Answer:
Step-by-step explanation:
The correct definition of perpendicular lines is option 1: "Two lines that intersect in a way that forms right angles."
When two lines intersect to form four right angles (90-degree angles), they are said to be perpendicular to each other. The point at which the lines intersect is called the point of intersection.
Therefore, option 1 is the correct definitation of perpendicular lines.
Answer: 1. Two lines that intersect in a way that forms right angles.
Step-by-step explanation:
Hope this helped! :)
The sides of a square are increased
by a scale factor of 3. The area of
the larger square is what percent of
the area of the smaller square?
So the area of the larger square is 900% of the area of the smaller square.
What is area?Area is a measure of the size of a two-dimensional surface or region. It is typically expressed in square units, such as square meters (m²) or square feet (ft²). To find the area of a shape, you need to measure the length and width of the surface or region and then multiply those measurements together.
Here,
If the sides of a square are increased by a scale factor of 3, then the new square will have sides that are 3 times as long as the original square. The area of a square is proportional to the square of its sides, so the area of the new square will be 3² = 9 times as large as the area of the original square. Therefore, the area of the larger square is 900% of the area of the smaller square.
Alternatively, we can use the formula for the area of a square, A = s², where A is the area and s is the side length. If the side length is increased by a scale factor of 3, then the new side length is 3s. Therefore, the area of the new square is:
A' = (3s)²
= 9s²
The ratio of the area of the new square to the area of the original square is:
A' / A = (9s²) / (s²)
= 9
Multiplying by 100% to convert to a percentage, we get:
A' / A = 900%
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On the map, , the distance is represented by a scale of 1:5000. If the distance between two buildings is shown as 3 cm on the map, then what is the actual distance between the two buildings in meter?
HELP ME PLEASE!!!!!!!!!!
Anyways, I can only offer 10 points!
The total distance between the buildings is 150 meters. In the event a map placed one is to 5000 scales then it projects one unit on the map represents 5000 units in the actual world.
We can apply this ratio to alter the distance on the map to the actual distance between the buildings or objects in the given case that the distance is shown as 3 centimeters then the actual distance in meters is followed 1 centimeter on the map represents 5000 centimeters in the real world.
1 cm on the map = 5000 cm in the actual world
3 cm on the map = (3 x 5000) cm in the actual world
= 15000 cm in the actual world
To alter cm to meters, we need to can apply division by 100 since there are 100 cm in a meter. So, the actual distance between the two buildings is:
15000 cm / 100 = 150 meters
The real distance between the two buildings is 150 meters.
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In ΔSTU, t = 260 cm, u = 850 cm and ∠S=166°. Find the area of ΔSTU, to the nearest square centimeter.
Answer:
1,110
Step-by-step explanation:
it's that because I added it all up in got thatv
I need assistance please.
Your Assignment
Mr. Paulsen challenges Olivia and Angelica to move figure ABCDE onto figure A"B"C"D"E" using a series of two different transformations. They give two different answers.
Answer the questions to investigate ways to transform ABCDE.
1. Olivia finds a combination of two different transformations that moves ABCDE onto A"B"C"D"E". What is one way she might have done this? (3 points)
2. Angelica reflects ABCDE over the y-axis and translates it up 8 units. Does her transformed figure match A"B"C"D"E"? If not, describe how her transformed figure compares to A"B"C"D"E". (3 points)
3. Michael says he can move ABCDE onto A"B"C"D"E" with one transformation by translating ABCDE diagonally so that it moves 8 units up and 10 units right. Is he correct? Explain why or why not. (4 points)
Olivia could have used a combination of a rotation and a translation to move ABCDE onto A"B"C"D"E".
Angelica's transformed figure will not match A"B"C"D"E" because reflecting ABCDE over the y-axis will change the order of the letters in the figure.
No, Michael is not correct.
