Find the surface area of the triangular priam, using a r
The surface area of the prism is square units
necessary
15
17
(The figure is not to scale)
Answer:
127.5
Step-by-step explanation:
multiply 15 and 17 divide by 2 and boom
Let sin (30°)
degrees, for cos(B) = 1/2.
=
Enter the angle measure (B), in degrees
Divide. Write your answer as a fraction or mixed number in simplest form 9÷4⅔
The graph of a function f is shown below. findf(-1)
please be detailed
The function f of the line is f(x) = 2x - 2 and f(-1) = -4.
What is a slope of a line?The slope of a line determines the steepness of the line and is calculated by dividing the vertical change (rise) between any two points on the line by the horizontal change (run) between those same two points. The formula for slope is (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) represent any two points on the line. The slope can be positive, negative, zero or undefined, depending on the direction and steepness of the line. If the line moves up from left to right, it has a positive slope, while a line that moves down from left to right has a negative slope.
From the graph we can take two points on the line (1,0) and (0,-2). Now we can find the equation of the line passing through these points, for that we can use the point-slope form of the equation of a line:
y - y₁ = m(x - x₁)
where m is the slope of the line and (x₁, y₁) is one of the points on the line.
First, we can find the slope:
m = (y₂ - y₁) / (x₂ - x₁) = (-2 - 0) / (0 - 1) = -2/-1 = 2
Next, we can choose either point and substitute the values into the point-slope equation:
y - y₁ = m(x - x₁)
Using point (1,0):
y - 0 = 2(x - 1)
Simplifying:
y = 2x - 2
Therefore, the equation of the line passing through points (1,0) and (0,-2) is y = 2x - 2. That is f(x) = 2x - 2.
f(-1) = 2 × -1 - 2 = -2 -2 = -4.
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Assume that adults have IQ scores that are normally distributed with a
mean of μ = 100 and a standard deviation o= 15. Find the probability
that a randomly selected adult has an IQ between 85 and 115.
Click to view page 1 of the table. Click to view page 2 of the table.
...
The probability that a randomly selected adult has an IQ between 85
and 115 is.
(Type an integer or decimal rounded to four decimal places as needed.)
Assume that adults have IQ scores that are normally distributed with a
mean of μ = 100 and a standard deviation o= 15. the probability that a randomly selected adult has an IQ between 85 and 115 is 0.6826.
How to find the probability?Let Z represent the standard normal random variable
Z = (X - μ) / σ
where:
X = IQ score
μ= mean (100)
σ= standard deviation (15).
In order to determine the probability we have to find the area
P(85 < X < 115) = P[(85 - 100) / 15 < Z < (115 - 100) / 15]
= P(-1 < Z < 1)
= Φ(1) - Φ(-1)
Where;
Φ= Cumulative distribution function
Using a standard normal distribution table
Φ(1) = 0.8413
Φ(-1) = 0.1587
So,
P(85 < X < 115) =0.8413 - 0.1587
= 0.6826
Therefore the probability is 0.6826.
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Downtown Mathville is laid out as a 6 x 6 square grid of streets (see diagram below). Your apartment is located at the southwest corner of downtown Mathville (see point H). Your math classroom is located at the northwest corner of downtown Mathville (see point M). You know that it is a 12-block walk to math class and that there is no shorter path. Your curious roommate (we’ll call her Curious Georgia) asks how many different paths (of length 12 blocks – you don’t want to back track or go out of your way) could you take to get from your apartment to the math class. It should also be clear that no shorter path exists. Can you solve Curious Georgia’s math problem?
Answer: 924 paths
Step-by-step explanation:
Since there is no shorter path, we know that the path must consist of 6 blocks to the north and 6 blocks to the east. Thus, the problem is equivalent to finding the number of ways to arrange 6 N's (for north) and 6 E's (for east) in a sequence such that no two N's are adjacent and no two E's are adjacent.
Let's denote N by 1 and E by 0. Then the problem is equivalent to finding the number of 12-digit binary sequences (i.e., sequences consisting of 0's and 1's) such that there are no consecutive 1's or consecutive 0's.
We can solve this problem using dynamic programming. Let F(n,0) be the number of n-digit binary sequences that end in 0 and have no consecutive 0's, and let F(n,1) be the number of n-digit binary sequences that end in 1 and have no consecutive 1's. Then we have the following recurrence relations:
F(n,0) = F(n-1,0) + F(n-1,1)
F(n,1) = F(n-1,0)
with initial values F(1,0) = 1 and F(1,1) = 1.
Using these recurrence relations, we can compute F(6,0) and F(6,1), and the total number of valid sequences is F(6,0) + F(6,1) = 132. Therefore, there are 132 different paths of length 12 blocks from your apartment to the math class.
Which table shows a proportional relationship between x and y?
Responses
x 1 2 3 4
y 4 10 12 16x 1 2 3 4 y 4 10 12 16 ,
x 2.5 3 5 6
y 5 6 10 15x 2.5 3 5 6 y 5 6 10 15 ,
x 7 14 28 35
y 1 2 4 5x 7 14 28 35 y 1 2 4 5 ,
x 1 3 4 7
y 2 5 8 14
(PLS HURRY I NEED TO GET THIS DONE)
(65 POINTS FOR THE RIGHT ANSWER)
The proportional relationship between x and y is shown by the table:
x 7 14 28 35
y 1 2 4 5
Explain about the proportional relationship:A connection among two factors that changes proportionally is referred to as a proportional relationship. If y=kx, where k is just the proportionality constant, can be used to represent two quantities, x and y, then they are said to be proportional.
This implies that the ratio between both always remains the same and that as x increases, y increases, and as x drops, y decreases.The proportional connection equation's graph is a line that passes directly through the origin.From the given options, consider the table:
x 7 14 28 35
y 1 2 4 5
As per proportional relationship.:
y=kx
k = y/x (must be same in all cases)
k = 1/7
k = 14/2 = 1/7
k = 4/28 = 1/7
k = 5/35 = 1/7
As all the k value for the given values of x and y are found equal.
Thus, the proportional relationship between x and y is shown by the table:
x 7 14 28 35
y 1 2 4 5
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homework i need help tho fr appreciate it!
1. Axis of symmetry : x= -5 2. Axis of symmetry : x =2
Vertex: (-5, 1) Vertex: (2, 8)
Domain: (-∞, ∞) Domain (-∞, ∞)
Ranges: [1, ∞) Ranges (-∞, 8]
3. Axis of symmetry : x = 1 4. Axis of symmetry x = -4
Vertex (1, -1) Vertex = (-4 0)
Domain (-∞, ∞) Domain (-∞, ∞)
Ranges [-1, +∞) Ranges (-∞, 0]
For 4. y = -x² - 8x -16
Axis of symmetry
x = -b / (2a)
x = -(-8) / (2 × -1) = 8 / (-2) = -4
Vertex
y = -(-4)² - 8(-4) - 16
= -16 + 32 - 16
= 0 therefore Vertex is (-4, 0)
Therefore range function (-∞, ∞)
The above answers are for the questions below as seen in the picture
1) y = x² + 10x + 26 2. y = -2x² + 8x 3. y = x² - 2x
Axis of symmetry :
Vertex
Domain
Ranges
4. y = -x² - 8x -16
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17. A babysitter charges a fee for every hour they work. Which statement below could be a
description of the point (1, 8) from this situation?
The point (1, 8) would then represent that the babysitter charges $8 per hour
Which statement could be a description of the point (1, 8)The point (1, 8) in this situation could mean that the babysitter charges $8 for one hour of work.
In general, when working with a fee-per-hour situation, we can use the slope-intercept form of a linear equation, y = mx + b,
Where y represents the total fee, x represents the number of hours worked, m represents the rate (fee per hour), and b represents the initial fee (fee for zero hours worked).If we assume that the initial fee is $0, then the equation for the babysitter's fee would be y = mx, where m is the hourly rate.
The point (1, 8) would then represent that the babysitter charges $8 per hour, since when x = 1 (one hour of work), y = 8 (the fee for one hour).
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F(x)=x-1/x+1 show that f(2x)=3f(x)+1/f(x)+3?
The proof that f(2x)=3f(x)+1/f(x)+3 is shown below.
Mathematical functionTo show that f(2x) = 3f(x) + 1/f(x) + 3, we substitute 2x for x in the expression for f(x):
f(x) = x - 1 / x + 1
f(2x) = 2x - 1 / 2x + 1
Next, we substitute x into the expression for f(x) and add the result to itself twice:
f(x) = x - 1 / x + 1
f(x) + f(x) + f(x) = (x - 1 / x + 1) + (x - 1 / x + 1) + (x - 1 / x + 1)
= 3x - 3 / 3x + 3
We can simplify the expression by dividing both the numerator and denominator by 3:
f(x) + f(x) + f(x) = x - 1 / x + 1
= (1/3) (3x - 3) / (1/3) (3x + 3)
= (x - 1) / (x + 1)
= f(x)
Now, we substitute f(x) and f(2x) back into the original equation:
f(2x) = 2x - 1 / 2x + 1
3f(x) + 1/f(x) + 3 = 3(x - 1 / x + 1) + 1/(x - 1 / x + 1) + 3
= (3x - 3 / x + 1) + (1 / (x - 1 / x + 1)) + 3
= (3x - 3 + (x + 1) / (x - 1)) / (x + 1)
= (2x + 2) / (x + 1)
= 2(x + 1) / (x + 1)
= 2
Thus, we have shown that f(2x) = 3f(x) + 1/f(x) + 3.
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Find the perimeter of the following shape,
given its curves are made from parts of
circles.
Give your answer in terms of TT.
6cm
30cm
14cm
The diagram is not drawn to scale.
The perimeter of the given shape in terms of pi is 22 cm + 25 pi cm.
How do you figure out perimeter?The circumference of the rectangle is equal to the sum of the lengths of its four sides. It is simple to do this because there are two of each side length; all that is needed is to sum the length and width and multiply the result by two.
By multiplying half of the semicircle's circumference by the diameter's length, one can determine the semicircle's perimeter. Thus, the semicircle's perimeter is as follows:
Perimeter of semicircle = 6 cm + (1/2) x pi x 6 cm
Perimeter of semicircle = 6 cm + 3 pi cm
Each quarter circle has a perimeter that is just one-fourth of its circumference. Consequently, the 14 cm quarter circle's perimeter is as follows:
Perimeter of quarter circle with radius 14 cm = (1/4) x 2 pi x 14 cm
Perimeter of quarter circle with radius 14 cm = 7 pi cm
And, the perimeter of the quarter circle with radius 30 cm is:
Perimeter of quarter circle with radius 30 cm = (1/4) x 2pi x 30 cm
Perimeter of quarter circle with radius 30 cm = 15 pi cm
Therefore, the total perimeter of the given shape is:
Perimeter = Perimeter of semicircle + Perimeter of quarter circle with radius 14 cm + Perimeter of quarter circle with radius 30 cm
Perimeter = (6 cm + 3 pi cm) + (7 pi cm) + (15 pi cm)
Perimeter = 22 cm + 25 pi cm.
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Luka and Dana are making cookies for the Westland pantry. They only have up to 6 hours to bake! They can bake 32 chocolate chip cookies in an hour(x), and 20 snickerdoodle cookies in an hour(y). They need it make at least 150 cookies. Which inequality represents the situation?
Option 3. x+y≤6 , 32x + 20y ≥ 150. The inequality 32x + 20y ≥ 150 ensures that they bake enough cookies to meet the requirement of making at least 150 cookies.
The right disparity that addresses what is happening is:
32x + 20y ≥ 150
To see the reason why, we want to consider the quantity of treats Luka and Dana can heat in every hour and the all out number of hours they need to prepare. We should expect they have H hours to prepare, where H = 6 for this situation.
Luka and Dana can prepare 32 chocolate chip treats in 60 minutes, so they can heat a sum of 32x treats in x hours. Likewise, they can prepare a sum of 20y snickerdoodle treats in y hours. To make no less than 150 treats, they need to prepare a mix of chocolate chip and snickerdoodle treats in every hour, with the end goal that the complete number of treats they make in H hours is something like 150.
Thus, the imbalance 32x + 20y ≥ 150 guarantees that they heat an adequate number of treats to meet the necessity of making somewhere around 150 treats.
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Let (-3, 4) be a point on the terminal side of 0. Find the exact values of sin 0, csc 0, and cot 0.
Therefore, sin θ = 4/5, csc θ = 5/4, and cot θ = -3/4 using trigonometric ratio.
Trigonometric ratio calculation.
We know that the point (-3, 4) is on the terminal side of the angle θ, and we can use the Pythagorean theorem to find the value of the hypotenuse:
r² = x² + y²
r² = (-3)² + 4²
r² = 9 + 16
r² = 25
r = 5
Now we can find the values of sin θ, csc θ, and cot θ:
sin θ = y/r = 4/5
csc θ = r/y = 5/4
cot θ = x/y = -3/4
Therefore, sin θ = 4/5, csc θ = 5/4, and cot θ = -3/4.
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Find a quadratic equation which has solutions x=square root of 10and x=-square root of 10. Write the quadratic form in the simplest standard form x^2+bx+c
The quadratic equation in standard form can be written as:
y = x² - 10
How to find the quadratic equation?Remember that for a quadratic equation whose solutions are x₁ and x₂, the quadratic can be written as:
y = (x - x₁)*(x - x₂)
Here the solutions are:
x = √10
x = -√10
Then we can write:
y = (x+ √10)*(x - √10)
Expanding that we will get:
y = x² + √10x - √10x + √10*-√10
y = x² - 10
That is the quadratic.
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HELLLLLLP!!! I WILL GIVE BRAINLIEST!!!
The expression that is equivalent to 6x2y + 2xy^5 include:
2(3x²y + xy^5).
2xy(3x + y⁴)
xy(6x + 2y⁴)
What is an expression?An expression can refer to a variety of things depending on the context in which it is used.
In mathematics and computer programming, an expression typically refers to a combination of numbers, variables, operators, and/or functions that are evaluated to produce a value. For example, "2 + 3" is an expression that evaluates to "5"
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100 Points! Algebra question, photo attached. Please show as much work as possible. Thank you!
Answer is down below!
Step-by-step explanation:
5 x2 =`5 xj2
Zoe makes a total of $72.85 selling cookies and cupcakes at a bake sale. If she sells 17 cupckaes for $3.25 each, how many cookies does she sell at $1,60 each?
PLEASE SHOW WORK
and I have to pass it pls
Answer: 11 Cookies
Step-by-step explanation:
let C be cookies
17($3.25) + 1.60C = $72.85
$55.25 + 1.60C = $72.85
1.60C = $17.60
C=11
She sells 11 cookies
Answer:
11
Step-by-step explanation:
To be able solve, you need to do 17 x 3.25, which would give you 55.25. Then you need to subtract 72.85 by 55.25, which is 17.60. Now divide 17.60 by 1.60. This should give you 11. Therefore, she sold 11 cookies.
I AM SO SORRY IF THIS DIDN'T MAKE SENSE!
Finding the Mean and Median 42,5,25,2,35
The mean of the given set of numbers is 21.8. and median is 25.
Define meanIn mathematics and statistics, the mean is a measure of central tendency that represents the average value of a set of numbers. It is calculated by adding up all the numbers in the set and then dividing by the total number of values. The mean is also known as the arithmetic mean or average.
To find the mean and median of the given set of numbers, we can follow these steps:
Arrange the numbers in order from smallest to largest: 2, 5, 25, 35, 42.
To find the mean, add up all the numbers and divide by the total number of numbers:
Mean = (2 + 5 + 25 + 35 + 42) / 5
= 109 / 5
= 21.8
Therefore, the mean of the given set of numbers is 21.8.
To find the median, we need to find the middle number in the ordered list. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.
In this case, there are 5 numbers, so the median is the middle number, which is 25.
Therefore, the median of the given set of numbers is 25.
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if k(x) = 3x, then f'(x)=? A. x³Ln3 B. 3xLn3 C. 3x/Lnx D. 3/3xLn3
The correct answer is not listed among the options. The correct answer is E. 1/x.
What is function?
In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.
To find f'(x), we need to differentiate the function f(x) with respect to x. Since we are given k(x) = 3x, we can use the chain rule to differentiate f(x) = ln(k(x)) = ln(3x) as follows:
f'(x) = d/dx [ln(3x)]
= 1/(3x) * d/dx [3x] (applying the chain rule)
= 1/(3x) * 3
= 1/x
Therefore, the correct answer is not listed among the options. The correct answer is E. 1/x.
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if a1 = 6 and an =5an-1 then find the value of a6
To find the value of a6, we need to first determine the value of a2, a3, a4, and a5 using the given recurrence relation:
a1 = 6
a2 = 5a1 = 5(6) = 30
a3 = 5a2 = 5(30) = 150
a4 = 5a3 = 5(150) = 750
a5 = 5a4 = 5(750) = 3750
Now, we can find a6 using the recurrence relation:
a6 = 5a5 = 5(3750) = 18750
Therefore, the value of a6 is 18750.
Surface area of this trapezoid prism
The surface area of the trapazoid based prism is 289.6 ft². The right option is b. 289.6 ft².
What is a prism?A prism is a solid shape that is bound on all its sides by plane faces.
To calculate the surface area of the trapazoid based prism, we use the formula below.
Formula:
S.A = c(a+b)+L(a+b+c+d)..................... Equation 1Where:
S.A = Surface area of the trapazoid based prismc = Height of the base of the prismL = Length of the prisma,b,d = The remaining sides of the trapezium.From the diagram,
Given:
c = 5 ftL = 9 fta = 8 ftb = 6 ftd = 5.4 ftSubstitute these values into equation 1
S.A = 5(6+8)+9(8+6+5+5.4)S.A = 70+219.6S.A = 289.6 ft²Hence, the right option is b. 289.6 ft².
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The perimeter of a rectangle is 42.4 inches. The length of the rectangle is three times its
width. What is the length of the rectangle?
The length of the rectangle is 15.9 inches. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
The four fundamental operations, often known as "arithmetic operations," can be used to explain any real number. Operations like quotient, product, sum, and difference come after operations like division, multiplication, addition, and subtraction in mathematics.
We are given that the perimeter of a rectangle is 42.4 inches and the length is three times its width.
Let the width be 'x'.
So, length will be 3x.
From this, we get
⇒ Perimeter = 2 (length + width)
⇒ 42.4 = 2 (3x + x)
⇒ 42.4 = 2 (4x) (Using addition operation)
⇒ 42.4 = 8x (Using multiplication operation)
⇒ x = 5.3 (Using division operation)
So,
⇒ Length = 3 * 5.3
⇒ Length = 15.9 inches
Hence, the length of the rectangle is 15.9 inches.
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A real estate company offered two plans to new employee: plan A is a salary of 2500 per month plus a 6% commission on sales. Plan B is a salary of 3000 per month plus a 4% commission on sales for what amount of monthly sales is plan A better then Plan B
In Linear equation, The of sales/month (x) has to exceed 25,000 units for Plan A to be superior to Plan B.
What is linear equation?
An algebraic equation with simply a constant and a first- order( direct) element, similar as y = mx b, where m is the pitch and b is the y- intercept, is known as a linear equation.
The below is sometimes appertained to as a" direct equation of two variables," where y and x are the variables. Equations whose variables have a power of one are called direct equations. One illustration with only one variable is where layoff b = 0, where a and b are real values and x is the variable.
Let x be # sales/month:
Plan A: $2500 + 6%•x
Plab B: $3000 + 4%•x
For Plan A to be better than Plan B: Plan A > Plan B
So inequality would be: $2500 + 6%•x > $3000 + 4%•x, then solve for x:
2%•x > $500 or x > $500/0.02
x > 25,000
Therefore, the of sales/month (x) has to exceed 25,000 units for Plan A to be superior to Plan B.
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In Linear equation, The of sales of the month (x) has to exceed 25,000 units for Plan A to be superior to Plan B.
What is linear equation?
A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. It is an equation of the form:
y = mx + b.
To solve this system of linear equations, we can use the method of elimination or substitution.
Let x be sales of the month:
Plan A: $2500 + 6% × x
Plan B: $3000 + 4% × x
For Plan A to be better than Plan B: Plan A > Plan B
So inequality would be: $2500 + 6%×x > $3000 + 4%×x
then solve for x:
=> 2500+0.06x > 3000+0.04x
=> 0.06x-0.04x > 3000-2500
=> 0.02x > 500
=> x > 500/0.02
=> x > 25000
Therefore, the of sales of the month (x) has to exceed 25,000 units for Plan A to be superior to Plan B.
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A person invested $840 in an account growing at a rate allowing the money to double every 10 years. How long, to the nearest tenth of a year would it take for the value of the account to reach $1,540?
It would take approximately 7.5 years (or 7 years and 6 months) for the value of the account to reach $1,540, assuming the money grows at a rate allowing it to double every 10 years.
HOW CAN WE CALCULATE THE AMOUNT?To solve this problem, we can use the formula for exponential growth:
[tex]A = P * (1 + r)^t[/tex]
where:
A = final amount (in this case, $1,540)
P = principal amount (initial investment, in this case, $840)
r = rate of growth (as a decimal, in this case, the rate at which the money doubles every 10 years, or 1/10 = 0.1)
t = time (in years, which we need to find)
Plugging in the values:
[tex]1,540 = 840 * (1 + 0.1)^t[/tex]
Dividing both sides of the equation by 840:
[tex]1.83333... = (1.1)^tTaking the natural logarithm of both sides:ln(1.83333...) = ln((1.1)^t)Using the property of logarithms that ln(a^b) = b * ln(a), we get:ln(1.83333...) = t * ln(1.1)Finally, dividing both sides by ln(1.1) to solve for t:t = ln(1.83333...) / ln(1.1)[/tex]
Using a calculator, we can find that t ≈ 7.5 (rounded to the nearest tenth of a year).
So, it would take approximately 7.5 years (or 7 years and 6 months) for the value of the account to reach $1,540, assuming the money grows at a rate allowing it to double every 10 years.
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A rectangular patio has a length of (1 + 2x) yards and a width of (2 - 3x) yards. Which correctly describes the area and perimeter of the patio?
Area of the patio is -6x² + x + 2 square yards and perimeter of the patio is 6 - 2x yards.
What is a yard?A yard is a unit of measurement used to measure length or distance in both the US customary system and the British imperial system. One yard is equal to 3 feet or 36 inches. In the US customary system, a yard is equal to 0.9144 meters, while in the British imperial system, it is equal to 0.9144 meters or 3 feet. Yards are commonly used for measuring larger distances, such as in construction or landscaping, as well as in some sports like American football and cricket.
The area of the rectangular patio is given by multiplying its length by its width, so the area is:
A = (1 + 2x)(2 - 3x)
Now using distributive property we get,
A = 2 - 3x + 4x - 6x²
Simplifying further, we get:
A = -6x² + x + 2
Therefore, the area of the patio is described by the quadratic equation -6x² + x + 2.
To find the perimeter of the patio, we add up the lengths of all four sides. The length and width are given as (1 + 2x) and (2 - 3x), respectively, so the perimeter is:
P = 2(1 + 2x) + 2(2 - 3x)
Simplifying this expression, we get:
P = 2 + 4x + 4 - 6x
P = 6 - 2x
Therefore, the perimeter of the patio is described by the linear equation 6 - 2x.
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Lauren works at a reception hall and is setting tables for a retirement party. She takes a basket of 98 soup spoons, and she places 8 soup spoons on every table she sets.
Write an equation that shows how the number of soup spoons remaining, y, depends on the number of tables Lauren sets, x.
y=
The equation that shows how the number of soup spoons remaining, y, depends on the number of tables Lauren sets, x, is:
y = 98 - 8x
The initial number of soup spoons, 98, is reduced by 8 for each table Lauren sets. Therefore, the number of soup spoons remaining after x tables have been set is 98 - 8x.
Given: △XYZ
and AY←→
is an auxiliary line that is parallel to XZ←→
Prove: The sum of the interior angles in △XYZ
is 180°
The answers are:
[tex]m \angle1+ m\angle2 + m\angle3=180^o[/tex] is the sum of interior angles in a triangle.
[tex]m \angle1+ m\angle5 = m\angle AYX[/tex] is Definition of parallel lines.
[tex]m \angle AYX+m\angle 4=180^o[/tex] Definition of a straight angle
[tex]m\angle5=m\angle2[/tex] is Substitution
[tex]m \angle1+ m\angle5 + m\angle4=m \angle AYX+m\angle 4[/tex] Substitution
Describe Angles?An angle in geometry is the measurement of the amount of rotation that occurs between two lines, rays, or line segments that have a shared endpoint, or vertex. Angles are expressed in terms of degrees, radians, or other angular measuring units.
A protractor, a tool with a semicircular or circular scale and degree markings, can be used to measure angles. Angles may also be labelled using symbols, such as ∠ABC or ∠PQR, in which the letter in the middle of the symbol designates the vertex of the angle.
An auxiliary line that is parallel to XZ given is the triangle formed by XYZ and AY.
[tex]m\angle 1+m\angle 2+m\angle3=180^o[/tex] Definition of the sum of interior angles in a triangle
[tex]m\angle1=m\angle AYX[/tex] Corresponding angles are congruent (alternate interior angles)
[tex]m \angle 2 = m \angle 4[/tex] Corresponding angles are congruent (alternate interior angles)
[tex]m \angle AYX + m \angle 4 = 180^o[/tex] Definition of a straight angle
[tex]m \angle 1 + m \angle 5 = m \angle AYX[/tex] Definition of parallel lines
[tex]m \angle 5 = m \angle 2[/tex] Substitution
[tex]m \angle 1 + m \angle 2 + m \angle 3 = m \angle 1 + m \angle 5 + m \angle 4[/tex] Substitution
[tex]m \angle 1 + m \angle 5 + m \angle 4 = m \angle AYX + m \angle 4[/tex] Substitution
[tex]m \angle 1 + m \angle 2 + m \angle 3 = m \angle AYX + m \angle 4[/tex] Transitive property of equality
[tex]m \angle 1 + m \angle 2 + m \angle 3 = 180^o[/tex] Substitution
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The figure shows ∠ABD is 90°, split by line BC. The measure of ∠ABC is x° and the measure of ∠DBC is (3x + 10)°. What is the value of x? Enter your answer in the box.
Answer:
From the picture,
∠ABC + ∠DBC = ∠ABD
Substituting with data,
x + (3x + 10) = 90
4x + 10 = 90
4x = 90 - 10
4x = 80
x = 80/4
x = 20
Step-by-step explanation:
In this 30°-60°-90° right triangle, the length of the long leg is 9√3
What is the measure of the hypotenuse n and the short leg m?
30°
9√3
n
m
Answer:
30°
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
In a 30°-60°-90° right triangle, the sides are always in the ratio of 1: √3:2, where 1 is the length of the short leg opposite the 30° angle, √3 is the length of the long leg opposite the 60° angle, and 2 is the length of the hypotenuse opposite the 90° angle1234.
In this case, we are given that the long leg is 9√3, so we can use this value to find the other sides by setting up a proportion:
short leglong leg=13
short leg93=13
Cross-multiplying and solving for the short leg, we get:
short leg=393×1=9
Similarly, we can use another proportion to find the hypotenuse:
long leghypotenuse=32
93hypotenuse=32
Cross-multiplying and solving for the hypotenuse, we get:
hypotenuse=32×93=18
Therefore, the measure of the hypotenuse n is 18 and the measure of the short leg m is 9.
Im doing my math homework and i need helpp
the power tells you how many times the base is multiplied.
1) 3^4 = 3 x 3 x 3 x 3
= 81