A perpendicular bisector is a bisector to a line segment which makes an angle of 90° with the line segment.
A perpendicular bisector is usually constructed by using a compass and a straightedge. It can also be constructed using a protractor.
Construction of perpendicular bisector using a compass and straightedge.
First draw the line segment, lets say AB.Using your compass measure a radius which is more than half of the line segment. We can measure this by keeping the compass ant point A, and take a measure beyond the mid point.Now place the compass at A, and draw an arc with the measured radius.Place the compass at B and draw an arc with the same radius.The arcs meet above and below the line. Take the straightedge and draw a line which passes through both the intersection of arcs.Thus we get the perpendicular bisector.
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What is the distance of the point (- 5 6 from the origin?
The point (-5,6), which is (0,0), is √61 units away from the origin.
What is coordinate?A pair of numbers called coordinates are used to locate a point or a shape in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane. The term "ordinate" refers to a point's separation from the x-axis when scaled with the y-axis. Coords are the collective noun for the abscissa and ordinate. The study of algebraic equations on graphs is known as coordinate geometry. The plotting of points, lines, and curves on an x and y axis is an illustration of coordinate geometry.
Here,
distance=√(y2²-y1²)+(x2²-x1²)
=√(6²-0²)+((-5)²-0²)
=√6²+-5²
=√36+25
=√61
The distance of the point (-5,6) from the origin that is (0,0) is √61 units.
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scores on an exam follow an approximately bell shaped distribution with a mean of 76.4 and a standard deviation of 6.1 points. approximately, what percentage of the data is less than 76.4?
The percentage of the data that is less than 76.4 will be 50% if scores of an exam follow an approximately bell-shaped distribution with a mean of 76.4 and a standard deviation of 6.1.
To determine by how many standard deviations the raw score is above or below the mean z score used.
z = (x - μ)/σ
x: raw score, σ: standard deviation, μ: mean
For x = 76.4 points:
z = (76.4 - 76.4)/6.1 = 0
Now, the percentage of data is less than 76.4:
P(x < 76.4) = P(z < 0)
We know that the area is equally distributed around the y-axis.
So, P(z<0) = 50 %
Therefore, the percentage of the data is less than 76.4 will be 50%.
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Question
Write the word sentence as an inequality. Then solve the inequality.
The quotient of a number x
and 4 is at most 5.
An inequality is
.
The solution of this inequality is
.
The solution that represents the given equality is x<= 20
What is Linear equation ?
Linear equation can be defined as the equation in which the highest degree is one.
The inequality that represents the word sentence is:
x/4 <= 5
The solution is x<=20
The quotient is the division of the first number by the second, thus the quotient of x and 4 is given by:
x/4
At most 5 means that the result is of 5 or less, thus, the inequality is:
x/4<=5
Solving it, similarly to an equation:
x <= 4*5
x <= 20
The solution is x<= 20 .
Hence, The solution that represents the given equality is x<= 20
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which statement is true regarding the rotated image?
The result will be A'B' ║ C'D' and A'D' ║ B'C'
What is rotational transformations?A rotation is a type of transformation which is a turn. A figure can be turned clockwise or counterclockwise on the coordinate plane. In both transformations, the size and shape of the figure stays exactly the same. A rotation is a transformation that turns the figure in either a clockwise or counterclockwise direction.
Given that parallelogram ABCD is being rotated by 180°
Since, we know that, rotating a figure gives the figures which is congruent to the original.
Therefore, the results will be,
A'B' ║ C'D'
A'D' ║ B'C'
Also,
AB = A'B'
CD = C'D'
AD = A'D'
BC = B'C'
And,
Corresponding angles are also equal,
Hence, ABCD ≅ A'B'C'D'
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A seagull is perched in a tree 62 feet above sea level. Directly below the seagull, an egret is flying 24 feet above sea level. Directly below the birds, a clown fish is swimming at 17 feet below sea level.
Select all TRUE statements.
A. The distance between the heights of the egret and the clown fish is 41 feet.
B. The difference in height between the egret and the clown fish is 41 feet.
C. The difference in height between the egret and the clown fish is -41 feet.
D. The difference in height between the egret and the seagull is -38 feet.
E. The difference in height between the egret and the seagull is 38 feet.
F. The distance in height between the egret and the seagull is -38 feet.
PLEASE ANSWER ONLY IF YOU KNOW ANSWERS. WILL VOTE BRAINLIEST IF ANSWERS ARE CORRECT. 15 POINTS.
Answer:
A. The distance between the heights of the egret and the clown fish is 41 feet.
B. The difference in height between the egret and the clown fish is 41 feet.
D. The difference in height between the egret and the seagull is -38 feet.
E. The difference in height between the egret and the seagull is 38 feet.
are TRUE statement.
In 3–5 sentences, explain 2 causes and 2 effects of the stock market crash of 1929.
The stock market crash of 1929 was caused by a combination of factors, including overvaluation of stocks and economic policies that favored the wealthy.
The effects of the crash were widespread and long-lasting, leading to the Great Depression and causing significant economic and social upheaval.
One of the causes of the stock market crash of 1929 was the overvaluation of stocks, where prices were much higher than the underlying value of the companies. Many investors were buying stocks on margin, which means they were borrowing money to buy stocks, this lead to the overvaluation of stocks. Another cause was the economic policies that favored the wealthy, such as the high tariffs on imported goods and the lack of regulations on the stock market, which allowed for speculation and manipulation.
The effects of the stock market crash of 1929 were far-reaching and long-lasting. One of the most significant effects was the Great Depression, which led to high unemployment, widespread poverty, and significant declines in industrial production and economic activity. The crash also led to a decline in consumer confidence, which further slowed economic growth and led to a decline in consumer spending. The crash also led to a decline in the standard of living for many Americans and the loss of savings for many investors.
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Name: Date: Period: Score: First attempt due: Practice Worksheet: Properties of Exponents Final corrections due: Simplify each expression completely using properties of exponents. Answers should have positive exponents only and all numbers evaluated, for example 5 3 = 125. Each set of problems will use the property listed above as well as a combination of properties attempted in previous sets. NEGATIVE EXPONENT AND ZERO EXPONENT PROPERTIES 1. ???? −7 = 2. (21c 18) −1 = 3. (3???? 2 ) 0 = 4. 5(x 0 )y −1 = PRODUCT OF POWERS PROPERTY 5. ???? 7???? 12 = 6. c 3 c 8 c −5 = 7. (2???? 7 )(−4???? 9???? 5 ) = 8. (9x 10y 3 )(−x 5y 3 ) = QUOTIENT OF POWERS PROPERTY 9. ???? 12 ????7 = 10. 6c 3 3c−5 = 11. 2???? 7 −4????9????5 = 12. 9x 10y 3 −x 5y3 = POWER OF A POWER PROPERTY 13. (???? 3 ) 4 = 14. (c −1 ) 3 = 15. (???? 5 ) −2 = 16. (6x 3y)(x 2 ) −2 = POWER OF A PRODUCT PROPERTY 17. (8???? 5 ) 2 = 18. (2c −1 ) −3 = 19. (−2???? 10) −2 = 20. (4x 2y 3 ) −2 (−x 10) 2 = POWER OF A QUOTIENT PROPERTY 21. ( ???? 2 ) 4 = 22. ( 25c −1 5 ) 2 = 23. ( −2???? 11???? 5 4????−2???? 2 ) 2 = 24. ( (−2x) 2 3xy2 ) 3 = MORE PRACTICE WITH MIXED PROPERTIES 25. ( ???? 2 ) 4 (8???? 5 ) 2 ????−1????10 = 26. ( 16c 6c −2 (2c 2) 3 ) −1 = 27. −2???? ????5 ( ???????? 5 −2???? 10) 2 = 28. ( (4x 2y 3) 0 −3x−1y2 ) 3 = BONUS QUESTIONS 29. ( 9 20 ???? 5 ) (2???? −2 ) ( 4 3 ???? 9 ) 30. 8(–m0???? 2) 3 (−???? 3) 2 m6????0(−2m−2????4) 3
The four basic properties of exponents are the negative exponent property, the product of powers property, the quotient of powers property, and the power of a power property.
The properties of exponents are a set of rules that allow us to simplify terms that contain exponents.
Negative exponent property states that when a negative exponent is present, the base and the exponent are switched and the sign of the exponent is changed. For example, x-2 = 1/x2.
The product of powers property states that when two terms with the same base are multiplied, the exponents are added together. For example, x3 x4 = x7.
The quotient of powers property states that when two terms with the same base are divided, the exponents are subtracted. For example, x6/x2 = x4.
The power of a power property states that when a term with an exponent is raised to another power, the exponents are multiplied. For example, (x3)2 = x6.
These properties can be used to simplify expressions that contain exponents. For example, the expression (−2m−2????4) 3 can be simplified using the power of a power property by multiplying the exponents. The expression simplifies to −2m−6????12.
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How do you find the derivative of log base 3?
In a right-angled triangle, the difference between two of the angles is 20°.
a ) Work out the size of the angles in the triangle.
b )How many solutions are there to part a? Explain why. C) For each solution to part a, write the ratio of the angles from smallest to biggest in its simplest form
On solving the provided question, we can say that since it is a right angle x + (x-20) + 90 = 180 => x = 35
what are angles?In Euclidean geometry, an angle is a shape made up of two rays, referred to as the angle's sides, that meet at a point in the middle known as the angle's vertex. Two rays can generate an angle that is in the plane where the rays are located. The meeting of two planes also creates an angle. They are referred to as dihedral angles. An angle is the shape created by two rays or lines that have a shared termination in plane geometry. The Latin word "angulus," which meaning "horn," is the source of the English term "angle." The vertex is the common terminal of the two rays, which are referred to as the sides of the angle.
difference between two of the angles is 20°.
since it is a right angle
x + (x-20) + 90 = 180
2x = 70
x = 35
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Find x.
5x
3x
X+ 12 12
Therefore , the solution of the given problem of equation comes out to be x=8 for the given equation.
What exactly is the equation?A mathematical formula between the two statements is employed to denote equality when the equivalent letter (=) is utilized. The equivalence of numerous mathematical variables is demonstrated using algebraic equations, which are statements of fact. For instance, the expression data d + 6 = 12 separates the values document d + 6 or 12 with an equal sign. One can quantify the number of syllables that each sides of each symbol corresponds to. A symbol's meaning usually runs counter to itself.
Here,
Given:
=> 5x/3x = x+12 /12
=> 5/3 = x/12 + 1
=> 5/3 -1 = x/12
=> 2/3 = x/12
=>2/3*12 = x
=> 24/3 =x
=>8=x
Therefore , the solution of the given problem of equation comes out to be x=8 for the given equation.
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Alguien que me ayude resolviendo , es ejercicio aritmético
-7+[-5+2 × (3-8×5)] - (-3) (-1) + 9
The result of the numeric expression is given as follows:
110.
How to solve the arithmetic expression?
The arithmetic expression for this problem is defined as follows:
-7+[-5+2 × (3-8×5)] - (-3) (-1) + 9
Outside the brackets, the multiplication takes precedence, hence:
(-3) x (-1) = 3.-(-3) x (-1) = -3.-7 - 3 + 9 = -10 + 9-10 + 9 = -1.Hence the expression can be simplified as follows:
-1 + [-5+2 × (3-8×5)]
Outside the parenthesis, we have that:
-5 + 2 = -3.
Inside the parenthesis, the multiplication takes precedence, hence:
3 - 8 x 5 = 3 - 40 = -37.
Hence:
-1 + [-5+2 × (3-8×5)] = -1 + [-3 x (-37)]
Applying the multiplication and the addition, the result of the expression is given as follows:
-1 + [-3 x (-37)] = -1 + 111 = 110.
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Solve.
The table shows how much money a concession stand
earns selling hamburgers. The graph shows how much
money the stand earns selling hot dogs. Find and
compare the rates of change for these two functions.
Hamburger Sales
Number of
Hamburgers Sold
1
2
3
4
Amount
Earned (5)
16
24
32
Amount Earned (5)
Hot Dog Sales
Company A: c-8h+ 10, where c- total cost
(in dollars) and h= number of hours
Company B: $15 per hour
12345 789
Number of Hot Dogs Sold
3 Two companies charge differently for canoe rentals,
as shown below. What is the rate of change for each
function? What is the cost to rent a canoe for 4 hours
from each company?
The graph shows a function. Write an equation with
the same initial value and a rate of change that is less
than the rate of change of the function shown in
the graph.
Y
S
7
Answer: iI dunno but its 56778888b a
Step-by-step explanation:
If f(x) =x/4 -3 and g(x) = 4ײ +2x−4, find (f+g)(x).
(f+g)(x)=4x2+94x−7Explanation:(f+g)(x)=f(x)+g(x)Substitute f(x)=x4−3:(f+g)(x)=x4−3+g(x)Substutitute g(x)=4x2+2x−4:(f+g)(x)=x4−3+4x2+2x−4Combine like terms:(f+g)(x)=4x2+94x−7
Please help
-6 (x + 7) = -30
X=?
Answer:
x = -2
Step-by-step explanation:
-6 ( x+ 7) = -30
-6x - 42 = -30
-6x = 12
x = -2
I hope this helps
Which symbol is used to symbolize represent function?
Answer:
The function symbol f(x)
Step-by-step explanation:
I need the work and the answer
Therefore , the solution of the given problem of percentage comes out to be she spend $39 on the sandals.
Define a percentage.A number or figure that is expressed as a fraction of 100 is known as a percentage in mathematics. There are also sporadic uses of the acronyms "pct.," "pct," and "pc." However, the "%" symbol used to represent it is often employed. No dimensions exist; the % amount is flat. Percentages are essentially fractions because their numerator is 100. A percent symbol (%) should be placed in front of a number to indicate that it is a percentage. For instance, if you answered correctly 75 out of questions in total on a test, you'd get a 75%.
Here,
Given :
Money = $80
Spent 25% on pair of shorts
=> 25/100 * 80 = 20
and
left money = 80 -20 =60
After that she spend 65% on sandals:
=> 65/100 * 60
=> 39
Thus , She spend $39 on the sandals.
Therefore , the solution of the given problem of percentage comes out to be she spend $39 on the sandals.
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Provide numerical measures of individuals. The values of a quantitative variable can be added or subtracted and provide meaningful results.
Quantitative variables offer measurable numerical values that can be added to or subtracted from to produce accurate results. Quantitative discrete variables have a finite or countable number of positive values.
Continuous variables are quantitative and have an endless range of uncountable possible values. Discrete and continuous data are both types of quantitative or numerical information. Measurements are often continuous, while counts are typically discrete. Discrete data are counts that can never be more precisely calculated. Usually, this entails integers.
A family's number of children would serve as an illustration. Individuals are complete, indivisible entities, hence this data is discrete. A family does not contain 1.7 or 2.3 children.
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the specification or description of the relationship between the dependent and independent variables is generally called
The specification or description of the relationship between the dependent and independent variables is generally called a function
A function describes the mapping from input variables to output variable.
The input variable is called independent variables, while the output is called dependent variable as its value depends on the values of the inputs.
Example:
y = f(x) = 2x + 1
In this function:
x = input = independent variable
y = output = dependent variable
An output can also be a function of several variables. For example, the cost of renting a car is a function of the number of renting days and the distance it travels. Hence, the cost is dependent variable, whereas the number of days and distance are the independent variables.
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Which of the following is the domain of the inverse function?
Answer:
X is an element of real numbers
Answer: The range of a function f(x) is the domain of the inverse function f−1(x). The domain of f(x) is the range of f−1(x)
Step-by-step explanation:
What is the domain and range
Domain and Range. The domain of a function is the set of values that we are allowed to plug into our function.
What is the Domain and Range?Range and Domain. The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
Important values that aid in defining a relation include domain and range. The collection of input values is the domain. These values are graphed on the axis of a coordinate graph and are represented by the independent variable. The collection of output values for a function is known as the range.
An further method to determine the domain and scope of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.
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How do you solve algebraic expressions Grade 9?
One can solve basic algebraic expressions by following these steps.
Students typically learn to solve basic algebraic expressions by following these steps:
Identify the variable and the coefficient (number in front of the variable) in the expression.
Use the order of operations (PEMDAS) to simplify any arithmetic within the expression.
Use the distributive property to combine like terms.
Isolate the variable on one side of the equation by using inverse operations (such as adding or subtracting the same value from both sides, or dividing or multiplying both sides by the same non-zero value).
Substitute in a value for the variable to find the numerical value of the expression.
It's good to practice with a lot of examples and check the solutions and ask for help if needed.
Example:
Solve for x: 3x + 2 = 12
variable is x, coefficient is 3
nothing to simplify
nothing to combine
subtract 2 from both sides: 3x = 10
divide both sides by 3: x = 10/3 or 3.3333
x = 3.3333
It's important to note that solving algebraic expressions can become more complex as the student progresses, but the basic steps remain the same.
Thus, One can solve basic algebraic expressions by following these steps.
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What is the only solution of 2x² 8x X² 16?
The only solution to an equation 2x² + 8x = x² - 16 is z = -4
Consider given equation.
2x² + 8x = x² - 16
Subtract x² from each side of equation.
2x² + 8x - x² = x² - 16 - x²
x² + 8x = -16
Add 16 to each side of equation.
x² + 8x + 16 = -16 + 16
x² + 8x + 16 = 0
We factorize above quadratic equation.
x² + 4x + 4x + 16 = 0
x(x + 4) + 4(x + 4) = 0
(x + 4) (x + 4) = 0
(x + 4)² = 0
x + 4 = 0
x = -4
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The complete question is:
What is the only solution of 2x^2 + 8x = x^2 - 16?
In a rectangle , the diagonal amount with the base is 72.
The diagonal is 2 cm bigger than the base.
Find the perimeter and S of the rectangle.
The rectangle in the example has a 173.70 cm perimeter.
What is Perimeter?The perimeter of a form is the space surrounding its edge. you can find the perimeter of various forms by summing the lengths of their sides.
Given, In a rectangle, the diagonal amount with the base is 72. The diagonal is 2 cm bigger than the base.
Since the Diagonal is 72 cm
and also given base = diagonal - 2
Base = 70
Because Diagonal ² = base² + height²
height² = 72² - 70²
Height² = 284
Height = 16.85
Thus the perimeter = 2*(base + height)
Perimeter of rectangle = 2 * (70 + 16.85)
the perimeter of the rectangle = 173.70
Therefore, the perimeter of the given Rectangle is 173.70 cm.
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So I'm in 6th-grade accelerated class learning 7th-grade math, and our subject is More Two-Step Equations. One of the questions is 8/11(n - 10) = 64. I have to find n, but what does n equal?
The value of n from 8/11(n - 10) = 64 is 98.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
8/11(n - 10) = 64.
Now, to find n first multiply both side by 11/8
8/11 (n- 10) x 11/8 = 64 x 11/8
n- 10 = 88
Now, add 10 both side
n - 10 + 10 = 88 + 10
n = 98
Hence, the value of n is 98.
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Can 2 acute and 1 right angle form a triangle?
A triangle with one right angle and two acute angles is called a right-angled triangle.
A right angle is one that is 90 degrees in length. It is the most frequently encountered angle in our daily lives. It can be noticed in room corners, box edges, mobile phone screens, and so on.
A square's and a rectangle's sides always make a right angle with each other. It is represented in radians as /2.
The angle formed by two lines that are perpendicular to each other is called a right angle. A right angle is equal to 90° and is in the shape of the letter "L". In the following figure, ray AB and BC form a right angle ABC.
Thus, a triangle with one right angle and two acute angles is called a right-angled triangle.
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8x11=(8x10)+(1x10) what is the answer
Answer:8*11=80
8*10+1*10=90
Step-by-step explanation:
Which parent functions have inverses which are also functions?
If any vertical line intersects a graph in at most one point, then that graph is the graph of a function.
A function is a set of ordered pairs in which for each x value, there is only one y value. A parent function is the simplest form of a function, with the basic form of the equation.
A parent function with an inverse that is also a function must have an equation that is invertible. In other words, the equation must be able to be rearranged so that the y variable is on one side and the x variable is on the other.
For example, let's look at the parent function f(x) = x^2. To find its inverse, we can rearrange the equation to make y the subject: y = x^2. Then, we can take the square root of both sides, giving us x = sqrt(y). This is the equation of the inverse of the parent function, which is also a function. Similarly, the parent function f(x) = ln(x) has an inverse of f-1(x) = e^x. This is also a function, as each x value has only one y value.
Therefore, for a parent function to have an inverse that is a function, the equation must be invertible. This means that the equation must be rearrangeable so that the y variable is on one side and the x variable is on the other.
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I really need help on this
Answer:
287 boxes
Step-by-step explanation:
Alan starts with $25 and wants to know how many bags of popcorn he must see, at $3,74 each, to accumulated at least the $1100 he needs for a deposit on a trip. The attched woksheet illustrates the steps Alan takes to determine he needs 287 boxes to make the deposit. More would be good, but 287 is a fine target.
Olivia started the school year with 14 pencils, and now has 28 pencils. She says, “This is a 200% increase because I have twice as many pencils as I started with!” Is she correct or incorrect? Why?
Answer: Olivia is incorrect.
Step-by-step explanation:
Since Olivia had twice as much, a 200% increase means x + 2x, which is basically 3x. She actually has a 100% increase, because she has 2x as much, not 2x more. If she actually had 200% more, she would have 42 pencils instead.
What is the slope of the line that passes through points E(6, 8) and F(6, −2)?
Answer:
Step-by-step explanation:
Answer:
-4
Step-by-step explanation:
m = y2 - y1/x2 - x1
m = (-2 - 6)/(8 - 6)
m = -8/2
m = -4