Answer:
a) To determine the monthly mortgage payment, we first need to calculate the amount of the loan, which is equal to the purchase price of the house minus the down payment. In this case, the loan amount is 250,000 * 0.8 = 200,000. Next, we need to calculate the monthly interest rate, which is equal to the annual interest rate divided by 12. In this case, the monthly interest rate is 0.12/12 = 0.01. Using the formula for the monthly mortgage payment (P = L[i(1+i)^n]/[(1+i)^n-1]), where P is the monthly payment, L is the loan amount, i is the monthly interest rate, and n is the number of payments (in this case, 30 years * 12 = 360), we can calculate the monthly payment as:
P = 200,000[0.01(1+0.01)^360]/[(1+0.01)^360-1] = 1326.91
b) To calculate the total amount of interest Ato Liku will pay over the life of the mortgage, we can subtract the original loan amount from the total amount of payments made over the life of the mortgage. In this case, that would be 360 * 1326.91 - 200,000 = 480,596.
c) To determine the amount of the mortgage Ato Liku will have paid after 10 years, we can multiply the monthly mortgage payment by the number of payments made in 10 years (10 years * 12 = 120). In this case, that would be 120 * 1326.91 = 159,223.20.
PLS HELPPPPPPPPPPPPPPOOP
how many 1/4 are in 3 inches
Answer:
12 inches
Step-by-step explanation:
3 inches / (1 / 4) = 12 inches
Kasey found a linear model for a data set. She believes her model is a good fit for the data based on the correlation coefficient. Which correlation coefficient best supports her claim?
r=-0.25
r=0.91
r=0.01
r=-0.79
Kasey's claim that her model is a good fit for the data is best supported by a correlation coefficient of r = 0.91. The correct answer would be an option (B).
What is the correlation coefficient?A correlation coefficient (r) is a number between -1 and 1 that measures the strength and direction of a linear relationship between two variables.
A coefficient of r = 1 indicates a perfect positive linear relationship, meaning as one variable increases, the other variable also increases.
A coefficient of r = -1 indicates a perfect negative linear relationship, meaning as one variable increases, the other variable decreases.
A coefficient of r = 0 indicates no linear relationship between the variables.
In this case, a coefficient of r = 0.91 is close to 1 which means that there is a strong positive linear relationship between the data and the model. On the other hand, the other coefficients -0.25, 0.01, and -0.79 are not close to 1, which means that there is no or weak linear relationship between data and the model.
Hence, the correct answer would be an option (B).
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If f and g are both even functions, is the product fg even? If f and g are both odd functions, is fg odd? What if f is even and g is odd?
F g - x hence equals -f x. -g x. It follows from this that f g - x = f g x. Given that f and g are two odd functions, it follows that f g is an even function. As a result, f g is not an unusual function.
What is meant by odd function?If the equation for every x and x in the domain of f holds, then a function f is odd. F(x)=F(x) or F(x)=F(x) An odd function has a graph that, geometrically speaking, is rotationally symmetric with respect to the origin, meaning that the graph is unaffected by a 180° rotation of the origin.
If f - x = f x, then a function f x is said to be even. These functions have symmetric properties around the y-axis.
F - x Equals F x if two functions f and g are two even functions.
g - x = g x
Now, the definition of the product function f g is as follows:
[tex]$f g x=f x \cdot g x$[/tex]
Analyze the fg at -x product function.
[tex]$f g-x=f-x \cdot g-x$[/tex]
The two functions are currently equal functions. Utilize the knowledge that f - x = f and g - x = g.
Consequently, f g - x = f x. g x It follows from this that f g - x = f g x. This suggests that f g, where f and g are two even functions, is an even function.
If f - x = -f x, then a function f x is said to be odd. These functions have symmetry at their origin.
If f and g are two odd functions, then f - x = -f x and g - x = -g x, respectively.
