Theta has a reference angle of 30° and is in Quadrant I or II.
Sin(theta) = ½
Basic angle: 30
What is the reference angle?
The acute angle between the terminal arm/terminal side and the x-axis. The reference angle is always positive. In other words, the reference angle is an angle sandwiched between the terminal side and the x-axis.
Angles: 30,
180-30 = 150
Because sin is positive in quadrants 1 and 2.
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ve questions from this section 18 A bus left Nairobi at 8.00am and traveled towards Busia at an average speed of 80km/hr. At 8.30 am a car left Busia for Nairobi at an average speed of 120km/hr. Given that the distance between Nairobi and Busia is 400km. ve questions from this section 18 A bus left Nairobi at 8.00am and traveled towards Busia at an average speed of 80km / hr . At 8.30 am a car left Busia for Nairobi at an average speed of 120km / hr . Given that the distance between Nairobi and Busia is 400km
The time that the bus arrived Busia is given as 1.00 pm
How to solve for the time of arrivalThe formula with which to solve for the time is given as
D/s = distance / by the speed.
Distance = 400km
Speed = 80km/hr
Time = 400/80
= 5 hours
Therefore the time of arrival from 8.00 am would be 1.00pm
Complete questionA bus left Nairobi at 8.00am and traveled towards Busia at an average speed of 80km / hr . At 8.30 am a car left Busia for Nairobi at an average speed of 120km / hr . Given that the distance between Nairobi and Busia is 400km
Calculate The time the car arrived in Busia
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given, what are the domain and range?
Factor the rational function,
.
.
.
.
Notice that the denominator and numerator both have x-1. This means that we have a removable discontinuity there so set x-1=0.
.
.
So our domain can be all reals except 1.
Range: First factor out the x-1. We will be left with
.
Since 1 isn't in the domain, plug in 1 to find the what won't be in the range
.
So 7 isn't in the range,
End Behavior:
Since the rational function numerator is a quadratic and the denominator is a linear function, the rational function will approach will not have a horizontal asymptotes.
A student begins a proof of the law of cosines. His work is shown.
(image below)
The student made an error in ___. To correct this error, he should ___.
After correcting this error, the student can use the ___ to relate sides x, y, z, and angle ___.
1st blank answers:
a, step 1
b, step 2
c, step 3
2nd blank answers
a, define side AY in terms of angle X
b, define side XY in terms of angle X
c, define side AX in terms of angle Y
3rd blank answers
a, tangent function
b, law of sines
c, Pythagorean theorem
4th blank answers
a, Z
b, X
c, Y
The student made an error in step 3. To correct this error, he should define side AY in terms of angle X. Pythagorean theorem relates sides x, y, z, and angle X
The law of cosine.In Trigonometry, law of cosine (cos) is given by this mathematical expression:
cosθ = Opp/Hyp
Where:
Opp is the opposite side of a right-angled triangle.Hyp is the hypotenuse of a right-angled triangle.θ is the angle.In this scenario, we can logically deduce that the student made an error in step 3. To correct this error, he should define side AY in terms of angle X.
After correcting this error, the student can use the Pythagorean theorem to relate sides x, y, z, and angle X.
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If the proportion of the total disposable income spent on consumer goods and services is 93 percent and if
consumers spend 85 percent of each additional dollar, what is
a. the apc?
b. the aps?
c. the mpc?
d. the mps?
Answer:
what?????????????????
Find the length of side AB.
Give your answer to 3 significant figures.
Answer:
[tex]\huge\boxed{\sf AB = 8.86 \ cm}[/tex]
Step-by-step explanation:
Given:θ = 41°
Hypotenuse = BC = 13.5 cm
Required:opposite = AB = ?
We will use the trigonometric ratio of sin.
Solution:[tex]\displaystyle sin \ \theta = \frac{opposite }{hypotenuse} \\\\sin \ 41=\frac{AB}{13.5} \\\\0.656 = \frac{AB}{13.5} \\\\0.656 \times 13.5 = AB\\\\8.86 \ cm = AB\\\\\boxed{ AB = 8.86 \ cm}\\\\\rule[225]{225}{2}[/tex]
Help please.. z zzz z Z z z z z z z z z z z z z zz
Find the midpoint of the line segment with end coordinates of:
(-1,7) and (3,-2)
Give coordinates as decimals where appropriate.