How to explain the transformationTranslating ABCDE diagonally by 8 units up and 10 units right will move each point in ABCDE the same distance horizontally and vertically, which will change the shape of the figure.
In order to match A"B"C"D"E", the transformation must preserve the order of the letters and the angles between the segments.
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What is the mean of 10, 10, 9, 9, 10, 8, 9, 10, 8, 0
Answer:
83
Step-by-step explanation:
Add them all together and then divide by 10 (which is the number of digits there are)
Answer:9.125
Step-by-step explanation:
Find the inequality represented by the graph.
The inequality represented by the given graph as required to be determined in the task content is; y ≥ 0.5x.
Which inequality is represented by the given graph?It follows from the task content that the inequality which is represented by the given graph is required to be determined.
By observation; the slope of the border line is; 0.5 and the y-intercept is; 0.
Ultimately, the corresponding equation to the border line is; y = 0.5x.
Hence, since the region above the line is shaded and the line is a solid line; the required inequality is; y ≥ 0.5x.
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A lottery game contains 28 balls numbered 1
through 28. What is the probability of choosing
a ball numbered 29?
The probability of choosing a ball numbered 29 is among the 28 balls numbered 1 through 28 is 0
Probability: Calculating the probability of choosing a ballFrom the question, we are to calculate the probability of choosing a ball numbered 29
From the formula for probability
P(A) = Number of favorable outcomes to A / Total number of possible outcomes
From the given information,
"A lottery game contains 28 balls numbered 1 through 28"
This means there are only 28 balls and they are numbered from 1, 2, 3, up until 28.
Now,
We are to determine the probability of choosing a ball numbered 29. Since there is no ball numbered 29,
Number of favorable outcomes = 0
Total number of possible outcomes = 28
Thus,
Probability of choosing a ball numbered 29 = 0/28
Probability of choosing a ball numbered 29 = 0
Hence,
Probability of choosing a ball numbered 29 is 0
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Which of the following explains why this inequality is true?
7 3/8 × 4/5 < 7 3/8
The answers I have to choose from are:
A. When 7 3/8 is multiplied by a number greater than 1, the product is more than 7 3/8
B. When 7 3/8 is multiplied by a number greater than 1, the product is less than 7 3/8
C. When 7 3/8 is multiplied by a number less than 1, the product is more than 7 3/8
D. When 7 3/8 is multiplied by a number less than 1, the product is less than 7 3/8.
The correct option is B: The result of multiplying 7 3/8 by a number larger than 1 is less than 7 3/8.
Explain about the term mixed fractions:Once kids have a firm grasp on right fractions, they are exposed to mixed numbers and improper fractions.
Divide the numerator and denominator to create a mixed fractions from an incorrect fraction. The solution to this problem is the whole number portion; the leftover portion is the numerator; its denominator stays the same.
We can convert the two fractions to decimal form in order to compare them.
7.375 is equivalent to 7 3/8, and
4/5 is equivalent to 0.8.
7.375 multiplied by 0.8 results in:
7.375 × 0.8 = 5.9
Since the result is 5.9, which is less than 7.375, it follows that 7 3/8 multiplied by 4/5 is less than 7 3/8.
Thus, the result of multiplying 7 3/8 by a number larger than 1 is less than 7 3/8.
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Josh is looking for the best deal on a refrigerator that has a wholesale price of $549. Help him compare the price of the
refrigerator at two different stores by completing the following.
(a)
(b)
Josh then looks at the refrigerator in a department store that marks up the refrigerator's wholesale price 50%. But
because of a customer loyalty program, he would receive a 10% discount off the in-store price. Ignoring tax, how
much would he pay for the refrigerator at this store?
(c)
Josh goes to a superstore that marks up the refrigerator's wholesale price 40%. Ignoring tax, how much would he
pay for the refrigerator at this store?
$0
Check
Select the true statement.
O Josh would pay more for the refrigerator at the superstore.
O Josh would pay more for the refrigerator at the department store.
O Josh would pay the same amount for the refrigerator at the department store and at the superstore.
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b) Josh would pay $741.15 for the refrigerator at the department store with 10% discount.
c) The true statement is: Josh would pay more for the refrigerator at the superstore.
(b) If the department store marks up the wholesale price of the refrigerator by 50%, then the price at the store would be:
Wholesale price + (50% x Wholesale price) = $549 + (0.5 x $549) = $823.50
If Josh would receive a 10% discount off the in-store price, then the price he would pay would be:
In-store price - (10% x In-store price) = $823.50 - (0.1 x $823.50) = $741.15
(c) If the superstore marks up the wholesale price of the refrigerator by 40%, then the price at the store would be:
Wholesale price + (40% x Wholesale price) = $549 + (0.4 x $549) = $768.60
Therefore, Josh would pay $768.60 for the refrigerator at the superstore.
Comparing the prices, we can see that Josh would pay less for the refrigerator at the department store after factoring in the discount:
Price at department store = $741.15
Price at superstore = $768.60
So the true statement is: Josh would pay more for the refrigerator at the superstore.
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Determine the line of Reflection. A(-3,3) B(-3,6) C(1,6) D(1,3) E(-1,1); A'(-5,3), B(-5,6), C(-9,6), D(-9,3) E(-7,1)
The line of reflection is the vertical line passing through (-5, 6), (-9, 6), (-9, 3), and (-7, 1).
What is line of reflection?A line of reflection is a line that acts as a mirror, reflecting a figure across it. Each point on the original figure is reflected over the line and the resulting image is the same size and shape as the original, but appears to be "flipped" or "mirrored" across the line of reflection. The line of reflection is the perpendicular bisector of the segment connecting each point on the original figure to its corresponding point on the reflected image.
In the given question,
To determine the line of reflection, we need to find the perpendicular bisector of each line segment between the point and its image.
First, we find the midpoint of the line segment between A and A': (A + A')/2 = (-3 + (-5))/2, (3 + 3)/2 = (-4, 3)
The perpendicular bisector of the line segment AA' is a vertical line passing through (-4, 3).
Similarly, we find the midpoints and perpendicular bisectors of the line segments BB', CC', DD', and EE'.
The perpendicular bisectors of the line segments BB', CC', DD', and EE' are also vertical lines passing through (-5, 6), (-9, 6), (-9, 3), and (-7, 1), respectively.
Therefore, the line of reflection is the vertical line passing through (-5, 6), (-9, 6), (-9, 3), and (-7, 1).
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The table shows the finishing times for each of the four swimmers on the men’s 100 meter freestyle relay US Olympic team in 2008. The team’s average time is 47 seconds. Estimate the team’s finishing time, in seconds, using cluster estimation.
Using cluster estimation, the team's finishing time is 188 seconds.
How to get the team's finishing time?We are given that the Team's average time is 47 seconds which means all players finishes in 47 seconds.
The Cluster Estimation means a method used to estimate sum & product when the numbers that we are adding or multiplying cluster near to a same number .
Here, all given time cluster near to the average time i.e., 47 seconds.
So, the team's finishing time will be:
= 47 + 47 + 47 + 47
= 4 × 47
= 188 seconds
Therefore, the team's finishing time is 188 seconds.
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The students in Mr. Anderson's class are growing bean plants from seeds. The heights of the plants are measured after 7 days and recorded in the histogram below.
The average height of the bean plants in Mr. Anderson's class after 7 days is approximately 7.41 centimeters.
How to solveHeight (in centimeters) Frequency
0 - 3 | 5
4 - 6 | 10
7 - 9 | 15
10 - 12 | 7
13 - 15 | 3
To find the average height, we can follow these steps:
Determine the midpoint of each height range.
Multiply the midpoint of each range by the frequency.
Add up the products from step 2.
Add up the frequencies.
Divide the sum from step 3 by the sum from step 4.
