Please help for number 8 I don't understand.
Answer:
8a. x = 16√3
8b. y = 8√3
Step-by-step explanation:
8a. Determination of the value of x
Adjacent = 24
Hypothenus = x
Angle θ = 30°
The value of x can be obtained by using cosine ratio as illustrated below:
Cos θ = Adjacent /Hypothenus
Cos 30 = 24 / x
√3/2 = 24/x
Cross multiply
x × √3 = 2× 24
x × √3 = 48
Divide both side by √3
x = 48/√3
Rationalise
x = 48/√3 × √3/√3
x = 48√3 / √3 × √3
x = 48√3 / 3
x = 16√3
8b. Determination of the value of y
Opposite = y
Adjacent = 24
Angle θ = 30°
The value of y can be obtained by using Tan ratio as illustrated below:
Tan θ = Opposite / Adjacent
Tan 30 = y / 24
1 / √3 = y /24
Cross multiply
y × √3 = 1 × 24
y × √3 = 24
Divide both side by √3
y = 24 /√3
Rationalise
y = 24 /√3 × √3/√3
y = 24 ×√3 / √3 × √3
y = 24√3 / 3
y = 8√3
Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. If the coffee has a temperature of 185 degrees Fahrenheit when freshly poured, and 3 minutes later has cooled to 167 degrees in a room at 60 degrees, determine when the coffee reaches a temperature of 137 degrees.
Answer:
9.4 secs
Step-by-step explanation:
From Newton's law of cooling;
T(t) = Ts + Do e^-kt
Where;
D0= initial temperature difference
Ts= Temperature of the surroundings
t= time
K = positive constant
Do = 185 - 60 = 125 degrees
167 = 60 + 125 e^-3k
167 - 60 = 125 e^-3k
107/125 = e^-3k
ln(e^-3k) = ln(107/125)
-3k = -0.1555
k = 0.1555/3
k = 0.0518
Substituting the value of k to find the time taken to reach 137 degrees
T(t) = Ts + Do e^-kt
137 = 60 + 125 e^-(0.0518t)
137 - 60 = 125 e^-(0.0518t)
77 = 125 e^-(0.0518t)
e^-(0.0518t)= 77/125
ln [e^-(0.0518t)] = ln(77/125)
-0.0518t = -0.4845
t = 0.4845/0.0518
t = 9.4 secs
What is the leading coefficient of the polynomial f(x) defined below
Answer:
1
Step-by-step explanation:
The answer is simply 1 as the leading term, x^4 has a coefficient of 1.
An opera theater has a sale: "Buy two tickets and get the third
ticket 60% off!" Peter uses the sale and spends $180 for three
tickets. What is the price of a ticket when there is no sale?
Answer:
$75
Step-by-step explanation:
let 'x' = full price ticket
x + x + 0.4x = 180
2.4x = 180
x = 75
PLEASE HELP!!
Questions and directions are in image!
Step-by-step explanation:
this is what I use go to your app store and get Math. way and type your answer in
Answer:
a) (c + 2)²
b) (x + 2)(x - 4)
c) (g + 2)(g + 6)
d) (x + 2)(x - 9)
e) (r + 9)(r + 1)
f) (x - 6)(x - 4)
Step-by-step explanation:
A car park holds 480 cars when full. The probability of a car in the car park being silver is 0.375.
On Friday morning the car park was full and Jamie counted 164 silver cars. Is this more or less
than expected?
Justify your answer by calculation
Answer:
164 is less than the expectation
Step-by-step explanation:
Given
[tex]n = 480[/tex] --- Cars
[tex]p = 0.375[/tex] --- Probability of silver
Required
Determine if 164 is more or less than the expectation
First, we calculate the expected value (E(x))
[tex]E(x) = n * p[/tex]
Substitute values for n and p
[tex]E(x) = 480 * 0.375[/tex]
[tex]E(x) = 180[/tex]
The expected number of silver cars is 180.
Hence, 164 is less than the expectation.
Solve the linear equation 3+5x=3
Step-by-step explanation:
the answer is
3+5x=3
5x=0
x=0
3 Choose Yes or No to tell whether the denominator of
each product is
early says that m ×(-1) is always equal to m ÷(-1) for all rational values of m. is he correct
Answer:
The equation are true.
Step-by-step explanation:
Given
[tex]m * (-1) = m / (-1)[/tex]
Required
True or false?
We solve this question from right to left:
[tex]m * (-1) = m / (-1)[/tex]
Express / as *
[tex]m * (-1) = m * 1/(-1)[/tex]
[tex]m * (-1) = m * (-1)[/tex]
The expression on both sides of the equation are true.
Find the equation of the exponential function represented by the table below:
Answer:
[tex]f(x)=5(4)^x[/tex]
Step-by-step explanation:
The exponential function is [tex]f(x)=ab^x[/tex]. [tex]a[/tex] is the initial value of the function, or the y-value when x=0. In this case, [tex]a[/tex]=5. If we enter that into the equation:
[tex]f(x)=5b^x[/tex]
Then we can use another point to solve for [tex]b[/tex].