Answer:
(1,2.5)
Step-by-step explanation:
On the graph, the (-1,7) lies in the top right grid. The (3,-2) lies in the bottom left grid. If you use a graphing calculator, the middle is hard to find but you will find (1, 2.5) or (1, 5/2).
Someone help me with this math word questions
2) The three ways of naming an angle are by the letter at the vertex, by placing a number or variable inside the angle, or by two letters with the vertex letter placed in the middle.
3) [tex]\angle WXY, \angle YXZ, \angle WXZ[/tex]
4) [tex]X[/tex]
Factorise x³ + 2x I can't understand this please give me the answer
Answer:
[tex]x(x^2+2)[/tex]
Step-by-step explanation:
Since x is the only common term, you factor that part out using the distributive property.
Solution:
Detailed explanation:
Hii! Let's factorise this expression!
Did you see that both terms, x^3 and 2x, have an x in common? That's what we are going to factor out, by dividing x^3 and 2x by x.
x^2+2 is what we obtain.
Now, this can't be the end of the process. We also need to put parentheses around x^2+2.
(x^2+2)
Next we put that x we factored out a short while ago outside the parentheses.
x(x^2+2). Did you get it?
________
Hope I helped, best wishes & happy studies!
Please reach out if any queries arise. Thankyou!!
_______
its math help me out
Answer:
each one is double the one before it so in year 5...
3912*2=7824
Hope This Helps!!!
Answer:
7824
Step-by-step explanation:
8 1/2 - 3/8=?
pls answer fast
Answer:
65/8
Step-by-step explanation:
1) Turn all numbers into improper fractions: 17/2 - 3/8 = ?
2) Make all denominators the same number by finding the least common factor, which is 8. Multiply the denominator in 17/2, which is 2, by 4 to match the other denominator. And then multiply the numerator (17) by 4 as well so that the fraction still has the same value: 68/8 - 3/8 = 65/8
3) Can not simplify since there are no common factors between 65 and 8.
DF=
Help me please:))
Answer:
[tex]\fbox {DF = 20}[/tex]
Step-by-step explanation:
Given :
ΔSDF ~ ΔRTY = 4 : 9 (Ratio of similitude)SF = RT - 2TY = RY + 9SD = 8Step 1 : Find RT
SD : RT = 4 : 98 : RT = 4 : 9RT = 18Step 2 : Find SF
SF = RT - 2SF = 18 - 2SF = 16Step 3 : Find RY
SF : RY = 4 : 916 : RY = 4 : 9RY = 36Step 4 : Find TY
TY = RY + 9TY = 36 + 9TY = 45Step 5 : Find DF
DF : TY = 4 : 9DF : 45 = 4 : 9DF = 20Answer:
DF = 20
Step-by-step explanation:
Triangle SDF has side lengths SD, DF, SF.
Triangle RTY has side lengths
RT = (9/4)SD
RY = (9/4)SF
TY = (9/4)DF
"SF is 2 less than RT" Given
SF = RT - 2
SF = (9/4)SD - 2
"SD = 8" Given
SF = (9/4)(8) - 2
SF = 16
"TY is 9 more than RY" Given
TY = RY + 9
(9/4)DF = (9/4)SF + 9
(9/4)DF = (9/4)(16) + 9
(9/4)DF = 45
DF = 45 × 4/9
DF = 20
if 9^x=25, what does 3^x equal?
Answer:
[tex]3^x=5[/tex]
Step-by-step explanation:
Given:
[tex]9^x=25[/tex]
Rewrite 9 as 3²:
[tex]\implies (3^2)^x=25[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 3^{2x}=25[/tex]
Apply the same exponent rule:
[tex]\implies (3^x)^2=25[/tex]
Square root both sides:
[tex]\implies \sqrt{(3^x)^2}=\sqrt{25}[/tex]
[tex]\implies 3^x=5[/tex]
Which ordered pair makes both inequalities true?
y < –x + 1
y > x
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, 0). Everything below and to the left of the line is shaded. The second dashed line has a positive slope and goes through (negative 1, negative 1) and (1, 1). Everything above and to the left of the line is shaded.
(–3, 5)
(–2, 2)
(–1, –3)
(0, –1)
Inequalities help us to compare two unequal expressions. The correct option is B.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
For the given inequalities, the graph can be plotted as shown below. Now when the coordinates have been plotted the point that will satisfy both the inequalities is (-2,2).
Hence, the correct option is B.
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5/8 divided by 15/32
Answer: [tex]\frac{4}{3}[/tex] or about 1.333
Step-by-step explanation:
We will use the "keep, change, flip" method to solve. Keep the first number the same, change the division to multiplication, and flip the second number so we have the reciprocal.
[tex]\displaystyle \frac{\frac{5}{8} }{\frac{15}{32} } \,\,\,\,\text{ becomes } \,\,\,\,\frac{5}{8} *\frac{32}{15} =\frac{5*32}{8*15} =\frac{160}{120} =\frac{4}{3}[/tex]
Answer: 4/3
Step-by-step explanation:
find the reciprocal of the divisor
15/32
32/15
Now multiply it with the dividend
5/8
15/32
=5/8
32/15
=5/32
8/15
=160/120
after reducing the fraction the answer is 4/3
in mix form 1 1/3
What are the solutions to the following system of equations?
y = x² + 7x - 5
2x - y = -9
Answer:
x= -7, y= -5 and
x= 2, y= 13
This may also be written as (-7, -5) and (2, 13).
Step-by-step explanation:
Start by labelling the two given equations:
y= x² +7x -5 -----(1)
2x -y= -9 -----(2)
Let's solve by substitution!
Making y the subject of formula in equation (2):
From (2): y= 2x +9 -----(3)
Substitute (3) into (1):
2x +9= x² +7x -5
x² +7x -5 -2x -9= 0
x² +5x -14= 0
Factorise:
(x +7)(x -2)= 0
x +7= 0 or x -2= 0
x= -7 or x= 2
Find the respective values of y.
Substitute into (1):
y= (-7)² +7(-7) -5 or y= (2)² +7(2) -5
y= 49 -49 -5 or y= 4 +14 -5
y= -5 or y= 13
Thus, the solutions are (-7, -5) and (2, 13).
Which graph represents the solution of x² + y² < 25 and y² <6x?
The graph is shown below
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
As, the equation x² + y² < 25 represents equation of circle.
So, the graph will be of the form circle.
and, y² <6x is the equation to represent parabola
So, the graph will represent a parabola.
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If price of 12 eggs is Rs. 192, how many eggs can be bought for Rs. 160?
Answer:
10
Step-by-step explanation:
First, divide 192 by 12, you get a unit rate of Rs. 16 per egg, then divide Rs. 160 by 16 and you get 10
The number of eggs that can be purchased at Rs. 160 is 10.
What is a division operator?The division operator ( / ) has the quotient of its operands where the left operand exists the dividend and the right operand exists the divisor.
The cost of 12 eggs = Rs. 192
The cost of 1 egg = 192/12 = Rs. 16.
The number of eggs that can be purchased is Rs. 160 = 160/16 = 10.
Therefore, the number of eggs that can be purchased at Rs. 160 is 10.
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Which algebraic expression is a trinomial?
Answer:
?
Step-by-step explanation:
because there is no picture or option
It costs $20 a day to rent a car and $30 for a full tank of gas. If Stacy fills up the tank 3 times and has the car rented for 14 days, how much does she owe?
Answer:
$20 × 14 days = $280
&30 × 3 = $90
&280 + $90 = $370
Answer:
For car she owes=
$20 x 14 = $280
For tank she owes=
$30 x 3 = $90
Therfore in total she owes,
$280 + $90 = $370
Is this pattern a net for the three-dimensional figure?
no
yes
Answer:
no
Step-by-step explanation:
the bet displays 3 hexagonal bases when in the figure there is only 2 bases.
Answer:
No.
Step-by-step explanation:
Examples of three-dimensional figures are: Cuboid, Cube, Cylinder, Sphere, Pyramid, and a Cone.
Write an equation for each translation of y=|x|
13 units down
y-13= |x|
y=1x1-13
y=1-13x1
y=1x1+13
The answer is y=|x|-13.
