Remember the chant "soh cah toa"
sine = opposite ÷ hypotheneus
cosine = adjacent ÷ hypotheneus
tangent = opposite ÷ adjacent
remember that hypotheneus is the slanty side, opposite and adjacent side is in COMPARISON with the angle you want to find.
In this case, tan B would be 15/8
sinB = 15/17
cosB = 8/17
Help asap! Ive tried many different things!
Answer: that realy saadddddddddd
Step-by-step explanation: 4xx 6y 9x
Answer: The slope is -1/5
Robin and Evelyn are playing a target game. The object of the game is to get an object as close to the center as possible. Each player’s score is the number of centimeters away from the center. Robin and Evelyn’s results from five rounds are shown.
Robin’s scores: 99, 108, 102, 107, 119
Evelyn’s scores: 125, 137, 138, 145, 145
The mean of Robin’s scores is 107. What is the mean of Evelyn’s scores?
it is 138
The mean of Evelyn’s scores based on the information will be 138.
How to calculate the mean?From the information, Robin and Evelyn are playing a target game, the object of the game is to get an object as close to the center as possible and each player’s score is the number of centimeters away from the center.
It should be noted that Robin and Evelyn’s results from five rounds are shown. The mean simply means the average of the numbers.
The mean of Evelyn’s scores based on the information will be:
= (125 + 137 + 138 + 145 + 145) / 5
= 690/5
= 138
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Pizza Palace pays Tony $40 a night +2 dollars for every delivery he makes which number line shows how many pieces Tony must deliver them to make at least $70 an hour. Please answer quickly
Analyzing the question, Tony must deliver them 35 pieces to make at least $70 an hour.
What is algebra?Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It is used to study mathematical structures that include numbers, as well as variables and other abstract concepts. Algebraic concepts include operations such as addition, subtraction, multiplication, and division, as well as the properties of operations such as distributivity and associativity. Algebraic concepts also include equations, inequalities, and functions.
According the question,
tony make 2 dollars for each delivery,
so, he need to do 70/2 = 35 delivery
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When the area in square units of an expanding circle is increasing twice as fast as its radius in linear units, the radius is.
1/π is the radius of an expanding circle that grows twice as fast as its radius in linear units.
What is area?The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina.
Here,
The area of a circle is: Ac = π×r² where r is the radius of the circle
If this area is expanding that mean Ac and r are a function of time and the speed is dA/dt and dr/dt can be found from the equation of the area
Then:
Ac = π×r²
dA/dt = 2×π×r×dr/dt
According to the problem statement
dA/dt = 2×dr/dt
By substitution
2×dr/dt = 2×π×r×dr/dt
Simplifying
1 = π×r
and
r = 1/π
The radius of expanding circle that is increasing twice as fast as its radius in linear units is 1/π.
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(8,3); y =-1/4 x+7 parallel lines
The equation parallel to the given line is y=-1/4 x+5.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
The given equation is y =-1/4 x+7 and the coordinate point is (8, 3).
Here, slope is -1/4
We know that, the slope of parallel lines are equal.
Now, substitute m=-1/4 and (x, y)=(8, 3) in y=mx+c, we get
3=-1/4 (8)+c
c=5
Substitute m=-1/4 and c=5 in y=mx+c, we get
y=-1/4 x+5
Therefore, the equation parallel to the given line is y=-1/4 x+5.
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Please please please help me!!!! 20+ points! Thank you :)
Answer:
m∠1 = 32
Step-by-step explanation:
∠WXZ = 115
m∠2 = m∠1 + 51
x + x + 51 = 115
2x + 51 = 115
2x = 64
x = 32
What is the exponential of 16?
The exponential of 16, also known as [tex]e^{16[/tex], is the value of the mathematical constant e (approximately equal to 2.71828) raised to the power of 16.
To calculate e^16, we would use the following formula:
[tex]e^{16[/tex] = e x e x e x e x e x e x e x e x e x e x e x e x e = 8.222838 x [tex]10^6[/tex]
So, the exponential of 16 is approximately 8.222838 x [tex]10^6[/tex].
It's important to note that the exponential value of any number is a real number, the value of e is raised to the power of that number. The mathematical constant e, also known as Euler's number, is an important number in mathematics and is used in various branches such as calculus, statistics and probability. It has also been used in physics and engineering, it appears naturally in many processes such as radioactive decay, natural growth and decay of populations, and more.
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A rectangule ha a preimeter of 446 feet. The rectangle ha a length of (13x-1) feet and a width of (9x 4) feet. Find the length and width of the rectangle
The rectangle has a length of 222 feet and a width of 150 feet.
A quadrilateral with parallel sides equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.
Rectangles can also be referred to as parallelograms since their opposite sides are equal and parallel.
We know that the perimeter of a rectangle is the sum of all four sides. So in this case:
Perimeter = 2(length) + 2(width)
Given that the perimeter is 446 feet, we can set up the equation:
446 = 2(13x-1) + 2(9x+4)
On Simplifying, we get:
446 = 44x + 6
Now we can solve for x by subtracting 6 from both sides:
440 = 44x
Finally, dividing both sides by 44:
x = 10 feet
Now that we know the value of x, we can substitute it back into the expressions for the length and width:
Length = (13x-1) = (13(10)-1) = 129 feet
Width = (9x+4) = (9(10)+4) = 94 feet
Therefore, the rectangle has a length of 129 feet and a width of 94 feet.
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Afia chool i plotted at -8, -3 on a coordinate plane. Her babyitter houe i located at 8 , -3. What i the ditance between Afia chool and her babyitter houe?
The distance between Afia's school and her babysitter's house is 16 units.
Distance is a measurement of how far away two things or locations are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in ordinary language.
The distance between two points in a coordinate plane can be found using the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Where (x1, y1) and (x2, y2) are the coordinates of the two points, and d is the distance between them.
In this case, the coordinates of Afia's school are (-8, -3) and the coordinates of her babysitter's house are (8, -3).
Plugging these values into the distance formula:
d = √((8 - (-8))^2 + (-3 - (-3))^2)
d = √((8 + 8)^2 + (0)^2)
d = √(16^2)
d = √(256)
d = 16 units
Therefore, the distance between Afia's school and her babysitter's house is 16 units.
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Is 4x an exponential function?
Yes, 4x is an exponential function. An exponential function is one where there is a constant being raised to a variable.
Exponential functions involves exponents. An exponential function has a constant as its base and a variable as its exponent but not the other way round. if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function. The exponential function is a type of mathematical function which are helpful in finding the growth or decay of population, money, price that are growing or decay exponentially. A basic exponential function from its definition is of the form f(x) = b x, where 'b' is a constant and 'x' is a variable. generally it refers to the positive valued function of a real variable. it can be extended to the complex numbers or generalized to other mathematical objects like matrices.
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How do you solve the midline theorem of a triangle?
The midline theorem claims that cutting along the midline of a triangle creates a segment that is parallel to the base and half as long.
The condition for the midline theorem is that the two triangles must have the same size and shape, so all three sides have the same length, and all three angles have the same measure.
For the theorem, we draw a line through two points on either side of the triangle and then we prove that the line divides the sides into equal halves. Once proven that the sides are in two equal halves using congruency it is proved that the base and midline are parallel.
Since the base and midline are parallel to each other using the SAS rule of congruency therefore according to the theorem the segment is half as long as the base.
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If point (x, y) is reflected over the x-axis, the resulting point is (-x, y)
The given statement "If point (x, y) is reflected over the x-axis, the resulting point is (-x, y)" is true.
What is the reflection on x-axis?When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the x-axis is (x, -y).
The given statement is "If point (x, y) is reflected over the x-axis, the resulting point is (-x, y)".
When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).
Therefore, the given statement is true.
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The shape below has rotational symmetry.
(b) Write down the order of rotational symmetry.
The order of rotational symmetry is the number of times a shape can be rotated and still look the same.
What is the order of rotational symmetry?Generally, The amount of times that a form may be rotated through 360 degrees with maintaining its appearance is referred to as its rotational symmetry.
For instance, a circle has an order of rotational symmetry of infinity, which means that it can be rotated any number of times and still look the same.
On the other hand, a square has an order of rotational symmetry of 4, which means that it can be rotated by 90 degrees four times while maintaining its original appearance.
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Point M is the midpoint of AB, the coordinates of point a or -7, 2 and the coordinates of M are -2, two what are the coordinates of point B
The coordinates of point B of the line AB with M as a midpoint are; (-11, 2)
How to find the midpoint between two coordinates?The formula for the midpoint between two coordinates is;
(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2
For the line AB, we are told that M is the point and that we have the coordinates as;
A(-7, 2) and M(-2, 2). Thus, plugging in the relevant values gives;
(-2, 2) = (7 + x₂)/2, (2 + y₂)/2
Thus;
(7 + x₂)/2 = -2
(7 + x₂) = -4
x₂ = -11
Similarly, we have;
(2 + y₂)/2 = 2
2 + y₂ = 4
y₂ = 2
B coordinate is (-11, 2)
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sb help♀️.. i got moree
The Pythagorean theorem and the above information can be used to deduce that the diagonal SU has a length of 13.
What does Pythagorean Theorem mean?For right-angled triangles, the theorem is applicable. The side opposing the right angle is the longest side in every right-angled triangle and is referred to as the hypotenuse. The square on the hypotenuse's area is equal to the sum of the squares on its two shorter sides, according to the theorem. Pythagoras of Samos, a mathematician and religious figure who held the view that everything in the cosmos was made up of numbers, is the subject of the Pythagorean Theorem.Given :
It is known that RS=12 and ST=5 in the rectangle RSTU.
The steps listed below can be used to calculate the diagonal SU's length:
The Pythagorean theorem can be used to calculate the diagonal SU's length in step 1.
Step 2 - The following is the Pythagorean theorem:
H² = B² + P²
Where B is the base, P is the perpendicular, and H is the hypotenuse.
Step 3: Replace the known terms' values in the aforementioned expression.
SU² = 12² + 5²
Step 4: Condense the previous expression.
SU = √144 + 25
SU = 13
So, the length of the diagonal SU is 13.
The complete question is:
In rectangle RSTU it is known that RS=12 and ST=5. What is the length of diagonal SU?
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What is the exponential form of 2 into 2 into a?
The Exponential form of the given expression "2 into 2 into a" is represented as [tex]2^{2} \times a[/tex] , and the value is 4a .
The Expression is given as : " 2 into 2 into a" ;
mathematically the given expression can be written as : ⇒ [tex]2\times 2\times a[/tex] ;
By using the Law Of Exponents , which states that : when the base of the exponents are same the power gets added ;
we see that , the base number 2 is same , So , we add the power of 2 ;
So , on adding the power ,
we get ;
⇒ [tex]2^{2} \times a[/tex] ;
So, the exponential form is [tex]2^{2} \times a[/tex] ;
and the value of this exponential expression is 4a .
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The castle tower has a height of 14 m.
Work out the height of the tree.
The height of the tree is 5 times of the castle. Then the height of tree is 70 m.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The castle tower has a height of 14 m. The height of the tree is 5 times of the castle.
The height of the tree is calculated as,
⇒ 14 x 5
⇒ 70 m
The height of the tree is 70 m.
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The complete question is given below.
The castle tower has a height of 14 m. The height of the tree is 5 times of the castle. Work out the height of the tree.
The sum and the product of the roots of 2x 2 − 6x + 10 = 0 respectively are
The sum of the roots of 2x² − 6x + 1 = 0 is 3 and the product is 0.5076.
