With a dilation factor of 1 / 4, Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), D(4, 4) would be: A(-1, 1.5), B(-0.5 , 0.5), C(1, -0.5), D(1 , 1). Second option
How to dilate the vertices to scaleThe solution to the problem would be the solution that is gotten when we divide these points by 1/4. This is the dilation factor
we would have:
A(−4, 6), B(−2, 2), C(4, −2), D(4, 4)
= (-4 * 1/4, 6 * 1/4) , B(-2 * 1/4, 2 * 1/4), C(4 * 1/4, -2 * 1/4), D(4 * 1/4, 4 * 1/4)
= A(-1, 1.5), B(-0.5 , 0.5), C(1, -0.5), D(1 , 1)
Hence the second option is correct.
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Answer:A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1).
Step-by-step explanation:
To dilate a point using a scale factor, you multiply both the x-coordinate and the y-coordinate of the original point by the scale factor.
Given the original vertices of the polygon ABCD and a scale factor of one fourth (1/4), we can find the coordinates of the dilated vertices A', B', C', and D':
Original vertex A(-4, 6):
x-coordinate of A': -4 * 1/4 = -1
y-coordinate of A': 6 * 1/4 = 1.5
So, vertex A' is (-1, 1.5).
Original vertex B(-2, 2):
x-coordinate of B': -2 * 1/4 = -0.5
y-coordinate of B': 2 * 1/4 = 0.5
So, vertex B' is (-0.5, 0.5).
Original vertex C(4, -2):
x-coordinate of C': 4 * 1/4 = 1
y-coordinate of C': -2 * 1/4 = -0.5
So, vertex C' is (1, -0.5).
Original vertex D(4, 4):
x-coordinate of D': 4 * 1/4 = 1
y-coordinate of D': 4 * 1/4 = 1
So, vertex D' is (1, 1).
Comparing the calculated coordinates with the options given:
A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1)
Among the given options, the correct vertices of polygon A′B′C′D′ are A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1).
A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.
Number of hours Total number of students
0 1
1 3
2 2
3 5
4 9
5 7
6 3
Determine the probability that a student studied for 1 hour.
1.0
0.9
0.3
0.1
the required probability is 0.1
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here: 3 students study for an hour and total students are 30
Thus P(1 hour) =3/30
=0.1
Hence, the required probability is 0.1
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Copy and complete the table of values for y=x²-3x - 2. What numbers replace A, B and C? X Y -1 A 0 1 2 3 B -4 C — 4
The numbers 2, -2, and -2 can replace the letters A, B, and C respectively in the table of values.
What is a table of valuesWe use table of values when we have to graph out a linear equation. We can make use of the table of values to map out the corresponding values of x and y for a given line equation.
For y = x² - 3x - 2:
when x = -1;
y = (-1)² - 3(-1) -2
y = 1 + 3 - 2
y = 4 - 2
y = 2
when x = 0;
y = (0)² - 3(0) -2
y = 0 - 0 - 2
y = -2
when x = 3;
y = (3)² - 3(3) - 2
y= 9 - 9 - 2
y = 0 - 2
y = -2
Therefore, the values 2, -2, and -2 replace letters A, B, and C respectively in the table of values for y = x² - 3x - 2.
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Graph the line that passes through the points (-6, -4) and (-5, -4) and
determine the equation of the line.
Answer:
Step-by-step explanation:
The equation of the line passing through the points [tex](x_{1},y_{1} ) and (x_{2} ,y_{2} )[/tex] is
[tex]y-y_{1}=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}*(x-x_{1} )[/tex]
plug the two points [tex](x_{1},y_{1} )=(-6,-4) and (x_{2} ,y_{2} )=(-5,-4)[/tex] into the equation.
[tex]y-y_{1}=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}*(x-x_{1} )\\y+4=\frac{-4-(-4)}{-5-(-6)} *(x+6)[/tex]
[tex]y-y_{1}=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}*(x-x_{1} )\\y+4=\frac{-4-(-4)}{-5-(-6)} *(x+6)\\y+4=0\\y=-4[/tex]
The equation of line that runs through the points (-6, -4) and (-5, -4) is y = -4.
What is the equation of the line that passes through the points (-6, -4) and (-5, -4)?The slope-intercept form is expresses as;
y = mx + b
Where m is slope and b is y-intercept.
Given that the line that passes through the points (-6, -4) and (-5, -4).
First, we find the slope.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( -4 - (-4) )/( -5 - (-6) )
Slope m = ( -4 + 4 )/( -5 + 6 )
Slope m = ( 0 )/( 1 )
Slope m = 0
Next, find the y-intercept b.
y = mx + b
Plug in slope m = = and point 1( -6, -4 )
-4 = 0(-6) + b
Solve for b
-4 = b
b = -4
Now, plug slope m = 0 and y-intercept b = -4 into the slope intercept form to determine the equation of the line.
y = mx + b
y = 0(x) + -4
y = -4
Therefore, the equation of line is y = -4.
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The price of a suit is reduced by 20%. By what percentage must the reduced price be increased so that the new price is 12% higher than the original price? Show how to use an equation to prove your answer.
Answer:
the reduced price must be increased by 32% to have a 12% higher price than the original price
The percentage that must the reduced in the reduced price so that the new price is 12% higher than the original price is 40%.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Let the price of the suit = 100
Reduced = 20%
Now,
The reduced price of the suit.
= 100 - (20% of 100)
= 100 - (20/100 x 100)
= 100 - 20
= 80 _____(1)
Now,
New price.
= 100 + (12% of 100)
= 100 + 12
= 112
Now,
From (1)
100% = 80
Multiply 112/80 on both sides.
112/80 x 100% = 112
140% = 112
This means,
40% increased
Thus,
40% increase in the reduced price.
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the cost of two star bars is the same as the cost of five toffee knobs . one star bar and one toffee knobs together cost 35 p . what do they each cost ?
Answer:
sorry I posted this question and never got and never got an answer
Out of 30 tudent urveyed, 17 have a dog. Baed on thee reult, predict how many of the 300 tudent in the chool have a dog?
170 out of 300 students in the school own a dog.
A word problem is a short passage presenting a "real-life" situation where an issue has to be solved using math.
Word problems are seen as an essential component of learning in the elementary curriculum because they require students to apply their understanding of various concepts to situations that are representative of "real-life" situations.
Given that,
Total number of students surveyed = 30
Total number of students that own a dog = 17
Total number of students in the school = 300
In order to find the equivalent of 17/30 with the bottom number 300
we get, 10 times of 30 is equal to 300 so based on this,
17/30 times 10/10 = 170/300
Thus, 170 out of 300 students in the school own a dog.
Correct question: Out of 30 students surveyed, 17 have a dog. Based on these results, predict how many of the 300 students in the school have a dog.
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A university's freshman class has 5400 students. 48% of those students are majoring
in Economics. How many students in the freshman class are Economics majors?
The number of students that are majoring in Economics is 2592 whose percentage is 48% of the total.
What is the percentage?
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”.
Examples of percentages are:
10% is equal to 1/10 fraction.20% is equivalent to ⅕ fraction.25% is equivalent to ¼ fraction.Now,
Total students=5400
Percentage of students doing majoring =48%
Hence,
The number of students that are majoring in Economics
=48/100*5400
=2592
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Recall that a reinforcement beam will extend from one trut to the other when the two trut are 2 feet apart. Algebraically determine the x -value of where the beam hould be placed. (15 point)
The x-value of where the beam should be placed is X = (x1+x2)/2.
Given: the distance between the two trusses is 2 feet and the reinforcement beam will extend from one truss to the other.
We can set up an equation using the distance formula to determine the x-value of where the beam should be placed.
The distance formula is: d = √((x2 - x1)² + (y2 - y1)²)
Let's assume that the trusses are located at point (x1, y1) and (x2, y2) and the beam is located at point (x, y).
We know that the distance between the trusses is 2 feet, so we can set d = 2.
We can use the coordinates of the trusses and the point where the beam is located to set up the equation:
d = √((x2 - x1)² + (y2 - y1)²) = 2
Since the trusses are located on the same line and only the x-coordinate changes, we can assume that y1=y2
Therefore the equation can be simplified to √((x2 - x1)²) = 2
Square both sides: (x2 - x1)² = 4
x2 - x1 = 2
Now we know that the difference between the x-coordinates of the two trusses is 2 feet.
So, to find the x-value of the point where the reinforcement beam should be placed, we can take the average of the x-coordinates of the two trusses.
x = (x1+x2)/2
We don't know the values of x1 and x2, so we can't solve for x. But we know that the reinforcement beam should be placed exactly in the middle of the trusses.
Thus, The x-value of where the beam should be placed is X = (x1+x2)/2.
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In the triangle below, suppose that mZS= (x+4)°, mZT= (x+4)°, and mU=(5x-3)°.
Find the degree measure of each angle in the triangle.
(5x - 3)
\-(x + 4)*
m Ls =
m2T =
0
0.
m2U = 0.
X
Ś
The measure of angle S = 29 degrees, angle T= 29 degrees, and angle U = 122 degrees.
What are internal angles?A triangle is a straightforward closed curve made up of three-line segments. An angle inside the form is known as an interior angle. The inner angles add up to a constant 180 degrees.
The sum of internal angle of the triangle is 180 degrees.
(x + 4) + (x + 4) + (5x - 3) = 180
7x + 5 = 180
7x = 175
x = 25
Substitute the value of x in each of the angle to find the measure of each angle as follows:
The value of angle S = x + 4 = 25 + 4 = 29 degrees.
The value of angle T = x + 4 = 25 + 4 = 29 degrees.
The value of angle U = 5x - 3 = 125 - 3= 122 degrees.
Hence, the measure of angle S = 29 degrees, angle T= 29 degrees, and angle U = 122 degrees.
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Please help me answer all of the questions! I'm sorry that it's so much but thank you to whoever helps me.
The surface areas for each of the cylinders are;
1) S = 10178.8 millimeters squared
2) S = 955.0 inches squared
3) S = 157.1 centimeters squared
4) S = 351 square inches
How to find the surface area of a cylinder?The formula for surface area of a cylinder is;
S = 2πr² + 2πrh
1) We are given;
radius; r = 30 mm
height; h = 24 mm
Thus;
S = 2π(30)² + 2π(30*24)
S = 10178.8 millimeters squared
2) We are given;
radius; r = 8 in
height; h = 11 in
Thus;
S = 2π(8)² + 2π(8*11)
S = 955.0 inches squared
3) We are given;
radius; r = 1 cm
height; h = 9 cm
Thus;
S = 2π(1)² + 2π(1*9)
S = 157.1 centimeters squared
4) We are given;
radius; r = 4 in
height; h = 10 in
Thus;
S = 2π(4)² + 2π(4*10)
S = 351 square inches
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Use the summation notation to rewrite the following expression.
1/2! + 2/3! + 3/4! + ...+ n/(n+1)! = [nΣk=1]
[nΣk=1]k/(k+1)! is the notation of the summation .
The summation notation is a compact way of expressing the sum of a series of terms. In this case, the series of terms is the expression "1/2! + 2/3! + 3/4! + ...+ n/(n+1)!" which can be represented using the summation notation as [nΣk=1]k/(k+1)!. It is saying the sum of all k/(k+1)! where k = 1, 2, 3, ...., n. The summation notation consists of three parts, the n, Σ and the k=1. The n represents the upper limit of the summation, the Σ (sigma) represents the summation operator and the k=1 represents the lower limit of the summation.
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Endpoint B is (9,4). The slope of AB is 1/3. Point P is 5/6 the directed path of BA.
A is (_,_) and P is (_,_)
P divides BA in the ratio of _:_
Endpoint A has coordinates (3,12) since the slope of AB is 1/3 and B is (9,4). Point P has coordinates (7,8) since P is 5/6 the directed path of BA.
Point P divides BA in the ratio of 5:6.
What is Ratio?How much of one quantity is in the other can be found by comparing two amounts of the same unit and calculating the ratio. Ratios can be categorized into two groups. Part to part ratio is the opposite of part to whole ratio. A two distinct things or groupings are related to one another as shown by the part-to-part ratio. For instance, the boy-to-girl ratio in a class is 12:15, but the part-to-whole ratio describes how one group of people compares to the total population. For instance, five out of ten people say they like to read. The ratio of the part to the whole is therefore 5: 10, which indicates that 5 out of every 10 people enjoy reading.
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I need help with this asap
The smallest y - intercept for the given equations is, (0, -6).
What is y - intercept?
A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis. This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points satisfy x = 0 because of this.
There are four function are given.
We have to find which function having smallest y - intercept.
Since, to find y - intercept we have to plug x = 0 in each equation.
Consider, the functions
1. g(x) = 2x - 6
Plug x = 0
g(0) = 0 - 6
g(0) = -4
⇒ The y - intercept is (0, -4).
2. f(x) = √x - 2
Plug x = 0
f(0) = 0 - 2
f(0) = -2
⇒ The y - intercept is (0, -2).
3. For 3 we get the equation, y = 2x + 1
Plug x = 0
y = 0 + 1
⇒ The y - intercept is (0, 1).
4. From graph the y - intercept is (0, -2).
Hence, the smallest y - intercept for the given equations is, (0, -6).
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Solve for nnn.
7n-4 = 317n−4=317, n, minus, 4, equals, 31
n =n=n, equals
The value of the variable, n is 5
What is an algebraic expression?An algebraic expression can simply be defined as an expression that is composed of variables, coefficients, factors, constants and terms.
These mathematical expression called algebraic expressions are also composed of arithmetic operations, such as;
BracketMultiplicationAdditionParenthesesDivisionSubtractionExamples of algebraic expressions are;
2x + 18
2x² + 4
3y + 6
From the information given, we have that;
7n - 4 = 31
collect like terms
7n = 31 + 4
Add like terms
7n = 35
Make 'n' the subject of formula
n = 35/7
n = 5
Thus, the value is 5
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Please Help me!!!!!!!!!!!!!!!!!!!!!!
Thank you !!!!!!!!!!!!!!!
Answer:
8 hours
Step-by-step explanation:
The rate at which the candle burns is:
5.5 in/11 hr = 0.5 in/hr
The 4 in candle burns at the same rate. Find the time for a 4 in candle to burn down:
time = (4 in) / (0.50 in/hr) = 8 hr
What is the additive inverse of 4 /- 7?
For the number -(4 / 7), the additive inverse would be (4 / 7).
The additive inverse of a number is the number that when added to the original number, the result is 0. In other words, it is the opposite of the original number.
To see this, let's add -(4 / 7) and (4 / 7) together:
-(4 / 7) + (4 / 7) = 0
This is because the negative sign in front of the fraction indicates that the fraction is the opposite of (4 / 7). So adding the two fractions together cancels out the opposite and results in 0.
In summary, the additive inverse of -(4 / 7) is (4 / 7) because adding the two fractions together results in 0, which is the definition of an additive inverse.
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Divide. Write your answer as a fraction in simplest form. −12÷(−25)
Answer:
4/9 in the simplest form
Step-by-step explanation:
When dividing by a negative number the sign of the quotient changes. so if the quotient is negative when the divisor and dividend have the same sign, it becomes positive when they have opposite sign. In this case -12 and -25 have opposite signs and the quotient will be positive, that's why the negative signs cancel out.
-12 / (-25) = 12/25 = 4/9 in the simplest form
Find the length of the third side. If necessary, write in simplest radical form
By using pythagorean theorem, the length of the third side is 3 unit.
What is simplest radical form?In mathematics, a number or an expression is said to be in its simplest radical form if it has no perfect square factors other than 1. For example, the square root of 12 can be simplified to 2√3 because 2 * 2 * 3 = 12, but 2 and 3 are not perfect squares. So the simplest radical form of √12 is 2√3.
what is pythagorean theorem?
The Pythagorean theorem is a fundamental result in Euclidean geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. It can be written as:
c^2 = a^2 + b^2
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5. Use the scatter plot to answer the question.
A. What grade would someone with 3 missing assignments
have?
B. After how many missing assignments will a student likely
have a zero for an average?
Average Grade
Number of Hissing Assignments
Therefore ,when the problem of expression is solved, we may state that the necessary inequality statement is 4.50x+1.75y 50.
Expression: What is it?An expression in mathematics consists of a statement, two or more variables or integers, but one or more mathematical functions. Numbers can be multiplied, divided, added, or subtracted using this mathematical operation. The construction of an expression is as follows: Expression: Math operator, variable or number, and math operator.
Here,
Cost per assignment is $4.50.
Therefore, "x" assignment cost equals 4.50x.
Cost per assignment: $1.75
Assignment "Y" cost is therefore 1.75Y.
Consequently, the sum of 4.50x+1.75y must be $50 or less.
Therefore, 4.50x+1.75y ≤ 50 is the necessary inequality statement.
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A pool i being drained by a pump at a rate of 4 gallon per minute. An identical pump wa added to help drain the pool. How doe the econd pump affect the rate of drainage?
A pool is being drained by a pump at a rate of 4 gallon per minute, then the second pump affect the rate of drainage = 8 minutes
For two identical pumps in parallel the flow rate doubles compared to single pump,
Single pump flow rate = 4 gallons per minute
When two pump act at same time, drain rate will be double,
Drain rate = 8 gallons per minute
The first pump can drain in 8 minutes, therefore:
Rate of the first pump = 1/8
Working together, they can drain the pool in 4 minutes, therefore:
Rate of both pumps = 1/4
Let the time taken by the second pump =t
Rate of the second pump = 1/t.
So,
We can write,
[tex]\frac{1}{8}[/tex] + [tex]\frac{1}{t}[/tex] = [tex]\frac{1}{4}[/tex]
[tex]\frac{1}{t}[/tex] = [tex]\frac{1}{4} -\frac{1}{8}[/tex]
[tex]\frac{1}{t}[/tex] = [tex]\frac{2-1}{8}[/tex]
[tex]\frac{1}{t}[/tex] = [tex]\frac{1}{8}[/tex]
t = 8 minutes
Therefore,
A pool is being drained by a pump at a rate of 4 gallon per minute, then the second pump affect the rate of drainage = 8 minutes
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What are the 4 problem-solving methods?
Students must possess both the growth mindset necessary for problem-solving and strong reading skills. Some of the problem-solving methods are described.
Define the 4 problem-solving methods?The capacity to solve math word problems is an essential component of math fluency.
Concentrate on using mathematical key words and phrases.
Putting an emphasis on words and phrases is the first step in assisting students with math word problems. For instance, the terms combined or increased by can refer to addition.Mark this sentence for deletion:
Along with underlining crucial words, students should make an effort to separate important information from irrelevant details. Ask your students to cross out the unnecessary distracting information in the problem to help emphasize what is important.Promote Question-Asking:
During the time you give them to read, give them time to ask questions about what they've read. They will learn what to focus on and what to ignore by asking questions.Sketch the issue.
Allowing your students to draw the issue on graph paper is an entertaining way to aid in their understanding.To know more about the problem-solving methods, here
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I need help please please
Answer:
[tex]0.7 \ m/s^2[/tex]
Step-by-step explanation:
Acceleration:From the graph, final speed = 9m/s
initial speed = 2 m /s
Time taken = 10 m
[tex]\sf \boxed{Acceleration=\dfrac{final \ speed - initial \ speed}{time \ taken}}[/tex]
[tex]\sf = \dfrac{9-2}{10}\\\\\\=\dfrac{7}{10}\\\\= 0.7 \ m/s^2[/tex]
The mapping diagram represents a relation where x represents the independent variable and y represents the dependent variable. A mapping diagram with one circle labeled x-values containing values negative 8, negative 5, negative 1, 1, and 12 and another circle labeled y values containing values negative 4 and negative 2 and arrows from negative 8 to negative 4, negative 5 to negative 2, negative 1 to negative 2, 1 to negative 2, 12 to negative 4, and 12 to negative 2. Is the relation a function? Explain. Yes, because for each input there is exactly one output Yes, because for each output there is exactly one input No, because for each input there is not exactly one output No, because for each output there is not exactly one input
Is the relation a function: C. No, because for each input there is not exactly one output.
How to determine the relationships that represent functions?In Mathematics, a function is typically used for uniquely mapping an independent value (input variable or domain) to a dependent value (range or output variable).
This ultimately implies that, an independent value represents the value on the x-axis of a cartesian coordinate while a dependent value represents the value on the y-axis of a cartesian coordinate.
Since the independent value (12) is mapped to multiple dependent values (-4 and -2), we can logically deduce that the relation does not represent a function.
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Which graph shows the solution to the system of linear inequalities?
y≤2x-5
y> -3x + 1
-532
Mark this and return
Save and Exit
Next
Submit
Therefore , the solution of the given problem of inequality comes out to be x > 6/5 and y > -13/5.
What does inequality really mean?In mathematics, an inequality is a linear connection or a collection of numbers even when there is no equal sign. Equity always comes after equilibrium. When two numbers are not equal, inequality exists. Between equality and inequality, there exist differences. The most common symbol was chosen because when parameters aren't the same or comparable (). Values can be compared using a variety of disparities, no matter how few or numerous they are. Many fundamental inequality problems can be addressed by flipping the two aspects until only the variables are left
Here,
Given :
=> y ≤ 2x-5
=> y > -3x + 1
and
=> y ≤ 2x-5
=> 2x - 5 > -3x + 1
=> 2x + 3x > 1 +5
=> 5x > 6
=> x > 6/5
=> y > -3(6/5) + 1
=> y > -18/5 + 1
=> y > -13/5
Therefore , the solution of the given problem of inequality comes out to be x > 6/5 and y > -13/5.
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which angles are vertical angles?
Answer:angle TSQ and angle UVX
Step-by-step explanation:
What is quadratic inequality form?
A quadratic inequality is an equation that takes the form of ax^2 + bx + c ≤ 0 or ax^2 + bx + c ≥ 0, where a, b, and c are real numbers and a is not equal to 0.
Solving Quadratic InequalitiesQuadratic inequalities are used to represent a relationship between two variables and can be used to solve a variety of problems. They can be used to find the maximum or minimum value of a function, or to determine the range of values for which a given equation is true. They can also be used to find the number of solutions to an equation and to compare the values of two functions. Quadratic inequalities are used widely in mathematics and other sciences and can help us to understand and solve many real-world problems.
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In a tournament, a professional golfer knows that she is 200 yards from the hole. A spectator is watching her play and is 140 yards away from the golfer. Triangle with vertices labeled golfer and spectator and hole, with the distance from the golfer to the spectator measuring 140 yards and the distance from the golfer to the hole measuring 200 yards and the vertex of the spectator measuring 120 degrees If the spectator has an angle of 120° between the golfer and the hole, what is the angle that the golfer has between the spectator and the hole?
The angle that the golfer has between the spectator and the hole is cos^-1((a^2 + b^2 - c^2)/(2ab))
How do we determine the angle?The angle that the golfer has between the spectator and the hole can be found using the Law of Cosines. The Law of Cosines states that for a triangle with sides a, b, and c and angle C opposite side c, the following equation holds:
c^2 = a^2 + b^2 - 2ab * cos(C)
In this case, we know that a = 140 (the distance from the golfer to the spectator), b = 200 (the distance from the golfer to the hole), and C = 120 (the angle between the golfer and the spectator).
We can use these values to solve for c, which is the distance from the spectator to the hole. Once we have this value, we can use the Law of Cosines again to find the angle between the golfer and the hole.
c^2 = 140^2 + 200^2 - 2 * 140 * 200 * cos(120)
c = sqrt(140^2 + 200^2 - 2 * 140 * 200 * cos(120))
Now we can use this value of c to find angle A:
A = cos^-1((a^2 + b^2 - c^2)/(2ab))
Note that the angle A is what we're looking for, the angle between the golfer and the hole.
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Find the equation of the linear function represented by the table below in slope-intercept form. x y 1 3 2 5 3 7 4 9
The equation of the linear function represented by the table is y = - x + 2 .
What is linear Equation ?
Linear equation can be defined as the equation in which the highest degree is one.
Given points,
(-1, 3), (1, 1), (3, -1), (5, -3)
Slope-intercept form:
y = mx + b
Finding the slope using slope formula and the first two points:
m = (1 - 3)/(1 - (-1))
= -2 / 2 = -1
Finding y-intercept using the slope and the first point:
3 = (-1)*(-1) + b
3 = 1 + b
b = 3 - 1
b = 2
Hence, The equation of the linear function represented by the table is
y = - x + 2 .
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is a perpendicular bisector of . What is true of any triangle created by points U, V, and any point on other than S
Quick Questions. True or False
1. is nine a factor of 777,777
2. 3 is not a factor of 12,345
3. 245+712 is a multiple of 5
4. 3a+15b is divisible by 3 for any values of a and b
5. 11 is not a factor of 11^3
6. 555 is divisible by three but not by 9
7. 2772 is a multiple of 9 but not of 3
Pls also explain why!!! is that
The statements regarding the multiplicity of the numbers are classified as follows:
1. Nine is a factor of 777,777: False.
2. 3 is not a factor of 12,345: False.
3. 245+712 is a multiple of 5: False.
4. 3a+15b is divisible by 3 for any values of a and b: True.
5. 11 is not a factor of 11^3: False.
6. 555 is divisible by three but not by 9: True.
7. 2772 is a multiple of 9 but not of 3: False.
What are the multiplicity rules?A number is divisible by 9 if the sum of the digits of the number is divisible by 9.
6 x 7 = 42 -> not divisible by 9 -> 9 is not a factor of 777,777.
A number is divisible by 3 if the sum of the digits of the number is divisible by 3.
1 + 2 + 3 + 4 + 5 = 15 -> divisible by 3 -> 3 is a factor of 12,345.
A number is a multiple of 5 if it finishes in either 0 or 5. 245+712 finishes in 7, hence it is not a multiple of 5.
3a+15b is divisible by 3 for any values of a and b, as the factors 3 and 15 are both divisible by 3.
11 is a factor of 11³, as:
11³/11 = 11².
As nine is a multiple of 3, all the multiples of 9 are also multiples of 3.
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