Step 1: Determine the midpoint of each height range.
Height Range Midpoint
0 - 3 | 1.5
4 - 6 | 5
7 - 9 | 8
10 - 12 | 11
13 - 15 | 14
Step 2: Multiply the midpoint of each range by the frequency.
Height Range Frequency Midpoint Midpoint x Frequency
0 - 3 | 5 | 1.5 | 7.5
4 - 6 | 10 | 5 | 50
7 - 9 | 15 | 8 | 120
10 - 12 | 7 | 11 | 77
13 - 15 | 3 | 14 | 42
Step 3: Add up the products from step 2.
7.5 + 50 + 120 + 77 + 42 = 296.5
Step 4: Add up the frequencies.
5 + 10 + 15 + 7 + 3 = 40
Step 5: Divide the sum from step 3 by the sum from step 4.
296.5 / 40 = 7.4125
The average height of the bean plants in Mr. Anderson's class after 7 days is approximately 7.41 centimeters.
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The students in Mr. Anderson's class are growing bean plants from seeds. The heights of the plants are measured after 7 days and recorded in the histogram below.
What is the average height of the bean plants in Mr. Anderson's class after 7 days?
Below is a model of the athletic field at IDEA Brentwood what is the area in square yards
The area in square yards of the athletic field at IDEA Brentwood would be 170. 24 yards ²
How to find the area ?The shape of the athletic field at IDEA Brentwood is shown to be a rectangle with two semi - circles attached.
The area of the athletic field at IDEA Brentwood is the sum of the areas of these shapes.
Area of rectangle :
= 15 x 8
= 120 yards ²
The area of the two semi - circles would be:
= π x radius x radius
= π x ( 8 / 2 ) x ( 8 / 2 )
= 50. 24 yards ²
The area of the athletic field at IDEA Brentwood is :
= 50. 24 + 120
= 170. 24 yards ²
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A 52 foot ladder is set against the side of a house so that it reaches up 48 feet. If Jevonte grabs the ladder at its base and pulls it 3 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 45 ft.) Round to the nearest tenth of a foot
The ladder will reach up the side of the house to a height of approximately 47.1 feet.
We can use the Pythagorean theorem to solve this problem. Let x be the distance between the base of the ladder and the house after Jevonte pulls the ladder 3 feet farther from the house. Then, we have a right triangle with legs x and 48 feet, and hypotenuse 52 feet (the length of the ladder).
Using the Pythagorean theorem, we have:
x² + 48² = 52²
Simplifying, we get:
x² + 2304 = 2704
x² = 400
x = 20
Therefore, Jevonte pulls the ladder 3 feet farther from the house, so the ladder is now 23 feet away from the house. The ladder will reach up the side of the house to a height of:
√(52² - 23²) = 47.1 feet (rounded to the nearest tenth)
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If the terminal point of 0 is (0, -1), what is tan 0?
A. Undefined
B. 1
C. -1
D. 0
If the terminal point of θ is (0, -1) then tanθ is undefined.
The point (0, -1) lies on the negative y-axis.
Since the tangent function is defined as the ratio of the opposite side to the adjacent side of a right triangle, and the adjacent side is zero for any point on the y-axis, the tangent of θ is undefined.
Therefore, if the terminal point of θ is (0, -1) then tanθ is undefined.
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how many flowers spaced every 6 inches are needed to surround a circular garden with a 18-foot radius?
The number of flowers needed is 226
What is circumference of a circle?The circumference is the perimeter of a circle or ellipse. The circumference is the outer body of a circle and it can also be called perimeter of a circle.
The circumference of a circle is expressed as!
C = 2πr , where r is the radius.
the radius of the garden is 18ft
C = 2 × 3.14 × 18
C = 113.04
This means the perimeter of the garden is 113.04
For a space of 6 inches, the flower needed is calculated as;
113.04 × 12/6 ( since 1 foot is 12 inches)
= 113.04 × 2
= 226 flowers ( nearest whole number)
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Calculate the net profit margin for boots sold for $80 that have a cost of $30 cost of goods sold and 20% operating expenses
The net profit margin for the boots is 42.5%.
