Answers
The note Micah made for the test on right triangles is correct by the Pythagoras rule.
What is the Pythagoras rule?The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
so by Pythagoras rule we can write:
For the first right triangle;
(x/√2)² + (x/√2)² = x²...(1)
from the left hand side of equation (1): (x/√2)² + (x/√2)²
x²/2 + x²/2
2(x²)/2 = x² {the right hand side of equation (1)}
and for the second right triangle;
(x√3/2)² + (x/2)² = x²...(2)
from the left hand side of equation (2): (x√3/2)² + (x/2)²
x²(3)/4 + x²/4
3x²/4 + x²/4
(3x² + x²)/4
4x²/4 = x² {the right hand side of equation (2)}
Therefore by Pythagoras rule the note Micah made for the test on right triangles is correct
Know more about Pythagoras here:https://brainly.com/question/343682
#SPJ1
Related Questions
In a town the bearing of the swimming pool from the bank is 138 degrees. What is the bearing of the bank from the swimming pool?
Answers
The bearing of the bank from the swimming pool is 42 degrees south of west.
What is temperature ?
Temperature is a measure of how hot or cold something is. More specifically, it is a measure of the average kinetic energy of the particles that make up a substance. When the particles in a substance move faster, their kinetic energy increases, and the temperature of the substance goes up.
Temperature is usually measured in degrees Celsius (°C) or degrees Fahrenheit (°F), although in scientific contexts, the International System of Units (SI) unit of temperature is the kelvin (K). The Celsius scale sets the freezing point of water at 0°C and the boiling point at 100°C, while the Fahrenheit scale sets the freezing point of water at 32°F and the boiling point at 212°F. The kelvin scale sets the zero point at absolute zero (-273.15°C or -459.67°F), the theoretical temperature at which all molecular motion ceases.
According to given condition:
The bearing of the swimming pool from the bank is 138 degrees.
The bearing is the angle measured clockwise from the north direction.
Therefore, to find the bearing of the bank from the swimming pool, we need to add 180 degrees to the given bearing of 138 degrees and then subtract 360 degrees (a full circle) to get the bearing within the range of 0 to 360 degrees.
So,
Bearing of bank from swimming pool = (138 + 180 - 360) degrees = -42 degrees
Therefore, the bearing of the bank from the swimming pool is 42 degrees south of west.
To know more about temperature visit:
https://brainly.com/question/27944554
#SPJ1
35:60 in its simple form
Answers
Answer:7/12
Step-by-step explanation:
Answer:
7/12
Step-by-step explanation:
I need some help thank you :)
Write an algebraic expression to represent the following situation: "Greg has nickels and pennies in his pocket. The number of pennies is 7 less than twice the number of nickels. Let N represent the number the nickels. Write an expression for the number of pennies."
Answers
An expression that is used to represent the number of pennies is; 2n - 7
How to solve Algebra word problems?Algebraic word problems are defined as questions that require translating sentences to equations, then solving those equations. The equations we need to write will only involve basic arithmetic operations.
Now, we are told that;
Number of pennies is 7 less than twice the number of nickels.
Thus. if n represents the number of nickels, then we can say that;
Number of Pennies = 2n - 7
Read more about Algebra Word Problems at; https://brainly.com/question/21405634
#SPJ1
Find the solution of the system of equations
3x+7y=-17
-3x+9y=-15
Answers
Answer: The solution of the system of equations is (x, y) = (-1, -2).
Step-by-step explanation:
We can solve this system of equations by using either elimination or substitution method. Here, we'll use elimination:
Adding the two equations, we get:
(3x + 7y) + (-3x + 9y) = -17 - 15
Simplifying the left side and right side:
16y = -32
Dividing both sides by 16:
y = -2
Now we can substitute y = -2 into either of the original equations and solve for x. Let's use the first equation:
3x + 7(-2) = -17
Simplifying:
3x - 14 = -17
Adding 14 to both sides:
3x = -3
Dividing both sides by 3:
x = -1
Mr. Yu applies 12 ounce of fertilizer to every 58 square meter of his lawn.
How many ounces of fertilizer does Mr. Yu use per square meter for his lawn?
Enter your answer in the box as a fraction in simplest form.
ounces per square meter
Answers
Answer: 0.20689655
Step-by-step explanation: because you take 12 divided by 58
Here is an equation: x + 3y = 6.
Use the whole numbers 0-6 without repeating to create two (x, y) coordinate pairs that are solutions and one that is not.
Answers
The two solutions of the linear equation are:
(0, 2)
(3, 1)
And a coordinate pair that is not a solution is:
(0, 5)
How to find the coordinate pairs?Here we have the linear equation:
x + 3y = 6
And we want to find two ordered pairs that are solutions.
To find them,wecan evaluate in two values of x and then find the correspondent values of y.
if x = 0
0 + 3y = 6
y = 6/3 = 2
if x = 3
3 + 3y = 6
3y = 6 - 3
3y = 3
y = 3/3 = 1
So the two solutions are (0, 2) and (3, 1)
And a point that is not a solution can be one with the same x-value than one of the above ones but a different y-value, like (0, 5)
Learn more about linear equations at:
https://brainly.com/question/1884491
#SPJ1
please answer the question below!
Answers
The values of x in f(x)=2x g(x)=2^x is x=2 and x=0.77.
What is the solution for an equation?
The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.
We are given that;
f(x) 2x and g(x)=2^x
Now,
To graph the functions on the same coordinate plane, we can plot some points and connect them with a line:
f(x) = 2x
(0, 0), (1, 2), (2, 4), (3, 6), ...
g(x) = 2^x
(0, 1), (1, 2), (2, 4), (3, 8), ...
To find the solutions to the equation f(x) = g(x), we need to set the two expressions equal to each other and solve for x:
2x = 2^x
x=2, 0.77
Therefore, the answer of the given equation will be x=2, 0.77
Learn more about solving equations here:
https://brainly.com/question/13072448
#SPJ1
URGENT ANSWER PLS
The explicit formula below describes a linear function, where n
is a positive integer.
f(n)=3n−8
Which recursive formula describes the same function?
A
a1=3an=an−1−8
B
a1=−5an=an−1+3
C
a1=3an=an−1−5
D
a1=−8an=an−1+3
Answers
Answer:
[tex]Option\ B[/tex]
Step-by-step explanation:
[tex]The\ explicit\ formula\ given:\\f(n)=3n-8\\Since\ n\ can\ be\ any\ positive\ real\ number\,\\The\ formula\ describes\ an\ AP\ whose\ d=3.\\Also,\ Substituting\ n=1:\\f(n)=3*1-8\\f(n)=-5\\Hence, a_1=-5[/tex]
[tex]However,\\We\ also\ know\ that,\\d=a_n-a_{n-1}\\Hence,\\a_n-a_{n-1}=3\\Or,\\a_n=a_{n-1}+3\\These\ conditions\ are\ appropriately\ specified\ on\ Option\ B.[/tex]
give example discrete variable
Answers
Discrete variables are a subset of variables that have a limited range of values. A variable that counts how many kids a family has, for instance, can only be a whole number, such as 0, 1, 2, etc.
Discrete variables, like integers or categories, are a form of variable that can only take specified, distinct values. For instance, a discrete variable is the number of siblings a person has because it can only be 0, 1, 2, 3, etc.Discrete variables are a subset of variables that have a limited range of values. A continuous variable, on the other hand, can accept any value within a range.Whole numbers like 0, 1, 2, 3, and so forth are frequently used as discrete variables. The number of kids in a household, the number of products in a shopping cart, or the number of individuals in a room are all examples of discrete variables.
Learn more about variable here
brainly.com/question/29583350
#SPJ4
Ernest has 16 math problems to do for homework. He has already finished p of them. Write an expression that shows how many math problems Ernest has left.
Answers
The mathematical expression that shows the number of math problem left for Ernest is 16-p
What is linear expressions?Linear expressions are expression that it's highest power in of it's variable is 1. Linear expression can have more than one variables.
Some of the examples of linear equations are 2x – 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, 3x – y + z = 3.
Ernest has 16 math problem , he has solved p out of it.
To actually know the remaining math problem left, we subtract the number he has done from the number of original problem
This means the number r of problem left = 16-p
therefore the expression is 16-p
learn more about linear expressions from
https://brainly.com/question/28732353
#SPJ1
How do you find the horizontal and vertical asymptote of a curve?
Answers
Answer: search it up
Step-by-step explanation:
Which graph has a slope of 4/5?
Answers
Answer:
B
Step-by-step explanation:
Rise over run should be 4 rise and 5 to the side run
Answer:
Step-by-step explanation:
The last one (placed below)
Just take two random points (x1,y1) and (x2,y2) from the graph and calculate the slope according to the expression:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
The graph placed below, passes through the points (5,4) and (0,0). So if we replace these coordinates within the formula:
[tex]m=\frac{5-0}{4-0}=\frac{5}{4}[/tex]
9,372,282 rounded to 1,000
Answers
- Hope this Helps
Answer: You would round down so 9,372,000
Step-by-step explanation: Since you are rounding to the nearest 1,000 it would be Answer: 9,372,000
Please give me branliest
Linda bought 6 pounds of rice for 4$ How many dollars did she pay per pound of rice
Answers
Answer: 24
Step-by-step explanation: 6*4=24
4+4+4+4+4+4=24
Answer:
she paid $1.50 / 1lb
Step-by-step explanation:
6lbs divided by $4 = 1.50 or $1.50 / 1lb
According to the midpoint method, the price elasticity of demand for apples between point X and point Y is approximately （0.02/0.1/0.2/5） , which suggests that the demand for apples is (elastic/inelastic) between points X and Y.
Answers
If the price elasticity of demand is equal to 0.02/0.1, then the demand for apples is inelastic and if the price elasticity of demand is equal to 0.2/5, then the demand for apples is elastic.
The price elasticity of demand is calculated using the midpoint method with formula:
Price Elasticity of Demand = (Percent Change in Quantity Demanded) / (Percent Change in Price)
The value of the price elasticity of demand tells us whether the demand for a product is elastic (sensitive to price changes), inelastic (insensitive to price changes), or unitary elastic (neither elastic nor inelastic). A value of price elasticity of demand greater than 1 indicates that the demand for the product is elastic, meaning that a small change in price leads to a large change in the quantity demanded. A value of price elasticity of demand less than 1 indicates that the demand for the product is inelastic, meaning that a small change in price leads to a small change in the quantity demanded.
If the price elasticity of demand is equal to 0.02/0.1, then the demand for apples is inelastic between points X and Y, meaning that a small change in price leads to a small change in the quantity demanded. If the price elasticity of demand is equal to 0.2/5, then the demand for apples is elastic between points X and Y, meaning that a small change in price leads to a large change in the quantity demanded.
To learn more about inelastic here:
https://brainly.com/question/15009640
#SPJ4
PLEASE HELP I REALLY NEED IT! Write an equation for the nth term of the geometric sequence 5,15,45,135,405,…
Then find a8
Answers
Answer:
An equation to represent the given geometric sequence would be [tex]a(x)=5*3^{x-1}[/tex], and a(8) of the geometric sequence will be 10,935.
Step-by-step explanation:
In order to write an equation for a geometric sequence, first we must analyze the sequence to find its starting value and its constant ratio. The starting value is simply the first term in the sequence, which is 5. As for the constant ratio, it is the rate of change that the equation uses. In this sequence, the constant ratio is 3. Now, we can write out an equation for this geometric sequence.
We know the first term of the sequence is 5, and the common ratio is 3, so we can write out a function for the geometric sequence, which will be [tex]a(n)=5*3^{n-1}[/tex]. NOTE that the exponential power is n - 1, and not n. This is because the first term of the sequence is 5, and not the "0th" term, therefore we must subtract 1 from n (the term number) to have the right sequence.
Lastly, we can use the equation [tex]a(n)=5*3^{n-1}[/tex] to find the 8th term of the sequence by replacing n with 8. So [tex]a(x)=5*3^{n-1}[/tex] would become [tex]a(8)=5*3^{8-1}[/tex], and you will get [tex]a(8)=5*3^{8-1}[/tex] ⇒ [tex]a(8)=5*3^{7}[/tex] ⇒ [tex]a(8)=5*2187[/tex] ⇒ [tex]a(8)=10,935[/tex]. Therefore, the equation for the nth term of the geometric sequence would be [tex]a(n)=5*3^{n-1}[/tex], and the 8th term of the sequence is 10,935.
Have a great day! Feel free to let me know if you have any more questions :)
a process in which a number is changed, such as by adding, subtracting, dividing or multiplying is called___
Answers
The process in which a number is changed, such as by adding, subtracting, dividing or multiplying is called mathematical operation.
A mathematical operation is a process that changes a number in some way. The most common mathematical operations are:
Addition is adding two or more numbers together to find their sum.
Subtraction is finding the difference between two numbers by subtracting one from the other.
Multiplication is finding the product of two or more numbers by multiplying them together.
Division is finding the quotient of two numbers by dividing one by the other.
In addition to these basic operations, there are also other mathematical operations such as modulo, exponentiation, and square roots.
These operations are used to perform various mathematical calculations and are fundamental to many areas of mathematics, including algebra, calculus, and geometry. They are also used in many real-world applications, such as in finance, engineering, and science.
To learn more about mathematical operations click on,
https://brainly.com/question/29146737
#SPJ4
how to convert torr to mmhg
Answers
Torr and mmHg are two units of pressure that are often used interchangeably. In fact, 1 mmHg is equal to 1 torr, which means that they are equivalent units of measurement.
