Answer:
The cosine function is f(t) = -30sin(π÷3)t + 20
Step-by-step explanation:
Given : The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius. The temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during a 6-hour period.
To find : What is a cosine function that models this reaction?
General form of cosine function is f(x) = A cos(Bx)+C
Where A is the amplitude
B=2π÷Period
C is the midline
Now, We have given
The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius.
A is the average of temperature,
i.e,
A=(-10-50)÷2 = -30
Period of 1 cycle is 6 hour
So,
B = 2π÷6 = π÷3
The temperature is at its lowest point when t = 0 and we know lowest point is -10
So,
f(t) = A cos t + C
-10 = -30 cos 0 + C
Therefore, C = 20
Substituting the values, we get
The cosine function is f(t) = -30sin(π÷3)t + 20
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x² +5-x when x = 5
Jamaymaykgajwnammagmaganhsnagm
Answer:
25
Step-by-step explanation:
you first solve for the expontes. 5 to the power of 2 is 25 plus 5 is 30. subtract 5 from that and we're back at 25
Answer:
25
Step-by-step explanation:
When we plug in 5 for x, we get 25+5-5=25.
can someone please help me?!? 25 points
please write wether each one is a function or a growth rate!!!
Answer:
See below
Step-by-step explanation:
There are 52 weeks in a year, so divide t by 52
= 120 (1.016)^(t/52)
then the % for one week = 1.016^1/52 = 1.0003 = .03%
The blue dot is at what value on the number line -3 -1
Answer:
It's +2
Step-by-step explanation:
As the positive occurs on the right side of the negatives in the number line so if we keep extending on the right side so we get +2
Here is the histogram of a data distribution. All class widths are 1.
Which of the following numbers is closest to the mean of this distribution?
A.3
B.5
C.7
D.9
E.4
hello, please help me match these!
Answer:
1)x+1
2)x-1
3)x+1,R-1
Step-by-step explanation:
please mark me as brainlest
S
Which triangle is similar to ABC if sin(A) = cos(A)=√15, and tan(A)=√1
R
5
12
13
T
D
3
12
f
3√15
O
2
K
√15
Σ.
M
O
3
L√6 N
X
6√15
N
O
24
6
Answer: Option 4
Step-by-step explanation:
Similar triangles have congruent angles, so this means that the sines, cosines, and tangents should be the same.
Thus, the side lengths of the triangle we want to find should be multiples of [tex]1, \sqrt{15}, 4[/tex].
This eliminates options (1) and (3).Between options 2 and 4, we know that the Pythagorean theorem is not satisfied by option (2), thus we should eliminate it.
This leaves us with option (4)
In 2009, there were 12,078 Burger King restaurants; in 2017, there were 16,717 Burger King restaurants. Calculate the average rate of change (slope) for the number of Burger King restaurants over this time period.
PLS HELP ME
Slope of the given data is 579.88
What is Slope?The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line.
Here, given data;
x₁ = 2009 y₁ = 12078 burger
x₂ = 2017 y₂ = 16717 burger
Now, Slope = (y₂ - y₁)/(x₂ - x₁)
Slope = (16717 - 12078) / (2017 - 2009)
Slope = 4639 / 8
Slope = 579.88
Thus, Slope of the given data is 579.88
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why is smallest possible angle of a 36-gon 5 degrees instead of 4.72222222222?
The smallest interior angle of the given regular polygon with 36 sides is; 170°
How to find the sum of interior angles of a polygon?The formula for calculating the sum of interior angles of a regular polygon is; S = (n − 2) × 180°
where n is number of sides of the polygon
We are told that number of sides of ploygon is 36. Thus;
S = (36 - 2) × 180°
S = 6120°
Thus;
Smallest possible angle of polygon = 6120/36 = 170°
Sum of external angles of a regular polygon is;
S = 360/n
S = 360/36
S = 10°
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S
2
Question 10 of 10
What is the value of p?
90
125
OA. 125°
O B. 55°
O C. 45°
O D. 35°
SUBMIT
Answer:
D
Step-by-step explanation:
You do 180-125 to find the angle (because its a straight line) and then you get 55, then you have a right angle so you have 90 and then you do:
55+90+p=180
and then you get
145 +p=180
180-145=35
p=35
Fill in the blank. In the triangle below, y=? Round your answer to two decimal places.
Answer:
z= 38°
Step-by-step explanation:
z= 90(from right angle)+52=142
180-142=38°
If the ordered pair (-5/2, y) lies on the graph of y=7-2x, find the value of y.
19/2
012
02
The correct answer is option B which is the value of Y will be 12.
What is an equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Given that:-
If the ordered pair (-5/2, y) lies on the graph of y=7-2x,
The value of Y will be calculated as:-
Y = 7 - 2x
Y = 7 - 2 ( -5/2 )
Y = 7 - ( - 5 )
Y = 7 + 5
Y = 12
Therefore the correct answer is option B which is the value of Y will be 12.
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Alina has $20 in her account she wants to purchase a purse shoes that cost $45 if the line makes the purchase which ener will represent the amount of money in the line of the account
The line represent the amount of money in the line of the account will be x + y = 45.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Alina has $20 in her account she wants to purchase a purse, shoes that cost $45.
If the line makes the purchase, Then the line represent the amount of money in the line of the account will be
x + y = 45
where x be the price of purse and y be the price of shoe.
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Move the slider on the graph on the right to graph each function:
For the function: y = StartRoot x minus 7 EndRoot + 1
The domain is : x ≥
The range is: y ≥
Answer:
domain: x ≥ 7 . . . [7, ∞) in interval notationrange: y ≥ 1 . . . [1, ∞) in interval notationStep-by-step explanation:
You want the domain and range of the function y = √(x -7) +1.
DomainThe domain is the horizontal extent of the graph. The graph of the given function extends to the right from x=7, which is included in the solution set.
The domain is x ≥ 7.
RangeThe range is the vertical extent of the graph. The graph of the given function extends upward from y=1, which is included in the solution set.
The range is y ≥ 1.
Answer: domain: 7
range: 1
Step-by-step explanation:
Gold has a density of 19.32 grams per cubic centimeter. How much does one-half of a cubic centimeter weigh? Gold has a density of 19.32 grams per cubic centimeter . How much does one - half of a cubic centimeter weigh ?
Substituting into the formula [tex]d=\frac{m}{v}[/tex],
[tex]19.32=\frac{m}{0.5}\\\\m=\boxed{9.66 \text{ grams}}[/tex]
The function g is related to one of the parent functions g(x) = |x − 1| + 5
a.) Identify the parent function f.
b.) Use function notation to write g in terms of f.
If the function f(x) is shifted right by one unit and upward by 5 units, then the function f(x) will be equal to the function g(x). Then the parent function is f(x) = |x|.
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
The absolute function is given as
f(x) = | x – h | + k
The function g is related to one of the parent functions g(x) = |x − 1| + 5.
Then the parent function f(x) will be
f(x) = |x|
If the function f(x) is shifted right by one unit and upward by 5 units, then the function f(x) will be equal to the function g(x).
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Find the equation of a line that contains the points (−2,−4) and (−5,4). Write the equation in slope-intercept form, using fractions when required.
The equation would be y+ 3/8x+9/4.
Lets try to explain in the further steps to calculate the equation,
Slope formula: (y₂ - y₁) / (x₂ - x₁)
First, plug in these values of the two given points.
[tex]= > (-5+2) / (4+4)\\= > -3/8[/tex]
Slope = -3/8
To find the equation of the line, (y- y1) = m* (x-x1)
So by putting the values into the above equation we get,
[tex]= > (y-4) = -3/8(x+5)\\= > y-4 = -3/8x - 15/8\\= > y + 3/8x + 4 - 15/8\\= > y + 3/8x + 9/4[/tex]
Hence the equation is [tex]y+ 3/8x+9/4.[/tex]
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Can someone please help me? I’ll give brainliest to the first person who gets it right
Answer:
128 degrees
Step-by-step explanation:
B = D
B = 128
Therefore, D = 128
This shape has these characteristics:
⇒ there are two sets of parallel sides
⇒ This shape is a parallelogram
Since this shape is a parallelogram:
⇒ meaning that angles opposite to each other
⇒ equal in measure
Since ∠B and ∠D are opposite each other
⇒ ∠D = 125°
Answer: ∠D = 125°
Hope that helps!
Vlad spent 20 minutes on his history homework and then completely solved x math problems that each took 2 minutes to complete. What is the equation that can be used to find the value of y, the total time that Vlad spent on his homework, and what are the constraints on the values of x and y?
y=2x+20; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20.
y=2x+20; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 20.
y=20x+2; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20.
y=20x +2; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 20
Answer:
y=2x+20
Step-by-step explanation:
x is any real number greater than or equal to 0, and y is any real number greater than or equal to 20
Hope this helps :)
Sketch the graph that has an area of 0.89 under the standard normal curve and to the right of the z-score. Then find the associated z-score.
The normal distribution is also known as the Gaussian distribution. The correct option is D, while the z-score is -2.29.
What is Normal Distribution?The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.
Since the normal distribution is symmetrical about the mean. Therefore, 0.89 area from the left will be equal to 0.11 area from the right. Therefore, the correct option is D, while the z-score is -2.29.
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what is the general term for sequence -6;3;15;30?
Answer:
[tex] \frac{3}{2} n {}^{2} + \frac{9}{2} n - 12[/tex]
Step-by-step explanation:
This sequence is a quadratic sequence meaning that we should find the difference and the constant second difference.
The difference between the 4 terms is in the sequence:
9;12;15
The constant second difference is 3.
Use your method of finding the general term:
2a=3 3a+b=9 a+b+c=-6
a=3/2 3(3/2)+b=9 3/2+9/2+c=-6
b=9/2 c=-12
Standard form for quadratic sequence:
[tex] {an}^{2} + bn + c[/tex]
Therefore your general term is the one stated above in the answer.
Hope that helps!
two variables x and y have corresponding values as shown in the table below. x=2,3,a and y=20,40,104 given that y varies directly as x power 2+1 find (a) value of k (b) value of a
The value of k is 4 and the value of a is 5
How to determine the value of k?The table of values is given as:
x=2,3,a
y=20,40,104
The variation is given as:
[tex]y\ \alpha\ x^2+1[/tex]
Express as an equation
y = k(x^2 + 1)
When x = 2, y = 20.
So, we have:
[tex]20 = k(2^2 + 1)[/tex]
Evaluate the sum
20 = 5k
Divide by 5
k = 4
Hence, the value of k is 4
How to determine the value of a?In (a), we have:
y = k(x^2 + 1)
Substitute 4 for k
y = 4(x^2 + 1)
When x = a, y = 104.
So, we have:
104 = 4(a^2 + 1)
Divide by 4
26 = a^2 + 1
Subtract 1 from both sides
a^2 = 25
Take the square root
a = 5
Hence, the value of a is 5
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square root of 12-square root of 8
Answer:
please tell me if im wrong!
Step-by-step explanation:
answer: 16 √ 3
Answer:
24√2
Step-by-step explanation:
if I'm correct the equation is
(√12)^2(√8)
we expand the surds
(√4x3)^2 (√4x2)
(2√3)^2 (2√2)
(4x3) (2√2)
12x2√2 =
24√2
The function y=(x-4)2+3 is a transformation of the function y=x2. How is the functions vertex affected by the transformation?
It is shifted 4 units right and 3 units up.
14)
Given a circle with a radius of 5, which equation expresses it as the ratio of the circumference of a circle to its diameter?
A)
B)
C)
D)
sin
- 7
10
216
C
Answer: 10
Step-by-step explanation: The diameter is twice the radius
Clara is building a triangular garden. She wants the length of the longest side to be three more than twice as long as the length of the shortest side, and the third side will be twelve feet long.
What expression could she write to determine the perimeter of the triangle if s represents the length of the shortest side?
The garden's perimeter = 3+2s+12+s.
The simpler version of the expression = 15+3s.
The variable's frequency in the abbreviated statement is 3.
Calculation of a triangle's perimeter:The triangle's perimeter is equivalent to the sum of its edges, where a, b, and c are its sides.
Let the triangle's longest edge be 'a'shorter one to be 's'the opposite side 'b'With the information provided, the formula will become 'a = 3+2s'
and 'b' is also 12 ft.
Triangle perimeter =the total of its edges
= a + b + s
= 3 + 2s + 12 + s
= 15 + 3s
As a result, the garden's perimeter = 3+2s+12+s.
Therefore,the simpler version of the formula is 15+3s.
The variable's coefficient in the abbreviated statement is 3.
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Figure ABCD is transformed to figure A prime B prime C prime D prime, as shown below:
A coordinate grid is shown from negative 5 to 0 to 5 on both x- and y-axes. A polygon ABCD has A at ordered pair 2, 3, B at ordered pair 4, 4, C at ordered pair 3, 1, D at ordered pair 2, 1. A polygon A prime B prime C prime D prime has A prime at ordered pair negative 1, 3, B prime at ordered pair negative 3, 4, C prime at ordered pair negative 2, 1, D prime at ordered pair negative 1, 1.
Which of the following sequences of transformations is used to obtain figure A prime B prime C prime D prime from figure ABCD?
Using translation concepts, the sequence that is used to obtain the translated image is:
Reflection over the y-axis.Shift right of one unit.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
For all the vertices, the transformations follow the given pattern:
(x,y) -> (-x,y) -> (-x + 1, y).In the step (x,y) -> (-x,y), the function is reflected over the y-axis. Then, in step (-x,y) -> (-x + 1, y), the function is shifted right one unit.
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A rope is broken up into 3 pieces. The first piece is three times bigger than the second piece and the third piece is eight feet more than the first piece. How big is each piece if the sun of all pieces is 64 feet ?
The scatter plot shows the relationship between the mass of a tree and the total mass of the vegetation within 100 square meters of the tree.
The regression equation is given by [tex]\overline{y}=50-0.01x[/tex]
We have given that,
The scatter plot shows the relationship between the mass of a tree and the total mass of the vegetation within 100 square meters of the tree.
What is the formula for slope?The slope =change in y/change in x
We have given the two points (100,40) and (25000,2)
Therefore the slope of the given point is,
[tex]=\frac{25-40}{2500-1000} \\=-0.01[/tex]
The y-intercept is the value of y when x=0 this implies that y=50
Therefore the regression equation is given by
[tex]\overline{y}=50-0.01x[/tex]
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Help me with this question please!! :)
Answer: 9516793/9765625
Step-by-step explanation:
We can subtract the probability none of them have been vaccinated from 1.
If 52% of people are vaccinated, then 48% of people are not vaccinated.
Thus, the probability is [tex]1-(0.48)^{5} =\frac{9516793}{9765625}[/tex]
A building has a height of 40 feet and a length of 20 feet. On a scale drawing of the building, the height is 20 centimeters. What is the length of the building on the scale drawing in centimeters?
Answer:
10 centimeters
Step-by-step explanation:
For the height:
40 ft / 20 cm = 2 ft / cm
With this ratio, we find the length as follows:
2 ft / cm = 20 ft / x cm
[tex]2 = \frac{20}{x} [/tex]
[tex]2x = 20[/tex]
[tex]x = 10[/tex]
Answer:
10 cm
Step-by-step explanation:
Look at the answer
