Answers
Part (a)
BC = opposite side (furthest leg from the reference angle)
AB = adjacent side (closest leg from the reference angle)
AC = hypotenuse (always opposite the 90 degree angle)
=============================================
Part (b)
i. False. Angle B is 90 degrees as shown by the square angle marker.
ii. False. Side AB is opposite angle C. Note how "C" is part of "BC", so that means we cannot have BC be opposite C.
iii. True. Leg AB is the closer leg to angle A. We have "A" in "AB" to see this without having to draw the diagram. Refer to part (a) above.
iv. False. The longest side of any right triangle is always the hypotenuse. The longest side of any triangle is always opposite the largest angle.
==============================================
Part (c)
cos(theta) = adjacent/hypotenuse = AB/AC
tan(theta) = opposite/adjacent = BC/AB
Refer back to part (a) to determine the opposite,adjacent and hypotenuse side lengths.
==============================================
Part (d)
The reference angle has changed, so the opposite and adjacent sides swap. The hypotenuse remains the same regardless of what reference angle you pick.
sin(C) = opposite/hypotenuse = AB/AC
cos(C) = adjacent/hypotenuse = BC/AC
tan(C) = opposite/adjacent = AB/BC
Note the tangent ratio is the reciprocal of what we found back in part (c).
Answer & Step-by-step explanation:
(a)
The hypotenuse is on line CA (the hypotenuse is always opposite the 90° angle (marked by a little square))
The adjacent is on the line BA (adjacent is next to the given angle, but NOT the hypotenuse)
The opposite is on the line CB (this is opposite the given angle)
(b)
i. false (b is a right angle)
ii. false (the side opposite C is BA)
iii. true
iv. false (the side opposite B is the hypotenuse, and the hypotenuse is always the longest side in a triangle)
(c)
cosine ratio: [tex]cos=\frac{adjacent}{hypotenuse}[/tex]
tangent ratio: [tex]tan=\frac{opposite}{adjacent}[/tex]
The cosine and tangent ratios of the given angle:
[tex]cos0=\frac{AB}{CA} \\\\tan0=\frac{CB}{AB}[/tex]
(d)
Remember SOH-CAH-TOA:
Sine=Opposite/Hypotenuse
Cosine=Adjacent/Hypotenuse
Tangent=Opposite/Adjacent
Using the angle C, plug in the appropriate sides:
[tex]sinC=\frac{BA}{CA}\\\\ cosC=\frac{CB}{CA}\\\\ tanC=\frac{BA}{CB}[/tex]
:Done
Related Questions
What is the the product of (-1 - 3i) and it’s conjugate?
Answers
Answer:
10
Step-by-step explanation:
(-1 - 3i)(-1 + 3i) = 1 - 3i + 3i -9i²
1 - 9i²; i² = -1, therefore 1 - 9(-1) = 1 + 9 = 10
The three-dimensional figure shown consists of a cylinder and a right circular cone. The radius of the base is 10 centimeters. The height of the cylinder is 16 centimeters, and the total height of the figure is 28 centimeters. The slant height of the cone is 13 centimeters. Which choice is the best approximation of the surface area of the figure? Use 3.14 to approximate pi.
Answers
Answer:
2,041 square centimeters
Step-by-step explanation:
surface area = (2 × π × r × h) + ((π × r) × (r+ (√(c² + r²))))+(π × r²)
where,
cylinder base radius (r) = 10 cm
height of cylinder (h) = 16 cm
total height = 28 cm
cone height (c) = total height - height of cylinder = 28 - 16 = 12cm
π = 3.14
surface area = (2 × 3.14 × 10 × 16) + ((3.14 × 10) × (10+ (√(12² + 10²))))+(3.14 × 10²)
surface area = 1004.8 + (31.4 * 25.6) + 314
surface area = 2122.64 cm²
therefore the approximate surface area given is 2,041 square centimeters
A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.m. At this time, he started pumping gas into the tank. At exactly 3:44, the tank was full and he noticed that he had pumped 6 gallons.
Answers
Answer:
3.625 gpm
Step-by-step explanation:
when the point ( k, 3 ) lies on each of these lines, find the value of k y= 3x+1 , y= 4x-2 , y=1/2x - 1 and 2x+3y=4
Answers
Answer:
see explanation
Step-by-step explanation:
Since (k, 3) lies on each of the lines, the point satisfies the equations.
Substitute x = k, y = 3 into each and solve for k
y = 3x + 1
3 = 3k + 1 ( subtract 1 from both sides )
2 = 3k ( divide both sides by 3 )
k = [tex]\frac{2}{3}[/tex]
-------------------------------------------------------
y = 4x - 2
3 = 4k - 2 ( add 2 to both sides )
5 = 4k ( divide both sides by 4 )
k = [tex]\frac{5}{4}[/tex]
--------------------------------------------------------
y = [tex]\frac{1}{2}[/tex] x
3 = [tex]\frac{1}{2}[/tex] k ( multiply both sides by 2 to clear the fraction )
k = 6
---------------------------------------------------------
2x + 3y = 4
2k + 3(3) = 4
2k + 9 = 4 ( subtract 9 from both sides )
2k = - 5 ( divide both sides by 2 )
k = - [tex]\frac{5}{2}[/tex]
Desmond is 2 inches taller than Niki. If we let w represent Nikis height in inches, write an algebraic expression for Desmonds height. Enter your answer as an expression. Example: 3x^2+1
Answers
Answer:
w + 2
Step-by-step explanation:
Niki's height = w in
Desmond height = w + 2
Answer:
w+2
Step-by-step explanation:
Since Desmonds is 2 inches taller than Niki, w+2 would make the most sense.
What is the value of x in the equation 3x-4y=65, when y =4 will give brainliest
Answers
Hello!
Answer:
[tex]\huge\boxed{x = 27}[/tex]
Given:
3x - 4y = 65 where y = 4;
Substitute in 4 for "y":
3x - 4(4) = 65
Simplify:
3x - 16 = 65
Add 16 to both sides:
3x - 16 + 16 = 65 + 16
3x = 81
Divide both sides by 3:
3x/3 = 81/3
x = 27.
Hope this helped you! :)
Answer:
x=27
Step-by-step explanation:
3x-4y=65
Let y=4
3x - 4(4) = 54
3x -16 = 65
Add 16 to each side
3x -16+16 = 65+16
3x = 81
Divide each side by 3
3x/3 =81/3
x =27
which one is irrational?
Answers
Basically everything but choice C
==========================================
Explanation:
sqrt is shorthand for square root
sqrt(4) = 2 = 2/1 showing that sqrt(4) is rational. We can write it as a fraction of two whole numbers, where 0 is not in the denominator.
-------
In contrast, we cannot write sqrt(2), sqrt(3), or sqrt(5) as a fraction of two whole numbers. Using your calculator, note how
sqrt(2) = 1.4142135623731
sqrt(3) = 1.73205080756888
sqrt(5) = 2.23606797749979
all of those decimal expansions go on forever without any pattern, which is a sign that those numbers are irrational. If they were rational, then a pattern would repeat at some point or the decimals would terminate at some point.
Answer:
a, b, d are irrational
Step-by-step explanation:
root 2 = 0.414.....
root 3 = 0.732.....
root 5 = 2.236.....
Hope this helps.....
Pls mark my ans as brainliest
If u mark my ans as brainliest u will get 3 extra points
A principal of $2600is invested at 6.75% interest, compounded annually. How much will the investment be worth after 14 years
Answers
Answer:
$6488.19
Step-by-step explanation:
To solve this problem we use the compounded interest formula:
[tex]amount = principal(1 + (r \n))^({n}{t})[/tex]
a = $2600(1+(0.0675/1))¹*¹⁴
a = $6488.19
$10,000 for 20 years at 5% compounded annually
Answers
Answer:
$26532.98
Step-by-step explanation:
Given:
Principal = $10000Profit rate = 5% PA compoundedTime = 20 yearsCompounds = 20*1 = 20Sum is:
10000*(1 + 5/100)²⁰ ≈ 26532.98Michael is using a number line to evaluate the expression –8 – 3. A number line going from negative 12 to positive 12. A point is at negative 8. After locating –8 on the number line, which step could Michael complete to evaluate the expression?
Answers
Answer:
move to the left 3 more spaces
Step-by-step explanation:
you are at -8 already. Therefore, you (-3) more spaces, so you go to the left three more spaces. Use the saying keep change change to help with this.
Keep the first number sign, change the next sign, and the next sign.
Answer:
d
Step-by-step explanation:
solve the following: - 3 raised to 1 by 5 the whole raised to 4 (3^1/5)^4
Answers
Answer:
8.30256
Step-by-step explanation:
Step 1: Write out expression
[tex]((-3)^{\frac{1}{5} })^{4(3^{\frac{1}{5} })^4[/tex]
Step 2: Use BPEMDAS to evaluate
[tex](-1.24573)^{4(3^{\frac{1}{5} })^4[/tex]
[tex](-1.24573)^{4(1.24573)^4[/tex]
[tex](-1.24573)^{4(2.40822)[/tex]
[tex](-1.24573)^{9.6329}[/tex]
= 8.30256
And we have our answer!
Mildred’s salary has increased from £24,600 to £25,338. By what percentage has her salary increase?
Answers
Answer:
The answer is 3%Step-by-step explanation:
To find the percentage increase we use the formula
[tex]Percentage \: change = \frac{ change}{original \: quantity} \times 100[/tex]
To find the change subtract the smaller quantity from the bigger one
From the question
original price = $24,600
Current price = $ 25,338
Change = $25,338 - $ 24,600
Change = $ 738
So the percentage increase is
[tex] \frac{738}{24600} \times 100[/tex]
[tex] = \frac{3}{100} \times 100[/tex]
We have the final answer as
Percentage increase = 3%Hope this helps you
Hey there please help me with this question
Answers
Answer:
see explanation
Step-by-step explanation:
sum the parts of the ratio, 2 + 1 = 3 parts , thus
81 cm² ÷ 3 = 27 cm² ← value of 1 part of the ratio
2 parts = 2 × 27 = 54 cm²
Area of A = 54 cm² and area of B = 27 cm²
The side of the original square = [tex]\sqrt{81}[/tex] = 9 cm
The width of both rectangles is 9 cm ( width remains unchanged after cut )
Thus
Rectangle A
9 × length = 54 ( divide both sides by 9 )
length = 6 cm
Rectangle B
9 × length = 27 ( divide both sides by 9 )
length = 3 cm
Rectangle A → length = 6 cm, width = 9 cm
Rectangle B → length = 3 cm , width = 9 cm
Answer:
Rectangle A Rectangle B
length = 9 cm length = 9 cm
width = 6 cm width = 3 cm
Step-by-step explanation:
Area of square At = 81 cm²
Square is cut into two pieces = A + B
The ration of area A to B = 2:1
Find
Rect A Rect B
length length
width width
---------------------------------
first, get the side of the square = A = s²
81 = s²,
s = √81
s = 9 cm
since the ratio is 2:1, therefore the side can be divided into 3
9 ÷ 3 = 3 cm ----- take note of this to get the Width
Rectangle A
L = 9 cm (which is the s = 9 cm)
W = 3 cm (2 ratio) = 6 cm
Rectangle B
L = 9 cm (which is the s = 9 cm)
W = 3 cm (1 ratio) = 3 cm
Proof:
At = A + B
81 = (9x6) + (9x3)
81 = 54 + 27
81 = 81 ----- OK
Nina is training for a marathon. She can run 4 1/2 kilometers in 1/3 of an hour. At this pace, how many kilometers can Nina run in 1 hour?
Answers
Answer:
Nina can run:
13 1/2 km in 1 hour
Step-by-step explanation:
4 1/2 = 4 + 1/2 = 8/2 + 1/2 = 9/2
proportions:
9/2 hours ⇔ 1/3 hour
N hours ⇔ 1 hour
N = (9/2)*1 / (1/3)
N = (9/2) / (1/3)
N = (9*3) / (2*1)
N = 27/2
27/2 = 26/2 + 1/2 = 13 + 1/2 = 13 1/2
Nina can run:
13 1/2 km/h
13 1/2 km in 1 hour
Nina can run [tex]13\frac{1}{2}[/tex] km in an hour
The distance Nina can run in an hour can be determined by dividing the distance she can run in 1/3 of an hour by 1/3
Distance Nina can run in an hour = distance run ÷ [tex]\frac{1}{3}[/tex]
[tex]4\frac{1}{2}[/tex] ÷ [tex]\frac{1}{3}[/tex]
Convert the mixed fraction to an improper fraction [tex]\frac{9}{2}[/tex] × 3 = [tex]\frac{27}{2}[/tex]
Convert the improper fraction back to an mixed fraction = [tex]13\frac{1}{2}[/tex] km
To learn more about fractions, please check:
https://brainly.com/question/21449807?referrer=searchResults
1. At the end of one school day a teacher had 17 crayons left. The teacher remembered
giving out 14 crayons in the morning, getting 12 crayons back at recess, and giving out
11 crayons after lunch. How many crayons did the teacher have at the start of the
day?
Answers
Answer:
30 crayons
Step-by-step explanation:
Let x be the number of crayons he started with
gave out 14 crayons
x-14
Got 12 back
x-14+12
Gave out 11 after lunch
x-14+12 -11
This equals 17
x-14+12 -11 =17
Combine like terms
x-13 = 17
Add 13 to each side
x -13+13 =17+13
x = 30
Answer: 30
Step-by-step explanation:
For this problem work backwards. Start from 17 and add 14. You should get 31. Then subtract 12, which equals 19. Finally add 11 to 19, which equals 30. Basically you are doing the inverse operation to get your answer. Hope this helps!
It is estimated that 52% of drivers text while driving . What is the probability the next driver texting while driving that a police officer pulls over is the fifth driver?
Answers
Answer:
0.0276
Step-by-step explanation:
The computation of the probability that the next driver is texting while driving is shown below:
= Fourth pull failure × fifth pull success
where,
Fourth pull failure is (1 - 0.52)^4
And, the fifth pull success is 0.52
Now placing these values to the above formula
So,
= (1 - 0.52)^4 × 0.52
= 0.0276
Hence, the probability is 0.0276
Plz Help I Will Mark Brainliest If Right!!!!!!!!!!!!!!!!!!!!!!!
Determine the domain of the function.
f as a function of x is equal to the square root of one minus x.
A). All real numbers
B). x > 1
C). x ≤ 1
D). All real numbers except 1
Answers
Hey There!!~
Your best answer choice is B). x > 1.
Good Luck!!
The fraction subtracted from 5/3 to get 1 is_____
Answers
Answer:
2/3
Step-by-step explanation:
I am not sure
Answer:
2/3Step-by-step explanation:
[tex]Let \:the \: unknown \: fraction \: be \: x\\\\\frac{5}{3} -x = 1\\\\\frac{5}{3}-x=1\\\\\mathrm{Subtract\:}\frac{5}{3}\mathrm{\:from\:both\:sides}\\\\\frac{5}{3}-x-\frac{5}{3}=1-\frac{5}{3}\\\\\frac{5}{3}-x-\frac{5}{3}=-x\\\\1-\frac{5}{3}=-\frac{2}{3}\\-x=-\frac{2}{3}\\\\x=\frac{2}{3}\\[/tex]
E
What is the value of x in the equation 3x.. by y 18, when y27
Answers
Answer:
x = 15
Step-by-step explanation:
We need to find the value of x in the equation 3x – y = 18 when y = 27.
To find the value of x, put y = 27 in the above equation.
So,
3x - 27 = 18
3x = 45
x = 15
So, the value of x is 15.
a rectangular garden is fenced on all sides with 128 feet of fencing. The garden is 4 feet longer than it is wide. Find the length and width of the garden
Answers
Answer:
Length = 34 feet
Breadth = 30 feet
Step-by-step explanation:
Perimeter= 128 ft
Let the breadth be = [tex]x[/tex]
Let the length be = [tex]x+4[/tex]
∴by the problem ,
2(length+breadth)= perimeter
[tex]2(x+4+x)=128\\2(2x+4)=128\\4x+8=128\\4x=128-8\\4x=120\\x=120/4\\x=30[/tex]
Therefore, length of the garden = 30+4= 34 feet
breadth of the garden = 30 feet
Sarah has $20 saved. She gets $10 per week for her allowance, and she saves her allowance for the next 3 weeks. At the end of the week, she gets $150 in birthday money. How much money will she have after the 3 weeks? Which of the following sets of equations represents this problem?
Answers
Answer:
$200
Step-by-step explanation:
We know that she already has $20. And we know that every week, for three weeks she gets $10.
20+3(10)+150=m
We add all of this up, and we find that at the end of 3 weeks Sarah has $200 saved.
A line passes through point (4,-3) and has a slope of 5/4. Write an equation in Ax + By = C
Answers
Answer:
The answer is
5x - 4y = 32Step-by-step explanation:
To write an equation of a line using a point and slope use the formula
y - y1 = m(x - x1)where
m is the slope
(x1 , y1) is the point
So we have
Equation of the line using point (4 , -3) and slope 5/4 is
[tex]y + 3 = \frac{5}{4} (x - 4)[/tex]
Multiply through by 4
4y + 12 = 5(x - 4)
4y + 12 = 5x - 20
5x - 4y = 20 + 12
The final answer is
5x - 4y = 32Hope this helps you
A debt of $12,000 with interest at 5% compounded monthly is to be repaid by equal payments at the end of each year for three years and nine months. What is the term of repayment? None 12 months 3.9 years 3.75 years
Answers
Answer:
3.75 years
Step-by-step explanation:
If the debt is to be paid in 3 years, 9 months, then the term of the loan is ...
3 9/12 = 3 3/4 = 3.75 . . . years
in the equation z=x^2-3y, find the value of z when x=-3 and y=4
Answers
Answer:
z=-3
Step-by-step explanation:
z=(-3)^2 - 3(4)
z=9 - 12
z=-3
Write the expression 12-2 in simplest form.
Answers
Answer:
convert into a whole number 6
Need to find the Domain and Range
Answers
Answer:
D: {x∈R | -2 ≤ x ≤ 2 }
R: {y∈R | 0 ≤ y ≤ 4 }
Step-by-step explanation:
The domain ranges between -2 and 2
The range ranges between 0 and 4
someone please expain how to do this, i’m really confused.
Answers
Answer:
13
Step-by-step explanation:
Basically, we have to plug in 4 for r into g(r). Doing so gives us g(4) = 25 - 3 * 4 = 25 - 12 = 13.
Some more examples:
g(6) = 25 - 3 * 6 = 25 - 18 = 7
g(1) = 25 - 3 * 1 = 25 - 3 = 22
Answer:g(4)=13
Step-by-step explanation:
g(4)=25-3r
25-3(4)
25-12
g(4)=13
inscribed angles. need answers asap , thank u!
Answers
Answer:
40°
Step-by-step explanation:
The circumference of a circle is equal to 360°
The arc AB is 180°, the arc AC is given as 100° so the arc CB is 80° and since <A is an inscribed angle it is equal to the half of the arc it sees
80 ÷ 2 = 40
4. The rental for a television set changed from $80 per year to $8 per month
What is the percentage increase in the yearly rental?
Answers
Answer:
16%
Step-by-step explanation:
rental charge per year = $80
rental charge at the rate $8 per year = 8 * 12 = 96
the increased amount = 96 - 80 = 16
% = 16 / 100 = 16%
One researcher wishes to estimate the mean number of hours that high school students spend watching TV on a weekday. A margin of error of 0.28 hour is desired. Past studies suggest that a population standard deviation of hours is reasonable. Estimate the minimum sample size required to estimate the population mean with the stated accuracy.
Answers
Complete question:
One researcher wishes to estimate the mean number of hours that high school students spend watching TV on a weekday. A margin of error of 0.28 hours is desired. Past studies suggest that a population standard deviation of 1.5 hours is reasonable. Estimate the minimum sample size required to estimate the population mean with the stated accuracy.
Answer:
111 students
Step-by-step explanation:
Given the following :
Margin of Error (E) = 0.28
Population standard deviation (sd) = 1.5
Recall:
Margin of Error(E) = Z * (sd/√n)
Taking a confidence interval of 95%
The Z value at a 95% confidence interval is 1.96
Plugging our values, we have :
Margin of Error(E) = Z * (sd/√n)
0.28 = 1.96 * (1.5/√n)
0.28 = 2.94 / √n
√n × 0.28 = 2.94
√n = 2.94 / 0.28
√n = 10.5
Square both sides to obtain n
n = 10.5^2
n = 110.25
