
(A) The number of miles on the first day:
[tex]\begin{gathered} \text{let x be the distance covered on first day:} \\ x,1.1x,1.21x,1.331x,\ldots. \\ \text{ This is a Geomatric sequence:} \\ S_n=\frac{a(r^n-1)}{r-1} \\ a=x \\ r=\frac{1.1x}{x}=1.1 \\ r=1.1 \\ n=7 \\ S_n=\frac{x((1.1)^7-1)}{1.1-1}\Rightarrow(0) \end{gathered}[/tex]Substituting the total miles covered on the 7th day in equation(0) gives:
[tex]\begin{gathered} 75.897=\frac{x((1.1)^7-1)}{1.1-1} \\ 7.5897=0.9487171x \\ x=7.9999612107761101807904590314647 \\ x\approx7.9999mi \end{gathered}[/tex]Therefore on the first day, the hiker covered about 7.99 miles:
(B) The equation for the S:
[tex]\begin{gathered} S_n=\frac{a(r^n-1)}{r-1} \\ S_n=\frac{7.99((1.1)^n-1)}{1.1-1}\Rightarrow(1) \end{gathered}[/tex]The equation (1) gives the number of miles hiked on the nth day.
(C) miles covered on 10th day:
The number of miles covered on the 10th day is calculated using the equation(1) as follows:
[tex]\begin{gathered} S_n=\frac{7.99((1.1)^n-1)}{1.1-1}\Rightarrow n=10 \\ S_{10}=\frac{7.99((1.1)^{10}-1)}{1.1-1} \\ S_{10}=127.340mi \end{gathered}[/tex]The number of miles covered on the 10th day is 127.340miles.
About the formula used:
[tex]\begin{gathered} S_n=\frac{a-ar^n}{1-r}\Rightarrow\text{ Your formula} \\ \text{Multiply by:} \\ \frac{(-1)}{(-1)} \\ \therefore\Rightarrow \\ S_n=\frac{(-1)}{(-1)}\times\frac{(a-ar^n)}{(1-r)}=\frac{(-1)\cdot(a-ar^n)}{(-1)\cdot(1-r)}=\frac{-a+ar^n}{-1+r}=\frac{ar^n-a}{r-1} \\ S_n=\frac{ar^n-a}{r-1}=\frac{a(r^n-1)}{r-1} \\ S_n=\frac{a(r^n-1)}{r-1}\Rightarrow\text{ My formula} \end{gathered}[/tex]In conclusion, the formula used is the same as the one that was required to be used.
Please help me work this out and explain it.
Answer:
a) DE = 15 cm
b) AB = 6 cm
Step-by-step explanation:
Explanation #a)
- Relating the triangle ABC with triangle DCE, a scale factor fomula is used;
[tex]{ \rm{ \frac{ \bar{DE}}{ \bar{BC} }} = \frac{ \bar{CE}}{ \bar{AC} } } \\ \\ { \rm{ \frac{\bar{DE}}{5} = \frac{24}{8} }} \\ \\ { \rm{\bar{DE}} = \frac{24 \times 5}{8} } \\ \\ { \rm{\bar{DE}} = 15 \: cm}[/tex]
Explanation #b)
[tex]{ \rm{ \frac{ \bar{CE}}{ \bar{AC}} } = \frac{ \bar{CD}}{ \bar{AB} }} \\ \\ { \rm{ \frac{24}{8} = \frac{18}{\bar{AB}} }} \\ \\ { \rm{\bar{AB} = \frac{18 \times 8}{24} }} \\ \\ { \rm{\bar{AB} = 6 \: cm}}[/tex]
- Therefore, the scale factor is 2, triangle CDE = 2ABC
[tex]{ \boxed{ \red{ \delta}}}{ \underline{ \red{ \mathfrak{ \: \: creed}}}}[/tex]
The average daily profit of an electronics store is $27,235. The company estimates that 15% is lost each day to returns, with a margin of error
of 13%. What is the maximum the company can expect for returned items?
O $3268.20
$3668.30
O$4425.60
O $4902.30
Using proportions, it is found that the maximum the company can expect for returned items is of:
$4,616.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations such as multiplication or division along with the unit rates in the context of this problem.
The lost amount to returns each day is of 15% of 27235, and this amount is calculated as follows:
0.15 x 27235 = $4,085.25
(the decimal equivalent of the percentage is multiplied by the original amount to find the equivalent amount).
The margin of error is of 13%, hence this amount can still be increased by 113, that is, multiplied by 1.13, hence:
4085.25 x 1.13 = $4,616.