To convert torr to mmHg, you can simply multiply the pressure value in torr by 1, since 1 torr is equivalent to 1 mmHg. For example, if you have a pressure of 760 torr, you can convert it to mmHg as follows:
760 torr x 1 mmHg/torr = 760 mmHg
Therefore, 760 torr is equivalent to 760 mmHg. Alternatively, you can also convert mmHg to torr by dividing the pressure value in mmHg by 1. For example, if you have a pressure of 760 mmHg, you can convert it to torr as follows:
760 mmHg ÷ 1 mmHg/torr = 760 torr
Therefore, 760 mmHg is equivalent to 760 torr.
Torr and mmHg are two units of pressure that are often used interchangeably. In fact, 1 mmHg is equal to 1 torr, which means that they are equivalent units of measurement.
To learn more about Torr:
https://brainly.com/question/13893899
#SPJ4
I don’t understand the questions
Answers
The solutions to the expressions using laws of exponents are;
17) y^(19/28)
18) 1/a^(5/9)
How to use Laws of Exponents?The product rule of exponents states that "To multiply two expressions with the same base, add the exponents while keeping the base the same". Thus;
y² × y³ = y²⁺³
= y⁵
17) y^(3/7) × y^(1/4)
Applying product rule of exponents gives;
y^(³/₇ + ¹/₄)
= y^(19/28)
18) The negative exponent rule states that: To convert any negative exponent into positive exponent, the reciprocal should be taken." Thus;
x⁻³ = 1/x³
Thus;
a^(-5/9) = 1/a^(5/9)
Read more about Laws of Exponents at; https://brainly.com/question/11761858
#SPJ1
Does someone mind helping me with this problem? Thank you!
Answers
Answer:3y +=7
=>3y-7-x
=>y=(7-x)/3 Step-by-step explanation:Solve for 'y' means, solve the equation to get the value of y and in terms of ,x means value of y not necessarily in pure constant form,but in the form of x.
Can someone help me with this please
Answers
The sides of the rectangle are
1. (x - 1)2. (x + 6)3. (x - 5)4. (x + 1)the codes are CFID
How to find the unknow part of the rectangleThe unknown part of the rectangle is solved using division of polynomial and the check is completed by multiplication of the polynomial involved
checking for the correct answers
1. 2(x + 5)(x - 1) = (2x + 10)(x - 1)
2x² - 2x + 10x - 10
2x² + 8x - 10
2. 3(x - 1)(x + 6) = (3x - 3)(x + 6)
3x² + 18x - 3x - 18
3x² + 15x - 18
3. 2(x + 1)(x - 5) = (2x + 2)(x -5)
2x² - 10x + 2x - 10
2x² - 8x - 10
4. 5(x - 1)(x + 1) = (5x -5)(x + 1)
5x² + 5x - 5x - 5
5x² - 5
Learn more about polynomials at:
https://brainly.com/question/4142886
#SPJ1
what does (0 -1)(1 -3) equal in y=a(b)^x form
Answers
The exponential equation that coordinate points formed is y = -(3)^x
Determining exponential function from coordinate pointsGiven the coordinate points (0 -1) and (1 -3), we need to determine the equivalent in the form y=a(b)^x
The equivalent simultaneous equation is:
-1 = ab^0 .......... 1
-3 = ab^1 ............ 2
From equation 1;
-1 = a(1)
a = -1
Substitute a = -1 into equation 2
-3 = (-1)b
b = 3
The required exponential equation is y = -1(3)^x
Learn more on exponential equation here: https://brainly.com/question/12940982
#SPJ1
Directions: Using the withholding tax tables for federal and state taxes on Figure 2.2, Figure 2.3, and Figure 2.4 of your textbook, complete the following phrases.
For a single person, 0 allowances, who made $295 last week
State withholding tax: $
Federal withholding tax: $
Answers
The amount of State withholding tax is, $20.65 and the amount of Federal withholding tax is, $17.7.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Assuming the State withholding tax to be 7% and the Federal withholding tax to be 6%.
Given, A person made $295 last week.
Therefore, The amount of Federal withholding tax is,
= $(6/100)×295.
= $17.7.
And, The amount of State withholding tax is,
= (7/100)×295.
= $20.65
learn more about percentages here :
https://brainly.com/question/24159063
#SPJ1
A candle maker is ordering wax. Each small candle uses 12 ounces of wax. Each large candle uses 18 ounces of wax. The candle maker wants to make 42 small candles and 38 large candles.
Which answer is the most reasonable estimate of the total amount of wax needed?
Answers
Answer:
1188
Step-by-step explanation:
12x42 + 18x38 = 1188
How many quart in a cubic feet ?
