Inverse operations, such as addition and subtraction, multiplication and division, are pairs of mathematical operations where one operation reverses the effect of the other. The term "inverse" refers to the reciprocal of a number, i.e., x - 1 = 1 / x. One results from multiplying a number by its reciprocal, or inverse.
Inverse operations, such as addition and subtraction, multiplication and division, are pairs of mathematical operations where one operation reverses the effect of the other. The term "inverse" refers to the reciprocal of a number, i.e., x - 1 = 1 / x. One results from multiplying a number by its reciprocal, or inverse.
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Yara is 8 years old. Yara's mother is 4n times older than Yara. How old
was Yara's mother 5 years ago in terms of n?
Yara's mother was 32n-5 years old 5 years ago in terms of n.
Yara's mother is 4n times older than Yara, and Yara is 8 years old, so we can set up the equation:
Mother's age = 4n * 8 years
We are also told that Yara's mother is 5 years older than she is now, so we can add 5 to the equation above:
Mother's age 5 years ago = 4n * 8 years - 5 years
Now we can simplify this equation:
Mother's age 5 years ago = 32n - 5 years
Now we can substitute the value of n to find the mother's age in terms of n.
To find the age of Yara's mother 5 years ago in terms of n, we need to know the value of n. But we don't have the value of n so we can't find the exact age but we can find it in terms of n which is 32n-5 years.
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When a=-1/2 and b=6, which expression:
has the largest value?
has the smallest value?
is the closest to zero?
When a=12 and b=-6, which expression:
has the largest value?
has the smallest value?
is the closest to zero?
When a=-6 and b=-12, which expression:
has the largest value?
has the smallest value?
is the closest to zero?
For an expression containing two variables, a and b, the expression with the largest value is a+b, the expression with the smallest value is a-b, and the expression closest to zero is either a+b or a-b, depending on the values of a and b.
For a=-1/2 and b=6, the expression with the largest value is a+b, which is equal to 5.5. The expression with the smallest value is a-b, which is equal to -7.5. The expression closest to zero is a+b, which is equal to 5.5.
For a=12 and b=-6, the expression with the largest value is a+b, which is equal to 6. The expression with the smallest value is a-b, which is equal to 18. The expression closest to zero is a-b, which is equal to 18.
For a=-6 and b=-12, the expression with the largest value is a+b, which is equal to -18. The expression with the smallest value is a-b, which is equal to 6. The expression closest to zero is a+b, which is equal to -18.
For an expression containing two variables, a and b, the expression with the largest value is a+b, the expression with the smallest value is a-b, and the expression closest to zero is either a+b or a-b, depending on the values of a and b.
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Circle C is inscribed with 5 lines. Point C is at the center of the circle. 3 lines come out of point C and make points D, A, and B on the edge of the circle. Another line comes out of point C and goes past the edge to point E. Another line connects points D and A.
Which geometric figures are drawn on the diagram? Check all that apply.
Line segment C A
Ray A C
∠ABC
∠BCE is drawn, line segment CA is drawn, Ray CA is drawn, For Circle C is drawn, Ray BE is not drawn.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Given that Circle C is inscribed with 5 lines
Point C is at the center of the circle
3 lines come out of point C and make points D, A, and B on the edge of the circle.
Another line comes out of point C and goes past the edge to point E.
For ∠ABC
The geometric figure is not drawn.
For ∠BCE
The geometric figure is drawn.
For line segment CA
The geometric figure is drawn.
For Ray CA
The geometric figure is drawn.
For Circle C
The geometric figure is drawn.
For Ray BE
The geometric figure is not drawn.
For Line segment AE
The geometric figure is not drawn.
Hence, ∠BCE is drawn, line segment CA is drawn, Ray CA is drawn, For Circle C is drawn, Ray BE is not drawn.
