The Law of Cosines can be used to calculate the angles of an isosceles triangle given three side lengths. Two of the angles are equal, while the third can be found by subtracting the two known angles from 180°.
Since you are given three sides of an isosceles triangle, you can use the Law of Cosines to calculate the angles of the triangle. The Law of Cosines states that for a triangle with side lengths a, b, and c and angle C opposite side c, the following equation holds:
c² = a² + b² - 2abcosC
Therefore, you can rearrange the equation to solve for angle C:
C = arccos((a² + b² - c²) / (2ab))
For an isosceles triangle, two of the angles will be equal, so you can calculate those two angles using the equation above, and the third angle can be found by subtracting the two known angles from 180°.
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Which variation is represented by this situation:
Lisa and Maria are at a convention. There is enough food at the convention to feed 300 attendees for 4 days. If 400 people attend the convention, how long will the food last?
If 400 people attend the convention,
the food will last for 3 days.
What is inverse proportion?Two quantities a and b are said to be in inverse proportion if an increase in quantity a, there will be a decrease in quantity b, and vice-versa. In other words, the product of their corresponding values should remain constant. Sometimes, it is also known as inverse variation.
That is, if ab = k, then a and b are said to vary inversely. In this case, if b1, b2 are the values of b corresponding to the values a1, a2 of a, respectively then a1 b1 = a2 b2 or a1/a2 = b2 /b1
Given,
Food for 300 people will Last for 4 days.
Attending people = 400
Let the food for 400 will last for x days.
According to the question,
300 × 4 = 400 × x
x = 300 × 4 /400
x = 3
Hence, the food will last 3 days,
if 400 people attend the convention.
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If there is a 50-50 chance of the Sneakers winning today's game, what are the chances that they win their next gam~
Solving the question asked, we can say: If you win tonight, your odds of winning the next game are [tex]$58.33\%$[/tex]. After that, if you lose, you have a [tex]$38.88 \%$[/tex] chance of winning the game.
What is probability?Probability theory is a branch of mathematics that measures the probability that an event or statement is true. The probability of an event is a number between 0 and 1, with approximately 0 indicating that the event is unlikely and 1 indicating that it is certain. Probability is a numerical representation of the disease that a particular event will occur. Another way to express probability is as a percentage from 0% to 100% or 0 to 1. Proportion of occurrences in the complete set of equally likely possibilities leading to a particular occurrence compared to the total number of outcomes.
[tex]$$\begin{aligned}& (2 / 3+1 / 2) / 2=X \\& 1,666 / 2=X \\& 0.58333=X \\& ((2 / 3+1 / 2 / 2) x 2 / 3=X \\& 0.58333 x 0.666=X .3888=X\end{aligned}$$[/tex]
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What is perimeter also called?
Perimeter is the total length of all sides of a shape, also known as the circumference.
Perimeter is a measure of the distance around a two-dimensional shape. It is the sum of the lengths of all the sides of a shape. Perimeter is also known as the circumference. When calculating perimeter, you measure the length of each side of the shape and add them together. For example, the perimeter of a square with sides of 4 inches each would be 16 inches. Perimeter is an important concept in geometry, and it can be used to calculate area, the space within a shape or figure. It can also be used to calculate the distance between two points. Knowing the perimeter of a shape can help you solve many problems in math, design, and science.
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How many incas did the spanish kill on november 16 1532 o 100 o 600 o 1000 6000?
Spanish killed nearly 6000 Incas.
The Spanish conquistador and explorer Francisco Pizarro springs a trap on Atahualpa, the monarch of the Incas, in the year 1532. Atahualpa allowed roughly 6,000 unarmed men to attend the feast despite having almost 80,000 soldiers with him in the mountains. It took the Spanish a long time and much violence to conquer the Inca Empire. Pizarro's soldiers massacred the 6,000 Incans in approximately one hour.
The lone Spanish wounded were received by Pizarro himself, who injured his hand while saving Atahualpa's life. Pizarro retained Atahualpa in captivity while he prepared plans to conquer his empire because he understood that the emperor was worthy alive than dead. Atahualpa responded by appealing to his hostages' avarice and supplying them with money and silver in exchange for their release.