How to calculate the net profit margin?Net profit margin is the measure of how much profit is generated as a percentage of revenue. It is the ratio of net profits to revenues.
Revenue from selling the boots is $80.
Total expenses = cost + operating expenses
The cost is $30, and the operating expenses is 20% of the revenue. That is:
2/100 * $80 = $16.
Total expenses = $30 + $16 = $46
net profit = $80 - $46 = $34
Net profit margin = (Net profit / Revenue) * 100
= (34 / 80) * 100
= 42.5%
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Rectangular prisim was 5mm tall, 40mm long and 20mm wide. Wjat is the answer
The surface area of the rectangular prism is 2200 square mm
What is the surface area of the rectangular prism?From the question, we have the following parameters that can be used in our computation:
Dimensions = 5 mm by 40 mm by 20 mm
The surface area of the rectangular prism is calculated as
Area = 2 * (5 * 40 + 5 * 20 + 40 * 20)
Evaluate
Area = 2200
Hence, the area is 2200 square mm
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In problem # 14 solve for y.
The required value of y is 14 units for the given right triangle.
14. It is required to find the value of y.
According to the attached figure, we have a right triangle that has:
Length of AB = x units
Length of BC = 7 units
Length of AC = y units
∠ABC = 90°
∠BAC = 30°
As per the sine ratio, it can be written as follows:
sin 30° = BC/ AC
1/2 = 7/y
Apply the cross-multiplication, and we get
y = (7)(2)
y = 14 units
Therefore, the required value of y is 14 units for the given right triangle.
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Which is a recursive formula for this geometric sequence?
-18
, -14
, -12
, -1, . . .
The recursive formula for the geometric sequence is given as follows:
[tex]a_1 = -\frac{1}{8}[/tex][tex]a_n = 2a_{n - 1}[/tex]What is a geometric sequence?A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.
The first term of the sequence is given as follows:
[tex]a_1 = -\frac{1}{8}[/tex]
Each term is the previous term multiplied by two, hence the common ratio is given as follows:
q = 2.
Then each term is the previous term multiplied by two, and the recursive rule is given as follows:
[tex]a_n = 2a_{n - 1}[/tex]
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1. Josh said that the square root of 100 is a perfect square and a perfect cube. Is Josh correct? Explain your reasoning.
Josh is incorrect because 100 is perfect square not a perfect cube.
We have the number 100.
Now, factorising the number 100 as
100 = 2 x 2 x 5 x 5
100= (2 x 5) x ( 2x 5)
100 = 10 x 10
As, 100 can be factorised as 10 x 10 which shows 100 is prefect square of 10.
But 100 is not a perfect cube because for the cube we need pair of three number.
Thus, Josh is incorrect.
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Please help me with this please
The subtraction of the two matrix is [31 6 12 -14 57 ]
[-19 -27 -18 18 27 ]
[ 47 14 -1 -40 9 ]
[10 12 -19 -15 -58]
[-14 -23 10 4 19]
What is the matrix subtraction?The subtraction of the two matrix is calculated as follows;
The result to 4 multiplied by D is calculated as;
4[D] = [28 -24 12 -32 -36]
[8 -36 -24 24 36]
[32 8 20 -40 -12]
[40 -12 -16 12 - 28]
[4 -8 16 -20 -8 ]
The result to 3 multiplied by B is calculated as;
3[B] = [-3 -30 -24 -18 21]
[27 -9 -6 6 9]
[-15 -6 21 0 -21]
[30 -24 3 27 30]
[18 15 6 -24 -27]
The subtraction of the two matrix is calculated as follows;
4[D] - 3[B] = [31 6 12 -14 57]
[-19 -27 -18 18 27 ]
[ 47 14 -1 -40 9 ]
[10 12 -19 -15 -58]
[-14 -23 10 4 19]
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Find the Taylor polynomial T3(x) for the function f centered at the number a.
f(x) = e^x, a = 1
The Taylor polynomial T3(x) for the function f centered at the number a.
f(x) = e^x, a = 1 is
[tex]T3(x0 = e + e(x-1) + e(x-1)^ 2/2 + e(x-1)^3/6[/tex]
How do we calculate?A polynomial is described as an expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.
The Taylor polynomial of degree n for a function f(x) centered at a is given by the formula:
[tex]pn(x)=f(c)+f′(c)(x−c)+f′′(c)2!....[/tex]
In this formula, f'(1), f''(1), f'''(1), and f^(n)(1) are the first, second, third, and nth derivatives of f(x), respectively, evaluated at a.
The symbol n! denotes the factorial of n, which is the product of all positive integers from 1 to n.
In the scenario above, we are given the function f(x) = e and a = 1.
The first derivative of e^x is e^x,
the second derivative is e^x,
and the third derivative is also eˣ.
We then evaluate these derivatives at a = 1, we get:
f(1) = e¹ = e
f'(1) = e¹ = e
f''(1) = e¹ = e
f'''(1) = e¹ = e
We substitute these values into the formula for the Taylor polynomial, and simplify to get Taylor polynomial T3(x) for the function:
[tex]T3(x0 = e + e(x-1) + e(x-1)^ 2/2 + e(x-1)^3/6[/tex]
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Write two numbers that multiply to the value on top and add to the value on bottom.
8
8
−
6
−6
×
×
+
+
Help please Jared uses two theorems together to make a conjecture about the sum of the interior angles of pentagons. What kind of reasoning is Jared using?
A)Inductive Reasoning
B)Deductive Reasoning
If Jared uses two theorems together to make a conjecture about the sum of the interior angles of pentagons, Jared is using deductive reasoning. Correct option is B.
Deductive reasoning is a logical process in which a conclusion is reached by applying general principles or known information to specific situations. In this case, Jared is using two theorems, which are general principles that have been proven to be true, to make a conclusion about a specific situation, the sum of interior angles of pentagons.
The conclusion that Jared makes is a conjecture, which is a hypothesis or a tentative conclusion that is based on limited evidence or observation.
In contrast, inductive reasoning is a logical process in which a conclusion is reached based on a series of observations or specific instances. Inductive reasoning involves making generalizations based on specific observations, which can lead to a hypothesis or a theory.
Therefore, Jared's use of two theorems to make a conclusion is an example of deductive reasoning. Correct option is B.
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Find the side lengths of each triangle.
Answer:
9) 36 36 and 36 (all three sides equal)
10) 3.1 3.1 and 3.3 (two sides equal)
Step-by-step explanation:
#9
This is an equilateral triangle so all three sides are equal
Expressions for two of the sides are 6y and 4y + 12
Set these expressions equal to each other and solve for y:
6y = 4y + 12
6y - 4y = 12
2y = 12
y =6
So the side with expression 6y becomes 6 · 6 = 36
Since it is an equilateral triangle, each of the three sides is 36
#10
This is an isosceles triangle with side 2x + 1.7 = x + 2.4
Solve for x:
2x + 1.7 = x + 2.4
2x - x = 2.4 - 1.7
x = 0.7
So the side with x + 2.4 = 0.7 + 2.4 = 3.1 same as the side with 2x + 1.7
The third side with 4x + 0.5 = 4(0.7) + 0.5 = 2.8 + 0.5 = 3.3
So the sides of this triangle are 3.1, 3.1 and 3.3
please help me with this problem
Answer:
X = 81
Y = 729
Step-by-step explanation:
Basically I simplified each expression by making both logarithms as one then converting it from logarithm to exponential (I hope you know how to do it, you must).. I then obtained 2 final equations labeled as equation 1 and equation 2. From there on its just Maths but I hope you understand what I did
Oak and Maple streets are parallel to each other. Main Street has a traffic
light at (5, 1) and is perpendicular to Oak and Maple. What is the equation
of the line representing Main Street?
