Answer:
r is -11
Step-by-step explanation:
Move the like terms to the same side. 4r-6r is -2r
14 + 8 is 22
22/-2 is -11
Julia examines the two triangles below and determines that Triangle F G H is similar to triangle L N M.
Triangle F G H. Angle F is 98.6 degrees and angle G is 61.1 degrees. Triangle L N M. Angle M is 18.3 degrees and angle L is 98.6 degrees.
Which best describes the accuracy of Julia’s solution?
Accurate. The triangles are similar and the congruent angles are listed in corresponding order.
Inaccurate. The triangles are not similar because the sum of the angles in each triangle is not 180º.
Inaccurate. The triangles are similar, but the triangles are named incorrectly. The vertices are listed out of corresponding order.
Inaccurate. The triangles are not similar because angle M is not congruent to angle H, and angle N is not congruent to angle G.
The correct option regarding whether the triangles are similar is given by:
Inaccurate. The triangles are not similar because angle M is not congruent to angle H, and angle N is not congruent to angle G.
What are similar triangles?Similar triangles are triangles that have congruent angles, that is, angles with the same measure.
Considering that the sum of the internal angles of a triangle is of 180º, the third angle of triangle FGH is given as follows:
98.6 + 61.1 + x = 180
x = 180 - (98.6 + 61.1)
x = 20.3º.
The second triangle has an angle of 20.3º, hence they are not similar, and the correct option is given by:
Inaccurate. The triangles are not similar because angle M is not congruent to angle H, and angle N is not congruent to angle G.
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If sin θ = cos θ, what are the possible values of θ from 0 < θ < 2π?
A.) π/4
B.) 3π/4
C.) 5π/4
D.) 7π/4
The possible values is θ = π/4 and 5π/4
What is Trigonometry?The branch of mathematics concerned with specific functions of angles and their application to calculations.
Given:
sin θ = cos θ
The above condition satisfied for θ = π/4 and 5π/4
sin π/4 = cos π/4 = 1/√2
sin 5π/4 = cos 5π/4 = -1/√2
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David is making a rectangular exercise yard for his turtle, Ralph. The perimeter of the yard is
16x² + 12x +18
3x
2x² + 6x +9
3x
inches in total. The length of the yard measures
inches. Find an expression to represent the measure of the width in inches
yd=
yd=
16x2+12x+18=3x=2x2+6x+9=3x=
sorry i try
Answer:
D
Step-by-step explanation:
we can tell that side DE is parallel to side....
A) AB
B) We can't be sure it's parallel to any side
By the converse of the basic proportionality theorem, we can say DE║AB.
We need to check whether DE is parallel to AB.
What is the converse of the basic proportionality theorem?If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.
In triangle ABC, we can see on side AC, D is midpoint (∵AD=DC) and on side BC, E is midpoint (∵BE=CE).
Therefore, by the converse of the basic proportionality theorem, we can say DE║AB.
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The proof is shown below:
What is Mid point theorem?The line segment joining the mid points of any two sides of a triangle is parallel to the third side.
△ABC in which D and E are the mid points of AB and AC,.
If D and E are the mid points of AB and AC,
then AD=DB and AE=EC.
Thus,
AD/DB = AE/ EC
by the converse of Thales theorem, DE∥BC.
As, by theorem we can say that DE∥BC.
So, there is no other side parallel to DE.
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The function f(x) = three-fourths(10)–x is reflected across the x-axis to create the function g(x). which ordered pair is on g(x)?
The ordered pair that is on g(x) is (2, -3/400)
determine the ordered pair:
The function is given as:
f(x)=3/4(10)∧-x
The rule of reflection across the x-axis is:
g(x) = -f(x)
So, we have:
g(x) = -3/4(10)∧-x
Set x = 2.
So, we have:
g(2) = -3/4(10)∧-2
Evaluate the exponent
g(2) = -3/4 * 1/100
Evaluate the product
g(2) = -3/400
This means that:
(x, y) = (2, -3/400)
Hence, the ordered pair that is on g(x) is (2, -3/400)
Ordered pairs are pairs of two numbers (or variables) that are enclosed in parentheses and separated by commas. For example, (1, 2) is an ordered pair. Coordinate geometry represents points, and set theory represents elements of relations / Cartesian products.
Ordered pairs are pairs of numbers in a particular order. For example, (1, 2) and (-4, 12) are ordered pairs. The order of the two numbers is important. (1, 2) is not equivalent to (2, 1)-(1, 2) ≠ (2, 1).
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Use the properties of 30-60-90 and 45-45-90 triangles to solve for x in each of the problems below. Then decode the secret message by matching the answer with the corresponding letter/symbol from the exercises.
The trigonometric function gives the ratio of different sides of a right-angle triangle. The given problems can be solved as given below.
What are Trigonometric functions?The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
1st.) x = 5 /Sin(30°)
x = 10
!) sin(45°) = 4/x
x = 4/sin(45°)
x = 4√2
I) Cos(45°) = √3 / x
x = √3 / Cos(45°)
x = √6
E) Tan(60°) = 3√3 / x
x = 3√3 / 3
W) For isosceles right-triangle, the angle made by the legs and the hypotenuse is always 45°.
x = 45°
N) x² + x² = (7√2)²
x = 7
V) Tan(60°) = 7 / x
x = 7√3/3
K) x² + x² = (9)²
x = 9/√2
Y) Sin(60°) = 7√3/x
x = 14
M) Sin(30°) = x/11
x = 11/2
T) Sin(45°) = x/√10
x = √5
A) x + 2x + 90° = 180°
x = 30°
O) Sin(45°) = √2 / x
x = 2
R) Tan(30°) = x / 4
x = 4/√3 = 4√3 / 3
S) Sin(60°) = x / (10/3)
x = 5√3 / 3
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Jacob made 93 cups of lemonade.
He and his sisters drank 5½ cups.
How much lemonade is left?
Give your answer as a mixed number in simplest form
Enter the number that belongs in the green box.
[?] cups
Answer:
I think it's 87.5 or 87½
Step-by-step explanation:
I hope it helps you.
Simplify (-8a¹b) (3a³b).
a) -24a7b²
b) -5a7b²
c) -5a¹26
d) -24a¹26²
What is the volume of the following rectangular prism? Volume ==equals units^3 3
The volume of the rectangular prism is 1/10 cubic units
Volume of a rectangular prismThe formula for calculating the volume of a rectangular prism is expressed as;
V = Bh
B is the base area
h is the height
Given the following parameters
B = 3/20 units²
h = 2/3 units
Substitute
V = 3/20 * 2/3
V = 2/20
V = 1/10 cubic units
Hence the volume of the rectangular prism is V = 1/10 cubic units
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Answer:8 1/2^3
Step-by-step explanation:
please answer this paper
The computation shows that the total number of chocolate bars when there are 280 orange flavored bars will be
How to compute the values?The total number of chocolate bars when there are 280 orange flavored bars will be:
= Coconut + Honeycomb + Coffee + Orange + Strawberry
= (4/6 × 280) + (5/6 × 280) + (1/6 × 280) + 280 + (4/6 × 280)
= 1033
The total number when there are 960 coconut bars will be:
= Coconut + Honeycomb + Coffee + Orange + Strawberry
= 960 + (5/4 × 960) + (1/6 × 960) + (6/4 × 960) + 960
= 960 + 1200 + 160 + 1440 + 960
= 4720
The mean of 7, 2, and 9 will be:
= (7 + 2 + 9)/3
= 6
The mean of 5, 6, 6, and 5 will be:
= (5 + 6 + 6 + 5)/4
= 22/4
= 5.5
The mean of 2, 1, 2, 3, 3, 1 will be:
= (2 + 1 + 2 + 3 + 3 + 1) / 6
= 15/6
= 2.5
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What is the solution to the system of equations? "-6x2/5y=8" 1/2x+3y=29
(10, –2)
(10, 2)
(2, 10)
(–2, 10)
The answer choice which represents a solution to the system of equations is; (–2, 10).
Which answer choice is a solution to the systems of equations?The system of equations as given in the task content is;
-6x - (2/5)y = 8
(1/2)x +3y = 29
Hence, by making x subject in equation 1 and substitution; we have;
x = (-0.4y -8)/6
Hence; (0.4y -8)/12 + 3y = 29.
(0.4y -8) + 36y = 348
35.6y = 356
y = 10
and x = (-0.4(10) -8)/6 = -2.
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Consider u = ⟨5, –2⟩ and v = ⟨10, –4⟩. what is the relationship between u and v?
Answer:
v = 2u
Step-by-step explanation:
note that
2u = 2 (5, - 2 ) ← multiply each component by 2
= (10, - 4) = v , then
v = 2u
5. Sally took money from her bank account to go
out of town for an audition. She spent $54.00
for a round-trip ticket and 1/2 of the remaining
money for her hotel bill. She spent $7.90 for
food and arrived home with $15.10. How much
money did Sally take from her bank account?
Answer:
110
Step-by-step explanation:
Sally takes $110 from her bank account if she spent $54.00 for a round-trip ticket.
What are expenses?It is defined as the money spends on the utility, the amount of money is required to buy something, in other words, it is the outflow of money from the sole earner's income or the money incurred by any organization.
We have:
Sally took money from her bank account to go out of town for an audition.
The expeses = (7.90 + 15.10) ÷ (1 - 1/2) = $46
Total money = 54 + 46
Total money = $110
Thus, Sally takes $110 from her bank account if she spent $54.00 on a round-trip ticket.
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Using the Addition Method, solve for x in the following system of linear equations.
2y + x = 4
y - 3x = 2
a.) x = 1
b.) x = 2
c.) x = 8
d.) x = 0
Answer:
c. x=8
Step-by-step explanation:
make me a brain list.
An isosceles triangle has a vertex angle of 21.21°. two sides of the triangle are each 17.91 ft long. find the area of the triangle.
The Area of triangle is A= 58.02 (ft)^2
According to statement
Let
B is the measure of the vertex angle of the isosceles triangle ABC
A and C is the two congruent sides of the isosceles triangle ABC
we know that
The area of a triangle applying the law of sines is equal to the
A= 1/2 *AC *SinB
we have
A=C= 17.91 ft
And
B= 21.21
Substitute these values in the formula
A= 1/2* 17.91* 17.91 * Sin(21.21)
A= 58.02 (ft)^2
So, the Area of triangle is A= 58.02 (ft)^2
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Find m given that the three angles of a triangle are (m plus18),(2m plus 28)and (3m plus 47)degree find all the angles
The value of m is 14.5 and the three angles of the triangle are 32.5°, 57°, and 90.5°.
How the angles of a triangle are related?There are three angles in a triangle. Consider as ∠A, ∠B, and ∠C.
The sum of all the three angles gives 180° in a triangle. I.e.,
∠A + ∠B + ∠C = 180°.
Calculation:The given triangle has three angles,
(m + 18)° , (2m + 28)°, and (3m + 47)°
On adding all these and equating to 180°,
(m + 18)° + (2m + 28)° + (3m + 47)° = 180°
⇒ 6m + 93 = 180
⇒ 6m = 180 - 93
⇒ 6m = 87
∴ m = 14.5
Then, the values of the three angles are:
(m + 18)° = (14.5 + 18)° = 32.5°
(2m + 28)° = (2 × 14.5 + 28)° = 57°
(3m + 47)° = (3 × 14.5 + 47)° = 90.5°
Therefore, the angles of the given triangle are 32.5°, 57°, and 90.5°.
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1. Taking your eyes off the road for ____ seconds at 60 miles per hour means you have traveled blindly for half the length of a football field.
Answer:
4.09 seconds
Step-by-step explanation:
simplify miles per hour to feet per second how many feet is a mile and how many seconds are in an hour you end up with 88 fps from 60 mph
now simply a football field is 360 feet so 360/88 is 4.09090909 etc
Your eyes off the road for 4.09 seconds.
What is speed?The rate of change of position of an object in any direction is called the speed.
Given that, Taking your eyes off the road for how many seconds at 60 miles per hour means you have travelled blindly for half the length of a football field,
Converting 60 mph into fps
60 mph = 88 fps
The length of a football field = 360 ft
Time = 350/88
= 4.09 seconds.
Hence, you travelled for 4.09 seconds.
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Find all solutions to the equation in the interval [0,2pi]. Enter the solutions in increasing order. sin 2x = sin x
please explain how you got the answer
Step-by-step explanation:
[tex]sin2x=sinx\\sin2x-sinx=0\\2*sinx*cosx-sinx=0\\sinx*(2*cosx-1)-0\\sinx=0 \\x=\pi n\ \ \ \ \ x\in[0;2\pi ]\ \ \ \ \Rightarrow\\x_1=0\ \ \ \ x_2=\pi .\\2*cosx-1=0\\2*cosx=1\ |:2\\cosx=\frac{1}{2} \\x=б\frac{\pi }{3} +2\pi n\ \ \ \ \ x\in[0;2\pi ]\ \ \ \ \Rightarrow\\x_3=\frac{\pi }{3} \ \ \ \ \ x_4=\frac{5\pi }{3}.\\[/tex]
[tex]Answer: x=0,\ \frac{\pi }{3} ,\ 1\pi ,\ \frac{5\pi }{3} .[/tex]
A circular swimming pool has a diameter of 8 m and a depth of 2 m. What is the volume of the swimming pool?
"-3pq^2+q^3" if p=2.9 and q=-1.3
7
Step-by-step explanation:
p = 1, q = 72 =49, q = 7
ookrndodnepwkpqq
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\mathbf{-3pq^2 + q^3}[/tex]
[tex]\mathbf{= -3(2.9)(-1.3)^2 + (-1.3)^3}[/tex]
[tex]\mathbf{= -3(2.9)(-1.3)^2 - 1.3^3}[/tex]
[tex]\mathbf{= -8.7(-1.3)^2 - 1.3^3}[/tex]
[tex]\mathbf{= -8.7(1.69) - 2.197}[/tex]
=[tex]\mathbf{ -14.703 -2.197}[/tex]
[tex]\mathbf{= -16.9}[/tex]
[tex]\huge\textbf{Thus, your answer should be: \boxed{\mathsf{-16.9}}}}\huge\checkmark[/tex]
[tex]\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}[/tex]
20² + 15¹ = ? Help me!!
Answer:
415
Step-by-step explanation:
20x20=400+15= 415
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathbf{20^2 + 15^1}[/tex]
[tex]\huge\textbf{Solving:}[/tex]
[tex]\mathbf{20^2 + 15^1}[/tex]
[tex]\mathbf{= 20\times 20 + 15\times 1}[/tex]
[tex]\mathbf{= 400 + 15}[/tex]
[tex]\mathbf{= 415}[/tex]
[tex]\huge\textbf{Answer:}[/tex]
[tex]\huge\boxed{\mathsf{415}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Question 10 How many cubic yards of sand will it take to fill a child's play area that measures 10 yards long, 8 yards wide, and 1/3 yard deep
Answer:
26.6 cubic yards
Step-by-step explanation:
Remark
What you have is a rectangle prism. It has an easy enough formula.
Formula
V = L *w * h
Givens
L = 10 yards
w = 8 yards
h = 1/3 yards
Solution
V = L*w*h
V = 10 * 8 * 1/3
V = 26.66 yds^3
Solve this identity, where the angles involved are acute angles.
[tex] \dfrac{\tan\theta}{1 -\cot\theta } + \dfrac{\cot\theta}{1 -\tan \theta } = 1 + \sec \theta \cosec\theta[/tex]
[tex]\therefore \sf{ LHS = \dfrac{tan \theta}{1 – cot \theta } + \dfrac{cot \theta}{1 – tan \theta}}[/tex]
[tex]\\[/tex]
[tex]\therefore\sf{ LHS = \dfrac{tan \theta}{1 – \dfrac{1}{tan \theta}} + \dfrac{ \dfrac{1}{tan \theta}}{1 – tan \theta} }[/tex]
[tex]\\[/tex]
[tex]\therefore\sf{ LHS = \dfrac{ tan^{2} \theta }{tan \theta – 1} + \dfrac{1}{tan \theta (1–tan \theta) } }[/tex]
[tex]\\[/tex]
[tex] \therefore\sf{ LHS = \dfrac{tan^{2} \theta}{tan \theta–1} – \dfrac{1}{tan \theta(tan \theta – 1 )}}[/tex]
[tex]\\[/tex]
[tex]\therefore \sf{LHS = \dfrac{tan^{3}\theta–1}{tan \theta(tan \theta –1)}}[/tex]
[tex]\\[/tex]
[tex]\therefore\sf{LHS = \dfrac{tan^{3}\theta–(1)^{3}}{tan\theta(tan\theta–1)}}[/tex]
[tex]\\[/tex]
[tex] \therefore\sf{ LHS = \dfrac{ (tan \theta -1)(tan^{2}\theta+tan\theta .1 + (1)^{2})} {tan \theta (tan\theta(tan \theta –1 )}}[/tex]
[tex]\\[/tex]
[tex] \therefore\sf{ LHS = \dfrac{(tan^{2} \theta×tan\theta .1+1)}{tan \theta}}[/tex]
[tex]\\[/tex]
[tex] \therefore\sf{ LHS = \dfrac{(sec^{2}\theta+tan\theta)}{tan\theta}}[/tex]
[tex]\\[/tex]
[tex] \therefore\sf{ LHS = \dfrac{sec^{2}\theta}{tan\theta} + \dfrac{tan \theta}{tan\theta}}[/tex]
[tex]\\[/tex]
[tex] \therefore\sf{ LHS = sec^{2}\theta \times cot \theta + 1 }[/tex]
[tex]\\[/tex]
[tex] \therefore\sf{ LHS = \dfrac{1}{cos^{2}\theta} \times \dfrac{cos \theta }{sin\theta}+1}[/tex]
[tex]\\[/tex]
[tex] \therefore\sf{ LHS = \left( \dfrac{ 1}{cos \theta} \times \dfrac{1}{sin \theta} \right) + 1}[/tex]
∴ LHS = 1 + secθ.cosecθ = RHS━━━━━━━━━━━━━━━━━━━━━━━We have proven that the trigonometric identity [(tan θ)/(1 - cot θ)] + [(cot θ)/(1 - tan θ)] equals 1 + (secθ * cosec θ)
How to solve Trigonometric Identities?We want to prove the trigonometric identity;
[(tan θ)/(1 - cot θ)] + [(cot θ)/(1 - tan θ)] = 1 + sec θ
The left hand side can be expressed as;
[(tan θ)/(1 - (1/tan θ)] + [(1/tan θ)/(1 - tan θ)]
⇒ [tan²θ/(tanθ - 1)] - [1/(tan θ(tanθ - 1)]
Taking the LCM and multiplying gives;
(tan³θ - 1)/(tanθ(tanθ - 1))
This can also be expressed as;
(tan³θ - 1³)/(tanθ(tanθ - 1))
By expansion of algebra this gives;
[(tanθ - 1)(tan²θ + tanθ.1 + 1²)]/[tanθ(tanθ(tanθ - 1))]
Solving Further gives;
(sec²θ + tanθ)/tanθ
⇒ sec²θ * cotθ + 1
⇒ (1/cos²θ * cos θ/sin θ) + 1
⇒ (1/cos θ * 1/sin θ) + 1
⇒ 1 + (secθ * cosec θ)
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Which triangles could not be similar to triangle ABC ?
triangle a b c where angle b is a right angle. side a b is 15 cm. side b c is 8 cm. side a c is 17 cm.
Select each correct answer.
(See image for details.)
Similar triangles are those triangles whose corresponding sides are in the same ratio. The triangles that are similar to ΔABC are ΔDEF and ΔJKL.
What are similar triangles?Similar triangles are those triangles whose corresponding sides are in the same ratio. And the corresponding angles measure the same.
For two triangles to be similar there sides should be in the same ratio.
For ΔABC ~ ΔMNO,
AB/MN should be equal to BC/NO,
AB/MN = 15/35 = 0.4286
BC/NO = 8/12 = 0.66
Thus, there are not similar triangles.
For ΔABC ~ ΔDEF,
AB/MN should be equal to BC/NO,
AB/DE = 15/22.5 = 0.66
BC/EF = 8/12 = 0.66
Thus, there are similar triangles.
For ΔABC ~ ΔGHI,
AB/GH should be equal to BC/HI,
AB/MN = 15/77 = 0.1948
BC/NO = 8/36 = 0.222
Thus, there are not similar triangles.
For ΔABC ~ ΔJKL,
AB/MN should be equal to BC/NO,
AB/JK = 15/60 = 0.250.25
BC/KL = 8/32 = 0.66
Thus, there are similar triangles.
Hence, the triangles that are similar to ΔABC are ΔDEF and ΔJKL.
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Write an equation that represents the line.
Use exact numbers.
The equation of the line passing through the points is y = x + 2
How to determine the equation?The points are (-1, 1) and (4, 6).
The slope is calculated using:
m= (y2 - y1)/(x2 - x1)
So, we have:
m = (6 - 1)/(4 + 1)
Evaluate
m = 1
The equation of the line is then calculated as:
y = m(x -x1) + y1
This gives
y = 1 *(x + 1) + 1
Evaluate
y = x + 2
Hence, the equation of the line passing through the points is y = x + 2
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Find the rate of change for the given table of values.
Answer:
-40
Step-by-step explanation:
First you have to look at the difference between 8 and 10. which is 80, then because it takes two steps to go from 8 to 10 you divide 80 by two, which is 40. And because the values are decreasing it is -40.
You are pouring canned sodas Into a cylindrical pitcher. Each can
of soda is 12 cm tall and has a diameter of 6.5 cm. The pitcher is
36 cm tall and has a diameter of 20 cm. How many cans of soda
will the pitcher hold?
Answer: 28.40 cans of soda
Step-by-step explanation:
Volume of cylinder: pi * r^2 * h
Volume of the can of soda = pi * 3.25^2 * 12 = 126.75 pi
Volume of the cylindrical pitcher = pi * 10^2 * 36 = 3600 pi
3600/126.75: 28.40 cans of soda
Answer:
28 whole soda cans or 28.4 soda cans (rounding to nearest tenth)
Step-by-step explanation:
The soda cans and the pitcher can be modeled as cylinders.
Volume of a cylinder
[tex]\sf Volume=\pi r^2h[/tex]
where:
r is the radiush is the heightDiameter of circle
[tex]\sf d= 2r[/tex]
[tex]\sf \implies r=\dfrac{1}{2}d[/tex]
Volume of Soda can
Given values:
d = 6.5 ⇒ r = 3.25 cmh = 12 cm[tex]\begin{aligned}\sf \implies Volume & = \sf \pi (3.25)^2 \cdot 12\\ & = \sf 126.75 \pi \:\:cm^3\end{aligned}[/tex]
Volume of Pitcher
Given values:
d = 20 ⇒ r = 10 cmh = 36 cm[tex]\begin{aligned}\sf \implies Volume & = \sf \pi (10)^2 \cdot 36\\ & = \sf 3600 \pi \:\:cm^3\end{aligned}[/tex]
To calculate how many cans of soda the pitcher will hold, divide the volume of the pitcher by the volume of one soda can:
[tex]\begin{aligned}\implies \textsf{Number of soda cans} & = \dfrac{\textsf{Volume of Pitcher}}{\textsf{Volume of one soda can}}\\\\&= \sf\dfrac{3600 \pi}{126.75 \pi}\\\\& = \sf 28.402366...\end{aligned}[/tex]
Therefore, the pitcher can hold 28 soda cans (nearest whole can), or 28.4 soda cans (nearest tenth).
Event A has a probability of occurring of 4/5 . Event B has a probability of occurring of 1/3. If events A and B are independent of one another, what is the probability of both events occurring?
The probability of both events occurring is 4/15
How to determine the probability?The given parameters are:
P(A) = 4/5
P(B) = 1/3
Because the events are independent, we have:
p(A and B) = P(A) * P(B)
This gives
P(A and B) = 4/5 * 1/3
Evaluate
P(A and B) = 4/15
Hence, the probability of both events occurring is 4/15
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convert the Function to Degrees Fahrenheit:
3. Suppose you want to represent the desert temperature in degrees Fahrenheit instead. How would you transform the function C(t) to make the new function, F(t)? (2 points: 1 point for each transformation)
Note: The conversion rule for Celsius to Fahrenheit is .
F(t)=95(-0.30(t-12)2+40)+32
f(t)=-0.54(t-12)2+72+32
4. Take your values from the previous chart (in question 2) and convert them from Celsius to Fahrenheit. Follow the example below, and use the conversion rule to fill out the chart for degrees Fahrenheit when t = 12 and t = 24. (2 points: 1 point for each row)
t
0
12
(12,24)
c(0)=95(24)+32
24
5. Use the conversion formula to write the equation for the new function, F(t).
(4 points: 2 points for setting up the equation, 2 points for the answer)
Hint: Substitute the equation for C(t) into .
6. Plot the points from the Fahrenheit chart in question 4 onto the graph below. Use the plotted points to sketch out the graph of F(t). (3 points: 2 points for correct coordinates, 1 point for correct shape)
7. Compare the graph in question 6 (F(t)) with the graph in question 2 (C(t)). What changes were made to the graph of C(t) to transform it to F(t)? (1 point)
The changes that transform C(t) to F(t) is that the function C(t) is stretched vertically to form the function F(t)
How to transform the function?The Fahrenheit function
The Celsius function is given as:
C(t) = -0.30 (t – 12)² + 40
The conversion from Celsius to Fahrenheit is
F(t) = 9/5 * C(t)
Hence, the Fahrenheit function is F(t) = 9/5 * C(t)
Convert values from Celsius to Fahrenheit
The values are t = 0, 12 and 24.
So, we have:
F(0) = -0.54(0 - 12)² + 72 = -5.76
F(12) = -0.54(12 - 12)² + 72 = 72
F(24) = -0.54(24 - 12)² + 72 = -5.76
The new function F(t)
The conversion from Celsius to Fahrenheit is
F(t) = 9/5 * C(t)
So, we have:
F(t) = 9/5 * (-0.30 (t – 12)² + 40)
Expand
F(t) = -0.54(t – 12)² + 72
Hence, the new function is F(t) = -0.54(t – 12)² + 72
The graph of function F(t)
See attachment for the graph of function F(t)
The changes that transform C(t) to F(t)
We have:
C(t) = -0.30 (t – 12)² + 40
F(t) = 9/5 * C(t)
The above implies that the function C(t) is stretched vertically to form the function F(t)
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The coordinates of the vertices of quadrilateral ABCD are A(−5, 1), B(−2, 5), C(5, 3), and D(2, −1). Drag and drop the choices into each box to correctly complete the sentences. The slope of AB¯¯¯¯¯ is Response area, the slope of BC¯¯¯¯¯ is Response area, the slope of CD¯¯¯¯¯ is Response area, and the slope of AD¯¯¯¯¯ is Response area. Quadrilateral ABCD is Response area because Response area.
Slope of AB = 4/3, Slope of BC = -2/7, Slope of CD = 4/3, Slope of AD = -2/7 and Quadrilateral ABCD is a parallelogram because both pairs of opposite sides are parallel.
How to find the slope of a quadrilateral?We are given the coordinates of the quadrilateral ABCD as;
A(−5, 1), B(−2, 5), C(5, 3), and D(2, −1).
Slope of AB = (5 - 1)/(-2 + 5) = 4/3
Slope of BC = (3 - 5)/(5 + 2) = -2/7
Slope of CD = (-1 - 3)/(2 - 5) = 4/3
Slope of AD = (-1 - 1)/(2 + 5) = -2/7
Thus we can see that both pairs of slope are equal which denotes that both pairs are parallel.
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