The function is decreasing in the interval (-∞,-3/2) and (3/2, ∞) and increasing in the interval (-3/2, 3/2).
What is a function?
A function is a mathematical relation between a set of inputs (often called independent variables, or the domain) and a set of outputs (often called dependent variables, or the range). A function assigns exactly one output for each input. It can be represented by an equation, such as y = f(x), where x is the input and y is the output.
To find the interval(s) in which the function is increasing and decreasing, we can first find the critical points of the function by setting the derivative equal to 0 and solving for x.
The derivative of y = |2x² + x - 6| is not a defined function, it is not differentiable, it is a piece-wise defined function, it has a break at x = -3/2
Hence, the function is decreasing in the interval (-∞,-3/2) and (3/2, ∞) and increasing in the interval (-3/2, 3/2).
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(X+2)(x+y+1)
Can someone help me with this one
Answer:
x^2 +xy+3x+2y+2
Step-by-step explanation:
(x+2)(x+y+1)
Apply the distributive property by multiplying each term of x+2 by each term of x+y+1.
x^2+xy+x+2x+2y+2
Combine x and 2x to get 3x
x^2 +xy+3x+2y+2
Answer: x^2+xy+3x+2y+2
Step-by-step explanation:
Expand and simplify
Convert 46.1031 to 4 significant figures
Converting 46.1031 to 4 significant figures, we have 46.10.
Rounding off to 4 significant figure.Rounding off numbers implies reducing the number of digits in a given number to a preferred length. The two modes are significant figures, or decimal places.
Decimal places requires reducing the numbers of digits in a given number to a required number but considering the position of the decimal point. In significant figures, the length of the given number is reduced to a required number by not considering the position of the decimal.
In the given question, we are to convert 46.1031 to 4 significant figures.
This can be done by counting four digits, and rounding off the digits after.
So that we have;
46.1031 = 46.10 (4 sf)
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The conversation of 46.1031 to 4 significant figures would be = 46.10
What is a four significant figures?A four significant figures are those figures that shows that all zeros to the right of the last significant zero after the decimal point.
From the given figure such as 46.1031, to convert to four significant figures, 46.10
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GH is tangent to both circle A and circle E. Determine the length of HE.1) 27 units2) 3 units3) 1.8 units4) 4 units
The length of HE is 4 units.
Given that GH is tangent to both circle A and circle E, we can use the property of tangents that states that a tangent line to a circle is perpendicular to the radius drawn to the point of tangency.
If we let r be the radius of circle A and circle E, and let HE be the length of the line segment from the center of the circles to the point of tangency, we can use the Pythagorean Theorem to determine the length of HE.
The Pythagorean theorem is a fundamental result in mathematics that states that 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.
Since GH is tangent to both circles, it is perpendicular to the radius of both circles and we can create a right triangle with legs HE and r. We can use the Pythagorean theorem to find the length of HE
HE^2 + r^2 = GH^2
We can use the information given to find the value of GH, then we can solve for HE using the equation above.
We know that GH is tangent to both circles, which means that GH is equal to the diameter of both circles. So GH = 2r
Substituting this value into the equation above:
HE^2 + r^2 = (2r)^2
HE^2 = 2r^2 - r^2 = r^2
HE = √(r^2) = r
Given that HE = r and r = radius of circle A and Circle E, HE = radius of Circle A = radius of Circle E.
Therefore, the length of HE = radius of Circle A or Circle E = 4 units.
So, the length of HE is 4 units.
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how to calculate calculate mean and standard deviation after transforming a random variable combining random variables
to calculate calculate mean and standard deviation after transforming a random variable combining random variables, use the formulae for both the expected and standard deviation of such a linear combination with random variables.
What is standard deviation?Data dispersion in regard to the mean is quantified by a standard deviation, or "σ". Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.
Because it makes measures easier to comprehend when the data is spread, standard deviation is significant. The data's standard deviation will increase as the data's distribution becomes more widely scattered. The deviation of each observed value from the mean is measured using this metric. The majority of data in any distribution will fall within a 2 standard deviation range of the mean.
