Answer: 12.8 cm
Step-by-step explanation:
Multiply 3.2 by the scale of 4 to get 12.8.
Given right triangle ABC with altitude
BD drawn to hypotenuse AC. If
AD = 12 and BD = 36, what is the
length of AC?
A
B
12D
36
Answer: AC =
Submit Answer
C
+
Can someone help and find the length of AC?
If AD = 12 and BD = 36 in the right triangle ABC with altitude BD was drawn to hypotenuse AC, then the length of AC is 12√82.
What is the similarity law for triangles?
It is defined as the law to prove that two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the complementary angles are congruent.
We can use the property of similar triangles to find the length of AC.
Since BD is an altitude of triangle ABC, we can write:
(AD)(DC) = (BD)²
Substituting the given values, we get:
12(DC) = 36²
Solving for DC, we get:
DC = (36)²/12 = 3 x 36 = 108
Now, using the Pythagorean theorem, we can write:
(AC)² = (AD)² + (DC)²
Substituting the given values, we get:
(AC)² = 12² + 108²
Simplifying and solving for AC, we get:
AC = √(12² + 108²) = √(12² x (1 + 9²)) = 12 x √(1 + 9²) = 12 x √(82)
Therefore, If AD = 12 and BD = 36 in right triangle ABC with altitude
BD was drawn to hypotenuse AC, then the length of AC is 12√82.
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Examine the right triangle below, solve for x, round to two decimal places if
necessary.
C
Answer:
Step-by-step explanation:
sinX = 18/32
sinX = 0.5625
X = 34.23
A lighthouse is situated 10m back from a 35m high cliff. If the beacon is 8m above the base of the lighthouse, how far from the cliff does the shadow extend?
Answer: the shadow will extend 43.75m
Step-by-step explanation:
A rancher raises milking cows and goats which he feeds with two types of mixes, type x and type y. Each bag of type x costs P400 and contains 100 units of calcium and 400 units of protein; each bag of type y costs P600 and contains 200 units of calcium and 200 units of protein. The livestock need a minimum of 6,000 units of calcium and 12,000 units of protein per day. What combination of mixes should the rancher buy to minimize daily feed cost?
The combination should be 20 of Brand A and 20 of Brand B.
What is Linear Programming?When a linear function is exposed to various constraints, it is maximised or reduced using the mathematical modelling technique known as linear programming. In commercial planning, industrial engineering, and—to a lesser extent—the social and physical sciences, this method has proven helpful for directing quantitative decisions.
Given:
Each bag of type x costs P400 and contains 100 units of calcium and 400 units of protein.
Each bag of type y costs P600 and contains 200 units of calcium and 200 units of protein.
So, Max Z = 400x + 600 y
Constraints:
100x + 200 y ≤ 6000
or, 400x + 200y ≤ 12000
Solving the Equation:
300x = 6000
x= 20
and, y= 20
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Please help me! Factor Each Polynomial Completely.
x^2-y^2-3.5(x+y)
The polynomial x^2-y^2-3.5(x+y) is factored completely to xy(x - y)
What are algebraic expressions?Algebraic expressions are defined as expressions that are made up of coefficients, variables, terms, factors and constants.
They are also composed of arithmetic operations, such as;
SubtractionMultiplicationDivisionAdditionBracketParenthesesx^2-y^2-3.5(x+y)
expand the brackey
x² - y² - 3.5x + 3.5y
Factor the common terms
xy(x - y - 3.5 + 3.5)
collect lie terms
xy(x - y)
Hence, the expression is xy(x - y)
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Sorting algorithms no unread replies.no replies. we are using and interacting with sorting algorithms in every day life. in your chapter reading this week, you reviewed many sorting algorithms. find an example of a place in real, everyday life where you interact with, implement or use one of the sorting algorithms covered in chapter 3. for example, while playing cards you may have found yourself implementing the insertion sort algorithm (without knowing it). for this peer interaction, post your example of a place in real, everyday life where you interact with, implement or use one of the sorting algorithms. be sure to provide your us with enough information so that we will thoroughly understand your example and use of a sorting algorithm. once you have made your post, please respond to at least two of your classmates interacting and communicating on the sorting algorithm use in real world context.
