The solution is, the situation can be modeled as y = 52 - 8x.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
Hiro painted his room. After 3 hours of painting at a rate of 8 square meters per hour, he had 28 square meters left to paint.
So, the total area to be painted is (28 + 3 × 8) = 52 square meters.
Let y represent the area (in square meters) left to paint after x hours of painting then the situation can be modeled as
y = 52 - 8x ................ (1) (Answer)
To learn more on equation click:
brainly.com/question/24169758
#SPJ1
If A = {3,5,9} and B
{2,4,5,6,9,12}, what is AU B?
For the given sets A = { 3, 5, 9 } and set B = { 2, 4, 5, 6, 9, 12 } then the value of AU B is equal to { 2, 3, 4, 5, 6, 9, 12 }.
Two different sets A and set B are equal to :
Set A = { 3, 5, 9 }
Set B = { 2, 4, 5, 6, 9, 12 }
Union of two different set A and B is defined as set having all the elements of set A and set B .
Union of two sets A and B is represented by AU B .
AU B
= { 3, 5, 9 } ∪ { 2, 4, 5, 6, 9, 12 }
= { 2, 3, 4, 5, 6, 9, 12 }
Therefore, the union of two given sets A and set B is given by :
AU B = { 2, 3, 4, 5, 6, 9, 12 }.
Learn more about sets here
brainly.com/question/18877365
#SPJ4
A building casts a 103-foot shadow at the same time that a 32-foot flagpole casts as 34. 5-foot shadow. How tall is the building (Round your answer to the nearest tenth. )
A building casts a 103-foot shadow at the same time that a 32-foot flagpole casts as 34. 5-foot shadow then the building is approximately 95.2 feet tall.
What is similar triangles ?
Similar triangles are useful in geometry and other fields because they allow us to solve problems involving unknown distances or heights. We can use the known lengths and angles of one triangle to find the lengths and angles of the other triangle, as long as we know that the two triangles are similar. This can be done using the properties of proportional relationships and the rules of similar figures.
Let's use similar triangles to solve this problem. The height of the building and the height of the flagpole are proportional to the lengths of their shadows. We can set up the following equation:
height of building / length of building's shadow = height of flagpole / length of flagpole's shadow
Let x be the height of the building. Then we have:
x / 103 = 32 / 34.5
Simplifying this equation, we get:
x = 103 * (32 / 34.5) ≈ 95.23
Therefore, the building is approximately 95.2 feet tall.
Learn more about similar triangles click here:
https://brainly.com/question/29782809
#SPJ1
Suppose p and q vary inversely and p = 14 when a = 4 Find p when q = 8 please show work
If p and q vary inversely and p = 14 when a = 4, then the work is q = 8, p = 7.
What is inverse proportionality?
Inverse proportionality occurs when x increases and y decreases, and when x decreases and y increases.
If p and q vary inversely, this means that their product is constant:
p * q = k
where k is a constant. We can use this relationship to solve the problem.
We are given that when a = 4, p = 14. This means that:
p * a = k
14 * 4 = k
56 = k
So we know that the product of p and a is 56.
To find p when q = 8, we can use the fact that p and q vary inversely. This means that:
p * q = k
We know that k = 56, so we can substitute:
p * q = 56
We are given that q = 8, so we can substitute this as well:
p * 8 = 56
Solving for p, we get:
p = 56 / 8 = 7
Therefore, when q = 8, p = 7.
To know more about inverse proportionality visit,
https://brainly.com/question/1266676
#SPJ1
$200 invested at 5% compounded quarterly after a period of 3 years
Given:-
[tex] \rm{Principal= \bold{200}}[/tex][tex] \rm{Time = \bold 3}[/tex][tex] \rm{Intrest \: Rate = \bold 5}[/tex]By using formula:-
[tex]\boxed { \color{green}\rm{Simple \: interest= \frac{Principal×Time×Rate}{100}}}[/tex]Solution:-
[tex] \rm{SI = \frac{PTR}{100} }[/tex][tex] \: [/tex]
[tex] \rm{SI = \frac{2\cancel{00}×3×5}{1\cancel{00}} }[/tex][tex] \: [/tex]
[tex] \rm{SI=2×3×5}[/tex][tex] \: [/tex]
[tex] \boxed { \rm \red{ SI = 30}}[/tex][tex] \: [/tex]
hope it helps! :)
What value represents the number of ways in which the expected classes are free to vary in the chi-square goodness-of-fit test?Degrees of Freedom.
Answer The formula df = (c – 1) (r – 1) is used to find the degree of freedom – The degree of freedom of the chi-square test is calculated by the formula df = (c – 1) (r – 1), where c represents the column number of cell and r represents the row number of the cell.
The United States Postal Service has an online guide to make life easy for people using their
postal service. This is an extract.
First Class Mail
First class mail must be used for handwritten or personal correspondence.
First Class Mail Rates - single piece rates
$0.44
First ounce (oz.) Letter size mail
Each additional oz. or fraction
First ounce Flat size mail **
Each additional oz. or fraction
First ounce Parcel ***
Each additional oz. or fraction
Standard Postcard ****
$0.17 per oz. up to 3.5 oz.
$0.88
$0.17 per oz. up to 13 oz.
$1.22
$0.17 per oz. up to 13 oz.
$0.28
* Letters: (min. dimension: 5" L, 3.5" H, 0.007" W; max. dimension: 11.5 L, 6.125" H, 0.25 W,
max. weight 3.5 oz). Letter size mai over 3.5 ounces, see Flat size prices.
**Flats: (min. dimension: 11.5 L, 6.125" H, 0.25"W; max. dimension: 15 L, 12 H, 0.75 W).
*** Parcels: Anything larger.
**** Postcards: (min. dimension: 5L, 3.5" H, 0.007"W; max. dimension: 61, 4.25 H, 0.016 W).
I want to send two items through the post using first class mail.
One fts into an envelope 20 L, 10°H and 4"W and weighs 10oz.
The other fits into an envelope 8 L, 5" H and 0.20 W and weighs 2.5oz.
How much are the items going to cost me to send?
Answer:
The first item that fits into an envelope 20 L, 10°H and 4"W and weighs 10oz is a "Flat size mail." According to the rate chart, the first ounce of Flat size mail costs $0.88 and each additional ounce costs $0.17. The cost for the 10 ounces of this item will be $0.88 + 9 x $0.17 = $1.83.
The second item that fits into an envelope 8 L, 5" H and 0.20 W and weighs 2.5oz is a "Letter size mail." According to the rate chart, the first ounce of Letter size mail costs $0.44 and each additional ounce costs $0.17. The cost for the 2.5 ounces of this item will be $0.44 + 1.5 x $0.17 = $0.75.
So, the total cost for both items will be $1.83 + $0.75 = $2.58.
Which equation is true?
O 6 ÷ 10 60
O 6 ÷ 100 = 60
O 6 ÷ 100.6
100
O 6100 = 0.6
of the value than the 6 in 25 division
Answer:sry
Step-by-step explanation:i need points
The equation which is true is 6 ÷ 100 = 0.06
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the first number be p = 6
Let the second number be q = 100
Substituting the values in the equation , we get
A = p/q
A = 6/100
The value of A = 0.06
Hence , the equation is A = 0.06 and is true
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ2
A probability model is a list of outcomes and the probability of each outcome. According to the following probability model, what is P(2)?
The value of the probability P(2) is 0.11
How to determine the value of the probabilityFrom the question, we have the following parameters that can be used in our computation:
The table of values
As a general rule:
The sum of probabilities must equal to 1
Using the above as a guide, we have the following:
0.1 + P(2) + 0.35 + 0.1 + 0.3 + 0.04 = 1
Evaluate the like terms
This gives
P(2) + 0.89 = 1
So, we have
P(2) = 0.11
Hence, the solution is 0.11
Read more about probability at
https://brainly.com/question/251701
#SPJ1
Given that 4ax² + 9x + c is always negative, what conditions must apply to the constants a and c?
Answer:
Step-by-step explanation:
According to question
[tex]4ax^{2} +9x+c < 0[/tex]
This means that the coefficient of the highest degree term
([tex]4ax^{2}[/tex]) must be positive
And the constant term (c) must be negative
So, the according to condition
4a must be positive,
which means a must be positive
And, c must be negative
[tex]a > 0\\c < 0[/tex]
Read more about quadratic equation:
https://amsi.org.au/teacher_modules/Quadratic_Equations.html
Please help thank you
The ocean current has a bearing of 19.1°E and travels at a speed of about 16.9 knots.
Why is math speed important?Math is made more fascinating and enjoyable using Speed Maths (Vedic Maths). by assisting the child in quickly performing some improbable computations. By combining the correct amount of enjoyment, memory, skills, memory recall, and formula application, your child will become a superstar performer.
Let's use the letters "c" for OC magnitude and "" for the angle between OC and OD (the present bearing). Next, we have:
c² = 28² + 20² - 2(28)(20)cos(106°)
c ≈ 16.9 knots
Using the law of sines, we can find the angle θ:
sin(53°) / c = sin(θ) / 20
sin(θ) = (20/c) sin(53°)
θ ≈ 19.1°
To know more about speed visit:-
https://brainly.com/question/7359669
#SPJ1
FIND THE PERIMETER AND AREA OF THE TRIANGLE BELOW
Answer:
perimeter = 8a³b + 4ab
area = 4a^4b²
Step-by-step explanation:
perimeter = 2a³b + 6a³b + 4ab
perimeter = 8a³b + 4ab
area = bh/2
area = 4ab × 2a³b / 2
area = 4a^4b²
A bus leaves the station every 12 minutes
A train leaves the station every 18 minutes
At 8am a bus and a train leave their stations at the same time.
a) when is the next time that a bus and a train leave at the same time?
b) Between 8am and 11am, on how many occasions does a bus and a train leave at the same time?
thank you so much for the help
Answer:
a) 8:32 am
b) 5 occasions
Find the image of (2,3) under a dilation with center at the origin and a scale factor of −3.
The image of (2, 3) under a dilation with center at the origin and a scale factor of −3 will be (-6, -9).
What is Image of a point ?
Dilation is the process of resizing or altering an object. With the aid of the specified scale factor, it is a transformation that reduces or enlarges the objects. The initial figure is referred to as the pre-image, while the new figure acquired after dilatation is known as the image.
Given point : (2,3)
the scale factor is -3 which means the point should be enlarged by -3 times to get the desired image.
So, we can write as : (a, b) where,
a = 2 × -3 = -6
and, b = 3 × -3 = -9
Hence, the coordinates of the image will be (-6, -9).
Learn more about Dilation from the given link:
https://brainly.com/question/3457976
#SPJ1
How many digits of the form x15y is di ivsble by 15
There are a total of 8 + 7 = 15 digits of the form x15y that are divisible by 15.
A number is divisible by 15 if and only if it is divisible by both 3 and 5.For a number of the form x15y to be divisible by 5, y must be either 0 or 5.
For a number of the form x15y to be divisible by 3, the sum of its digits must be divisible by 3. Since the sum of the digits is x + 1 + 5 + y = x + y + 6, x + y must be either 0, 3, 6, 9, 12, or 15.
So, we need to find all possible values of x and y such that x + y is one of these six values, and y is either 0 or 5.
If y = 0, then x must be one of the numbers 0, 3, 6, 9, 12, 15, 18, or 21, for a total of 8 possibilities.
If y = 5, then x must be one of the numbers 2, 5, 8, 11, 14, 17, or 20, for a total of 7 possibilities.
Therefore, there are a total of 8 + 7 = 15 digits of the form x15y that are divisible by 15.
To know about Divisibilty:
https://brainly.com/question/11374214
#SPJ4
A group of students atten a math club. Half of them students are boys 4/9 of them boys have brown eyes
The fraction of the group are boys with brown eyes with total group of students who attend the math club is equals to the 2/9.
Let us assume that total number of students who attend the math club be 'x'. Now, according to problem, half of students who attend the math are boys. So, boys students out of total students who attend the math club, B = ( 1/2)x --(1)
Also, 4/9 of them boys have brown eyes. That is the boys students have brown eyes out of boys students who attend the math club, E = 4/9 of B
=> (4/9)B --(2)
We have to determine the relationship between boys with brown eyes (E) and the group of students (x). so, let's replace B in second equation with the expression present in eqution (1).
=> E = (4/9)(x/2)
For simplification, multiply the two fractions, that denominator with denominator and numerator with numerator.
=> E = 4x/18
For further simplification, simply dividing both the numerator and denominator by their common factor, ( 4, 18 ) = 2,
=> E = 2x/9
so, the required relationship between E and x is 2/9. Hence, required value is 2/9.
To learn more about fraction, refer:
https://brainly.com/question/1878884
#SPJ4
Complete question :
a group of students attend a math club half the students are boys and 4/9 of the boys have brown eyes what fraction of the group are boys with brown eyes.
It is a point that divides a segment into two congruent segments.
A.Point
B.Midpoint
C.Bisector
D.Ray​
The point that divides a segment into two congruent segments is called the midpoint. Therefore, the answer is B) midpoint.
In geometry, a midpoint is a point that divides a line segment into two equal parts. It is the point on the line segment that is equidistant from both endpoints. The midpoint is important in geometry as it can be used to construct other geometric figures, such as perpendicular bisectors, which are lines that pass through the midpoint of a line segment and are perpendicular to it. For example, if we have a line segment AB, the midpoint M is the point that is exactly halfway between A and B, such that AM = MB. This can be found by drawing a perpendicular bisector of AB, which is a line that passes through the midpoint M and is perpendicular to AB. The perpendicular bisector will intersect AB at the midpoint M. It is important to note that the midpoint is not a bisector, ray, or point on a line. A bisector is a line, segment, or ray that divides an object into two congruent parts, while a ray is a part of a line that extends infinitely in one direction. The midpoint is simply the point that divides a line segment into two equal parts, and it is denoted by a symbol, such as a small vertical line with a hat on top, or by labeling the midpoint as a letter, such as M in the example above
To learn more about congruent segments click here
brainly.com/question/29550003
#SPJ4
Some girl needs to earn R500 in interest so she will have enough to buy a used bicycle. She puts R2000 into an account that earns 5% per year simple interest. How long will she need to leave her money in the account to have enough money for the bicycle?
The money needs to be in the account for 5 years on simple interest at the rate 5% to earn R500.
What is simple interest?The interest on a loan or principal amount can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more. When you pay back a loan, the monthly interest is deducted first, and any remaining funds are applied to the principle.
Let us suppose the time period as x.
The simple interest is given as:
SI = PRT/100
Where,
SI = Simple Interest = 500
P = Principal = 2000
R = Rate = 5%
T = x
Substituting the values:
500 = (2000)(5)(x) / 100
500 = 100x
x = 5 years
Hence, the money needs to be in the account for 5 years on simple interest at the rate 5% to earn R500.
Learn more about simple interest here:
https://brainly.com/question/25845758
#SPJ1
What is the scale factor?
6
3
1/3
1/6
Answer:
3
Step-by-step explanation:
You multiply the pre-image by 3 to get the image numbers.
Answer:
B.3
Step-by-step explanation:
The scale factor is 3 because all of the images are dilated 3 times larger than the preimage.
12. Tickets to a school play cost $5.00 for general
admission (g) and $3.50 with a student ID (s). On
opening night, 400 tickets were sold for a total of
$1580. How many of each kind of ticket were sold?
Gimme Brainliest!!!
Gimme Brainliest!!!
Gimme Brainliest!!!
Gimme Brainliest!!!
Gimme Brainliest!!!
Gimme Brainliest!!!Gimme Brainliest!!!Gimme Brainliest!!!Gimme Brainliest!!!Gimme Brainliest!!!Gimme Brainliest!!!Gimme Brainliest!!!Gimme Brainliest!!!Gimme Brainliest!!!Gimme Brainliest!!!Gimme Brainliest!!!Gimme Brainliest!!!Gimme Brainliest!!!Gimme Brainliest!!!Gimme Brainliest!!!
Answer:
120 general admission
280 with student with a student ID
Step-by-step explanation:
x is tickets for general admission
y is tickets with a student ID
5x+3.5y=1580
x+y=400
y=400-x
5x+3.5(400-x)=1580
5x+1400-3.5x=1580
1.5x=180
x=120
120+y=400
y=280
On a test that has a normal distribution, a score of 34 falls two standard deviations above the mean, and a score of 22 falls one standard deviation below the mean. Determine the mean of this test.
The mean of this data set is 65.
What is the mean absolute deviation?The average distance between each data item and the mean is known as the mean absolute deviation.
The gap between each data value and the mean in absolute terms is represented by this average.
Let the mean be 'x' and the standard deviation be 'y'
3 standard deviations the mean means that we are taking away 3 standard deviations from the mean
Mathematically, we have that as;
x - 3y = 41...(i)
73 is 1 standard deviation above the mean
Mathematically;
x + y = 73...(ii)
So let us solve both equations simultaneously
Simply multiply equation (ii) by 3 then add to (i)
x - 3y = 41
3x + 3y =219
4x = 41 + 219
4x = 260
x = 260/4
x = 65.
learn more about standard deviations here :
https://brainly.com/question/23907081
#SPJ9
Answer: 26
Step-by-step explanation:
How much is 5$? please I need help because I just dont know how much is it im so confused!!!!
5 dollars equals 500 pennies, once 5 dollars times 100 equals 500. What's 5 dollars in cents? 5 dollars equals 500 cents, once 5 dollars times 100 equals 500.
Q9.
Gavin bought 3 pairs of jeans in the USA.
He paid a total of $72
Gavin sold the 3 pairs of jeans in England,
He sold each pair of jeans for £34.50
£1 = $1.34
Work out Gavin's percentage profit.
Give your answer correct to the nearest whole number.
Answer:
Gavin made a Profit of $66.69 that is 93% Profit
Step-by-step explanation:
First, we calculate the Selling Price of Jeans after converting from GBP to USD on the given rate:
Rate: £1 = $1.34
Quantity: 3
Price in USD = Selling Price per pair * Rate in USD
£34.50 * 1.34 = $46.23 per pair of jeans.
Total Selling Price = Price Per Pair * Quantity
= 46.23 * 3
= $138.69
Total Profit = Total Selling Price - Total Cost Price
= $138.69-$72
= $66.69
Percentage of Profit = Total Profit / Total Cost Price
=66.69 / 72
=92.65
Therefore, the Profit Percentage is 92.65 % the nearest whole number would be 93%
To calculate Gavin's percentage profit, find the difference between the selling price and the buying price, and calculate the percentage of the buying price that the profit represents.
Explanation:To calculate Gavin's percentage profit, we need to find the difference between the selling price and the buying price, and then calculate the percentage of the buying price that the profit represents.
First, convert the selling price of each pair of jeans from pounds to dollars. Since £1 = $1.34, each pair of jeans sold for $34.50 x 1.34 = $46.23.Next, calculate the total selling price by multiplying the selling price of each pair by the number of pairs: $46.23 x 3 = $138.69.Then, calculate the profit by subtracting the total buying price from the total selling price: $138.69 - $72 = $66.69.Finally, calculate the percentage profit by dividing the profit by the total buying price and multiplying by 100: ($66.69 / $72) x 100 ≈ 92.6%.Gavin's percentage profit is approximately 92.6%.
Learn more about Percentage Profit here:https://brainly.com/question/35552199
#SPJ2
one of my factors are 4, when you pair me with 32 we have an lcm of 32, i am greater than 4 and less the 15. what is the mystery number?
The mystery number is 8. It is the number that is greater than 4 and less than 15 which when paired with 32 has an LCM of 32.
The mystery number is 8. To find this number, we first need to determine the Least Common Multiple (LCM) of two numbers. The two given numbers are 4 and 32. To find the LCM, we can list out the multiples of each number until we find a common multiple. The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, and so on. The multiples of 32 are 32, 64, 96, 128, and so on. We can see that 32 is the first common multiple of 4 and 32. Therefore, the LCM of 4 and 32 is 32. We are then told that the mystery number is greater than 4 and less than 15. This means the mystery number must be 8, since it is the only number between 4 and 15 that when paired with 32, has an LCM of 32.
Learn more about number here
https://brainly.com/question/28210925
#SPJ4
how many decimeters are in 3.6 millimeters
Final Answer:
There are 0.036 decimeters in 3.6 millimeters.
Explanation:
To convert from millimeters to decimeters, we can use the following measurement conversion:
1 millimeter = 0.01 decimeters
So, to find out how many decimeters are in 3.6 millimeters, we can multiply 3.6 by 0.01:
3.6 * 0.01 = 0.036
Therefore, there are 0.036 decimeters in 3.6 millimeters.
The balance in an account after several transaction is shown in the table. Is the relationship between the balance and the number of withdrawals of linear? Blank If so, find the constant rate of change. Write the slope as a unit rate and explain your reasoning.
It should be noted that the relationship between the balance and the number of withdrawals is linear, because there is a constant amount of $10 per withdrawal.
How to express the relationshipTo confirm this, we can calculate the differences in balance for each pair of withdrawals:
Between withdrawals 3 and 2: 170 - 140 = 30
Based on the information, the starting amount is $200.
The equation to illustrate the withdrawal will be:
= 200 - 10w
where w = withdrawal.
These differences are constant, which means the rate of change of the balance is constant too.
Learn more about linear on:
https://brainly.com/question/2030026
#SPJ1
Write a similarity transformation that maps ∆ABC to ∆DEF
Answer:
Reflect ABC over the y axis. Translate ABC 1 unit to the right. C is the center, dilate ABC with a scale factor of 2.
Step-by-step explanation:
Howard's pencil is 75 cm long. How many millimeters long is Howard's pencil?
Answer:
Howard's pencil is 750 millimeters
Step-by-step explanation:
[tex]\begin{array}{|l}\underline{km~}\\~~~~~\underline{|hm~}\\~~~~~~~~~~~\underline{|dam}~~~~~~~~\nwarrow~\div10\\~~~~~~~~~~~~~~~~~\underline{|m~~}\\~~~~~~~~~~\searrow~~~~~~~\underline{|dm~}\\~~~\times10~~~~~~~~~~~~~~~~~~\underline{|cm~}\\\underline{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~|mm~}\end{array}\\~~~~~~~~~~~\rm Converting ~Length ~ Unit[/tex][tex]~[/tex]
Step-by-step:
75 cm = 75 × 10 mm
75 cm = 750 mm
Find the nth term of this number sequence 1, 7, 13, 19, .. .
Answer:
[tex]a_{n}[/tex] = 6n - 5
Step-by-step explanation:
there is a common difference between consecutive terms in the sequence
7 - 1 = 13 - 7 = 19 - 13 = 6
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 1 and d = 6 , then
[tex]a_{n}[/tex] = 1 + 6(n - 1) = 1 + 6n - 6 = 6n - 5
How do I do this? I need all these problems solved pls I really need help and don't care about the process as much but when you put the answers please just put the numbered question they go to
The missing sides of right triangles are, respectively:
Case 1: x = 18.910
Case 2: x = 23.584
Case 3: x = 15.890
Case 4: x = 16.659
Case 5: x = 24.111
And the angles of the right triangles are, respectively:
Case 6: 32°
Case 7: 31°
Case 8: 71°
Case 9: 71°
Case 10: 32°
The exact values of trigonometric functions:
Case 11: cos A = 12 / 13
Case 12: tan C = 3 / 4
Case 13: tan A = 3 / 4
And the trigonometric ratios of right triangles are:
Case 14: tan X = 1.3333
Case 15: sin A = 0.6000
Case 16: cos C = 0.3243
How to analyze right triangles by trigonometric functions
In this question we find 16 cases of right triangles that must be analyzed by trigonometric functions. Trigonometric functions is an important tool to determine missing sides and angles and relationships with sides. Most important trigonometric functions are described below:
sin θ = y / r
cos θ = x / r
tan θ = y / x
Where:
x, y - Legsr - Hypotenuse.Please notice that hypotenuse is the longest side of a right triangle.
The first five cases implies the determination of missing lengths in five right triangles:
Case 1
x = 20 · cos 19°
x = 18.910
Case 2
x = 20 / cos 32°
x = 23.584
Case 3
x = 10 / cos 51°
x = 15.890
Case 4
x = 15 / tan 42°
x = 16.659
Case 5
x = 19 / sin 52°
x = 24.111
The following five cases implies the determination of angles by means of direct and inverse trigonometric functions:
Case 6
tan θ = 16 / 26
tan θ = 8 / 13
θ = 31.608° (32°)
Case 7
tan θ = 6 / 10
θ = 30.964° (31°)
Case 8
tan θ = 76 / 26
θ = 71.114° (71°)
Case 9
tan θ = 67 / 23
θ = 71.053° (71°)
Case 10
tan θ = 26 / 42
θ = 31.759° (32°)
The next three cases implies the computation of the exact values of trigonometric functions:
Case 11
cos A = 24 / 26
cos A = 12 / 13
Case 12
tan C = 24 / 32
tan C = 3 / 4
Case 13
tan A = 27 / 36
tan A = 3 / 4
And the last three triangles implies the values of trigonometric ratios:
Case 14
tan X = 36 / 27
tan X = 4 / 3 (1.3333)
Case 15
sin A = 30 / 50
sin A = 3 / 5 (0.6000)
Case 16
cos C = 12 / 37 (0.3243)
To learn more on trigonometric functions: https://brainly.com/question/25618616
#SPJ1
The lengths of the sides, measures of the angles and the values of the trigonometric ratios are as follows;
1) x ≈ 18.9
2) x ≈ 23.1
3) x ≈ 15.9
4) x ≈ 16.7
5) x ≈ 23.1
6) x ≈ 32°
7) x ≈ 31°
8) x ≈ 71°
9) x ≈ 71°
10) x ≈ 32°
11) cos(A) ≈ 0.9
What are trigonometric ratios?Trigonometric ratios are expressions that specify the relationships between two sides of a right triangle and an interior angle of the triangle.
1) The opposite side = 20 × sin(19°) ≈ 6.5
The adjacent side = 20 × cos(19°) ≈ 18.91
2) cos(30°) = 20/x
cos(30°) = (√3)/2, therefore;
(√3)/2 = 20/x
x = 20/((√3)/2) = 40·√3/3 ≈ 23.1
x ≈ 23.1
3) cos(51°) = 10/x
Therefore;
x = 10/(cos(51°)) ≈ 15.9
4) tan(42°) = 15/x
Therefore;
x = 15/(tan(42°)) ≈ 16.7
x ≈ 16.7
5) sin(52°) = 19/x
Therefore;
x = 19/(tan(52°))
x = 20/(cos(30°)) ≈ 23.1
x ≈ 23.1
6) tan(x) = 16/26
tan(x) = 16/26 = 8/13
x = arctan(8/13) ≈ 32°
7) tan(x) = 6/10
tan(x) = 6/10 = 3/5
x = arctan(3/5) ≈ 31°
8) tan(x) = 76/26
tan(x) = 76/26 = 38/13
x = arctan(38/13) ≈ 71°
9) tan(x) = 67/23
x = arctan(67/23) ≈ 71°
x ≈ 71°
10) tan(x) = 26/42
tan(x) = 26/42 = 13/21
tan(x) = 13/21
x = arctan(13/21) ≈ 32°
11) The trigonometric ratios for cosine indicates that we get;
cos(A) = 24/26 ≈ 0.9
12) Trigonometric ratio for tangent indicates that we get;
tan(C) = 24/32 = 0.75
13) tan(A) = 27/36
27/36 = 3/4
Therefore; tan(A) = 3/4 = 0.75
14) tan(x) = 36/27 = 4/3
tan(x) = 4/3 = 1 1/3
15) sin(A) = 30/50 = 3/5
sin(A) = 3/5 = 0.6
16) cos(C) = 12/37 ≈ 0.32
Learn more on trigonometric ratios here: https://brainly.com/question/16663616
#SPJ1
PLS HELP ITS A TESTTTT
Answer:
14)37
15)16
16)38
17)C
Step-by-step explanation:
14)7*4+9=28+9=37
15)42/7+10=6+10=16
16)-5*(-6)+8=30+8=38
