Triangle 1: 80°, 62° Triangle 2: 62°, 38° - Similar
Triangle 1: 29°, 47° Triangle 2: 91°, 76° - Nοt Similar
Triangle 1: 100°, 45° Triangle 2: 25°, 45° - Nοt Similar
What is Similarity οf Triangles?Twο triangles are similar if their cοrrespοnding angles are cοngruent and their cοrrespοnding sides are prοpοrtiοnal, meaning that they have the same shape but nοt necessarily the same size.
Triangles Similar οr Nοt Similar
Triangle 1: 80°, 62° Triangle 2: 62°, 38° - Similar
Triangle 1: 29°, 47° Triangle 2: 91°, 76° - Nοt Similar
Triangle 1: 100°, 45° Triangle 2: 25°, 45° - Nοt Similar
Tο determine if twο triangles are similar, we need tο check if their cοrrespοnding angles are cοngruent and their cοrrespοnding sides are prοpοrtiοnal.
In the first pair οf triangles, the measures οf the twο angles in Triangle 2 are cοrrespοnding angles tο the twο angles in Triangle 1, sο if we subtract the angle measures frοm 180 degrees, we can see that the third angles in bοth triangles are cοngruent:
Angle 1 in Triangle 1 = 80 degrees, Angle 2 in Triangle 1 = 62 degrees, Angle 3 in Triangle 1 = 180 - 80 - 62 = 38 degrees
Angle 1 in Triangle 2 = 62 degrees, Angle 2 in Triangle 2 = 38 degrees, Angle 3 in Triangle 2 = 180 - 62 - 38 = 80 degrees
Since the cοrrespοnding angles are cοngruent, the triangles are similar.
In the secοnd pair οf triangles, nοne οf the angles are cοngruent and the side lengths are nοt prοpοrtiοnal, sο the triangles are nοt similar.
In the third pair οf triangles, the measures οf twο angles in Triangle 1 are 100 degrees and 45 degrees, while the measures οf twο angles in Triangle 2 are 25 degrees and 45 degrees. The angles are nοt cοngruent, sο the triangles are nοt similar.
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What is the volume of the prism?
Enter your answer, as a mixed number in simplest form, in the box.
cm³
Answer:
40 5/8
Step-by-step explanation:
6 1/2 × 2 1/2
13/2 × 5/2= 65/4
65/4 × 2 1/2
65/4 × 5/2 = 325/8
325/8= 40 5/8
Answer:
40 5/8
Step-by-step explanation:
6 1/2 × 2 1/2
13/2 × 5/2= 65/4
65/4 × 2 1/2
65/4 × 5/2 = 325/8
325/8= 40 5/8
16 Extend Your Thinking Suppose you cut a square shape
in half, as shown. How can you find the area of one part
of the figure?
52 yd
Identifying the values a, b, and c is the first step in using the Quadratic Formula to find solution(s) to a quadratic equation. What are the values a, b, and c in the following quadratic equation? -3x^2 -5x +9 =0
Answer:
The quadratic equation is in the standard form: ax^2 + bx + c = 0. To use the quadratic formula to find the solutions, we need to identify the values of a, b, and c in the equation:
a is the coefficient of the x^2 term, which is -3 in this case.
b is the coefficient of the x term, which is -5 in this case.
c is the constant term, which is 9 in this case.
Therefore, the values of a, b, and c in the quadratic equation -3x^2 - 5x + 9 = 0 are:
a = -3
b = -5
c = 9
A survey was conducted that asked 1015 people how many books they had read in the past year. Results indicated that x=10.5 books and s=16.6 books. Construct a 95% confidence interval for the mean number of books people read. Interpret the interval.
Construct a 95% confidence interval for the mean number of books people read and interpret the result. Select the correct choice below and fill in the answer boxes to complete your choice.
A. There is a 95% probability that the true mean number of books read is between ? and ?
B. If repeated samples are taken, 95% of them will have a sample mean between ? and ?
C. There is 95% confidence that the population mean number of books read is between ? and ?
A 95% confidence interval that the t population mean number of books is between 9.89 and 11.11 books.
What is confidence interval ?
A confidence interval is a statistical range that provides an estimate of the likely range of values for a population parameter (such as a mean, proportion, or standard deviation) based on a sample of data. It is calculated using a specific level of confidence, which represents the probability that the true population parameter falls within the calculated range.
Confidence intervals are typically expressed as a range of values with a margin of error or standard error. The margin of error represents the amount of random variation that is expected due to sampling error, while the standard error reflects the variability of the sample data.
According to the question:
C. There is 95% confidence that the population mean number of books read is between a lower bound of approximately 9.89 books and an upper bound of approximately 11.11 books.
To construct the confidence interval, we can use the formula:
[tex]CI =\bar x \± z* (s/\sqrt{n})[/tex]
substitute the values, we get:
CI = 10.5 ± 1.96 * (16.6/√1015)
CI = (9.89, 11.11)
This means that we are 95% confident that the population mean number of books is between 9.89 and 11.11 books.
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if x = 3/4y and y = 8 what is 3x-4
measure the diameter of the tin in mm and write down the real diameter in mm
The diameter of the tin is 2/5D and the circumference of the tin is 0.4πD
How to determine the circumference and the diameterGiven the the scale factor of dilation is
Container = 2/5 smaller than in reality
This means that
Scale factor = 2/5
So, we have
Diameter = 2/5D where D = diameter in reality
Also, we have
Height = 2/5H where H = height in reality
The circumference is then calculated as
C = πD
So, we have
C = π * 2/5D
Evaluate
C = 0.4πD
Hence, the circumference is 0.4πD
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Complete question
The Ricoffy tin container with no dimensions indicated.The container is 2,5 times smaller than what it is in reality
Diameter of the tin on the picture = ? Height of the tin on the picture = ? Actual weight of coffee = 750 g 1.1 Measure the diameter of the tin in mm and write down the real diameter in mm
The function f(x) is defined below. What is the end behavior of f(x)?
f(x) =-156x + 44x^2 - 4x^3 + 180
As x approaches negative infinity (i.e., x → -∞), the term -4x³ dominates the expression and becomes increasingly positive. Therefore, the end behaviour of f(x) as x → -∞ is f(x) → +∞.
What is behaviour of function?The behavior of a function refers to how the function changes or behaves as the input values (usually denoted as x) approach certain values, typically positive infinity, negative infinity, or a critical point.
According to question:To determine the end behaviour of the function f(x), we need to examine the highest-degree term of the polynomial, which is -4x³.
As x approaches positive infinity (i.e., x → ∞), the term -4x³ dominates the expression and becomes increasingly negative. Therefore, the end behaviour of f(x) as x → ∞ is f(x) → -∞.
Similarly, as x approaches negative infinity (i.e., x → -∞), the term -4x³ dominates the expression and becomes increasingly positive. Therefore, the end behaviour of f(x) as x → -∞ is f(x) → +∞.
In summary, the end behaviour of f(x) is:
As x → +∞, f(x) → -∞As x → -∞, f(x) → +∞To know more about behaviour of function visit:
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I don't understand this as much as I went through it , pls help, very much appreciated
The cost per ride is $1.50: True.
The situation can be represented by the equation y = 15x + 15: False, it can be be represented by y = 1.5x + 15.
The initial entrance fee was $15: True.
How to calculate the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the slope formula, we have the following;
Slope (m) = (18 - 15)/(2 - 0)
Slope (m) = 3/2
Slope (m) = 1.50.
At data point (0, 15), a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 15 = 1.50(x - 0)
y - 15 = -1.50(x)
y = 1.50(x) + 15
When x = 0, the y-intercept is given by;
y = 1.50(x) + 15
y = 1.50(0) + 15
y = 15.
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Jacque bought 2.5 pounds of dark chocolate covered pecans at $0.30 per ounce. In dollars and cents, what was the cost of these pecans?
Answer:
$12.00
Step-by-step explanation:
We know that 1 pound = 16 oz. Thus, we can create a proportion to find how many ounces (x) is 2.5 pounds:
[tex]\frac{1}{16}=\frac{2.5}{x}\\ x=(2.5*16)\\ x=40[/tex]
Since 2.5 pounds = 40 oz, we can now multiply 40 by 0.30 to find the price of 40 ounces of peacans priced at $0.30/ounce:
40 * 0.30 = $12.00
is the statement for a set of decimals, the longest numeral will belong to the largest number?
The statement “For a set of decimals, the longest numeral will belong to the largest number” is false because it doesn't determine the value of a number.
What is a numerical data?In Mathematics and statistics, a numerical data can be defined as a data set that is primarily expressed in numbers only. This ultimately implies that, a numerical data refers to a data set consisting of numbers rather than words.
In Mathematics and statistics, a numeral simply refer to the symbol and numerical figure that is used for representing or denoting a numerical data (number).
For instance, by using the numerical data (numbers) 8 and 9;
8 is represented as VIII in Roman numerals while 9 is represented as IX in Roman numerals. However, the numeral VIII for 8 is longer than the numeral IX for 9, but IX for the number 9 is greater than VIII for the number 8.
In conclusion, we can logically deduce that the given statement is false.
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Complete Question:
Is the statement “For a set of decimals, the longest numeral will belong to the largest number” true or false?
Solve the equation √y+3=√y +√ 3
Step-by-step explanation:
so, it is
sqrt(y + 3) = sqrt(y) + sqrt(3)
first we square both sides :
y + 3 = y + 3 + 2×sqrt(y)×sqrt(3) =
= y + 3 + 2×sqrt(3y) =
= y + 3 + sqrt(4×3y) = y + 3 + sqrt(12y)
0 = sqrt(12y)
we square again :
0² = 12y
0/12 = 0 = y
Find the quotient. What is the remainder?
233 ÷ 6
Answer:
When you divide 233 by 6 using long division, you get:
38
---
6|233
216
---
17
Therefore, 233 ÷ 6 = 38 with a remainder of 17
Answer:
38.83 (the 3 goes on and on)
please help me!
Mark reads 42 pages of a book every 3/4 hour. Write an equation that models the relationship between x, the number of hours Mark reads, and y, the number of pages of the book he reads.
The linear equation that models the number of pages that he reads is:
y = 56*x
How to write the equation?So we know that Mark reads 42 pages every 3/4 of an hour, and we want to write an equation that models the number of pages y that mark reads in x hours, to do so we needto get the unit rate.
Take the quotient between the number of pages and the time above to get:
u = (42 pages)/(3/4 hours) = 56 pages per hour.
Then the number of pages that he can read in x hours is modeled by the linear equation:
y = 56*x
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[tex]8x ^{2} y + 12xy - 16xz[/tex]
Factorize the expression
The factοrs οf the expressiοn is 4x(2xy+3y-4z).
What is factοrizatiοn?Tο factοrise an algebraic statement, we first identify the terms' highest cοmmοn factοrs and then arrange the terms intο grοups in accοrdance with thοse grοups. In plain English, factοrizatiοn is the prοcess thrοugh which an algebraic expressiοn gets expanded in the οppοsite directiοn.
Here the given expressiοn is ,
=> [tex]8x^2y+12xy-16xz[/tex]
Nοw factοrizing the given expressiοn then,
=> 4×2×x×x×y+4×3×x×y-4×4×x×z
=> 4x(2xy+3y-4z)
Hence the factοrs οf the expressiοn is 4x(2xy+3y-4z).
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An investor has an account with stock from two different companies. Last year, her stock in Company A was worth $5150 and her stock in Company B was worth $5250. The stock in Company A has increased 24% since last year and the stock in Company B has increased 20%. What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth (if necessary).
the total percentage increase in the investor's stock account is 22%.
How much is a percentage?In mathematics, a ratio or figure that can be expressed as a fraction of 100 is known as a percentage. If we want to calculate a percentage of a number, we should split it by 100 before multiplying it by the original number. Therefore, the percentage relates to a component per 100. The term percent means "per 100". It is represented by the symbol "%". In mathematics, a percentage is a number or ratio that is represented as a fraction of 100. Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most commonly used to denote it. A percentage is a number that has neither measurements nor a defined unit of measurement.
In the given question,
Increase in stock A= 24% of $5150 = 1236
Increase in stock = 20% of $5250 = 1050
The total percentage increase in the investor's stock account= {(1236+1050)/(5150+5250)* 100=
= 21.98%
≈22%
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B(t) = 100 · [tex]2^{\frac{t}{20} }[/tex]
How many minutes will it take for the culture to achieve 10,000 bacteria
Therefore, it will take about 46.5 minutes for the culture to achieve 10,000 bacteria.
What is expression?In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, x, ÷, etc.) that represents a mathematical quantity or relationship. Expressions can be as simple as a single number or variable, or they can be complex and involve multiple terms and operations. Examples of expressions include 2x + 5, 3y - 7, and (a + b)(c - d).
Here,
We can set up an equation to solve for t:
B(t) = 100 ·[tex]2^{t/20}[/tex]
= 10,000
Dividing both sides by 100, we get:
[tex]2^{t/20}[/tex] = 100
Taking the logarithm of both sides with base 2, we get:
t/20 = log2(100)
t = 20 · log2(100)
Using a calculator, we can simplify this to:
t ≈ 46.5 minutes
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What is the domain of the square root function graphed below?
Assume lines n and m are parallel. If μ(∠1) =147°, find the following angle measures.
Hence, the angles' measurements are as follows: ∠1 = 147° , ∠2 = 33° and ∠3 = 147° as Interior angles on the same side of the transversal.
what is angles ?A geometric shape known as an angle is created by two rays or line segments that have a shared termination, or vertex. Angles, which express how much of a turn or rotation there is between two rays or line segments, are measured in degrees or radians. They are frequently employed in physics, engineering, geometry, trigonometry, and other disciplines.
given
The characteristics of parallel lines and transversals allow us to determine that:
Interior angles on the same side of the transversal: 1 + 2 = 180°; 2 + 3 = 180°.
We know that (1) = 147°, thus we can apply the first equation to determine 2:
∠1 + ∠2 = 180°
147° + ∠2 = 180°
∠2 = 33°
We can apply the second equation to determine 3 now that we know 2:
∠2 + ∠3 = 180°
33° + ∠3 = 180°
∠3 = 147°
Hence, the angles' measurements are as follows: ∠1 = 147° , ∠2 = 33° and ∠3 = 147° as Interior angles on the same side of the transversal.
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- 1 and combining like terms
(x² - 4x+9)-(3x² - 6x-9)
Combining the like terms of the expressions (x² - 4x+9)-(3x² - 6x-9) gives -2x² + 2x + 36
What are algebraic expressions?Algebraic expressions are simply described as those mathematical expressions that are known to consist of certain variables, coefficients, terms, factors and constants.
Algebraic expressions are also identified with arithmetic operations. These arithmetic operations are;
SubtractionBracketDivisionParenthesesMultiplicationAdditionFrom the information given, we have;
(x² - 4x+9)-(3x² - 6x-9)
First, expand the bracket
x² - 4x + 9 - 3x² + 6x + 27
Now, collect the like terms
x²- 3x² - 4x + 6x + 9 + 27
Add or subtract
-2x² + 2x + 36
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solve for me please
(5xy+3x-7)+(3xy-xy+3y+4)
Answer:
Step-by-step explanation:
7xy+3x+3y−3
Translate the point (- 8, - 6) to the new origin given (h, k). Given center (h, k) = (5, 4), find point (x', y').
(13, 10)
(-13, -10)
(-3, -2)
Translation of the point (-8, -6) to the new origin (5, 4) is thus (-13, -10). Hence, the response is (-13, -10).
what is coordinates ?A sequence of numbers known as coordinates is used to describe the location of a point or object in space or on a plane. Coordinates in two-dimensional space typically have two values, which are typically written as (x, y), where x denotes the horizontal position and y denotes the vertical position. Coordinates in three dimensions can have three values, denoted as (x, y, z), where x, y, and z stand for the position along the x, y, and z axes, respectively. In many different fields, such as geometry, physics, and computer graphics, coordinates are used.
given
The coordinates of the new origin must be subtracted from the given point in order to translate the point (-8, -6) to the new origin (h, k) = (5, 4).
x' = -8 - 5 = -13
y' = -6 - 4 = -10
Translation of the point (-8, -6) to the new origin (5, 4) is thus (-13, -10). Hence, the response is (-13, -10).
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Can someone help me please
Answer: X=55 and Y=125
Step-by-step explanation:
y is an external angle
so according to external angle property sum of two angles is equal to external angle. two angles are given- 35 and 90
90+35=y
y=125
now with angle sum property
90+35+x=180
125+x=180
x=55
please mark it brainliest
1.1.3 Quiz: Exponents
Question 2 of 10
Simplify (6^7)³.
Answer:6^21
Step-by-step explanation:
What is the symbolic representation for this argument?
If a polygon has exactly three sides, then it is a triangle.
Jeri drew a polygon with exactly three sides.
Therefore, Jeri drew a triangle.p
The fact that Jeri drew a polygon with precisely three sides serves as the representation of this claim.
Describe a polygon.A polygon is a closed shape made of line segments rather than curves on a two-dimensional plane.
A minimum of three line segments need to be joined end to end to produce a closed figure. As a result, a triangle and a 3-gon are both terms for a polygon with at least three sides.
The polygons are divided into many categories based on the sides and angles, including:
Normal PolygonUneven PolygonPolygon Convexrounded polygonsIn this instance, Jeri's drawing of a polygon with precisely three sides serves as the symbolic expression of this argument.
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Question
Brian invests his money in an account paying 8% interest compounded semiannually. What is the effective annual yield on
this account? Enter your response as a percentage rounded to two decimal places and omit the percent sign (7.25%
should be input as 7.25.)
Step-by-step explanation:
Semi-annual means an interest period is 1/2 year
1/2 *8% = 4% = .04
effective annual interest rate is then
(1+ .04)^2 - 1 = .0816 or 8.16 (%)
Eliana opened a savings account and deposited $700.00 as principal. The account earns 4%
interest, compounded monthly. What is the balance after 10 years?
Answer:
We can use the formula for compound interest to find the balance in Eliana's savings account after 10 years:
A = P(1 + r/n)^(nt)
where A is the balance, P is the principal (initial deposit), r is the annual interest rate as a decimal, n is the number of times interest is compounded per year, and t is the time in years.
Substituting the given values, we get:
A = $700(1 + 0.04/12)^(12*10)
Simplifying, we get:
A = $700(1.0033333)^120
Using a calculator, we get:
A ≈ $1,038.81
Therefore, the balance in Eliana's savings account after 10 years is approximately $1,038.81.
Gianna is going to throw a ball from the top floor of her middle school. When she throws the ball from 48feet above the ground, the function h(t)=-16t^2+32t +48 models the height,h, of the ball above the ground as a function of time, t. Find the zero of this function that tells us when the ball will hit the ground.
The 12 students in the after-school gaming club are all wearing hats. The hats are
either red, blue, green, or black. There are 2 red hats and 1 blue hat. If you select a
student at random, it is likely that the student has a green hat. What is the greatest
possible number of black hats in the group? Explain.
The probability of the maximum number of black hats that could be present in the group is 2.
Since the probability of selecting a student with a green hat is the highest, it is likely that there are more green hats than any other color. Let's assume that there are 7 green hats. If there are 7 green hats, then there are only 5 hats left for the remaining colors. However, we know that there are only 2 red hats and 1 blue hat, leaving a maximum of 2 hats for the black color. Therefore, the greatest possible number of black hats in the group is 2, which would give a total of 2 red hats, 1 blue hat, 7 green hats, and 2 black hats. In conclusion, if the probability of selecting a student with a green hat is the highest, then the greatest possible number of black hats in the group is 2.
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A bag with 8 marbles has 8 blue marbles. A marble is chosen from the bag at random.
Easy simultaneous equation question - help me i cba :)
Answer:
Let x be the cost of 1 kg of mushrooms and y be the cost of 1 kg of turnips.
From the given information, we can form two equations:
2x + 2.5y = 8.55 (Equation 1)
3x + 4y = 13.10 (Equation 2)
To solve for x and y, we can use the method of elimination. Multiplying Equation 1 by 4 and Equation 2 by -2, we get:
8x + 10y = 34.20 (Equation 3)
-6x - 8y = -26.20 (Equation 4)
Adding Equation 3 and Equation 4, we get:
2x + 2y = 8
Simplifying this equation, we get:
x + y = 4 (Equation 5)
Now we have two equations: Equation 2 and Equation 5. We can solve for x and y using substitution or elimination. Here, we will use substitution.
From Equation 5, we can express x in terms of y as:
x = 4 - y
Substituting this expression for x into Equation 2, we get:
3(4 - y) + 4y = 13.10
Simplifying and solving for y, we get:
y = £1.50
Substituting this value for y into Equation 5, we can solve for x:
x + £1.50 = 4
x = £2.50
Therefore, the cost of 1 kg of mushrooms is £2.50 and the cost of 1 kg of turnips is £1.50.
a) The cost of 1 kg of turnips is £1.50.
b) The cost of 1 kg of mushrooms is £2.50.