Answer:
1/2
Step-by-step explanation:
Given right triangle ABC with right angle A and tan(B) = 1, you want the value of the expression tan(C) -sin(B)cos(C).
AnglesAngle A is given as 90°.
Angle B is found from ...
tan(B) = 1 ⇒ B = arctan(1) = 45°
Angle C is its complement:
C = 90° -B = 45°
Trig functionsThe relevant trig functions are ...
tan(C) = tan(45°) = 1
sin(B) = sin(45°) = 1/√2
cos(C) = cos(45°) = 1/√2
ExpressionThen the value of the expression is ...
tan(C) -sin(B)cos(C)
= 1 -(1/√2)(1/√2) = 1 -1/2
= 1/2
Evaluate x/y for x=1/6 and y=1/3.
1/18
1/2
1/9
9
Answer:
soln:
x/y=1/6/1/3
=1/6×3/1
=1/2
Therefore x/y = 1/2
How to teach area Grade 5?
On the basis of their sides, we may similarly determine the areas of various shapes like rectangles, parallelograms, triangles, and any polygon.
The space the thing occupies is known as the area. Any shape can call this area home. We solely take into account the side's length when calculating the square's area. A square's area is equal to the sum of its squared sides since all of its sides are equal.
Similar to triangles, we can determine the area of any polygon based on its sides, as well as the areas of other forms like rectangles, parallelograms, and triangles. The radius of the surface, or the separation of the outer line from the axis for curved surface objects, is used to compute the area of the surface.
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a normal population has a mean of 59.8 and a standard deviation of 18.0. a sample of 10 will be taken. find the probability that the sample mean will be greater than 59.8. a) calculate the z score. (round your answer to 2 decimals.) b) find the probability that the sample mean will be greater than 59.8. (round your answer to 4 decimals.)
The z-score is 0 and the probability that the sample mean will be greater than 59.8 is 0.5000
How to determine the probability?From the question, the given parameters about the distribution are
Mean value of the set of data = 59.8Standard deviation value of the set of data = 18.0The actual data value = 59.8The z-score
The z-score of the data value is calculated using the following formula
z = (x - mean value)/standard deviation
Substitute the given parameters in the above equation
z = (59.8 - 59.8)/18.0
Evaluate
z = 0
The probability
The probability that the sample mean will be greater than 59.8 is then calculated as:
P(x > 59.8) = P(z > 0)
From the z table of probabilities, we have;
P(x > 59.8) = 0.5
Hence, the probability is 0.5000
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What is an example of perpendicular equations?
An example of perpendicular equations are:
f(x)=2x+4
g(x)=[tex]\frac{-1}{2}\\[/tex]x+2
A straight line passing through a point is called a perpendicular line. It forms a 90-degree angle with a specific place where the line passes. The need for determining the perpendicular line is coordinates and a line equation.
Think about a line with the equation ax + by + c = 0 and the coordinates (x1, y1). The slope should be a/b. Let m1 and m2 represent the slopes of two lines; their product will be -1 if the lines are perpendicular to one another.
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
m = Δy/Δx = dy/dx = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line may be shown as
tan θ = Δy/Δx
A line's slope often indicates the steepness and direction of the line.
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Think about a line with the equation ax + by + c = 0 and the coordinates (x1, y1). The slope should be a/b. Let m1 and m2 represent the slopes of two lines; their product will be -1 if the lines are perpendicular to one another.
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
m = Δy/Δx = dy/dx = change in y/change in x
where "m" represents a line's slope.
How many solutions does the pair of equations y 0 and y =- 5 have class 10?
If there were two equation, one on top of the other, there would be infinitely many solutions. but here no solution
If there were two lines that intersected at one point, there would be one solution.
y=0 and y=-5 don't have any solutions. When you ask if a pair of equations have a solution, that means there is an intersection of the equations. The 2 equations will meet somewhere, and that is the solution. To find the solution, you set the equations equal to each other.
0≠-5
It is obvious that 0 and -5 are not equal to each other. Therefore, there is no solution. Also, y=0 and y=-5 are horizontal lines that are parallel to each other. They will never meet, which means there will be no intersection. No intersection means no solutions
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Is 3x² a polynomial?
The expression given in question is not a polynomial because it could not satisfy the criteria for polynomial.
What is polynomial?The algebraic expression that contains two or more terms having different power of the same variables along with subtraction, addition or multiplication sign is termed as polynomial.
such as x² - 4x+7
In the above expression, there are different power of same variable x,
or x³+ 3x²+x-5
The terms are separated by either addition or subtraction sign.
What is the degree of a polynomial?We know that a polynomial expression contains different terms in where there is different power of same variables. The highest power is called the degree of polynomial.
As example, 4x³+2x²-3x+2
we have highest power 3 so this is called 3-degree polynomial.
What are the criteria of polynomial?We stated earlier that an expression can be said a polynomial whenever two or more terms which contain numbers and variables along with addition or subtraction operator. From the question we have a term 3xA² that contain a number and two variable x and A. There is no addition or subtraction sign. So, the term could not satisfy the criteria for polynomial. It is called monomial.
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Which congruence theorem can be used to prove △ ABC ≅ △ DEF?
The ASA criterion might be the most appropriate, as it states that two triangles are congruent if two angles and the included side are congruent.
To use a congruence criterion in the given situation, you will need to determine which criterion is most appropriate based on the information provided. There are several congruence criteria that can be used to determine whether two triangles are congruent, including the Side-Side-Side (SSS) criterion, the Side-Angle-Side (SAS) criterion, the Angle-Side-Angle (ASA) criterion, and the Angle-Angle-Side (AAS) criterion.
In this case, the ASA criterion might be the most appropriate, as it states that two triangles are congruent if two angles and the included side are congruent. Given that ∠A=∠C=90∘ and AE=CB, you can use the ASA criterion to conclude that triangles AEB and CED are congruent.
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The question is -
Which congruence theorem can be used to prove EB = BD, AE = CB, ∠ A = ∠ C = 90°?
URGENT!
in how many ways can 7 books be arranged in a shelf if three particular books must stay together?
Answer:
5040 ways
Step-by-step explanation:
We need to place 3 particular books so that they are always together.
let 3 books are one books
we have 5 books
these can be arranged in ⁵P5 = 5! = 12O
total books = 3 × 2 = 6
Required no. of books are 120×6 = 720.
find and sketch the domain of the function. f(x, y, z) = ln(144 − 9x2 − 16y2 − z2)
The domain of the function f(x, y, z) = ln(144 − 9x² − 16y² − z²) is x ∈ (-4, 4), y ∈ (-3, 3) and z ∈ (-12, 12). It forms an ellipsoid.
Domain of a function is the set of all values possible for the input parameters for real output parameter or output parameter in given range.
f(x, y, z) = ln(144 − 9x² − 16y² − z²)
For f(x, y, z) to be real, 144 − 9x² − 16y² − z² should be greater than 0. So,
144 − 9x² − 16y² − z² > 0
9x² + 16y² + z² < 144
x²/ 4² + y²/ 3² + z²/ 12² < 1
So the domain is an ellipsoid.
Therefore x ∈ (-4, 4)
y ∈ (-3, 3)
z ∈ (-12, 12)
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What are the 6 angle types?
Angles are 6 types.
What are different types of angles?1.Acute Angle: An acute angle is any angle that is less than 90 degrees and is between 0 degrees and 90 degrees.
2.Obtuse Angle: Opposite of an acute angle is an obtuse angle. In other terms, an obtuse angle is one that is larger than 90 degrees and less than 180 degrees. It is the angle that is between 90 degrees and 180 degrees.
3. Right Angle: A right angle is always 90 degrees in length. Acute angles are those that are less than 90 degrees, whereas obtuse angles are those that are higher than 90 degrees.
4. Straight Angle: A straight angle has a measured angle of 180 degrees. Since the angle between its arms is 180 degrees, you can see that it is simply a straight line.
5.Reflex angle: The arms make an acute angle because this measurement is less than 90 degrees. What about the angle on the opposite side, though? What is the name of the larger angle that complements the acute angle? It is referred to as a reflex angle.
A reflex angle is any angle having a dimension higher than 180 degrees but less than 360 degrees (which corresponds to 0 degrees).
6.Complete Rotation: Entire rotation or full angle refers to an angle with a value of 360 degrees. When one of the arms extends completely, it is created.
Angles are 6 types.
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Will mark brainliest the first answer with explanation!!!
Consider a game in which each play costs one nickel (5¢). During each play, the game dispenses a coin to the player to keep. The game machine contains equal numbers of pennies (1¢), nickels, dimes (10¢), and quarters (25¢). The nickels that the player inserts do not go into the same pool of "reward" coins. What is the expected profit, in cents, for a player who plays five games in a row?
The expected profit, in cents, for a player who plays five games in a row, is given as follows:
26.25 cents.
How to obtain the expected profit?The distribution that models the profit of a player for a single game is given as follows:
P(X = -4 cents) = 0.25. -> pays 5 cents, wins 1 cent, loses 4 cents.P(X = 0 cents) = 0.25. -> pays 5 cents, wins 5 cents.P(X = 5 cents) = 0.25. -> pays 5 cents, wins 10 cents.P(X = 20 cents) = 0.25. -> pays 5 cents, wins 25 cents.The expected value of a discrete distribution is calculated as the sum of each outcome multiplied by it's respective probability, hence:
E(X) = -4 x 0.25 + 0 x 0.25 + 5 x 0.25 + 20 x 0.25 = 5.25 cents.
For five games, the expected value is obtained as the multiplication of the expected value of a single game by five, hence:
5E(X) = 5 x 5.25 = 26.25 cents.
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find an equation of the tangent line to the curve at the given point. y = 4ex cos(x), (0, 4)
The equation of the tangent line to the curve at the given point, y = 4ex cos(x), (0, 4) as calculated is y' = 0.
In order to find the equation we will have to differentiate y = 4ex cos(x)
On differentiating we get the differential as ,
y' = - 4eˣsin(x)
given the value of x as 0 and y as 4
y' = -4e⁰sin(0)
= 0 because sin( 0 ) = 0
Therefore ,the required equation is , y' = 0.
Differentiation is a technique which is used to find the derivative of a function . Differentiation is a mathematical procedure it determines the rate of change of a function based on one of its variables.
Other than differentiation calculus also has a branch known as integration.
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Make a sketch if you need to and solve this problem using similar triangles. A telephone pole has a shadow of 16 ft. When a person 5 ft. Tall has a shadow of 6 ft. How tall is the pole? write answer as a fraction. X = ft.
The height of the poll is 40/3 and 13.3ft.
Let us assume that the Height of an object is h.
Let us assume that the shadow of an object is y.
(As the shadow is always proportional to height .)
Thus y∝h
y = kh
As given
when a person 5 ft. tall has a shadow of 6 ft.
h = 5 ft and y = 6 ft
Put in y = kh
6 = 5k
[tex]k=\frac{6}{5}[/tex]
As given
A telephone pole has a shadow of 16 ft.
Let us assume that the height of the pole is x.
h = x and y = 16 ft
16 = hk compare the value of k
[tex]k=\frac{16}{x} \\\\\frac{6}{5} =\frac{16}{x} \\\\x=\frac{16*5}{6} \\\\x=\frac{80}{6} \\\\x=\frac{40}{3} ft[/tex]
0r
x=13.3ft
Therefore, The height of the poll is 13.3ft
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The function V(x)=x3−6x2 repreent the volume (in cubic inche) of the box hown. The function W(x)=V(12x) repreent the volume (in cubic inche) when x i meaured in feet. Write a rule for W. Then find W(2)
The rule for transformed function W(x ) = V(12x) is, W(x) = 1728 x³ - 864 x² and the value of W(2) is 10368 in³.
What is transformed polynomial function?Transforming a function means that the curve representing the graph "moves left, right, up and down" or "stretches " or "mirrors". For example, the graph of the function f(x) = x² + 3 can be obtained by simply shifting the graph of g(x) = x² up by 3 units. We have , function of Volume of box in cubic inches, V(x) = x³- 6 x² --(1)
also, an another function, W(x) = V(12x) repreent the volume (in cubic feet ) when x is meaured in inches. Now , understand the problem,
We are a function V whose inputs are in inches and whose outputs are in cubic inches . We are provide an another function W whose inputs are in inches and whose outputs are in cubic feet., W(x) = V(12x) makes sense because there are 12 inche in 1 feet. We are asked to write a rule for W and interpret the output for an input. Write the transformed function W(x) ,
W(x) = V(12x)
=> W(x) = (12x)³ - 6 (12x)²
=> W(x) = 1728 x³- 6× 144 x²
=> W(x) = 1728 x³ - 864 x²
Now, calculate W(2)
W(2) = 1728 (2)³ - 864 (2)²
=> W(2) = 13824 - 3456
=> W(2) = 10368 in³
When x is 2 feet , the volume of the is 8100 cubic inches.
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Complete question:
The function V(x)=x3−6x2 repreent the volume (in cubic inche) of the box hown. The function W(x)=V(12x) repreent the volume (in cubic feet) when x i meaured in inches. Write a rule for W. Then find W(2)
consider the following hypothesis test: h0: ha: m $ 20 m , 20 a sample of 50 provided a sample mean of 19.4. the population standard deviation is 2. a. compute the value of the test statistic. b. what is the p-value? c. using a 5 .05, what is your conclusion? d. what is the rejection rule using the critical value? what is your conclusion?
As a result, the test is significant and we can draw this conclusion that the population mean is less than 20.
A test statistic is what?A test statistic is a statistic used for testing statistical hypotheses. A test statistic, which is a tally of a data set that can be used to conduct the test and boils the data down to a single figure, is a common way to characterize a hypothesis test.
a) Here, the test statistic is calculated as:
Z= [tex]\frac{p'-p}{\sqrt{(p(1-p)/n} }[/tex]
Z=[tex]\frac{19.4-20}{\sqrt{(20(1-20)/50} }[/tex]
Z= -2.12
Therefore -2.12 is the required test statistic value here.
b) Given that this is a one-tailed test, the following p-value was calculated using standard normal tables: p = P(Z -2.12) = 0.0169
The necessary p-value in this case is therefore 0.0169.
c) The test is significant in this case, and the null hypothesis can be rejected because the p-value is 0.0169 0.05, which is the level of significance. This means that there is enough data to conclude that the mean is less than 20.
d) For a significance level of 0.05, we have the following data from normal standard tables:
P(Z < -1.645) = 0.05
Therefore, the following is the rejection criteria in this case: Reject H0 if Z -1.645.
We can reject the null hypothesis here and draw the same conclusion as in the previous section because the test statistic value is -2.12 -1.645. As a result, the test is significant and we can draw this conclusion that the population mean is less than 20.
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What are the 2 formulas for volume?
Answer:
length x width x height or probably like area x height
Step-by-step explanation:
At 8 a.m., the hobbit left Beorn's and headed towards the Misty Mountains at 3 mph. 2
hours later, Gandalf left Beorn's and headed in the same direction. If Gandalf was 5 miles
ahead at noon, what was his speed?
Answer:
8.5 mph
Step-by-step explanation:
First find how far Hobbit traveled in 4 hrs (8AM - Noon)
3 mph x 4 hr = 12 miles
Now find Gandalf's speed:
Galdalf traveled the same 12 miles that Hobbit did PLUS 5 more miles in 2 hours (10AM -Noon) for a total of 17 miles
Speed = 17 mi / 2 hr = 8.5 mph
How do you find the total from 1 to 100?
The total number from 1 to 100 is found by addition
What is addition in math ?
Combining things and counting them as one big group is done through addition.
In math, addition is the process of adding two or more integers together.
Addends are the numbers that are added, and the outcome of the operation, or the final response, is referred to as the sum.
In the problem the addends are the numbers 1 2 3 4 5 6 .......97 98 99 100
The applying the addition operation the sum is calculated to be 5050. calculator will make the operation easier
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what is the relationship between the servings of blueberries and the number of calories? Answer in a complete sentence
i will give brainless to some that answers right and fast
Answer:
Each blueberries serving contain 21 calories or the slope of this is 21
Step-by-step explanation:
The slope is rise/run
We see that when the x increase by 1, the y increase by 21, so the slope is 21.
What are 2 examples of arithmetic sequences in real life?
Stacking chairs and sitting around table are examples of arithmetic sequence in real life
What is simple arithmetic?
The foundational subject in mathematics is arithmetic, which covers operations with numbers. These include multiplication, division, addition, and subtraction. One of the key areas of mathematics, arithmetic serves as the cornerstone for students studying the topic of mathematics.
How is arithmetic sequence used in daily life?
There are numerous applications for arithmetic sequences in daily life. The clock, for instance, demonstrates properties of an arithmetic sequence. The standard deviation of a clock's time is 1. Other examples of arithmetic sequences can be seen in daily life, such as our age.
Among these there are many other examples of arithmetic sequence is real life like fencing and perimeter examples.
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A canoe travels 4 miles per hour downstream and 2 miles per hour upstream.
Let x represent the canoe's speed with no water current (still water) and y
represent the speed of the water current, in miles per hour. Then the situation
can be represented by this system of equations:
Choose the two correct options.
x + y = 4
x - y = 2
A. The speed of the water current is 1 mile per hour.
B. The speed of the canoe in still water is 3 miles per hour.
C. The speed of the canoe in still water is 1 mile per hour.
D. The speed of the water current is 3 miles per hour.
Answer:
A, B
Step-by-step explanation:
Given the system of equations, we should first solve for x and y so we can answer this question:
equation 1: x + y = 4, equation 2: x - y = 2 ⇒ add both equations together
x + y + x - y = 4 + 2 ⇒ combine like terms
2x + 0y = 6 ⇒ divide both sides by 2
x = 3 ⇒ plug into the x + y = 4 equation to solve for y
3 + y = 4 ⇒ subtract 3 from both sides
y = 4 - 3 = 1
Since we know y is the speed of the water current and x is the canoe's still water speed, we know that the water current's speed is 1 mph and the canoe's still water speed is 3 mph
This corresponds with choices A and B
Find the characteristic polynomial and the eigenvalues of the matrix. 6 3 3 6 The characteristic polynomial is □ (Type an expression using λ as the variable. Type an exact answer, using radicals as needed.) Select the correct choice below and, if necessary, fill in the answer box within your choice 0 A. The real eigenvalue(s) of the matrix is/are (Type an exact answer, using radicals as needed. Use a comma to separate answers as needed. Type each answer only once.) B. The matrix has no real eigenvalues.
The characteristic polynomial is P(λ) = λ² - 12λ + 27.
The real eigenvalues of the matrix are 3, 9. Answer A.
The full question is in the attachment. The characteristic polynomial from a matrix is P(λ) = |A - λI|
[tex]Matrix\:A\:=\: \left(\begin{array}{cc}6&3\\3&6\end{array}\right)[/tex]A - λ
[tex]A \:-\: \lambda I \:=\: \left(\begin{array}{cc}6&3\\3&6\end{array}\right) \:-\: \lambda \left(\begin{array}{cc}1&0\\0&1\end{array}\right)[/tex]
[tex]A \:-\: \lambda I \:=\: \left(\begin{array}{cc}6&3\\3&6\end{array}\right) \:-\: \left(\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right)[/tex]
[tex]A \:-\: \lambda I \:=\: \left(\begin{array}{cc}6 \:-\: \lambda&3\\3&6 \:-\: \lambda\end{array}\right)[/tex]
If matrix P [tex]\left(\begin{array}{cc}a&b\\c&d\end{array}\right)[/tex] than determinant of matrix P = |P| = ad - bc
P(λ) = |A - λI
P(λ) = (6 - λ) (6 - λ) - (3 × 3)
P(λ) = 36 - 12λ + λ² - 9
P(λ) = λ² - 12λ + 27
The eigenvalues
P(λ) = 0
λ² - 12λ + 27 = 0
(λ - 3) (λ - 9) = 0
λ - 3 = 0 or λ - 9 = 0
λ₁ = 3 λ₂ = 9
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Is cleaning the measuring instrument not necessary?
It is necessary to clean the measuring instrument the moving parts of the measuring device may be harmed if airborne dust or dirt gets inside of it. Additionally, if any foreign objects are present between the measurement target and the measuring device, precise measurements may be affected.
what is measuring instrument?A measuring instrument is a tool used to quantify anything tangible. The act of obtaining and comparing physical amounts of actual objects and occurrences is known as measuring in the physical sciences, quality control, and engineering. Vernier calipers, micrometers, dial gauges, gauges of various types, bubble levels, protractors, and rulers are some of the primary goods that fall under the category of measurement instruments. These equipment are employed in the production process and for quality assurance.
It is necessary to clean the measuring instrument the moving parts of the measuring device may be harmed if airborne dust or dirt gets inside of it.
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Snooty had to solve the following
equation for x:
x² = 64
Someone told Snooty there are actually
2 solutions! This confused Snooty. Can
you explain to Snooty why there are 2
solutions for x in this equation?
Type a response
0.
Answer:
8, -8
Step-by-step explanation:
There are 2 answers for the solution because x² = 64 can equal 8, and -8. It can equal 8 because 8 x 8 = 64. It can also equal -8 because -8 x -8 is a positive 64.
Devon is considering taking out a 75000 loan for a 15 year period. How many monthly payments he has to make for the life of the loan?
Devon's monthly payment will be about 416.6
To make for the life of the loan.
What is interest ?
Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. The three types of interest include simple (regular) interest, accrued interest, and compounding interest.
Have given,
He considered to take lone about 75,000 for a 15 year period,
In 1 year he will be paid [tex]\frac{75,000}{15}[/tex] = 5000
Then in 1 month he will be paid [tex]\frac{5000}{12}[/tex] = 416.6
Devon's monthly payment will be about 416.6
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ralph records the time it takes for each of his classmates to run around the track one time. as he analyzes the data on the graph, he locates the mean and median time. which component of data analysis is ralph utilizing?
The component of data analysis that Ralph is utilizing is the overall spread of the data. That is option D.
What is data analysis?Data analysis is defined as the method a researcher uses to collect, clean, sort, and process raw data in a way that it's representation can be understood by the reader.
The mean of a data set is defined as the addition of all the data set which is then divided by the number of the data set.
The median of a data set is the number that falls at the middle of the set after being arranged in an ascending or descending order.
Therefore, to find the mean and median of a data set will depend on the spread out of the data.
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Complete question:
Ralph records the time it takes for each of his classmates to run around the track one time. As he analyzes the data on the graph, he notices very little variation between his classmates' times.
Which component of data analysis is Ralph observing?
A. An outlier in the data set
B. The overall shape of the data
C. The center of the data set
D. The overall spread of the data
Answer:
The overall spread of the data.
Step-by-step explanation:
Got it right on the test.
f(x) = -3 |x-1| +5; Find f(3)
Answer: f(3) = -1
Step-by-step explanation:
f(x) = -3 |x-1| +5
f(3), we just need to put 3 in for both the x
f(3) = -3 |3-1| +5
f(3) = -9 + 3 +5
f(3) = -1
If g(x) = - 4x^2 - 3x + 2, determine g(-2).
Show your work.
Answer:
g(-2) = -8
Step-by-step explanation:
If [tex]g(x) = - 4 x^2 - 3x +2[/tex], determine g(-2):
[tex]g(-2) = - 4 (-2)^2 - 3(-2) +2\\g(-2) = - 4 (4) - (-6)+2\\g(-2) = -16 + 6 + 2 \\[/tex]
g(-2) = -8
Given the arithmetic sequence:
5, 9, 13,...
Part A: What is the common difference AND how do you find it?
Part B: What are the 4th and 5th terms of this sequence?
Part A: The common difference is 4.
Part B: The 4th term is 17 and the 5th term is 21 of this sequence.
What do you mean by arithmetic sequence?
The difference between each term in an arithmetic sequence is a constant. To put it another way, we just add the same value repeatedly, indefinitely.
According to the given question,
We have the given information:
The arithmetic sequence:
5, 9, 13,...
Now, we need to find the common difference and we will find it in this way,
The common difference is the difference between two consecutive terms in a sequence. To find it, we just need to do simple subtraction.
d = t2 - t1
= 9-5 = 4
So, the common difference is 4.
Then, we need to find the 4th and 5th terms of this sequence,
t4 = t3 + d
= 13+4
= 17
t5 = t4 + d
=17 + 4
=21
Therefore, the 4th term is 17 and the 5th term is 21.
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The common difference of this arithmetic sequence is 4 and 4th, 5th term of this arithmetic sequence is 17 and 21.
What in mathematics is an arithmetic sequence?Each phrase in an arithmetic sequence increases by adding or subtracting a specific constant, k. Each word in a geometric sequence is raised by either multiplying by or dividing by a certain constant, k.
Briefing:Part A:
The constant difference between consecutive terms of an arithmetic sequence is called the common difference and its is denoted by d.
Therefore, the common difference (d) is equal to 9 - 5 = 4.
The 4th and 5th terms of this sequence are
Part B:
Using Arithmetic progression formula,
aₙ = a + (n- 1)d
where
n = nth term
a (first term = 5
d = common difference = 4
4th term of the sequence
a₄ = a + (n- 1)d
a₄ = 5 + (4 - 1)4
a₄ = 17
5th term of the sequence
a₅ = a + (n- 1)d
a₅ = 5 + (5 - 1)4
a₅ = 21
Hence the 4th and 5th term of this arithmetic sequence is 17 and 21.
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When two angles and a non-included side of one triangle are congruent to the corresponding pieces of another triangle?
The correct answer is option b) AAS
What is meant by triangle ?A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point.Polygons of the form with three sides and three vertices are called triangles. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. Tri-, which means "three," and angulus, which means "angle or corner," are the roots of the Latin word triangulus, which means "three-cornered" or "having three angles."According to the AAS congruence theorem, if two angles and the non-included side of one triangle are congruent with the corresponding components of another triangle, then the two triangles are congruent.
Therefore, option B is the correct answer.
"AAS congruence" theorem an be used to prove that the triangles are congruent .
The complete question is:
Two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle. Which congruence theorem can be used to prove that the triangles are congruent?
a) SSS
b) AAS
c) SAS
d) HL
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