c) tan²0 - cot²0 = sec²0 (1- cot²0)
Prove that LHS = RHS So that LHS will be the sec²0 (1- cot²0)
Answers
Answer:
Maybe this could help?
Related Questions
The EYE company spends $4,000,000 to refurbish its prescription-sunglasses factory. Each pair of sunglasses sells for $99. Labor and materials cost $30 per pair and marketing cost another $19 per pair. How many pairs of sunglasses, s, will the company need to sell so that it makes a profit?
Answers
The number of pair of sunglasses that the company needs to sell in order to make profit is 80,000.
What is Break-even Point?In economics, business, and especially cost accounting, the break-even point is the point at which total cost and total income are equal, i.e. "even". There is no net loss or gain, and one has "broken even," despite the fact that opportunity costs were incurred and capital got the risk-adjusted, expected return.
In order to make profit the organization needs to be at breakeven. Therefore, firstly they need to make profit that is equal to the refurbish cost.
The Profit on per pair of glass = Selling price per pair - Labor and material cost per pair - marketing cost per pair
The Profit on per pair of glass = $99 - $30 - $19
The Profit on per pair of glass = $50
Now, the breakeven point can be found as,
Break even quantity = Refurbish Cost / Profit on a pair of sunglasses
= $4,000,000 / $50
= 80,000
Hence, the company needs to sell 80,000 pair of sunglasses.
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Which statement is true about the function f(x)=4x-4
Answers
Answer: The statement that is true about the function f(x)=4x-4 is:
It is a linear function, as it is a straight line in the form of y=mx+b where m is 4 and b is -4
The y-intercept of this line is -4, which means when x=0, y=-4
The slope of this line is 4, which means for every 1 unit increase in x, y increases by 4 units
The domain of this function is all real numbers and the range is all real numbers except -4
The equation of the line is y = 4x - 4
The graph of this function is a line with a slope of 4 and y-intercept of -4.
Step-by-step explanation:
What 2 numbers multiply to get 0 and add to get 7
Answers
Answer:
There is no such set of two numbers that multiply to get 0 and add to get 7. Since any number multiplied by 0 is 0, it is impossible for two numbers to multiply to 0 and add to 7 as adding two numbers that multiply to 0 will always result in zero.
Answer:
Step-by-step explanation:
the numbers are 0 and 7 itself.
Multiply : 0*7 = 0
Add : 0+7 = 7
The equation for line d is 4x + 2y = 18. Line c is perpendicular to line d and intersects line d
at the point (1,7).
Write the equation for line c in slope-intercept form.
Answers
Which equations are equivalent to Negative one-fourth (x) + three-fourths = 12 Select all that apply. (StartFraction negative 4 x over 1 EndFraction + three-fourths = 12 Negative 1 (StartFraction x over 4 EndFraction) + three-fourths = 12 StartFraction negative x + 3 over 4 EndFraction = 12 One-fourth (x + 3) = 12 (StartFraction negative x over 4 EndFraction + three-fourths = 12
Answers
The equations which are equivalent to -1/4(x) + 3/4 = 12 are -1(x/4) + 3/4 = 12 and -x/4 +3/4 = 12. Choose the 2nd and 5th options
How determine which equations are equivalent?Equivalent equations are equations that work the same way even though they look different
The given equation is -1/4(x) + 3/4 = 12 which can simplified as:
-1/4(x) + 3/4 = 12
(-x + 3)/4 = 12
Compare with options:
1. 4x/1 + 3/4 = 12
4x/1 + 3/4 = 12
This is not equivalent
2. -1(x/4) + 3/4 = 12
-1(x/4) + 3/4 = 12
-x/4 + 3/4 = 12
(-x + 3)/4 = 12
This is equivalent
3. -(x+3)/4 = 12
-(x+3)/4 = 12
This is not equivalent
4. 1/4(x+3) = 12
1/4(x+3) = 12
This is not equivalent
5. -x/4 +3/4 = 12
-x/4 +3/4 = 12
(-x+3)/4 = 12
This is equivalent
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Answer:it’s b and d
Step-by-step explanation:
The weights and heights of six mathematics students are given in the following table: Weight (in pounds)
165 123 212 175 165 147
Height (in centimeters)
172 157 183 178 163 167
State whether weight is a function of height for the six students and explain.
a. Yes, height is a function of weight because two students weigh 165 pounds but have different heights.
b. No, height is not a function of weight because two students weigh 165 pounds but have different heights.
c. Yes, weight is a function of height because for each value of height there is one corresponding value of weight.
d. No, weight is not a function of height because there is not enough data to determine a function.
