Answer:
1.8
3 percent of 60 is 1.8
Please answer the attached picture
Answer:
25
Step-by-step explanation:
(f+g)(x) also stated as f(x)+g(x)
2x²+3x-2
where x=3
2(3)²+3(3)-2
2(9)+9-2
18+7
25
Is tonys addition correct or wrong and why?
Step-by-step explanation:
Customers eat 7/8. Tony says it's 14/16
[tex] \frac{7}{8} = \frac{14}{16} [/tex]
because 7 times 2 is 14 and 8 times 2 is 16, so he got to the correct conclusion
Tony says...
[tex] \frac{1}{7} + \frac{1}{14} = \frac{14}{16} [/tex]
There's no way to get this answer because neither 7 or 14 goes evenly into 16.
Tony got the correct answer, but his addition is incorrect for that said reason
Answer:
Tony's addition is correct.
Step-by-step explanation:
Tony needs to add 7 two times, since the customers ate 7 slices of out both pizzas. And, 7 + 7 is 14, and you need to also count the total slices of pizza, which is 16. So, the fraction would be 14/16, which can be simplified into 7/8, which is just 14/16 multiplied by 2.
The x distribution must be normal in order to use a chi-square distribution to test the variance. What are some methods you can use to assess whether the x distribution is normal?
Hint: Try utilizing a goodness-of-fit test. (Select all that apply.)
a)Look at a normal quantile plot to check for a straight line.
b)Use a histogram or boxplot to check for symmetry and outliers.
c)Look at a normal quantile plot to check for a curved line.
d)Use a goodness-of-fit test to see if the distribution follows the empirical rule.
e)Look at a residual plot for a parabolic pattern.
The required methods we can use to assess whether the x distribution is normal is mentioned in (a) and (b). Options (A) and (B ) are correct
What is a normal distribution?Normal distributions can be altered to standard normal distributions by the formula:
Z = (X - μ)/σ
Where x is a value from the initial normal distribution, μ is the mean of the initial normal distribution, and σ is the standard deviation of the initial normal distribution. The standard normal distribution is periodically called the z distribution.
Here,
The methods to assess whether the x distribution is normal are:
a) Look at a normal quantile plot to check for a straight line.
b) Use a histogram or boxplot to check for symmetry and outliers.
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Angel has two baby guinea pigs, Whiskers and Scamp. The sum of their weights is 1 7/8 pounds Whiskers weighs 3/8 pound less than Scamp. How much does each guinea big weigh?
Answer:
[tex]\frac{9}{8} [W]\ and \ \frac{3}{4} [S].[/tex]
Step-by-step explanation:
1. if the weight of Whisters is 'w', then the weight of Scamp is 'w-3/8'; then
2. it is possible to make up the equation:
[tex]w+w-\frac{3}{8}=1\frac{7}{8};[/tex]
3. if to solve this equation, then w=9/8 - this is the weight of Whiskers;
the weight of Scamp is 9/8-3/8=6/8=3/4 [pounds].
(4)/(9)((3)/(2)z^(2)y^(3))^(5)
???
how do i do this ??
Answer:
The expression can be solved using algebraic methods. The result is -(2^7)z^2y^3.
Step-by-step explanation:
The solution to the equation 4/(9)((3/2)z^2y^3)^5 is y^15z^10. This can be solved by using the steps of algebraic manipulation. First, the parentheses can be simplified by multiplying the numerator and denominator together, resulting in 4/27z^2y^3. Then, the exponent can be applied to both terms, resulting in y^15z^10. Finally, this answer can be checked by substituting it into the original equation and verifying that it is true.
Tell weather DEF and GEF can be proven congruent.
A) Yes, DEF and GEF can be proven congruent by SSS.
B) No, DEF and GEF aren’t congruent because they share a side.
C) No, there isn’t enough information provided.
D) Yes, DEF and GEF can be proven congruent by HL.
Answer:
D) Yes, DEF and GEF can be proven congruent by HL.
Step-by-step explanation:
Given triangles DEF and GEF with sides DF and GF marked congruent, and a right angle at E, you want to know if congruence can be proved, and how.
CongruenceThe hypotenuses of the right triangles are marked congruent. The shared leg EF is congruent to itself, so enough information is provided to claim congruence by the HL theorem.
__
Additional comment
Sides DE and GE are not marked congruent, so you only can make claims about 2 of the sides. SSS congruence cannot apply.
The HL theorem only applies to right triangles, which these are.
2.4 divided by 0.75
The answer is 3.2
But I don’t know how to get there I only get 3 with a remainder of 15
I need to see the work please help.
Hi There! Here's your answer:
To make it easier, let's write this in fraction form:
[tex]\frac{2.4}{0.75}[/tex]
Now, multiply the numerator and denominator by 100 to remove the decimal point.
[tex]\frac{2.4}{0.75}[/tex] × [tex]\frac{100}{100}[/tex] = [tex]\frac{240}{75}[/tex]
Now, you can either divide using long division, or you can take out common factors and simplify the fraction that way.
Upon common factor simplification, we get the final fraction to be:
[tex]\frac{240}{75}[/tex] = [tex]\frac{48}{15}[/tex] (Common factor 5) = [tex]\frac{16}{5}[/tex] (Common factor 3)
Therefore, we get the final fraction as [tex]\frac{16}{5}[/tex] which is 3.2.
HOPE IT HELPS!
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 6.7 years, and standard deviation of 1.7 years. The 7% of items with the shortest lifespan will last less than how many years?
Answer:
4.2 years
Step-by-step explanation:
If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:
[tex]\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]
Given:
Mean μ = 6.7Standard deviation σ = 1.7Therefore, if the lifespans of an item are normally distributed:
[tex]\boxed{X \sim\text{N}(6.7,1.7^2)}[/tex]
where X is the lifespan of the item.
Converting to the Z distribution
[tex]\boxed{\textsf{If }\: X \sim\textsf{N}(\mu,\sigma^2)\:\textsf{ then }\: \dfrac{X-\mu}{\sigma}=Z, \quad \textsf{where }\: Z \sim \textsf{N}(0,1)}[/tex]
To find the number of years that 7% of the items with the shortest lifespan will last less than, we need to find the value of a for which P(X < a) = 7%:
[tex]\implies \text{P}(X < a) =0.07[/tex]
Transform X to Z:
[tex]\text{P}(X < a) = \text{P}\left(Z < \dfrac{a-6.7}{1.7}\right)=0.07[/tex]
According to the z-tables, when p = 0.07, z = -1.47579106...
[tex]\implies \dfrac{a-6.7}{1.7}= -1.47579106...[/tex]
[tex]\implies a-6.7= -2.50884480...[/tex]
[tex]\implies a=4.19115519...[/tex]
[tex]\implies a=4.2\; \sf years[/tex]
Therefore, the 7% of items with the shortest lifespan will last less than 4.2 years.
Prove by contradiction that for any positive two real numbers, x and y, if x · y ≤ 50, then either x < 8 or y < 8.
The assumption must be false, which means that either x < 8 or y < 8 must hold true.
What is the Proof by Contradiction?
A proof by contradiction is a method of proof in which we assume the opposite of what we want to prove, and then show that this assumption leads to a contradiction. The contradiction then serves as evidence that the assumption must be false, and therefore the original statement must be true.
In this case, we want to prove that for any positive real numbers x and y, if x · y ≤ 50, then either x < 8 or y < 8.
Suppose for the sake of contradiction that x and y are positive real numbers such that x · y ≤ 50 and x ≥ 8 and y ≥ 8. Then, since x and y are positive, we have x · y = xy ≥ 64, which contradicts the assumption that x · y ≤ 50.
Therefore, we have shown that the assumption that x and y are positive real numbers such that x · y ≤ 50 and x ≥ 8 and y ≥ 8 leads to a contradiction.
Hence, the assumption must be false, which means that either x < 8 or y < 8 must hold true.
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Let V be the space spanned by the two functions cos(t) and sin(t). Find the matrix A of the linear transformation T(f(t))=f′′(t)+3f′(t)+7f(t) from V into itself with respect to the basis {cos(t),sin(t)}.
Answer: The matrix A of the linear transformation T(f(t)) = f''(t) + 3f'(t) + 7f(t) from the space spanned by the functions cos(t) and sin(t) into itself with respect to the basis {cos(t), sin(t)} can be found by computing the images of the basis vectors under T and expressing those images as linear combinations of the basis vectors.
We have:
T(cos(t)) = -cos(t)'' - 3cos(t)' - 7cos(t) = -cos(t) - 3(-sin(t)) - 7cos(t) = -8cos(t) - 3sin(t)
T(sin(t)) = -sin(t)'' - 3sin(t)' - 7sin(t) = -sin(t) - 3cos(t) - 7sin(t) = -8sin(t) + 3cos(t)
So, with respect to the basis {cos(t), sin(t)}, the matrix A is:
A = [ -8, -3; 3, -8 ]
This is the matrix representation of the linear transformation T with respect to the basis {cos(t), sin(t)}.
Step-by-step explanation:
Help meeeeeeeeeeeeeeee
Answer: If you help me I will help you Cuz I been screaming for help all day
Step-by-step explanation:
In the diagram, the ratios of two pairs of corresponding
sides are equal.
N
3
M
X 6 Z
9
To prove that ALMN-AXYZ by the SAS similarity
theorem, it also needs to be shown that
O
O ZN ZX
O ZL ZZ
O ZL ZY
Since you have two sets of side lengths that are in the same ratio, you need the included angles. The included angle of two sides is the angle formed by the two sides. ∠N ≅ ∠Z
What is the SAS similarity theorem?Two triangles are said to be comparable if the two sides of one are in proportion to the two sides of another triangle and the angles that the two sides inscribe in each triangle are equal.
Hence, if you align both triangles' equations, option A A. ∠N ≅ ∠Z is the answer.
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1.11. Let a and b be positive integers (a) Suppose that there are integers u and v satisfying au + bv 1. Prove that gcd(a, b) = 1(b) Suppose that there are integers u and v satisfying au + bu = 6. Is it necessarily true that gcd(a, b) = 36? If not, give a specific counterexample, and describe in general all of the possible values of gcd(a,b)?
(a) gcd(a, b) must equal 1.
(b) No, it is not necessarily true that gcd(a, b) = 6 just because au + bv = 6.
What do you mean by integer?An integer is a whole number that can be positive, negative, or zero. It is a number without any fractional or decimal component. Integers include the counting numbers (1, 2, 3, ...) and their negatives (-1, -2, -3, ...), as well as 0. Examples of integers are -5, -3, -1, 0, 1, 2, 3, 5, and so on. Integers are used in a variety of mathematical operations, such as addition, subtraction, multiplication, and division, and they play a key role in many areas of mathematics, including number theory, algebra, and discrete mathematics.
(a) Suppose that gcd(a, b) is not equal to 1. Then, there exists a positive integer k such that k divides both a and b. Let a = ka' and b = kb', where a' and b' are relatively prime.
Since there are integers u and v satisfying au + bv = 1, it follows that ka'u + kb'v = k(a'u + b'v) = k. But this means that k divides 1, which is a contradiction. Hence, gcd(a, b) must equal 1.
(b) No, it is not necessarily true that gcd(a, b) = 6 just because au + bv = 6. Consider the counter example a = 4 and b = 2. In this case, we have 2u + 4v = 6, but gcd(a, b) = 2, not 6.
In general, if there are integers u and v satisfying au + bv = k, then gcd(a, b) divides k. However, the converse is not necessarily true; that is, just because gcd(a, b) divides k does not mean there are integers u and v satisfying au + bv = k.
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Gcd(a,b) can take on any value from 1 to the minimum of a and b (inclusive). For example, if a = 6 and b = 1, then au + bu = 6, but gcd(6,1) = 1.
What is GCD?GCD is an abbreviation for Greatest Common Divisor. It is the greatest positive integer that divides two or more numbers without a remainder. It is used to simplify fractions and solve linear Diophantine equations. The Euclidean algorithm or the prime factorization method can be used to compute GCD.
(a) Assume u and v are integers such that au + bv = 1. So a and b must have no common factor, because the only way to add two integers and obtain 1 is if they have no common factors. As a result, gcd(a,b) = 1.
(b) No, it is not always the case that gcd(a,b) = 6. For example, if an is 6 and b is 1, au + bu equals 6, while gcd(6,1) equals 1. In general, gcd(a,b) can have any value between 1 and the minimum of a and b. (inclusive).
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Stories in the World's Tallest Buildings
The number of stories in each of a sample of the would's 29 tallest building follows. Construct a grouped frequency distribution and
a cumulative frequency distribution with 9 classes.
70 55 100 60 70 85 64 69 80 75
88
65 80 102 55 75 72 60 79 88
55 78 77 71 105 88 90 54 56
a. Find the class limits. The first lower class limit is 54.
b. Find the class boundaries.
c. Find the class frequency.
Class Limits
54-
Class boundaries
Frequency
The class limit or the Class width is 6.
What is measure of dispersion?Data scattering is indicated by a measure of dispersion. It provides a clear picture of their distribution while explaining the discrepancy between the data from different sources. The measure of dispersion illustrates and provides information on the range and centre value of a single item.
Dispersion, then, is the degree to which values in a distribution deviate from the distribution's mean. It offers us a sense of how different each item is from the main value and from one another.
Arrange the data in increasing order:
54 55 55 55 56 60 60 64 65 69 70 70 71 72 75 75 77 78 79 80 80 85 88 88 88 90 100 102 105
Class width = range/no of classes
No of classes=9
range=Maximum value-Minimum value=54-105=51
Class width = 51/9 = approx. 6
Hence, the class limit or the Class width= 6.
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The following data give the estimated prices of a 6-ounce can or a 7.06-ounce pouch of water-packed tuna for 14 different brands, based on prices paid nationally in supermarkets. 1.04 1.95 1.23 0.83 0.70 0.48 1.45 1.14 0.58 0.64 0.69 0.63 0.62 0.67 Find the range. Find the sample variance. (Round your answer to four decimal places.) Find the sample standard deviation. (Round your answer to three decimal places.)
For the given data, the range, variance, and standard deviation is 1.47, 0.1716, and 0.414, respectively.
To find the range, subtract the minimum value from the maximum value in the set of data. The minimum value is 0.48 and the maximum value is 1.95, so the range is: 1.95 - 0.48 = 1.47.
To find the sample variance, follow these steps.
1. Calculate the mean of the data set.
2. Subtract the mean from each value in the data set.
3. Take the summation of the squares of the result.
4. Divide the sample size minus 1.
Upon calculation, the sample variance is 0.1716.
Lastly, to find the sample standard deviation, take the square root of the sample variance: √0.1716. = 0.414.
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Listed here are some items found in the financial statements of Finzelberg. Indicate in which financial statement each item would appear.A. service revenueB. equipmentC. advertising expenseD. accounts receivableE. common stockF. interest payable
The correct answer is:
(a) Income Statement ; (b) Balance Sheet ; (c) Income Statement ; (d) Balance Sheet ; (e) Balance Sheet ; (f) Balance Sheet.
Income statementThe income statement, which is one of the so-called basic financial statements, shows how the company arrived at its financial or accounting results, which could be a profit or loss, and may be shown as a profit or loss.
In order to calculate the utility from the income the company has obtained—from which costs and expenses have been incurred—a number of processes must be taken.
Balance SheetThe balance sheet is a statement of a company's financial position at a specific time, such as at the end of the month, quarter or year. The balance sheet shows the assets and lists the responsibilities, creating a statement of what the business owns and owes.
(a) Service revenue - Income statement
(b) Equipment - Balance sheet
(c) Advertising expense - Income statement
(d) Accounts receivable - Balance sheet
(e) Common stock - Balance sheet
(f) Interest payable - Balance sheet
An investor use the information about the companies future strategy and opportunities before buying and selling of any stock . This data illustrates the dividend trend for the company.
A bank keeps track of a corporation's dividend information since it will have an impact on the balance sheet and enable banks to more effectively manage loan risk.
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Select any to represent a and use it to complete the puzzle on the left.
Pls, help.
Please find attached the completed equation puzzle with the number 8 representing a, created with MS Word.
What is an equation?An equation is an expression of equivalence of the two expressions, quantities and or numbers, which are joined by the '=' sign.
The puzzle can be completed using both variables and values that satisfies equations created in the puzzle as follows;
Let a = 8, starting from top left of the puzzle, we get;
3·a + 4 = 3 × 8 + 4 = 28
The vertical column in the top middle with 28 at the top, indicates that we get the following equation;
28 + 4·a = 28 + 4 × 8 = 60
The row that crosses the middle of the vertical row above indicates that we get;
4·a + 4·a - 3·a = 5·a
The value, 3·a, obtained above is evaluated as; 3·a = 3 × 8 = 24
The vertical column with 6·a is evaluated as follows;
4·a + x = 6·a + a = 7·a
x = 7·a - 4·a = 3·a
x = 3·a
Therefore, we get; 4·a + 3·a = 6·a + a = 7·a
The values left blank are evaluated as follows;
a + 6·a - 3·a = 4·a
2·a + 4·a = 6·a
a + 6·a = 7·a
60 - 2·a = y - 5·a
y = 60 - 2·a + 5·a = 60 + 3·a = 60 + 3 × 8 = 84
84 - 5·a = 84 - 5 × 8 = 44
2·a + 4·a = 6·a
a + 6·a = 7·a
Please find attached the values obtained from the above evaluation of the puzzle, inputed in a similar puzzle created with MS Word.
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What is the period of this graph?
Answer:
4π
Step-by-step explanation:
The Period, as measured from crest-to-crest (or from trough-to-trough), is 4π, as read directly from the graph
Which expression is equivalent to (1 + cos(x))2Tangent (StartFraction x Over 2 EndFraction) )?
The expression that is equivalent to (1 + cos(x))2Tangent (StartFraction x Over 2 EndFraction) ) is option D. (1 + cos(x))(sin (x))
How are the expressions equivalent?The expression (1 + cos(x))2Tangent (StartFraction x Over 2 EndFraction) is equivalent to (1 + cos(x))(sin (x)) because of the double angle identity for tangent.
here, we have,
The double angle identity states that tangent of 2 times an angle is equal to 2 times the tangent of that angle divided by 1 minus the square of the tangent of that angle. In other words,
tan(2θ) = 2tan(θ)/(1 - tan2(θ))
In this expression, we have tangent of x/2,
so substituting θ = x/2 gives us:
tan(x) = 2tan(x/2)/(1 - tan2(x/2))
Since cos(x) = 1 - 2sin2(x/2),
we can simplify the expression to:
(1 + cos(x))2tan(x/2) = (1 + 1 - 2sin2(x/2))2tan(x/2)
= (2 - 2sin2(x/2))(2sin(x/2)/(1 - sin2(x/2)))
Expanding the product of the two factors gives us the final result:
(1 + cos(x))2tan(x/2) = (2 - 2sin2(x/2))(sin(x)) = (1 + cos(x))(sin(x))
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7x - y = 7
x + 2y = 6
Answer:
x = 4/3
y = 7/3
Step-by-step explanation:
7x - y = 7
x + 2y = 6
Times the second equation by -7
7x - y = 7
-7x - 14y = -42
-15y = -35
y = 7/3
Now put 7/3 back in for y and solve for x
x + 2(7/3) = 6
x + 14/3 = 6
x + 14/3 = 18/3
x = 4/3
Let's check
4/3 + 2(7/3) = 6
4/3 + 14/3 = 6
18/3 = 6
6 = 6
So, x = 4/3 and y = 7/3 is the correct answer.
A bank offers 3 mortgage . Option1: Fixed rate mortgage at 4% for 15 years. Option 2: Adjustable rate mortgage at 2.99% for 15 years with terms
Fixed rate only have fixed payments for at least the first 6 years. Therefore, option A is the correct answer.
What is fixed rate mortgage?A fixed-rate mortgage is a home loan option with a specific interest rate for the entire term of the loan. Essentially, the interest rate on the mortgage will not change over the lifetime of the loan and the borrower's interest and principal payments will remain the same each month.
An adjustable-rate mortgage, also called an ARM, is a home loan with an interest rate that adjusts over time based on the market. ARMs typically start with a lower interest rate than fixed-rate mortgages, so an ARM is a great option if your goal is to get the lowest possible mortgage rate starting out.
A balloon mortgage begins with fixed payments for a specific period and ends with a final lump-sum payment. The one-time payment is called a balloon payment because it's much larger than the beginning payments.
Therefore, option A is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
A bank offers 3 mortgage.
Option1: Fixed rate mortgage at 4% for 15 years.
Option 2: Adjustable rate mortgage at 2.99% for 15 years with terms 6/1 and a cap of 2/5
Option 3: Balloon mortgage at 5% with terms 15/5.
Which mortgage (s) will have fixed payments for at least the first 6 years?
A) Fixed rate only
B) Fixed rate and the balloon only
C) Fixed rate and adjustable rate only
D) Fixed rate, adjustable rate, and balloon.
The standard long jump pit is approximately 9 feet 2 inches wide and 30 feet 2 inches long. The sand to fill the pit needs to be 30 inches deep.
a. How much wood will you need to surround the pit?
b. How much sand will you need to fill the pit?
Can you answer and explain how you got it please.
Therefore, we will need volume approximately 694.4 cubic feet of sand to fill the pit to a depth of 30 inches.
Describe volume.The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Two instances of cubic units are cm3 and in3. To the contrary hand, a measurement of a thing's mass indicates how much material it includes. Typically, the weight of an item is measured in mass units the same as pounds or kilograms.
Here,
a.
Length: 30 feet 2 inches
Width: 9 feet 2 inches
Height: 30 inches (since the sand needs to be 30 inches deep)
To calculate the amount of wood required, we need to find the perimeter and area of the base of the frame.
Perimeter = 2(Length + Width) = 2(30 ft 2 in + 9 ft 2 in) = 2(39 ft 4 in) = 78 ft 8 in
Area of the base = Length × Width = (30 ft 2 in) × (9 ft 2 in) = 275 ft²
The amount of wood needed to surround the pit can then be calculated by finding the total surface area of the wooden frame.
Total surface area = 2(L × H) + 2(W × H) + Area of the base
= 2(30 ft 2 in × 30 in) + 2(9 ft 2 in × 30 in) + 275 ft²
≈ 240.5 square feet
Therefore, we will need approximately 240.5 square feet of wood to surround the pit.
b.
Length: 30 ft 2 in = (30 × 12) + 2 = 362 inches
Width: 9 ft 2 in = (9 × 12) + 2 = 110 inches
Depth: 30 inches
The volume of sand needed to fill the pit can be calculated using the formula:
Volume = Length × Width × Depth
Substituting the values, we get:
Volume = 362 in × 110 in × 30 in
= 1,198,800 cubic inches
To convert cubic inches to cubic feet, we divide by 12^3 (since there are 12 inches in a foot, and we need to cube this conversion factor):
Volume = 1,198,800 in³ ÷ (12³ in³/ft³)
= 694.4 ft³ (rounded to one decimal place)
Therefore, we will need approximately 694.4 cubic feet of sand to fill the pit to a depth of 30 inches.
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Use the function B(t) = 45422 + 34.26t find the inverse of the linear model; write your function using function notation
Answer: A linear function is one whose graph is a straight line. Given the linear function B(t) = 45422 + 34.26t, its inverse function can be found by switching the places of x and y and then solving for y.
The inverse function, written in function notation, can be represented as:
B^(-1)(t) = (1/34.26)(t - 45422)
So the inverse of the linear model B(t) = 45422 + 34.26t can be written as B^(-1)(t) = (1/34.26)(t - 45422) in function notation.
Step-by-step explanation:
Which equation has the solution set {3, −4}?
x²+x-12=0 is the equation have the solution {3, -4}
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
(x-3)(x-4)=0
x=3 and x=4
So the equation does not have the solution {3, -4}
x²+x-12=0
x²+4x-3x-12=0
x(x+4)-3(x+4)
(x-3)(x+4)=0
x=3 and x=-4
x²+x-12=0 the equation have the solution {3, -4}
(x+3)(x-4)=0
x=-3 and x=4
(x+3)(x-4)=0 does not have the solution {3, -4}
x²-x-12=0
x²-4x+3x-12=0
x(x-4)+3(x-4)=0
(x+3)(x-4)=0
x=-3 and x=-4 does not have the solution {3, -4}
Hence, x²+x-12=0 is the equation have the solution {3, -4}
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Two numbers (x & y) add up to 20 and have a difference of 6.
a. Set up a system of equations for this problem.
b. Solve for the values of x & y.
c. Verify that these are the correct values of x & y.
A system of equations are x+y=20 and x-y=6 and the solution is (13, 7).
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Two numbers x and y add up to 20.
x+y=20 --------(I)
Two numbers x and y have a difference of 6.
x-y=6 --------(II)
x=6+y
Substitute x=6+y in equation (I), we get
6+y+y=20
6+2y=20
2y=14
y=7
Substitute y=7 in equation (I), we get
x+7=20
x=13
So, the solution is (13, 7)
Therefore, a system of equations are x+y=20 and x-y=6 and the solution is (13, 7).
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30-60-90 and 45-45-90 triangles
The value of a and b are 4 and 3 respectively
What are trigonometry ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
60°, 45° ,30° are special angles with definite values
To solve for a;
sin60 = 2√3/a
√3/2 = 2√3/a
a = 2√3/√3/2
a = 2√3 ×2/√3
a = 2× 2 = 4
tan 60 = 2√3/5-b
√3 = 2√3/(5-b)
(5-b) = 2√3× 1/√3
5-b = 2
b = 3
therefore the value of a and b are 4 and 3 respectively
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Math triangle word problem:
The height of the mountain above the level plain is 4465.2 feet
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
Trigonometric ratio is used to show the relationship between the sides and angles of a right triangle.
Let h represent the height of the mountain. Let d represent the distance from the plain to the mountain base
Using trigonometric ratio:
tan(32) = h/d
h = d * tan(32)
Also:
tan(36) = h / (d - 1000)
h = (d - 1000) * tan(36)
Equating:
d * tan(32) = (d - 1000) * tan(36)
d = 7145.9 feet
h = d * tan(32) = 7145.9 * tan(32) = 4465.2 feet
The height of the mountain is 4465.2 feet
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Solve the right triangle using the given information.
a= 76.5 yd, b=40.1 yd
c= 86 yd
(Simplify your answer. Type an integer or a decimal. Round to the nearest tenth if needed.)
A=00'
(Simplify your answers. Type integers. Round to the nearest ten minutes if needed.)
8='
(Simplify your answers. Type integers. Round to the nearest ten minutes if needed.)
II
B
The triangle is not a right triangle because the Pythagorean Theorem (c² = a² + b²) is not satisfied.
What is the Pythagorean Theorem?
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base, and Hypotenuse.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side, which is opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the given values of a and b do not satisfy the equation:
c² = a² + b²
(86)² = (76.5)² + (40.1)²
7396 = 5862.25 + 1608.01
7396 = 7470.26
This means that the triangle with sides a = 76.5 yd, b = 40.1 yd, and c = 86 yd is not a right triangle.
Hence, The triangle is not a right triangle because the Pythagorean Theorem (c² = a² + b²) is not satisfied.
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For triangle XYZ, m∠X = (2g + 16)° and the exterior angle to ∠X measures (4g + 38)°. Find the measure of ∠X and its exterior angle. Interior angle = 122°; exterior angle = 58° Interior angle = 58°; exterior angle = 122° Interior angle = 82°; exterior angle = 38° Interior angle = 38°; exterior angle = 82°
Answer:
Step-by-step explanation:
the sum of the interior and the exterior angle must be 180°.
7g + 12 + 2g + 60 = 180
9g + 72 = 180
9g = 108
g = 12
interior angle = 7×12 + 12 = 96°
exterior angle = 2×12 + 60 = 84°
Given △ABC, AD and BE are medians, AD ∩BE=G. prove GD=1/3 AD
Answer: In a triangle, the medians divide the triangle into six smaller triangles with equal area. This can be proven using the fact that the medians of a triangle are concurrent, meaning they all intersect at a single point called the centroid.
Let's assume that AD = 2BE, then the area of △ADG is equal to four times the area of △BEG. This can be expressed as follows:
Area(△ADG) = 4 * Area(△BEG)
Since GD is one of the medians, it must be equal to one-third of AD. So, we can write:
GD = AD/3
Since the area of △ADG is equal to four times the area of △BEG, we can write:
Area(△ADG) = 4 * Area(△BEG)
(2BE)^2/2 * GD / 2 = 4 * BE^2/2 * EG / 2
Expanding and simplifying the above equation gives us:
BE^2 * GD / 2 = 4 * BE^2/2 * EG / 2
And, finally, dividing both sides of the equation by BE^2/2, we get:
GD = 1/3 * AD
This result holds true regardless of the relative lengths of AD and BE. Hence, the conclusion that GD = 1/3 AD is always true for any triangle △ABC where AD and BE are medians.
Step-by-step explanation: