The values of x that satisfy the equation are x = -8 and x = 1.
To find all values of x that satisfy the equation x-(x+5)/(x+8)=(3)/(x+8), we can follow the steps below:
1. Multiply both sides of the equation by (x+8) to eliminate the fractions:
(x+8)(x) - (x+5) = 3
2. Distribute the (x+8) on the left side of the equation:
x^2 + 8x - x - 5 = 3
3. Combine like terms on the left side of the equation:
x^2 + 7x - 5 = 3
4. Subtract 3 from both sides of the equation to get the equation equal to zero:
x^2 + 7x - 8 = 0
5. Factor the left side of the equation:
(x+8)(x-1) = 0
6. Set each factor equal to zero and solve for x:
x+8 = 0 or x-1 = 0
x = -8 or x = 1
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How do I draw a parabola when given the directix and focus
The distance between any point on the parabola and the directrix is equal to the distance between that point and the focus. This property is what defines a parabola.
How to draw a parabola when given the directix and focus?To draw a parabola given the directrix and focus, follow these steps:
Draw the directrix as a straight line.Mark the focus point on the opposite side of the directrix from the vertex.Find the midpoint between the focus and the directrix, which is also the vertex of the parabola.,Draw a perpendicular line from the vertex to the directrix. This is the axis of symmetry of the parabola.Measure the distance between the focus and the vertex. This distance is called the focal length and is denoted by "p".From the vertex, mark a point "p" units above and below the vertex along the axis of symmetry. These points are called the "endpoints of the latus rectum."Draw lines through each endpoint of the latus rectum perpendicular to the axis of symmetry, extending to intersect the directrix. These two lines will be parallel to each other and equidistant from the axis of symmetry.Finally, draw a smooth curve through the focus point that passes through each endpoint of the latus rectum. This curve is the parabola.Learn more about parabola here: https://brainly.com/question/25651698
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Styles Editing Voice Sensitivity 3. Given are three arbitrary three-dimensional shapes. Use these to complete the following table to see if Euler's Formula holds for these shapes (11 points) a. b. c. Figure F V F+ V E a. b. C. А. If you answered "NO" for any Do all of them satisfy Euler's Formula? of them, explain your reasoning [1 point) B B A polyhedron has 10 edges and 6 vertices. How many faces does it have? Sketch a polyhedron that satisfies these conditions and name the polyhedron you drew. [2 points)
A Polyhedron with 10 edges and 6 vertices has 4 faces.
A. Yes, all of the shapes satisfy Euler's Formula, which states that F + V - E = 2, where F is the number of faces, V is the number of vertices, and E is the number of edges. The following table shows that each shape satisfies this formula:
B. A polyhedron with 10 edges and 6 vertices has 4 faces. The polyhedron that satisfies these conditions is a regular tetrahedron.
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If the value of a is negative and the value of b is negative, which best describes the translation?
Best describes the translation of the figure moves Left and down.
Describe the term translation?A translation is a transformation that moves every point of a figure or object by the same distance and in the same direction without changing its shape, size, or orientation. It is a type of rigid transformation that preserves the distance between points and angles between lines.
A translation can be described using the horizontal and vertical shift or displacement of the object. If a point (x, y) is translated by a distance of 'a' units to the right and 'b' units upwards, the new location of the point would be (x + a, y + b).
Question says that a figure is translated using the mapping (x, y) → (x + a, y + b).
If the value of 'a' is negative and the value of 'b' is negative in the mapping (x, y) → (x + a, y + b), it means that the figure is being translated to the left and downwards.
The x-coordinates are being decreased by the absolute value of 'a', which means that the figure is moving left. Similarly, the y-coordinates are being decreased by the absolute value of 'b', which means that the figure is moving downwards.
Therefore, the best description of the translation is "the figure moves left and down"
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Problem 7. Given a in Quadrant III, with cot a = 7, find the exact values of sin 0 and cos 0. Problem 8. Suppose sin a = - 24/25 and cos a =-7/ 25 and consider the angle B = Phi - a. (a) Find sin B and cos B (b) Indicate the quadrant the angle B belongs to
a) sin B = y/r = -1/5sqrt(2) and cos B = x/r = 7/5sqrt(2) (b) Since sin B is positive and cos B is negative, we found that angle B belongs in Quadrant II.
