how can you tell when an equation in one variable has infinitely many soultions or no solution
In each triangle ABC, angle C is a right angle. Find the value of the trig function indicated.
As given triangle ABC, angle C is a right angle if a=6, c=10 then value of trigonometric function is sin A = 3/5.
As given in the question,
In triangle ABC,
∠C = 90°
Side a is opposite to angle A
c is the hypotenuse opposite to angle C
a = 6
c = 10
sin A = ( opposite side) / Hypotenuse
⇒sin A = a/c
⇒sin A = 6/10
⇒sin A = 3/5
Therefore, as given triangle ABC, angle C is a right angle if a=6, c=10 then value of trigonometric function is sin A = 3/5.
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Use differentials to estimate the amount of metal in a closed cylindrical can that is 22 cm high and 10 cm in diameter if the metal in the top and the bottom is 0.4 cm thick and the metal in the sides is 0.05 cm thick. (Round your answer to two decimal places.) cm3
Answer:
97.43cm³
Step-by-step explanation:
h = 22cm
d = 10cm
r = d/2
= 10/2
= 5
dh = 2(0.4)
= 0.8
dr = 0.05
V = πr²h
dV = d(πr²h)
Such that
πd(r²h)
= π[(r²dh + hd(r²)]
dV = π[(r²dh + 2rhdr]------(1)
When we put the values above in this equation 1 above:
dV = π[(5)²*0.8 + 2*5*22*0.05]
= π(25*0.8+11)
= π31cm³
Multiply the value of pi with 31cm³
= 97.43cm³
sgshnsjmsngtjsdyjhsksykhm
i can't read it, its too blurry
anyways have a great day/night :)
Nick bought 5 tickets to go to the amusement park for $65. If he wanted to buy 8 tickets, what would that cost him?
Answer:
$104
Step-by-step explanation:
First find how much 1 ticket costs
65/5= 13
Times that by 8
8x13=104
Marbles question:
John is told to find 3 specific marbles within a box of 60 marbles. The room is dark and he can’t see the marbles properly. He pours out 20 of these marbles, and blindly chooses 3 of them.
What are the chances he chooses the 3 specific marbles he was told to find?
The chances he chooses the 3 specific marbles he was told to find is 1/20.
How to calculate the probability?It should be noted that there are 60 marbles and he wants to find 3.
In this case, he poured out 20. Therefore, his chances of picking the three marbles will be 1 out of 20.
Therefore, the chances will be 1/20.
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Question
A globe of Earth is in the shape of a sphere with a radius of 14 inches. Find its a volume and b surface area.
Round the answers to the nearest hundredth.
Answer:
[tex]Volume = 11488.21[/tex]
[tex]Area = 2461.76[/tex]
Step-by-step explanation:
Given
[tex]Radius, r = 14\ in[/tex]
Shape: Sphere
Solving (a): The Volume
This is calculated as:
[tex]Volume = \frac{4}{3}\pi r^3[/tex]
Take [tex]\pi[/tex] as 3.14 and substitute 14 for r
[tex]Volume = \frac{4}{3} * 3.14 * 14^3[/tex]
[tex]Volume = \frac{4}{3} * 3.14 * 2744[/tex]
[tex]Volume = \frac{4 * 3.14 * 2744}{3}[/tex]
[tex]Volume = \frac{34464.64}{3}[/tex]
[tex]Volume = 11488.21[/tex]
Solving (b): The Surface Area
This is calculated as follows:
[tex]Area = 4\pi r^2[/tex]
Take [tex]\pi[/tex] as 3.14 and substitute 14 for r
[tex]Area = 4 * 3.14 * 14^2[/tex]
[tex]Area = 4 * 3.14 * 196[/tex]
[tex]Area = 2461.76[/tex]
Calculate the constant of proportionality, k, for the given table.
Answer:
k = y/x
Step-by-step explanation:
1/5, 2/10, 3/15 . . . all equal to 1/5 which is what the value of k is; 'k' stands for constant of proportionality
Who likes my banana⤵️⤵️⤵️⤵️⤵️⤵️
Answer:
damm thats really good
Step-by-step explanation:
Answer:
ooooooo me :)
X
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Simplify the following expression.
4(20+12)+(5-3)
Answer:
[tex] = 4(32) + (2) \\ = 128 + 2 \\ = 130[/tex]
HOPE THIS HELPS
Which shape is similar to shape x?
Answer:
the c oneStep-by-step explanation:
hope it will helpAnswer:
Step-by-step explanation:
Probably C but I sure wouldn't bet the farm on it. It looks like C is about 1.5 times the size of X
Please I need some answers
What are the roots of f(x)=x^3-x^2-5x-3?
Answer:
x=3 and x=-1
Step-by-step explanation:
Given Descartes' Rule of Signs, there is only one positive root and one negative root.
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient.
So P could be +1, -1, +3, or -3, while Q could be 1 or -1.
Therefore, P/Q could be +1, -1, +3, or -3.
Then we use synthetic division to find the correct factor(s):
1 | 1 -1 -5 -3
___ 1_0_ -5
1 0 -5 | -8
So (x-1) is not a factor
-1 | 1 -1 -5 -3
___-1_2_ 3
1 -2 -3 | 0
So (x+1) is a factor where the quotient is x^2-2x-3 or (x-3)(x+1)
3 | 1 -1 -5 -3
___ 3_6_ 3
1 2 1 | 0
So (x-3) is a factor where the quotient is x^2+2x+1 or (x+1)^2
Given (x-3) and (x+1) are factors, we now use the Zero Product Property:
(x-3)(x+1)=0
x-3=0
x=3
x+1=0
x=-1
So the roots are x=3 and x=-1
A penguin walks 10 feet in 6 seconds. How far does the penguin walk in 45 seconds
Answer:
70 ish
Step-by-step explanation:
Please I need help with the question
Answer: Yes please tell us the question.
Step-by-step explanation:
Two people are pulling on a rope in order to get a 2250-kg car out of a mud puddle. One person pulls with a force of 600 N and the other pulls with a force of 800 N. There is a resistive frictional force of 1200 N. What will the acceleration of the car be? (answer with 3 digits, units will be m/s/s, DO NOT put them. ) *
Assuming both people are pulling in the same direction, the net force on the car is, according to Newton's second law,
600 N + 800 N - 1200 N = (2250 kg) a
Solve for the acceleration a :
200 N = (2250 kg) a
a = (200 N) / (2250 kg)
a ≈ 0.0889 m/s/s
The function W(t) = 40e^–0.35t models the healing of a wound after t hours, where W(t) represents the wound area in square millimeters. What relationship do W(t) and t have?
when t = 0, W(t) > 40
when t = 0, W(t) 0, W(t) > 40
when t > 0, W(t) < 40
ASAP I'm taking test
Answer:
Pretty sure its D.
Step-by-step explanation:
Whenever I made t something higher than 0 I got something less than 40|
(Sorry if I didn't make it in time and if I did I'm taking the same test rn gl homie)
The value of function W(t) will be less then 40 if t > 0 thus option (D) is correct.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.
As per the given function,
W(t) = 40[tex]e^{-0.35t}[/tex]
By the law of indices,
W(t) = 40/[tex]e^{.035t}[/tex]
When t > 0 the value of [tex]e^{.035t}[/tex] > 1
Thus, t > 0 the value of W(t) < 40
Hence "The value of function W(t) will be less then 40 if t > 0".
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A ball is thrown from an initial height of 4 feet with an initial upward velocity of 30ft/s. The balls height h (in feet) after t seconds is given by the following. H=4+30t-16t^2n
The maximum height of the ball is at 18.0625 feet which occurs at 0.9375 s
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let h represent the height of the ball after t seconds, hence:
h(t) = 4 + 30t - 16t²
The maximum height is at h'(t) = 0, hence:
h'(t) = 30 - 32t
-32t + 30 = 0
t = 0.9375 s
h(0.9375) = 4 + 30(0.9375) - 16(0.9375)² = 18.0625 feet
The maximum height of the ball is at 18.0625 feet which occurs at 0.9375 s
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Plz help me with this!?!? I will mark you brainliest plz and thank you!
Answer:
9
Step-by-step explanation:
Ceecee and Jose ate at a restaurant.
Ceecee gave a 20% tip on an $85 dinner bill.
Jose gave a 18% tip on a $80 dinner bill.
Who (Ceecee or Jose) gave the larger tip?
If Max wants to build a rectangular walkway 4 ft wide by 1.5 ft deep by 20 ft long
from the house to the storage shed, what is the area of the walkway?
Square Feet
Answer:
80 ft^2
Step-by-step explanation:
The area of a rectangular walkway = L x W = 20 ft x 4ft = 80 ft
Evaluate 4^2 - 6 ÷ 2 + 3=
Answer:The correct answer is 16
Step-by-step explanation:
4^2= 16
16-6/2+3
16-3+3
13+3=16
At 60 km per hour it takes archie 10 hours to travel from his house in Manila to his house in the province. If his rate will be 120 km per hour, how long will it take him to reach his house in the province from Manila
A. 5 hours
B. 8.5 hours
C. 6 hours
D. 7.5 hours
Pls i need it now
Answer:
a
Step-by-step explanation:
5 hours
(PLEASE HELP THIS IS TIMED!!!)
