To know if a triangle is a 30-60-90 triangle, you must check if the triangle's angles measure 30°, 60°, and 90°. Additionally, the sides of a 30-60-90 triangle will have a specific ratio. The longest side of the triangle is always double the length of the shortest side, and the side opposite the 60° angle is always the square root of 3 times the shortest side.
1. Measure the angles of the triangle.
2. Check if the angles measure 30°, 60° and 90°.
3. Measure the sides of the triangle.
4. Check if the longest side is double the length of the shortest side and if the side opposite the 60° angle is the square root of 3 times the shortest side.
To know if a triangle is a 30-60-90 triangle, you must check if the triangle's angles measure 30°, 60°, and 90°. Additionally, the sides of a 30-60-90 triangle will have a specific ratio. The longest side of the triangle is always double the length of the shortest side, and the side opposite the 60° angle is always the square root of 3 times the shortest side.
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Consider y =f(x)=-3x+2 . Using space below, determine the equation that represents the inverse f(x)
Answer: [tex]f^{-1}(\text{x}) = \frac{2-\text{x}}{3}[/tex]
Explanation:
Swap x and y, then solve for y to get the inverse.
[tex]f(\text{x}) = -3\text{x}+2\\\\\text{y} = -3\text{x}+2\\\\\text{x} = -3\text{y}+2\\\\\text{x}-2 = -3\text{y}\\\\\text{y} = \frac{\text{x}-2}{-3}\\\\\text{y} = \frac{2-\text{x}}{3}\\\\f^{-1}(\text{x}) = \frac{2-\text{x}}{3}\\\\[/tex]
Jessica and Josh are selling entertainment books to raise money for the art room after school one book sells for $18 Jessica receive the prize for selling the most books in the school Jessica sold 13 times more books than Josh together they sold 280 books how many did each of them sell
Based on the question above, Jessica sold 260 books and Josh sold 20 books.
What is the math equation about?Let x be the number of books Josh sold
We know that:
Jessica sold 13x books
Together they sold 280 books
So we can set up an equation:
x + 13x = 280
14x = 280
x = 20
Josh sold 20 books
Jessica sold 13 * 20 = 260 books
Therefore Jessica = 260 books sold and Josh = 20 books sold.
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At a certain zoo, the average mass of one cow is measured to be 410410 kilograms. Use scientific notation to express the mass of 6060 cows
The scientific notation to express the mass of 60 cows is 2.46 × 10⁴ kg. It is determined after multiplying the mass of one cow by the number of cows.
What is scientific notation?Scientific notation is a way of expressing very small or very large numbers in a simpler form.
In scientific notation, the number is written as
a.b × 10ⁿ
Where
1 ≤ a < 10n is an integerIf the mass of one cow is 410 kg, find the mass of 60 cows in scientific notation!
The mass of 60 cows would be
= number of cows × mass of one cow
= 60 × 410 kg
= 24,600 kg
In scientific notation, it is
24,600 kg = 2.46 × 10,000
24,600 kg = 2.46 × 10⁴ kg
Hence, the mass of 60 cows in scientific notation is 2.46 × 10⁴ kg.
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A and B are vertical angles. A=(x+15) B=(5x−17) the measure of b
Simplifying algebraic expressions
Answer:
Step-by-step explanation:
Plug in 5 for h
6(5)+7(5)
30+35=65
65
Answer:
[tex] \sf \: 6h + 7h = 65[/tex]
Step-by-step explanation:
Given information,
→ 6h + 7h
→ h = 5
Now the final value will be,
→ 6h + 7h
→ 6(5) + 7(5)
→ 30 + 35
→ 65 => final value
Hence, the answer is 65.
28 = 4/5x - 8 what value of x makes the equation true?
Answer:
1.6285
Step-by-step explanation:
28 = 4/5x-8
Cross multiply
140x-224=4
140x =224+4
140x = 228
x = 228/140
x = 1.6285
An amusement park has a collection of scale models, with ratio 1:20, of buildings and other sights from around the country. The height of the United States Capitol is 289 feet. What is the height in feet of its replica at this park, rounded to the nearest whole number
The height in feet of its replica at this park, rounded to the nearest whole number is 14 feet.
What connection exists between height and separation?Distance is the measurement of an object's horizontal distance from a specific location, whereas height is the measurement of an object's height in the vertical direction.
Since the heights of real buildings are 1:10 times higher than those of model buildings, this is evident. We also know that the actual height of the US Capitol is 289 feet, so we divide that figure by 20 to determine the model's height. That amounts to 14.45, rounding to 14. Thus, the duplicate is 14 feet, rounded up to the nearest whole number.
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2. Which of the following. are solutions to 5.7 + x = -3.5? Choose as many as
apply.
A. -3.5+5.7
B. 3.5-5.7
C. -3.5-(-5.7)
D.-3.5-5.7
Answer:
option D is correct
5.7+x=-3.5
x= -3.5-5.7
Answer:
D
Step-by-step explanation:
5.7 + x = - 3.5 ( subtract 5.7 from both sides )
x = - 3.5 - 5.7 ( x = - 9.2 )
Don’t know need help
Answer:
37?
I am SO sorry if this is wrong
A mountain on a tropical island experiences changes in its height due to volcanic activity. Its current height is 2,827 meters, which is 10% taller than it was when the mountain was last measured. How tall was it then?
Answer:
2,570 meters
Step-by-step explanation:
110% of what number is 2827
1.1x = 2827 Divide both sides by 1.1
[tex]\frac{1.1x}{1.1}[/tex] = [tex]\frac{2827}{1.1}[/tex]
x = 2570
e:f =2:5 f:g=3:4 work out e:g in simpliest form
After a work out, the simplest form of e:g is 3:10.
What is a ratio?Ratio is an expression which shows the relationship between two numbers or variables. It can generally be expressed in two forms, viz; a:b or a/ b.
To work out the simplest form of e:g as required in the question,
e/ f = 2/ 5
2f = 5e ........... 1
f/g = 3/ 4
3g = 4f ........... 2
From equation 1,
f = 5e/2
substitute the value of f in equation 2
3g = 4(5e/2)
3g = 10e
Therefore, e:g is given as;
3/ 10 = e/ g
3:10 = e: g
Thus in its simplest form, e:g = 3:10
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Buffalo New York had 2ft of snow on the ground before a snowstorm during the storm snow fell at an average rate of % in hr
The expression when Buffalo New York had 2ft of snow on the ground before a snowstorm is 2 - 0.25h.
How to illustrate the expression?From the information, Buffalo New York had 2ft of snow and we want to find the. expression based on the information given.
An expression have at least two terms which have to be related by through an operator.
Since Buffalo New York had 2ft of snow on the ground before a snowstorm during the storm snow fell at an average rate of 25% in every hr. The expression will be:
2 - (25% × h)
= 2 - 0.25h
h = number of hours.
The expression is 2 - 0.25h.
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Complete question
Buffalo New York had 2ft of snow on the ground before a snowstorm during the storm snow fell at an average rate of 25% in every hr. Illustrate the expression
Can you help me with this
a) The ordered pair so that the set still remains the function is (-5, 17)
b) The ordered pair so that the set does not remain the function is (-26, 15).
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
A Relation is said to be a function if the input value or the x- value is unique and have their corresponding output.
But if the input value repeats then it may no longer be a function.
First, Add a ordered pair so that the set still remains the function as
(-5, 17)
and, Add a ordered pair so that the set does not remain the function as
(-26, 15).
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What is the midpoint of the x intercepts of x 4 )( x 4?
The midpoint of the x-intercepts of f(x) = (x - 4)(x + 4) is (0, 0).
The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.
A compass and straightedge setup can be used to locate the midpoint of the line segment they determine given two points of interest. By initially building a lens out of circular arcs with equal radii centered at the two endpoints and joining the cusps of the lens, one can determine the midpoint of a line segment immersed in a plane. The midpoint of the segment is then the place where the line joining the cusps intersects the segment.
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How do you explain 2 3?
This is a coordinate pair of a point. 2 and 3 denotes X and Y coordinate respectively.
What is coordinate system?The system that is used to represent the location of points in the space is termed as coordinate system. There are two types of coordinate system such as polar and cartesian. In case system there are two reference axes which are perpendicular to each other.
In the cartesian system points are represented with respect to a vertical axis named Y axis and a horizontal axis named X axis.
How do we explain 2 3?We stated earlier that in the cartesian system a location of a point is identified by a pair of numerical terms.
So, 2, 3 indicates a pair of numerical terms. 2 denotes the X coordinate of the point and 3 denotes the Y coordinate of that point.
In the next, the distance of the point from X axis is 3 unit and distance from Y axis is 2 unit.
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Complete question is: In the point (2,3) which point denotes the y-coordinate.
find the gradient of a line passing through each of the following pair of points (0,-5) and (6,3)
30 students went on a field trip to the science museum. 60% of the students tried the new Gravity Buster ride at the museum.
What will make the expression x² 4x+ a perfect square trinomial?
In order for an expression, such as x² + 4x + , to become a perfect square trinomial, it must be in the form of a² + 2ab + b².
What is perfect squares?Perfect squares are whole numbers that are the result of multiplying a given number by itself. For example, 4 is a perfect square because it is the result of multiplying 2 by itself. Similarly, 9 is a perfect square because it is the result of multiplying 3 by itself. Other examples of perfect squares include 16 (4x4), 25 (5x5), 36 (6x6), and so on.
To do this, you must factor the expression. In this case, the expression can be factored into (x + 2)².
Once the expression has been factored into a perfect square trinomial, it can be written as (x + 2)².
This is a perfect square trinomial because it represents the area of a square, as the length of each side is equal to (x + 2).
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Which strategies can be used to find the product of 1,587 x 1,000? Select two options
Answer:
Step-by-step explanation:
you can multiple and get 1,587,000]and then you divide to get 8 [tex]\sqrt{1587000[/tex]A stone was thrown into a pond from 8 feet above the surface of the water in the pond. Justin wrote 8 feet to represent the height from which the stone was thrown. What does 0 represent in this situation
prove that (4x-5)2 -5x(3x-8) is a positive for all values of x
To prove that (4x - 5)^2 - 5x(3x - 8) is positive for all values of x, we can start by expanding the expression:
(4x - 5)^2 - 5x(3x - 8) = 16x^2 - 40x + 25 - 15x^2 + 40x = -14x^2 + 80x - 25
Now, we can complete the square to find that this expression is always positive:
-14x^2 + 80x - 25 = (-14x^2 + 80x) - 25
= (-14x^2 + 80x + (80/2)^2 - (80/2)^2) - 25
= (-14x + 40)^2 - 25 - 40^2 + 40^2
= 15^2 - 25
= (15 - 5)(15 + 5)
= 10(20)
= 200
Since this expression is equal to 200, which is a positive number, we can conclude that (4x - 5)^2 - 5x(3x - 8) is positive for all values of x.
What is the perimeter of a 30 60 90 triangle whose shorter leg is 5 inches long?
The perimeter of the triangle is 23.66 inches
According to the 30-60-90 triangle theorem, the hypotenuse is twice as long as the shorter leg. Additionally, the sides of this particular triangle have a ratio of 1:2: [tex]\sqrt{3}[/tex].
Now in the question
As shown in the diagram, if the shorter leg of the triangle at 30°, 60°, and 90° is extended in the direction of the right angle by an amount equal to itself and connected to the third point, we obtain a triangle that is congruent with the original triangle. It is clear that the combined triangle is an equilateral triangle with equal sides and angles.
The greatest leg, AB, in the picture is therefore twice as long as the shortest leg of the original triangle and equal to base BC.
Therefore according to the question
given that the shorter leg is 5 inches,
hypotenuse = 5*2 = 10 inches.
the longest leg = 5[tex]\sqrt{3}[/tex], and
The perimeter is thus 5 + 10 + 5[tex]\sqrt{3}[/tex] = 15 + 5[tex]\sqrt{3}[/tex] = 23.66 inches
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Can someone please explain how to do inequalities in math.
please add an example too.
Adrianne is reading a book. She reads 275 pages and has 155 pages to go. How many pages p is Adrianne’s book? Write and solve an equation to find the book’s length in pages
There will be a total of 430 pages in the book or the length of the book in pages = 430.
Adrianne reads 275 pages
She is left with 155 pages.
So, for converting the above in form of an equation,
Let us assume that the total pages in the book be x
Let us assume that the total number of pages she read = a
Assuming that the total remaining pages that she does not read = b
So, the total number of pages will be = total pages which she read + total remaining pages.
=> x = a+b
Now, solving the values given in the questions,
The value of a = 275 and the value of b = 155
So, the total number of pages in the book = 275+155 = 430
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What is the example of zero polynomial?
A polynomial in which the degrees of all the variables is 0 is called a zero degree polynomial .
The zeros of a polynomial p(x) are all the x-values that make the polynomial equal to zero.
For example- 6 x 0 , − 9 a 0.
Polynomial
A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division .
Degree of polynomial
The degree of a polynomial is defined as the highest exponent of a monomial within a polynomial. Thus, a polynomial equation having one variable which has the largest exponent is called a degree of the polynomial .
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1.12 less the product of m and n.
2.the product of two numbers decreased by their sum.
3.two thirds of a number subtracted from the square of the same number.
4.the sum of the product and quotient of two numbers decreased by 10.
5.the cube of the sum of a number and 2.
6.twice the difference between four times b and twice x.
7.the sum of 5 times y and 6 divided by twice a.
8.three-fourths of x added to thrice of x is equal to twelve.
Pa Help
Answer:
1.12 < mn
xy - x + y
2/3x - x²
xy + x/y - 10
(x + 2)³
2(4b - 2x)
The Reed family is selecting a furniture set. A furniture set has a bed, a desk and a dresser. There are 4 beds, 3 desks, and 1 dresser to select from. How many different furniture sets could they select?
Answer:
12.
Step-by-step explanation:
right!!
2x + 4y = -16
solve for y
Answer: y = -1/2x -4
Step-by-step explanation:
To solve for y, subtract 2x on both sides
2x-2x + 4y = -16 - 2x
Simplify
4y = -16 - 2x
Divide by 4 on both sides to get y by itself
4y/4 = -16 - 2x/4
Simplify
y = -4 - 1/2x
Switch the right-side terms to write them in slope-intercept form
y = -1/2x -4
What is the largest prime factor of 999?
Answer:
37
Hope this helps :)
What does log of e mean?
The Power e is to which a number should be raised to get the specified number is called the logarithm of that specific number. For example, the logarithm to the base of 10 of 1000 is 3 because 10 raised to the power 3 is 1000.
The logarithmic function is the reverse of the Mathematical function of the exponential function. The logarithmic function is log ax = y is equal to x = ay.
There are mainly two types of logarithms normally used in Mathematics. They are one is common logarithms and second natural logarithms.
The log number ‘e’ is an irrational Mathematical constant and is mostly used as the base of natural logarithms. The number ‘e’ is the only unique number in mathematics whose value of natural logarithm is equal to unity.
The value of log ‘e’ was calculated in 1683 by Jacob Bernoulli.
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