Given that cot a = 7, we know that tan a = 1/7. Since tan a = y/x, we can let x = 7 and y = -1 (since a is in Quadrant III and both x and y values are negative in this quadrant).
Using the Pythagorean Theorem, we can find r:
r = sqrt(x^2 + y^2) = sqrt(7^2 + (-1)^2) = sqrt(50) = 5sqrt(2)
Now we can find sin B and cos B:
sin B = y/r = -1/5sqrt(2)
cos B = x/r = 7/5sqrt(2)
We can use the double angle formulas for sine and cosine, sin B and cos B: sin B = sin(Phi - a) = sin Phi cos a - cos Phi sin a = (0)(-7/25) - (1)(-24/25) = 24/25 cos B = cos(Phi - a) = cos Phi cos a + sin Phi sin a = (1)(-7/25) + (0)(-24/25) = -7/25.
Since sin B is positive and cos B is negative, we know that angle B is in Quadrant II.
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17. Find the quotient using long division. Express the quotient as a rational expression.
O 2x + 15
O 2x-15
x-5
O 2x + 15
x-5
x-52x²-10x+15
O 2x² + 15x
O
O
2x+
15
x-5
The polynomial 2x² - 10x + 15 will have a quotient 2x and remainder of 15 when divided by x - 5 and the result can be written in the form 2x + 15/(x - 5).
How to divide the polynomialUsing the long division method will require us to; divide, multiply, subtract, bring down the next number and repeat the process to end at zero or arrive at a remainder
We shall divide the polynomial 2x² - 10x + 15 by x - 5 as follows;
2x² divided by x equals 2x
x - 5 multiplied by 2x
2x(x - 5) = 2x² - 10x
subtract 2x² - 10x from 2x² - 10x + 15
2x² - 10x + 15 - (2x² - 10x)
2x² - 10x + 15 - 2x² + 10x = 15.
Therefore, the polynomial 2x² - 10x + 15 will have a quotient 2x and remainder of 15 when divided by x - 5 and the result can be written in the form 2x + 15/(x - 5).
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what is 7.5= to in mm?
Answer:
7.5 inches is equal to 190.5 millimeters (mm).
To convert from inches to millimeters, we can use the conversion factor of 1 inch = 25.4 millimeters.
So, 7.5 inches x 25.4 millimeters/inch = 190.5 millimeters.
Find the exact value of each of the remaining trigonometric functions of e. sin 0 3 and tan 0 0 4 cos 0 = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expre tan 0 = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expres csc = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the express sec 0 = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expressic cote = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression Find the lengths and area A 80 15 yd 2 com The longth of the artis yards (Round to three decimal places as needed.) The area of the sector square yards Round to three decimal places as needed.) 1 of 2 comples Find the distance from A to C across the gorge illustrated in the figure. 170 n The distance from A to C's foot. (Do not round until the final answer. Then round to two decimal places as needed.) Name the quadrant in which the angle o lies. sin 0 <0, coto > 0 The angle o lies in which quadrant? IV 11 =
The angle o lies in quadrant IV because sin 0 < 0 and cot 0 > 0. The question is a bit unclear and has multiple parts, so I will answer each part separately.
Part 1: Find the exact value of each of the remaining trigonometric functions of e.
sin 0 = 3/5
cos 0 = 4/5
tan 0 = 3/4
csc 0 = 5/3
sec 0 = 5/4
cot 0 = 4/3
Part 2: Find the lengths and area A.
The length of the arc is 80 * (15/360) = 3.333 yards.
The area of the sector is (80^2 * (15/360))/2 = 266.667 square yards.
Part 3: Find the distance from A to C across the gorge illustrated in the figure.
The distance from A to C is sqrt(170^2 + 170^2) = 240.42 feet.
Part 4: Name the quadrant in which the angle o lies.
The angle o lies in quadrant IV because sin 0 < 0 and cot 0 > 0.
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A school staff meeting had 30 teachers in attendance, 30% of whom were first-year teachers. How many first-year teachers were in the meeting?
Answer:
There were 30 x 30/100 = <<30*30/100=9>>9 first-year teachers at the meeting.
Answer: 9.
Answer:
9
Step-by-step explanation:
30% of 30 is 9. Therefore there are 9 teachers how were first year teachers.
Hope this helps :)
Question 40
5
NUMBER THEORY The sum of the digits of a two-digit number is 11. If the digits are reversed, the new number is 45 more than the original
number. Find the number.
The original number would be 3.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Consider that the 10s digit = x
And the units digit = y
x +y = 11
The Sum of the digits = 11
10x + y + 45 = 10y + x
Then Reversed number is 45 more than original,
10x - x + y + 45 = 10y
9x + y + 45 = 10y
9x + 45 = 10y - y
9x + 45 = 9y
Now, Put x + y = 11 into the equation just found.
9x + 45 = 9(11 - x)
x + 45/9 = 11 - x
2x + 5 = 11
2x = 11 - 5
2x = 6
x = 6/2
x = 3
Therefore, we have;
x + y = 11
3 + y = 11
y = 11 - 3
y = 8
Henece, we can conclude that the original number is 38 and the new number is 83 which the digits are reversed.
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The enrollment at high school R has been increasing by 15 students per year.Currently High School R has 200 students attending.High school T currently has 400 students,but it’s enrollment is decreasing in size by average of 10 students per year. If the two schools continue their current enrollment trends over the next few years, how many years will it take the schools to have the same enrollment.
So it will take 20 years for High School R and High School T to have the same enrollment.
What is enrollment?Enrollment is the process of registering for classes at a college or university. The process usually involves submitting an application and providing transcripts and other documents to the school.
The enrollment at High School R is increasing by 15 students per year while High School T is decreasing by 10 students per year. To figure out how many years it will take for both schools to have the same enrollment, we need to calculate the difference between the two schools.
High School R currently has 200 students and High School T has 400 students. The difference between the two schools is 200 students (400-200 = 200).
Since High School R is increasing by 15 students per year and High School T is decreasing by 10 students per year, it will take 20 years for the two schools to have the same enrollment.
To calculate this, we divide the difference between the two schools (200 students) by the difference between the two schools' enrollment growth (15 students - 10 students = 5 students). This gives us 200/5 = 40. Since 40 years is too long, we divide 40 by 2 and get 20, which is the answer. So it will take 20 years for High School R and High School T to have the same enrollment.
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Use the pattern of the differences of consecutive y-values to write an expression for y when x=6.
y=?
When x=6, the value of [tex]y=ax^2[/tex] is 11a.
What is expression?
One or more variables or numbers are combined with one additional action to form an expression.
Assuming that the function [tex]y=ax^2[/tex] is defined for all real numbers x, we can use the pattern of the differences of consecutive y-values to write an expression for y when x=6.
The differences of consecutive y-values for the function y=ax^2 are given by:
[tex]a(2^2 - 1^2), a(3^2 - 2^2), a(4^2 - 3^2), ...[/tex]
Simplifying these expressions, we get:
3a, 5a, 7a, ...
We can see that the differences between consecutive values are all the same, namely 2a. Therefore, we can express any y-value of the function
[tex]y=ax^2[/tex] as:
y = y(1) + (x-1)Δy
where y(1) is the value of y when x=1, and Δy is the common difference between consecutive y-values, which in this case is 2a.
Substituting the values x=6, y(1)=a(1^2)=a, and Δy=2a into this expression, we get:
y = a + (6-1)(2a) = a + 10a = 11a
Therefore, when x=6, the value of [tex]y=ax^2[/tex] is 11a.
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evaluate xy^-4 with positive exponents
By answering the above question, we may state that Hence, [tex]xy{(-4)}[/tex]is x exponents divided by y raised to the power of 4.
what are exponents?The mathematical process of exponentiation, frequently referred to as "b raised to the nth power," is symbolised by the symbol bn and includes two numbers: a base number, b, and an exponent, or power, n. Exponents demonstrate the number of times that a number has been multiplied by itself. For example, 2-3 (written as 23) means: 2 x 2 x 2 = 8. 2 + 3 does not equal 6, nor does 23. Remember that an integer whose power is one is equal to itself. Exponents can be used as a way to express large numbers as powers. Therefore, the exponent is the measurement that shows how many times a number has been multiplied by itself. For instance, multiplying 6 by 4 results in the values 6 x 6 x 6. .