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Help me plisssss,I need this for tomorrow
Answer:
slope=-5/2 and equation of line y=-5/2x+3
Step-by-step explanation:
we find the slope by using formula =y2-y1/x2-x1
a magazine publisher always mails out a questionnaire six months before a subscription ends. this questionnaire asks its subscribers if they are going to renew their subscriptions. on average, only 10% of the subscribers respond to the questionnaire. of the 10% who do respond, an average of 44% say that they will renew their subscription. this 10% who respond to the questionnaire are known as what?
Therefore , the solution of the given problem of average comes out to be the box is the population for selecting 8 cables from that box.
Specify AverageThe exact number in the mean of an ordered dataset is known as the median value. A maximum likelihood measure, often known as an average, is the difference between the min and max 50% of the data. The median and mode are calculated using various formulae depending on whether there are an odd or perhaps even number of data points.
Here,
Since every member of the population has a newspaper subscription, all but 8% of them make up the sample.
A sample is (B)
4, where the population to be sampled is one box chosen from the available 4. C) The one of the four boxes that was randomly selected.
The population for choosing a box seems to be of size 4, and the box is the population for selecting 8 cables from that box.
Therefore , the solution of the given problem of average comes out to be the box is the population for selecting 8 cables from that box.
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Answer the following questions using what you've learned from this lesson. Write your responses in the space provided.
For questions 1-3, state the similarity theorem that shows that AABC-ADEF.
Answer:
Not too sure about the name of specific theorem but:
1. ABC = DEF, BCA = EFD and CAB = FDE
Same angles
2. The ratio of 2 sides is the same
[tex]\frac{ab}{ac} = \frac{de}{df} \: \\ \frac{2}{3} = \frac{4}{6} [/tex]
3. The ratio of 2 sides is the same
[tex]\frac{ab}{ac} = \frac{de}{df} \: \\ \frac{2}{4} = \frac{10}{20} [/tex]
rewrite the triple integral ∫10∫x0∫y0f(x,y,z)dzdydx as ∫ba∫g2(z)g1(z)∫h2(y,z)h1(y,z)f(x,y,z)dxdydz
A new form of the triple integral [tex]\int\limits^1_0\int\limits^x_0\int\limits^y_0 {f(x,y,z)} \, dzdydx[/tex] as a = 0, b = 1, g2(z) = 1, h2(y,z) = 1.
In other words, we want the integration order to be totally reversed for
[tex]\int\limits^1_0\int\limits^x_0\int\limits^y_0 {f(x,y,z)} \, dzdydx[/tex]
Keep in mind that this area is quite simple to define. The planes z = y and y = x, as well as the coordinate planes x=y=z=0 , define our boundaries. We essentially have upper bounds z = y = x = 1 because x ∈[ 0, 1 ]. Therefore, we can alternatively express the region as:-
0 ≤ x ≤ y
0 ≤ y ≤ z
z∈ I0,1I. So
[tex]\int\limits^1_0\int\limits^x_0\int\limits^y_0 {f(x,y,z)} \, dzdydx = \int\limits^1_0\int\limits^z_0\int\limits^y_0 {f(x,y,z)} \, dxdydz[/tex]
Remember that a double integral could be set up in two different ways. Our number of alternative orders of integration increases from two to six when we include that third integral. We will rewrite the supplied integral in one of the other five possible orders in this exercise.
hence,
[tex]\int\limits^1_0\int\limits^x_0\int\limits^y_0 {f(x,y,z)} \, dzdydx = \int\limits^1_0\int\limits^z_0\int\limits^y_0 {f(x,y,z)} \, dxdydz[/tex]
Therefore, the new form of the triple integral [tex]\int\limits^1_0\int\limits^x_0\int\limits^y_0 {f(x,y,z)} \, dzdydx[/tex] as a = 0, b = 1, g2(z) = 1, h2(y,z) = 1.
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3x² + 2 × 3x × 5 - 5²
Qui pourait m'expliquer svp ?
Answer:
Step-by-step explanation:
3x² + 2 * 3x * 5 - 5²
= 3x^2 +2 * 3x * 5 - 25 ( then do 2*3x*5 = 30x)
=3x^2+30x-25
When point F ( , ) is reflected in the line y=x, the image is located at F’(−7, 1).
Answer:
(1, -7)
Step-by-step explanation:
(x,y) ⇒ (y, x)
(1,-7) ⇒(-7,1)
Consider the inheritance pattern for the ABCC11 gene. This pedigree follows the inheritance of dry and wet earwax. Match the following individuals with their genotype.
II-3 --> aa
I-2 --> Aa
III-1 --> Cannot determine
II-6 --> Aa
II-2 --> Cannot determine
II-4 --> Cannot determine
What is inheritance?In object-oriented programming, inheritance is the technique that allows one object or class to be based on another while keeping comparable implementation. Also described as deriving new classes from existing ones, such as a superclass or a baseclass, and then organizing them into a class hierarchy. Inheritance refers to the assets that a person leaves to their loved ones when they die. An inheritance may include cash, stock or bond investments, and other assets such as jewelry, vehicles, art, antiques, and real estate.
Here,
II-3 --> aa
I-2 --> Aa
III-1 --> Cannot determine
II-6 --> Aa
II-2 --> Cannot determine
II-4 --> Cannot determine
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The match of the following will be:
II-3 --> aa
I-2 --> Aa
III-1 --> Cannot determine
II-6 --> Aa
II-2 --> Cannot determine
II-4 --> Cannot determine
What is inheritance?In object-oriented programming, inheritance is the technique that allows one object or class to be based on another while keeping comparable implementation. Also described as deriving new classes from existing ones, such as a superclass or a baseclass, and then organizing them into a class hierarchy. Inheritance refers to the assets that a person leaves to their loved ones when they die. An inheritance may include cash, stock or bond investments, and other assets such as jewelry, vehicles, art, antiques, and real estate.
Here,
II-3 --> aa
I-2 --> Aa
III-1 --> Cannot determine
II-6 --> Aa
II-2 --> Cannot determine
II-4 --> Cannot determine
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A tree that is 11 feet tall is growing at a rate of 2 1/2
feet each year. A tree that is 15 feet tall is growing at a rate of 2 feet each year.
Enter the number of years it will take the two trees to reach the same height.
Answer:
it should be 8 years and at 8 years they will both be 31 ft tall
Step-by-step explanation:
What is the approximate yield to maturity of a 7000 bond bearing 6%interest bought at 90 with 15yrs left to maturity
The yield to maturity on the bond, give the face value, and the price the bond was bought at, is 7. 11%.
How to find the yield to maturity ?You can find the Yield to Maturity using a Yield to Maturity calculator. You would have to input the Face Value as the value of $ 7, 000.
The bond price is the amount the bond was purchased for :
= Face value x buying percentage
= 7, 000 x 90%
= $ 6, 300
The coupon rate if the 6% interest bearing and the years to maturity is 15 years.
The Yield to Maturity is then 7. 11%.
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Let's assume that bacteria doubles every 10 minutes. If the culture starts with 4 bacterial cells, how many bacterial cells will be present after 1 hour? (Hint: Enter the answer only, and don't forget your units!)
Answer: 256 bacterial cells
Step-by-step explanation:
Using the half-life formula, the number of bacteria after [tex]t[/tex] minutes is [tex]4(2)^{\frac{t}{10}}[/tex].
Setting [tex]t=60[/tex] (since there are 60 minutes in an hour), we get there are [tex]4(2)^{\frac{60}{10}}=256[/tex] bacterial cells.
30 POINTS BRAINLIEST HELPWhich number is rational? A-2.1010010001... b.-0.8974512... c.1.2547569... d. 5.3333333...
Answer:
Step-by-step explanation:
A rational number is a number that can be expressed as a ratio of two integers, or as a fraction. A rational number is any number that can be written in the form a/b, where a and b are integers and b is not equal to zero.
In this case, the correct answer is d. 5.3333333.... This number can be written as a fraction in the form 5 3/9, which is a ratio of two integers and thus a rational number.
The other three choices are not rational numbers because they are repeating decimals, or irrational numbers. An irrational number is a number that cannot be written as a ratio of two integers. Irrational numbers are numbers that are not rational.
An electronics wholesaler must sell at least $4000 worth of computers and printers per day to stay profitable. Each printer costs $300 and each computer costs $900. The store can ship a maximum of 25 items per day. If c represents the number of computers and p represents the number printers, which THREE statements are correct? Select 3 correct answer(s) Question 4 options: c + p ≥ 25 and 900c + 300p ≤ 4000 models the situation c = 5 and p = 15 is a viable solution c = 15 and p = 5 is a viable solution c + p ≥ 25 and 900c + 300p ≥ 4000 models the situation c + p ≤ 25 and 900c + 300p ≥ 4000 models the situation
Answer:
A,B,D
Step-by-step explanation:
(A) is correct because 5*900+15*300>4000
(B) is correct because 15*900+5*300>4000
(D) is correct because C+P must be less than or equal to 25
Calculate the percentage by which the orangutan population has changed from 1900 when there were 85,000 orangutans to the present day when there are about 6,600 orangutans. Give your answer to 2 decimal places.
The percentage by which the orangutan population has changed is 92.23%
We know that the formula for the relative change.
R = |x2 - x1| ÷ x1
where x2 is the final value
and x1 is the initial value
R is the relative change
Here, the orangutan population has changed from 1900 when there were 85,000 orangutans to the present day when there are about 6,600 orangutans.
This means, x1 = 85000 and x2 = 6600
So, the relative change would be,
R = |6600 - 85000| ÷ 85000
R = 78400 / 85000
R = 0.9223
and the percentage change would be,
P = R × 100
P = 0.9223 × 100
P = 92.23%
Therefore, the percentage change = 92.23%
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The ratio of the length to width of a picture is 5:2 the picture is enlarged so that it’s length is 15 inches now what is the width of the enlarged picturea. 5inb. 6inc. 7ind. 8in
We may use the ratio of length to width and the new length of the image to determine the width of the enlarged image.
Step 1: The original image's length to width ratio is 5:2, which may be expressed as 5/2.
Step 2: We are aware that the enlarged image is 15 inches long.
Step 3: We may apply the formula length/width = new length/new width to determine the width of the enlarged image. The known values of the original ratio and the new length can be substituted in: 5/2 = 15 inches / new width.
Step 4: To find the new width, we must cross multiply and divide, so multiply the new width by 5/2 to get 15 inches, and divide both sides by this number to get 6 inches.
Therefore, The expanded image has a 6 inch width.
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Carey's extreme sports is an ecommerce store specializing in selling extreme sports products.The products include equipment, apparel, and other items related to extreme sports. Founded in 2015 in Arizona, US, the company has grown from a high-end sports gear equipment company into a national extreme sports brand with operations in 50 States and close to 1000 employees working for the company. The world of Carey's Extreme has traditionally conjured up images of inclusivity, sophistication, and elegance, attracting both wealthy and not-so-wealthy crowds, including college students.
According to the Pareto study, the brands Adidas, Hyperlite, Mongoose, Schwinn, and Aquaronotman account for around 80 percentage of the profit.
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a
fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used.
Pareto analysis is based on the notion that 20% of the work is necessary to produce 80% of the benefits of a project. It is regarded as a strong instrument for decision-making and quality maintenance in larger commercial organizations. We might say that it is a technique for gathering the necessary data and information for establishing priorities.
As a result, we may claim that it is a technique employed in both welfare economics and corporate decision-making. The '80-20 rule' forms the basis of it. When used as a decision-making tool, Pareto analysis statistically identifies a small number of either acceptable or unpleasant input characteristics that have the most influence on an output.
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The complete question is " Carey's Extreme Sports Is An Ecommerce Store Specializing In Selling Extreme Sports Products.
Carey's extreme sports is an ecommerce store specializing in selling extreme sports products.
The products include equipment, apparel, and other items related to extreme sports. Founded in 2015 in Arizona, US, the company has grown from a high-end sports gear equipment company into a national extreme sports brand with operations in 50 States and close to 1000 employees working for the company. The world of Carey's Extreme has traditionally conjured up images of inclusivity, sophistication, and elegance, attracting both wealthy and not-so-wealthy crowds, including college students. "
a normal coin is tossed ten times and the result, heads or tails, is recorded for each toss. how many of the possible outcomes have three heads and seven tails? (we mean to count the different orderings on the 10 flips, and not simply the number of heads and tails that appear)
i used nCr and i got the answer 120 oucomes. is that correct?
Answer:
120 is correct and the formula to be used is 10C₃ or 10C₇ both of which work out to 120
Step-by-step explanation:
That appears to be correct . Since only one of two possibilities exist for each toss, for 10 tosses we determine if 3 heads appear that would be the same as 7 tails appearing for the 10 tosses
Number of ways r heads can appear in n tosses is indeed nCr
For r= 3 heads and n = 10 tosses this would be
10C₃ = 120
This should be the same as 10C₇ which works out to 120 also
the radis of circle A is three feet les than twice the diameter of Circle b. If the sum of the diameters of bothj circles is 49 feet, find the area and circumferance of circle A
The required area and circumference of circle A are 1,134.57feet² and 119.43 feet.
What is a circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle.
In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
So, the area and circumference of circle A:
d = the circumference of circle B
r = radius of circle A
r = 2d - 3
Diameter of circle A = 2 x (2d - 3) = 4d - 6
By figuring out d, we may find the diameter of circle B.
4d - 6 + d = 49
5d = 55
d = 11
Diameter of circle A = 4(11) - 6 = 38
Radius of circle A = 38/2 = 19 feet
Area of a circle = πr²
22/7 x 19² = 1,134.57 feet²
Circumference of a circle = πD
22/7 X 38 = 119.43feet
Therefore, the required area and circumference of circle A are 1,134.57feet² and 119.43 feet.
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Determine whether each function has a constant or variable rate of change. Use rates of change to determine whether each function is linear or nonlinear. answer
We can also check if the function's equation is in the form y = mx + b.
What is function's equation ?
A function's equation is a mathematical statement that defines the relation between the input (also known as independent variable) and output (also known as dependent variable) of a function. The equation is typically represented by the letter "y" for the output, and one or more letters for the input (usually "x").
To determine whether a function has a constant or variable rate of change, we need to find the slope or rate of change between two points on the function. If the slope remains the same no matter what two points we choose, the function has a constant rate of change and is linear. If the slope changes depending on the two points we choose, the function has a variable rate of change and is nonlinear.
To determine whether a function is linear or nonlinear, we can also check if the function's equation is in the form y = mx + b, where m and b are constants. If it is, the function is linear, otherwise it is nonlinear.
It's important to mention that, in order to have a definitive answer, we need the function to be defined.
We can also check if the function's equation is in the form y = mx + b.
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List and explain at least three popular sixteenth-century dance types, including the style, common instrumentation, and use in court, society, or both.
One of the most popular dance types of the sixteenth century was the pavane, another one are galliard and allemande.
What is instruments?Instruments in math are tools or processes used to perform mathematical operations and calculations. Examples of instruments in math include calculators, rulers, compasses, protractors, and computers. These instruments can be used to solve problems, analyze data, and understand mathematical concepts. Additionally, instruments in math can be used to teach students about problem-solving and allow them to gain a deeper understanding of mathematics.
This was a slow, stately dance, usually in duple meter, that was popular in courts and societies across Europe. It was usually accompanied by lute or harpsichord and sometimes with viols. The pavane was often used as a ceremonial dance in courts and was usually performed by couples.
Another popular dance type of the sixteenth century was the galliard. This was a lively, energetic dance, usually in triple meter, that was popular in courts and societies across Europe. It was usually accompanied by lute or harpsichord and sometimes with viols. The galliard was often used as a dance for entertainment and was usually performed by couples.
The third popular dance type of the sixteenth century was the allemande. This was a slow, stately dance, usually in duple meter, that was popular in courts and societies across Europe. It was usually accompanied by lute or harpsichord and sometimes with viols. The allemande was often used as a ceremonial dance and was usually performed by couples. It was usually danced in a line or circle formation, with each dancer taking the lead in turn.
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if a bar of soap cost $2,49 in 2003 how much did a bar of soap cost in 2005
Therefore , the solution of the given problem of unitary method comes out to be the cost of soap after 2005 is $ 2.6145.
A unitary method is precisely what?To finish a work using the unitary strategy, multiply the quantity with two after determining the size of a small slice. The unit variable technique, to put it simply, works to isolate a coded object from a specific group or sets of sets. For instance, 40 pens would cost 400 pounds (expression $1.01) = Rs. There is a chance that one nation will have complete control over the technique used to do this. Almost all living things have a unique trait..
Here,
Given :
=> Cost of soap $2.49 in 2003
=> Cost of soap in 2005
=> 2.49 + 5/100 * 2.49
=> 2.49 + 0.1245
=> 2.6145
Therefore , the solution of the given problem of unitary method comes out to be the cost of soap after 2005 is $ 2.6145.
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the student population of school is 480. 85% participate in atleast one extra-curricular activity. how many students participate in at least one extra-curricular activity ?
Answer: 408
Step-by-step explanation:
85% is equal to 0.85 in decimal form.
So, the answer is [tex](480)(0.85)=408[/tex] students.
Answer:
408
Step-by-step explanation:
In decimal notation, 85% is 0.85.
saul plans to complete more than 225 hours of volunteer work during a 9-month period. he has already completed 36 hours of volunteer work. which inequality describes all the additional numbers, h, of hours of volunteer work that saul could complete each month to meet his goal?
The inequality that satisfies the number of hours of volunteer work that saul could complete each month to meet his goal is 21 hours.
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
Different types of inequalities are represented by a variety of notations, including:
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that an is bigger than b.
Given,
Hours Saul plans to volunteer in the 9-month period = 225 hours
Also,
Hours of volunteering he has already completed = 36 hours
=> Number of hours left = 225 - 36 =189 hours
Number of months= 9
=> Minimum number of hours he has to volunteer per month
=> [tex]\frac{Number of hours left}{Number of months}[/tex]
=>[tex]\frac{189}{9}\\ 21 hours[/tex]
=>Minimum number of hours saul has to volunteer per month ≥ 21 hours
Therefore, The number of hours of volunteer work that saul could complete each month to meet his goal is 21 hours.
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which segment is the shortest?
The shortest segment in the given figure is EF
Geometric Relationship Between Sides and Interior Angles:
When two rays are united at a common point, then an angle is created. The two rays are referred to as the arms of the angle, while the common point is referred to as the vertex.
The geometric relationship between sides and interior angles is defined by the angle-side relationship theorem.
According to the angle-side relation theorem,
1. The lowest angle in each triangle lies opposite the shortest side.
2. The largest side is located across from the largest angle.
3. The opposite of the second-largest side is the second-largest angle.
Here we have
EFGH is a quadrilateral and the given angles are
∠HEG = 68°, ∠EFG = 65°, ∠EGF = 55°, and ∠HGE = 71°
The smallest angle in the given figure is ∠EGF = 55° which is opposite to the line segment EF
Therefore,
The shortest segment in the given figure is EF
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Use a calculator to determine the measure of 0, in degrees, given that Csc (0) = 1.7894
If Csc(θ) = 1.7894 then θ = 34°.
What are the trigonometric identities?Equations using trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities.
Given:
Csc(θ) = 1.7894
To find the value of θ:
θ = Csc⁻¹(1.7894)
By the Cosecant calculator,
θ = 34°
Therefore, the value of θ = 34°.
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the cost of a movie ticket was $10 . it increased by 15% . how much is the movie ticket now ?
you were in the garden, there are 34 people in the yard. 30 people left. how many people are in the garden.
you were in the garden, there are 34 people in the yard. 30 people left. 35 people are in the garden. This can be solved using addition.
What is addition?Mathematically, addition is the process of merging several numbers together. The numbers that are being added are known as addends, and the outcome of the addition process, or the answer we ultimately obtain, is known as the sum. It is a fundamental mathematical operation that we employ on a daily basis. We add numbers in many different contexts. In arithmetic sums, the plus sign (+) is used to indicate addition.
The combination of at least two integers constitutes basic addition. Once a student has mastered counting, they may begin to study basic addition. By locating the addend at the top of the chart and tracing down to the row of the second addend, they may utilize an addition chart as a learning tool.
Given that,
there are 34 people in the yard.
Among them 30 people left.
Thus, (30 dead + 4 living + you ) = 35 people are in the garden.
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