To solve this problem, we can use the Law of Cosines. The Law of Cosines states that for a triangle with sides a, b, and c and the angle C opposite side c, the following equation holds:
c^2 = a^2 + b^2 - 2abcos(C)
In this problem, we are given the measure of angle C and the lengths of sides b and c. We can use this information to find the length of side a and the measures of angles A and B.
First, we can use the Law of Cosines to find the length of side a. Plugging in the given values, we get:
a^2 = c^2 - b^2 + 2bc cos(C)
Substituting in the given values, we get:
a^2 = 151^2 - 181^2 + 2 * 151 * 181 * cos(60.0°)
Solving this equation gives us a = 143 m.
Now that we have the length of side a, we can use the Law of Sines to find the measures of angles A and B. The Law of Sines states that for a triangle with sides a, b, and c and angles A, B, and C opposite these sides, the following equation holds:
a/sin(A) = b/sin(B) = c/sin(C)
We are given the lengths of sides a and b and the measure of angle C. We can use this information to find the measures of angles A and B.
First, we can use the Law of Sines to find the measure of angle A. Plugging in the given values, we get:
a/sin(A) = b/sin(B)
Solving for sin(A), we get:
sin(A) = a * sin(B) / b
Substituting in the given values, we get:
sin(A) = 143 m * sin(B) / 181 m
To find the measure of angle A, we can use the inverse sine function (sin^-1). This gives us:
A = sin^-1(sin(A))
= sin^-1(143 m * sin(B) / 181 m)
Similarly, we can use the Law of Sines to find the measure of angle B:
B = sin^-1(143 m * sin(A) / 181 m)
Since we have two unknowns (A and B) and two equations, there is a unique solution for this triangle.
Therefore, the number of solutions is 1, and the measures of angles A and B are A = 38.5° and B = 101.5°. The length of side a is 143 m.
The angle below measures 2.4 radians, and the circle centered at the angle's vertex has a radius 3 units long. 2.21 (x, y) 11 2.4 rad Determine the exact coordinates of the terminal point (2,y). • 2 = cos(2.4) * Preview • y= sin(2.4)
The exact coordinates of the terminal point (x,y) is = (-2.212185 , 2) .
In the question ,
it is given that ,
the measure of the angle in the figure is = 2.4 radians ,
From graph ,
we can see that the y - coordinate is = 2 unit , So , y = 2 .
Now , for the x - coordinate ,
we draw a right triangle ABO ,
where the height is 2 units and hypotnuse is = 3 units (radius) ,
the angle 2.4 radian in degree is = 137.51° ,
So , from the trigonometric ratio ,
Cos(θ) = base/hypotnuse ,
Cos(137.51) = x/3 ,
x = 3*Cos(137.51)
x = 3*(-0.737395)
x = -2.212185
Therefore , the exact point (x,y) is = (-2.212185 , 2) .
The given question is incomplete , the complete question is
The angle below measures 2.4 radians, and the circle centered at the angle's vertex has a radius 3 units long. Determine the exact coordinates of the terminal point (x , y) .
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Given the functions:
f(x)=2x g(x)=|x-3| h(x)=1/x-7
Evaluate the function (f-g)(x) for x = -2.
(f-g)(-2) is.
Answer:
-9
Step-by-step explanation:
[tex]f(-2)=2(-2)=-4 \\ \\ g(-2)=|-2-3|=5;\\ \\ (f-g)(2)=-4-5=-9[/tex]
A machine is designed to dispense 20 mg of d-desoxyephedrine into each capsule of a medicine. 13
pills are tested, and it's found that they have a mean drug content of 20.2 mg, with a standard
deviation of 2.4 mg. To a 1% level of significance, can it be asserted that the standard deviation of
the process (in general) is over 2 mg?
[Assume that the drug contents of all the pills are normally distributed.]
Answer: To answer this question, we need to perform a hypothesis test. The null hypothesis is that the standard deviation of the process is 2 mg or less, and the alternative hypothesis is that the standard deviation of the process is over 2 mg.
To test this hypothesis, we need to calculate the test statistic, which is the z-score. The z-score tells us how many standard deviations a given data point is from the mean. In this case, the z-score is calculated by subtracting the mean of the sample from the hypothesized mean of the population, and dividing that difference by the standard deviation of the sample:
z = (20.2 - 20) / 2.4 = 0.1
Since the z-score is positive, we know that the mean of the sample is greater than the hypothesized mean of the population. However, we need to compare this z-score to the critical value to determine whether it is statistically significant.