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How to solve y-2=-2(x+3) when x equals -3
Estimate how many times larger 6.1 • 10^7 is than 2.1 • 10^-4
Answer:
Estimation: 300 Billion times bigger
Actual: 290 Billion times bigger
Step-by-step explanation:
Lets group the coefficients together and the exponents together.
[tex](\frac{6.1}{2.1})(\frac{10^7}{10^{-4} })[/tex]
We can round 6.1 to 6.
We can round 2.1 to 2.
[tex](\frac{6}{2})(\frac{10^7}{10^{-4} })[/tex]
[tex](3)(\frac{10^7}{10^{-4} })[/tex]
Subtract the exponent from the denominator from the exponent of the numerator.
[tex](3)(10^{7-4*1} )[/tex]
[tex](3)(10^{7+4} )[/tex]
[tex](3)(10^{11} )[/tex]
[tex]3*10^{11}[/tex]
[tex]10^{11}[/tex] is 100 billion.
3 times 100 billion is 300 billion.
Fill in the blank question.
Miss Wade's science class of 20 students is going on a field trip to the zoo. Each student will also take a train ride around the zoo. Mr. Sexton's class of 25 students is going on a field trip to the state park and will take a canoe trip. Admission to the zoo is twice that of the state park's entry fee as shown in the table. Each group will spend the same total amount of money.
The admission fee for the zoo and for the state park is given as follows:
Zoo: $13.State park: $6.5.How to model the situation?For the zoo, the costs are divided as follows:
Admission: 2x per student.Train ride: $3.25 per student.20 students are going to the zoo, hence the total cost spent at the zoo is given as follows:
20(2x + 3.25) = 40x + 65.
For the state park, the costs are divided as follows:
Admission: x per student.Train ride: $6.50 per student.25 students are going to the state park, hence the total cost spent at the state park is given as follows:
25(x + 6.50) = 25x + 162.50.
The costs spent at both parks are the same, hence the value of x can be obtained as follows:
40x + 65 = 25x + 162.5
15x = 97.5
x = 97.5/15
x = 6.5.
Hence the admission fees are given as follows:
Zoo: $13, as 2x = 13.State park: $6.5, as x = 6.5.Missing InformationThe table is given by the image presented at the end of the answer.
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is the relationship between the variables in the table an inverse variation or a direct variation? write an equation to model it.
x= 2 6 7 14
y= 21 7 6 3
The relationship between the variables in the table is an inverse variation The equation to model is y = 42/x.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x = 8 is an equation.
We have,
x: 2 6 7 14
y: 21 7 6 3
Now,
When x = 2, y = 21
This can be written as,
y = kx
21 = 2k
k = 21/2
The equation is y = (21/2)x _____(1)
or
y = k/x
21 = k/2
k = 42
The equation is y = 42/x _____(2)
Now,
We will check which equation fits the table.
From (1)
y = (21/2)x
When x = 6,
y = (21/2) x 6 = 21 x 3 = 63
From (2),
When x = 6,
y = 42/6 = 7
When x = 7,
y = 42/7 = 6
When x = 14,
y = 42/14 = 3
This equation satisfies the table.
Thus,
The relationship is an inverse variation.
The equation is y = 42/x.
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What is the simplified form of StartRoot 144 x Superscript 36 Baseline EndRoot?
The simplified form of expression is, 12x⁶.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ √144 x³⁶
Now, By the property of square root;
⇒ √ ab = √a × √b
We get;
⇒ √144 x³⁶ = √144 × √x³⁶
And, By using the exponent property, we get;
⇒ xᵃᵇ = xᵃ × xᵇ
So, We get;
⇒ √144 x³⁶ = √144 × √x³⁶
= √144 × √x⁶ × √x⁶
= √12×12 × √x⁶ × √x⁶
= 12 × x⁶
= 12x⁶
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Evaluate the function.
ƒ(x) = 2x + 1
f(x) = 7
Answer:
Read below
Step-by-step explanation:
Step 1: Multiply 2 by x: 2x
Step 2: Add 1 to 2x: 2x + 1
Step 3: Substitute x with 7: 2(7) + 1
Step 4: Multiply 2 by 7: 14 + 1
Step 5: Add 1 to 14: 14 + 1 = 15
The graph shows the number of each kind of CD in Dante's music collection. What is
the probability that a randomly choosen CD will be country?
Pop
10
Types of Music CDs
Rock
6
Jazz
4
Country
12
Hip-Hop
Answer: 1/8
Step-by-step explanation: To calculate the probability, we first need to add up the total amount of CDs. 10+6+4+12 = 32. After this, we divide 4 by 32, getting 4/32 which can be simplified to 1/8
What is associative property in math?
Answer:
This law simply states that with addition and multiplication of numbers, you can change the grouping of the numbers in the problem and it will not affect the answer. Subtraction and division are NOT associative.
Step-by-step explanation:
A circular mirror is surrounded by a square metal frame. The radius of the mirror is 3x. The side length of the metal frame is 15x. What is the area of the metal frame? (Type your answer in factored form. Type an exact answer in terms of pi.
The area of the frame is __ square units
The area of the frame is 196.73 x²
What is area ?
The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.
Area is a phrase used to describe how much room a 2D form or surface occupies. Area is measured in square units, such as cm2 or m2. The area of a form is computed by dividing its length by its breadth.
(15x)^2 = 225x^2
Area of the frame
= π (3x)²
= 28.27 x²
Metal area surrounding the frame
225 x² - 28.27 x²
= 196.73 x²
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The four-digit numeral $3AA1$ is divisible by $9$. What digit does $A$ represent?
When the four - digit numeral is divisible by nine is given by 3AA1 the digit A represents 7
Properties of numbers divisible by 9A number itself is divisible by 9 if its digit's sum is also divisible by 9.
In mathematics, multiples are the results of multiplying an integer by a given number. number divisible by 9 is multiple of 9
using the above property we have that
3 + A + A + 1 = 9, OR 18, OR 27
4 +2A = 9, OR 18, OR 27
assuming 18
2A = 18 - 4
2A = 14
A = 7
hence the number is 3771
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DEFG is a square with vertices at D(1, 1), E(1,6), F(6, 6), and G(6, 1). DEFG is reflected in the line x = 1. Find the coordinates of
D',E,F, and G'.
By considering the reflection, the coordinates of the reflected square D'E'F'G' are:
D'(0,1) , E'(0,6), F'(5,6) and G'(5,1)
What is square?A square is a two-dimensional geometric shape that has four equal sides and four right angles. It is a type of rectangle, but with all sides equal. The opposite sides of a square are parallel and of equal length. A square can be defined by its side length or by the coordinates of its vertices.
What is reflection?Reflection is a type of transformation in geometry in which a shape is flipped over a given line, called the line of reflection. The image that is created is a mirror image of the original shape. The line of reflection can be a horizontal line, a vertical line, or any line that is not parallel to the axes. Reflecting a shape over a line involves taking the coordinates of each point of the shape and applying a specific rule (such as multiplying or adding a constant) to the x or y coordinate, depending on the line of reflection. This rule is often simple and easy to apply, such as reflecting over x = 1. The reflected shape will be in the same plane as the original shape but with a different orientation or position.
When a square is reflected in the line x=1, each of the points on the square will have their x-coordinate replaced by 1 subtracted from their original x-coordinate.
The coordinates of the reflected square D'E'F'G' can be found by applying this rule to the original coordinates of square DEFG:
D(1,1) => D'(1-1,1) => D'(0,1)
E(1,6) => E'(1-1,6) => E'(0,6)
F(6,6) => F'(6-1,6) => F'(5,6)
G(6,1) => G'(6-1,1) => G'(5,1)
So the coordinates of the reflected square D'E'F'G' are:
D'(0,1) , E'(0,6), F'(5,6) and G'(5,1)
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During lockdown down period people work very puzzled and their decided to play some game firstly they collect the 17 cards and write the numbers 1 to 17 put them in a box people make a bet from the chance of drawing the number either the prime or even number
etc.
From the universal set; N = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17}
Probability of drawing an even or prime number will be 15/17.
What is Probability?Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event. The probability of all the events in a sample space adds up to 1.
N = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17}
Prime = {1,2,5,7,11,13,17}
Even = {2,4,6,8,10,12,14,16}
Pr(Prime) = 7/17
Pr(Even) = 8/17
Pr(Prime or even) = 7/17 + 8/17
Pr(Prime or even) = 15/17
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10 Two cyclists are traveling along a track in the same direction. Their motions are described
by the linear equations d = 10t and d-8t= 2, where t hours is the time and d miles is the
distance from a point on the track.
b When will the cyclists meet?
Answer:
They will meet in 1 hour
Step-by-step explanation:
(1) d = 10t
(2) d - 8t = 2 rearrange this equation to: d = 8t + 2
Set equation (1) equal to equation (2):
10t = 8t + 2
Solve for t:
10t - 8t = 2
2t = 2
t = 2/2 = 1 hr
For what value of k is the system of equations KX 3y K 2 12x Ky K inconsistent?
The system of equations is inconsistent for any value of k.
If we subtract the first equation from the second one, we get 0 = 12x, which is inconsistent no matter what value k is. This means that the system of equations has no solution and is therefore inconsistent.
The system of equations KX + 3y = K + 2 and 12x + Ky = K is inconsistent for any value of k. This is because when we subtract the first equation from the second one, we get 0 = 12x, which is an inconsistent equation no matter what value k is. This means that the system of equations has no solution and is therefore inconsistent. No matter what value we assign to k, the equations cannot be solved simultaneously and so the system of equations is inconsistent.
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[tex]w + 29 = 250 \div 5 - 20[/tex]
Find the value of w
Answer:
I don't know I am sorry bro
(I need the answer as FAST as possible so if anybody could help that would be greatly appreciated)
What is the domain of the function y √ x?
The domain of the function y = √ x is x ≥ 0.
The domain of a function is the set of all input values for which the function is defined. The square root function, represented by √, is only defined for non-negative real numbers. This is because the square root of any negative number is not a real number, it becomes an imaginary number. Therefore, the domain of √ x is the set of all real numbers greater than or equal to zero.
This means that any input value less than zero would result in an undefined output for the square root function. In this case, since the square root is the only function, the domain of the function y = √ x is x ≥ 0. This means that the function can only take non-negative real numbers as input and will output a non-negative number.
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Please help me with my HW
Answer: 4k^7
Step-by-step explanation:
How do you use sin Cos in C?
We can use the sin (), and cos () functions in C programming to find the sine and cosine values of any problem.
sin( ), cos( ) and tan( ) functions in C are used to find sine, cosine and tangent values.
sinh( ), cosh( ) and tanh( ) functions are used to find hyperbolic sine, cosine and tangent values.
exp( ) function is used to find the exponential “e” to the xth power. log( ) function is used to find the natural logarithm and the log10( ) function is used to find the base 10 logarithms.
The” math.h” header file supports all these functions in the C language.
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8. Sarah has a cube with a volume of 2,197 cubic centime
of Sarah's cube?
volume of 2,197 cubic centimeters, which square represents the faces
15 cm
25 cm
13 cm
10 cm
The side of the cube, the faces will be 13 cm.
What is cube?
The term "cube" refers to a solid three-dimensional shape in mathematics or geometry that has six square faces, eight vertices, and twelve edges. It is also asserted to be a conventional hexahedron. You must be familiar with the three-by-three Rubik's cube, which is the most prevalent example in daily life and can help to increase brain capacity. Similar to this, you'll run into a lot of real-world examples, like 6 sided dice, etc. Solid geometry is the study of three-dimensional objects with surface areas and volumes. Cube, cylinder, cone, and sphere are some of the other solid shapes. Here, we'll talk about its definition, attributes, and relevance to mathematics.
Sarah has a cube with a volume of 2,197 cubic cm.
side is ∛(2197) =13 cm
So the side of the cube will be 13 cm.
Hence, the side of the cube, the faces will be 13 cm.
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What is irrational statement?
An irrational statement is a kind of genuine number that can't be addressed as a basic portion. It can't be communicated in that frame of mind of a proportion. If N is silly, N isn't equivalent to p/q where p and q are numbers and q isn't equivalent to 0. Model: √2, √3, √5, √11, √21, π(Pi) are nonsensical.
A number can't be communicated as a portion of any numbers and. . Unreasonable numbers have decimal developments that neither end nor become occasional. Each supernatural number is irrational.
If a square root is not an ideal square, then it is viewed as an unreasonable number. These numbers can't be composed as a portion because the decimal doesn't end (non-terminating) and doesn't rehash an example (non-repeating).
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A cup of tea costs $3.25 at a local cafe. Alan and his wife, Patty, have a coupon for $1 off their order. Alan says the expression 3.25t - 1 represents the cost for t cups of tea. Patty says the expression 3t + (-1) represents the cost. Are their expressions equivalent? Explain.
Answer:
Step-by-step explanation:
The expressions are not equivalent. A cup of tea costs $3.25. $3.25t reprensents the total cost for the number of cups of tea (t) in one order. Subtracting the $1 coupon or adding the coupon as a negative results in the same discount. But Patty is using the wrong cost for a cup of tea, $3 instead of $3.25. Resulting in expressions that are NOT equivalent.
March Madness Movies served 2323 lemonades out of a total of 111111 fountain drinks last weekend. Based on this data, what is a reasonable estimate of the probability that the next fountain drink ordered is a lemonade?
23/111 is a reasonable estimate of the probability that the next fountain drink ordered is a lemonade.
What do you mean by Probability?Probability theory deals with numerical evaluations of the likelihood that an event will occur.
Probabilities are mathematical explanations of the likelihood that an event will occur or that a proposition is true. The likelihood of an event is represented by a number between 0 and 1, with 0 typically signifying impossibility and 1 typically signifying certainty.
A probability represents the likelihood or chance that a particular occurrence will take place. Probabilities can be expressed as ratios between 0 and 1, or as percentages between 0% and 100%.
March Madness Movies served 23 lemonades out of a total of 111 fountain drink last weekend.
The probability that the a fountain drink ordered is a lemonade will be :-
P= [tex]\frac{Number of lemonade}{Total fountain drink}[/tex]
= 23/111
Based on this data, the reasonable estimate of the probability that the next fountain drink ordered is a lemonade = 23/111.
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483000 in standard form
Answer:
483000
Step-by-step explanation:
To write a linear expression in standard form, rearrange the terms in alphabetical order.
Answer:
48300000
We can write the above number as
4.83 x 10000000
=4.83 x 10 ^7
12. Sarah uses long division to convert
a rational number 2 to a decimal.
P
Which of the following statements
cannot be true?
A. The decimal form of P
q
terminates with a zero in the
tenths place.
B. The decimal form of P
eventually repeats.
C. The decimal form of never
terminates or repeats.
D. The decimal form ofis 0.
On solving thr provided question, by help of arithmetic progression, we got to know that a10 = 207
what is arithmetic progression?There are two approaches to define arithmetic progressions (AP): The difference between any two successive terms in an arithmetic sequence must always be equal, and it is sometimes referred to as a series in which all terms except the first are created by adding a predetermined number to the preceding term.
9,15,25..............
15-9 = 6
25-15 = 10
a4 - 25 = 14 => a4 = 39
frequently referred to as a series in which all terms save the first are formed by adding a predefined number to the preceding term since the difference between any two succeeding terms in the sequence must always be equal.
a5-39 = 18 => a5 = 57
a6-57 = 22 => a6 79
...
...
...
...
...
a10 - 169 = 38 => a10 = 207
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What is the slope of the line passing through the points
(-8, 5) and (7,0)?
Therefore, the slope of the line passing through the points (-8, 5) and (7,0) is -1/3.
The slope of the line passing through the points (-8, 5) and (7,0) can be found by using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
So, using the coordinates (-8, 5) and (7,0), we have:
m = (0 - 5) / (7 - (-8)) = -5 / 15 = -1/3
Therefore, the slope of the line passing through the points (-8, 5) and (7,0) is -1/3.
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