What is roots?The values of variables that satisfy the given quadratic equation are known as its roots. In other words, x = α is a root of the quadratic equation f(x) if f(α ) = 0. The real roots of an equation f(x) = 0 are the x-coordinates of the points where the curve y = f(x) intersects the x-axis.
To find sum and the product we first need to find roots/zeroes of the quadratic equation 2x² − 6x + 1 = 0, i.e.
⇒ 2x² − 6x + 1
⇒ 2x²−6x + 1
Putting them in quadratic equation
[tex]$ \Rightarrow x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}[/tex]
[tex]$ \Rightarrow x={\frac {-(-6)\pm {\sqrt {(-6)^{2}-4(2)(1)}}}{2(2)}}[/tex]
[tex]$ \Rightarrow x = \frac{3 -\sqrt{7} }{2}[/tex], [tex]$ \Rightarrow x_2 = \frac{3 +\sqrt{7} }{2}[/tex]
⇒ x = 0.177124, x₂ = 2.822876
⇒ x = 0.18, x₂ = 2.82
The sum of the equation roots of 2x² − 6x + 1 = 0 is
0.18 + 2.82 = 3
The Product of the equation roots of 2x² − 6x + 1 = 0 is
0.18 × 2.82 = 0.5076
Thus, The sum of the roots of 2x² − 6x + 1 = 0 is 3 and the product is 0.5076.
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I’ll give brainliest please help! Using point slope form find the equation of the line with the given slope that passes through the given point
Answer:
Below
Step-by-step explanation:
Point -4, 6 slope = - 3
Point slope form of the line : ( y-y1) = m (x - x1)
(y-6) = -3 (x - -4)
y - 6 = -3 (x+4)
how do i solve n - 4 < 5
=> n-4<5
=> n-4+4<5+4
=> n<9
While playing a board game, Mary noticed that the die landed on the number 4 more often than usual. Please Hurry!!!!! Will mark brainliest for explanation of all parts.
Part A: Describe a simulation that could be run to test how many times out of 100 a fair die should land on the number 4. State the representations and possible outcomes. Be sure to give enough detail that another person could replicate your simulation. (7 points)
Part B: While running a simulation, the die landed on the number 4 a total of 32 times out of the 100 rolls. Construct and interpret a 95% confidence interval for the true proportion of rolls that will land on the number 4. Show all work. (7 points)
Part C: Does the confidence interval in part B support Mary's suspicions that the die is not fair? Explain your reasoning. (6 points)
Part A:
We want to see how often the number 4 comes up when we roll a fair dice 100 times. We will use a dice with numbers 1,2,3,4,5,6. We will keep track of how many times 4 comes up and we think it should be around 16 times because there are 6 numbers on the dice.
Part B:
We rolled the dice 100 times and got 4 32 times.
-We want to know if that is normal or if something is wrong with the dice.
-We use special numbers to check if this is normal, it's called the confidence interval
-The confidence interval tells us if 32 times is normal or not.
Part C:
The confidence interval tells us that 32 times is not normal, it's unlikely that it happened by chance. So, the dice might not be fair.
Macy made a 220 grooming dogs one day in her mobile grooming business she charges 60 per appointment and 40 earned in tips write an equation to represent the situation and solve the equation to determine how many appointments Messi had part B Logan made a profit of 300 as a mobile groomer he charge $70 per appointment and received $50 in tips but he had to pay a rental fee for the truck of $20 per appointment write an equation to represent the situation and solve the situation to determine how many appointments Logan had (32 points)
We can see that:
Part A: 3 appointments
Part B: 5 appointments
What is an equation?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
Part A
Let x = number of dog grooming appointments Macy had in one day.
Given information:
Charge per appointment = $60
Total amount earned = $220
Total amount of tips earned = $40
Create an equation with the given information:
⇒ 60x + 40 = 220
Solving the equation:
Subtracting 40 from bothsides, we have:
⇒ 60x + 40 - 40 = 220 - 40
⇒ 60x = 180
⇒ 60x ÷ 60 = 180 ÷ 60
⇒ x = 3 appointments.