Oak St.: y =
A. Y
1
22
+3 Maple St.: y = 22
C. y = -2x + 11
B.y=2x-9
D. y = -2x + 15
+6
The equation of the line representing Main Street is option C. y = -2x + 11
How did we arrive at this equation?The slope of the parallel lines is ½. The Main Street is perpendicular to Oak and Maple. So, the slope of Main Street is -2.
[The product of slopes of perpendicular Lines is -1.)
y - 1 = -2 (x -5)
y - 1 = -2x +10
y = -2x + 10 + 1
y = -2x + 11
Therefore, the best choice is option C. y = -2x + 11
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Since Main Street is perpendicular to Oak and Maple, its slope will be the negative reciprocal of the slope of Oak and Maple. Let's first find the equation of Oak Street.
We don't have enough information to determine the equation of Oak Street, so we need to make an assumption about its equation. Let's assume that Oak Street passes through the point (0,3) and has a slope of 2 (since the options suggest that Oak Street has a positive slope).
Using the point-slope form of a line, we have:
y - 3 = 2(x - 0)
y - 3 = 2x
y = 2x + 3
Now we can find the slope of Maple Street by noticing that it is parallel to Oak Street. Since parallel lines have the same slope, Maple Street also has a slope of 2.
To find the equation of Main Street, we need to use the fact that it passes through the point (5,1). Using the point-slope form of a line, we have:
y - 1 = -1/2(x - 5)
y - 1 = -1/2x + 5/2
y = -1/2x + 7/2
Therefore, the equation of the line representing Main Street is y = -1/2x + 7/2. The answer is (D).
Geometry simplifying square roots
(2/√3) can be rationalized by multiplying both the numerator and the denominator by √3 to get (2√3/3) .
What is mean by Square root and how to find it ?The square root is the value that gives a prime number multiplied by itself. Four methods can be used to find the square root: prime factorization, repeated subtraction, long division, and the evaluation method.
In geometry, we often encounter the square root when calculating the size of shapes, such as the length, area or volume of certain geometric shapes. Simplifying square roots can make calculations much easier and more efficient.
Here are some rules for simplifying square roots:
Simplify perfect squares under the radical sign: For example, √9 = 3 and √25 = 5. Multiplying or dividing a number outside the radical sign: For example, 2√3 can be simplified to √12. Adding or subtracting like terms: For example, 3√2 2√2 = 5√2.
You can rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator: For example, (2/√3) can be rationalized by multiplying both the numerator and the denominator by √3 to get (2√3/3) .
Applying these rules, we can simplify the square root and make calculations easier and more accurate in geometric problems..
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For the following exercises, convert the angle measures to degrees.
9π/5 b) - π/3
(round to two decimal places)
a) The measure of 9π/5 radians in degrees is approximately 324 degrees.
b) The measure of -π/3 radians in degrees is approximately -60 degrees.
To convert the given angle measures from radians to degrees, we can use the formula:
angle in degrees = (angle in radians) × (180/π)
a) To convert 9π/5 radians to degrees, we can substitute the given value in the above formula as:
angle in degrees = (9π/5) × (180/π) ≈ 324 degrees (rounded to two decimal places)
b) To convert -π/3 radians to degrees, we can substitute the given value in the above formula as:
angle in degrees = (-π/3) × (180/π) ≈ -60 degrees (rounded to two decimal places)
In general, we can convert an angle measure from radians to degrees by multiplying it by 180/π. Since π is an irrational number, the conversion factor 180/π is an irrational number as well. Therefore, when we round the result to two decimal places, we are actually approximating the true value of the angle measure.
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