Answers
The volume of a cubic foot is equal to 29.9220779 US liquid quarts. This conversion factor is based on the definitions of the cubic foot.
So the volume of a cubic foot is equal to 29.9220779 US liquid quarts. This conversion factor is based on the definitions of the cubic foot as a unit of volume equal to a cube with sides that are one foot in length and the quart as a unit of volume in the US customary system.
The quantity of cubic feet can be multiplied by 29.9220779 to get the conversion to quarts. For instance, if you have a container with a 2 cubic foot volume, the quantity of quarts in that container would be:2 cubic feet multiplied by the US liquid quart density of 29.9220779 gives 59.8441558 US quarts. The volume of a cubic foot is equal to 29.9220779 US liquid quarts. This conversion factor is based on the definitions of the cubic foot as a unit of volume equal to a cube with sides that are one foot in length and the quart as a unit of volume in the US customary system.
Learn more about volume here:
https://brainly.com/question/1578538
#SPJ4
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
Answers
Answer:
Option 2 Is Correct
Step-by-step explanation:
The following statements are true about the function and its graph:
The graph of the function is a parabola.
The graph contains the point (0, 0).
The graph does not contain the point (20, -8).
Option 1 is true because the function is a quadratic function, and all quadratic functions have a parabolic graph.
Option 2 is true because the y-intercept of the function is (0,0).
Option 3 is false because the function opens upwards
Please help!!!!!Triangle ABC is similar to triangle FGH. Given the following angle measures, find the
missing angle measures.
Answers
The measures of angles in similar triangles are ∠ F = 22°, ∠ G = 75° and ∠ H = 83°
What are similar triangles?Similar triangles have the same corresponding angle measures and proportional side lengths.
Given that, Triangle ABC is similar to triangle FGH, we need to find the measures of the angles,
The sum of interior angles of a triangle = 180°
Considering Δ ABC,
∠ A + ∠ B + ∠ C = 180°
∠ C = 180°-(22°+75°)
∠ C = 83°
Since, we know that the similar triangles have congruent corresponding angles,
Therefore,
∠ A = ∠ F, ∠ B = ∠ G and ∠ C = ∠ H
Therefore, the measures of angles in Δ FGH are ∠ F = 22°, ∠ G = 75° and ∠ H = 83°
Learn more about similar triangles, click;
https://brainly.com/question/29731302
#SPJ9
Which values of x make the following statement true? Choose all correct
answers.
x-9.5 = a negative number
X = 9
X = -9.5
x = -9
x = 10
X = -10
x = 10.5
Answers
The values of x make the statement true are x = 9 X = -9.5 x = -9 and x = -10
Which values of x make the statement true?From the question, we have the following parameters that can be used in our computation:
x-9.5 = a negative number
Using the above as a guide, we have the following:
x - 9.5 < 0
Make x the subject
x < 9.5
This means that the values of x are less than 9.5
From the options, we have:
x = 9 X = -9.5 x = -9 and x = -10
Read more about equation at
https://brainly.com/question/2972832
#SPJ1
What are the measures of the angles? Please help 55 points.
Answers
Answer: 5
Step-by-step explanation:
Opposite angles of parallelograms are always equal, thus resulting in the equation, 20 + 2x = 6x simplified to 20 = 4x, so x is equal to 5. Hope this helps!
Answer:
The answer is a) 5
Step-by-step explanation:
In excerise 13-16 find the measures of the numbered angles in rhombus DEFG image it’s only one question image below
Answers
The measures of the numbered angles in rhombus DEFG are m ∠ 1 = m ∠ 2 = m ∠ 4 = 27°, m ∠ 3 = 90° and m ∠ 5 = m ∠ 6 = 63°
What is a rhombus?A flat shape with 4 straight sides that are all equal length. Also opposite sides are parallel and opposite angles are equal. It is a type of parallelogram.
Given is a rhombus DEFG, we need to find the measures of the numbered angles,
We know that, diagonals of a rhombus bisect each other at right angle, and also bisects the vertex angles,
Also, the opposite angles are equal,
Therefore,
m ∠ 1 = m ∠ 2 = m ∠ 4 = 27°
m ∠ 3 = 90°
m ∠ 5 = m ∠ 6 = 90° - m ∠ 1
m ∠ 5 = m ∠ 6 = 90° - 27° = 63°
m ∠ 5 = m ∠ 6 = 63°
Hence, the measures of the numbered angles in rhombus DEFG are m ∠ 1 = m ∠ 2 = m ∠ 4 = 27°, m ∠ 3 = 90° and m ∠ 5 = m ∠ 6 = 63°
Learn more about rhombus, click;
https://brainly.com/question/27870968
#SPJ1