[tex]20=5b^1[/tex]
Since anything raised to the power of 1 remains the same, we can continue to solve algebraically.
[tex]20=5b\\\frac{20}{5}=\frac{5b}{5}\\b=4[/tex]
Now that we have both the [tex]a[/tex] and [tex]b[/tex] value, we can return to the exponential function and fill in the blanks.
[tex]f(x)=5(4)^x[/tex]
I hope this helps!
5+=8
How do I solve this
Answer: 3
Reason: 5 + 3 = 8
Answer:
t = 0.625
Step-by-step explanation:
Assuming this is 5t = 8:
5t = 8 | Given
t = 0.625 (5/8, divide 5 by 8 to separate the coefficient 5 from the variable t.)
sketch the graph of each function. Then State the domain, range and increasing, decreasing intervals. Part 2
Problem 17
The graph is shown below.
The domain is [tex]x \ge -1[/tex] which is found by solving [tex]x+1 \ge 0[/tex]. This is done to ensure that the stuff under the square root is not negative. Note the left-most point of the graph has x = -1 as its x coordinate.
The domain in interval notation is [tex][-1, \infty)[/tex] we have a square bracket at -1 and a curved parenthesis at infinity.
The range is [tex]y \le 3[/tex] based on what the graph shows. This is directly tied to the +3 at the end of the function. The parent's function max value is y = 0, so that plus 3 shifts everything up 3 units so that the new translated function has a max of y = 3.
The range in interval notation is [tex](-\infty, 3][/tex] we use a square bracket to include 3 as part of the interval.
Throughout the entire function, the curve is going downhill as we move from left to right. The graph shows this. We could also use a table of values to see that as x gets bigger, y gets smaller.
So the function is never increasing. The function decreases on the interval (-1, infinity) which is the entire domain.
=====================================================
Problem 18
The graph is shown below. It's in a separate attachment.
The domain and range are the set of all real numbers. The graph shows that the curve extends forever to the left and right. Also, the graph extends forever upward and downward (regardless if that growth seems really slow).
The domain and range in interval notation is [tex](-\infty, \infty)[/tex] to indicate the entire real number line.
The graph goes uphill as we read from right to left, so the function is increasing on the interval [tex](-\infty, \infty)[/tex]. In other words, no matter where you are, you're going uphill if you move from left to right. This rules out the function ever decreasing.
We can use a table of values to see that the function is increasing if we cannot rely on the graph. As x gets bigger, so does y.
Answer:
1)
The angle of inclination is the angle between the horizontal and the ramp.
Using the sine ratio in the right triangle formed by the ground and the ramp
let x be the angle of inclination, then
sinx = \frac{opposite}{hypotenuse}
hypotenuse
opposite
= \frac{0.7}{4.2}
4.2
0.7
, then
x = sin^{-1}sin
−1
(\frac{0.7}{4.2}
4.2
0.7
) ≈ 10° ( to the nearest degree )
(2)
Again there is a right triangle between the ground and the vertical height of the kite, with hypotenuse being length of string.
let y be the height of the kite and x the horizontal distance, then
sin27° = \frac{opposite}{hypotenuse}
hypotenuse
opposite
= \frac{y}{176}
176
y
( multiply both sides by 176 )
176 × sin27° = y , then
y ≈ 80m ( to the nearest metre ) ← height of kite
and
cos27° = \frac{adjacent}{hypotenuse}
hypotenuse
adjacent
= \frac{x}{176}
176
x
( multiply both sides by 176 )
176 × cos27° = x , then
x ≈ 157m ( to the nearest metre ) ← horizontal distance
Pls i need this asap
Answer:
It would have to be (C) 50.27 because 25 is too short for a diameter of 8 seeing it would be 8x4 to get 32 in which 25 is not long enough for. So the answer is C.
FAST PLEASE!! Emma weighs half as much as Sonya. Sonya weighs 120 pounds. How much
does Emma weigh? Write the expression and solve
Answer:
I think it would be 120
Step-by-step explanation:
You add 120+120 and it would equal 240. Then 240 dived by 2 which will equal 120.
(120 + 120)= 240 dived by 2= 120 I might be wrong
9) Linda and Maria share £200. Linda has 4 times as much money as Maria.
How much money does Maria have?
Answer:
40
Step-by-step explanation:
maria is x
linda is 4x
x+ 4x = 200
5x = 200
x= 40
Find the area of the composite figure.
Eva is going to the amusement park, where she has to pay a set price of admission and another price for tickets to go on each of the rides. The total amount of money Eva will spend is given by the equation y=26+1.5x. , where y represents the total amount of money, in dollars and cents, and represents the number of rides Eva goes on . What could the number 1.5 represent in the equation ?
Answer:
B. The change in the total amount if money for every one additional ride she goes on
Step-by-step explanation:
Given,
y = 26 + 1.5x, where,
y = total amount of money Eva will spend
x = number of rides Eva rides on
Thus,
Set price of admission into the amusement park = $26
Price per ride = $1.5
Therefore, the 1.5 I'm the equation can be said to be "the change in the total amount if money for every one additional ride she goes on".
