Answers
The area of the triangle is 60 in²
How to find the area of an isosceles triangle?
An isosceles triangle is a triangle with two equal sides. The area of an isosceles triangle is given by:
A = 1/2[√(a² − b² ⁄4) × b],
Where a is the measure of equal sides and b is the base of triangle
From the given info, a = KL = LM = 13 in and b = KM = 10 in
A = 1/2[√(13² − 10² ⁄4) × 10]
A = 1/2[√(169 − 100 ⁄4) × 10]
A = 1/2[√(169 − 25) × 10]
A = 1/2[√(144) × 10]
A = 1/2[12 × 10]
A = 1/2[120]
A = 60 in²
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Related Questions
you were taking a multiple-choice test that has six questions. Each of the questions has five answer choices, with one correct answer per question. If you select one of these choices for each question and leave nothing blank, and how many ways can you answer the questions?
Answers
The number of ways to answer the questions is given as follows:
15,625.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the number of outcomes for each trial as presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For this problem, there are six questions, each with five possible options, hence the number of ways to answer the questions is calculated as follows:
5^6 = 15,625 ways.
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13. FURNITURE Sai is rearranging his furniture. He wants his couch to sit along the 20-foot wall,
labeled AC on the diagram. He wants the left side of his couch to sit at a point B so that the
ratio of AB to BC is 1:2. What distance from the left side of the wall should Randall place the left side of his couch?
Answers
The value of distance after calculating are AB = 4 ft and BC = 16 ft.
What is ratio?
A ratio is a comparison between two numbers or quantities. It is typically expressed as a fraction, with the first number being divided by the second number. Ratios are often used to compare values or to express a portion of a whole.
It is given in the question, that Ladd is rearranging his living room furniture. He wants his couch to sit along the 20-ft wall.
To find the length of AB and BC we need to relate them using the equations.
AB + BC = 20 ft (from the diagram) ----------- (Equation 1)
∵ AB : BC = 1 : 4
⇒ 4AB = BC
Substituting, BC = 4AB into equation 1.
AB + 4AB = 20 ft
5AB = 20 ft
AB = 4 ft
Plugging AB = 4 ft into equation 1.
4 + BC = 20
BC = 20 ft - 4 ft
BC = 16 ft
Thus, the value of sides AB = 4 ft and BC = 16 ft , and here AB and BC are in ratio 1:4.
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help me pls , thanks :)
its about funtions and i rlly need help on this
Answers
The given relations are:
1) It is a function.
2) not a function.
3)it is a function.
4) not a function.
Are the relations functions or not?A function is a relation that maps inputs into outputs, such that each output needs to be mapped into a single input.
1) For example, the first relation each input (left row) is mapped into a single output, thus, it is a function.
2) Here theinput 9 is mapped into two different outputs, then it is not a function.
3) The notation used here is (input, output), so we can see that no input is repeated,so it is a functon.
4) The input 9 is mapped into 3 different outputs, then it is not a function.
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a number increased by 7 given 20
Answers
Answer:
13
Step-by-step explanation:
A sign on the roadway at the top of a mountain indicates that for the next 4 miles the grade is 9. 5° (see figure). Find the change in elevation for a car descending the 4-mile stretch. (Round your answer to two decimal places. )
Answers
The change in elevation of the car is 0.66mile.
Now, According to the question:
Trigonometric functions are immensely useful when real-life examples form a right triangle. In such cases, sine, cosine, or tangent functions are used based on the given information to determine the unknown value. For example, suppose we are looking at the top of a building and we know the height of the building and our distance from the base of the building, using the tangent function, we can easily calculate the angle made by the line of sight above the ground.
d = 4 miles is the distance covered by the car on the inclined road.
θ = 9.5° is the angle made by the road above the horizontal.
Let:
h be the change in elevation of the car.
Using the sine function, we write:
[tex]sin\theta= \frac{opposite side}{hypontenuse}[/tex]
[tex]sin\theta =\frac{h}{d}[/tex]
h = dsinθ
h = (4 mile)(Sin(9.5°))
h ≈ 0.66 mile
Therefore, the change in elevation of the car is 0.66mile.
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can someone help me please?
Answers
Answer:
Step-by-step explanation:
a) A(11) > M(11)
45 > 40
Go to x axis where t=11 then go straight up to find the y values (temp.) on each line
b) Look for where the lines intersect. This is where t≈47, t≈60
c) M(t) < A(t) where t=2, t=11
Look for where the Minn. line (dashed orange) is BELOW the Aspen line (solid blue)
Please help with this problem!
Answers
The maximized value of the objective function is 3
How to maximize the objective functionFrom the question, we have the following parameters that can be used in our computation:
C = x + y
Subject to
y >= 0
x >= 0
4x + 2y <= 8
2x - y <= 0
When the graphs of these inequalities are plotted (see attachment), we have the following feasible regions
(x, y) = (0, 0) and (1, 2)
This means that
C = 0 + 0 = 0
C = 1 + 2 = 3
3 is greater than 0
Hence, the maximized value is 3
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5x+y=9
10x−7y=−18
in substitution
Answers
Substitution is a method for solving systems of equations that involves solving for one variable in one equation and then substituting that value into the other equation.
Here's how we can use substitution to solve the system of equations:
5x+y=9
10x−7y=−18
Solve one equation for one variable, for example:
y = 9 - 5x
Substitute this expression of y into the other equation:
10x - 7(9 - 5x) = -18
Solve the equation resulting from the substitution
10x - 63 + 35x = -18
45x = 45
x = 1
Substitute this value of x back into one of the original equations to find the value of y.
5(1) + y = 9
y = 4
So the solution is (x,y) = (1,4)
You can check this solution by substituting it back into both original equations.
students who score within 22 points of the number 78 will pass a particular test. write this statement using absolute value notation and use the variable x for the score.
Answers
The statement using absolute value notation will be x - 78 ≤ 22.
The student will pass the test which scores 22 points for the number 78
Absolute values are any digit's value without taking the sign into an account. Therefore, all negative numbers will be regarded as positive for absolute value. The absolute value of -5, for instance, will be 5, whereas that of -7, will be 7.
In essence, the absolute value calculates the distance from zero. Putting an absolute value on something does not imply that they are the same number but that they are the same distance from 0.
Le the score of student be = x
Forming the absolute value notation -
This can be expressed as,
x - 78 ≤ 22.
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What is the slope of the line through the points (4,10) and (2, 20)
Answers
Explanation: y2 - y1. 20 - 10
—————- = ——————
x2 - x1 2 - 4
= 10/-2 = -5
Can someone please help me on this?
A linear function is plotted on the coordinate plane with the following points: (0, 3) and (2, 7). What is the rate of change (slope) and the initial value (y-intercept) for the linear function?
Answers
The rate of change for the linear function is 2.
The initial value for the linear function is 3.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The points on the coordinate plane:
(0, 3) and (2, 7)
Now,
The equation of the line.
y = mx + c
Slope = m
m = (7 - 3) / (2 - 0)
m = 4/2
m = 2
Now,
(0, 3) = (x, y)
3 = 2 x 0 + c
3 = 0 + c
c = 3
The y-intercept is 3.
Thus,
The rate of change is 2.
The initial value is 3.
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y-0.8x=0.5
5y-2.5-4x
Answers
Answer:
x = -1
Step-by-step explanation:
y-0.8x=0.5
5y-2.5-4x
Get y by itself.
y = 1.3
Put 1.3 into the second equation
5(1.3) - 2.5 - 4x
6.5-2.5 - 4x
4 - 4x = 0
Get x by itself
-4x = 4
x = -1
I hope this was able to help you :D
simplify the algebraic expressions completely.
7. (4-4). K
and
simplify the algebraic expression completely.
d+12-8/4+5
Answers
Answer:
see below
Step-by-step explanation:
7. (4-4). K =0
d+12-8/4+5 = d+12-2+5 =d+15
A line has a slope of –1/3 and a y-intercept of 5/3. Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
Answer:
The answer in intercept form will be
[tex] - 1 \div 3 = 5 \div 3x + c \\ [/tex]
Brick San Antonio playing a game of counter Rick ha ome counter Selma ha twice a many counter a Rick Tony ha ix counter Leton Selma in total they have 54 counter the number of count a Rick ha: the number of count a Tony ha = 1: P work out the value of paid
Answers
The number of counters Rick has is equal to 12 counters.
The number of counters Tony has is equal to 1:1.5.
The value of p is 1.5.
In order to solve this word problem, we would assign variables to the unknown numbers and then translate the word problem into algebraic equation as follows:
Let R represent the number of counters Rick has.
Let S represent the number of counters Selma has.
Let O represent the number of counters Tony has.
Let T represent total number of counters.
Translating the word problem into an algebraic equation, we have;
S = 2R .....equation 1.
O = 2R - 6 ......equation 2.
T = R + S + O ......equation 3.
Substituting equation 1 and equation 2 into equation 3, we have:
T = R + S + O
54 = R + 2R + 2R - 6
54 = 5R - 6
5R = 54 + 6
5R = 60
R = 60/5
R = 12 counters.
For Tony, the number of counters is given by:
O = 2R - 6
O = 2(12) - 6
O = 24 - 6
O = 18 counters.
In ratio form, we have:
O = 1:P
O = 1:(18/12)
O = 1:1.5
The number of counters Rick has is equal to 12 counters.
The number of counters Tony has is equal to 1:1.5.
The value of p is 1.5.
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are the following statements true or false? false 1. if two row interchanges are made in sucession, then the determinant of the new matrix is equal to the determinant of the original matrix. false 2. if is zero, then two rows or two columns are the same, or a row or a column is zero. false 3. the determinant of is the product of the diagonal entries in . false 4. .
Answers
Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.
What is matrix ?
A matrix is a rectangular array of numbers or other mathematical objects, typically arranged in rows and columns. Matrices are often denoted using capital letters, such as A, B, and C. Each element of a matrix is identified by its row and column indices,
1) False, If two row interchanges are made in succession, the determinant of the new matrix is the negative of the determinant of the original matrix.
2) False, If the determinant of a matrix is zero, it does not necessarily mean that two rows or two columns are the same or a row or column is zero, it only means that the matrix is singular, i.e. non-invertible and it also can mean that the matrix is linearly dependent.
3) False, The determinant of a matrix is not always equal to the product of the diagonal entries, it is a scalar value calculated through a specific method called matrix expansion which is based on the entries of the matrix and it depends on the size of the matrix.
4) False, The determinant of a matrix is a scalar value, it cannot be equal to another matrix.
Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.
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How many solutions does this system have? x + 4 y = 6. y = 2 x minus 3a. one b. two c. an infinite number d. no solution
Answers
According to the graph, the system of equations x + 4y = 6 and y = 2 x -3 has one solution that is (2,1)
In math the term called graph is defined as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.
Here we know that the following equation are known:
=> x + 4y = 6
=> y = 2x - 3
And here we need to find the number of solution for the equations.
Here we have to plot the equation on the graph then we get the graph like the following.
While we looking into the graph, we have identified that the intersection point in the graph is (2,1) and there is no other intersecting point.
Therefore, option (a) is correct.
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A newspaper charges a flat
fee plus a charge per day to
place a classified ad.
Number
of Days
2
4
6
Total
Charges
($)
8
13
18
Answers
Answer: This problem can be represented by the equation y = mx + b, where y is the total charges, x is the number of days, m is the charge per day, and b is the flat fee.
To find the values of m and b, we can use the given data points to solve for the equation.
For x = 2, y = 8, so 8 = m * 2 + b
For x = 4, y = 13, so 13 = m * 4 + b
For x = 6, y = 18, so 18 = m * 6 + b
We can then use a system of equations to solve for m and b:
m * 2 + b = 8
m * 4 + b = 13
m * 6 + b = 18
Using substitution or elimination methods:
m = 2
b = 2
Therefore, the equation is: y = 2x + 2
This means that the flat fee is $2 and the charge per day is $2.
Step-by-step explanation:
Multiselect Allce takes an art class after school once a week. At each class,
she buys a bottle of juice for $1.25 and a bag of pretzels for $0.85. Select all
expressions that represent the amount of money, in dollars, Alice spends after
attending 8 art classes.
Answers
Answer:
$16.8
Step-by-step explanation:
u got to trust me
Answer: $16.8
im sure its this it has to be
what is the product for (2x+1) and (5-x)
Answers
The product for (2x+1) and (5-x) is -2x²+9x+5.
What is Fraction?A fraction represents a part of a whole.
We have to find the product of (2x+1)(5-x)
We use distributive property to find the product.
2x(5-x)+1(5-x)
10x-2x²+5-x
-2x²+10x-x+5
Add the like terms
-2x²+9x+5
Hence, the product for (2x+1) and (5-x) is -2x²+9x+5.
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You spin a ball of mass 0.18 kg that is attached to a string of length 0.98 m at ω = 5.2 rad/s in a circle. What is the ball’s angular momentum?
Answers
The angular momentum of the the ball is 4.16kgrad/sec
What is angular momentum?Angular momentum is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity. This means that the total angular momentum of a closed system remains constant. Angular momentum has both a direction and a magnitude, and both are conserved. It is measure d in kgrad/sec
angular momentum = mass × angular velocity
mass = 0.18kg
angular velocity = 5.2 rad/s
therefore angular momentum = 0.18× 5.2
= 4.16 kg rad/s
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At the third step, Han subtracts 39 from 39. How do you know that these numbers represent hundredths?
Answers
Answer: Because 2 places to the right of the the decimal.
Step-by-step explanation:
5/10 the students in Sam's class are girls. Of the girls, of them wear glasses. What
fraction of the student's wear glasses?
Answers
As 5/10 are Girls in Class And 1/5 of the girls wear glasses So on overall girls wear glasses is 1/10 in the whole class.
The fraction 5/10 is equal to 1/2 of the total and 1/5 of the girls wear glasses so if you multiply 1/2 and 1/5 you get 1/10, To get a total fraction of girls who wear glasses overall will be by multiplying both the fraction. So,
1/5*1/2 = 1/10
Here the answer is produced by multiplying the numerator with the numerator and similarly denominator with the denominator to get the answer of total friction of girls wearing glasses in the whole class.
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What percent of the area under the tandard normal ditribution lie within two tandard deviation of the mean?
Answers
Approximately 95.45% of the area under the standard normal distribution lies within two standard deviations of the mean.
Area Under Standard Normal Distribution Within Two Standard Deviations of the MeanThe standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. This means that 68.27% of the area under the standard normal distribution lies within 1 standard deviation of the mean, and 95.45% of the area under the standard normal distribution lies within 2 standard deviations of the mean.
This is because the standard deviation is a measure of the spread of the data; the larger the standard deviation, the more spread out the data is.
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Multi step trig problem
Answers
The value of x is 14.28 units, this is determined using the trigonometric functions.
What are trigonometric functions?Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the connection between the sides and angles of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.
Consider the smaller triangle:
Sin (30) = Opposite side ÷ Hypotenuse
0.5 = Opposite side ÷ 10
Opposite side = 5
Consider the bigger triangle:
Sin (22) = Opposite side ÷ Hypotenuse
0.37 = 5 ÷ x
x = 5 / 0.35
x = 14.28
Hence, the value of x is 14.28 units, this is determined using the trigonometric identities.
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A group of students were asked which club they planned to join.
Club Percent of Students
Garden Club 0.1
Robotics Club 0.2
Technology Club 0.5
Zoology Club 0.2
Compare the probabilities of a randomly selected student joining a club and interpret the likelihood. Choose the statement that is true.
The student will be more unlikely to join the Robotics Club than the Garden Club because P(Robotics) < P(Garden).
The student will be equally likely to join the Zoology Club or Robotics Club because P(Robotics) = P(Zoology).
The student will be more likely to join the Zoology Club than the Robotics Club because P(Zoology) > P(Robotics).
The student will be more likely to join the Garden Club than the Robotics Club because P(Garden) > P(Robotics).
Answers
The statement that is most likely to be true in the question that we have here is that : The student will be equally likely to join the Zoology Club or Robotics Club because P(Robotics) = P(Zoology). Option 2
What is meant by probability?Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, if we are unclear of how an event will turn out. Statistics is the study of occurrences subject to probability.
In the question the probability of robotics is 0.2 while the probability of zoology club is 0.2 as well.
They have equal probability
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Answer: Answer B
Step-by-step explanation:
what is the probability that two randomly generated strings of length 9 in the dna alphabet ({a, c, g, t}) are identical?
Answers
The probability that two randomly generated strings of length 9 in the DNA alphabet is 729.
We have to find the probability that two randomly generated strings of length 9 in the DNA alphabet (a, c, g, t) are identical.
Probabilities are based on occurrences, and events can result from one or more observations or experiment results.
The total number of alphabet in word DNA is 3.
So, the probability that two randomly generated strings of length 9 in the DNA alphabet = 9 × 9 × 9
The probability that two randomly generated strings of length 9 in the DNA alphabet = 729
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An angle of 2. 5 radians is subtended by an arc of a circle with a radius of 10cm. What is the length, in cm, of the arc?
Answers
The length of the arc of the given circle with radius 10 cm and an angle of 2.5 radians subtended by an arc of a circle is equal to 25 cm.
Let 'y' represents the length of the arc of the given circle.
Radius 'r' of the given circle is equal to 10 cm
Angle 'α' subtended by an arc of a circle is equal to 2.5 radians.
length of the arc = Angle subtended by an arc × Radius of the circle
⇒ y = rα
⇒ y = 10 × 2.5
⇒ y = 25 cm
Therefore, the length of the arc of a circle for the given radius 10cm and subtended angle 2.5 radians is equal to 25 cm.
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Given reflections R₁ and Rk where "h" is a line with equation
x = -3 and "k" is a line with equation x = 2, how can you determine
the distance of the translation resulting from the composition
Rk Rh
Answers
The distance of the translation resulting from the composition of the two reflections Rk and Rh is equal to |1 + 2x|
How to determine the distance of the translationTo determine the distance of the translation resulting from the composition of two reflections Rk and Rh, we can calculate the difference in x-coordinates of the pre-image and image points.
Reflection Rk reflects points over the line x = 2,
So the x-coordinate of a point and its reflection would have a difference of 2 - x, where x is the x-coordinate of the original point.
Reflection Rh reflects points over the line x = -3,
So the x-coordinate of a point and its reflection would have a difference of -3 - x
When we compose the two reflections
The x-coordinate of a point and its image will have a difference of (2 - x) - (-3 - x)
Evaluate
Distance = 5
Hence, the distance is 5 units
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It costs $5 per hour to rent a snowboard from a certain ski rental company, plus a $50 deposit. Another ski rental company charges $10 per hour to rent a snowboard, plus a $25 deposit. For what number of hours is the cost to rent a snowboard the same at each company? What is the cost of renting a snowboard for this number of hours?
Answers
The number of hours for which the cost is the same would be 5 hours.
The cost of renting a snowboard for 5 number of hours would be same as that point i.e. $5
By costs, what do you mean?
Costs are really the monetary value of purchases made for use by a company or other accounting entity of supplies, service, labor, products, equipment, and other items.
The cost of renting a snowboard from the first company is $5 per hour + $50 deposit = $5x + $50.
The cost of renting a snowboard from the second company is $10 per hour + $25 deposit = $10x + $25. To find the number of hours for which the cost is the same, we set the two costs equal to each other and solve for x:
$5x + $50 = $10x + $25
$5x - $10x = $25 - $50
$5x = $25 - $50
$5x = -$25
x = -5
As we will not take cost in negative so it would be 5
So, we can say that the cost is same at any point of time.
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