Now, the definition of the product function f g is as follows:
[tex]$f g x=f x \cdot g x$[/tex]
Evaluate the product function f g at -x
[tex]$f g-x=f-x \cdot g-x$[/tex]
The two functions are now peculiar functions. Utilize the knowledge that f-x = -f-x and g-x = -g-x.
F g - x hence equals -f x. -g x. It follows from this that f g - x = f g x. Given that f and g are two odd functions, it follows that f g is an even function. As a result, f g is not an unusual function.
Assume that g is odd and f is even. G - x = -g x and f - x = f x, respectively.
The following is a definition of the product function:
[tex]f g-x & =f-x \cdot g-x \\[/tex]
[tex]& =f x \cdot-g x \\[/tex]
[tex]& =-f x \cdot g x \\[/tex]
[tex]& =-f g x[/tex]
Because f is even and g is odd, f g is an odd function.
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D and T are points on a polygon.
D' are T' points of the polygon under a translation. Determine the translation. Write your answer as .
D(5,-10) T(-9,-6)
D'(0,-1) T'(-14,3)
The polygon was translated 5 units left and 9 units up using the rule for (x, y) ⇒ (x - 5, y + 9)
What is an translation?Translation is the movement of a point in the coordinate plane either up, left, down or right. Translation is a type of rigid transformation because it preserves both the shape and size of the figure.
Other types of rigid transformations are reflection and rotation.
The points D(5, -10) and T(-9, -6) were translated to give D'(0,-1), T'(-14,3). This means that the translation was 5 units left and 9 units up.
The rule for this translation is (x, y) ⇒ (x - 5, y + 9)
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otherwise, x is possible but uncertain, and 0 < p(x) < 1. in the die example, the probabilities of each of the six outcomes are equally likely (so long as the die is fairly balanced), so p(1)
The probability of rolling an odd number on a fair six-sided die is P(odd) = (1/6) + (1/6) + (1/6) = 3/6 = 1/2. This is because there are three odd numbers (1, 3, and 5) out of the six possible outcomes, and they are each equally likely to occur.
The probability of rolling a number divisible by 3 on a fair six-sided die is P (divisible by 3) = (1/6) + (1/6) = 2/6 = 1/3. This is because there are two numbers (3 and 6) out of the six possible outcomes that are divisible by 3, and they are each equally likely to occur.
It's important to note that in both of these examples, we are assuming that the die is fair and unbiased, which means that each of the six possible outcomes has an equal chance of occurring. If the die is not fair, the probabilities of each outcome could be different.
Complete question:
More probability Aa Aa An event's probability measures the likelihood of its occurrence. The probability that an event X occurs is between 0 and 1, inclusive, and is denoted by P(X). If it is impossible for X to occur, then P(X) Rolling a standard six-sided die, the probability of rolling a 7 is zero, P(7)-0. If X is the set of all possible outcomes in the experiment, then X is certain to occur and P(X)1 In the die example, X could be that an integer is rolled, which must occur, and thus P(integer)-1 Otherwise, X is possible but uncertain, and 0<P(X) 1. In the die example, the probabilities of each of the six outcomes are equally likely (so long as the die is fairly balanced), so P(1)-P(2)-P(3)-P(4) = P(5)-P(6)- 1/3. If possible, you want to identify all the possible outcomes, called the If you are rolling a 1/6). fair die, your outcomes range from 1 to 6, with equal probability (P The probability of rolling an odd number is the probability of rolling a number divisible by 3 is
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let $n$ be the number of ordered triples $(a,b,c)$ of integers satisfying the conditions (a) $0\le a
The total number of ordered triples $(a,b,c)$ satisfying the conditions [tex]$0\le a \le b \le c \le 10$[/tex] is 10275.
The total number of ordered triples $(a,b,c)$ satisfying the conditions [tex]$0\le a \le b \le c \le 10$[/tex] is given by
[tex]$n= \sum_{a=0}^{10}\sum_{b=a}^{10}\sum_{c=b}^{10} 1$$= \sum_{a=0}^{10}\sum_{b=a}^{10} (c-b+1)$$= \sum_{a=0}^{10}\sum_{b=a}^{10} c - \sum_{a=0}^{10}\sum_{b=a}^{10} b + \sum_{a=0}^{10}\sum_{b=a}^{10} 1$$= \sum_{a=0}^{10}\sum_{b=a}^{10} 10 - \frac{10(11-a)(a+1)}{2} + \sum_{a=0}^{10} (b-a+1)$$= \sum_{a=0}^{10} 105 - \frac{10(11-a)(a+1)}{2} + \frac{10(a+1)}{2}$$= \sum_{a=0}^{10} \frac{185 + 10a^2}{2}$$= \frac{(185 + 10\times 100) \times 10}{2}$ $= \frac{2055 \times 10}{2}$ $= 10275$[/tex]
Therefore, the total number of ordered triples $(a,b,c)$ satisfying the conditions [tex]$0\le a \le b \le c \le 10$[/tex] is 10275.
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Convert mixed number into an improper fraction 2 1/8
Answer:
[tex]\frac{17}{8}[/tex]
Step-by-step explanation:
[tex]2\frac{1}{8} = (2*8)+1 =17= \frac{17}{8}[/tex]
Answer:
17/8
Step-by-step explanation:
40,512 rounded to the nearest thousand
Answer: 41,000
Step-by-step explanation:
If the hundreds column 5 or more than it rounds up if it is lower it rounds down
x² - 2x - y² + 4y-3 , x² + 2x - y² + 8y-15 find hcf
To find the highest common factor (HCF) of two polynomials, we can use the Euclidean algorithm or the method of factoring the polynomials and comparing their common factors.
The first polynomial is x² - 2x - y² + 4y-3 and the second polynomial is x² + 2x - y² + 8y-15
x² - y² is common in both polynomials, let's factor it out.
x² - y² = (x-y)(x+y)
so the first polynomial can be written as (x-y)(x+y) - 2x + 4y - 3
and the second polynomial can be written as (x-y)(x+y) + 2x + 8y - 15
So the HCF of these two polynomials is (x-y)(x+y)
It is important to note that the HCF of polynomials is not unique, there can be more than one factorization.
Popcorn at a concession stand comes in two different-sized containers. The dimensions of the small container with a diameter of 4 in. are shown below.
A popcorn container shaped like a cylinder is shown. A dashed line across the top of the container is labeled four inches. The height of the container is labeled four and five tenths inches.
The large container of popcorn has the same height as the small container, but its diameter is 1.5 times greater. How do the volumes of the two containers of popcorn compare? Use 3.14 for π.
Select the answers from the drop-down lists to correctly complete each sentence.
The volume of the large container of popcorn is _______ in.^3
OPTIONS FOR BLANK : A) 56.52 B) 84.78 C)127.17 D) 169.56
This is ______ times the volume of the small container.
OPTIONS FOR THIS BLANK : A) 2.88 B) 2.25 C) 1.8 D) 1.5
The volume of the large container is given as follows:
113.04 in³.
The ratio of the volumes is of:
B) 2.25
How to obtain the volume of a cylinder?The volume of a cylinder of radius r and height h is given by the equation presented as follows:
V = πr²h.
The diameter of the smaller cylinder is of:
4 inches.
Hence the diameter and radius of the larger container is of:
Diameter: 4 x 1.5 = 6 inches.Radius: 0.5 x 6 = 3 inches.As the height of the cylinder is of 4 inches, the volume is given as follows:
V = 3.14 x 3² x 4
V = 113.04 in³.
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HELP!! Quadrilateral ABCD is inscribed in circle P. Complete the following.
The measures of the angles are (a) 180-C, and 180-A (b) 180 (c) 180 and supplementary.
What is a cyclic quadrilateral?You should understand that cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle
For better understanding note the following
Opposite angles of a cyclic quadrilateral are supplementaryopposite angles of a cyclic quadrilateral = 180 degrees(a) m<A = 180 - m<C
m<C = 180 - m<A
(b) m<A + m<C = 180 .......... (opposite angles are supplementary)
(c) m<A + m <C = 180 (Sum of opposite angles = 180⁰)
(d) <A and <C are supplementary angles
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Triangle LMN is similar to triangle OPQ. Find the measure of side OP. Round your
answer to the nearest tenth if necessary.
Triangle LMN is similar to triangle OPQ. The measure of side OP is 12.6
How to find the measure of side OP?Triangle LMN is similar to triangle OPQ.
Similar forms or figures have corresponding sides that are proportionate to one another. The ratio of their matching sides would be identical because LMN OPQ. Thus:
MN/PO = LN/OQ
LN = 31
OQ = 8
MN = 49
RO = ?
Put the values in.
31 / 8 = 49 / PO
multiply by cross
31 * PO = 49 * 8
31 * PO = 392
PO = 392 / 31
PO = 12.6
Triangle LMN is similar to triangle OPQ. The measure of side OP is 12.6
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sharon has at most $25 to spend on her sister's birthday gift. she already bought a knitting machine for her, which cost $14.99. she would also like to get her sister some skeins of yarn to go with it. each skein costs $2.75.
Three skeins are the most Sharon can afford to purchase because a number of skeins have to be a whole number.
For her sister's birthday present, Sharon has a budget of no more than $25. Sharon is therefore limited to spending no more than $25. She has paid $14.99 for a knitting machine for her. She wants to get her sister some yarn skeins to go with it as well. Cost per skein is $2.75. Let y be the number of yarn skeins.
The necessary inequality is:
14.99 + 2.75y ≤ 25
2.75y ≤ 25 - 14.99
2.75y ≤ 10.01
y ≤ 10.01 / 2.75
y ≤ 3.64
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What equation do I write?
Answer:
[tex]y=-\dfrac{1}{30}x+12[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
The y-intercept is the y-value of the point at which the line crosses the y-axis.
Therefore, from inspection of the given graph, the y-intercept is 12:
b = 12The slope of a line is the change in y over the change in x.
From inspection of the given graph, the change in y is -3 and the change in x is 90. Therefore, the slope is:
[tex]\sf m=\dfrac{-3}{90}=-\dfrac{1}{30}[/tex]Substitute the found values of m and b into the slope-intercept formula to create an equation of the line:
[tex]y=-\dfrac{1}{30}x+12[/tex]
Solve the compound inequality.
- 4x + 2
3
-3≤
≤4
Answer:
The inequality can be solved by isolating the variable x on one side of the inequality. To do this, we can first add 4x to both sides of the inequality:
-2 ≤ 4x + 3 ≤ 4
Next, we can subtract 3 from both sides of the inequality:
-5 ≤ 4x ≤ 1
Finally, we can divide both sides of the inequality by 4 to solve for x:
x ≥ -5/4 and x ≤ 1/4
So the solution of the compound inequality is x ≥ -5/4 and x ≤ 1/4
We can also express this solution in interval notation: [-5/4, 1/4]
Note that the compound inequality has two separate inequality signs, indicating that the solution is the set of all x-values that make both inequalities true.
Step-by-step explanation:
An open box is to be constructed from a square piece of sheet metal by removing a square of side 3 feet from each corner and turning up the edges. If the box is to hold 300 cubic feet, what should be the dimensions of the sheet metal?
If an open box is to be constructed from a square piece of sheet metal by removing a square of side 3 feet from each corner and turning up the edges. the dimensions of the sheet metal is 16 feet.
How to find the dimension?Let x represent the dimension of the sheet metal
So,
Volume =3×(x-2×3)×(x-2×3) = 300
Volume =3×(x-6)×(x-6) = 300
(x -6)² = 300/3 = 100
x-6 = √100 =10
x = 10 +6
x = 16 feet
Therefore the dimensions of the sheet metal is 16 feet
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Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) f(x)=x [-/1 Points]. Find the most generat antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) r(θ)=sec(θ)tan(θ)−5e θ3. [-/1 Points] Find 1. f(x)=(x)=1+2 x ,f(4)=24
4. [-/1 Points] 4.9.061 A paricle is moving with the given gata. Find the position of the particle.
1. The antiderivative would be x.
2. The antiderivative would be sec(θ)tan(θ)−5e^(θ^3).
3. The antiderivative would be 1+2x.
What is the antiderivative of the function?
An antiderivative of a function is a function whose derivative is equal to the original function. It is also known as an indefinite integral of a function with respect to its variable. The process of finding an antiderivative is called integration.
1. The most general antiderivative of the function f(x)=x is F(x) = (1/2)x^2 + C, where C is the constant of the antiderivative. To check this, we can differentiate F(x) using the power rule for derivatives and see if we get back f(x) = x: d/dx [(1/2)x^2 + C] = d/dx (1/2)x^2 + d/dx C = x
2. The most general antiderivative of the function r(θ)=sec(θ)tan(θ)−5e^(θ^3) is R(θ)=∫sec(θ)tan(θ)−5e^(θ^3) dθ = -ln(cos(θ))+5e^(θ^3)/3+C, where C is the constant of the antiderivative. To check this, we can differentiate R(θ) using the rules of integration by substitution, and see if we get back r(θ) = sec(θ)tan(θ)−5e^(θ^3): d/dθ [-ln(cos(θ))+5e^(θ^3)/3+C] = sec(θ)tan(θ)−5e^(θ^3)
3. The most general antiderivative of the function f(x)=1+2x is F(x) = x+x^2 + C, where C is the constant of the antiderivative. To check this, we can differentiate F(x) using the power rule for derivatives and see if we get back f(x) = 1+2x: d/dx (x+x^2 + C) = d/dx x+d/dx x^2 + d/dx C = 1+2x
Hence,
1. The antiderivative would be x.
2. The antiderivative would be sec(θ)tan(θ)−5e^(θ^3).
3. The antiderivative would be 1+2x.
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which of the following shows a correct stacked bar chart with store location on the horizontal axis and percentage of time spent on each task on the vertical axis?
A correct stacked bar chart would show store location on the horizontal axis, and the percentage of time spent on each task on the vertical axis. Each store location would be represented as a separate bar, with each bar displaying the percentage of time spent on each task as stacked sections within the bar.
A stacked bar chart is a type of graph that is used to visualize data. It is a bar chart that displays the relative contribution of different data points to the whole. It is particularly useful for comparing the contribution of different data points across different categories. For example, a stacked bar chart can be used to show the percentage of time spent on different tasks at different store locations. The horizontal axis would represent the store locations, while the vertical axis would represent the percentage of time spent on each task. Each store location would then be represented as a separate bar, with each bar displaying the percentage of time spent on each task as stacked sections within the bar. The colors used to represent each task can be used to make the chart more visually appealing, and help viewers differentiate between the tasks. The stacked bar chart is a useful tool for analyzing data over multiple categories, and can be used to quickly identify trends and patterns.
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The complete question is
which of the following shows a correct stacked bar chart with store location on the horizontal axis and percentage of time spent on each task on the vertical axis Store Location Task
3 bottle of water of wine and four bottled water costs N450 if each bottle water cost 35 naira how much is spent on the wine
Answer:
N103. 33
Step-by-step explanation:
let the cost of bottle of water be represented by B
Let the cost of wine be represented by W
3×W + 4×B =N450
3W+4B=450....(1)
one bottle of water(B)Costs N35
3W+ 4(N35)= N450
3W + 140=450
collect the.like terms
3W= 450-140
3W = 310
divide through by 3
W= N103.33
The probability that amaka and David will pass statistic exams are 2/3 and 4/7 find the probability that one of them will pass the exam ?
Answer:
Amaka passes hers 2/3
Step-by-step explanation:
she just will
given 1 is congruent to 2 prove. p is parallel to q
Answer:
Step-by-step explanation:
Given : ∠1 ≅ ∠2
To prove : p║q
Solution :
In the figure attached,
Statements Reasons
1). m∠1 ≅ m∠2 1). Given
2) m∠1 ≅ m∠3 2). Vertical angles
3) m∠2 ≅ m∠3 3). Transitive property of congruence of the angles
4). Line p║q 4). Corr
There are 36 tables set up for the
annual pancake breakfast. Each table
is 8 feet long. The students plan
to cover each table with a paper
tablecloth that extends an extra
4 inches over each end so they can
tape it underneath. What is the total
length of paper needed to cover all
the tables?
The total length of paper needed to cover all the tables is equal to 10 tables multiplied by 104 inches per table, which is equal to 1040 inches.
What is Pythagorean theorem?According to the Pythagorean theorem, the hypotenuse's square length is equal to the sum of the squares of the two legs' lengths in a right triangle. The formula for this is a2 + b2 = c2, where a and b represent the lengths of the two legs, respectively, and c represents the length of the hypotenuse.
The theory used in this question is the Pythagorean theorem.
Number of tables:
Let's say there are 10 tables.
Length of each table plus 8 inches:
Each table is 8 feet long, which is equal to 96 inches. The extra 8 inches makes it 104 inches per table.
Total length of paper needed:
The total length of paper needed to cover all the tables is equal to 10 tables multiplied by 104 inches per table, which is equal to 1040 inches.
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3. expressing the binomial coefficients in terms of factorials and simplifying algebraically, show that (a) nr
Expressing the binomial coefficients in terms of factorials and simplifying algebraically. we have proved that
[tex]$\left(\begin{array}{l}n \\ r\end{array}\right) = \dfrac{n-r+1}{r} \cdot \left(\begin{array}{c}n \\ r-1\end{array}\right)[/tex]
What is binomial coefficients?The binomial coefficient [tex]\left(\begin{array}{l}n \\ k\end{array}\right)[/tex] is the number of ways of picking k unordered outcomes from n possibilities, also known as a combination or combinatorial number. The symbols [tex]_nC_k[/tex] and [tex]\left(\begin{array}{l}n \\ k\end{array}\right)[/tex] are used to denote a binomial coefficient, and are sometimes read as "n choose k."
[tex]$$In general, $\left(\begin{array}{l}n \\ r\end{array}\right) \neq\left(\begin{array}{c}n \\ r-1\end{array}\right)$To solve (a), simply expand LHS.$$\left(\begin{array}{l}n \\r\end{array}\right)=\frac{n !}{r ! \cdot(n-r) !}=\frac{n !}{r \cdot(r-1) ! \cdot(n-r) !}$$Multiply numerator and denominator by $(n-r+1)$, then,$$\left(\begin{array}{l}n \\r\end{array}\right)=\frac{n-r+1}{r} \cdot \frac{n !}{(r-1) ! \cdot(n-r+1) !}=\frac{n-r+1}{r} \cdot\left(\begin{array}{c}n \\r-1\end{array}\right)$$[/tex]
Thus, Expressing the binomial coefficients in terms of factorials and simplifying algebraically. we have proved that
[tex]$\left(\begin{array}{l}n \\ r\end{array}\right) = \dfrac{n-r+1}{r} \cdot \left(\begin{array}{c}n \\ r-1\end{array}\right)[/tex]
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Full question:
Expressing the binomial coefficients in terms of factorials and simplifying algebraically, show that:
(a) [tex]$\left(\begin{array}{l}n \\ r\end{array}\right) = \dfrac{n-r+1}{r} \cdot \left(\begin{array}{c}n \\ r-1\end{array}\right)[/tex]
what is the mean number of cakes jenny bakes in a month. Numbers of cake are 100, 200, 300, 400, 500, 600, 700
Answer:
400
Step-by-step explanation:
[tex]100 + 200 + 300 + 400 + 500 + 600 + 700 = 2800 [/tex]
There are 7 numbers ( No. of cakes in a month)
Therefore, we should divide it by sum of the cakes
[tex]2800 \div 7 = 400[/tex]
SO MEAN NUMBER IS 400//
A long year-end status report for work is 127 pages long. You need to print 18 copies for a meeting next week. How much is the paper going to cost for those reports? Paper is sold in reams (500 pages) for $3.77 each.