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at a local restaurant the amount of time that customers have to wait for their food is normally distributed with a mean of 32 minutes what is the probability that a randomly selected customer
The probability that a randomly selected customer will have to wait between 32 minutes and 37 minutes is 59.81%
What is meant by probability?How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability. Look up all the related responses.
The likelihood that an event will happen is quantified by probability. An event's likelihood is determined by how frequently it will occur over the long run. Probabilities are all digits that fall between 0 and 1, inclusive—that is, all digits that fall between 0 and 1.
Let the equation of Z score be:
z = (raw score - mean) / standard deviation
Given mean of 36 minutes and a standard deviation of 3 minutes.
If x = 32:
z = (32 - 36)/3 = -1.33
and x = 37:
z = (37 - 36)/3 = 0.33
P(-1.33 < z < 0.33) = P(z < 0.33) - P(z < -1.33)
= 0.6179 - 0.0198
= 0.5981
A consumer selected at random has a 59.81% chance of having to wait between 32 and 37 minutes.
The complete question is:
At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 36 minutes and a standard deviation of 3 minutes. What is the probability that a randomly selected customer will have to wait between 32 minutes and 37 minutes, to the nearest thousandth?
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When Edna's phone is fully charged, it can operate for up to 18 hours before running out of battery. It has been 6 hours since Edna's phone was fully charged. Let x represent how many more hours Edna's phone can operate without running out of battery. Which inequality describes the problem? 6 + x < 18 6 +xs 18 Solve the inequality. Then, complete the sentence to describe the solution. Edna's phone can operate for up to more hours without running out of battery.
Edna's phone can operate for up to 12 more hours without running out of battery.
In Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.
fully charged
T = 18Hr
It has been 6 hours since Edna's phone was fully charged.
remaining battery =18- 6= 12Hr
x=12Hr
6 + x < 18
6 +x > 18
neither nor.
both equations are wrong.
6 +x = 18
Edna's phone can operate for up to 12 more hours without running out of battery.
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i need help with this
*im second guessing*
Answer:
A) 5
B) X-3
C) 2X+Y
step by step:
base x height = area
A Height= (5x+20) ÷ (x+4)= 5
B Base= (8x-24) ÷ 8 = x-3
C Height= (12x+6y) ÷ 6 = 2x+y
The solution is
Parallelogram A : Base = x + 4 ; Height = 5
Parallelogram B : Base = x - 3 ; Height = 8
Parallelogram C : Base = 6 ; Height = 2x + y
What is a Parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
The four types are parallelograms, squares, rectangles, and rhombuses
Properties of Parallelogram
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent.
Same-Side interior angles (consecutive angles) are supplementary
Each diagonal of a parallelogram separates it into two congruent triangles
The diagonals of a parallelogram bisect each other
Given data ,
Let the area of the parallelogram be A = Base x Height
So , Substituting the values in the equation , we get
a)
Let the parallelogram be A
Now , Area = 5x + 20
Base = x + 4
So , the height = Area / Base
Height = 5
b)
Let the parallelogram be B
Now , Area = 8x - 24
Height = 8
So , the Base = Area / Height
Height = x - 3
c)
Let the parallelogram be C
Now , Area = 12x + 6y
Base = 6
So , the height = Area / Base
Height = 2x + y
Hence , the equations are solved
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The average monthly salary of 10 male staffs and 5 female staffs of a manufacturing company are Rs. 20,000 and Rs. 18,000 respectively. Find the average monthly salary of all staffs taken together.
The average monthly salary of all the staff is going to be 19,333.34 ₹.
Average is the value obtained by dividing the sum total of a set of figures by the number of figures. In this question, we have to find the average monthly salary of all the staff taken together,
So the sum total of the set of figures here will be (20,000 × no. of males + 18,000 × no. of males) ₹ and the number of figures here will be no. of males + no. of females. It's given that
No. of males=10
No. of females=5
So, the total no. of figures = 15
Sum total of set of figures = (20,000 × 10 + 18,000 × 5 )₹ and the average will be
=(20,000 × 10 + 18,000 × 5) ₹/15
=(200,000+90,000)/15₹
=290,000/15 ₹
=19,333.34 ₹
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What does the slope of a log-log graph represent?
The Slope of log - log graph represents the power of the relationship, and a straight line which indicates that there exists a definite power relationship .
What is Logarithm ?
The Logarithm is defined as power to which a number must be raised to get some other number .
A log-log plot is the plot in which both the x-axis and y-axis use a log scale.
The plot of logarithms of variables helps in extracting the information about the power relationship. The case of freely falling object is used to illustrate a log - log plot.
A plot of the logarithm of freefall distance as a function of logarithm of time gives a straight line of slope 2.
Therefore , The slope of log-log plot gives the power of relationship, and a straight line indicating that a definite power relationship exists.
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Write a rule to describe each transformation.
J(2, 2), (3, 4), H(4,3), G(3,0)
to
J'(-1,2), I'(0, 4), H'(1, 3), G'(0, 0)
The only difference is a -2 in x in 1 transformation in 2 transformation. The function is shifted up by b units with f (x) + b.
what are transformations ?Transformations can be divided into four categories: translation, reflection, rotation, and dilation. Rotate, reflect, or translate the geometric figures on a coordinate plane. The label given to a function, f, that maps to itself is the transformation, or f: X X. The pre-image X is transformed into the picture X after the transformation. It is possible to utilize any operation, or a combination of operations, in this transformation, including translation, rotation, reflection, and dilation.
given
J(2, 2), (3, 4), H(4,3), G(3,0) to J'(-1,2), I'(0, 4), H'(1, 3), G'(0, 0)
in 2 transformation as the only change is that -2 in x in 1 transformation
The function is shifted up by b units with f (x) + b.
The function is shifted downward by b units when f (x) b.
The function is moved left by b units when f (x + b) is used.
The function is moved right b units by the expression f (x b).
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Triangle ABC was rotated to form triangle A'B'C'. Triangle A'B'C' was reflected across the x-axis to form Triangle A"B"C".
Which of the following statements correctly describes the relationship between Triangle ABC, Triangle A'B'C', and Triangle A"B"C"? Select all that apply.
Group of answer choices
Triangle ABC has greater angle measurements than Triangle A"B"C".
Triangle ABC is congruent to Triangle A"B"C".
Triangle A'B'C' has greater angle measurements than Triangle A"B"C".
Triangle ABC has greater side lengths than Triangle A"B"C".
Triangle A'B'C' is congruent to Triangle A"B"C".
Therefore , the solution of the given problem of triangle comes out to be ΔA"B"C "≅ ΔABC is congruent.
Explain the triangle.The fact that a triangle has sides or vertices qualifies it as a polygon. It is an elementary geometric form. The name given to a triangle with vertices A, B, & C is Triangle ABC. A singular planes and triangle are obtained in Euclidean geometry when the vertices are not collinear. Any triangle that has three sides and three corners is a polygon.
Here,
Triangle A'B'C' is created by reflecting triangle ABC across the y-axis.
Afterward, it was dilated by a ratio of 1/3 to create triangle A "B"C".
Find the right answer for the triangles ABC and A"B"C."
So,
We are aware that reflection undergoes a rigorous transformation, meaning the shape and size of the original object do not change.
As a result, after reflection, figures always match their pictures.
"ABC," "A'B'C," etc (i)
The process of dilation is flexible. Although the size is changed, the shape is still the same.
Figures after dilatation therefore always resemble their photographs.
ΔA'B'C' ≅ ΔA "B"C" ... (ii)
With I and (ii), we obtain
ΔA"B"C "≅ ΔABC
Similar triangles include ABC and ABC.
As a result, choice A is the right one.
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How do you solve basic equations in algebra 1
The sides of a triangle are 68, 61, and 46. Use the Pythagorean Theorem to determine if the triangle is right, acute, or obtuse.
Answer: Acute
Step-by-step explanation:
The Pythagorean Theorem is [tex]a^2+b^2=c^2[/tex]. A and b are legs while c is hypotenuse. Hypotenuse is also the longest side. Let's plug them in and see if they are equal to each other.
[tex]46^2+61^2=68^2[/tex] [exponent]
[tex]2116+3721=4624[/tex] [add]
[tex]5837\neq4624[/tex]
Since they are not equal, then it is not a right triangle.
To tell is a triangle is acute, if the sum of the two shorter sides squared is greater than the longest side squared, then the triangle is acute.
At the end of the Pythagorean Theorem, we got 5837≠4624. 5837>4624, so that tells us that the triangle is acute.
True or false:
If f(x) is a cubic function
and f(1) = 0, f(3) = 0 and
ƒ(4) = 0,
then f(5)=8
Answer:
FALSE
Step-by-step explanation:
It is not necessarily true that ƒ(5)=8 just because ƒ(1)=0, ƒ(3)=0, and ƒ(4)=0. In fact, it is possible for ƒ(x) to be a cubic function and for ƒ(5) to equal any number, depending on the specific form of the function and the values of its coefficients.
How do you solve 3 equations with 3 unknowns on a Casio calculator?
The process to solve 3 equations with 3 unknown is explained below.
The term equation is known as a mathematical statement that is made up of two expressions connected by an equal sign.
The process of 3 equation with 3 unknown variable is explained step by step as follows:
First of all we have to write all the equations in standard form cleared of decimals or fractions.
And then we have to choose a variable to eliminate them then we have to choose any two of the three equations and eliminate the chosen variable.
After that we have to select a different set of two equations and eliminate the same variable as in Step 2.
Now, we have to solve the two equations from steps 2 and 3 for the two variables they contain.
And then we have to substitute the answers from Step 4 into any equation involving the remaining variable.
And then finally we have to check the solution with all three original equations.
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The local sports team donated 200 meal vouchers and 24 jerseys for a fundraising event. 125 vouchers and 20 jerseys were part of a raffle . The ratio of tickets sold to raffled items was 8:1; each ticket was sold for $3.50. How much money was raised from the raffle
On solving the provided question, we can say that by linear equation $249.67 money was raised from the raffle
What is a linear equation?A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
here,
the linear equation that can be formed is
200x + 24 y = 3.50
125 x + 20y = 5
ratio = 8:1
so, $249.67 money was raised from the raffle
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What is the Pythagorean theorem rounding of 16 and 18
The Pythagorean theorem rounding of 16 and 18 would be = 24 (approximately)
What is Pythagorean theorem?Pythagorean theorem is defined as the theorem that expresses the relationship that exists between the three side of a right angle triangle.
The relationship states that the square of the longest side is equal to the sum of the square of the other two sides.
That is, c² = a² + b²
Where, a = 16
b = 18
c² = 16²+18²
c² = 256 + 324
c² = 580
C =√580
C = 24.1
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Choose the equation that represents the line passing through the point (-3,-1) with a slope of 4.
y=4x-11
y = 4x + 11
y = 4x + 7
y=4x-7
On solving the provided question, we can say that - in the linear equation here the value will be
What is a linear equation?The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
here,
y = 4x + 11
x = 8
y = 32 + 11
y = 43
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The medical treatment cost $3000, and the insurance pays 90% less deductible of $300. Write how much money the patient pays and how much the insurance company pays. Describe the mathematics involved.
Based on the question above, the patient pays $600 and the insurance company pays $2400.
What is the arithmetic operations about?To calculate how much the patient pays, we first need to calculate how much the insurance pays. We can do this by taking the total cost of the treatment ($3000) and multiplying it by the percentage that the insurance pays:
(90% = 0.9).
$3000 x 0.9 = $2700
This means that the insurance pays $2700 of the cost of the treatment. But we also need to subtract the $300 deductible from this amount.
$2700 - $300
= $2400
So the insurance pays $2400 for the medical treatment.
To find out how much the patient pays, we can subtract the amount paid by the insurance from the total cost of the treatment:
$3000 - $2400
= $600
Therefore, the mathematics involved in solving this problem is very straightforward. We used basic arithmetic operations such as multiplication and subtraction to find the amounts paid by the insurance company and the patient.
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On a assembly line, 2 parts can be made per minute. There are 8 parts already made. To determine how many more minutes (x) it will take to make y total parts, the equation y=2x + 8 is written. What is the description of a solution to this problem?
The description of a solution to the problem modeled by the function y = 2x + 8 is given as follows:
The time needed to complete 40 parts is of 16 minutes.
What is the interpretation for the function in this problem?The function for this problem is defined as follows:
y = 2x + 8.
In which the variables are defined as follows:
x is the time in minutes.y is the number of parts produced.Hence, solving the function for x, we are going to obtain the time needed to produce y parts, giving the description of a solution for this problem.
When y = 40, the solution for x is given as follows:
40 = 2x + 8
2x = 32
x = 32/2
x = 16 minutes.
The interpretation of this solution is that a time of 16 minutes is needed to obtain a production of 40 parts.
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You found that the area of the quarter circle is 78.50 cm squared. You are right. How was this answer found?
Please help me! It's basically asking how to find the area of this quarter circle. I also have to show how I know that the answer is correct by using these steps to get the area of 78.50 cm squared.
The area of the quarter of the circle is 78.50 squared centimeters.
How to find the area of quarter of a circle.A circle is a 2 dimensional plane shape that is bounded by a curve. Its area can be determined by;
area of a circle = [tex]\pi r^{2}[/tex]
where r is the value of the radius of the circle.
The radius of a circle is given as the half of its diameter.
Thus, a quarter of a circle is the 4th part of a given circle. This implies of fraction selected when a circle is divided into 4 equal part.
So that;
area of quarter of a circle = area of a circle/ 4
= [tex]\pi r^{2}[/tex]/ 4
The area of quarter of then given circle = ((22/7)*(10)^2)/ 4
= 78.50 squared centimeters
Therefore, the answer to the area of the quarter circle was found as explained above.
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Please help due in 20 min
5^-1/-9^0
Answer: -0.2 hope this answer helps you good luck
Answer:
-0.2
Step-by-step explanation:
[tex] \frac{ {5}^{ - 1} }{ { - 9}^{0} } = \frac{ \frac{1}{5} }{ - 1} = \frac{1}{5} \times \frac{ - 1}{1} = \frac{ - 1}{5} = - 0.2[/tex]
How do you find the length of the third leg of a triangle?
The third side of the triangle can be found out by using the Pythagoras theorem or the Heron's formula.
When there is a right angle triangle (A triangle whose on angle is of 90 degrees) then we use the Pythagoras theorem to find the third side.
The relation says that the sum of the square of the base and perpendicular is equal to the square of the hypotenuse.
In case of the scalene triangle the heron's formula is used to find out the value of the third side of the triangle.
There are several methods also present to find the value of the third side of the triangle.
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2. Rabbit Problem
When rabbits were first brought to Australia last
century, they had no natural enemies so their numbers increased
rapidly. Assume that there were 60,000 rabbits in 1865, and that by
1867 the number had increased to 2,400,000. Assume that the num-
ber of rabbits increased exponentially with the number of years that
elapsed since 1865.
Write the particular equation for this function,
b. How many rabbits would you predict in 1870?
c. According to your model, when was the first pair of rabbits in-
troduced into Australia?
According to the exponential function,
a) The function that models the given situation is f(rabbits) = 65000(√500/13)ˣ
b) The number of rabbits in 1870 is 6.5
c) According to your model, the first pair of rabbits introduced into Australia is 19th century
Here we have given that during the 19th century, here rabbits were brought to Australia.
And here we also know that the rabbits had no natural enemies on that continent, their population increased rapidly.
And we have given that there were 65,000 rabbits in Australia in 1865 and 2,500,000 in 1867.
Then according to the exponential function that could be used to model the rabbit population y in Australia in terms of x, the number of years since 1865 is to be determined.
Then the exponential function can be written as,
=> f(rabbits) = 65000(√500/13)ˣ
When we plot these on the graph then we get the graph like the following.
Through the graph we have identified that the value of rabbits in 1870 is 6.5
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If sin 0<0 and cos0>0, then the terminal point determined by 0 is in :
Answer: The statement "if sin 0 < 0 and cos 0 > 0" is not true, as both the sine and cosine of an angle of 0 degrees are equal to 0. Therefore, the statement is not meaningful and the question cannot be answered.
It is important to note that sine, cosine, and all the trigonometric functions are defined in radians and not degrees and the value of sin(0) and cos(0) is not zero but 1
Please provide more context or specify what you are asking about in order to give a more accurate answer.
Step-by-step explanation:
Is 10 12 15 a Pythagorean triple?
No, 10 12 15 is not a Pythagorean triple. A Pythagorean triple is a set of three positive integers a, b, and c such that a^2 + b^2 = c^2.
To determine whether 10 12 15 is a Pythagorean triple, we need to calculate a^2 + b^2.
In this case, 10^2 + 12^2 = 100 + 144 = 244. Since 244 ≠ 15^2, 10 12 15 is not a Pythagorean triple. We can also confirm this by plugging 10, 12, and 15 into the Pythagorean Theorem, a^2 + b^2 = c^2.
10^2 + 12^2 = 100 + 144 = 244
244 ≠ 15^2
Therefore, 10 12 15 is not a Pythagorean triple.
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How do you find the sides of an acute triangle?
To find the missing side length of the acute angled triangle apply the cosine law as follow:
a² = b² + c² - 2bccosA
b² = a² + c² - 2accosB
c² = b² + a² - 2abcosC
As given in the question,
Given triangle is acute angled triangle.
Let us consider the measure of two sides and its included angle of the acute angled triangle is given.
Let the triangle be ABC,
Side opposite to ∠A, ∠B , and ∠C are a , b, and c respectively.
Apply cosine law to find the measure of the missing side in the acute angled triangle:
a² = b² + c² - 2bccosA
b² = a² + c² - 2accosB
c² = b² + a² - 2abcosC
Therefore, to get the measure of the missing side length in the acute angled triangle apply cosine law.
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50 POINTS!!!
I NEED STEPS
Answer:
[tex]\dfrac{3}{a-6}\quad \textsf{if}\;\;a \neq -6,a \neq 6[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{a}{a-6}-\dfrac{3}{a+6}+\dfrac{a^2}{36-a^2}[/tex]
Rewrite the third fraction:
[tex]\implies \dfrac{a^2}{36-a^2}=\dfrac{-a^2}{-(36-a^2)}=\dfrac{-a^2}{a^2-36}[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Difference of two squares }\\\\$x^2-y^2=(x-y)(x+y)$\\\end{minipage}}[/tex]
Apply the difference of two squares to the denominator of the third fraction:
[tex]\implies a^2-36=a^2-6^2=(a-6)(a+6)[/tex]
Therefore the expression can be written as:
[tex]\implies \dfrac{a}{a-6}-\dfrac{3}{a+6}+\dfrac{-a^2}{(a-6)(a+6)}[/tex]
[tex]\implies \dfrac{a}{a-6}-\dfrac{3}{a+6}-\dfrac{a^2}{(a-6)(a+6)}[/tex]
The least common multiplier (LCM) of the denominator is (a - 6)(a + 6).
Adjust the fractions based on the LCM:
[tex]\implies \dfrac{a(a+6)}{(a-6)(a+6)}-\dfrac{3(a-6)}{(a-6)(a+6)}-\dfrac{a^2}{(a-6)(a+6)}[/tex]
Simplify:
[tex]\implies \dfrac{a^2+6a}{(a-6)(a+6)}-\dfrac{3a-18}{(a-6)(a+6)}-\dfrac{a^2}{(a-6)(a+6)}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}-\dfrac{d}{c}=\dfrac{a-b-d}{c}:[/tex]
[tex]\implies \dfrac{a^2+6a-(3a-18)-a^2}{(a-6)(a+6)}[/tex]
Simplify:
[tex]\implies \dfrac{3a+18}{(a-6)(a+6)}[/tex]
Factor out 3 from the numerator:
[tex]\implies \dfrac{3(a+6)}{(a-6)(a+6)}[/tex]
Cancel the common factor (a + 6):
[tex]\implies \dfrac{3}{a-6}[/tex]
Therefore:
[tex]\dfrac{a}{a-6}-\dfrac{3}{a+6}+\dfrac{a^2}{36-a^2}=\dfrac{3}{a-6}\quad \textsf{if}\;\;a \neq -6,a \neq 6[/tex]
A=?cm
What is the total area of the tiles Felix needs to buy?
Therefore , the solution of the given problem of surface area comes out to be Felix is required to purchase 10 parallelogram-shaped tiles for an area totaling 80cm2.
Definition of surface areaIts surface area is a gauge of the space it takes up overall. A three-dimensional shape's entire environment is considered part of its surface area. Surface area is the total area of a thing. By adding up the faces on each of its six rectangle sides, a cuboid's volume of water can be calculated. The following formula could be used to calculate the dimensions of the box: Surface is the same for 2lh, 2lw, and 2hw (SA). The muti shape's surface area serves as a representation of the entire region.
Here,
Given: One parallelogram-shaped tile has a base of 4 cm and a height of 2 cm.
4 x 2 cm is the area of a single parallelogram-shaped tile.
8 cm2 is the size of one parallelogram-shaped tile.
The total area of the five black and five white tiles is 10 8cm2.
Total tile area is 80cm2 for the 5 black and 5 white tiles.
Felix is therefore required to purchase 10 parallelogram-shaped tiles for an area totaling 80cm2.
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Use the given confidence interval to find the margin of error and the sample mean
(12.7, 19.5)
The margin of error and the sample mean of the confidence interval are given as follows:
Margin of error: 3.4.Sample mean: 16.1.How to obtain the margin of error and the sample mean of the confidence interval?The confidence interval is defined as follows:
(12.7, 19.5).
The definition of a confidence interval is that it is obtained as the sample mean plus/minus the margin of error.
Hence the sample mean is calculated as the mean of the bounds of the interval, hence:
(12.7 + 19.5)/2 = 16.1.
The margin of error is calculated as the absolute value of the difference of each bound from the sample mean, hence:
|19.5 - 16.1| = |12.7 - 16.1| = 3.4.
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Karl invests $100 in a savings account, which earns interest yearly.
Select the TWO changes that would earn Karl more money from this savings account.
The two changes that would Karl earn more money are "Karl increases his initial investment" and "Karl deposits more money into the account every year" (options B and D).
What factors affect the amount of money Karl can get?In this case, the amount of money Karl can get depends on both the amount of money he invest and the interest rate. Here are some examples:
If he invest $100 and the interest rate is 10% he will get $10
If the invest $1000 and the interst rate is the same (10%) he will get $1000
Moreover, if the interste rate increases he can get more money: If the invest $100 but the interst rate is 12% he gets $12
This means he can get more profit if the investment is higher or the rate increases. Based on this, the two options that would increase his amount of money are increasing the initial investment or depositing more money (option B and D).
Note: This question is incomplete; here is the missing section:
A. The bank decreases the interest rate.
B. Karl increases his initial investment.
C. The bank adds a fee to keep the account active.
D. Karl deposits more money into the account every year.
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