Q5.
Machine A and machine B both make car parts.
Machine A makes 6 parts every 10 minutes.
Machine B makes 13 parts every 15 minutes.
On Monday
machine A makes parts for 12 hours
machine B makes parts for 10 hours
Work out the total number of parts made by the two machines on Monday.
Answer:
A=432 B=520
Step-by-step explanation:
alright so there are 60 minutes in a hour so every 10 you get 6 so 6x6=36 per hour so 36x12 equals 432 parts
15 x 4 = 60 so 13 x 4 =52 per hour so 52 x 10 = 520
what is 6/5÷7/1 can u tell me pls
Answer:
6/35
Step-by-step explanation:
6/5÷7/1=6/5 x 1/7 = 6/35
Answer:
6/35
Step-by-step explanation:
ङ-आपको कौन-सी ऋतु पसंद है और क्यों ?
Answer:
हेलो मेरा पसंदीदा मौसम गर्मियों का है, मैं इसे प्यार करता हूं क्योंकि मैं अपने दोस्तों के साथ तैराकी करता हूं और मुझे तैराकी पसंद है क्योंकि मैं ट्रैक रन करता हूं, मुझे सिर्फ गर्मी से प्यार है
Step-by-step explanation:
What is (f o g) (3) if f (x) =3x-1 and g(x) = 4x^2 -9?
Answer:
4x+1
Step-by-step explanation:
Suppose y varies directly as x. If x = 24 when y = 8, then what is the constant of variation
Direct variation is represented by the formula [tex]\frac{y}{x} = k[/tex]
where k is the constant of variation.
So here, since we know that x = 24 and y = 8,
the constant of variation must be equal to 8/24.
if we write 8/24 in lowest terms, we have 1/3.
So 1/3 = k.
How many 1/2 inch cubes would it take to fill up a 6 inch cube.
Answer:
1
Step-by-step explanation:
Answer:396
Step-by-step explanation:your volume is 5.5 * 3 * 3 = 5.5 * 9 = 45 + 4.5 = 49.5 cubic inches. multiply that by 2*2*2 = 8 and you get 49.5 * 8 = 396 half cubic half inches. let's see if that makes sense. 11 half inches * 6 half inches * 6 half inches = 396 cubic half inches.brainliest?
(3a+9)+(6a+6) =
What is the answer to this??
Maria needs $2.35 to buy a magazine. The only money she has is a jar of nickels and dimes. Write an equation in standard form for the different amounts of nickels and dimes she could use.
Answer:
Step-by-step explanation:
sorry need the points
What’s 9+10 I need help
Answer:
9+10=19 but if you are talking about the meme 21
Step-by-step explanation:
x + 7 = 9
What does X equal?
3x3 - 7x2 + 6x - 14
Explain
Answer:
Step-by-step explanation:
x^2(3x - 7) + 2(3x - 7)
(x^2 + 2)(3x - 7)
[tex]\huge\text{Hey there!}[/tex]
[tex]\bold{Factor: 3x^3 -7x^2+6x -14}[/tex]
[tex]\bold{Step-by-step\downarrow}[/tex]
[tex]\bold{x^2(\dfrac{3x^3}{x^2}-\dfrac{7x^2}{x^2})+2(\dfrac{2\times3x}{2}-\dfrac{2\times7}{2})}[/tex]
[tex]\bold{= x^2(3x^{3-2}-7)+2(3x-7)}[/tex]
[tex]\bold{= x^2(3x-7)+2(3x-7)}[/tex]
[tex]\bold{= (3x-7)(\dfrac{x^2(3x-7)}{3x-7}+\dfrac{2(3x-7)}{3x-7})}[/tex]
[tex]\bold{= \underline{(3x -7)(x^2+2)}}[/tex]
[tex]\boxed{\boxed{\bold{Answer: (x^2+2)(3x-7)}}}\huge\checkmark[/tex] [tex]\underline\bold{(Option\ C.)}[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
-2x - 6 = 2 - 4x - (x - 1)
solve
Answer:
Step-by-step explanation:
-2x - 6 = 2 - 4x - x + 1
-2x - 6 = 3 - 5x
3x - 6 = 3
3x = 9
x = 3
alguien me ordena estás fracciones 1/10 4/10 6/10 14/10 10/10 8/10 de menor a mayor porfa doy corona
Responder:
[tex]\frac{1}{10},\frac{4}{10},\frac{6}{10},\frac{8}{10},\frac{10}{10},\frac{14}{10}[/tex]
Explicación paso a paso:
Dado que los denominadores son iguales, organice los numeradores.
Answer:
[tex]\frac{1}{10} ,\frac{4}{10}, \frac{6}{10}, \frac{8}{10}, \frac{10}{10}, \frac{14}{10}[/tex]
¡Espero que ayude!
Lo siento si es mal español. No soy un hablante nativo. :P
Step-by-step explanation: