Side angle side formula is used to prove congruent triangles.
What are congruent triangles?
Congruent triangles are triangles that are precisely the same size and shape. The word congruent has a symbol ≅. When the three sides and three angles of one triangle match the same dimensions as the three sides and three angles of another triangle, two triangles are said to be congruent.
Side angle side rule:
The triangles are congruent if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.
There are four rules of congruent triangles.
1) Side angle side
2) Side side side
3) Angle angle angle
4) Angle side angle
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Drag the tiles to the boxes to form correct pairs. Polygon ABCD has sides with these lengths: A B ¯ , 5 units; B C ¯ , 4 units; C D ¯ , 4.5 units; and A D ¯ , 7 units. The slope of A B ¯ is 5, the slope of B C ¯ is 0.25, the slope of C D ¯ is -2, and the slope of A D ¯ is 0. The polygon is dilated from point A by a scale factor of 1.2 to form polygon A′B′C′D′. Match the slopes and lengths of the sides of polygon A′B′C′D′ to their values.
The required match for the dilation of the polygon from ABCD to A'B'C'D',
The slope of A'B' = 5
Length of C'D' = 5.4
Length of A'D' = 8.4
The Slope B'C' = 0.25
The scale factor is defined as the ratio of the modified change in length to the original length.
here,
After the dilation of the polygon from ABCD to A'B'C'D',
The slope of A'B' = 5
[scale dilation does not affect the orientation of geometry.]
Length of C'D' = 5.4 [length of C'D' = 1.2 × CD]
Length of A'D' = 8.4 [length of A'D' = 1.2 × AD]
The Slope B'C' = 0.25
[scale dilation does not affect the orientation of geometry.]
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What is the Area of the Hexagon?
The region included by a hexagon's sides is known as the area of the hexagon.
What is a hexagon?
A hexagon is a two-dimensional shape with six sides, six angles, nine diagonals, and a total of 720 degrees in its inner angles.
The space included within the polygon's sides is referred to as the hexagon's area.
The area of a regular hexagon is calculated using the formula
(3√3s^2)/2, where 's' is the length of a hexagonal side.
The fact that all the sides are the same length should be noted since we are discussing a regular hexagon.
Hence, area of hexagon is the region included by a hexagon's sides.
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choose h and k such that the system has (a) no solution, (b) a unique solution, and (c) many solutions. h k
Choosing h and k in the given system of linear equations such that they they have no solution, a unique solution, and many solutions is determined by the augmented matrix.
The augmented matrix is
[1 h 2
4 8 k].
Reduce matrix to row echelon form
a)We need to determine the values of h and k such that the system has no solution
8 - k =/ 0 and h -2 = 0
Hence, The System has No solution only when h=2, and k not equal to 18.
b)We need to determine the values of h and k such that the system has unique solution when
h - 2 =/ 0
The System has a Unique Solution only when h not equal to 2 and k is any Real number
c)We need to determine the values of h and k such that the system many solution when
8 - k = 0 and h -2 = 0
The system has many solutions only when h=2 and k= 8
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The complete question is :
choose h and k such that the system has (a) no solution, (b) a unique solution, and (c) many solutions. h & k
x1 + hx2 = 2
4x1 + 8x2 = k
for what value of a does 9= [1/27]^a+3?
Note that the value of a for which 9 is equal to the equation (1/27)ᵃ⁺³ is a = -11/3.
What is an equation?An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol "=".
Note that the given equation is:
9 = (1/27)ᵃ⁺³
In order to find the value of a for which both sides of the equation become equal, we can revise the equation as:
9 = 27⁻¹⁽ᵃ⁺³⁾
that is:
3³ = 3⁻³⁽ᵃ⁺³⁾
Because the bases are equal, we can cancel out to derive:
2 = -3(a + 3)
2 = -3a - 9
2+9 = -3a
-3a = 11
a = -11/3
Thus it is correct to state that the value of a for which 9 = (1/27)ᵃ⁺³ is:
a = -11/3.
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within which interval would you expect to find the largest number of observations?
By organizing the data into intervals and counting the frequency of observations, we can identify the range of values in which the most data points are located.
In statistics, an interval is a range of values within which we expect to find a certain amount of observations.
The number of observations within an interval is known as the frequency, and it can be used to determine where the majority of values lie in a data set.
When we are looking for the interval with the largest number of observations, we are trying to find the range of values in which the most data points are located.
In order to do this, we need to first organize the data into intervals, often called bins, and then count the frequency of observations within each bin.
For example, if we have a data set of 100 heights of people, we could create 10 bins with a range of 10 cm each. The first bin would cover the range of heights from 0-10 cm, the second bin from 10-20 cm, and so on. After counting the number of people in each bin, we can easily see which bin has the largest frequency, and therefore the interval with the largest number of observations.
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Tyreick wants to fill six containers
with 3/4 of a cup of lemonade. How
much lemonade will he need to fill
the six containers?
4.5 cups of lemonade is required to fill 6 containers.
Multiplication is a mathematical operation that embodies the fundamental concept of repeated addition of the same integer.
The multiplied numbers are known as the factors, and the outcome of the multiplication of two or more numbers is known as the product of those numbers.
Multiplication is used to make repetitive adding of the same number easier.
As per the data given in the questions,
We have,
To fill one container, Tyreick needs 3/4 of a cup of lemonade.
So, to fill 6 containers, he will need 6 * 3/4 = 4.5 cups of lemonade.
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For positive acute angles A and B, it is known that sin A = 4/5 and tan B = 45/28
Find the value of sin(A + B) in simplest form. Please HELP
Answer:
Step-by-step explanation:
.
For positive acute angles A and B, it is known that sin A= 4/5 and tan B= 45/28 . Find the value of IIT A+B in simplest form. Question. user avatar image ...
the solution of sin(A + B) in simplest form is 27/35.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now, We use the trigonometric identity as;
sin(A + B) = sin A cos B + cos A sin B
Hence, we need to find cos A and cos B.
Here, We know that;
⇒ sin A = 4/5,
By use the Pythagorean identity;
sin²A + cos² A = 1
sin² A + cos² A = 1
(4/5)² + cos² A = 1
16/25 + cos² A = 1
cos² A = 9/25
cos A = 3/5
And, we can use the identity;
tan B = sin B / cos B
to find sin B:
tan B = sin B / cos B
45/28 = sin B / √(1 - sin² B)
(45/28)² = sin² B / (1 - sin² B)
sin² B + (45/28)² sin² B = (45/28)²
sin² B (1 + (45/28)²) = (45/28)²
⇒ sin B = 3/7
Now that we have sin A, cos A, sin B, and cos B,
We can put them into the formula for sin(A + B):
sin(A + B) = sin A cos B + cos A sin B
sin(A + B) = (4/5)(45/28) + (3/5)(3/7)
sin(A + B) = 27/35
Therefore, the solution of sin(A + B) in simplest form is 27/35.
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math ridle a 12 hour clock loses 1 minute every hour suppose it shows the correct time now what is the least number of hours from now when it will again show the correct time?
The least number of hours from now when the clock will again show the correct time is 720 minutes
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
According to the data problem,
The clock will show the correct time again when it lost 12 hours
As every hour it loses 1 minute, the clock have to lose 12 hours in minutes, so we get:
12 hour * (60 minutes / 1 hour) = 720 minutes
Therefore, the least number of hours from now when the clock will again show the correct time is 720 minutes.
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Mason bought 16 tickets to a baseball game. The group rate saved him $5. 75 per ticket. He paid a total of $296. 00 for the tick.
The regular price of a ticket to the game is: $24.25
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
According to the data problem,
Total paid = $296Number of tickets = 16saved per ticket = $5.75Calculating the cost per tickets we get:
Cost per tickets = 296/16 = $18.5
Calculating the regular price we have:
regular price = $18.5 + $5.75 = $24.25
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Correctly written question:
Mason bought 16 tickets to a baseball game. The group rate saved him $5.75 per ticket He paid a total of $296.00 for the tickets. What was the regular price of a ticket to the game?
Geometric Constructions Using Technology Go to https://www.geogebra.org/geometry
The goal for this assignment is to record the process and explanation of 4 geometric constructions using technology.
You can record by using programs such as screencastomatic.com or use your phone to make a video of your computer screen as you use geogebra.
Remember your final constructions should be labeled properly. Your recorded explanation should explain each step of the construction. Also during your explanation be sure to include the difference between a paper/pencil/compass construction and the geogebra technology constructions that you are creating. Assignment will be graded by the rubric below. Reach out to your teacher if you have any questions.
Construct the following 4 geometric constructions using technology:
RUBRIC -10 points
1. Congruent Segments
2. Perpendicular bisector of a segment
3. Congruent Angles
4. Angle Bisector
For congruent segments, the following are required:
Draw a segment using a stylus or mouse on a digital platform such as Geogebra, Cabri, or Sketchpad.Create a copy of the segment using the copy and paste tool or duplicate tool on the platform.Use the measurement tool to verify that both segments have the same length.The segments are congruent if they have the same length.How to explain the constructionPerpendicular Bisector of a Segment:
Draw a segment on a digital platform.Use the midpoint tool to find the midpoint of the segment.Use the perpendicular line tool to draw a line passing through the midpoint and perpendicular to the segment.The perpendicular line is the perpendicular bisector of the segment.Congruent Angles:
Draw two rays that share a common endpoint on a digital platform.Use the angle measurement tool to measure the angles created by the rays.The angles are congruent if they have the same measure.Angle Bisector:
Draw two rays that share a common endpoint and form an angle on a digital platform.Use the angle bisector tool to draw a line that bisects the angle created by the rays.The bisector line divides the angle into two congruent angles.Learn more about geometry in:
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Find the P-value for a right-tailed hypothesis test with a test statistic of z = 1.58. Decide whether to reject the null hypothesis H0 if the level of significance is 0.05. Choose two answers below.
Answers
A. Fail to reject H0
B. 0.943
C. Reject H0
D. 0.114
E. 0.057
Since 0.0493 < 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis.
How to find the P-value for a right-tailed hypothesis test?The P-value for a z-score of 1.58 can be found using a standard normal table or a calculator with a cumulative distribution function. The P-value is the area to the right of the z-score, or in this case, 1 - the area to the left of 1.58.
Using a standard normal table or calculator, we find that the P-value is approximately 0.0493.
If the level of significance is 0.05, we compare the P-value to the significance level. If the P-value is less than the significance level, we reject the null hypothesis (H0), and if it's greater than or equal to the significance level, we fail to reject the null hypothesis.
Since 0.0493 < 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis.
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plplplpllplplpl help asasp
The number of different rectangles with an area of 5 sq cm is 2
How to determine the number of rectanglesFrom the question, we have the following parameters that can be used in our computation:
Area = 5 sq cm
The length of each square box is given as
Length = 1 cm
Assume the box cannot be divided
Then the number of rectangles to draw is 2
This is so because the height of the grid is 5 cm and it cannot take more than 5 cm
Also, because the square boxes cannot represent fractions
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If Gino sold 42 more Red tomatoes then yellow tomatoes last week, how many red tomatoes did he sell?
Answer: x+42
Step-by-step explanation:
If red tomatoes was 42 more than yellow, it would be x=yellow tomatoes, x+42 because we do not know how many yellow tomatoes there are.
you have been hired by an industrial company to lead a project to help improve their custom safety training course. the course is intended to prepare the candidates for a globally recognized certification. to help rate the effectiveness of the course, you create a scatter diagram and compare the hours of preparation (x-axis) with the final score (y-axis) of previous employees. from the diagram, it is determined that there is a negative linear correlation. which conclusion can be made using the data from this chart? answers a. the more time that was used to prepare, the lower the score b. the data is inconclusive; statistical sampling should be used instead c. the amount of preparation time does not directly affect the candidate's score d. the more time that was used to prepare, the higher the score
The conclusion can be made using the data in option A the negative linear correlation means that as the preparation time increases, the final score decreases in a linear pattern.
The conclusion that can be made from the data in the scatter diagram is that the more time that was used to prepare, the lower the score (answer A). The negative linear correlation means that as the preparation time increases, the final score decreases in a linear pattern. This suggests that there may be a relationship between the amount of preparation time and the final score, but further investigation and statistical analysis is needed to confirm this relationship.
Linear correlation refers to the relationship between two variables that can be represented by a straight line on a scatter plot. The relationship between the two variables can be positive, negative, or neutral. Positive linear correlation means that as one variable increases, the other variable also increases in a linear pattern. Negative linear correlation means that as one variable increases, the other variable decreases in a linear pattern. A neutral linear correlation means that there is no relationship between the two variables.
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The conclusion can be made using the data in option A the negative linear correlation means that as the preparation time increases, the final score decreases in a linear pattern.
The conclusion that can be made from the data in the scatter diagram is that the more time that was used to prepare, the lower the score (answer A). The negative linear correlation means that as the preparation time increases, the final score decreases in a linear pattern. This suggests that there may be a relationship between the amount of preparation time and the final score, but further investigation and statistical analysis is needed to confirm this relationship.
Linear correlation refers to the relationship between two variables that can be represented by a straight line on a scatter plot. The relationship between the two variables can be positive, negative, or neutral. Positive linear correlation means that as one variable increases, the other variable also increases in a linear pattern. Negative linear correlation means that as one variable increases, the other variable decreases in a linear pattern. A neutral linear correlation means that there is no relationship between the two variables.
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Which of the following DOES NOT belong to the group?
Answer:
i think it is the second one?
Step-by-step explanation:
i hope it helped!
Reagan needs to rent a pickup truck for one day, so she is comparing different rental companies' rates.
- One rental company charges $55 per day to rent a pickup, with no additional charge per mile driven.
- Another company's charge of $34 per day includes up to 150miles. Beyond that, the renter is charged $0.25 per mile.
If Reagan drives a certain distance, d, the total charges from the two rental companies will be the same amount. Which equation can Reagan use to find d?
The equation that can be used to find d is 0.25d - 3.50 = $55.
What is the equation?The first step is to determine the total cost when the distance travelled is d.
Total cost when the first rental company drives d miles = $55
Total cost when the second rental company drives d miles = cost per day + [cost per mile x (d - 150)
= $34 + [$0.25 x (d - 150)]
$34 + 0.25d - 37.50
0.25d - 3.50
When the total charges are the same, the two equations would be equal
0.25d - 3.50 = $55
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Given the quadratic equation y=ax^2+bx+c, find the axis of symmetry when b=0.
The axis of symmetry of the graph of the quadratic function represented by the equation is x=-b/2a
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
The standard formula for a quadratic equation is expressed as
y=ax^2+bx+c
where a, b and c are the coefficientx and y are the variablesAll quadratic functions have an axis of symmetry and they are expressed according to the equation x=-b/2a
Hence the axis of symmetry of the graph of the quadratic function represented by the equation is x=-b/2a
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Cindy is designing a rectangular fountain in the middle of a courtyard. The rest of the courtyard will be covered in stone. The part of the courtyard that will be covered in stone has an area of 246 square feet. A. What is the width of the fountain? B. What fraction of the area of the courtyard will be occupied by the fountain?
The width of the fountain will be 3 feet and the fraction of the area of the courtyard will be occupied by the fountain is 3/44
What is the area?Is the measure of the space occupied by a body bounded by an environment called perimeter, the same is expressed in units of squared side. Example: ft^2, m^2
The formula and procedure to solve this geometry exercise is:
A(rectangle) = length * width
Information about the problem:
A(stone) = 246 ft^2
A(fountain) = ?
Width = ?
Calculating the area of the fountain we get:
Area of fountain = area of the rectangle - 246
Area of fountain = (12 x 22) - 246
Area of fountain = 264 - 246
Area of fountain = 18 ft^2
Calculating the width of the fountain we have:
A(rectangle) = length * width
18 = W x 6
W = 18/6
W = 3 feet
Calculating the fraction of the area of the courtyard will be occupied by the fountain we get:
Fraction = Area of fountain / area of the rectangle
Fraction = 18 ft^2 /264 ft^2
Fraction = 18/264
Simplifying we have:
Fraction = 3/44
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The turtle’s distance from the starting point is increasing for seconds.
Between 10 and 12 seconds, the turtle’s distance is.
Between 12 and 14 seconds, the turtle is
The turtle’s distance from the starting point is increasing for 18 seconds, and the distance between 10 and 12 seconds, the turtle, is -10cm, and the distance between 12 and 14 seconds, the turtle, is 0 cm.
The turtle’s distance from the starting point is 16+(20-16)*1/2=16+2=18sec.
To calculate the distance between 10 and 12 seconds, the turtle is as per the graph shown below we can consider the turtle is in 12:30 cm and 10:30 cm so 30-40=-10cm
To calculate the distance between 12 and 14 seconds, the turtle is as per the graph shown below we can consider the turtle is in 14:30 cm and 12:30 cm so 30-30=0cm
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Answer:The turtle’s distance from the starting point is increasing for
✔ 10
seconds.
Between 10 and 12 seconds, the turtle’s distance is
✔ decreasing
.
Between 12 and 14 seconds, the turtle is
✔ standing still
.
Step-by-step explanation:
Clay Why bark, . a soft-drink vendor at Hard Rock Cafe's annual Rockfest, created a table of conditional values for the various alternatives (stocking decision) and states of nature (Size of crowd): The probabilities associated with the states of nature are 0.3 for a big demand, 0.5 for an average demand, and 0.2 for a small demand. a) Determine the alternative that provides Clay Why bark the greatest expected monetary value (EMV). b) Compute the expected value of perfect information (EVPI). Raymond Jacobs owns a health and fitness center, the Muscle-Up, in Ashland. He is considering adding more floor space to meet increasing demand. He will either add no floor space(N), a moderate area of floor space that doubles the size of the facility (D). Demand will either stay fixed. increase slightly. or increase greatly. The following are the changes in Muscle-Up's annual profits under
a) The alternative that provides Clay Whybark the greatest expected monetary value (EMV) is an alternative to Large Stock.
b) The expected value of perfect information (EVPI) is $13,800.
a) The alternative large stock's expected monetary value (EMV) = 22000 × 0.3 + 12000 × 0.5 - 2000 × 0.2
The alternative large stock's expected monetary value (EMV) = $12,200.
Expected Financial Value of Alternative Average Stock = 14,000 × 0.3 × 1000 × 0.5 × 6000 × 0.2
Expected Financial Value of Alternative Average Stock = $ 10,400
Expected Financial Value of an Alternative Small Stock = 9,000 × 0.3 + 8,000 × 0.5 + 4,000 × 0.2
Expected Financial Value of an Alternative Small Stock = $7,500
b) The expected value with perfect information (EVPI) = 22000 × 0.3 + 12000 × 0.5 + 6000 × 0.2
The expected value with perfect information (EVPI) = $13,800
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Jarett's puppy weighed 33 ounces at birth.
At one week old, the puppy weighed 5 ounces.
At two weeks old, the puppy weighed 6 ounces.
If the weight gain continues in this pattern, how
much will the puppy weigh at three weeks old?
8.
Answer: 8 ounces
Step-by-step explanation:
the puppy will weigh 8 ounces at three weeks old if the weight gain continues in the same pattern (33 ounces - 5 ounces + 6 ounces).
What is the value of x?
Answer:
x=64 degrees
Step-by-step explanation:
because triangle IHG is isosceles, angle HIG is 58 degrees. the sum of angles in a triangle is 180 degrees, and 180-58-58=64
Answer:
x= 64
Step-by-step explanation:
180-58-58=64
please help i need it
The missing value in the table is 12.
How to complete the table?We assume that there is a proportional relation between the two variables, which can be written as:
y = k*x
Where k is a constant.
The first pair is:
x = 2
y =3
Replacing that we get:
3 = k*2
3/2 = k
(you will get the same value of k if you use any one of the pairs on the table).
Now to complete the table we need to evaluate in x = 8.
y = (3/2)*8
y = 3*4
y = 12
That is the missing value.
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The missing value in the table of values is 12.
How to complete the table of valuesFrom the question, we have the following parameters that can be used in our computation:
The table of values
From the table of values, we can see that
The relationship between x and y is:
The product of 1.5 and x gives y
Mathematically, this can be represented as
y = 1.5x
When the value of x is 8, we have
y = 1/5 * 8
Evaluate the product
y = 12
Hence, the missing value is 12
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IfA1-3 -3 4 and AB- 1-128 determine the first and second columns of B. Let b, be column 1 of B and b2 be column 2 of B
The first column of matrix B is -3, -1 and the second column of matrix B is 4, 128.
First Column of B (b1): -3, -1
Second Column of B (b2): 4, 128
A1-3 is the first row of matrix A, so b1 = -3.
A2-4 is the second row of matrix A, so b2 = 4.
AB-1 is the first row of matrix B, so b1 = -1.
A2B-128 is the second row of matrix B, so b2 = 128.
The first column of matrix B (b1) is determined by the first row of matrix A (A1-3) and the first row of matrix B (AB-1). The first value of b1 is -3, which comes from the first row of matrix A, and the second value of b1 is -1, which comes from the first row of matrix B. The second column of matrix B (b2) is determined by the second row of matrix A (A2-4) and the second row of matrix B (A2B-128). The first value of b2 is 4, which comes from the second row of matrix A, and the second value of b2 is 128, which comes from the second row of matrix B. To summarize, the first column of matrix B is -3, -1 and the second column of matrix B is 4, 128.
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Which boundary marker did the organizers of New York City's annual India Day Parade use to exclude a particular group from participating
Sexuality is boundary marker that organizers of New York City's annual India Day Parade use to exclude a particular group from participating.
What exactly do you mean by groupism?The proclivity to think and act as members of a group: the proclivity to conform to a group’s cultural pattern at the price of individualism and cultural variety. Groupism… is founded not on evident group emergencies, but on the nebulous unease of lonely individuals. Mr. David Riesman.
Tangible culture (such as buildings, monuments, landscapes, literature, works of art, and artifacts), intangible culture (such as folklore, traditions, language, and knowledge), and natural heritage are all examples of cultural heritage (including culturally significant landscapes, and biodiversity).Sexuality, gender, religion, race, socioeconomic status, and area are examples of cultural identities.
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Please help me with this math problem
The sample space when 3 coins are tossed is given as follows:
{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.
The outcomes in which the first coin is tails is given as follows:
THH, THT, TTH, TTT.
What is a sample space?A sample space is a set that contains all possible outcomes in the context of an experiment.
In this problem, we have three trials, each with two possible outcomes, hence the cardinality of the sample space is obtained as follows:
2³ = 8.
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Gillian has a board that is 2 meters long. She cuts the board into 5 equal pieces, and then measures them with a tape measure that only measures in customary units. To the nearest inch, what is the length of each piece?
The length of each of piece of board is 40 cm or 0.4 m.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Gillian has a board that is 2 meters long.
She cuts the board into 5 equal pieces.
Now, the length of each piece is
= 200 cm /5
= 40 cm
Hence, the length is 40cm or 0.4 m.
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In a rhombus, all the side lengths are $10,$ and one of the angles is equal to $120^\circ. $ Find the area of the rhombus
The area of the rhombus would be [tex]$\mathbf{5 0} \sqrt{3}$[/tex].
What is meant by rhombus?A parallelogram has a unique variation known as a rhombus. A rhombus has opposing sides that are parallel and opposing angles that are equal. A rhombus also has equal-length sides and diagonals that are at right angles to one another. The term "rhombus" can also refer to a diamond or rhombus.
Given:
Each side length in a rhombus is $10, and one of the angles is equal to $120 circumference.
If the angle is 120 degrees, its half, 60 degrees, creates a right-angled triangle.
[tex]& \sin 60=\text { Height } / 10 \\[/tex]
[tex]& \sqrt{3} / 2 * 10=\text { height } \\[/tex]
[tex]& \text { height }=5 \sqrt{3} \text {. } \\[/tex]
Let the equation be
[tex]& \text { Area of rhombus = base }* \text { height } \\[/tex]
simplifying the above equation, we get
[tex]& =10 * 5 \sqrt{3} \\[/tex]
[tex]& =50 \sqrt{3}[/tex]
Therefore the area of the rhombus is [tex]$\mathbf{5 0} \sqrt{3}$[/tex].
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PLSSS HELP IF YOU TURLY KNOW THISSS
Answer:
x = 24
Step-by-step explanation:
Now we have to,
→ find the required value of x.
The equation is,
→ x/12 = 2
Then the value of x will be,
→ x/12 = 2
→ x = 2 × 12
→ [ x = 24 ]
Hence, the value of x is 24.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{x}{12} = 2}[/tex]
[tex]\mathsf{\dfrac{1}{12}x = 2}[/tex]
[tex]\large\text{MULTIPLY 12 to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{1}{12}x\times 12 = 2 \times 12}[/tex]
[tex]\large\text{Simplify it}[/tex]
[tex]\mathsf{x = 12\times 2}[/tex]
[tex]\mathsf{x = 24}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x = 24}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Find a point Q = (x_1, y_1, z_1) at which f and l are perpendicular. Give an equation for the set of all points at which f and l are perpendicular.
The point Q = (-12, 1, 24) is a point at which the vector field F and the line l are perpendicular, and the equation for the set of all points at which f and l are perpendicular is 6x₁ + 3y₁ + 4z₁ = 0.
To find a point at which the vector field F and the line l are perpendicular, we need to find the point at which the dot product of the vector F and the direction vector of the line l is zero.
The direction vector of the line l is given by:
d = (1, 1, 4)
The vector F at the point (x₁, y₁, z₁) is given by:
F(x₁, y₁, z₁) = x₁ i + (x₁ + y₁) j + (x₁ - y₁ + z₁) k
The dot product of F and d is:
F(x₁, y₁, z₁) ⋅ d = x₁ + (x₁ + y₁) + 4(x₁ - y₁ + z₁)
Setting this equal to zero, we have:
x₁ + (x₁ + y₁) + 4(x₁ - y₁ + z₁) = 0
Expanding, we get:
6x₁ + 3y₁ + 4z₁ = 0
We can substitute x₁ = 3 - 5t, y₁ = t - 4, and z₁ = 4 + 4t into this equation to find t:
6(3 - 5t) + 3(t - 4) + 4(4 + 4t) = 0
Expanding, we get:
72 - 30t + 3t - 12 + 16 + 16t = 0
Simplifying, we get:
100 = 20t
So, t = 5.
Substituting t = 5 back into x₁ = 3 - 5t, y₁ = t - 4, and z₁ = 4 + 4t, we get:
x₁ = 3 - 5 * 5 = -12
y₁ = 5 - 4 = 1
z₁ = 4 + 4 * 5 = 24
The point Q = (-12, 1, 24) is a point at which the vector field F and the line l are perpendicular.
The set of all points at which F and l are perpendicular is given by the equation:
6x₁ + 3y₁ + 4z₁ = 0
This represents a plane in 3-dimensional space, perpendicular to the vector F at all points.
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--The given question is incomplete; the complete question is
"Let F = (x)i + (x+y)j + (x-y+z)k. Let the line l be x = 3 - 5t, y = t - 4, z = 4 + 4t. Find a point Q= (x₁, y₁, z₁) at which F and l are perpendicular. Give an equation for the set of all points at which F and I are perpendicular."--