Answers
The input variable is "Height," while the output variable is "Weight."
Explain about the independent variable?A variable that is independent is precisely what it sounds like. It is a stand-alone variable that is unaffected by the other variables you are attempting to assess. Age, for instance, could be an independent variable.
The cause is the independent variable. Its value is unaffected by the other study variables. Effect is the dependent variable. Changes in the independent variable affect its value.
When doing an experiment, the independent variable is what you alter, and the dependent variable is what changes as a result of that change. This is an easy way to conceive of independent and dependent variables. The independent variable can alternatively be viewed as the cause, and the dependent variable as the result.
The input and output variables are "Height" and "Weight," respectively.
Detailed explanation:
"Weight and height are related"
As we all know, the independent variable in a function of the form y=f(x) is x, and the dependent variable is y.
In other words, after substituting the values of "x," we are getting the values of the quantity "y."
As a result, we can infer from the assertion that,
We are getting the values of "Weight" after substituting the values of "Height."
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A repair person charges a travel fee to visit a home and an hourly fee for the time spent fixing a leak.
A repair that takes 2 h costs $100. A repair that takes 6 h costs $260.
Write an equation to represent the total cost of a repair, y, as a function of the
number of hours spent fixing a leak.
Answers
So on solving the provided question, we can say that y = a + xb is the necessary equation for the total fee the repairman charged, y = 260 + 6x
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
Here,
Let the total amount charged by the repairman be y and the total number of hours worked be x,
[tex]y = a + xb[/tex]
a is as travel fee
b is as hourly rate
Therefore, y = a + xb is the necessary equation for the total fee the repairman charged.
y = 260 + 6x
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What is the function of for loop explain with example?
Answers
For loop is a type of looping structure that is used in programming to repeat a sequence of codes until a certain condition is met.
What is function?In mathematics, a function is a relation between a set of inputs and a set of outputs, such that each input is related to exactly one output. Functions are often represented as mathematical expressions, or as a graph or table. The input to a function is known as the argument, while the output is known as the value. Functions are used to describe physical phenomena, and to model relationships between different variables.
It is commonly used to go through each element in an array or a list without having to write the same code multiple times. For example:
// Initialize array
int arr[] = {1, 2, 3, 4, 5};
// For loop to print out each element in the array
for (int i = 0; i < 5; i++) {
System.out.println(arr[i]);
}
In this example, the for loop will print out each element of the array until it reaches the condition that i is less than 5, which is the length of the array.
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LOTS OF POINTS PLEASE HELP
Three Algebra 1 students are comparing how fast their social media posts have spread. Their results are shown in the following table:
Student Amber Ben Carter
Description Amber shared her photo with 3 people. They continued to share it, so the number of shares increases every day, as shown by the function. Ben shared his post with 2 friends. Each of those friends shares with 3 more every day, so the number of shares triples every day. Carter shared his post with 10 friends, who each share with only 2 people each day.
Social Media Post Shares f(x) = 3(4)x
Day Number of Shares
0 2
1 6
2 18 Carter shared his post with 10 friends, who each share with only 2 people each day.
Graph each function using at least three points for each curve. All graphs should be placed together on the same coordinate plane, so be sure to label each curve. You may graph your equation by hand on a piece of paper and scan your work, or you may use graphing technology.
Answers
A graph of each of the exponential equation is shown in the image attached below.
What is an exponential function?In Mathematics, an exponential function can be modeled by using this mathematical expression:
f(x) = ab^x
Where:
a represents the initial value or y-intercept.x represents time.b represents the rate of change.Since Amber shared her photo with 3 people who continued to share it, an exponential function that models the situation is given by:
f(x) = 3(4)^x
Similarly, Ben's post was shared with 2 friends and each of them shared it with 3 more every day, tripling the number of shares every day, an exponential function that models the situation is given by:
g(x) = 2(3)^x
Lastly, an exponential function that represents the spread of Carter's social media post is given by:
h(x) = 10(2)^x
In this scenario, we would use an online graphing calculator to graph each function as shown in the image attached below.
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They continued to share it, so the number of shares increases every day, as shown by the function.
Social Media Post Shares f(x) = 3(4)x
Day Number of Shares
0 2
1 6
2 18 Carter shared his post with 10 friends, who each share with only 2 people each day.
Heila either walk or cycle to chool
the probability he walk to chool i 0. 65
if he walk to chool, the probability he i late i 0. 4
If he cycle to chool, the probability he i late i 0. 1
work out the probability that on any one day heila will not be late for chool
Answers
The probability that on any one day, Heila will not be late for school is 0.69 or 69%.
We can use conditional probability to find the probability that Heila will not be late for school on any one day.
Let W be the event that Heila walks to school, and L be the event that Heila is late for school.
We know that:
P(W) = 0.65 (the probability that Heila walks to school)
P(L | W) = 0.4 (the probability that Heila is late for school given that he walks to school)
P(L | W') = 0.1 (the probability that Heila is late for school given that he cycles to school)
The probability that Heila is not late for school is the complement of the event that he is late for school. So:
P(L') = 1 - P(L)
We can use the formula for conditional probability to find the probability that Heila is not late for school:
P(L' | W) = 1 - P(L | W) = 1 - 0.4 = 0.6
P(L' | W') = 1 - P(L | W') = 1 - 0.1 = 0.9
We also know that the total probability of the outcomes must be equal to 1. Therefore, we can find the probability that Heila walks to school, P(W) by using the following equation:
P(W) + P(W') = 1
We know that P(W) = 0.65, so we can find P(W') by subtracting P(W) from 1:
P(W') = 1 - P(W) = 1 - 0.65 = 0.35
Now, we can use the formula of Total Probability to find the probability that Heila will not be late for school:
P(L') = P(L' | W) * P(W) + P(L' | W') * P(W')
P(L') = 0.6 * 0.65 + 0.9 * 0.35 = 0.69
Therefore, the probability that on any one day, Heila will not be late for school is 0.69 or 69%.
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Which of the following is the equation of the circle with center C and a point P on the circle, as shown in the graph?
(x – 4)2 + (y + 5)2 = 10
(x + 2)2 + (y – 3)2 = 10
(x – 2)2 + (y + 3)2 = 100
(x + 4)2 + (y – 5)2 = 100
Answers
The equation of the circle center, C(2, -3), with the point on the circle, P(-4, 5), is the option;
(x - 2)² + (y + 3)² = 100What is the standard form of the equation of a circle?The standard form of the equation of a circle is presented as follows;
(x - h)² + (y - k)² = r²
Where;
(h, k) = The coordinates of the center of the circle
r = The length of the radius of the circle
The location of the specified center of the circle, C = (2, -3)
The location of the point P = (-4, 5)
The radius of the circle found using the distance formula used for finding the distance between two points is therefore;
r = √((-4 - 2)² + (5 - (-3))²) = √((-6)² + (8)²) = 10
The radius of the circle, r = 10
Therefore;
The center of the circle, (h, k) = (2, -3)
The equation of the circle = (x - 2)² + (y - (-3))² = 10²
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The sum of Lisa's age and Myra's age is 40. In 10 years, Lisa will be 3
times as old as Myra. How old is each person now?
Answers
Answer:
Lisa: 35Myra: 5Step-by-step explanation:
You want Lisa's and Myra's ages if the sum of their ages is 40 and in 10 years, Lisa will be 3 times as old as Myra.
10 years henceThe current sum of their ages is 40. In 10 years, 10 will be added to each of their ages, so the sum will be 60.
At that time Lisa's age is 3 times Myra's age, so will be 3/(3+1) = 3/4 of the total.
Lisa's age in 10 years = (3/4)(60) = 45
Lisa is 35 now, and Myra is 5 now.
__
Additional comment
We could write some equations, but we find a mental solution based on ratios to be quick and easy. Here is a solution using equations:
L + M = 40
(L +10) = 3(M +10) . . . . . . age relation in 10 years
(40 -M) +10 = 3M +30 . . . . substitute for L
20 = 4M . . . . . . . . . add M-30
M = 5; L = 40-M = 35
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Give an example of a quartic trinomial.
Give an example of a quintic polynomial.
Answers
Answer:
quartic trinomial : 3x4 – 2x3 + x2 + 8, a4 + 1, and m3n + m2n2 + mn.
quintic polynomial: x5 – x3 + x, y5 + y4 + y3 + y2 + y + 1, and 42a3b2.
Step-by-step explanation:
Quartic Polynomial
A polynomial of degree 4.
Examples: 3x4 – 2x3 + x2 + 8, a4 + 1, and m3n + m2n2 + mn.
a quintic function is defined by a polynomial of degree five.
Because they have an odd degree, normal quintic functions appear similar to normal cubic functions when graphed, except they may possess one additional local maximum and one additional local minimum.
The quartic trinomial having a degree of 4 and the quintic polynomial having a degree of 5.
Quartic Trinomial:
A quartic trinomial is a polynomial expression of degree four that consists of three terms.
The general form of a quartic trinomial is:
[tex]ax^4 + bx^2 + c[/tex]
Example:
Let's consider the quartic trinomial:
[tex]2x^4 - 5x^2 + 3[/tex]
In this example, the term "[tex]2x^4[/tex]" is the highest degree term (degree 4), the term "-[tex]5x^2[/tex]" is the second highest degree term (degree 2), and the constant term "3" has no variable.
So, the quartic trinomial has three terms.
Quintic Polynomial:
A quintic polynomial is a polynomial expression of degree five that may contain multiple terms.
The general form of a quintic polynomial is:
[tex]ax^5 + bx^4 + cx^3 + dx^2 + ex + f[/tex]
Example:
Let's consider the quintic polynomial:
[tex]3x^5 - 2x^4 + 4x^3 + x^2 - 7x + 2[/tex]
In this example, the term "[tex]3x^5[/tex]" is the highest degree term (degree 5), the term "-[tex]2x^4[/tex]" is the second highest degree term (degree 4), and so on. The quintic polynomial has six terms, including the constant term "2".
Hence the quartic trinomial having a degree of 4 and the quintic polynomial having a degree of 5.
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how could you use a 1/4 cup measuring cup to to measure
the water
Answers
Answer:
Step-by-step explanation:
1 you would pour the water in the cup and see what dash it lands on
let's say you pour the water and it lands on the 1/8 mark it would be one 1/8
Hope this help if not sorry
What is the coefficient of y² in the expression 3y² 4x *?
Answers
So, on solving the provided question, we can say that coefficient of y² in the expression 3y² - 4x is 3
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 y² in the expression 3y² - 4x is 3
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What is the 4 sequence in math?
Answers
The four types of Sequence are Arithmetic Sequence , Geometric sequence , Harmonic Sequence and Fibonacci Sequence .
What is a Sequence ?
The Sequence is defined as an arrangement of objects or a set of numbers in a particular order which are followed by some rule .
The Four Types of Sequences are :
(i) Arithmetic Sequence : It is defined as a type of sequence in which every term of the series is created by adding or subtracting a fixed number to preceding number .
(ii) Geometric Sequence : It is defined as a type of sequence in which every term is obtained by multiplying or dividing a fixed number with the preceding number .
(iii) Harmonic Sequence : It is defined as a type of sequence in which the reciprocals of the terms follows the Arithmetic Progression .
(iv) Fibonacci Sequence : It is defined as a type of sequence in which every element is obtained by adding the two preceding elements and the sequence starts with 0 and 1 .
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Ben solves this equation
14 + 12x - 6 = 18 - 4x + 4
His work is shown:
Step 1: 8 + 12x = 22 - 4x
Step 2: 8x = 14
Step 3: x = 4
Step 2 is Incorrect.
Enter the correct equation for step 2.
Answers
The correct equation of step 2 is 16x = 14
How to determine the correct equation of step 2?from the question, we have the following parameters that can be used in our computation:
14 + 12x - 6 = 18 - 4x + 4
When the like terms on each side are Evaluated, we have
Step 1: 8 + 12x = 22 - 4x
When the like terms on all sides are Evaluated, we have
Step 2: 16x = 14
Hence, the correct equation is 16x = 14
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A cuba diver tart at ea level and travel to a poition that i a little lower than −18
-
18
feet. Ue the drop-down menu to complete the tatement about the cuba diver' poition
Answers
As per the given statement, the scuba diver's position means the distance he traveled is below 18 feet at the sea level.
Here we have given that a scuba diver starts at sea level and travels to a position that is a little lower than -18 feet.
Now, we need to find the scuba diver's position means the distance he traveled.
While we consider that the scuba driver travelled on -18 feet.
Here the negative term is defined that the the traveler goes on the bottom level.
Therefore, here we said that the person is going to below the sea level.
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What is the formula for finding the sides of a triangle?
Answers
Therefore , the solution of the given problem of trigonometry comes out to be we can find the sides of triangle by trigonometry ratios.
What does trigonometry mean?The area of mathematics known as trigonometry explores the correlation between square side length and As a result of the combination of astronomy and geometry studies, the field initially emerged inside the Nineteenth century, most likely there in third century BC. Precise methods of mathematics cover a number of geometric equations and possible applications to calculations.
Here,
To find the all sides of a triangle
By using trigonometry ,
We can:
Apply the law of sines or trigonometry to find the right triangle side lengths: a = c × sin(α) or
a = c × cos(β)
b = c × sin(β) or
b = c × cos(α)
Therefore , the solution of the given problem of trigonometry comes out to be we can find the sides of triangle by trigonometry ratios.
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Can I simplify a function?
Answers
The following actions must be taken in order to simplify the rational function f (x) = p (x) q (x): Where q (x) = 0, identify the values of x.
what is functions ?The study of mathematics include the study of numbers, formulas and related structures, forms and the environments in which they exist, quantities and their variations, and the environments in which they exist. A function is an association between a number of inputs, each of which has an output. Simply described, a function is a relationship between inputs and outputs in which each input leads to a single, distinct result. Usually, the letter f is used to denote functions (x). input consists of x. There are four different types of functions. based on the following elements: one-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.
given
The following actions must be taken in order to simplify the rational function f (x) = p (x) q (x): Where q (x) = 0, identify the values of x.
If so, all real values, with the exception of these roots, are in the domain of f (x).
It may be necessary to factor by grouping or by applying the factor theorem in order to fully factor both p (x) and q (x).
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what is 200000x 20456
Answers
The workers at a bakery must make 12 batches of bagel dough an hour to meet the customers needs. The number of batches of dough, y, that each worker needs to mix in one hour is inversely proportional to the number of workers, x.
Answers
The value for constant of proportionality and inverse proportionality is k=12 and x=12/y respectively.
What is constant of proportionality and inverse proportionality?
The ratio between two proportional quantities' constant values is known as the constant of proportionality. When either their ratio or their product gives a constant, two changing values are said to be in a proportionate relationship.
When the value of one item rises in relation to a fall in the other or vice versa, two values are said to be inversely proportionate. This indicates that the natural behaviour of these two quantities is contrary
In a bakery workers must make 12 batches of bagel dough an hour.
The number of batches of dough, y, that each worker needs to mix in one hour is inversely proportional to the number of workers, x.
Lets find the constant of proportionality first.
According to the graph -
The point given in the graph is (6,2).
x=6 and y=2
(where 'x' denotes no of workers and 'y' denote no. of bagel dough batches).
Equation for constant of proportionality is -
x×y=k
6×2=k
k=12 is the constant of proportionality.
Now find the equation for inverse proportionality.
No. of workers (along x-axis) = x
No. of the bagel dough batches (along y-axis) = y
The algebraic equation relating both = x×y=k
The constant of proportionality is k=12.
x×y=12
xy=12
x=12/y
Therefore, the equation of inverse proportionality is x=12/y.
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1. What is the expression for the perimeter of the entire gardening area based on Lisa’s measurements?
Answers
The expression for the perimeter of the gardening area is 10x+16
What is perimeter?A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.
The perimeter of the garden will be the sum of all the sides of the garden.
left side = x+3+x = 2x+3
right side = x+3x+x =2x+3
top side = x+3+x+3+x = 3x+6
bottom side = 3x+6
therefore this shot the garden as a rectangular shape.
The perimeter of a rectangle = 2(L+B)
= 2((2x+3)+3x+6)
= 2( 5x+8)
therefore the expression that best represents the perimeter of the garden is 10x+16
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This relationship can also be shown in a table. Complete the equation that represents the relationship between n and w.
Answers
An equation that represents the relationship between n and w is w = 10n + 8.
How to write the required equation?Mathematically, the slope-intercept form of a line can be represented by using this linear equation:
y = mx + c
Where:
m represents the slope.c represents the y-intercept.x and y are the data points.Next, we would determine the slope of the data points in this table (see attachment) as follows;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (78 - 68)/(7 - 6)
Slope, m = 10/1
Slope, m = 10.
At point (6, 68), an equation of this line can be calculated in slope-intercept form as follows:
y - y₁ = m(x - x₁)
y - 68 = 10(x - 6)
y - 68 = 10x - 60
y = 10x - 60 + 68
y = 10x + 8 ≡ w = 10n + 8.
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Hilda went hiking and used the app on her phone to track her progress. When she looked back, she discovered she had hiked down 230 feet, up 602 feet, down 183 feet, and up 762 feet to get to the lake. What is her elevation in relation to where she started?
Answers
Answer: 951 ft
Step-by-step explanation:
-230 + 602 - 183 + 762
= 951 ft
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
Answers
Answer:
See explanation below.
Step-by-step explanation:
2.3p – 10.1 = 6.5p – 4 – 0.01p?
2.3p -6.5p + 0.01p= – 4 + 10.1
-4.19p = 6.1 [Combine like terms and moved from one side to the other]
p = -1.456
Select two options.
The options seem to run together. Where does one equation stop and the other begin?
Are these the equation options?
2.3p – 10.1 = 6.4p – 4
2.3p – 10.1 = 6.49p – 4
230p – 1010 = 650p
– 400 – p 23p – 101 = 65p – 40
– p 2.3p – 14.1 = 6.4p – 4
These don't look correct. Please review the derivation of p=-1.456 and find the option(s) that provide the same result.
Plot the x-intercept of the function f(x) = (x + 4)².
y
-6 -4 -2
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Click or tap the graph to plot a point.
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Answers
By graphing a plot point using the x-intercept form, the function (x + 4)2 is shown to be x2 + 16 + 8x.
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
given
(x + 4)²
= x2 + 16 + 8x
By graphing a plot point using the x-intercept form, the function (x + 4)2 is shown to be x2 + 16 + 8x.
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Which among the following are solution of the equation 2x+3y=8a) x=0,y=5b) x=3,y=2c) x=-5,y=6d) x=-1,y=-2
Answers
(C) x=-5, y=6 is the solution of the equation 2x+3y=8
To find out which among the following options are solutions of the equation 2x+3y=8, we can substitute the values of x and y in the equation and see if it holds true or not.
a) x=0, y=5 : 2(0) + 3(5) = 0 + 15 = 15 != 8
b) x=3, y=2 : 2(3) + 3(2) = 6 + 6 = 12 != 8
c) x=-5, y=6 : 2(-5) + 3(6) = -10 + 18 = 8 = 8
d) x=-1, y=-2 : 2(-1) + 3(-2) = -2 + -6 = -8 != 8
so the value of left hand side and right hand side of a), b) ,d) is not equals to each other and hence they won't be the equation solution .
So the correct answer is (c) x=-5, y=6
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Triangle ABC is translated by the rule (x, y) → (x - 1, y + 6) then reflected across the y- axis. What are the coordinates of A”,B”, and C”?
Answers
The coordinates of A'', B'' and C'' are (-1, 4), (-4, 3) and (-1, 2) respectively.
What is Geometric Transformation?Transformation of geometrical figures or points is the manipulation of a given figure to some other way.
Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.
Given triangle has coordinates,
A(2, -2), B(5, -3) and C(2, -4).
First the triangle is translated by the rule (x, y) → (x - 1, y + 6)
A(2, -2) becomes A'(2 - 1, -2 + 6) = A'(1, 4).
B(5, -3) becomes B'(5 - 1, -3 + 6) = B'(4, 3)
C(2, -4) becomes C'(2 - 1, -4 + 6) = C'(1, 2)
Then the translated triangle is reflected across the Y axis.
When reflected a point (x, y) across the Y axis, y coordinate remains same and x coordinate flips.
A'(1, 4) becomes A''(-1, 4)
B'(4, 3) becomes B''(-4, 3)
C'(1, 2) becomes C''(-1, 2)
Hence the vertices of the triangle after undergoes translation and reflection becomes A''(-1, 4), B''(-4, 3) and C''(-1, 2).
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what does -2/3 slope look like on a graph
Answers
On solving the provided question, we can say that the provided slope is -2/3 equation of line 2x + 3y -7 = 0
what is slope?A line's slope determines how steep it is. A mathematical equation for the gradient is called "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical change (rise) between two points to the horizontal change (run) between those same two spots. When a straight line's equation is written as y = mx + b, the slope-intercept form of an equation is employed to express it. The y-intercept is located at a location where the line's slope is m, b is b, and (0, b). For instance, the slope of the equation y = 3x - 7 and the y-intercept (0, 7).The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).
the provided slope is -2/3
let us assume x1 = 2 and y1 = 1
equation of line =>
y-1 = -2/3(x-2)
y-1 = -2x/3 + 4/3
3y-3 = -2x + 4
2x + 3y -7 = 0
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