Answer:
Step-by-step explanation:
[tex]\displaystyle\\\frac{tan32^0+tan88^0}{1-tan32^0tan88^0} \ \ \ \ (1)\\\\Let\ \alpha =32^0\ and\ \beta =88^0\\\\Hence,\ expression\ (1)\ will \ look\ like\ this:\\\\\frac{tan\alpha +tan\beta }{1-tan\alpha tan\beta }\\[/tex]
The trigonometric formula for adding angles for a tangent is as follows:
[tex]\displaystyle\\\\\boxed {tan(\alpha +\beta )=\frac{tan\alpha +tan\beta }{1-tan\alpha tan\beta }}[/tex]
Thus,
[tex]\displaystyle\\\frac{tan32^0 +tan88^0 }{1-tan32^0 tan88^0 }=tan(32^0+88^0)\\\\\\\frac{tan32^0 +tan88^0 }{1-tan32^0 tan88^0 }=tan120^0[/tex]
Calculate the value of tan120°:
[tex]tan120^0=tan(90^0+30^0)\\\\tan120^0=-cot30&^0\\\\tan120^0=-\sqrt{3}[/tex]
So,
[tex]\displaystyle\\\frac{tan32^0 +tan88^0 }{1-tan32^0 tan88^0 }\equiv-\sqrt{3}[/tex]
The diagram shows a convex polygon.
What is the sum of the interior angle measures of this polygon?
The sum of the interior angle measures of the given polygon will be equal to 360°.
What is a Polygon?A polygon is described in geometry as a compact, two-dimensional shape having three or more straight lines.
Poly, which means "many," and gon, which means "angle," make up the Greek word "Polygon." Polygons of several kinds can be seen all around us.
As per the given information in the question,
Use the formula of the sum of an interior angle of the polygon,
180(n - 2) (i)
Here, n is the number of sides.
As per the given figure, n = 4
Put n = 4 in equation (i)
180 (4 - 2)
180 (2)
= 360°
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How do you find holes and asymptotes?
To find holes, look for places where the function is undefined. To find asymptotes, look for where the function approaches infinity or negative infinity. Additionally, look for places where the function has a vertical or horizontal line, as these are also potential asymptotes.
To find holes in a function, look for places where the function is undefined. This can occur when the denominator of a fraction is equal to zero, as the fraction becomes undefined. Additionally, look for places where the function is not continuous, as this can indicate a hole in the graph. To find asymptotes, look for places where the function approaches infinity or negative infinity. This can occur when the denominator of a fraction is equal to zero and the numerator is not. Additionally, look for places where the function has a vertical or horizontal line, as these can also indicate potential asymptotes. Asymptotes are also present when the degree of the numerator is higher than the degree of the denominator. By looking for these areas, you can identify potential holes and asymptotes in a function.
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what is the slope between (-2,-19) and (-12,11)
Answer:
m = -3
Step-by-step explanation:
The slope is rise/run or (y2 - y1) / (x2 - x1)
We see the y increase by 30 and the x decrease by 10, so the slope is
-30/10 = -3
So, m = -3
Answer:
Slope = -3
Step-by-step explanation:
Formula of slope,
→ Slope(m) = (y2 - y1)/(x2 - x1)
Now the slope will be,
→ m = (y2 - y1)/(x2 - x1)
→ m = (11 -(-19))/(-12 -(-2))
→ m = (11 + 19)/(-12 + 2)
→ m = 30/-10
→ m = -(30/10)
→ [ m = -3 ]
Hence, the slope is -3.
Work out the fraction that is halfway between 0 and 3/4
The work out fraction that is halfway between 0 and 3/4 is 1/2
In math, what are fractions?
A fraction is a part of the whole. In a quotient, where the numerator and denominator are divided, the number is mathematically expressed. In a straightforward fraction, both are integers. A complicated fraction has a fraction in either the numerator or denominator. In a correct fraction, the numerator is smaller than the denominator.
What seven types of fractions are there?
Proper fractions, improper fractions, mixed fractions, like fractions, unit fractions, equivalent fractions, and same numerator fractions are the seven different types of fractions.
A midway fraction is defined.
Halfway of Two Fractions is what? Exactly halfway between 2/3 and 3/4, a fraction cannot be smaller than 2/3 or larger than 3/4. Nothing is halfway but the average of two fractions.
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What is the leading coefficient of the polynomial function if?
Observing the polynomial and the coefficient provided, The leading coefficient of the polynomial function is the coefficient of the highest degree term.
What do you mean by a polynomial?Sums of terms with the form kxⁿ, where K is any number and N is a positive integer, are known as polynomials.
What do you mean by leading coefficient?The term with the greatest x power is the leading term in a polynomial function. The leading coefficient is the coefficient of the leading phrase.
polynomial of the form [tex]ax^{2}+bx+c[/tex].
Since, The degree is 2 and the coefficient of [tex]x^{2}[/tex] is a.
The leading coefficient is 'a'.
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How many types of quadrilaterals are there?
Answer:
There are 6 types of quadrilaterals
Step-by-step explanation:
6 types are: Parallelogram, Trapezium, Rhombus, Rectangle, Square, Kite
8/x = 12/30 Solve for x
Answer:
The value of x is 20
Step-by-step explanation:
This question has to do with an equation. The information is given thus:
8/x = 12/30
Cross multiply
12x = 30 × 8
12x = 240
Divide
x = 240 / 12
x = 20
What value of x would make these two solids similar? X = 27 x = 30 x = 7.75 x = 31
The value of x is 31 mm, which makes given prisms similar.
What is similarity?Similarity of a triangle is the ratio of their corresponding sides or angles which are equal.
In the given prisms,
The length of the large prism = 29 mm,
And width = x mm.
In small prism, the length = 14.5 mm,
And width = 15.5 mm.
According to given condition,
Both the prisms are similar.
By property of similarity,
The in similar figure, the ratio of corresponding sides are equal.
For the given prisms,
29 / x = 14.5 / 15.5
x = 2 × 15.5
x = 31
The required value of x is 31 mm.
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the graph of this equation is which of the following
x² + y² - 2x + 3y + 8 = 0
a) parabola
b) circle
c) hyperbola
d) ellipse
e) point
someone help me please!!
Answer:
Step-by-step explanation:
What are the domain and range of y = -2(x-4)² + 1?
A. D: x > 4 and R: all real numbers
B. D: x ≤ 4 and R: all real numbers
C. D: all real numbers and R: y ≤ 1
D. D: all real numbers and R: y ≥ 1
Answer:
he correct answer is D: all real numbers and R: y ≥ 1.
Step-by-step explanation:
a researcher wants to find out how much a person watches television causes a person to like bourbon whisky more. to do this she asks each participant if they watch tv more or less than 2 hours per day and then has them take a likert scale of how much they like bourbon whisky. which test statistic would you use?
chi-square test statistic is statistically significant.
What is Test Statistic?
A statistic employed in statistical hypothesis testing is known as a test statistic. A test statistic, which can be thought of as a numerical summary of a data set that condenses the data into a single value that can be used to conduct the hypothesis test, is how a hypothesis test is commonly expressed.
To determine whether the amount of television a person watches is related to their liking for bourbon whisky, the researcher could use a chi-square test of independence.
The chi-square test is a statistical test that is used to determine whether there is a significant association between two categorical variables.
In this case, the two variables of interest are television watching (more or less than 2 hours per day) and liking for bourbon whisky (measured using a Likert scale).
The chi-square test statistic is calculated based on the observed frequencies of each combination of television watching and liking for bourbon whisky, and it is used to determine whether the observed frequencies are significantly different from the frequencies that would be expected if the two variables were independent.
If the chi-square test statistic is statistically significant, it indicates that there is a significant association between the two variables, and the researcher can conclude that television watching is related to liking for bourbon whisky.
Hence, chi-square test statistic is statistically significant.
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Can someone please help me I’ll mark you as brainlist
A=
B=
Answer:
A = 14
B = 4
Step-by-step explanation:
You want to know the values of A and B consistent with ∆EFG being congruent to ∆HJI, given that EF=14B-15, FG=9A-28, HJ=7B+13, JI=7A.
CongruenceCorresponding sides of congruent triangles have the same measure, so we have ...
FG = JI
9A -28 = 7A
2A = 28 . . . . . . add 28-7A
A = 14 . . . . . divide by 2
and ...
FE = JH
14B -15 = 7B +13
7B = 28 . . . . . . . . add 15-7B
B = 4 . . . . . . divide by 7
The values of A and B are 14 and 4, respectively.
PLEASE HELP ASAP
At a local high school, the student population is growing at 12% a year. If the original population was 242 students, how long will it take the population to reach 300 students? Round to the nearest tenth of a year.
A. 0.7 Years
B. 3.2 Years
C. 1.9 Years
Answer:
c is the closest
Step-by-step explanation:
it should take about 2 years
12.2: Postage Stamps
The relationship between the postage rate and the weight of a letter can be defined by a
piecewise function.
The graph shows the 2018 postage rates
for using regular service to mail a letter.
1.67
postage (dollars)
$10.55
0.45
1.5
1.25
1
0.75-
0.50
0.25
0.5
1
1. What is the price of a letter that has the following weight?
a.
1 ounce
0.50
b. 1.1 ounces
c. 0.9 ounce
2. A letter costs $0.92 to mail. How much did the letter weigh?
1.5 2 2.5 3 3.5 4
weight (ounces)
The price of the letter with the given weights are;
a) 1 ounce = $0.5
1.1 ounces = $1.1
0.9 ounces = $0.5
b) At a cost of $0.92 , weight is 3 ounces
How to Interpret Piecewise function Graphs?A piecewise function is defined using different expressions for different intervals in its' domain.
Now, from the graph, we see two line end points. One that is shaded circle and one that is not shaded circle but we will make use of the shaded one because it implies that is the output.
a) At one ounce, we can trace on the graph that the postage price is $0,5.
At 1.1 ounces, we can trace on the graph that the postage price is approximately $0.71
At 0.9 ounces, we can trace on the graph that the postage price is approximately $0.50
b) At a cost of $0.92 to mail, the weight must be more than 2 ounces but less than or equal to 3 ounces.
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How do you prove two shapes are similar?
According to the value of scale factor, we have to prove that the two shapes are similar.
The term shape in math is defined as the object that the form of an object or its outline, outer boundary or outer surface.
Here we have to find the way to prove two shapes are similar.
Here we have given that there are two shapes are given, in order to prove that those two shapes are similar, we must consider that the two shapes are considered to be "similar figures" if they have the same shape, congruent corresponding angles which means the angles in the same places of each shape are the same and equal scale factors.
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What is direct and inverse property?
The direct proportion means that two numbers increase or decrease together and in the same ratio and the inverse proportion means that if one number increases the other decreases and vice versa.
Direct Proportion: Two numbers or quantities are said to be in direct proportion if they increase or decrease together in the same ratio.
If a and b are in direct proportion, they can be written as
a ∝ b
Inverse Proportion: Two numbers or quantities are said to be in inverse proportion if one increases when the other decreases and vice versa.
If a and b are in inverse proportion, they can be written as
a ∝ 1 / b
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How many term of the A. P. 16,14,12,. Are needed to give the um 60? explain why do we get two anwer
The sum of first five or twelve term in the A.P given the value 60.
The term AP refers a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value.
Here we have given that A. P. 16,14,12,.
And we need to find the number of term to get the value of 60.
While we looking into the given question we have identified that the common difference d of the A.P. is − 2
Here we also know that the terms of the A.P. are in descending order.
Now, we have to take n = 5 then then first 5 terms are 16,14,12,10,8.
Here we have identified that the sum is 60.
Similarly, here by taking n = 12 , then the last 7 terms ( 12 − 5 ) (12-5) are 6 , 4 , 2 , 0 , − 2 , − 4 , − 5 6,4,2,0,-2,-4,-5
Here we have identified that the sum of these seven terms is 0.
Therefore, sum of first 12 terms is also 60.
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What is the translation formula?
Use P′(x+a,y+b) to translate the point P(x,y), a unit to the right, and b unit up. Use P′(x−a,y−b) to translate the point P(x,y), a unit to the left and b unit to the lower.
Whenever an object is moved from one location to the next without changing its size, shape, or orientation, a translation takes place. If we know which way and how far the figure to be moved, we can draw the translation in the coordinate plane.
Use P′(x+a,y+b) to translate the point P(x,y), a unit to the right, and b unit up. Use P′(x−a,y−b) to translate the point P(x,y), a unit to the left and b unit to the lower.
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What is an example of a geometric term?
An example of geometric term is ar².
When a set of numbers follow a particular order, they are said to be in sequence.
A set of numbers are said to be in geometric sequence if the ratio between second and first term is same as the ratio between third and second term and so on. The geometric sequence is presented as
Geometric Sequence = a, ar, ar², ar³, ......, arⁿ⁻¹, arⁿ.
where,
The first term is a.
Every two consecutive terms, r is the common ratio.
The number of terms is n.
Let us take an example.
The numbers 2, 6, 18, 54 are in geometric sequence because 6:2 = 18:6 = 54:18 and when we will write it as 2 + 6 + 18 + 54, it will become a geometric series and 2, 6, 18, 54 are geometric terms.
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What does a square of 1 mean?
Since 1 is a square of 1, or square of 1, we receive a new number when we multiply 1 by 1.Since a square number is a number multiplied by itself, 1 is likewise a square number.
what is square ?Four of its sides are equal in length, making a square a two-dimensional shape. A square has four right angles and opposing sides that are parallel to one another. Some examples of square-shaped objects in daily life include paper napkins, chess boards, cheese slices, floor tiles, and so forth.
here
When you multiply any integer by itself,
the answer is a square number.
Let's multiply one by itself as an example: 1 * 1 = 1
so since 1 is a square of 1, or square of 1, we receive a new number when we multiply 1 by 1.
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The following histogram shows the number of items sold at a grocery store at various prices:
Histogram titled Items Sold with Price Range on the x axis and Number of Items Sold on the y axis. Bar 1 is 0 to 2 dollars and 50 cents and has a height of 2. Bar 2 is 2 dollars and 51 cents to 5 dollars and has a height of 4. Bar 3 is 5 dollars and 1 cent to 7 dollars and 50 cents and has a height of 0. Bar 4 is 7 dollars and 51 cents to 10 dollars and has a height of 1.
Which of the following data sets is represented in the histogram?
{0.50, 2.00, 2.52, 3.37, 4.53, 5.00, 8.99}
{2, 4, 0, 1}
{2.50, 2.51, 5.00, 5.01, 7.50, 9.00, 10.00}
{0.50, 2.50, 2.50, 5.00, 5.00, 5.00, 7.51}
Answer:
i think 2.oo or 7.51 not sure
Answer:
the answer to this is a.
Step-by-step explanation:
What is inequality examples?
An example of inequality is 3 < 5.
How to illustrate the inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal.
They are denoted by the symbols ≥ < > ≤. An example of inequality is 3 < 5. This simply means that 3 is less than 5.
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How do you find the perpendicular line of a linear equation?
Ways to find the perpendicular line of a linear equation are by solving for y, convert the equation of the given line into slope-intercept form.
Describe perpendicular.A straight line that forms a 90° angle with another line is said to be perpendicular. A small square is placed between two perpendicular lines, as seen in the illustration, to indicate a right angle, also known as a 90° angle. The two lines in this instance are considered to be perpendicular to one another because they intersect at a straight angle.
Given
Ways to find the perpendicular line of a linear equation are,
First, by solving for y, convert the equation of the given line into slope-intercept form.
You obtain y = -2x + 5, indicating a -2 slope. Since the slopes of perpendicular lines are opposite-reciprocal, the slope of the line we're looking for is 1/2.
By entering the supplied point into the formula y = 1/2x + b and solving for b, we arrive at the value b = 6.
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A recipe for a cucumber salad includes 13cup tomatoes for 6 servings. how many cups of tomatoes are needed for 27 servings?
Answer:
PROPORTION:
13:6 = x/27
6x = 27(13)
6x = 351
x = 58.5
Therefore, cucumber salad need 58.5 cups of tomatoes to make 27 servings.
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-The figure below is made up of a rectangle and a half of a circle find the perimeter of the figure to the nearest tenth show ur work please use 3.14?for pi
The figure's circumference, as seen in the diagram, is 60.84 m.
What are some instances of perimeters?
The perimeter of an object is the space surrounding it. For instance, your house has a fenced-in yard. The perimeter is the length of the fence. If the yard is 50 feet by 50 feet, your fence is 200 feet long.
The formula below is used to determine the figure's perimeter.
Formula:
Equation 1: P = 2L + W + W / Equation 1:
P = The figure's perimeter
L is the figure's length.
W is the figure's width.
Considering the query,
Given:
L = 15 m\sW = 12 m\sπ = 3.14
Replace the values in equation 1 with these ones.
P = (15×2)+12+(12×3.14/2)
P = 30+12+18.84
P = 60.84 m
As a result, the figure's perimeter is 60.84 meters.
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What is the value of 3 √ 4 √ x when x 4096?
The value of 3 √ 4 √ x is 48
A number's square root is a value that, when multiplied by itself, yields the original number. The other way to square an integer is to find its square root. Squares and square roots are hence related concepts.
Assuming that x is the square root of y, the equation would be written as x=y or as x2 = y. The radical symbol for the number's root is "" in this instance. The square of the positive number is represented by multiplying it by itself. The original number is obtained by taking the square root of the square of a positive number.
As per the question, 3 √ 4 √ x when x =4096
first we need to calculate square root of 4096 by prime factorisation method
4096 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
4096 = (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2)
√4096 = √((2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2))
√4096 = 2 × 2 × 2 × 2 × 2 × 2
√4096 = 64
Therefore the square root of 4096 = 64.
x=64
now putting the value of x in 3 √ 4 √ x
= 3 √ 4 √ 64
= 3 √ 256
=3×16
=48
so the value of 3 √ 4 √ x is 48
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Assuming that x is the square root of y, the equation would be written as x=y or as x2 = y. The radical symbol for the number's root is "" in this instance. The square of the positive number is represented by multiplying it by itself. The original number is obtained by taking the square root of the square of a positive number.
4096 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
4096 = (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2)
√4096 = √((2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2))
√4096 = 64
x=64
= 3 as 4 as 64
= 3 as 256
=3×16
=48
The question is in the picture
Order from least to greatest. .46 4/6 .046 1/10 -4
(/ means fraction)
Answer:
-4, 0.046, 1/10, 0.46, 4/6
Step-by-step explanation:
First, we know that -4 is the least because it is a negative number.
Next, we need to convert the fractions to decimals. 1/10 is 0.1, and 4/6 is 0.66.
Then, we order the decimals.
0.046 is the next smallest, because it is a hundredth, and the remaining decimals are tenths and therefore greater.
We compare the remaining decimals, which are 0.10, 0.46, and 0.66. These are easy to compare and order.
Now, we've compared and ordered all the numbers. We can convert the fractions back into their original form.
Is a triangle congruent if 1 angle of the triangle is congruent and 2 sides are congruent?
The triangles are congruent if there are two pairs of corresponding angles and one pair of corresponding sides.
What is meant by congruent ?If two shapes are congruent, we can also state that their mirror images are identical. If one of the geometric figures can be superimposed on the other so that their entire surface coincides, then the two are said to be congruent, or to be in the relation of congruence. Congruent refers to objects that are precisely similar in size and shape. The forms stay equal no matter how they are rotated, flipped, or turned. Create two circles with the same radius, cut them out, and stack them.To learn more about congruent refer to:
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mark and kevin own 1/4 and 1/3 of the books on a shelf, respectively lori owns the rest of the books. if kevin owns 9 more books than mark, how many books does lori own ?
The total number of books Lori owns is 45.
To find the total number of booksLet x be the total number of books.
Mark owns 1/4 of x
Kevin own 1/3 of x
Kevin owns 9 more than Mark, so;
1/4x - 1/3x = 9
Multiplying both sides by 12
4x - 3x = 108
x = 108
The total number of books is 108
but;
Mark owns 1/4 of x = 1/4 x 108
Mark = 27
while Kevin owns 1/3 x 108
Kevin = 36
Therefore, Lori would own
108 - 36 - 27 = 45
Lori's number of books will be 45.
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