The critical value is the z-score that marks the cutoff between the region of acceptance and the region of rejection of the null hypothesis. For a 1% level of significance, the critical value is the z-score that marks the 99th percentile of the normal distribution. Since the normal distribution is symmetrical, this means that the critical value is 2.58 standard deviations from the mean.
Since the z-score we calculated is less than the critical value, we cannot reject the null hypothesis. This means that we cannot assert that the standard deviation of the process is over 2 mg at a 1% level of significance.
Max is thinking of a number, which he calls n. He adds 8 and then doubles the sum.
Write an expression to represent Max's number.
Answer:
2n + 16
Step-by-step explanation:
he adds 8 then doubles the sum
2(n + 8) which is 2n + 16
Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. Group of answer choices 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x + 9) = –3 + 9 2(x2 + 6x) = –3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x) = 3
The following are the actions she could take to solve the quadratic equation: 2(x² + 6x + 9) = 18 + 3.
Define the term quadratic equation?In relation to squares, the square operation, concepts of a second degree, including equations or formulas containing such terms, something is said to as quadratic.Following is the determination of the quadratic equation's solution;
2x² + 12x - 3 = 0
2x² + 12x = 3
Divide equation by 2.
x² + 6x = 3/2
Add both of the equation's sides after squarely multiplying the x-coefficient by half:
(x + 3)² = 3/2 + 3²
x² + 6x + 9 = 9 + 3/2
2(x² + 6x + 9) = 18 + 3
Thus, in order to calculate the quadratic equation, she could follow these steps: 2(x² + 6x + 9) = 18 + 3.
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Adult tickets to the fall play cost $8 and student tickets cost $4. The drama class sold 20 more adult tickets than student tickets to the fall play. If
the class collected $880 from ticket sales, how many adult tickets were sold?
The drama class sold
adult tickets.
The solution is
Answer: 110
Step-by-step explanation: If the drama class sold 20 more adult tickets than student tickets to the fall play, and adult tickets cost $8, then the number of adult tickets sold can be calculated by adding 20 to the number of student tickets sold and multiplying by $8. We can set up an equation to represent this relationship, where A represents the number of adult tickets sold and S represents the number of student tickets sold:
A = S + 20
A * 8 = $880
We know that the total amount collected from ticket sales was $880, and we know that adult tickets cost $8, so we can divide $880 by $8 to find the number of adult tickets sold:
A = $880 / $8
A = 110
Therefore, the drama class sold 110 adult tickets to the fall play.
26. The graph shows a polynomial function f. Polynomial function g=x^2(6-x). Compare the maximum values and the end behavior of the functions f and g when x>0
The end behavior of the polynomial is, rises to the left and falls to the right.
What is end behavior of polynomial?
A polynomial function typically behaves at its end in the same way that its leading term, or the term with the largest exponent, does at its end.
Look at the leading term of the polynomial function to understand its end behavior. Given that the leading term has the highest power, its behavior will dominate the graph because it will grow much more quickly than the other terms as x gets very large or very small.
Consider, the given polynomial g(x) = x^2 (6 - x)
From the graph of the polynomial function we can see that the maximum point of the polynomial is at its vertex.
The vertex of the polynomial is (10, 90).
So this is the maximum value of the function is (10, 90).
Now to find the end behavior of the polynomial.
The degree of the polynomial is 3 and the leading coefficient of the polynomial is, -1.
By using: Odd degree and Negative leading coefficient the graph Rises to the left and falls to the right.
Hence, the end behavior of the polynomial is, rises to the left and falls to the right.
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During a clearance sale at a sporting goods store, skateboards were marked down 30%. On Saturday, an additional 25% was taken off the already reduced prices of the skateboards. If a skateboard originally cost $119.50, what was the final price after all discounts? Round to the nearest cent.
The final cost of a skateboard after all the discounts and reductions is $53.775.
Given that, during a clearance sale at a sporting goods store, skateboards were marked down 30%. On Saturday, an additional 25% was taken off already reduced prices of skateboards.
We need to find the final price after all discounts had been taken.
What is the discount?
The basic way to calculate a discount is to multiply the original price by the decimal form of the given percentage rate. To calculate the sale price of any item, we need to subtract the discount from the original price.
Given, that the original cost of the skateboard is $119.50.
Now, 30+25=55
So, the total decrease in percentage is 55%.
The final cost of a skateboard=119.50-55% of 119.50
=119.50-0.55 × 119.50
=119.50-65.725
=$53.775
Therefore, the final cost of a skateboard after all the discounts and reductions is $53.775.
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Solving Equations and Inequalities
The error occur from line 2 to line 3(optionB)
What is a linear equation?An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent more than 1. The graph of a linear equation forms a straight line.
A linear equation can have one or two variables. For example 5 = y+ 3y is an example of linear equation with one variable and y = 5 +3x is an example of linear equation with two variables.
8x-4= 2(4x+1)-6
8x-4= 8x+2-6
8x-4= 8x-4
Therefore the error is made where the parentheses is been solved, 2 is to multiply both 4x and 1.
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Jimmy began deriving the quadratic formula. ax² + bx + c = 0 x2+bax+ca=0 x2+bax=−ca x2+bax+(b2a)2=−ca+(b2a)2 What step should Jimmy do next? Responses Subtract b2a from each side. Subtract , b over 2a, from each side. Factor the trinomial. Factor the trinomial. Add x² to each side. Add , x, ² to each side. Subtract x² from each side.
The required step to be taken is to factor the trinomial in the derivation.
What is a quadratic equation?The general form of a quadratic equation is given as ax^2 + bx + c = 0.
Here, a ≠ 0 and b and c are integers.
The degree of a quadratic equation is 2.
It can be factorized by completing square method.
The given problem can be solved as follows,
The derivation made by Jimmy is given as,
ax² + bx + c = 0
=> x² + (b/a)x + c/a = 0
=> x² + (b/a)x = -c/a
=> x² + (b/a)x + (b/2a)² = -c/a + (b/2a)²
Now, in order to solve the equation the trinomial on the LHS can be factored as follows,
(x + b/2a)² = -c/a + (b/2a)²
Hence, the next step taken by jimmy should be to factorize the trinomial on LHS.
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write an equation for the money they collect,y,as a function of the number of t-shirts they sell,x.
Answer:
Step-by-step explanation:
There are several ways to write an equation for the money collected as a function of the number of t-shirts sold. One possible equation is $y = x \cdot p$, where $p$ is the price of each t-shirt. This equation says that the total amount of money collected is equal to the number of t-shirts sold multiplied by the price of each t-shirt.Another possible equation is $y = p \cdot (x - c)$, where $c$ is the cost of producing each t-shirt. This equation says that the total amount of money collected is equal to the price of each t-shirt multiplied by the number of t-shirts sold minus the cost of producing each t-shirt.These are just two examples of how to write an equation for the money collected as a function of the number of t-shirts sold. The exact equation will depend on the specific details of the situation.
Which proportion could be used to prove that HJ || KL?
The correct proportion used to prove that HJ || KL is [tex]\frac{GK}{HK} = \frac{GL}{LJ}[/tex].
What is the proportion theorem of two similar lines?
According to this theorem, if you draw a line parallel to one side of a triangle that divides the other sides into two separate points, the line will proportionally divide the other sides. In addition, a line is parallel to the third side if it divides any two triangle sides in the same ratio.
We have,
HJ || KL
If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.
And in the given triangle, HJ is parallel to KL, So HJ divided the two sides in proportion, that is
[tex]\frac{GK}{HK} = \frac{GL}{LJ}[/tex]
The correct option is the fourth option.
So, The correct proportion could be used to prove that HJ || KL
[tex]\frac{GK}{HK} = \frac{GL}{LJ}[/tex]
Hence, the correct proportion used to prove that HJ || KL is [tex]\frac{GK}{HK} = \frac{GL}{LJ}[/tex].
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Pls help me is fast rapidly more fast answer fast of khan academy
The different possibilities
5 + 4/105 + 3/10 + 10/100 5 + 2/10 + 20/1005 + 1/10 + 30/1005 + 0/10 + 40/100What is place value?The value of each digit in a number is known as place value. Every digit in a number has a distinct value depending on where it is located. The value of a digit depends on its position in the number, which might result in a number having two comparable digits with distinct values.
Given:
5.4
Now, filling with different possibilities
5 + 4/105 + 3/10 + 10/100 5 + 2/10 + 20/1005 + 1/10 + 30/1005 + 0/10 + 40/100Tens Ones Tenths Hundredths
0 5 4 0
0 5 3 10
0 5 2 20
0 5 1 30
0 5 0 40
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If sin (0) = -3.29, what is sin ( + 0)?
A.
-2.39
B. -3.29
C. 2.39
D. 3.29
Answer:
Step-by-step explanation:
B
Prepare a manifesto in which you propose alternatives to overcome discrimination in the case of activity 2. Consider the following
the needs and rights of those involved. What do you think are the reasons for not discriminating against these groups?
to seek equality in dignity and rights. What would you do to avoid this discrimination?
Avoiding discrimination is extremely important because this is an attitude that goes against human dignity and different values.
1. Alternatives to overcome discriminationSome alternatives to overcome discrimination are:
Promote good values, such as respect. Raise awareness about the negative effects of discrimination.2. What do you think are the reasons for not discriminating against these groups?No group should be discriminated against because discrimination promotes negative values and does not allow the correct development of people.
3. What would you do to avoid this discrimination?To avoid discrimination you can:
Seek to raise awareness about why we should not discriminate. Promote good values such as respect.Promote inclusion.¡Hope this helped!
the lengths of two sides of a triangle are 4 cm and 13 cm. identify the range of possible lengths for the third side.
a. 4 cm < x < 13 cm b. 5 cm < x < 12 cm c. 9 cm < x < 17 cm d. 3 cm < x < 14 cm
Because the range is supplied as the difference between the side and the total of the sides given, option C, which is 9 cm<x<17 cm, is the right choice.
What is triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
Here,
The range of possible lengths for the third side,
13-4<x<13+4
9<x<17
The correct option is C that is 9 cm < x < 17 cm because the range is given in difference between the side and sum of sides given.
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what does it mean by element c32
Answer:
2 (the first choice)
Step-by-step explanation:
This is a matrix of size 3 rows and 5 columns (3 x 5)
Any element of the matrix can be reference by row and column number
C₃₂ refers to the element in the 3rd row, 2nd column which is 2
Questions 6-10. Suppose Calvin Cordozar Broadus, Jr. (aka Snoop Doggy Dogg) is
considering moving his family to Manhattan. His real estate agent has managed to locate a
penthouse apartment that overlooks Central Park for $2.4 million. He will have $2.1 million
from the sale of his current home as a down payment. Snoop would like to finance the
remainder of the cost and his banker has presented two options: a 30-year fixed-rate
mortgage at 8% or a 20-year fixed-rate mortgage at 7.5%.
How much will snoop have to finance?
Answer:
The price of the Penthouse is $2.4 million
Down Payment is $2.1 Million
So the amount that must be financed is $2.4 million - $2.1 million = $0.3 million or $300,000
Step-by-step explanation:
The manager of a medical center wants to schedule staff based on a pattern of 5 days working and 2 consecutive days off. Based on the history of their workload, below is their weekly staff requirement: Day Monday Tuesday Wednesday Thursday Friday Saturday Sunday Staff needed 6 5 4 4 6 5 3 a. Determine what days employee 3 does not need to work. multiple choice A) Sunday and Monday B) Monday and Friday C) Tuesday and Thursday D) Wednesday and Friday b. Determine the minimum number of full time staff. c. Determine the minimum number of part time staff.
The correct option A) Sunday and Monday, is the days employee 3 does not need to work.
Explain the term frequency table?A frequency table is a list of objects with the frequency of each item shown in the table.The distribution of sightings based on a variable's possible values is displayed in a frequency table. To understand which alternatives appear more or less frequently in the dataset, frequency tables are useful.This is useful for better understanding each variable and determining whether or not variables must be recoded.For the stated question-
A medical center's manager wants to schedule employees so that they work 5 days and take 2 days off in a row.
Thus, they are reportedly mandated to have consecutive days off on Saturday and Monday, and there is no better option than A.
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The fox population in a certain region has an annual growth
estimated that the population in the year 2000 was 25800.
rate of 4 percent per year. It is
(a) Find a function that models the population t years after 2000 (t = 0 for 2000).
Your answer is P(t) =
(b) Use the function from part (a) to estimate the fox population in the year 2008.
Your answer is (the answer should be an integer)
The function and the estimated value for the given population of fox are obtained as P(t) = P₀(1 + r)^t and 35346 respectively.
How to model a population growth function?In order to model the population growth first find the value of the growth rate then substitute it into the expression P(t) = P₀(1 + r)^t.
Now, the value of P₀ can be found for t = 0 and thus the function is obtained.
The given problem can be solved as follows,
(a) The population of fox in year 2000 is given as 25800.
And, the growth rate is 4%.
Suppose t = 0 for year 2000.
And for some value of t, the population is P(t).
Now, the following expression for the population can be written as,
P(t) = P₀(1 + r)^t
Where P₀ is the population at the year 2000.
Thus, the expression can be written as,
P(t) = 25800(1 + 4/100)^t
(b) In the year 2008, the value of t is 8.
Substitute t = 8 in the expression of the population to get,
P(t) = 25800(1 + 4/100)^8
⇒ 25800 × 1.37
⇒ 35346
Hence, the function that models the population and the estimated population for year 2008 are given as P(t) = P₀(1 + r)^t and 35346 respectively.
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4
BOOKMARK
Simplify each of the following expressions:
-5 - 2 + 8 =
Answer:
1
Step-by-step explanation:
-5 -2=-7
Keep in mind that negative is below zero. by adding eight we have reach 1 point to the right of zero. Thus, explaining tha answer of positive 1.
-7+8=1
Final Answer: 1
A hypothesis test is used to test a claim. On a right-tailed hypothesis test with a 1.6257 critical value, the collected sample's test statistic is calculated to be 1.3994. Which of the following is the correct decision statement for the test?
a. Claim the null hypothesis is true
b. Claim the alternative hypothesis is true
c. Reject the null hypothesis
d. Fail to reject the null hypothesis
The correct part is (d) i.e. Fail to reject the null hypothesis.
What is hypothesis testing?
By evaluating whether or not the observed test statistic is more extreme than would be anticipated if the null hypothesis were true, the critical value approach determines whether something is "likely" or "unlikely." This means that the alternative hypothesis is accepted in place of the null hypothesis when the observed test statistic is more extreme than a cutoff number, known as the "critical value." The null hypothesis is not disproved if the test statistic does not deviate significantly from the crucial value.
Here, The critical value is 1.6257 and the sample's test statistic value is 1.3994.
We can see that the sample's test statistic value is not extreme as the critical value, So the null hypothesis should not be rejected.
Hence, It fails to reject the null hypothesis.
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Determine if the expression 7 y-6 y²-y⁵ is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.
The given expression ______ a polynomial.
Since the Polynomial has three non zero terms then the type of the polynomial is Trinomial
What are Polynomials?
A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
Solution:
Yes the mentioned Ploynomial
7y - 6y² - y^5 is a Polynomial
Since the Polynomial has three non zero terms then the type of the polynomial is Trinomial
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It says my answer is correct over a part of the domain of the integrand, but undefined on another part of the domain. Entered Answer 3*In(\n(7*x))+C
Preview Message 3 ln(ln(7x)) +C
Your answer is correct over part of the domain of the integrand, but is undefined on another part of the domain Evaluate the indefinite integral: 1 x In (18) 3 dx x In(7x) = 3*ln[In(7x)]+C
Answer:
3 ln(abs ln(7x)) +C
Step-by-step explanation:
Do not forget to add the absolute value!
State the third congruence that must be given to prove that △ ≅ △, using the indicated postulate or theorem. Select the two corresponding sides or angles that must be congruent.
(Explanation would be appreciated!)
Answer:
<A ≅ <X
<B ≅ <Y
Method
AAS Congruence Theorem
Step-by-step explanation:
Please solve the question in Image
Answer:
y(0.1) = 0.05, y(0.2) = 0.09
what is modified Euler method?Modified Euler's method is a numerical method used to solve ordinary differential equations (ODEs). It is a variation of Euler's method that is more accurate than the original, but still relatively simple to implement. It works by taking a single iteration of the Euler method, then using the midpoint between the current and previous points to calculate the next point in the sequence. This is done in order to reduce the error.