A sorting algorithm is defined as an algorithm that sorts the elements of a list. The most commonly used sequences are numerical sequence and lexicographical sequence, ascending or descending.
A sorting algorithm is used to reorder an array or list of elements according to an element comparison operator. Comparison operators are used to define a new order of elements in that data structure. Consider example, The above list of characters is sorted in ascending order by their value. That is, characters with lower values are placed before characters with higher values. It is important in real life because it supports the development of the scientific concept that things can be owned and organized into distinct groups (e.g. creatures, cars, weather types, etc.). We will now discuss some real-world examples of using sorting algorithms.
1) Your phone's contact list is sorted. This means that your data is organized in this way so you can easily access the contacts you want from your phone. That is, "I ordered."
2) Paper sorting : Imagine a teacher sorting students' work alphabetically by student name. This type of operation is similar to the functionality of sorting algorithms such as bucket sort. Sorting is more efficient process.
3) Traffic lights : Traffic lights are a good example of how algorithms are used in the real world around us. Next time you get stuck in a car at a red light, think about the algorithm that traffic lights run." Most traffic lights don't automatically switch between green, yellow, and red. This algorithm is a well-established turn-by-turn algorithm that directs traffic correctly. It's in order (it may not seem that way when you're sitting at a red light).
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1. Fill in the missing Statement/Reason for the following proof:
Given: LN bisects ZMLO and LM = LO
Prove: ALMN = ALON
M
STATEMENT
1.
2.
3.
4. LN = LN
5.
ALMN a ALON
REASON
N
1.
2.
3. def of Angle Bisector
4.
5.
| In
The triangles are congruent using: 1. LM = LO - segments of the same length as given. 2. LN = LN - common segment. 3. Angle MLN = Angle OLN - LN bisects the angle. 4. ΔMLN ≅ ΔOLN - SAS criteria.
What are congruent triangles?A triangle is a closed polygon with three line segments that intersect at each of its three angles.
When the sides and angles of two triangles match, the triangles are said to be congruent. Thus, two triangles can be placed side by side and angle by angle on top of one another.
Given that the segments LM = LO, and LN bisects angle MLO.
Thus,
1. LM = LO - segments of the same length as given.
2. LN = LN - common segment
3. Angle MLN = Angle OLN - LN bisects the angle.
4. ΔMLN ≅ ΔOLN - SAS criteria.
Hence, the triangles are congruent using: 1. LM = LO - segments of the same length as given. 2. LN = LN - common segment. 3. Angle MLN = Angle OLN - LN bisects the angle. 4. ΔMLN ≅ ΔOLN - SAS criteria.
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The weight of potato chips in a medium sized bag is stated to be 10 ounces. The amount that
the packaging machine puts in these bags is believed to be normally distributed with a mean of 10.2
ounces and a standard deviation of 0.12 ounces. Is it unusual for a bag to contain 9.8 ounces of
chips? Explain your answer and show work
Answer:
Step-by-step explanation:
Let me explain each step in more detail.
Step 1: Calculate the Z-score
The Z-score is a measure of how many standard deviations a value is from the mean. To calculate the Z-score, we use the following formula:
Z = (x - μ) / σ
Where:
x = 9.8 ounces (the value we want to examine)
μ = 10.2 ounces (the mean of the distribution)
σ = 0.12 ounces (the standard deviation of the distribution)
Plugging in the values, we get:
Z = (9.8 - 10.2) / 0.12 = -3.33
This Z-score tells us that 9.8 ounces is 3.33 standard deviations below the mean of 10.2 ounces.
Step 2: Look up the cumulative probability from a Z-table
A Z-table is a table that lists the cumulative probabilities for various Z-scores. The cumulative probability tells us the probability of getting a value less than or equal to a certain Z-score. To use the Z-table, we need to know the Z-score and whether we want the cumulative probability to the left (for values less than) or to the right (for values greater than). In this case, we want the cumulative probability to the left because we want to find the probability of getting a weight less than or equal to 9.8 ounces.