Considering that the phrase is:
[tex]xy^{-4}[/tex]
We may simplify the case when x and y both have positive exponents as follows:
[tex]xy^{(-4)} = x / y^4[/tex]
This is due to the negative exponents rule, which claims that y(-n) = 1/yn, which indicates that [tex]y(-n) = 1/yn.[/tex]
Hence, [tex]xy{(-4)}[/tex]is x divided by y raised to the power of 4.
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The following list shows the number of new memberships that a gym has sold each day over the past week: 4, 2, 9, 2, 0, 3, 8. Which of the following is not a true statement?
Show quoted text
The median of the data is 2 is not a true statement. (second option).
What is the median?Mean is the average of a set of numbers.
Mean = sum of numbers / total numbers
(0 + 2 + 2 + 3 + 4 + 8 + 9) / 7 = 28 / 7 = 4
Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order.
The numbers in ascending order is: 0, 2, 2, 3, 4, 8, 9
Median = 3
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Determine if the vectors are linearly independent. Justify your answer. [[4],[0],[0]],[[9],[3],[-6]],[[6],[6],[-18]]
The vectors [[4],[0],[0]],[[9],[3],[-6]],[[6],[6],[-18]] are linearly independent.
To determine if the vectors are linearly independent, we can use the determinant of the matrix formed by the vectors. If the determinant is not equal to 0, then the vectors are linearly independent.
The matrix formed by the vectors is:
\begin{bmatrix}
4 & 9 & 6\\
0 & 3 & 6\\
0 & -6 & -18
\end{bmatrix}
The determinant of this matrix is:
\begin{vmatrix}
4 & 9 & 6\\
0 & 3 & 6\\
0 & -6 & -18
\end{vmatrix} = 4\begin{vmatrix}
3 & 6\\
-6 & -18
\end{vmatrix} - 9\begin{vmatrix}
0 & 6\\
0 & -18
\end{vmatrix} + 6\begin{vmatrix}
0 & 3\\
0 & -6
\end{vmatrix} = 4(-54-(-36)) - 9(0-0) + 6(0-0) = 4(-18) = -72
Since the determinant is not equal to 0, the vectors are linearly independent. Therefore, the vectors [[4],[0],[0]],[[9],[3],[-6]],[[6],[6],[-18]] are linearly independent.
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In Exercises 3-10 \( \square \), find the inverse of the given matrix. 3. \( \left[\begin{array}{ll}7 & 2 \\ 3 & 1 \\ 2 & 3 \\ \text { 4. } 5 .\end{array}\right] \)
(\begin{bmatrix}\frac{1}{5} & -\frac{2}{5} \\-\frac{3}{5} & \frac{7}{5}\end{bmatrix}\)
To find the inverse of the given matrix 3. \( \left[\begin{array}{ll}7 & 2 \\ 3 & 1 \\ 2 & 3 \\ \text { 4. }
5 .\end{array}\right] \), use the following steps:
1. Find the determinant of the matrix by using the formula det \(A = ad-bc\). The determinant of the given matrix is \((7*1) - (2*3) = 5\).
2. Find the adjoint of the matrix by using the formula
\(A^T = \begin{bmatrix}
a & b \\c & d\end{bmatrix}^T = \begin{bmatrix}d & -b \\-c & a\end{bmatrix}\)
The adjoint of the given matrix is \\begin{bmatrix}1 & -2 \\-3 & 7\end{bmatrix}\)
3. Find the inverse of the matrix by using the formula \(A^{-1} = \frac{1}{det(A)} \cdot A^T\).
The inverse of the given matrix is \(\begin{bmatrix}\frac{1}{5} & -\frac{2}{5} \\-\frac{3}{5} & \frac{7}{5}\end{bmatrix}\)
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SSD Provided Links EXPONENTS AND POLYNOMIALS Multiplying conjugate binomials: Multiva Multiply. (4y+5x)(4y-5x) Simplify. your answer.
The simplified answer is 16y² - 25x².
When multiplying conjugate binomials,
We use the formula (a+b)(a-b) = a²-b².
In this case, a = 4y and b = 5x. So,
We can pluggin these values into the formula and simplify:
(4y+5x)(4y-5x) = (4y)² - (5x)²
= 16y² - 25x²
Therefore, the simplified answer is 16y² - 25x². This is the final answer, and there are no further steps to simplify.
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based on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole number
The solution is: standard deviation. So, correct option is C.
Here, we have,
Explanation:
However, note that the mean of a sample from a normal population (that is, a type of "standard deviation" known as "standard deviation from a sample mean", is an "unbiased estimator" of the "population mean".
We shall represent the "sample mean" as: X ;
(pronounced: "x-bar"; that is; "ex-bar"); this is the usual symbol used;
We shall represent the sample size as "n" ;
(This is the usual variable used; note that
"n" is a numeric value).
The standard deviant from the sample mean:
(n * X) / (n + 1) is a "biased estimator of the mean" that becomes "unbiased" as the sample size increases; since as "n" increases in values; the value of the entire entire expression becomes smaller (i.e the standard deviation becomes smaller.
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Complete question:
Which biased estimator will have a reduced bias based on an increased sample size? mean median standard deviation range
What is the lateral and total surface area
Answer:A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]
Step-by-step explanation:A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]
Write a polynomial in factored form whose solutions are x =
-3, 5/2, and
and - 5i.
The polynomial in factored form whose solutions are x = -3, 5/2, and -5i is 2(x + 3)(2x - 5)(x² + 25).
What is the polynomial in factored form whose solutions are x = -3, 5/2, and - 5i?Given the solutions;
x = -3x = 5/2x = -5iTo have the solutions at x = -3 and x = 5/2, the polynomial must have factors of (x + 3) and (2x - 5), respectively.
Also, to have a solution at x = -5i, there must be a factor of (x+5i) and its complex conjugate (x-5i):
Hence;
(x + 3)(2x - 5)(x + 5i)(x - 5i)
Multiplying out these factors gives:
(x + 3)(2x - 5)(x + 5i)(x - 5i)
(x + 3)(2x - 5)(x² + 25)
= (2x² + x - 15)(x² + 25)
= 2x⁴ + x³ - 15x² + 50x² + 25x - 375
= 2x⁴ + x³ + 35x² + 25x - 375
So the polynomial in factored form is:
= 2(x + 3)(2x - 5)(x + 5i)(x - 5i)
= 2(x + 3)(2x - 5)(x² + 25)
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Using the numbers 1 to 9 (one time each), fill in the boxes to make
the equation true.
0:0=00:0=00:00
The complete equation using the numbers from1 to 9 will be:
2:2 = 3×3:9 = 4×4 =16.
What do you mean by proportion?A contrast between two numbers in arithmetic, this is referred to as a proportion. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.
In the question given:
By using the digits 1 to 9 at one time each, we have to form the equation to make the equality true.
Now,
All the numbers from 1 to 9 are = 1, 2 ,3, 4, 5, 6, 7, 8 and 9
Let the proportion be = 1
Hence, the equivalent ratios are:
1:1, 2:2. 3:3
Now, according to the question the required equation will be:
2:2 = 3×3:9 = 4×4 =16.
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Lowest common factors and highest common factors
The Lowest Common Factor (LCF) and Highest Common Factor (HCF) are concepts used in mathematics to find the factors that are common to two or more numbers.
The LCF is the smallest factor that two or more numbers have in common, while the HCF is the largest factor that two or more numbers have in common.
For example, consider the numbers 12 and 18--
The factors of 12 are 1, 2, 3, 4, 6, and 12.
The factors of 18 are 1, 2, 3, 6, 9, and 18.
The common factors of 12 and 18 are 1, 2, 3, and 6.
Therefore, the LCF of 12 and 18 is 6, and the HCF of 12 and 18 is 3.
Note that the LCF and HCF are also called the Lowest Common Denominator (LCD) and Highest Common Factor (HCF) respectively.
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In the figure above, R is the midpoint of QS and U is the midpoint of QT. If ST = 70, what is RU?
The value of RU, considering the Triangle Midsegment Theorem, is given as follows:
RU = 35.
How to obtain the value of RU?The value of RU is obtained applying the proportions in the context of the problem.
A proportion is applied as the Triangle Midsegment Theorem states that the midsegment of a triangle is parallel to it's base, and has the length half as long.
The length of the base is of ST = 70, hence the length of the midsegement is given as follows:
RU = 0.5ST
RU = 0.5 x 70
RU = 35.
(the length of the midsegment is half the length of the base, hence we apply the proportion multiplying by 0.5).
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The reciprocal of 5/11 is:
The reciprocal of 20 is:
The reciprocal of 5/11 is: 11/5
The reciprocal of 20 is: since 20=20/1 so the reciprocal is 1/20
Answer: 11/5, 1/20
Step-by-step explanation:
The reciprocal of a value is the numerator and denominator of that value switched.
When you look at 5/11, we see that 5 is the numerator and 11 is the denominator. The reciprocal(switch numerator and denominator) is 11/5.
The reciprocal of 20 can be tricky because it isn't written with a denominator. But we know intuitively that 20 is also equal to 20/1.
Therefore we apply the same steps as in the first instance and we get that the reciprocal of 20/1 is 1/20.
How do I find the X and Y for this equation using elimination method?
6x+6y=54
2x - 6y= 2
Answer:
X=7 Y=2
I will lead you through it and show you how you can find x through eliminating y, and finding y through eliminating x! So, both ways! :)
Step-by-step explanation:
When looking to use the elimination method, either all x OR y coefficients must be equal before finding one or another. That might sound a little confusing so let me explain!
Finding x by eliminating y: (they already set it up for us, this way!)
6x+6y=54 6y and -6y will cancel each other out!
2x - 6y= 2
6x=54 Add both lines!
2x=2
8x=56 Now, divide 8 on both sides to find x!
x=7 The product is x equals 7! Plug into a line to find y!
6(7)+6y=54
42+6y=54 Subtract both sides by 42
6y=12 Divide both sides by 6
y=2
So, X=7 and Y=2 ! To check that this is true, plug both variables into one line!
2(7)-6(2)=2
14-12=2
2=2 2 equals 2, so this is true! Lets check the other line to make
sure!
6(7)+6(2)=54
42+12=54
54=54 Yes, this is also true! That means we found the true value of the variables. :)
Finding y by eliminating x: Now, how do we find X and Y using the elimination method if the terms are not equal? We will continue to use this problem since it meets the standards of unequal terms! However, we will find y by eliminating x!
We must get the x terms to be equal to they can cancel each other out! So, we will multiply a line by a certain variable until it matches the x term on the other line. We will multiply line 2 until it matches line 1's x term, but make sure the signs (positive/negative) are opposite so they cancel out! In other problems, one line's term may not be able to be multiplied until it reaches its term since it is not a factor of it! So, both lines would be multiplied b a specific number until they have a common multiple! Confusing? Just focus on the underlined portion of this paragraph as that is what you will need for this question. Lets work hard now! :)
6x+6y=54 Multiply line 2 by -3 so the x term will be cancel out line 1's x!
2x - 6y= 2
6x+6y=54
(2x - 6y= 2) -3 Yes, all of it!
6x+6y=54
-6x+18y=-6 Add both lines
24y=48 Divide 24 by both sides!
y=2 y is equivalent to 2! Plug value into a line!
6x+6(2)=54
6x+12=54 Subtract 12 on both sides!
6x=42 Divide 6 on both sides.
x=7 X is equal to 7!
So, X=7 and Y=2 , just like we found and even checked before! I hope this helped. Elimination method is my favorite method and overall favorite lesson in Algebra, for me, since it is pretty easy once you get a hang of it! Goodluck all! :)
calculate the side of the unknown side of this right angled triangle 17cm 9cm
The side of the unknown side of this right angled triangle is 14cm
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The given two sides of the triangle are 17cm and 9cm.
We have to find the unknow side of the triangle.
By Pythagoras theorem we find the length of unknown side.
The sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
17²=9²+x²
289-81=x²
208=x²
Take square root on both sides
x=√208
x=14.42 cm
Hence, the side of the unknown side of this right angled triangle is 14cm
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The cost of 4 shirts is $36. At this rate, what is the cost of 9 shirts?
Answer:
$81
Step-by-step explanation:
36/4 = 9
We can deduce that each shirt costs $9 so...
9x9 = 81
help, it is dpecial products of polynomials and or just polynomias
The solution is, (x + 6) and (2x - 5) are the factors of polynomial
2x^2 + 7x - 30.
What are Polynomials?Polynomials are sums of k-xⁿ terms, where k can be any number and n can be any positive integer.
3x+2x-5, for example, is a polynomial.
A binomial is a two-term polynomial.
For instance, x²ˣ-2ˣ² and x⁶ˣ-6ˣ⁶ are both binomials.
here, we have,
given that,
2x^2 + 7x - 30 is the polynomial .
now, we have to factorize it.
so, we get,
2x2 + 7x - 30
2x2 + 12x - 5x - 30
2x( x + 6) - 5( x + 6)
so, we have,
(x + 6) and (2x - 5) are the factors.
Hence, The solution is, (x + 6) and (2x - 5) are the factors of polynomial
2x^2 + 7x - 30.
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Please help me to solve this math problem:
-From a port P, a ship sails 46 km on a
bearing of 104 followed by 32 km on a
bearing of 310%.
a Calculate the distance and bearing of
the ship from P after this journey.
b The ship travels west until it is due
north of P, The captain says they they are
now less than 10 km from P.
Is he correct?
Since the distance between P and S is greater than 10 km, the captain is incorrect. The ship is still more than 10 km away from P.
What is function?In mathematics, a function is a rule that maps a set of inputs (domain) to a set of outputs (codomain) in such a way that each input is associated with exactly one output. A function can be represented using various notations, including equations, graphs, and tables. A function can be thought of as a machine that takes an input and produces an output. The input is usually represented by the variable x, and the output is represented by the variable y. The relationship between the input and output is defined by the function rule. Functions are used in many areas of mathematics, science, and engineering to describe various phenomena, such as motion, growth, and decay. They are also used to model and analyze data in statistics and economics, and to design and control systems in engineering and computer science.
Here,
a) To solve this problem, we can use the Law of Cosines to find the distance and the Law of Sines to find the bearing.
First, let's label the points as follows:
P: the starting point
Q: the point reached after sailing 46 km on a bearing of 104
R: the final destination reached after sailing 32 km on a bearing of 310
To find the distance QR, we can use the Law of Cosines:
QR² = PQ² + PR² - 2(PQ)(PR)cos(QPR)
where PQ is the distance sailed on the first leg, PR is the distance sailed on the second leg, and angle QPR is the angle between the two legs.
We can calculate PQ and PR using basic trigonometry:
PQ = 46cos(14)
PR = 32cos(50)
Substituting these values into the Law of Cosines, we get:
QR² = (46cos(14))² + (32cos(50))² - 2(46cos(14))(32cos(50))cos(206)
Simplifying this expression using a calculator, we get:
QR ≈ 67.7 km
To find the bearing of QR, we can use the Law of Sines:
sin(QRP) / QR = sin(QPR) / PR
where angle QRP is the bearing we want to find.
Substituting the known values, we get:
sin(QRP) / 67.7 = sin(310 - 50) / (32sin(14))
Solving for sin(QRP) and taking the inverse sine, we get:
sin(QRP) ≈ 0.493
QRP ≈ 30.1°
Therefore, the ship is approximately 67.7 km away from P on a bearing of 30.1°.
b) If the ship travels west until it is due north of P, it will reach a point S that forms a right triangle with P and Q. Let's label the angles as follows:
angle QPS: the angle between PQ and PS
angle PQS: the angle between PS and QS
angle QSP: the right angle at S
We know that angle QPS is 90° (since the ship travels due north) and that PQ = 46 km. To find PS, we can use basic trigonometry:
PS = PQtan(QPS)
PS = 46tan(90-104)
PS ≈ 26.8 km
To check if the captain is correct, we need to find the distance between P and S. We can use the Pythagorean theorem:
PS² + SP² = PQ²
SP² = PQ² - PS²
SP² = (46)² - (26.8)²
SP ≈ 38.5 km
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Does the point (2, –2) satisfy the equation y = x? whats the answer
The point (2, –2) with x-coordinate value 2 and y-coordinate value -2, is not satisfied the equation y = x.
We have an equation, y = x --(1) and point (2,-2). We have to check that point (2, –2) satisfy the equation y = x or not. To check that, we need to put the values of the point in the equation. If the equation satisfies them, the point belong to the line. Substituting the coordinates of the given point, i.e., x = 2 and y = -2, into the defining equation(1), we get, y = x
L.H.S, y = -2
R.H.S, x = 2
but -2 ≠ 2 so, L.H.S ≠ R.H.S
We now see from the above substitution and the resultant calculation that the coordinates (x, y) of the point (2, -2) does not make the equation y = x
Hence, the point ( 2,-2) does not satisfied equation y= x .
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Could someone help me with these questions?
Anstoo blurry
Step-by-step explanation:
