6. The diagram on the right shows right-angled triangles POR
and PRS. Given that tan 0 =
3
4
in em, the length of
(a) PR
(b) RS
Q
9 cm
R
Answers
Answer:
The answer is below
Step-by-step explanation:
Trigonometric ratios shows the relationship between the sides of a right angled triangle and its angles. Some trigonometric ratios are:
sinθ = opposite / hypotenuse, cosθ = adjacent / hypotenuse; tanθ = opposite / adjacent.
In triangle PQR:
tanθ = QR / PQ
substituting gives:
3/4 = 9 / PQ
PQ = 9 * 4 / 3 = 12 cm
Applying Pythagoras in triangle PQR gives:
PR² = PQ² + QR²
PR² = 12² + 9²
PR² = 144 + 81 = 225
PR = 15 cm
Also in triangle PRS:
PS = (5/3)PR = (5/3)*15 = 25 cm
PS² = PR² + RS²
25² = 15² + RS²
625 = 225 + RS²
RS² = 400
RS = 20 cm
Related Questions
Write an equation of a line through the point (2, -1) parallel to y = 4x - 3.
Answers
Answer:
y = 4x - 9
Step-by-step explanation:
y = 4x + b
-1 = 4(2) + b
-1 = 8 + b
-9 = b
which are the slope and the y-intercept linear function that is represented by the graph?
Answers
Answer:
See explanation
Step-by-step explanation:
The question is incomplete, as the graph is not given.
The general step to calculate slope and y intercept is as follows;
Assume any two points on the graph are:
[tex](x_1,y_1) = (5,1)[/tex]
[tex](x_2,y_2) = (1,4)[/tex]
The slope (m) is:
[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{4 -1}{1-5}[/tex]
[tex]m = \frac{3}{-4}[/tex]
[tex]m = -\frac{3}{4}[/tex]
The equation of the graph is:
[tex]y = m(x - x_1) + y_1[/tex]
This gives:
[tex]y = -\frac{3}{4}(x - 5) + 1[/tex]
[tex]y = -\frac{3}{4}x +\frac{15}{4} + 1[/tex]
[tex]y = -\frac{3}{4}x +\frac{15+4}{4}[/tex]
[tex]y = -\frac{3}{4}x +\frac{19}{4}[/tex]
To calculate the y intercept; set [tex]x = 0[/tex]
[tex]y = -\frac{3}{4}*0 +\frac{19}{4}[/tex]
[tex]y = \frac{19}{4}[/tex] ---- y intercept
there are 105 teachers in a school 19 more are femal than male how what is the proprtion of female teachers
Answers
Explanation: 105 - 19 = 86 (Find out how much the college would have without the more)
86 ÷ 2 = 43 (Find out male and female teachers in a seperate way without more)
43 + 19 = 62 (Female teachers)
You bought a shirt for 13.50 that was originally 45.00 in terms of percent what discount did you get the shirt?
Answers
31.5/45x100= 70%
You got the shirt 70% discounted.
I am not too sure if it’s correct though, I might be wrong.
The base of an open rectangular box is of length (2x + 5) cm and width x cm.
The area of this base is 58 cm
The height of the open box is (x - 2) cm.
a) Show that 2x + 5x -58 = 0
) Solve the equation 2x + 5x -58 = 0, giving your answers correct
to 2 decimal places
D) Hence calculate the volume of the box, stating the units of your answer.
Answers
Answer:
a) x = 8.29 cm
D) V = 1125.27 cm³
Step-by-step explanation:
a) We can solve the equation as follows:
[tex] 2x + 5x - 58 = 0 [/tex]
[tex] 2x + 5x = 58 [/tex]
[tex] x = \frac{58}{7} = 8.29 [/tex]
D) The volume of the box is given by:
[tex] V = l*w*h [/tex]
Where:
l: is the length
w: is the width
h: is the height
The length of the rectangular box is:
[tex] l = (2x + 5) cm = (2*8.29 + 5) cm = 21.58 cm [/tex]
The width is x = 8.29 cm.
And the height is:
[tex] h = (x - 2) cm = (8.29 - 2) cm = 6.29 cm [/tex]
Hence, the volume is:
[tex] V = l*w*h = (21.58*8.29*6.29) cm^{3} = 1125.27 cm^{3} [/tex]
I hope it helps you!
If a ⋆ b = ab² - a²b, then 2 ⋆ 3 = i don't kno the answer
Answers
Hello,
We know that :
a * b = ab² - a²b
We know that : 2 * 3 = 6 but we want to try this formula.
We have :
a = 2 and b = 3
So :
2 * 3
= 2 * 3² - 2² * 3
= 2 * 9 - 4 * 3
= 18 - 12
= 6
It works :)
Which region represents the solution to the given system of inequalities?
{y < -1/2x }
[y ≥ 2x+3 }
A
B
C
D
Answers
The region D represents the solution of the given system of inequalities.
What is the system of linear inequalities?
A system of linear inequalities is a collection of linear inequalities in the same variables.
How to shade the graph of inequalities?Rearrange the equations so "y" is on the left and everything else on the right. Plot the "y≤ ,y≥ ,y> or y< " line.Shade above the line for a " greater then" and below for the "less than".According to the given equation.
We have system of inequalities.
[tex]y < \frac{-1}{2}x[/tex]
and [tex]y \geq 2x + 3[/tex]
Also, the graph of the inequalities.
Since, y is less than [tex]-\frac{1}{2} x[/tex] shade below the line.
And, for the second inequality.
y is greater than and equal to 2x + 3 therefore, shade the above the line.
So, the common region D we get after the shading.
Hence, region D represents the solution of the given system of inequalities.
Find out more information about system of inequalities:
https://brainly.com/question/19526736
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Can someone help me?It's urgent and thank you!
Answers
Answer:
x = 9
Step-by-step explanation:
square each side first to get:
8x - 8 = 64
8x = 72
x = 9
Miguel made $286 for 13 hours of work.
At the same rate, how much would he make for 7 hours of work?
Answers
Answer:
Step-by-step explanation:
The key here is to find out how much he makes per hour. We can find that out using the info given.
286 = 13x so
x = 22 dollars per hour. For 7 hours of work then,
7(22) = $154
Find the unit rate of dollars per hour:
286 ÷ 13 = 22
So the unit rate is $22 per hour of work
Either way, the answer is right
Hope this helps!
lines that intersect and form four right angles are called?
Answers
Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect. Perpendicular lines are lines that intersect at a right (90 degrees) angle.
4days : 2 weeks simplify
Answers
Answer:
2:7
Step-by-step explanation:
ratio as a fraction in simplest form. 2 weeks = 14 days, so 4/14 = 2/7.
Answer:
2 : 7
Step-by-step explanation:
7 days = 1 week
y days = 2 weeks
[tex]\frac{1}{7} :\frac{2}{y}[/tex]
1 × y = 2 × 7
y = 14
4 days : 14 days
4 = 2 × 2
14 = 2 × 7
GCF = 2
4 ÷ 2 = 2
14 ÷ 2 = 7
2 : 7
Evaluate x2+9/x2 for each of the given values.
What is the value of the expression when x = 3?
2
3
10
undefined
What is the value of the expression when x = 1?
2
3
10
undefined
What is the value of the expression when x = 0?
2
3
10
undefined
Answers
Answer:
ok so we just substate the number in so
6+9/6
6+1 1/3 = 7 1/3
so for part a the answer is 7.33
for part b
2+9/2
3+4 1/2 =7 1/2
so the answer is 7.5
A:7.33
B:7.5
Hope This Helps!!!
Answer:
A, 2
B, 10
C, undefined
Step-by-step explanation:
Just did the assignment E2021
NEED HELP; A group of friends goes out to dinner. The total bill, without tax, is $63. If tax on the meal is 6% and if an 18% tip is left on the $63 total bill, what is the total amount paid?
A. $78.12
B. $78.80
C. $66.78
D. $74.34
Answers
Find the next term of the sequence.
21, 15, 9, 3, . .
6
−6
0
−3
Answers
Answer:
-3
Step-by-step explanation:
You need to substract 6 to get the next term.
I HOPE THIS HELPS :)
Answer:
-3
Step-by-step explanation:
21 - 6 = 15
15 - 6 = 9
9 - 6 = 3
3 - 6 = -3
Ifthe fish commission states that the mean length of all fish in spring run is mean =15cm,withthe standard deviation of variance=4cm,what will be the probability that a fish is caught in spring run :between 15cm&19cm?
Answers
Answer:
Step-by-step explanation:
z(lower) = (15-15)/4 = 0
z(upper) = (19-15)/4= 1
z at 0 = .5
z at 1 = 0.841344746
(look these up in a Z table)
probability "between" = 0.841344746 - .5 = 0.3841344746
0.384 is the probability that a fish is caught in spring run between 15cm and 19cm
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given that fish commission states that the mean length of all fish in spring run is mean =15cm
the standard deviation of variance=4cm,
We need to find the probability that a fish is caught in spring run :between 15cm and 19cm
The z score formula is z=x-µ/σ
z(lower) = (15-15)/4 = 0
z(upper) = (19-15)/4= 1
From the table of z values we get
z at 0 is 0.5
z at 1 is 0.841344746
probability between 0.841344746 -0 .5 is 0.3841344746
Hence, 0.384 is the probability that a fish is caught in spring run between 15cm and 19cm
To learn more on Statistics click:
https://brainly.com/question/29093686
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part ion even know of the hardest test
Answers
Given:
The equation of a line is:
[tex]y=-\dfrac{5}{7}x+2[/tex]
A line passes through the point (-5,-3) and perpendicular to the given line.
To find:
The equation of the line.
Solution:
Slope intercept form of a line is:
[tex]y=mx+b[/tex] ...(i)
Where, m is the slope and b is the y-intercept.
We have,
[tex]y=-\dfrac{5}{7}x+2[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]m=-\dfrac{5}{7}[/tex]
We know that the product of slopes of two perpendicular lines is always -1.
[tex]m_1\times m_2=-1[/tex]
[tex]-\dfrac{5}{7}\times m_2=-1[/tex]
[tex]m_2=\dfrac{7}{5}[/tex]
Slope of the required line is [tex]\dfrac{7}{5}[/tex] and it passes through the point (-5,-3). So, the equation of the line is:
[tex]y-y_1=m_2(x-x_1)[/tex]
[tex]y-(-3)=\dfrac{7}{5}(x-(-5))[/tex]
[tex]y+3=\dfrac{7}{5}(x+5)[/tex]
Using distributive property, we get
[tex]y+3=\dfrac{7}{5}(x)+\dfrac{7}{5}(5)[/tex]
[tex]y+3=\dfrac{7}{5}x+7[/tex]
[tex]y=\dfrac{7}{5}x+7-3[/tex]
[tex]y=\dfrac{7}{5}x+4[/tex]
Therefore, the equation of the line is [tex]y=\dfrac{7}{5}x+4[/tex]. Hence, option A is correct.
Apothem=
A) 4 units
B) 4 (square root) 2 units
C) 4 (square root) 3 units
Answers
Answer:
Step-by-step explanation:
c
what is 69/2 as a mixed number
Answers
Answer:
I think it's 34
Step-by-step explanation:
69/2 = 34.5 = 34
Which angle would be complementary to
Answers
He average price of a home in a neighborhood of mostly leased properties is $259,000. The average monthly rent is $2,500. One home in the neighborhood is leased for $2,800. Using a GRM, what is the value of that home?
Answers
Answer:
$290,080
Step-by-step explanation:
Given:
Average price = 259,000
Average monthly rent = 2500
Monthly rent of home = $2800
Gross Rent Multiplier = price per monthly rent
GRM = Price / monthly rent
The GRM = 259000 ÷ 2500
= $103.60
The price = GRM * Monthly rent
Price = $103.60 * $2800
Price = $290,080
The function h(t) = -16t^2 + h, 0 gives the height (in feet) of a ball dropped from a height of h, 0 after t seconds. A ball is dropped from a height of 12 feet. After how many seconds does the ball hit the floor?
could someone explain how to solve the equation? I know it's h(t) = -16^2 + 12
Answers
Answer:
Step-by-step explanation
the answee
Which of the following describes the parabola with the equation y = −x2 − 3x + 6?
A) The axis of symmetry is x = 1.5 and the vertex is (1.5, 12.75).
B) The axis of symmetry is x = −1 and the vertex is (−1, −3).
C) The axis of symmetry is x = −1.5 and the vertex is (−1.5, 8.25).
D) The axis of symmetry is x = 0 and the vertex is (0, 6).
Answers
Answer:
C) The axis of symmetry is x = −1.5 and the vertex is (−1.5, 8.25).
Step-by-step explanation:
The axis of symmetry is x = − b/2a
= -(-3) / 2(-1)
= 3/(-2)
= -1.5
the vertex => x = -1.5
y= -(-1.5)²-3(-1.5)+6 =
-2.25 +4.5+6= 8.25
due today pls helppppp
Answers
====================================================
Work Shown:
tan(angle) = opposite/adjacent
tan(C) = AB/BC
tan(theta) = x/BC
tan(23) = (8.1)/BC
BC*tan(23) = 8.1
BC = (8.1)/tan(23)
BC = 19.0824041631723
BC = 19.1
In this case, rounding to 3 sig figs means we round to the nearest tenth.
Make sure your calculator is in degree mode.
Una empresa fabrica protectores faciales, según los estudios de mercado que se han hecho, se ha de vender a S/.9 la unidad. La empresa tiene unos gastos fijos mensuales de local y personal de S/.9000, y además, fabricar cada unidad protector facial cuesta S/. 3. ¿Cuántas unidades ha de vender mensualmente si no quiere tener pérdidas?
Answers
Answer:
The number of units sell is 2.
Step-by-step explanation:
selling cost of one unit = $ 0.9
Monthly expense = $ 0.9
Manufacturing cost = $ 0.3
Let the number of unit sell is x.
So,
0.9 x = 0.9 + 0.3 x
0.6 x = 0.9
x = 1.5
So, the number of units sell to get no loss is 2.
When x = 1 and y = –2, z =
Answers
Answer:
No solution is possible from the information provided
Step-by-step explanation:
Please help us help you by including enough information to answer your question.
Answer:
z = -10
Step-by-step explanation:
trust me
Complete the sentence:
The intersection of a circle and a triangle can be
A. Six Points
B. Twelve Points
C. Eight Points
D. Circle
Answers
Answer:
A. Six Points
Step-by-step explanation:
Type the correct answer in the box.
Consider the table below.
х у
-3 0.5
-2
1
-1 2.5
0
5
18.5
Complete the standard form equation representing the quadratic relationship displayed above, where a, b, and care constants.
Answers
Answer:
Step-by-step explanation:
Use the standard form equation along with 3 of the coordinates from the table. I used (-1, 2.5), (0, 5), and (1, 8.5). Begin always with the coordinate where you have a 0:
[tex]5=a(0)^2+b(0)+c[/tex] and we get immediately that c = 5. We can use that value as move forward with the next coordinate pair.
[tex]8.5=a(1)^2+b(1)+5[/tex] and
8.5 = a + b + 5 and
3.5 = a + b Hold that thought while we come up with the second equation for this system.
[tex]2.5=a(-1)^2+b(-1)+5[/tex] and
2.5 = a - b + 5 and
-2.5 = a - b Now solve this system using the method of eliination:
a + b = 3.5
+ a - b = -2.5
so
2a = 1 and a = 1/2 Now we can plug that in and solve for b:
a + b = 3.5 becomes
1/2 + b = 3.5 so
b = 3 and the equation is
[tex]y=\frac{1}{2}x^2+3x+5[/tex]
given f(x)=2/5(6-x)^2 what is the value of f(6)?
Answers
Answer:
0
Step-by-step explanation:
f(x) = 2/5(6 - x)²
f(6) = 2/5[6 - (6)]²
f(6) = 2/5(0)²
f(6) = 0
A hot air balloon is released and it rises at a speed of 15 mph. A
weather pattern introduces a wind headed west at 20 mph. The
hot air balloon is now redirected. What is the new direction of the
hot air balloon?
Answers
Answer:
The direction is 37 degree north of west.
Step-by-step explanation:
velocity of balloon, v = 15 mph upwards
velocity of wind, v' = 20 mph west wards
The direction is given by
[tex]tan\theta = \frac{15}{20}\\\\\theta = 37^o north of west[/tex]
Find the equation of the line passing
through the points (2, 4) and (3,2).
Answers
Answer:
y=-2x+8
Step-by-step explanation:
first is to find the slope
m=(y2-y1) /(x2-x1)= (2-4)/(3-2)=-2/1= -2
now using the line formula of y=m*x+b, put in one of the points and solve for b.
2= -2*3 + b
2= -6 + b
8 = b
so y= -2*x+8