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Answer:
The answer is D $4902.30
Step-by-step explanation:
. If g= 12 and h = 19, what is the value of3h(h-g)?A. 13B. 43C. 252D. 399
Solution
For this case we have the following:
g = 12 and h=19
And we want to find 3h(h-g)
If we replace we got:
3*19 (19-12) =57*7=399
Then the answer would be:
D. 399
HELP PLEASE!!! WILL AWARD BRAINLIEST xx
Based on the graph of the function shown, we can logically deduce the following:
Domain = -2 ≤ x < 0.Range = 0 ≤ x < 2.The relation is a continuous function.How to identify the range and domain of this graph?The vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
Similarly, the horizontal extent of a graph represents all domain values and they are also read and written from smaller to larger numerical values, and from the left of the graph to the right.
By critically observing the graph of the given function shown above, we can reasonably and logically deduce the following:
The domain is equal to -2 ≤ x < 0.The range is equal to 0 ≤ x < 2.In conclusion, the function which this graph represent is a continuous function because both the domain and range is defined for all set of values in the interval above.
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400 in savings for 20 years compounded 5% monthly
Answer:1,086
Step-by-step explanation: Initial Deposit
$400
Contributions
$0
Investment Time Span
20
Estimated Rate of Return
5.00%
In an office building, 42 offices are currently being rented. This represents 30% of the total units. How many offices are there in the building?
Let the total number of offices in the building be x.
We can represent the information provided in the question mathematically as:
[tex]30\text{ \% of x = 42}[/tex]Solving for x:
[tex]\begin{gathered} \frac{30}{100}\text{ }\times\text{ x = 42} \\ \frac{30x}{100}\text{ = 42} \\ \end{gathered}[/tex]Cross-Multiply:
[tex]\begin{gathered} 30x\text{ = 4200} \\ \text{Divide both sides by 30} \\ \frac{30x}{30}\text{ = }\frac{4200}{30} \\ x\text{ = 140} \end{gathered}[/tex]Hence, there are 140 offices in the building.
Answer: 140 offices
Write the equation of the line with a slope of -3 that passes through (-5,20)
SUBSTITUTE THE KNOWNS IN THE GIVEN GENERAL EQUATION BELOW AND SIMPLIFY TO GET c
[tex]y = mx + c \\ 20 = - 3( - 5) + c \\ 20 = 15 + c \\ c = 20 - 15 \\ c = 5[/tex]
Meaning
[tex]y = - 3x + 5[/tex]
IS THE EQUATION
Tristan is building steps up to a deck that is 1 yards above the ground. The steps must all be the same height. If he wants to make 8 steps, how high should he make each step?
Tristan should make 8 pieces of length 0.125 yards each to make a steps to the deck 1 yards above.
What is division?Division is breaking a number up into an equal number of parts. Mathematically, we can write "[a] divided by [b]" as a ÷ b. The division algorithm is given by -
D = dq + r
[D] - Dividend
[d] - Divisor
[q] - Quotient
[r] - remainder
Given is Tristan who is building steps up to a deck that is 1 yards above the ground. The steps must all be the same height an he wants to make 8 steps.
Total number of steps to be made = [n] = 8
Height of deck = [h] = 1 yard.
Now, we have to divide 1 yard into 8 equal parts. Therefore, assume
that -
A = 1 ÷ 8
A = 1/8
0.125
We get the length of each step to be 0.125 yards.
Therefore, Tristan should make 8 pieces of length 0.125 yards each to make steps to the deck 1 yards above.
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Alicia has 10 paintings and wants to hang them side by side on the wall. How many ways can she hang the paintings?
The total number of ways she can hang the painting is 720 after applying the concept of permutation and combination.
What are permutation and combination?The variety of possible arrangements of a set is its permutation however order is important in permutations but not in combinations.
It is given that:
Alicia wants to place her ten paintings side by side on the wall.
We can get the factorial of 6 and use that knowledge to calculate how many ways there are to multiply 6 by multiplying it by all positive integers that are more than or equal to that number, in this case, 6.
Alicia can arrange her six paintings:
6! = 6x5x4x3x2x1
6! = 720
Thus, the total number of ways she can hang the painting is 720 after applying the concept of permutation and combination.
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Write the correct equation for the following statement.
The quotient of x and seven is twelve
Answer:
Step-by-step explanation:
x/7=12
Simplify the fractiom
7/21
4/38
Need help with a statistics question please!
Ben has £24
He gives £16 to Rhys.
a) What fraction of the £24 does Rhys get?
