Answer:
[tex] \huge \boxed{ \red{ \boxed{\begin{cases} \theta = {45}^{ \circ} \\ \theta= {60}^{ \circ} \end{cases} }}}[/tex]
Step-by-step explanation:
to understand thisyou need to know about:trigonometryPEMDASlet's solve:distribute tan(θ):
=>tan²(θ)-(tan(θ)+√3tan(θ))+√3=0
remove parentheses:
=>tan²(θ)-tan(θ)-√3tan(θ)+√3=0
so this equation is now in standard form i.e ax²+bx+c=0
we can solve by factoring as we solve quadratic equation
factor out tanθ:
=>tan(θ)(tan(θ)-1)-√3tan(θ)+√3=0
factor out -√3:
=>tan(θ)(tan(θ)-1)-√3(tan(θ)-1)=0
group:
=>(tan(θ)-√3)(tan(θ)-1)=0
separate it as two different equation:
[tex] \implies \begin{cases} \tan( \theta) - 1 = 0 \\ \tan( \theta) - \sqrt{3} = 0 \end{cases}[/tex]
add 1 and √3 to both sides to first and second equation respectively:
[tex] \implies \begin{cases} \tan( \theta) - 1 + 1 = 0 + 1 \\ \tan( \theta) - \sqrt{3} + \sqrt{3} = 0 + \sqrt{3} \end{cases} [/tex]
[tex] \implies \begin{cases} \tan( \theta) = 1 \\ \tan( \theta) = \sqrt{3} \end{cases} [/tex]
[tex] \therefore \begin{cases} \theta = {45}^{ \circ} \\ \theta= {60}^{ \circ} \end{cases} [/tex]
TOURS The table shows the activities of two visitors at a park. You want to take the boat tour for 2 hours and the walking tour for 3 hours. Can you determine how much you will pay? Explain.
Answer:
Step-by-step explanation:
State if the triangle is acute, obtuse, or right
Answer:
right angle triangle
A total of 50,000 contestants are chosen for a survey. A
computer randomly eliminates 20% of the participants
each day.
Which function models the survey?
Answer:
you are correct do not say any other answer
Answer:
The answer is either
y=50000 x 0.8^x
or
y=50000(20%)^x but this just seems wrong
Step-by-step explanation:
I NEED HELP PLEASE !!
Answer:
all 3 sides are the same length
SOMEONE PLEASE HELP!
Figures 1 and 2 below show two polygonal regions used to approximate the area of the given shape. Find the average area, in square units, of the given shape using figures 1 and 2.
Answer:
figure 1 is 8.5 units^2 and figure 2 is 3 units^2 and the average are is 5.25 units^2
The overestimated area, the underestimated area, and the average area will be 8.5 units², 3 units², and 2.75 units², respectively.
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
Since the area is covered with either a square or a triangle. Therefore, we can write the area of this two as,
Area of a square = 1 unit × 1 unit = 1 unit²
Area of triangle = 0.5 × 1 unit × 1 unit = 0.5 units²
The overestimated area, the number of square and triangles are,
Number of square = 6
Number of triangle = 5
Total overestimated area = (6×1unit²) + (5×0.5unit²) = 8.5 unit²
The under estimated area, the number of square and triangles are,
Number of square = 2
Number of triangle = 2
Total Underestimated area = (2×1unit²) + (2×0.5unit²) = 3 unit²
Furthermore, the average area is,
Average area = (Total overestimated area - Total Underestimated area)/2
= (8.5 units² - 3 units²) / 2
= 5.5 units² / 2
= 2.75 units²
Hence, the overestimated area, the underestimated area, and the average area will be 8.5 units², 3 units², and 2.75 units², respectively.
Learn more about Area here:
https://brainly.com/question/1631786
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What percent of 54 is 28?
52%
192%
19%
0.52%
?
Answer:
52%
happy to hep ya :)
Step-by-step explanation:
halp me pleaze................
factorise fully :
4(x - y)^2 - 9(x + y)^2
Answer:
- ( 5x + y ) ( x + 5y )
or
-5x^2 - 5y^2 - 26xy
Answer:
Step-by-step explanation:
4(x^2-2xy+y^2)-9(x^2+2xy+y^2)
4x^2-8xy+4y^2-9x^2-18xy-9y^2
-5x^2-26xy-5y^2
-5x^2-xy-25xy-5y^2
-x(5x+y)-5y(5x+y)
(-x-5y)(5x+y) or you can also remove the negative one to get
-(x+5y)(5x+y)
What is the equation of the line that goes through the points (4,-1) and
(2,3)?
Answer:
y = -2x + 7
Explanation:
y = mx + b
m = slope
b = y-intercept
y = a given y coordinate
x = a corresponding x coordinate
First, we need to find the slope (m).
1) (4, -1)
2) (2/3)
m = slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = [tex]\frac{3-(-1)}{2-4}[/tex] = [tex]\frac{4}{-2}[/tex] = -2
plug in the values to the equation y = mx + b
-1 = -2(4) + b
-1 = -8 + b
7 = b
now, we can substitute in m and b into the equation y = mx + b
y = -2x + 7
please also answer this one rlly fast!!
Answer:
4
Step-by-step explanation:
1 ÷ 0.25 = 4
HELP giving brainlest for first person that answers and extra points
Given right triangle ABC with altitude BD drawn to hypotenuse AC. If BC=6 and DC=4, what is the length of AC ?
Step-by-step explanation:
BC^2 + DC^2 = AC^2
6^2 + 4^2 =AC^2
36 + 16 = AC^2
52=AC^2
√52=AC
AC=7.2111
May someone please help me with this :)
I really need help!!!!
Answer:
No
Step-by-step explanation:
You can't use the perpendicular bisector theorem because it doesn't intersect it at a right angle, (meaning it isn't perpendicular)
Your friend Alex has won a scholarship to study abroad. (Congratulations!) Alex has only 8 weeks to earn enough money to buy a plane ticket, and he wants to work at an amusement park over the summer to acheive this goal
What’s the question?
Step-by-step explanation:
?
what's
[tex] \sqrt{45 + 36} [/tex]
help
What is an equation of the line that passes through the points (-4, 4) and (8.1)?
Answer:
y = -1/4x +3
Step-by-step explanation:
Hope this helps!
quick test 2+2x68(8)=y
2176
Step-by-step explanation:
2+2=4 68(8)= 544
4× 68×8= 2176
Eight years ago, Manny was 4 years old. Let m equal Manny's age now. Circle every equation that shows Manny's age now.
Answer:
4+8=M or 4+8=12 or just 12
Step-by-step explanation:
there isnt anything to circle so but since he was 4, 8 years ago, you would add 4 and 8.
which graph represents the function
A golf course has 18 holes. A guidebook provided to golfers includes useful information about each hole, as shown below. A 4-column table with 6 rows. Column 1 is labeled hole number with entries 1, 2, 3, 4, 5, 6. Column 2 is labeled yards with entries 312, 530, 147, 350, 410, 185. Column 3 is labeled bunkers with entries 2, 5, 1, 0, 2, 1. Column 4 is labeled difficulty level with entries moderate, moderate, easy, moderate, hard, moderate. What are the individuals in this data set? holes yards bunkers difficulty levels
Answer:
Holes got it right :)
Step-by-step explanation:
Answer
difficulty levels
Step-by-step explanation:
took the test
sorry different question
Write the following FRACTIONS in order of size (SMALLEST to LARGEST)
70% , 2/3 , 0.62 , 13/20 , 0.6
Answer:
is this helpful?? i guess it is
6 - 4 (6n + 7 ) > 122 giving brainlest to whoever shows work
Answer:
n<-6
Step-by-step explanation:
6-24n-28>122
-22-24n>122/:(-2)(devide the whole equation by (-2), when u devide by a negative number > changes to <)
11+12n>-61
12n<-72
n<-6
Can u help me with my work pls
Answer:
The mountain is 8.
The map is 96.
The compass is 6.
The hiker is 54.
The train is 14.
The a corn is 26
Hope this helps.
Help me please thanks
Answer:
3.64 × 10¹⁵
Step-by-step explanation:
Hey!
==================================================================
We always follow these rules when we are Multiplying and Dividing numbers with Scientific Notation.
1. If the numbers are not in scientific notation, convert them.
2. Regroup the numbers using the commutative and associative properties of exponents.
3. Now multiply the two numbers written in scientific notation, you work out the coefficients and the exponents separately.
-Use the product rule; aⁿ × aᵇ = a⁽ⁿ⁺ᵇ⁾ to multiply the bases.
4. If the product of the coefficients is greater than 9, convert it to scientific notation and multiply by the new power of 10.
5. Join the new coefficient to the new power of 10 to get the answer.
--------------------------------------------------------------------------------------------------------------
Let's start!
Our equation:
(5.2 × 10⁶)(7 × 10⁸)
--------------------------------------------------------------------------------------------------------------
1. If the numbers are not in scientific notation, convert them.
They are in scientific notation, so we go on to step 2.
2. Regroup the numbers using the commutative and associative properties of exponents.
(5.2 × 7)(10⁶ × 10⁸)
3. Now multiply the two numbers written in scientific notation, you work out the coefficients and the exponents separately.
-Use the product rule; aⁿ × aᵇ = a⁽ⁿ⁺ᵇ⁾ to multiply the bases.
5.2 × 7 = 36.4
10⁶ × 10⁸= 10⁽⁶⁺⁸⁾ = 10¹⁴
4. If the product of the coefficients is greater than 9, convert it to scientific notation and multiply by the new power of 10.
36.4 = 3.64 × 10¹
5. Join the new coefficient to the new power of 10 to get the answer.
3.64 × 10¹ × 10¹⁴
3.64 × 10⁽¹⁺¹⁴⁾ = 3.64 × 10¹⁵
==================================================================
3.64 × 10¹⁵
Hope I Helped, Feel Free to ask any questions to clarify :)
Have a fantastic day!
-Aadi x
24 college students were hired as ushers for a concert. This is 30% of the students who applied for the job. How many college students applied to be ushers
Answer:
80 students applied
Explanation:
24 ÷ 30 × 100
= 0.8 × 100
= 80
i hope this helps! :D do comment if you need any clarification.
Answer:
80 students
Step-by-step explanation:
if 30%=24
100%=?
100%/30%*24
=80
Find area of circle circumference or area
Answer:
closest option B (50.24)
Step-by-step explanation:
A=πr²
= π×4×4
=π×16
=50.265m²
Area:
50.24 m^2
Explanation:
The formula for the area of a circle is A = πr²,
where:
A = area, r = radiusDiagram:
[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 4\ m}\end{picture}[/tex]
Plug in the data. I'll use 3.14 for pi.
[tex]\bf{A=\pi \times4^2}\\\bf{A=3.14\times16}\\\bf{A=50.24\:m^2}[/tex]
Hence, area = 50.24 m^2
ALEGBRA 1 ! help. me. please. this. is. so. hard. i dont. understand it.
Answer:
Part a) to find the maximum height of the snowball, you have to differentiate the function. Therefore you get ----> dh/dt= -32x-8 . Now equate this to zero and solve for x. x= (-1)/4 now sub this value in to find h(x) [note: i'm talking about the original function] . I got h max = h((-1)/4) = 9 which is the max height.
Step-by-step explanation:
I'm not too sure about the other questions. Sorry
Solve for x
Literally forgot how to do this..
Answer:
x = 114 ur welcome
Step-by-step explanation:
Answer:
x = 114
Step-by-step explanation:
Given
[tex]\frac{x+18}{4}[/tex] = 33 ( multiply both sides by 4 to clear the fraction )
x + 18 = 132 ( subtract 18 from both sides )
x = 114
15 is 20% of what number? Enter your answer in the box.
Answer:
75
Step-by-step explanation: