The value of both the interior angles of the triangle is calculated as 70° and 35°.
What is the exterior angle property?If a triangle side is formed, the exterior angle made is equal to the sum of a 2 interior opposite angles.
When an equivalent angle is chosen to take at each vertex of the triangle, this same exterior angles always add up to 360°.Each exterior angle equals 180° minus the interior angle. If the relating interior angle is given, this formula can be used. Exterior angle = Sum of opposite angles on the inside. When the exterior angle's distant interior opposite angles are given, this formula can be used to find it.Now, as per the given question;
The exterior angle of a triangle is 105°.
Let one of the interior angle is 'x'.
Then, the other interior angle is 35 degree less; x - 35°.
By the exterior angle property.
Sum of interior angles = exterior angle
x + x - 35° = 105°
2x = 105° + 35°
2x = 140°
x = 70°
The other interior angle is; x - 35°
= 70° - 35°
= 35°
Therefore, the two interior angles of the triangles are estimated as 70° and 35°.
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A is 50% acid sulotion. And B is an 80% sulotion determin how much of each sulotion he need to create 200 ml of 68% sulotion
Solving a system of equations we can see that we need to use 120 ml of the 80% solution, and the other 80ml are of the 50% solution.
How much of each we should mix?
Let's define the variables:
x = ml of A solution used.y = ml of B solution used.We know that we want to make 200ml, then:
x + y = 200
And the concentration of these 200ml must be of 68%, then the concentrations in the left side and in the rigth side must give the same value, so we can write:
x*0.5 + y*0.8 = 200*0.68
(the concentrations are written in decimal form)
Then we have the system of equations:
x + y = 200
x*0.5 + y*0.8 = 200*0.68
To solve it we start by isolating x in the first equation:
x = 200 - y
Replacing that in the other equation we get:
(200 - y)*0.5 + y*0.8 = 200*0.68
Now we can solve this for y, we will get:
100 - y*0.5 + y*0.8 = 136
y*0.3 = 136 - 100 = 36
y = 36/0.3 = 120
So we need to use 120 ml of the 80% solution, and the other 80ml are of the 50% solution.
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True or False: In –6x – 20 = –2x + 4(1 – 3x)
Given [tex]-6x-20[/tex]
Proof that it is equal to the [tex]-2x + 4(1 - 3x)[/tex] or not
[tex]-2x + 4(1 - 3x)[/tex]
Distribute
[tex]-2x+ 4-12x[/tex]
[tex]4-14x[/tex]
Not equal to the [tex]-6x-20[/tex] [tex]\neq[/tex] [tex]4-14x[/tex]
So, it is false
What is Distribute in math?
To "distribute" anything is to divide it up or to give someone a piece of it.
What does the mathematical distributive property mean then?
The distributive property is the distributive law of multiplication over operations in fundamental arithmetic, such as addition and subtraction.
Distributive property: What Is It?
This property states that multiplying the total of two or more addends by a number will provide the same outcome as multiplying each addend by the number separately and then adding the results together.
In other words, an expression of the type A (B + C) can be resolved as A (B + C) = AB + AC in accordance with the distributive property.
This characteristic also holds for subtraction.
A(B-C) = AB-AC
This demonstrates that the other two operands share operand A.
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Add:
4⁄6 + 2⁄4 + 3⁄5 =
Answer:
Step-by-step explanation:
[tex]\frac{4}{6} + \frac{2}{4} + \frac{3}{5} = \frac{80}{120} + \frac{60}{120} + \frac{72}{120} = \frac{212}{120}[/tex]
simplest form : [tex]\frac{53}{30}[/tex]
find the perimeter of ABC with vertices A(-4,4), B(2,-2), and C(-4,-2). Round your answer to the nearest hundredth.
The perimeter of ABC with vertices A(-4,4), B(2,-2), and C(-4,-2) is 20.848 units.
We are given the vertices:
A(-4,4), B(2,-2), and C(-4,-2).
We need to find the perimeter of ABC.
AB = √ ( 2 + 4)² + (-2 - 4)²
AB = √ 6² + 6²
AB = √72
AB = 6 √2 units
BC = √ (-4 - 2)² + ( -2 + 2)²
BC = √ 6²
BC = 6 units
AC = √ ( -4 + 4)² + (-2 - 4)²
AC = √ 6²
AC = 6 units.
Perimeter = AB + BC + AC
Perimeter = 6 √2 + 6 + 6 units
Perimeter = 12 + 6 √2 units.
Perimeter = 12 + 6(1.414) units
Perimeter = 12 + 8.848 units
Perimeter = 20.848 units
Therefore, the perimeter of ABC with vertices A(-4,4), B(2,-2), and C(-4,-2) is 20.848 units.
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Select all the correct locations on the figures.
Select two angles, one from each triangle, that must be congruent for the triangles to be congruent by the SAS criterion.
For the two triangles to be congruent by the side angle side (SAS) criterion, then the angle in between the two marked sides must be congruent.
What are congruent triangles?Two triangles are said to be congruent if they have the same shape and their corresponding sides are also equal. Therefore, their corresponding angles would also be congruent.
For the two triangles to be congruent by the side angle side (SAS) criterion, then the angle in between the two marked sides must be congruent.
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Answer:
as shown on the screen shot
the table gives info about number of people voting for each part at an election there are 52852 people who can vote target was 88% of people who can vote was the target met maths soulotion
The target of achieving 88% votes from people is not achieved
Given that the golden party got 12598 votes, the pink party got 9112 votes, the brown party got 20059 votes and the purple party got 4466 votes. and 52,852 people can vote
The total number of people participated in voting=12598 + 9112 + 20059 + 4466
The total number of people who participated in voting=46,235
Percentage of people who participated in voting= [tex]\frac{46235}{52852}[/tex]×100
The percentage of people who participated in voting=87.5%
The target is 88%, 88%>87.5% i.e. lesser than the actual voting percentage
Therefore, The target of achieving 88% votes from people is not achieved
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What is the sequence of transformations that maps △ABC to △A′B′C′? Select from the drop-down menus to correctly identify each step. Step 1: Choose... Step 2: Choose... Two triangles on the coordinate plane. Triangle A B C has vertex A at negative 1 comma 2, vertex B at negative 2 comma 5, and vertex C at negative 5 comma 1. Triangle A prime B prime C prime has vertex A prime at 3 comma negative 2, vertex B prime at 4 comma negative 5, and vertex C prime at 7 comma negative 1.
Answer:
Step-by-step explanation:
Any 1 of the following transformations will work. There are others that are also possible.
translation up 4 units, followed by rotation CCW by 90°.
rotation CCW by 90°, followed by translation left 4 units.
rotation CCW 90° about the center (-2, -2).
Step-by-step explanation:
The order of vertices ABC is clockwise, as is the order of vertices A'B'C'. Thus, if reflection is involved, there are two (or some other even number of) reflections.
The orientation of line CA is to the east. The orientation of line C'A' is to the north, so the figure has been rotated 90° CCW. In general, such rotation can be accomplished by a single transformation about a suitably chosen center. Here, we're told there is a sequence of transformations involved, so a single rotation is probably not of interest.
If we rotate the figure 90° CCW, we find it ends up 4 units east of the final position. So, one possible transformation is 90° CCW + translation left 4 units.
If we rotate the final figure 90° CW, we find it ends up 4 units north of the starting position. So, another possible transformation is translation up 4 units + rotation 90° CCW.
Of course, rotation 90° CCW in either case is the same as rotation 270° CW.
_____
Answer:
Step-by-step explanation:
The orientation of line CA is to the east. The orientation of line C'A' is to the north, so the figure has been rotated 90° CCW. In general, such rotation can be accomplished by a single transformation about a suitably chosen center. Here, we're told there is a sequence of transformations involved, so a single rotation is probably not of interest.
If we rotate the figure 90° CCW, we find it ends up 4 units east of the final position. So, one possible transformation is 90° CCW + translation left 4 units.
Find the value of x, given that m4 POS = 119°.
Answer: x=4.7°
Step-by-step explanation:
[tex]m\angle PQS=119^0\\\angle PQR+\angle RQS=\angle PQS\\72^0+(10x)^0=119^0\\72^0+(10x)^0-72^0=119^0-72^0\\10(x^0)=47^0\\[/tex]
Divide both parts of the equation by 10:
[tex]x=4.7^0[/tex]
Yasmin is the youngest of three siblings who ages are consecutive integers. If the sum of their ages is 57, find Yasmin's age. 17 18 19 20
Answer: 18
Step-by-step explanation:
18
If Yasmin is the youngest of three siblings who ages are consecutive integers then Yasmin's age is 18, option B is correct.
Let's assume Yasmin's age is represented by the variable "Y".
Yasmin is the youngest, so her age is the smallest integer among the three siblings' ages.
Since their ages are consecutive integers, we can represent the ages of the three siblings as Y, Y+1, and Y+2.
According to the given information, the sum of their ages is 57.
So we can write the equation:
Y + (Y+1) + (Y+2) = 57
Now, let's solve for Y:
3Y + 3 = 57
Subtract 3 from both sides:
3Y = 54
Divide both sides by 3:
Y = 18
So, Yasmin's age (Y) is 18 years old. Option B is correct.
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Need the answer please
Answer:
5
Step-by-step explanation:
This uses the Pythagorean theorem ([tex]f^2 + g^{2} =h^2[/tex]). So you would take your values 3 and 4 and plug them into the equation. [tex]3^2+4^2=h^2[/tex]. This becomes [tex]9+16=h^2[/tex]. Simplify and this becomes [tex]25=h^2[/tex]. If you take the square root of both sides you will end with 5 = h. Therefore your answer is 5.
Answer:
H=5
Step-by-step explanation:
Since it's a right triangle, you can use the Pythagorean Theorem which is [tex]a^2 + b^2 = c^2[/tex] or in this case: [tex]f^2 + g^2 = h^2[/tex]
Substitute 3 in for f and 4 in for g: [tex]3^2 + 4^2 = h^2[/tex]
Add 9 and 16 together, it's 25 and then find the square root of 25 and the square root of h and the answer is 5
[tex]f^2 + g^2=h^2\\3^2 + 4^2 = h^2\\9 + 16 = h^2\\25 = h^2\\\sqrt25 = \sqrt h^2\\5 = h[/tex]
GOOD LUCK! :)
A hospital stores one type of medicine in 222-decagram containers. Based on the information given in the box above, how many 111-milligram doses are there in one 222-decagram container?
Answer:
2,220,000 mlg
Step-by-step explanation:
This question can be solved by a simple conversion calculation. Thankfully we're converting between two units of measurement with the same base!
So First, let's convert 222 decagrams to grams, and then convert grams to milligrams.
The conversion rates we need are:
1 decagram = 10 grams
1 gram = 1000 milligrams
Now for the math!
[tex]222 dg *\frac{10g}{1dg} =2220g\\then...2220g * \frac{1000mlg}/1g\\\\\\=2,220,000 mlg[/tex]
56+85+95+42= i need help from Zoe witthans
Answer:
278
Step-by-step explanation:
First, add 85+95=180.
Then, add 56+42=98
Add 180+98=278
Suki is trying to solve the equation 62.75 + x = 92.
Determine whether Suki could use each statement below to reason and solve the equation.
Choose Yes or No for each statement.
A) Suki can add 62.75 to both sides of the equation.
[ Select ]
B) Suki asks, "What number can be added to 62.75 to get 92?"
[ Select ]
C) Suki thinks, "x is the difference between 92 and 62.75."
[ Select ]
D) Suki can divide 92 by x to get a value equal to 62.75.
[ Select ]
E) Suki knows that 62.75 + 0.25 = 63 and 63 + 29 = 92, so x must be 29.25.
[ Select ]
Answer:
picle scoops ina lane
Step-by-step explanation:
Answer:
29.25
Step-by-step explanation:
PLEASE HELP!! STUCK ON THIS! Do you think the amount of water wasted by the leaky faucet over the course of 1 day is closer to the estimate of 1 cup, 1 gallon, or 1 shower? Explain your reasoning.
Screen Shot 2022-
I think the amount of water wasted will be closer to a __________ measure because:
Answer: I would say 1 gallon
Step-by-step explanation: 1 gallon because 1 gallon would be closer then a shower or a cup
If we know the distance of an object from earth, we can determine the size of the object by measuring its parallax. True or false?.
False, If we know the distance of an object from earth, we can determine the size of the object by measuring its parallax.
The size of an object can be calculated by measuring its parallax if we know how far it is from Earth. According to the heliocentric theory of the universe, Earth is the center of the universe, and everything else revolves around it. A planet's speed is unaffected by the location of the planet within its orbit.
What is parallax explain?
Particularly: the angular difference in direction of a celestial body as measured from two places in the earth's orbit. the apparent displacement or the difference in apparent direction of an object as observed from two separate points that are not on a straight line with the object.Learn more about parallax
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Write the equation in simplest terms
f(g(x))
Disclaimer:
The equations were not given in the question.
So, take random examples for the functions f(x) and g(x) to simplify.
f(g(x)) denotes the composition function.
Important note:
After computing the composition function we must define the domain of the new function.
Example 1:
f(x) = x² and g(x) = x + 4, here the domain of f and g is the set of all real numbers.
⇒ f(g(x)) = f(x + 4) = (x + 4)²
⇒ f(g(x)) = x² + 8x + 16
This new function is also defined for all the real numbers.
Example 2:
f(x) = 5/x and g(x) = x² - 4, here the domain of g is the set of all real numbers and the domain of f is the set of all real numbers except x=0.
⇒ f(g(x)) = f(x² - 4)
⇒ f(g(x)) = 5/(x² - 4) = 5/((x - 2)(x + 2))
The domain for the new function is the set of all real numbers except x=2 and x=-2.
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Genes a and b are 10 mu apart. a man has an ab/ab genotype. his father was ab/ab. he marries a woman who is ab/ab. what is the likelihood they will have an ab/ab child?
The probability that they will have an ab/ab child is 5%
Probability is how likely an event is to happen. It is measured by the ratio of the number of good cases to the total number of cases that could happen.
ab/ab (female) x ab/ab (male)
Possible alleles: [Find the alleles of the parents first, because the rest can be mixed]
AB (parental)
ab (parental)
Ab (recombinant)
aB (recombinant)
The m.u. tells us that recombinant alleles happen 10% of the time. If a child is (Ab/ab), then (ab) would come from the father, and (Ab) would come from the mother.
Given the mother has allele ab/ab looking at probabilities there is 50%chance that the child will inherit the allele and a 10% chance for the recombination to happen.
P(ab/ab)= (50%) (10%) = 5%
hence the answer is 5%
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which of the following expressions has a coefficient of 10 and a constact of 5
Answer:
2
Step-by-step explanation:
y(a-b)=c(y+a) what's the answer
Linear equation: a, b, c, and r are real numbers (and if a, b, and c are not all equal to 0)
then ax + by + cz = r is called a linear equation in three variables. (The
“three variables” are the x, the y, and the z.)
The numbers a, b, and c are called the coefficient of the equation. The
number r is called the constant of the equation
y(a-b)=c(y+a)
ya-yb=cy+ca
ya-yb-cy=ca
y(a-b-c)=ca
[tex]y=\frac{ca}{a-b-c}[/tex]
case 1:
if either C and a are zero the y is zero,
case 2:
if
[tex]c\neq 0 \\a\neq 0\\y\neq 0[/tex]
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FIND THE GCF. Mathematics
The G.C.F of the given algebraic expression is; ⁴⁹/₆a xy
What is the G.C.F (Greatest Common Factor)?The greatest common factor (GCF or GCD or HCF) of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder. For example, for the set of numbers 18, 30 and 42 the GCF = 6.
We are given the algebraic expression;
(3 x y * 4x²y * ¹/₁ * 5x³y ^ z * 4)7a * 1/1 * 7*6
Expanding this further gives;
⁴⁹/₆a((3xy * 4x²y * 20x³y ^ z )
Now, the GCF of the terms inside the bracket would be x y. Thus, expanding the GCF we have;
⁴⁹/₆a xy((3 * 4x * 20x²y^(z - 1))
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a small furniture factory makes three types of tables coffee tables dining tables and end tables. The factory needs to make 54 tables each day. The number of dining tables made per day should equal the number of coffee tables and end tables combine. The number of coffee tables maybe she should be three more than the number of end tables. write and solve a system equation to find the numbers of table of each type of factory should make each day.
Using a system of equations, the numbers of each machine made are given as follows:
Dining: 19Coffee: 19End: 16.What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.
For this problem, the variables are given as follows, considering the situation described:
Variable x: Number of dining tables made.Variable y: Number of coffee tables made.Variable z: Number of end tables made.The factory needs to make 54 tables each day, hence:
x + y + z = 54.
The number of dining tables made per day should equal the number of coffee tables, hence:
x = y.
Then, on the first equation:
2y + z = 54.
The number of coffee tables should be three more than the number of end tables, hence:
y = z + 3.
Replacing in the equation 2y + z = 54:
2(z + 3) + z = 54
3z = 48
z = 16.
Then:
y = z + 3 = 19.x = y = 19.The numbers of each machine made are given as follows:
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Please help! (Level middle school)
The box and whisker plot shows he number of points Carl made during each game last season. What is the range of points Carl had?
Answer:
The range = 14
Step-by-step explanation:
Definition: (range of a data set)
the range of a data set is the difference between the greatest and smallest value.
In a box plot :
We should notice the maximum (generally located at the top right) and the minimum value (generally located at the top left)
Then we make the difference.
97.
In our case :
Max value = 24
Min value = 10
Therefore
The range = 24 - 10 = 14
solve the following quadratic equations by using square roots
(x-2)² = 0
(x-2)² =36
9a²-100 =0
Answer:
Step-by-step explanation:
no solution
Vocabulary Activity
constraint
dimensional analysis
equation
equivalent equations
formula
1. A(n)
Use the words from the word bank to complete each sentence.
Some terms may be used more than once.
5. A(n)
6. A(n)
identity
literal equation
margin of error
multi-step equation
proportion
2. A formula or equation that involves several variables is a(n)
quantities.
3. A(n) equation is a mathematical statement that contains two expressions and an
equal sign.
sample
solution
solve an equation
survey
4. A statement that two ratios are equivalent is a(n) equivalent equation
is a condition that a solution must satisfy.
9. Salve an equation
statement.
is an equation that expresses a relationship between certain
is an equation that is true for every value of the variable.
7. An equation that uses more than one property of equality to solve it is a(n)
8. Equations that have the same solution are
• equivalent equation
to find all values of the variable that make the equation a true
10. The process of performing operations with units is called
Module 1 Review Writing and Solving Equations 61
Systems of equation that have the same solution are called equivalent systems.
Given a system of two equations, we can produce an equivalent system by replacing one equation by the sum of the two equations, or by replacing an equation by a multiple of itself.
In contrast, we can be sure that two systems of equations are not equivalent if we know that a solution of the one is not a solution of the other.
Note: This idea of equivalent systems of equations pops up again in linear algebra. However, the examples and explanations in this article are geared to a high school algebra 1 class.
Example 1
We're given two systems of equations and asked if they're equivalent.
System A
−12x+9y=7
9x−12y=6
system B
−12x+9y=7
3x−4y=2
If we multiply the second equation in System B by 3, we get:
3x−4y=2
3(3x−4y)= 3(2)
9x−12y=6
Replacing the second equation of System B with this new equation, we get an equivalent system:
−12x+9y=7
9x−12y=6
Whoa! Look at that! This system is the same as System A, which means system A is equivalent to System B
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Match each business message to the best delivery method.
We are writing to thank you for providing the support we
needed to meet our delivery targets last week.
Listen up: The Big Shoe store is announcing a storewide
clearance sale!
All employees must obey these updated company Internet
usage policies.
Follow us to learn more about our scuba diving classes for
beginning and advanced divers!
letter
arrowRight
memo
arrowRight
social media
arrowRight
radio
arrowRight
Answer:
The correct pair matching each type of letter to its correct description would be as follows:
send it to favorably influence employers’ decision on hiring you - thank you letter
state how you meet the job requirements - cover letter
send 3-5 days after submitting your application or résumé - follow-up letter
express your desire to work for a particular company - letter of interest
A 'thank you' letter is a letter written to admit gratefulness for a favor that has been done. It can also be written in anticipation of a favor to be done. Hence, writing it to a potential employer after an interview is a way of trying to influence the employer's decision on hiring you.
A cover letter, as it relates to job application, is a letter written to express how one meets the requirement for a job. In it, a job seeker would state their qualifications, skills, and experience as it relates to the job they are applying for.
A follow-up letter is usually written to follow up with a situation that one expects that a response should have been given or written just to further emphasize one's interest in something. Writing a follow-up letter after submitting an application for a job is a way of reminding potential employers of one's desire to take up a job in their firm.
A letter of interest is written to show a desire to work in a particular organization or company irrespective of whether they have got a vacancy.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Simon invested $2600 into a simple interest account for 2 years if account yielded $234 at the end of two year what was the interest rate write your answer as a percent
Answer:
4.5%
Step-by-step explanation:
I = prt
234 = 2600 × r × 2
r = 234/5200
r = 0.045
r = 4.5%
Answer:
4.5%
Step-by-step explanation:
$234 is interest for 2 years
interest for 1 year will be 234/2 = 117
117/2600 = 0.045 which is 4.5%
A rectangle with a total of 80 square feet has been broken into two rectangles with areas of 56
square feet and 24 square feet as shown. The common length of the two smaller rectangles is
a whole number that is greater than either width 1 or width 2, which are both whole numbers.
From this information, determine the length, width 1, and width 2. Explain how you found
your answers.
The length of the rectangle is 8 feet, width 1 is 7 feet and width 2 is 3.
A rectangle of area 80 square feet is broken and forms two square rectangles of area 56 square feet and 24 square feet, which has a common length.
Area of the rectangle = length × width
Now suppose the length is x feet, and let width 1 be a and width 2 be b.
Therefore we get that
rectangle first is of area = x a
rectangle second is of area = x b
Therefore original rectangle area = area of first rectangle + area of the second rectangle
80= x a + x b
80 = x( a + b)
As it is given that the length is common and is greater than both the width of the rectangle
56 = 8 × 7
24 = 8 × 3
So we will take x = 8 and a =7, b= 3
Now put these numbers in the equation to see if they fulfill the criteria
80 = 8( 7 + 3)
80 = 80
Therefore we get a length is 8, a width of 1 is 7, and a width of 2 is 3.
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A continuous variable _____ (does/does not) allow fractional amounts. a discrete variable _____ (does/does not) allow fractional amounts.
A continuous variable does allow fractional amounts. a discrete variable does not allow fractional amounts.
Which variables require boundaries, also known as real limits, in their measurement scales?
A researcher must utilize genuine limits, which are boundaries that are exactly halfway between adjacent categories, to specify the units for a continuous variable.
What distinguishes a ratio scale from an ordinal scale?
Ordinal: The information is classifiable and rankable. The data can be equally spaced, categorized, and rated. Ratio: The data is evenly spaced, categorizable, rankable, and has a natural zero.For continuous data, what kind of data would you use?
Line graphs, skews, and other data analysis techniques are used to measure continuous data. One of the most popular kinds of continuous data analysis is regression analysis.
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Find the area of the parallelogram with vertices k(2, 2, 1), l(2, 3, 3), m(6, 9, 3), and n(6, 8, 1).
Let [tex]\vec K,\vec L,\vec M,\vec N[/tex] be vectors pointing the vertices K, L, M, and N, respectively.
The side KL is parallel to and has the same length as the vector
[tex]\vec L - \vec K = (2\,\vec\imath + 3\,\vec\jmath + 3\,\vec k) - (2\,\vec\imath+2\,\vec\jmath+\vec k) = \vec\jmath + 2\,\vec k[/tex]
Similarly, the side KN is parallel and as long as
[tex]\vec N - \vec K = (6\,\vec\imath+8\,\vec\jmath+\vec k) - (2\,\vec\imath+2\,\vec\jmath+\vec k) = 4\,\vec\imath+6\,\vec\jmath[/tex]
These vectors have magnitudes
[tex]\|\vec L - \vec K\| = \sqrt{0^2 + 1^2 + 2^2} = \sqrt5[/tex]
[tex]\|\vec N - \vec K\| = \sqrt{4^2 + 6^2 + 0^2} = 2\sqrt{13}[/tex]
and their dot product is
[tex](\vec L - \vec K) \cdot (\vec N - \vec K) = 0\cdot4 + 1\cdot6+1\cdot0 = 6[/tex]
The parallelogram spanned by the vectors [tex]\vec L-\vec K[/tex] and [tex]\vec N-\vec K[/tex] has area equal to the magnitude of their cross product, for which we have the identity
[tex]\bigg\|(\vec L - \vec K) \times (\vec N - \vec K)\bigg\| = \|\vec L - \vec K\| \|\vec N - \vec K\| \sin(\theta) \\\\ \implies \text{area} = 2\sqrt{65} \, \sin(\theta)[/tex]
where [tex]\theta[/tex] is the angle between the sides KL and KN.
From the dot product identity, we have
[tex](\vec L - \vec K) \cdot (\vec N - \vec K) = \|\vec L - \vec K\| \|\vec N - \vec K\| \cos(\theta) \\\\ \implies 6 = 2\sqrt{65} \cos(\theta)[/tex]
Then
[tex]\cos(\theta) = \dfrac3{\sqrt{65}} \implies \sin(\theta) = \sqrt{1-\cos^2(\theta)} = 2\sqrt{\dfrac{14}{65}} \\\\ \implies \text{area} = 2\sqrt{65} \cdot 2\sqrt{\dfrac{14}{65}} = \boxed{4\sqrt{14}}[/tex]
Which of the following could be measured in meters? weight of a bag, height of a building,time it takes to reboil or temperature on a hot day
Answer:
Step-by-step explanation:
height of the building