Answers
Answer:
(fg)(x)= (x²+6)(x²-x+9)
multiply the terms:
(fg)(x)= x²(x²-x+9) +6(x²-x+9)
add the like terms:
(fg)(x)= (x⁴-x³+9x²)+(6x²-6x+54)
and you get your final answer:
(fg)(x)= x⁴-x³+15x²-6x+54
Related Questions
Find the area of the shaded region
Answers
Answer:
17.5
Step-by-step explanation:
The triangle is an equilateral triangle since all sides are equal
Area of a equilateral triangle is:
[tex]ar(triangle) = \frac{a^2\sqrt{3} x}{4}[/tex]
[tex]=\frac{5^2\sqrt{3} }{4} \\\\=\frac{25\sqrt{3} }{4} \\[/tex]
the sde of the square = diameterof the circle(d)
d = 6
r = d/2 = 3
ar(circle) = πr²
= π * 3²
= 9π
= 9*22/7
= 198/7
ar(shaded region) = ar(circle)-ar(triangle)
[tex]= \frac{198}{7} - \frac{25\sqrt{3} }{4}[/tex]
= 17.5
Suppose 150 mL (milliliters) of a medication is administered to an infected patient. It is estimated that 8%
of this person’s cells are infected with a virus.
1. Suppose 2 mL of the medication contains 2.3 × 103 antiviral proteins. How many antiviral proteins were
injected into this person? Express your answer in scientific notation.
2. There are about 1 × 1014 cells in the average adult human body. What percentage of this person’s cells
can be affected by the administered medication?
3. How many mL of medication would need to be administered to the patient in order to have 1 antiviral
protein for every infected cell? How many liters is this equivalent to?
Answers
Answer:
Step-by-step explanation:
To find the number of antiviral proteins injected into the person, we can set up a proportion:
2 mL contains 2.3 × 10^3 antiviral proteins
x mL contains how many antiviral proteins?
The proportion can be written as:
2 mL / 2.3 × 10^3 = x mL / (unknown number of antiviral proteins)
We can solve this proportion by cross-multiplication:
2 mL * (unknown number of antiviral proteins) = 2.3 × 10^3 antiviral proteins * x mL
x = (2.3 × 10^3 antiviral proteins * x mL) / 2 mL
Simplifying, we get:
x = 1.15 × 10^3 * x mL
Therefore, the number of antiviral proteins injected into the person is 1.15 × 10^3.
The total number of cells in the person's body is approximately 1 × 10^14. If 8% of the person's cells are infected with the virus, we can calculate the percentage of cells that can be affected by the medication:
Percentage of cells affected = (Number of infected cells / Total number of cells) * 100
Number of infected cells = 8% of 1 × 10^14 cells
Number of infected cells = (8/100) * 1 × 10^14
Number of infected cells = 8 × 10^12
Percentage of cells affected = (8 × 10^12 / 1 × 10^14) * 100
Percentage of cells affected = 8 × 10^-2 * 100
Percentage of cells affected = 8%
Therefore, the administered medication can affect 8% of the person's cells.
To find the amount of medication needed to have 1 antiviral protein for every infected cell, we can set up a proportion:
2.3 × 10^3 antiviral proteins in 2 mL
1 antiviral protein in x mL
The proportion can be written as:
2.3 × 10^3 antiviral proteins / 2 mL = 1 antiviral protein / x mL
We can solve this proportion by cross-multiplication:
(2.3 × 10^3 antiviral proteins) * x mL = 2 mL * 1 antiviral protein
x = (2 mL * 1 antiviral protein) / (2.3 × 10^3 antiviral proteins)
Simplifying, we get:
x = 0.8696 mL
Therefore, to have 1 antiviral protein for every infected cell, approximately 0.8696 mL of medication needs to be administered. This is equivalent to 0.0008696 liters.
Solve this ASAP PLS HELP
Answers
Answer:
(2, -1)
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}y=-2x+3\\y+9=4x\end{cases}[/tex]
To solve the given system of equations, we can use the method of substitution.
Substitute the first equation into the second equation to eliminate the y term:
[tex](-2x+3)+9=4x[/tex]
Solve for x:
[tex]-2x+3+9=4x[/tex]
[tex]-2x+12=4x[/tex]
[tex]-2x+12+2x=4x+2x[/tex]
[tex]12=6x[/tex]
[tex]\dfrac{12}{6}=\dfrac{6x}{6}[/tex]
[tex]2=x[/tex]
[tex]x=2[/tex]
Substitute the found value of x into the first equation and solve for y:
[tex]y=-2(2)+3[/tex]
[tex]y=-4+3[/tex]
[tex]y=-1[/tex]
Therefore, the solution to the system of equations is (2, -1).
To verify the solution by graphing the system, find two points on each line by substituting two values of x into each equation. Plot the points and draw a line through them. The solution is the point of intersection.
Graphing y = -2x + 3
[tex]\begin{aligned} x=0 \implies y&=-2(0)+3\\y&=0+3\\y&=3\end{aligned}[/tex] [tex]\begin{aligned} x=-2 \implies y&=-2(-2)+3\\y&=4+3\\y&=7\end{aligned}[/tex]
Plot points (0, 3) and (-2, 7) and draw a straight line through them.
Graphing y + 9 = 4x
[tex]\begin{aligned} x=0 \implies y+9&=4(0)\\y+9&=0\\y&=-9\end{aligned}[/tex] [tex]\begin{aligned} x=3 \implies y+9&=4(3)\\y+9&=12\\y&=3\end{aligned}[/tex]
Plot points (0, -9) and (3, 3) and draw a straight line through them.
The solution to the graphed system of equations is the point of intersection of the two lines: (2, 1).
Order these from least to greatest.
Answers
Answer:
Least to greatest:
√143
4π
√79 + √63
Step-by-step explanation:
√79 + √63 = 16.82
4π = 12.57
√143 = 11.96
2. Sandra's house is located at the point (2,2). The school is located at the point (7, 10). Each
unit on the graph represents 1 mi. How far is the school from Sandra's house? Remember to
show your work.
Plot and label your points on the coordinate plane (1 point)
Use the Pythagorean Theorem to calculate the diagonal distance between the two
points, express your answer as a radical and as a decimal rounded to nearest
hundredths.
Answers
Answer:
Step-by-step explanation:
peter is 24 years younger than his father. In 5 years time, his father will be 3 times as old as peter? a). how old is peter. b). how old will peter's father be in 25 year's time?
Answers
Step-by-step explanation:
Let Peter's present age be "p" and his father's age be "x"
So, p = x-24 ;
5 years from now,
Peter's age will be (x-24) + 5 = x-19
His father's age will be x+5.
It is given that 3(x-19)= x+5.
3x - 57 = x + 5 => 2x = 62.
On solving, his father's present age (x) is 31.
So Peter's present age is (p) is x - 24 = 31 - 24 = 7.
Now going in the reverse oder to check the answer.
Peter's present is 7.
5 years from now, it will be 12.
His father's age is 31.
5 years from now, his age will be 36 (which is 3x12).
Hence , the answer to the given problem is 7
Ms. Lee used two dozen Mud Bugs in her suit the recipe makes 20 cups of soup approximately how many Mud Bugs are in each cup of soup round off the answer to the nearest whole number
Answers
Answer:
1
Step-by-step explanation:
So, 1 dozen is 12. Two dozen is 24.
She used 24 Mud Bugs in this soup.
This soup makes 20 cups.
So, 24 Mud Bugs are in 20 cups of soup.
To find the amount of Mud Bugs in each cup of soup, you divide the amount of Mud Bugs by the number of cups.
24/20
Which equals 1.2
You asked for the nearest whole number, so there is 1 Mud Bug per sup of soup.
please answer i am stuck
Answers
The correct answer choice is: A. The system has exactly one solution. The solution is (13, 5).
The correct answer choice is: A. all three countries had the same population of 5 thousand in the year 2013.
How to solve this system of equations and interpret the answer?Based on the information provided above, the population (y) in the year (x) of the counties listed are approximated by the following system of equations:
-x + 20y = 87
-x + 10y = 37
y = 5
where:
y is in thousands.x = 10 corresponds to 2010.By solving the system of equations simultaneously, we have the following solution:
-x + 20(5) = 87
x = 100 - 87
x = 13
-x + 10(5) = 37
x = 50 - 37
x = 13
Therefore, the system of equations has only one solution (13, 5).
For the year when the population are all the same for three countries, we have:
x = 2010 + (13 - 10)
x = 2013
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Please help me with this question
Answers
Answer:
try (gauth math) could be helpful take screen shot and upload it it may be there or not hopefully it is
Based on the two data sets represented below, complete the following sentences. DATA SET K DATA SET K 0 0 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 DATA SET L DATA SET L 0 0 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 The center of Data Set K is than the center of Data Set L. The spread of Data Set K is than the spread of Data Set L.
Answers
Based on the provided data sets, it can be observed that both Data Set K and Data Set L have identical values. Therefore, their centers and spreads are also identical.
The center of a data set can be measured using various statistical measures such as the mean, median, or mode. Since the data sets have the same values, all these measures will yield the same result for both sets.
In this case, the center of Data Set K is equal to the center of Data Set L.
Similarly, the spread of a data set refers to the measure of variability or dispersion within the data. Common measures of spread include the range, variance, and standard deviation.
However, since the data sets are exactly the same, all these measures will yield identical results for both sets. Thus, the spread of Data Set K is the same as the spread of Data Set L.
In summary, both the center and the spread of Data Set K are the same as those of Data Set L. Therefore, there is no difference between the two data sets in terms of their central tendency or variability.
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Calc II Question
Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x axis
x = 4y^2 - y^3
x = 0
Answers
V = 2π ∫[0,1] y(4y^2 - y^3) dy
Simplifying the integrand, we get:
V = 2π ∫[0,1] (4y^3 - y^4) dy
Integrating, we get:
V = 2π [(y^4 - (1/5)y^5)]|[0,1]
V = 2π [(1 - (1/5))] = (8/5)π
Therefore, the volume of the solid is (8/5)π cubic units.
Copy the axes below.
a) By completing the tables of values to help
you, plot the lines y = 2x + 1 and
y = 10x on your axes.
b) Use your diagram to find the solution to the
simultaneous equations y = 2x + 1 and
y = 10 - x.
y = 2x+1
x012
Y
y = 10-x
x012
Y
Y
-3 -2 -1
10
2987
65
6
-5
4
3
NW
21
1
-14
--2
73
1 2 3 4 5 6 7 8 9 10 x
Answers
The solution to the simultaneous equations is x = 3 and y = 7
Finding the solution to the simultaneous equationsFrom the question, we have the following parameters that can be used in our computation:
y = 2x + 1
y = 10 - x
Subtract the equations
So, we have
3x - 9 = 0
This gives
3x = 9
So, we have
x = 3
Next, we have
y = 10 - x
y = 10 - 3
Evaluate
y = 7
Hence, the solution is x = 3 and y = 7
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find the surface area of the composite figure 12cm x 2cm x 10cm x 3cm x 6cm x 8cm SA=
Answers
Answer:
If you are in Acellus trust me the answer is 394
Step-by-step explanation:
SA = 2 ( 2 x 12 ) + 2 ( 2 x 10 ) + ( 8 x 6 ) + 2 ( 3 x 8 ) + ( 3 x 6 ) + ( 12 x 16 )
SA = 48 + 40 + 48 + 48 + 18 + 192
SA = 394 square cm.
Given the set of data
4
10
2
18
15
would finding the best predicted value for x = 20 be an example of interpolation or extrapolation?
a. Extrapolation since 20 is not within the range.
b. Extrapolation since 20 is within the range.
Answers
The correct answer is b. Extrapolation since 20 is within the range.
In this scenario, finding the best predicted value for x = 20 would be an example of extrapolation. Extrapolation involves estimating values outside the given range of data based on the trend or pattern observed within the existing data.
Given the data set: 4, 10, 2, 18, 15, we can see that the values provided are not in any particular order. To perform extrapolation, it is generally helpful to first examine the trend or pattern within the data. However, without additional information or context, it is difficult to determine the underlying trend in this case.
Since the given data set does not explicitly indicate any pattern or trend, any estimation made for x = 20 would be considered extrapolation. Extrapolation involves projecting or extending the existing trend or pattern beyond the known data points. In this case, the value of 20 falls outside the range of the given data set, so estimating its corresponding value would require extending the trend beyond the known data points.
Consequently, the appropriate response is b. Extrapolation since 20 is within the range.
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Qué porcentaje de 200 es 164
Answers
Si hacemos una regla de tres
Se multiplica 164*100
Y después el resultado de divide entre 200
Espero que te sirva
Here is a unit circle with point P at (1, 0) Find the coordinates of P after the circle rotates the given amount counter clockwise around its center
1. 1/3 of a full rotation: ?
2 1/2 of a full rotation: ?
3. 2/3 of a full rotation: ?
Answers
1/3 of a full rotation: (-0.5, √3/2)
1/2 of a full rotation: (-1, 0)
2/3 of a full rotation: (0.5, -√3/2)
These are the coordinates of point P after the corresponding rotations around the unit circle's center.
To find the coordinates of point P after the unit circle rotates a certain amount counter-clockwise around its center, we can use the properties of the unit circle and the trigonometric functions.
1/3 of a full rotation:
A full rotation in the unit circle corresponds to 360 degrees or 2π radians. Therefore, 1/3 of a full rotation is equal to (1/3) * 360 degrees or (1/3) * 2π radians.
When the unit circle rotates 1/3 of a full rotation, point P will end up at an angle of (1/3) * 2π radians or 120 degrees from the positive x-axis.
In the unit circle, the x-coordinate of a point on the circle represents the cosine of the angle, and the y-coordinate represents the sine of the angle.
At an angle of 120 degrees or (1/3) * 2π radians, the cosine is -0.5 and the sine is √3/2.
Therefore, the coordinates of point P after rotating 1/3 of a full rotation are (-0.5, √3/2).
1/2 of a full rotation:
Similarly, 1/2 of a full rotation is equal to (1/2) * 360 degrees or (1/2) * 2π radians.
When the unit circle rotates 1/2 of a full rotation, point P will end up at an angle of (1/2) * 2π radians or 180 degrees from the positive x-axis.
At an angle of 180 degrees or (1/2) * 2π radians, the cosine is -1 and the sine is 0.
Therefore, the coordinates of point P after rotating 1/2 of a full rotation are (-1, 0).
2/3 of a full rotation:
Again, 2/3 of a full rotation is equal to (2/3) * 360 degrees or (2/3) * 2π radians.
When the unit circle rotates 2/3 of a full rotation, point P will end up at an angle of (2/3) * 2π radians or 240 degrees from the positive x-axis.
At an angle of 240 degrees or (2/3) * 2π radians, the cosine is 0.5 and the sine is -√3/2.
Therefore, the coordinates of point P after rotating 2/3 of a full rotation are (0.5, -√3/2).
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In circle I, IJ = 9 and m/JIK = 140°. Find the length of JK. Express your answer as a fraction times pie.
Answers
The calculated length of the arc JK is 7π
Finding the length of the arc JKFrom the question, we have the following parameters that can be used in our computation:
Central angle = 140 degrees
Radius, IJ = 9 inches
Using the above as a guide, we have the following:
JK = Central angle/360 * 2 * π * Radius
Substitute the known values in the above equation, so, we have the following representation
JK = 140/360 * 2 * π * 9
Evaluate
JK = 7π
Hence, the length of the arc is 7π
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Determine the equation of the midline of the following graph.
Answers
Answer:
3
Step-by-step explanation:
midline is the distance or the midway between the highest point and the lowest one or between maximum and minimum,
for the given graph,
maximum point = 5
minimum point = 1
midline = 5 +1 / 2 = 6 / 2 = 3
consider the graph function below
Answers
The equation of the red graph is g(x) = f(x) - 5
How to calculate the equation of the red graphFrom the question, we have the following parameters that can be used in our computation:
The functions f(x) and g(x)
Where, we have
f(x) = -x
i.e.. the parent equation of the function
From the graph, we can see that
The function is shifted down by 5 units
This means that
g(x) = f(x) - 5
This means that the equation of the red graph is g(x) = f(x) - 5
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Team A and Team B together won 50% more games than Team C did. Team A won 50% as many games as Team B did. The three teams won 60 games in all. How many games did each team win?
Answers
Let x be the number of games won by Team A.
Let y be the number of games won by Team B.
Let z be the number of games won by Team C.
From the given information, we can form the following equations:
Equation 1: x + y + z = 60 (The total number of games won by the three teams is 60.)
Equation 2: x = (1/2)y (Team A won 50% as many games as Team B.)
Equation 3: x + y = 1.5z (Team A and Team B together won 50% more games than Team C.)
Now, let's solve this system of equations:
Substituting Equation 2 into Equation 3, we get:
(1/2)y + y = 1.5z
(3/2)y = 1.5z
y = (1.5z) * (2/3)
y = z
Substituting y = z into Equation 1, we have:
x + y + z = 60
x + y + y = 60
x + 2y = 60
Substituting y = z into Equation 3, we have:
x + y = 1.5z
x + y = 1.5y
x = 0.5y
Now, we can substitute x = 0.5y and y = z into Equation 1:
0.5y + 2y = 60
2.5y = 60
y = 60 / 2.5
y = 24
Substituting y = 24 into x = 0.5y:
x = 0.5 * 24
x = 12
Substituting y = 24 into the equation y = z:
z = 24
Therefore, Team A won 12 games, Team B won 24 games, and Team C won 24 games as well.
{y=4x−19.4
y=0.2x−4.2
Answers
Answer:The solution of the linear equations y = 4x − 19.4 and y = 0.2x − 4.2 will be (4, -3.4). Then the correct option is A.
What is the solution to the equation?
The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The equations are given below.
y = 4x − 19.4 ...1
y = 0.2x−4.2 ...2
From equations 1 and 2, then we have
4x - 19.4 = 0.2x - 4.2
3.8x = 15.2
x = 4
Then the value of the variable 'y' will be calculated as,
y = 4 (4) - 19.4
y = 16 - 19.4
y = - 3.4
The solution of the linear equations y = 4x − 19.4 and y = 0.2x − 4.2 will be (4, -3.4). Then the correct option is A.
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NEED HELP ASAP
Y
B
^^
CX
A
Previous Activity
N
Which would prove that AABC~ AXYZ? Select two
options.
OBA-BC-A
=
YX
YZ XZ
OBA = BC₁
YX
YZ
O
AC
XZ
=
=
BA
XX.
YX
AC
BC
BA = AE = 8C
YX
YZ
XZ
OBC=BA ₁ <=
XY
ZX
Next Activity
Answers
The two options that would prove that ΔABC ~ ΔXYZ include the following:
A. BA/YX = BC/YZ = AC/XZ
C. AC/XZ = BA/YX, ∠A≅∠X
What are the properties of similar triangles?In Mathematics and Geometry, two triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Based on the side, side, side (SSS) similarity theorem, we can logically deduce the following congruent angles and similar triangles:
BA/YX = BC/YZ = AC/XZ (ΔABC ≅ ΔXYZ)
Based on the side, angle, side (SAS) similarity theorem, we can logically deduce the following congruent angles and similar sides:
AC/XZ = BA/YX, ∠A≅∠X
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¿Cuál es el costo de un plátano si el racimo de 22 plátanos cuesta $23.10?
Answers
The cost of a single unit is given as follows:
$1.05.
El costo de un plátano es el seguiente:
$1.05.
How to obtain the cost of a single unit?The cost of a single unit is obtained applying the proportions in the context of the problem.
The cost of 22 units is of $23.10, hence the cost of a single unit is obtained dividing the total cost by the number of units, as follows:
23.1/22 = $1.05.
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Which equation, when graphed with the given equation, will form a system that has an infinite number of solutions?
77110
03-x--2
- 3-4-x
Oy+4x-1
Mark this and retum
C
Save and Exit
€
6
Next
Submit
Answers
The equation 2y + 8x - 2 = 0 will satisfy the condition of having an infinite number of solutions when graphed with the given equation.
How to determine the equation, when graphed with the given equation, will form a system that has an infinite number of solutionsTo form a system of equations that has an infinite number of solutions when graphed with the given equation, we need to find an equation that represents the same line or is a multiple of the given equation.
The given equation is: y + 4x - 1 = 0
To find an equation with an infinite number of solutions, we can multiply the given equation by a non-zero constant.
Let's multiply the given equation by 2:
2(y + 4x - 1) = 2(0)
2y + 8x - 2 = 0
The equation 2y + 8x - 2 = 0, when graphed with the given equation y + 4x - 1 = 0, will form a system that has an infinite number of solutions. The two equations represent the same line, just with different coefficients.
Therefore, the equation 2y + 8x - 2 = 0 will satisfy the condition of having an infinite number of solutions when graphed with the given equation.
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4/5 x 5/7 x 7/9 x 9/11 x 11/13 x 13/15 x 15/17 x 17/19 x 19/21 x 21/23 x 23/25 x 25/27 27/28 x 29/37 x 31/35 x 33/33 x 35/31 x 37/29
Answers
The product of the given fractions is 224/61.
To calculate the product of the given fractions, let's simplify and cancel out any common factors.
We have:
(4/5) x (5/7) x (7/9) x (9/11) x (11/13) x (13/15) x (15/17) x (17/19) x (19/21) x (21/23) x (23/25) x (25/27) x (27/28) x (29/37) x (31/35) x (33/33) x (35/31) x (37/29)
Starting from the numerator and denominator of the first fraction, we observe the following cancellations:
5 in the numerator and denominator cancel out.
7 in the numerator and denominator cancel out.
9 in the numerator and denominator cancel out.
11 in the numerator and denominator cancel out.
13 in the numerator and denominator cancel out.
15 in the numerator and denominator cancel out.
17 in the numerator and denominator cancel out.
19 in the numerator and denominator cancel out.
21 in the numerator and denominator cancel out.
23 in the numerator and denominator cancel out.
25 in the numerator and denominator cancel out.
27 in the numerator and denominator cancel out.
Now, let's multiply the remaining fractions:
(4/1) x (1/28) x (29/37) x (31/1) x (1/35) x (37/29)
This simplifies to:
(4 x 1 x 29 x 31 x 37) / (1 x 28 x 37 x 29 x 35)
Simplifying further:
(4 x 29 x 31) / (28 x 35)
We can calculate this to get the final result:
(4 x 29 x 31) / (28 x 35) = 3584 / 980 = 224 / 61.
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21. In each of these problems, determine a suitable form for Y (t) if the method of undetermined coefficients is to be used. Do not evaluate the constants.
a. y"" - 2y" + y' = t³ + 2e^t
b. y''' - y' = te^-t + 2cost
c. y^4 - 2y'' + y = e^t + sin(t)
d. y^4 + 4y" = sin 2t + te^t + 4
e. y^4 - y''' - y" + y' = t² + 4 + tsin(t)
f. y^4 + 2y''' + 2y" = 3e^t + 2te^-t + e^-t sin(t)
Answers
Answer:
a. Y(t) = At³ + Be^t + Ct² + Dt + E
b. Y(t) = At + B + Ce^t + Dsin(t) + Ecos(t)
c. Y(t) = Aet + Bte^t + Csin(t) + Dcos(t)
d. Y(t) = At³ + Bt² + Ct + D + Ecos(2t) + Fsin(2t)
e. Y(t) = At² + Bt + C + Dsin(t) + Ecos(t) + Fsin(t) + Gcos(t)
f. Y(t) = Aet + Bte^-t + Ccos(t) + Dsin(t) + E + Ft + G
Find the exact value of cos 105⁰.
a. √√√2-√6
4
b.
√2+√6
4
C.
4
d. √2+√6
4
Answers
Answer:
[tex]\dfrac{\sqrt{2}-\sqrt{6} }{4} }[/tex]
Step-by-step explanation:
Find the exact value of cos(105°).
The method I am about to show you will allow you to complete this problem without a calculator. Although, memorizing the trigonometric identities and the unit circle is required.
We have,
[tex]\cos(105\°)[/tex]
Using the angle sum identity for cosine.
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Angle Sum Identity for Cosine}}\\\\\cos(A+B)=\cos(A)\cos(B)-\sin(A)\sin(B)\end{array}\right}[/tex]
Split the given angle, in degrees, into two angles. Preferably two angles we can recognize on the unit circle.
[tex]105\textdegree=45\textdegree+60\textdegree\\\\\\\therefore \cos(105\textdegree)=\cos(45\textdegree+60\textdegree)[/tex]
Now applying the identity.
[tex]\cos(45\textdegree+60\textdegree)\\\\\\\Longrightarrow \cos(45\textdegree+60\textdegree)=\cos(45\textdegree)\cos(60\textdegree)-\sin(45\textdegree)\sin(60\textdegree)[/tex]
Now utilizing the unit circle.
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{From the Unit Circle:}}\\\\\cos(45\textdegree)=\dfrac{\sqrt{2} }{2}\\\\\cos(60\textdegree)=\dfrac{1}{2}\\\\\sin(45\textdegree)=\dfrac{\sqrt{2} }{2}\\\\\sin(60\textdegree)=\dfrac{\sqrt{3} }{2} \end{array}\right}[/tex]
[tex]\cos(45\textdegree)\cos(60\textdegree)-\sin(45\textdegree)\sin(60\textdegree)\\\\\\\Longrightarrow \Big(\dfrac{\sqrt{2} }{2}\Big)\Big(\dfrac{1 }{2}\Big)-\Big(\dfrac{\sqrt{2} }{2}\Big)(\dfrac{\sqrt{3} }{2}\Big)[/tex]
Now simplifying...
[tex]\Big(\dfrac{\sqrt{2} }{2}\Big)\Big(\dfrac{1 }{2}\Big)-\Big(\dfrac{\sqrt{2} }{2}\Big)(\dfrac{\sqrt{3} }{2}\Big)\\\\\\\Longrightarrow \Big(\dfrac{\sqrt{2} }{4} \Big)-\Big(\dfrac{\sqrt{6} }{4} \Big)\\\\\\\therefore \cos(105\textdegree)= \boxed{\boxed{\frac{\sqrt{2}-\sqrt{6} }{4} }}[/tex]
what is the value of f(x)=-1/3x-1/3 when x=-1/2
Answers
Answer:
f(-1/2) = -1/6
Step-by-step explanation:
To find the value of f(x) when x = -1/2, we substitute -1/2 for x in the expression for f(x) and simplify:
f(x) = (-1/3)x - 1/3
f(-1/2) = (-1/3)(-1/2) - 1/3
= 1/6 - 1/3
= -1/6
So, f(-1/2) = -1/6.
The cost of capsaicin arthritis rub is $21 for a
physical therapist who works with chronic arthritis patients, you need to buy
42 ounces of capsaicin. How many tubes will you need to purchase?
Answers
You will need to purchase approximately 1/42 of a tube, which is less than a full tube. In practical terms, you would need to purchase at least one tube to meet your requirement of 42 ounces of capsaicin arthritis rub.
To determine the number of tubes of capsaicin arthritis rub you will need to purchase, we can divide the total required quantity by the quantity in each tube.
Given that the cost of capsaicin arthritis rub is $21 and you need to buy 42 ounces, we need to find out how many ounces are in each tube.
Let's assume that each tube contains x ounces of capsaicin arthritis rub.
Now we can set up a proportion to solve for x:
42 ounces / x tubes = 1 tube / x ounces
Cross-multiplying gives us:
42x = 1 * x
Simplifying the equation:
42x = x
Dividing both sides of the equation by x (since x cannot be zero):
42 = 1
Since this equation is not true, it means that there is an error in our assumption. We need to revise our assumption.
Let's assume that each tube contains 1 ounce of capsaicin arthritis rub.
Now we can set up a new proportion:
42 ounces / x tubes = 1 tube / 1 ounce
Cross-multiplying gives us:
42x = 1 * 1
Simplifying the equation:
42x = 1
Dividing both sides of the equation by 42:
x = 1/42
As a result, you will need to buy less than a full tube—roughly 1/42 of a tube. In order to get the 42 ounces of capsaicin arthritis rub you need, you would essentially need to buy at least one tube.
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You read online that a 15 ft by 20 ft brick patio would cost about $2,275 to have professionally installed. Estimate the cost of having a 25 by 26 ft brick patio installed.
Answers
Answer:
$4929
Step-by-step explanation:
I assume the cost is proportional to the area.
15 ft × 20 ft = 300 ft²
25 ft × 26 ft = 650 ft²
650/300 = x/$2275
300x = 650 × $2275
x = $4929
Answer: $4929
