i need help with this question... it's about special right triangles. The answer should not be a decimal.
Answers
4) The given triangle is a right angle triangle. Taking 30 degrees as the reference angle,
hypotenuse = 34
adjacent side = x
opposite side = y
We would find x by applying the Cosine trigonometric ratio which is expressed as
Cos# = adjacent side/hypotenuse
Cos 30 = x/34
Recall,
[tex]\begin{gathered} \cos 30\text{ = }\frac{\sqrt[]{3}}{2} \\ \text{Thus, } \\ \frac{\sqrt[]{3}}{2}\text{ =}\frac{x}{34} \\ 2x=34\sqrt[]{3} \\ x\text{ = }\frac{34\sqrt[]{3}}{2} \\ x\text{ = 17}\sqrt[]{3} \end{gathered}[/tex]To find y, we would apply the Sine trigonometric ratio. It is expressed as
Sin# = opposite side/hypotenuse
Sin30 y/34
Recall, Sin30 = 0.5. Thus
0.5 = y/34
y = 0.5 * 34
y = 17
Related Questions
In the diagram below , ^PQR = ^STR . Complete the statement
Answers
Given:
[tex]\Delta\text{PQR}\cong\Delta\text{STR}[/tex]Since it is given that triangles PQR and STR are congruent, the corresponding angles of the triangles are equal.
Hence,
Therefore, option D is correct.
4) At a fundraising event, there is a raffle. A total of 165people bought a raffle ticket. The ratio of losing ticketsto winning tickets is 12:3. How many people wonsomething in the raffle?
Answers
In order to determine the number of people which won something, it is necessary to write the following system of equations:
x + y = 165
y/x = 12/3
x is the people won and y the people lost.
The first equation represents tha total number of people in the event.
The second equation represents the ratio of losing tickets to winning people.
First, solve the second equation for y, and then replace the expression for y into the first equation:
y = 12/3 x
x + 12/3 x = 165
next, solve the last equation for x:
(3+12)/3 x = 165
15/3 x = 165
5x = 165
x = 165/5
x = 33
x is the number of people who won something in the event.
Hence, the number of people was 33
Solve by applying the zero product property.m^2= 27-6m
Answers
To apply the zero product property we first need to write all the terms of the equation on side:
[tex]\begin{gathered} m^2=27-6m \\ m^2+6m-27=0 \end{gathered}[/tex]Now we need to factorise the expression on the right:
[tex]\begin{gathered} m^2+6m-27=0 \\ (m+9)(m-3)=0 \end{gathered}[/tex]The last line indicates that the product of two numbers is equal to zero this means that one of them has to be zero (this is the zero product property), then we have:
[tex]\begin{gathered} m+9=0 \\ m=-9 \\ or \\ m-3=0 \\ m=3 \end{gathered}[/tex]Therefore, the solutions of the equation are m=-9 and m=3
30. Landscaping Calculate the area (in square feet) of a flower garden shaped like a circular sector withradius 60 ft and central angle 33 degrees.31. In problem 30; if shrubs are planted every 2 ft along the outer border of the garden, how many shrubsare needed?
Answers
Explanation
the area of a circular sector is given by
[tex]\begin{gathered} \text{Area}_{sc}=\frac{\theta}{360}\pi r^2 \\ \text{where r is the radius and }\theta\text{ is the angle in degr}ees \end{gathered}[/tex]then
Step 1
Let
[tex]\begin{gathered} \text{radius}=\text{ 60 ft} \\ \text{angle}=33\text{ \degree} \end{gathered}[/tex]now, replace in the formula
[tex]\begin{gathered} \text{Area}_{sc}=\frac{\theta}{360}\pi r^2 \\ \text{Area}_{sc}=\frac{33}{360}\pi(60ft)^2 \\ \text{Area}_{sc}=1036.72ft^2 \\ \text{rounded} \\ \text{Area}_{sc}=1036.72ft^2 \end{gathered}[/tex]Step 2
if shrubs are planted every 2 ft along the outer border of the garden, how many shrubs
are needed?
to figure out this, we need to take the perimeter of the circular sector and divide by 2 ft, to get the total number of shrubs in the border
so,
[tex]\text{perimeter}=(2\cdot\text{radius)}+length\text{ of arc}[/tex]so, we need to find the length of the arc
the length of the arc is given by
[tex]l=\frac{2\pi r}{360}\cdot\theta[/tex]replace.
[tex]\begin{gathered} l=\frac{2\pi r}{360}\cdot\theta \\ l=\frac{2\pi\cdot60}{360}\cdot33 \\ l=34.55 \end{gathered}[/tex]finally, replace in the perimeter formula
[tex]\begin{gathered} \text{perimeter}=(2\cdot\text{radius)}+length\text{ of arc} \\ \text{perimeter}=(2\cdot60ft\text{)}+34.55 \\ \text{perimeter}=120\text{ ft+34.55 ft} \\ \text{Perimeter}=154.55\text{ ft} \end{gathered}[/tex]divde by 2 to know the numbers of shrubs
[tex]\begin{gathered} Numbver\text{ of shrubs=}\frac{\text{ perimeter}}{2})=\frac{154.55\text{ ft}}{2} \\ Numbver\text{ of shrubs=}77.275\text{ ft} \\ Numbver\text{ of shrubs=}78 \end{gathered}[/tex]
Need help finding the volume and rounding to nearest whole number.
Answers
For a cylinder, the volume can be calculated using the formula:
[tex]V=\pi r^2h[/tex]Where r is the radius of the base and h is the height. From the problem, we identify:
[tex]\begin{gathered} r=\frac{16}{2}=8\text{ yd} \\ \\ h=10\text{ yd} \end{gathered}[/tex]Then, using these values to calculate the volume of the cylinder:
[tex]\begin{gathered} V=\pi(8)^2(10)=\pi(64)(10)=640\pi \\ \\ \therefore V=2011\text{ yd}^3 \end{gathered}[/tex]Sara is 33 years younger than Rolando. The sum of their ages is 105. Select the system of equations if Sara’s age is represented by S and Rolando’s age is represented by R.
Answers
Given:
Sara's age is represented by S and Ronaldo's age is represented by R.
Since,
Sara is 33 years younger than Ronaldo, then;
S= R - 33
Now, the sum of ages of Sara and Ronaldo is 105 then
[tex]R+S=105[/tex]Hence, from above,
[tex]\begin{gathered} S+R=105 \\ S=R-33 \end{gathered}[/tex]Therefore, second option is correct.
"People who are generous help those in need however they can."
To which theory of ethics is the person who made this statement likely appealing?
Conventionalism
Virtue-based ethics
Kantian deontology
Egoism
Answers
Answer: Conventionalism
Step-by-step explanation:
The person who made the statement, "People who are generous help those in need however they can," is appealing to virtue-based ethics.
What is Virtue ethicsVirtue ethics is a way of thinking about what is right and wrong. It focuses on becoming a good person and practicing good qualities.
This focuses on helping people develop good qualities such as being generous, caring, and kind. In this situation, the statement means that being kind and helping people who need it is seen as doing the right thing.
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find the volume or missing value 3ft, 2.5ft, 6ft
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The formula to find the volume of a rectangular prism is
[tex]\begin{gathered} V=l\cdot w\cdot h \\ \text{ Where V is the volume}, \\ l\text{ is the length,} \\ w\text{ is the width and} \\ \text{h is the height of the rectangular prism} \end{gathered}[/tex]Graphically,
So, in this case, you have
[tex]\begin{gathered} l=3ft \\ w=2.5ft \\ h=6ft \\ V=l\cdot w\cdot h \\ V=3ft\cdot2.5ft\cdot6ft \\ V=45ft^3 \end{gathered}[/tex]Therefore, the volume of the rectangular prism is 45 cubic feet.
hailey is going to rent an apartment for $864 a month in addition to the first month's rent when moving in a security deposit of $216 is required what will be the total payments required when moving in
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We are given that a total amount is $864, if a deposit of $216 is given, then the total amount to pay is the following:
[tex]864-216=648[/tex]Therefore, there is $648 to pay.
number serieswhat number comes next in the following series 27, 28, 32, 41, 57, 82, ?
Answers
Answer:
The number that comes next is;
[tex]118[/tex]Explanation:
Given the series;
[tex]27,28,32,41,57,82[/tex]From the series, if we observe the series closely we can see a relationship between the difference between consecutive terms.
[tex]\begin{gathered} 28-27=1=1^2 \\ 32-28=4=2^2 \\ 41-32=9=3^2 \\ 57-41=16=4^2 \\ 82-57=25=5^2 \end{gathered}[/tex]We can see that the difference follows the same pattern.
So, the next term would be the sum of the last term and the square of 6;
[tex]\begin{gathered} 82+6^2 \\ =82+36 \\ =118 \end{gathered}[/tex]Therefore, the number that comes next is;
[tex]118[/tex]URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100 POINTS!!!!!
Answers
Answer:
option 3
Step-by-step explanation:
As long as both lines are rotated the same direction and the same angle, then the angle between the two lines will not change.
3. The function f(x) has the coordinates below. State the changes made to f(x) which result in the function g(x). Write the (x,y) rule that would transform the coordinates of f(x) to the coordinates of g(x). g(x) = -2f(x + 1) - 4
Answers
Problem
The function f(x) has the coordinates below. State the changes made to f(x) which result in the function g(x). Write the (x,y) rule that would transform the coordinates of f(x) to the coordinates of g(x). g(x) = -2f(x + 1) - 4
Solution
From this table we know that
f(-1) = 5, f(2) = 1, f(6)=0
The rule for this case would be:
y= 13/84x^2 -125/84x +47/14
We also know that we have the following transformation
g(x) = -2f(x + 1) - 4
The corresponding coordinates of x on g(x) are:
0, 3, 7
So we have this:
f(0) = 47/14
f(3)= 2/7
f(7) = 11/21
And the corresponding y coordinates are:
-2(47/14) -4=-75/7
-2(2/7) -4=-3277
-2(11/21) -4=-106/21
Jess's age is six years less than three times Ethan's age. The product of their ages is 45. What are their ages? Hint: Write an equation to represent the product of their ages, using x to represent Ethan's age, then solve this quadratic equation. Connect each person to their correct age.
Answers
Jess's age is six years less than three times Ethan's age. The product of their ages is 45. What are their ages?
Hint: Write an equation to represent the product of their ages, using x to represent Ethan's age, then solve this quadratic equation. Connect each person to their correct age.
Let
x ------> Ethan's age
y -----> Jess's age
we have that
y=3x-6 -------> equation A
xy=45 ------> equation B
substitute equation A in equation B
x(3x-6)=45
solve for x
3x^2-6x=45
3x^2-6x-45=0
Solve using the formula
so
a=3
b=-6
c=-45
substitute
[tex]x=\frac{-(-6)\pm\sqrt[]{-6^2-4(3)(-45)}}{2(3)}[/tex][tex]\begin{gathered} x=\frac{6\pm\sqrt[]{576}}{6} \\ \\ x=\frac{6\pm24}{6} \end{gathered}[/tex]the solutions for x are
x=5 and x=-3 (is not a solution)
Find the value of y
y=3(5)-6
y=9
therefore
Ethan's age is 5 years
Jess's age is 9 years
With the information given, find the lenght of the prism
Answers
Answer:
The lenght of the prism is 22 cm.
Step-by-step explanation:
From the given drawing, we can conclude that a one-unit line measures 2 cm. Since the prism is 11 unit lines long, we can conclude that it is 22 cm.
Classify the following conic section from its standard equation: 4y2 - 6x +16y - 21 = 0.My
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it is a parabolla because only variable is quadratic and the other is linear.
What’s the correct answer answer asap for brainlist
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Answer: 3 years it started in Europe in 1914 and the USA got involved in 1917
Step-by-step explanation:
Solve the system of two linear inequalities graphicallySysx-2y) -5x + 10Step 1 of 3: Graph the solution set of the first linear inequalityAnswerKeypadKeyboard ShortcutsThe line will be drawn once all required data is provided and will update whenever a value is updated. The regions will be added once the line is drawn.Enable Zoom/PanChoose the type of boundary line:Solid (-) Dashed (-)Enter two points on the boundary line:10-Select the region you wish to be shaded:Submit Answer
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Given:
[tex]\begin{gathered} y\leq x-2 \\ \\ y>-5x+10 \end{gathered}[/tex]Find-: Solution set of the first linear inequality.
Sol:
Graph of first inequality is:
Graph of inequality of:
[tex]y>-5x+10[/tex]Graph of the given inequality is:
The solution of inequality is:
[tex]\begin{gathered} x=2 \\ y=0 \end{gathered}[/tex]What is the equation in slope-intercept form of the line that passes through the point (1,5) and is parallel to the line represented by 3x-y=4?
Answers
Answer:
[tex]3x - 14[/tex]
Step-by-step explanation:
-y= -3x+4
-1 because de y no have a number in front
-1y÷-1= -3x÷-1 4÷-1
Approximate when the function is positive, negative, increasing, or decreasing.
Describe the end behavior of the function.
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The function y = - | x | + 1 is increasing on ( - ∞, 0 ) and decreases on ( 0, ∞ ).
A relationship between a group of inputs with each output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
Consider the function,
y = - | x | + 1
The non-negative value of a real number x, represented by the symbol |x|, is the absolute value or modulus of x, regardless of its sign.
From the graph, we can approximate that the function is increasing from negative infinity to zero and the function decreases from zero to infinity.
Increasing on: ( - ∞, 0 )
Decreasing on: ( 0, ∞ )
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Find all x-intercepts of the following function. Write your answer or answers as
coordinate points. Be sure to select the appropriate number of x-intercepts.
f(x)
3x + 30
25x2 - 49
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Given: The function below
[tex]f(x)=\frac{3x+30}{25x^2-49}[/tex]To determine: All x-intercepts of the given function
The x-intercept is a point where the graph crosses the x-axis
We would substitute the function equal to zero and find the value of x
[tex]\begin{gathered} f(x)=\frac{3x+30}{25x^2-49},f(x)=0 \\ \text{Therefore} \\ \frac{3x+30}{25x^2-49}=0 \\ \text{cross}-\text{ multiply} \\ 3x+30=0 \end{gathered}[/tex][tex]\begin{gathered} 3x=-30 \\ \frac{3x}{3}=\frac{-30}{3} \\ x=-10 \end{gathered}[/tex]Therefore, the coordinate of the x-intercept is (-10, 0)
You live 3 miles from collage and 2 miles from the business where you work.Let d represent the distance between your work and the collage write an inequality involving d.
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The inequality involving the distance is 3 > d > 2.
What is an inequality?An inequality is simply used to illustrate the expressions that aren't equal. This can be illustrated through the use of greater than, less than, etc.
When you live live 3 miles from collage and 2 miles from the business where you work. This will be expressed thus
Let d represent the distance between your work and the collage and the inequality is 3 > d > 2.
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An electronics store sends an email survey to all customers who bought tablets. The previous month, 570 people bought tablets. Surveys were sent to 300 of these people, chosen at random, and 138 people responded to the survey. Identify the population and the sample. (4 points)The population is 570. The sample is 138.The population is 570. The sample is 300.The population is 300. The sample is 138.The population is 138. The sample is 570.The population is 138. The sample is 300.
Answers
Answer:
The population is 300. The sample is 138.
Explanation:
In statistics, population refers to the entire group of persons or things that a study is to be carried out on. Looking at the given question, we can see that, even though there were 570 people that bought tablets, the surveys were only sent to 300 people chosen at random. It shows that only 300 of the 570 people are to be surveyed, therefore, the population is 300.
A sample is the particular/specific group of persons or things that data is to be received from.
Looking at the given question, we can see that, out of the 300 people that the surveys were sent to, only 138 people responded to the survey. So the sample is 138.
HelpWhich equation can be used to solve for x in the following diagram?
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The sum of the angles is 90° because is a right angle because the square on the angle means it
then if we sum the angles 30° and 2x° we have 90°
[tex]30+2x=90[/tex]or
[tex]2x+30=90[/tex]then right option is A
How much higher is the summit of Mt. McKinley than the summit of Mt. Kosciuszko?
Answers
Based on the heights of the summits of Mt. McKinley and Mt. Kosciuszko, we find that Mt. McKinley is higher than Mt. Kosciuszko by 13,000 ft
What are the heights of Mt. Kosciuszko and Mt. McKinley?Mt. McKinley is reputed to be the tallest mountain in the North American continent which makes sense considering it has a summit with the height of 20,310 feet.
Mt. Kosciuszko on the other hand, is not that tall and stands at a height of 7,310 ft and is located in Australia.
The difference between both summits is:
= 20,310 - 7,310
= 13,000 ft
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PLEASE ANSWER ASAP1. The length of a bookshelf is 5 ft. The length of a model of this bookshelf is 3 ft. Find the scale of the model to the bookshelf. Enter your answer in the box.2. A rectangular garden has a length of 8 ft and a width of 4 ft. A smaller garden was made, using a scale of 3:4 . Find the dimensions of the smaller garden. Enter your answers in the boxes.
Answers
1.
The scale factor would be:
[tex]3\colon5[/tex]2.
Divide each original dimension by 4 and then multiply by 3, as following:
[tex]\begin{gathered} \frac{8ft}{4}\cdot3=6ft \\ \\ \frac{4ft}{4}\cdot3=3ft \end{gathered}[/tex]The smaller garden has a length of 6 ft and a widht of 3 ft
Note:enter your answer and show all steps that you use to solve this problem3.jaoquin buys 3 dozen lightbulbs.after changing the lightbulbs in his house, he has 15 lightbulbs left how many lightbulbs did he use?*btw the not is the same thing to my question I have for number 6*6. the empire state building in new York City is 1,250 feet tall. it has 103 floors. rounded to the nearest whole, what is the height of each floor?
Answers
Answer: Number of lightbulbs that he used = 21 lightbulbs
1 dozen of light bulbs = 12 light bulbs
Jaoquin buys 3 dozens
3 dozens of lightbulbs = 3 * 12 lightbulbs
3 dozens of lightbulbs = 36 lightbulbs
This means that :
The number of light bulbs Jaoquin bought = 36
The number of lightbulbs that remain = 15
The number of lightbulbs that he used = (Number of lightbulbs that he buys) - (Number of lightbulbs that remains)
Number of lightbulbs that he used = 36 - 15
Number of lightbulbs that he used = 21 lightbulbs
Select all the correct locations on the image.Which statements are logically equivalent to (p q)?
Answers
-(p ∧ q ) is logically equivalent to
-pv-q
Simplify and express in " a + bi " form.Show Detailed Step By Step Calculations
Answers
So, let's simplify
(8 - 10i) - (22 - 6i) =
8 -10i -22 +6i = (adding like terms)
-4i -14i
if angle 2 = 106 degrees, what is the measurement of angle 6 ? ( better explanation in picture )
Answers
angle 2 and angle 6 are corresponding angles.
Since the lines crossed by the trnasversal are parallel, corresponding angles are congruent. (equal)
angle 6 = 106°
the circle below is centered at the point (2,-1 ) and had a radius of length 3 what is its equation
Answers
The standard equation for a circle is
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ \text{where} \\ a=2 \\ b=-1 \\ r=\text{radius}=3 \\ (x-2)^2+(y-(-1))^2=3^2 \\ (x-2)^2+(y+1)^2=3^2 \\ \end{gathered}[/tex]