Solution
We have, y(0) = 0
dy/dt = 1 – y
h = 0.1
Using modified Euler's method,
y(0.1) = y(0) + (1/2) h (f(t0, y0) + f(t0 + h, y0 + hf(t0, y0)))
= 0 + (1/2) (0.1) [(1 - 0) + (1 - 0 + 0.1)]
= 0.05
Similarly,
y(0.2) = 0.1 + (1/2) (0.1) [(1 - 0.05) + (1 - 0.1 + 0.1)]
= 0.0975
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which of the following assets is not an example of a fixed asset for a manufacturer of road building equipment? group of answer choices employee parking lot production equipment for assembling engines shipping area for finished goods and receiving area for component parts cans of yellow paint for refurbishing equipment warehouse building for storing finished equipment
The following assets is not an example of a fixed asset for a manufacturer of road building equipment is " cans of yellow paint for refurbishing equipment warehouse building for storing finished equipment " .
Given :
which of the following assets is not an example of a fixed asset for a manufacturer of road building equipment group of answer choices employee parking lot production equipment for assembling engines shipping area for finished goods .
What is fixed asset ?
A fixed asset is a long-term tangible property or piece of equipment that a company owns and uses in its operations to generate income.
It is clear that the paints cans cannot a property so it is not an example of fixed assets .
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The height y (in feet) of an arrow t seconds after it is shot from a bow can be modeled by the function y=-16t² + 112t + 2.
a. Write the function in vertex form.
Y
b. Find the maximum height of the arrow.
The maximum height of the arrow is
feet.
c. How long does it take the arrow to hit the ground? Round your answer to the nearest second.
It takes about seconds for the arrow to hit the ground.
a) The function in vertex form is; y = -16(x - 3.5)² + 198
b) The maximum height if the arrow is; 198 feet
c) The time that it takes the arrow to hit the ground is; 16 seconds
How to write the quadratic equation in vertex form?We are given the function as;
y = -16t² + 112t + 2.
where;
y is the height (in feet) of an arrow
t is the time in seconds after it is shot from a bow
This is the equation of a vertical parabola open downward
The vertex is a maximum
The general form of a quadratic equation in vertex form is;
y = a(x - h)² + k²
where (h, k) is the vertex coordinate
a) y = -16t² + 112t + 2
This is in standard form and using completing the square, we can write in vertex form as;
y = -16(x - 3.5)² + 198
b) The vertex is the point (3.5, 198)
The maximum height of the arrow represents the y-coordinate of the vertex of the function
Thus, the maximum height of the arrow is 198 feet
c) We know that when the arrow hits the ground, the value of y is equal to zero. Thus, at y= 0, we have;
-16(x - 3.5)² + 198 = 0
Rearranging gives;
(x - 3.5)² = (198/16)
(x - 3.5) = ±√(198/16)
(x - 3.5) = ±12.375
x = 12.375 + 3.5
x = 15.875 ≈ 16 seconds which is the time it will take to hit the ground.
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Really need help on this
We need to see how far the figure has moved in translation and directions and angles in rotational transformation.
What is transformation?
A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.
Given is a triangle ABC,
In translation transformation, the original image is congruent to the transformed one hence, we need to see how far the shape has moved to the left or right and how many it has moved up or down.
In rotational transformation, the original figure is not necessarily congruent to the image hence, we need to see direction (clockwise CW or counterclockwise CCW) angle in degrees and Center point of rotation (turn about what point)
Hence, we need to see how far the figure has moved in translation and directions and angles in rotational transformation.
Learn more about transformation;
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What is the equation of a line that is parallel to -3x + 4y = 4 and passes through the point (4, 0)?
Enter your answer as a slope intercept equation (y=mx+b) in the box.
Answer:
y = [tex]\frac{3}{4}[/tex] x - 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + b ( m is the slope and c the y- intercept )
given
- 3x + 4y = 4 ( add 3x to both sides )
4y = 3x + 4 ( divide through by 4 )
y = [tex]\frac{3}{4}[/tex] x + 1 ← in slope- intercept form
with slope m = [tex]\frac{3}{4}[/tex]
• Parallel lines have equal slopes , then
y = [tex]\frac{3}{4}[/tex] x + b ← is the partial equation of the parallel line
to find b substitute (4, 0 ) into the partial equation
0 = 3 + b ⇒ b = 0 - 3 = - 3
y = [tex]\frac{3}{4}[/tex] x - 3 ← equation of parallel line