Answer:
y=|x|-13
Step-by-step explanation:
ZY = 34, WY = 38, and m/ZXY = 34° find WZ
The value of the WZ will be 28.18. The given figure is quadrilateral.
What is the definition of geometry?It is concerned with the geometry, region, and density of various 2D and 3D shapes.
In ΔZXY
∠Z+∠X+∠Y=180
∠Z+34°+90°=180°
∠Z = 56°
In Δ WZY
sin Θ = WZ/ZY
sin 56° = WZ/34
WZ= 28.18
Hence, the value of the WZ will be 28.18.
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The side WZ = 30.4.
What are alternate angles?The angles which lie on the alternate side of the line between two parallel lines.
Given a geometry in which ZY = 34, WY = 38, and ∠ZXY = 34°
In this geometry, opposite sides are equal.
WZ = XY and WX = ZY.....................(1)
The diagonal are perpendicular to each other.
∠XVY = 90°
Diagonal form four right angle triangles. Take ΔXVY
VY = WY/2
VY = 38/2
VY = 17
Using trigonometric property,
sin X° = VY / XY
sin 34° = 17/XY
XY = 30.4
From equation 1, we have
WZ = 30.4
Thus, the value of WZ is 30.4.
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can disjunction introduction (either ∨il or ∨ir ) be used to derive any type of formula other than a disjunction?
It is impossible to use a disjunction introduction to derive any other type of formula besides disjunctive formulas.
What is Disjunction Introduction?A rule of inference in propositional logic and virtually every other deduction system is referred to as disjunction introduction.
It is right to state that it is not possible to use a disjunction introduction to derive any other type of formula besides disjunctive formulas.
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The pipe has a length 29cm, internal diameter 6.5cm and thickness 0.5cm. What is the Volume
Answer:
Length of pipe = 21 cm
Internal diameter = 4 cm
Internal radius = \frac{4}{2} = 2 cm24=2cm
Thickness = 0.5 cm
Outer radius = 2+0.5=2.5 cm
Volume of pipe =\pi R^2 h - \pi r^2 hπR2h−πr2h
Volume of pipe =\frac{22}{7} (2.5)^2 (21)-\frac{22}{7}(2)^2(21)=148.5 cm^3
=\frac{22}{7} (2.5)^2 (21)-\frac{22}{7}(2)^2(21)=148.5 cm^3722(2.5)2(21)−722(2)2(21)=148.5cm3
Hence The volume is 148.5 cubic cm.
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The thickness of a metal pipe is 1.5cm. The inner diameter is 21cm. What is the volume of metal required for a pipe of length 7cm
vanessa deposited money into a bank account yhat earned 1.25% simple interest after each year. after 1/2 year she earned $5 in interest on the account. how much was her initial deposit
The initial amount is $800.
What is interest?
Interest is the price you pay to borrow money or the cost you charge to lend money.
Given:
Simple interest = 1.25% = 0.0125
So, interest in half a year.
=0.0125 ÷ 2
= 0.00625
Now,
=5 / 0.00625
= 800
Hence, the initial deposit was $800
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the sum of the 10th and 11th terms of an arithmetic sequence is 65 what is the sum of its first 20th terms
Answer:
this is the answer
Step-by-step explanation:
a 65
b 650
c 52
d 3
HELPP
Simplify the expression 6^3+ 5(4 − 2).
28
36
226
234
Answer:
BODMAS
[tex] {6}^{3 } + 5(4 - 2) = 216 + 5(2) \\ = 216 + 10 \\ = 226[/tex]
Answer: Answer is 226
Step-by-step explanation: Do math
describe the effect of the transformation (x,y) to (x,y+4)
A. vertical stretch without reflection
B. horizontal translation of 4 units
C. vertical stretch with reflection
D. Vertical translation of 4 units
Lily sold 18 items at the street fair. she sold bracelets for $6 each and necklaces for $5 each for a total of $101. which system of equations can be used to find b, the number of bracelets she sold, and n, the number of necklaces she sold? b n = 101 6b 5n = 18 b n = 101 5b 6n = 18 b n = 18 6b 5n = 101 b n = 18 5b 6n = 101
Answer:
[tex]b + n = 18[/tex]
[tex]6b + 5n = 101[/tex]