Part B
Let x = number of dog grooming appointments Logan had.
Given information:
Charge per appointment = $70
Total amount earned = $300
Total amount of tips earned = $50
Rental fee per appointment = $20
Create an equation with the given information:
⇒ 70x - 20x + 50 = 300
Solve the equation:
⇒ 50x + 50 = 300
⇒ 50x + 50 - 50 = 300 - 50
⇒ 50x = 250
⇒ 50x ÷ 50 = 250 ÷ 50
⇒ x = 5 appointments.
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Whats the value of x
Answer:
x = 50
Step-by-step explanation:
These two angles are supplementary angles which means their sum is equal to 180°.
We can write the following equation based on this information:
3x+5+x-25 = 180
Add like terms4x - 20 = 180
Add 20 to both sides4x = 200
Divide both sides by 4x = 50
3) Mary works at a factory assembling auto parts. She earns a fixed salary for the first 40
hours and then additional pay for any time over 40 hours. During one week, she worked 47
hours and earned $613.75. Another week she worked 51 hours and earned $678.75. What
is Mary's weekly salary and overtime pay per hour?
So on solving the provided question we cans ay that by unitary method earns 47 hours = 15.34375 * 47 = $721.15625
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
so here,
She earns a fixed salary for the first = 40hours.
he worked and earned $613.75
earns per hour = 613.75/40 = 15.34375
earns 47 hours = 15.34375 * 47 = $721.15625
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what is angle of sides are 60.5,216 and 169.26
Using the law of cosines we know that the outfielder throws the ball 169.26 feet away.
What was the law of cosines?The law of cosines in trigonometry establishes a relationship between a triangle's side lengths and the cosine of one of its angles.
According to the Law of Cosines, c2=a2+b22ab cosC.
With the exception of the third component, which equals zero if C is a straight angle and the Pythagorean Theorem results, this is similar to the Pythagorean Theorem.
So, here, the pitcher's mound is 60.5 feet away from home plate.
Additionally, the ball traveled 216 feet when it was struck by the bat.
Allow the outfielder to toss the ball x feet away.
According to the diagram below:
x² = 216² + 60.5² - 2 * 216 * 60.5 * cos34°
x = 169.258748677 ⇒ 169.26 feet
Therefore, using the law of cosines we know that the outfielder throws the ball 169.26 feet away.
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Correct question:
Use the law of cosines to solve the problem. On a baseball field, the pitcher's mound is 60.5 feet from home plate. During practice, a batter hits a ball 216 feet. The path of the ball makes a 34° angle with the line connecting the pitcher and the catcher, to the right of the pitcher's mound. an outfielder catches the ball and throws it to the pitcher. how far does the outfielder throw the ball?
What is the coefficient of x² in 3x³ 2x² x 1?
So on solving the provided question we can say that here, coefficient of x² in 3x³+ 2x² -x+ 1 is 2
What is the coefficient?A coefficient in mathematics is a polynomial, a series, or the multiplicative coefficient of a particular term in an expression. Typically numeric, however any expression is permitted. The term "parameter" can also refer to the coefficients themselves if they are variables. A number times a variable equals a coefficient. Coefficient examples include: The coefficient is 14 in phrase 14c 14c 14c. The coefficient is 1 for word g. multiplies the variable by this amount. example Given that "z" is a variable and that 6z is the definition of the term, the coefficient is 6. One is the coefficient of the square of x.
here,
coefficient of x² in 3x³+ 2x² -x+ 1 is 2
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Here are the first four terms of a sequence.
28 23 18 18
Find the nth term of the sequence.
Answer:
8, 3
Step-by-step explanation:
28, 23, 18, 13
Subtract each term from the next term.
23 - 28 = -5
18 - 23 = -5
13 - 18 = -5
All differences are equal. When all differences are equal, you have an arithmetic sequence. The equal differences are called the "common difference." To find a new term, add the common difference to the previous term.
13 + (-5) = 13 - 5 = 8
8 + (-5) = 8 - 5 = 3
Answer: 8, 3
What is the difference between circumcenter and centroid?
The intersection of a triangle's three medians is known as the centroid, and the point at which the perpendicular bisectors of its three sides meet is known as the circumcenter.
What is called centroid and circumcenter?The object's centre is represented by its centroid. The centroid of a triangle is where the triangle's three medians connect. The junction of all three medians is another way to describe it. The middle point of a side and the opposing vertex of a triangle are connected by a line known as the median.
The circumcenter of a triangle is the point where three perpendicular bisectors of its sides meet. A triangle's circumcenter is defined as the point at which the perpendicular bisectors of its own sides cross. In all other senses, the circumcenter is the point at which a triangle's sides intersect to form a bisector.
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someone explain, i did a and its just 12x + 36 but for part b I don't understand half a thing, I did something I did in a, I did x^2 + 12x + 36 -144 but then the answer was wrong someone please help me I have final exam tmrw and I'm gonna do really bad :(
Answer:
a. x²
b. 144 cm²
Step-by-step explanation:
You want to know an expression for the area of the four white triangles in the given figure, and you want to know that area when x = 12 cm.
a. Triangle areaIf you draw horizontal and vertical lines through the middle of the figure, you can see that for each white triangle there is a matching shaded triangle. That is, the shaded area is equal to the white area.
The shaded area is the square of the length of the side of the shaded square, so is ...
shaded area = x²
The white area is the same, so is ...
white area = x²
b. Area for x=12 cmUsing x = 12 cm, the formula from part (a) tells us ...
white area = (12 cm)² = 144 cm²
The total area of the four white triangles is 144 cm².
__
Additional comment
The relation between the side lengths of the shaded area and the side length of the total area is ...
2x/√2 = x+6
This has one solution: x = 6/(√2 -1) ≈ 14.485281 (cm).
The figure cannot be drawn to scale for any other value of x, so it is impossible for x=12 cm, unless the outside length is (x+4.97056...)
If you take the white triangles to be isosceles right triangles, each will have an area of A = 1/2bh = 1/2(x/√2)(x/√2) = x²/4. The four of them will have an area of 4(x²/4) = x². If you take the white area to be the overall area less the area of a square of side length x, then the area of the four triangles will be (x+6)² -x² = 12x+36. You will notice that these expressions give different values of the area of the white triangles when x=12. (See the previous comment about the value of x.)
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Amber and Jeica go out for lunch. Amber’ lunch cot $11. 70, and he tip 18%. Jeica’ lunch cot $12. 30, and he tip 15%
Amber and Jeica go out for lunch. Amber’ lunch cot $11. 70, and he tip 18%. Jeica’ lunch cot $12. 30, and he tip 15%, then the percentage of tip is = 33.9%
Define Percentage :
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means.
Given that the Amber’ lunch cot is $11.70.
There is a 18% tax.
Therefore the tax on $11.70 is,
= $11.70×18%
= $2.106
The Amber’ lunch cot with tax is $(11.70 + 2.106)
= $13.806.
The Jeica’ lunch cot is $12.30.
There is a 15% tax.
Therefore the tax on $12.30 is,
= $12.30×15%
= $1.845
The Amber’ lunch cot with tax is $(12.30 + 1.845)
= $14.145.
The tip that is given is $(14.145 - 13.806)
= $0.339
The percentage of tip is
= $0.339 * 100
= 33.9%
Therefore,
Amber and Jeica go out for lunch. Amber’ lunch cot $11. 70, and he tip 18%. Jeica’ lunch cot $12. 30, and he tip 15%, then the percentage of tip is = 33.9%
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amber - $13.81
jeica - $1.85
so, jeica paid $11.96 less than amber