Give your answer in its simplest form.
b) What fraction of the £24 does Ben have now?
Give your answer in its simplest form.
Answer:
[tex]\frac{2}{3}[/tex] and [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
(a)
fraction Rhys gets is [tex]\frac{16}{24}[/tex] = [tex]\frac{2}{3}[/tex]
(b)
Ben is left with £24 - £16 = £8
then fraction Ben has left is
[tex]\frac{8}{24}[/tex] = [tex]\frac{1}{3}[/tex]
Kathy Runde, age 66 and retired, receives a $20,000 partial distribution from her 401(k) plan. The plan does not pay out an annuity. Immediately before the distribution, her account balance is $50,000, including $10,000 in nondeductible contributions. How much of the $20,000 distribution must Kathy include in gross income?
The whole twenty thousand dollars that were distributed has to be accounted for as part of the gross revenue.
This is further explained below.
What is gross income?Generally, A person's or a household's gross income is the whole amount of money earned before any deductions or taxes are taken out of that income. This includes all wages, salaries, profits, interest payments, rentals, and other types of earnings.
Because it is treated as regular income, the amount that was withdrawn is subject to taxation at the same rate as ordinary income under the federal income tax system.
If, on the other hand, Kathy makes the decision to convert her 401(k) to a Roth 401(k), then any money she takes out of the account will not be subject to taxes.
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One batch of pink paint uses 2 cups of red paint and 7 cups of white paint. Mai made a
large amount of pink paint using 14 cups of red paint.
a. How many batches of pink paint did she make?
Answer:
7
Step-by-step explanation:
14/2=7
<1 is in a triangle work <4 and a 53° angle . what is the sum of the measures of these two angles
In the small triangle
There are a right angle and an acute angle of measure 53 degrees
Since the sum of the angles of a triangle is 180 degrees
Then 90 + 53 + < 1 = 180 degrees
Then 143 + < 1 = 180
Subtract 143 from both sides
Then < 1 = 37 degrees
Since <2 is an exterior angle of the small triangle
Then its measure = the sum of <1 and 90 degrees
Then < 2 = 37 + 90 = 127 degrees
In the triangle of angles 2, n3 and 30
< 2 + < 3 + 30 = 180
127 + < 3 + 30 = 180
Add 127 and 30
157 + <3 = 180
<3 = 23
The answer is < 2 = 127 degrees and < 3 = 23 degrees
Which number comes first
5
1/3 -1. √3. - 12/21
6
3.4
-3.4 is the number which will come first.
What is simplifying?To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. the act of simplifying something such that it is simpler to carry out or understand, or the thing that is the product of this simplifying process: The group offers suggestions for streamlining business processes. This grossly oversimplifies what actually transpired.
Given Data
5, 1/3 -1. √3. - 12/21,6,3.4
Simplifying,
5, [tex]\frac{1}{3}[/tex] - 1, √3. -[tex]\frac{12}{21}[/tex], 6, -3.4
5, -0.6 , [tex]\sqrt{3}[/tex] , -0.5 ,6,-3.4
-3.4 is the number which will come first.
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School Supplies Pencils $0.25 each Notebooks $2.50 each Backpacks $32 each- . Hugh bought x notebooks. Write an expression for the cost of the notebooks.
Pencils: $0.25 each
Notebooks: $2.50 each
Backpacks: $32 each
The cost of the notebooks (C) must be equal to the price of each notebook (2.50) multiplied by the number of notebooks bought (x)
C = 2.50x
Find the product of 21 and the difference between one whole number 1/2 and -1/2
The product of 21 and the difference between one whole number 1/2 and -1/2 is; 42
What is the product of the two numbers?We want to find the product of 21 and the difference between one whole number 1/2 and -1/2. This can be expressed as;
21 * (1¹/₂ - (-¹/₂))
Let us first solve the bracket out using the order of operations rule named PEMDAS which stands for P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction to get;
1¹/₂ - (-¹/₂)
= 1¹/₂ + ¹/₂
= 2
Thus;
21 * (1¹/₂ - (-¹/₂)) = 21 * 2
= 42
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Find an equation in point-slope form for the line having the slope m=-3 and containing the point (4,2).
The equation of a line in point-slope form is given by
[tex]y-y_1=m(x-x_1)[/tex]Where
[tex]\begin{gathered} m=-3 \\ y_1=2 \\ x_1=4 \end{gathered}[/tex]Thus, if we substitute the above values into the equation:
[tex]y-2=-3(x-4)[/tex]the domain of a function is all of the second value of ordered pairs
true or false?
Answer:
False
Step-by-step explanation:
Domain is the x-axis, range is the y-axis. In an ordered pair, the x-values go first, not second.
If you roll a 6-sided die 72 times, what is the best prediction possible for the number of times you will roll a one?
The prediction of outcomes of the number of 1 is 12
How to determine the number of times?The given parameters are
Device = A die
Number of rolls = 72
From the question, the die is six-sided
This means that the sample space is
S = {1, 2, 3, 4, 5, 6}
So, the probability of rolling a 1 is
P(1) = 1/6
When the die is rolled 72 times, the number of outcomes of 1 is
Outcomes = P(1) * n
Where n = 72
So, we have
Outcomes = 1/6 * 72
Evaluate
Outcomes = 12
Hence, the prediction is 12
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Are the triangles similar! If yes state how?are the triangles similar if yes State how
Part 1
Remember that
If two triangles are similar , then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
so
Verify the proportion
38.5/14=22/8
38.5*8=14*22
308=308 -----> is true
that means
the triangles are similarPart 3
Verify the proportion
22/9=30/12=25/10
2.44=2.5=2.5 ------> is not true
that means
the triangles are not similarIf you could please help me with this it makes no sence to me.
Answer:
A = 7986 m²
Step-by-step explanation:
the field is in the form of a trapezium.
the area (A) of a trapezium is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the perpendicular distance between the bases b₁ and b₂
here h = 66 , b₁ = 102, b₂ = 140 , then
A = [tex]\frac{1}{2}[/tex] × 66 × (102 + 140) = 33 × 242 = 7986 m²
Answer:
7986 m²
Step-by-step explanation:
The field geometric shape is a trapezoid whose bases are 102 m and 140 m and height of 66m
The equation for the area of a trapezoid is given by
[tex]A = \dfrac{a + b}{2} h\\\\[/tex]
where a and b are the two sides and h is the height
Here a = 102, b = 140 and h = 66
Substitute these values directly into the equation for area
[tex]A = \dfrac{102 + 140}{2} \times 66\\\\A = (102 + 140) \times \dfrac{66}{2}\\\\\\102 + 140 = 242\\\\\dfrac{66}{2} = 33\\\\\\A = 242\ \times 33 = 7986\; m^2[/tex]
4/5 equals blank over 100
We solve as follows:
[tex]\frac{4}{5}=\frac{x}{100}\Rightarrow x=80[/tex]So, the value of "blank" is 80.
For each of the variables described below, indicate whether it is a quantitative or a categorical (qualitative) variable. Also, indicate the level of measurement for the variable: nominal, ordinal, interval, or ratio. Make sure your responses are the most specific possible.
Part A.
From the given table, we can see that the variable occupation is a Categorical variable becasue the occupation can divide a set of people into groups. Then, the level of measurement is Nominal because the occupation describes the objects by labels, with no quantitative value.
Part B.
Temperature is a Quantitave variable because we can measure the temperature of an object. Regarding the level of measurement, the temperature is an Interval variable because zero temperature is not the lowest possible temperature.
Part C.
The price is a Quantitative variable because the price is a numerical value with a meaningful order. Regarding the level of measurement, the price is a Ratio variable because it has a true zero, meaning that we can take ratios of values.
A country's education department reported that in 2015, 64.8% of students enrolled in college or a trade school within 12 months of graduating high school. In 2017, a random sample of 179 individuals who graduated from high school 12 months prior was selected. From this sample, 112 students were found to be enrolled in college or a trade school. Complete parts a through c. a. Construct a 90% confidence interval to estimate the actual proportion of students enrolled in college or a trade school within 12 months of graduating from high school in 2017.
The confidence interval has a lower limit of
and an upper limit of
(Round to three decimal places as needed.)
Answer:
Step-by-step explanation:
Nicholas is typing a book report at an average of 30 words per minute. Which equation could Nicholas use to find tea the amount the amount of time in minutes he will spend typing his report has W words?
The equation could Nicholas use to find tea the amount the amount of time in minutes he will spend typing his report has W words is w = 30t .
What is speed?In contrast to velocity, which describes the speed and direction of an object's movement, speed is the rate of movement along a path. Alternatively, velocity is a vector while speed is a scalar quantity. Velocity and speed are denoted by the letters v and v, respectively (boldface). The symbol has a bar over it for average values. How swiftly something is going, being done, or something that is moving quickly is measured in terms of speed. Driving an automobile 45 miles per hour is an illustration of speed. Someone cleaning a room in 10 minutes would be an example of quickness. the definition of speed. a direction or speed at which an object's location changes.
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