Which graph represents the inequality x > 6?
Answer:
The last one
Step-by-step explanation
x is greater than six so you would go to the right and it has to be an open dot since it can't be the same as 6
Answer:
hello
Step-by-step explanation:
Dreyfus cashed a check for $145. The teller gave him five $20 bills, two $20 bills, and f $1 bills. How many $1 bills did he get?
Answer:
5 singles
Step-by-step explanation:
5 $20= 100
2 $20= 40
remainder is 5 singles
Answer:
5 $1 bills.
Step-by-step explanation:
The expression to reflect this problem is:
145 = 20(5) + 20(2) + 1x
145 = 100 + 40 + 1x
145 = 140 + 1x
145 - 140 = 140 + 1x - 140
5 = 1x
5 ÷ 1 = 1x ÷ 1
5 = x
I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!
Evaluate. 1 1/2÷4
A. 2 1/2
B. 12/2
C. 3/8
D. 6
the correct answer is C. 3/8
Given the quadratic function f(x) = 4x^2 - 4x + 3, determine all possible solutions for f(x) = 0
Answer:
The solutions to the quadratic function are:
[tex]x=i\sqrt{\frac{1}{2}}+\frac{1}{2},\:x=-i\sqrt{\frac{1}{2}}+\frac{1}{2}[/tex]
Step-by-step explanation:
Given the function
[tex]f\left(x\right)\:=\:4x^2\:-\:4x\:+\:3[/tex]
Let us determine all possible solutions for f(x) = 0
[tex]0=4x^2-4x+3[/tex]
switch both sides
[tex]4x^2-4x+3=0[/tex]
subtract 3 from both sides
[tex]4x^2-4x+3-3=0-3[/tex]
simplify
[tex]4x^2-4x=-3[/tex]
Divide both sides by 4
[tex]\frac{4x^2-4x}{4}=\frac{-3}{4}[/tex]
[tex]x^2-x=-\frac{3}{4}[/tex]
Add (-1/2)² to both sides
[tex]x^2-x+\left(-\frac{1}{2}\right)^2=-\frac{3}{4}+\left(-\frac{1}{2}\right)^2[/tex]
[tex]x^2-x+\left(-\frac{1}{2}\right)^2=-\frac{1}{2}[/tex]
[tex]\left(x-\frac{1}{2}\right)^2=-\frac{1}{2}[/tex]
[tex]\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}[/tex]
solving
[tex]x-\frac{1}{2}=\sqrt{-\frac{1}{2}}[/tex]
[tex]x-\frac{1}{2}=\sqrt{-1}\sqrt{\frac{1}{2}}[/tex] ∵ [tex]\sqrt{-\frac{1}{2}}=\sqrt{-1}\sqrt{\frac{1}{2}}[/tex]
as
[tex]\sqrt{-1}=i[/tex]
so
[tex]x-\frac{1}{2}=i\sqrt{\frac{1}{2}}[/tex]
Add 1/2 to both sides
[tex]x-\frac{1}{2}+\frac{1}{2}=i\sqrt{\frac{1}{2}}+\frac{1}{2}[/tex]
[tex]x=i\sqrt{\frac{1}{2}}+\frac{1}{2}[/tex]
also solving
[tex]x-\frac{1}{2}=-\sqrt{-\frac{1}{2}}[/tex]
[tex]x-\frac{1}{2}=-i\sqrt{\frac{1}{2}}[/tex]
Add 1/2 to both sides
[tex]x-\frac{1}{2}+\frac{1}{2}=-i\sqrt{\frac{1}{2}}+\frac{1}{2}[/tex]
[tex]x=-i\sqrt{\frac{1}{2}}+\frac{1}{2}[/tex]
Therefore, the solutions to the quadratic function are:
[tex]x=i\sqrt{\frac{1}{2}}+\frac{1}{2},\:x=-i\sqrt{\frac{1}{2}}+\frac{1}{2}[/tex]
Which fraction shoes unit rate that is equal to the ratio 18:2
Answer: 9/1
Step-by-step explanation:
Which of the following ratios is not equivalent to the other three 2/3 4to6 8to12 4/5
Answer:
The non-equivalent ratio is 4:5.
Step-by-step explanation:
2/3 4/6 and 8/12 are equivalent because they are all multiples of each other.
Which of the following equations is equivalent to 4x-2=38
A. 5x=-50
B. X-20=30
C. 5x=50
D. 2x=10