The cumulative probability for a Z-score of -3.33 is approximately 0.0004. This means that there is a 0.0004 (or 0.04%) chance of getting a weight of 9.8 ounces or less in a bag of chips.
Step 3: Interpret the results
Since the cumulative probability is very small, it is highly unlikely that a bag of chips would contain 9.8 ounces or less of chips. Therefore, we can conclude that it is unusual for a bag of chips to contain 9.8 ounces or less.
If my answer met your requirements, please rate it AWESOME BRAINLY ANSWER.
Proper subset is a set that contains elements contained in another set but not equal
to that set.
True or false
Answer: A proper subset of a set A is a subset of A that is not equal to A
Step-by-step explanation:
What does a rising sequence do in a piece of music?
A. Increases the dynamic
B. Adds drama and tension
C. Decreases the dynamic
D. Decreases the tempo
WILL MARK BRAINLIST A one of a kind necklace is worth $3200. The value of the necklace increases by 9% each year.
Which explicit and recursive formulas can be used to model the situation.
Drag and drop each formula to the corresponding box.
The Formula will be in form of exponential function that is y=$3200(1.09)ˣ
where x= no. of years.
What exactly are exponential functions?
An exponential function is a mathematical function with the formula f (x) = aˣ, where "x" is a variable and "a" is a constant that is termed the function's base and must be greater than zero. The transcendental number e, which is approximately equal to 2.71828, is the most often used exponential function basis.
Growth that is exponential
The amount expands extremely slowly at first, then rapidly in Exponential Growth. The rate of change accelerates with time. As time passes, the pace of growth accelerates. The quick expansion is designed to represent a "exponential rise".
The exponential growth formula is: y = a (1+ r)ˣ, where r is the growth percentage.
Now,
Initial value=$3200
% increase=9%
then
Amount in x years will be =3200(1+9/100)ˣ
=3200(109/100)ˣ
=3200(1.09)ˣ
Hence,
The Formula will be in form of exponential function that is y=$3200(1.09)ˣ
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The graph shows Felix's English scores versus the number of hours he studies:
What will Felix's English scores most likely be if he spends 7 hours a week studying English?
a 64 points
b 72 points
c 84 points
d 92 points
Felix's English score would be around 72 points if he spends 7 hours a week studying English.
the answer is option b, 72 points.
What is a graph of an equation?
A graph of an equation is a visual representation of the relationship between the variables in that equation. In mathematics, an equation typically involves one or more variables, and the graph of that equation shows how the value of one variable changes as the value of another variable change.
Look at the horizontal axis of the graph to find the point that corresponds to 7 hours of studying per week. In this case, it is approximately halfway between 6 and 8, so we can estimate it to be around 7.
From that point, draw a vertical line up to the graph to find the corresponding English score.
Follow the line until it intersects with the blue line representing Felix's English scores.
From that intersection point, draw a horizontal line over to the y-axis to read the corresponding score.
Based on this analysis, we can estimate that Felix's English score would be around 72 points if he spends 7 hours a week studying English.
Therefore, Felix's English score would be around 72 points if he spends 7 hours a week studying English.
the answer is option b, 72 points.
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if the ratio of two sample variances exceeds the critical value of f at a defined confidence level, then___
if the ratio of two sample variances exceeds the critical value of f at a defined confidence level, then the level of confidence also exceeds the critical level.
All tests that make use of the F-distribution are collectively referred to as "F Tests." The F-Test to Compare Two Variances is often what is meant when the term "F-Test" is used. However, a number of tests, including regression analysis, the Chow test, and the Scheffe test, use the f-statistic. If we are conducting an F-Test, we might employ a variety of technological tools. since doing an F-test manually while accounting for variations is a difficult and time-consuming operation.
if the ratio of two sample variances exceeds the critical value of f at a defined confidence level, then the level of confidence also exceeds the critical level.
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Triangle GHI has coordinates G(-5, -2), H(3, 8), and I(2, 1). If the triangle is translated 1 unit up, what are the coordinates of H'?
The coordinates of point H' will be: H'(3, 9)
What is Translation ?We know that a translation is basically a transformation that occurs when an object is moved from one place to another place.
The original object's dimensions, orientation, or shape are unaffected by translation.
Translating a point P(x, y) 1 unit up means we need to add to use P'(x, y+1), that is adding 1 unit to the y-coordinate of the point P'(x, y).
Now we have to translate the triangle 1 unit up. So, use the formula
P(x, y) → P'(x, y + 1)
Thus, the coordinates of point H' will be:
H( 3, 8) → H'( 3, 8+1) → H'(3, 9)
Therefore, the coordinates of point H' will be: A'(3, 9).
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Solve for x with the given measures
The measured value x = 13.
What is parallelogram?
A unique variety of quadrilateral made up of parallel lines is known as a parallelogram. A parallelogram can have any angle between its adjacent sides as long as its opposite sides are parallel. If two opposite sides of a quadrilateral are parallel and congruent, it will be a parallelogram. Consequently, a quadrilateral in which both pairs of opposite sides are parallel and equal is known as a parallelogram.
We can solve this easily using alternative interior angles. A parallelogram's interior is always 360 degrees, right?
In the given parallelogram the side vy = yx
VY = YX = 80 = 6x+2
6x = 80-2=78
x = 78/6= 13
Hence The measured value x = 13.
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A roller-coaster car is at the top of a hill. The car and its passengers have a combined mass of 1,088 kilograms. If the hill is 62 meters tall, how much potential energy does the car have?
PE=mgh
A) 67,456 J
B) 330,534.4 J
C) 1,159.8 J
D) 661,068.8 J
The potential energy of the roller coaster car at the top of a hill is 661,068.8 J.
The correct answer choice is option D
What is potential energy?Potential energy is a form of energy which is dependent on the relationship between different system components.
The gravitational constant, g = 9.8 m/s².
Mass, m = 1088 grams
Height, h = 62 meters
So, The amount of potential energy the car has;
PE = mgh.
PE = 1088 × 9.8 × 62
PE = 661,068.8J
Ultimately, the car has a potential energy of 661,068.8J.
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Can you please help me!!!Please
The company will be able to purchase enough pens while staying within the budget by purchasing 10 mugs only not more than that.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given;
A company has a budget of $305
Company needs to purchase either a mug or a pen for each of its 100 clients.
Price per Mug $5.55 Price per Pen $2.50
Now,
Price of pen = 100*2.50=250
When the number of employees are 10
=10*5.50=55.0
Mugs can be purchased
When the number of employees are 15
=15*5.50=82.5
Mugs cannot be purchased
Therefore, by algebra the answer will be 10 mugs only.
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Enter the letter of the graphed function(image)
The given graph is represented by the function ( x + 2 )(x - 1 )³(x - 3 ). The correct option is A.
What is a function?The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.
Graphing functions involve drawing a curve on the coordinate plane that represents the function. Every point on a curve (graph) that represents a function satisfies the function equation.
The graph is represented by the function,
( x + 2 )(x - 1 )³(x - 3 )
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5. Now, that you have your answers for questions 1 & 2. Explain what the difference between finding the
mean of the given numbers and finding the value that is half-way between a given set of numbers.
It should be noted that finding the mean gives the average value of a set of numbers, while finding the halfway point gives a value that is equidistant between the two extreme values in the set.
How to explain the meanFinding the mean of a set of numbers involves adding up all the numbers in the set and then dividing the sum by the total number of numbers in the set. The mean represents the average value of the set.
Finding the value that is halfway between a set of numbers involves taking the two extreme values in the set and finding the arithmetic average (i.e., adding the two values and dividing by 2). This value represents the midpoint between the two extremes.
In summary, finding the mean gives the average value of a set of numbers, while finding the halfway point gives a value that is equidistant between the two extreme values in the set.
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find the size of angle x 164
Note that the size of angle x = 115°. This is a problem relating to the sum of angles in a circle. See the computation below.
What is the sum of angles in a circle?The sum of angles in a circle is always equal to 360 degrees or 2π radians.
This means that the sum of the measures of the angles formed by any number of rays or line segments that meet at a common point, or vertex, and whose endpoints lie on the circle, will always add up to 360 degrees or 2π radians. This property is often used in geometry and trigonometry to solve problems involving circles and angles.
With regard to the above problem,
We are given three angles in a circle named as follows:
a) 81°
b) 164°
c) x
The above rule state that
81 + 164 + x = 360°
thus, x = 360 - 81 - 164
x = 360 -245
x = 115°
Thus the value of ∠x is 115°
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Full Question:
See attached image.
Lis price: $5,227.00 , Options: $1,625.00, Destination charges: $200.00 , Subtotal: $7,052.00, Tax: $431.58
Less trade in: $2,932.00, Amount to be financed: $4,691.03, 10% interest for 48 months: $1,501.63, Total: $6,192.66, Monthly payment: $129.00
Please round your answer to one decimal place(tenth place). Enter only the number without % sign.
The annual percentage rate is 19.59%.
What is an expression?An expression contains terms with addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Repayment months = 48
Interest rate = 10%
The annual percentage rate.
= (2 x repayment months x interest rate) ÷ (repayment months + 1)
= (2 x 48 x 10/100) / (48 + 1) x 100
= (2 x 48 x 0.10) / 49 x 100
= 9.6/49 x 100
= 0.1959 x 100
= 19.59%
Thus,
The annual percentage rate is 19.59%.
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f(x) =
-x² + 3x
4(x)³
x+5
x-1
x≤-2
-2 < x < 1
x ≥ 1
The value of the piecewise function f(-2) + 2f(-1) - f(3) is -14
How to determine the value of the piecewise functionFrom the question, we have the following parameters that can be used in our computation:
The definition of a piecewise function
Given that
f(-2) + 2f(-1) - f(3)
Using the definition of the piecewise function and the domain values. we have
f(-2) + 2f(-1) - f(3) = -(-2)^2 + 3(-2) + 2(4(-1)^3) + [(3 + 5)/(3 - 1)]
Evaluate
f(-2) + 2f(-1) - f(3) = -14
Hence, the solution is -14
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What equation would you use to solve x
Answer: X^2+6.8^2=10.6^2
Step-by-step explanation:
The pythagorean theorem can be used to find the missing sides of triangles.
The formula is:
a^2+b^2=c^2, where c^2 is always the hypotenuse (the biggest and diagonal line) and a^2 and b^2 are the other side lengths
In this problem, plug in the values. So in this case, you have:
a^2+6.8^2=10.6^2
Hope this helps
Can someone please help me with this equation
The measure of the angles m∠BOX = 77.5° and m∠AOX = 77.5°.
What is the angle bisector of an angle?
The angle bisector of an angle is a line or line segment that divides the angle into two equal parts, creating two smaller angles that are congruent (i.e., have the same measure). The angle bisector starts from the vertex of the angle and extends to the opposite side or ray of the angle, dividing the angle into two smaller angles that have the same number of degrees.
By the definition of the angle bisector of an angle, the angle bisector divides the angle in two equal measures.
As m∠AOB = 155°
m∠BOX = 1/2 * m∠AOB
m∠BOX = 1/2 * 155
m∠BOX = 77.5°
also m∠AOX = 77.5°
Hence, the measure of the angles m∠BOX = 77.5° and m∠AOX = 77.5°.
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Consider the following ordered data. 10 13 13 14 15 15 16 17 18 Find the low, Q_1, median, Q_3, and high. low ________ Q_1 ___________ median _________ Q_3 ___________ high ___________ Find the interquartile range. _________
The low Q₁ is 13 and the median Q₃ is 16.5, the high is 18 and the interquartile range is 3.5
The interquartile range is a measure of dispersion that tells us how spread out the middle 50% of a dataset is. To calculate the IQR, we first need to find the quartiles of the dataset. Quartiles divide a dataset into four equal parts, with the first quartile (Q₁) representing the 25th percentile, the second quartile (Q₂) representing the 50th percentile (also known as the median), and the third quartile (Q₃) representing the 75th percentile.
To find the quartiles of the dataset {10, 13, 13, 14, 15, 15, 16, 17, 18}, we first need to order the data in ascending order:
10, 13, 13, 14, 15, 15, 16, 17, 18
The low is the smallest value in the dataset, which is 10.
To find Q₁, we need to find the value that is 25% of the way through the dataset. Since we have 9 values in our dataset, 25% of 9 is 2.25. This means that Q₁ lies between the 2nd and 3rd values in the dataset, which are both 13. To find the exact value of Q₁, we can take the average of these two values:
Q₁ = (13 + 13) / 2 = 13
The median is the middle value in the dataset, which is 15.
To find Q₃, we need to find the value that is 75% of the way through the dataset. 75% of 9 is 6.75, which means that Q₃ lies between the 6th and 7th values in the dataset, which are 16 and 17, respectively. To find the exact value of Q₃, we can take the average of these two values:
Q3 = (16 + 17) / 2 = 16.5
The high is the largest value in the dataset, which is 18.
Now that we have found the quartiles, we can calculate the IQR by subtracting Q1 from Q₃:
IQR = Q₃ - Q₁ = 16.5 - 13 = 3.5
Therefore, the interquartile range of the dataset {10, 13, 13, 14, 15, 15, 16, 17, 18} is 3.5. This tells us that the middle 50% of the dataset is relatively tightly clustered around the median, with values ranging from 13 to 16.5.
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The price of a math book after a discount of 25% is $30.
Answer:
7.5dollars
Step-by-step explanation:
25%/100×$30
Erin has a set of 10 index cards. Each index card is 3 ½ inches long. If she were
to lay the index cards in one long row, how long would the row be?
*
If Erin were to lay the index cards in one long row, the row would be 35 inches long.
What is Multiplication?
Multiplication is an arithmetic operation that is used to find the result of combining equal groups of a given quantity. It involves repetitive addition of equal groups, where one factor represents the number of groups, and the other factor represents the number of items in each group.
Solution:
If Erin has 10 index cards, and each index card is 3 ½ inches long, then the total length of the row would be:
10 cards x 3 ½ inches per card = 35 inches
Therefore, if Erin were to lay the index cards in one long row, the row would be 35 inches long.
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What is the solution to the system of equations?
{y=5x−10
{y=−3x+14
Enter your answer as the correct ordered pair, like this: (42, 53)
multiply the second equation by -1, you get
y=5x-10
-y=3x-14
add both of the equations together
0=8x-24
then
24=8x
x=3
to find y replace x in one of the original equations
y=5x-10
y=5(3)-10
y=15-10
y=5
(x,y)
(3,5)
Does the following table represent equivalent ratios?
Answer:
D
Step-by-step explanation:
We can see that we are not increasing by the same amount.
[tex]\frac{1}{25}= \frac{2}{50} \neq \frac{3}{70} \neq \frac{5}{168}[/tex]
Find the value of each variable. Round to the nearest tenth, if necessary.
16.7, 6.7 and 22 degrees respectively are the measures of a, c and m<C
Solving trigonometry identityThe given diagram is a triangle with the following sides
Hypotenuse = AC = 18
m<A = 68 Degrees
We need to determine the measure of a, b and m<C
Using the trigonometry identity
sin 68 = a/18
a = 18sin68
a = 16.7
Similarly;
cos68 = c/18
c = 18cos68
c = 6.7
Since the sum of angles in a triangle is 180 degrees, hence:
m<C = 90 - m<A
m<C = 90 - 68
m<C = 22 degrees
Hence the measure of a, c and m<C is 16.7, 6.7 and 22 degrees respectively.
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