$
Answer:
$18.85
Step-by-step explanation:
1. 127*18 = 2286 pages.
2. 2286/500 = 4.6 (approx.)
3. You need to buy 5 reams of paper 500 pages each.
It will cost 5*$3.77 = $18.85
I Need help please….
The distance between two points on a line segment .
What is the formula for graph length?Learn how to use the distance formula to calculate the distance between two points, which is an application of the Pythagorean theorem. To calculate the distance between any two points, we may rewrite the Pythagorean theorem as d=((x 2-x 1)2+(y 2-y 1)2). Sal Khan and the CK-12 Foundation created it.
A line segment is delimited by two separate points on a line in geometry. A line segment is a section of a line that links two locations. A line has no endpoints and stretches in both directions indefinitely, but a line segment has two defined or definite endpoints.
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solve for x in the right triangle. 915 a right triangle is given. the first side has length 9. the second side has length x. the third side of length 15 is opposite the right angle. g
The length of the second side, x, is 12.
What is Pythagoras' theorem?
In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs of the triangle). This theorem is usually represented by the equation: a^2 + b^2 = c^2, where c is the length of the hypotenuse, and a and b are the lengths of the legs.
In this case, the first side has a length of 9, the second side has a length of x, and the third side has a length of 15, which is the hypotenuse. We can use the Pythagorean theorem to solve for x:
x^2 + 9^2 = 15^2
x^2 = 15^2 - 9^2
x^2 = 225 - 81
x^2 = 144
x =√144
x = 12
Hence, the length of the second side, x, is 12.
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The given points lies on the terminal side of an angle (θ)in standard position. Find the values of six trig functions of (θ).(2,−4).
The values of six trig functions are:
sinθ=− √5/5, cosθ=2√5/5, tanθ=-1/2, cot θ=−2, secθ=√5/2, cscθ=−√5
The relationship between the angles and sides of a triangle is given by these trig functions.
There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).
The point's coordinates are:
x=2, y=−4
To calculate the functions we have to calculate the distance between the point and the origin:
r=√x²+y²=√2²+(−4)²=√16+4=√20
r=2√5
Now we can calculate the functions:
sinθ=y/r=−2/2√5=−√5/5
cosθ=x/r=4/2√5=2/√5=2√5/5
tanθ=y/x=−2/4=−1/2
cotθ=x/y=4/−2=−2
secθ=r/x=2√5/4=√5/2
cscθ=r/y=2/√5−2=−√5.
Hence, the values of trig functions are calculated.
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The stem & leaf diagram shows the
number of emails received by Colin
each day.
8016
9 2 3 5 6 7789
10 0 1 2 3 4
11 1 3
12 3 8
Key:
10 3 means 103 emails
Find the median.
To find the median of the data set, we first need to arrange the data in numerical order. We can do this by grouping the digits in the stem & leaf diagram according to the key:
8016
92 35 67
100 124 34
113
123 8
Then we will arrange them in order as: 8016 92 35 67 100 124 34 113 123 8
To find the median we have to identify the middle value of the data set, considering that we have 12 data points. The middle value is the 7th value in the set which is 100, therefore the median is 100.
