The expression as product is sin(a)(4 + 2cos(a) - 4sin²(a))
How to express as productFrom the question, we have the following parameters that can be used in our computation:
sin(a)+sin(2a)+sin(3a)
By sine rule, we have
sin(a)+sin(2a)+sin(3a) = sin(a) + 2sin(a)cos(a) + sin(3a)
Factor out sin(a)
sin(a)+sin(2a)+sin(3a) = sin(a)(1 + 2cos(a)) + sin(3a)
Expanding sin(3a), we have
sin(a) + sin(2a) + sin(3a) = sin(a)(1 + 2cos(a)) + 3sin(a) - 4sin³(a)
So, we have
sin(a) + sin(2a) + sin(3a) = sin(a)(1 + 2cos(a) + 3 - 4sin²(a))
Evaluate the like terms
sin(a) + sin(2a) + sin(3a) = sin(a)(4 + 2cos(a) - 4sin²(a))
Hence, the product expression is sin(a)(4 + 2cos(a) - 4sin²(a))
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What is the arc measure of major arc BAC in degrees? no
Answer: 360 = 7n + 12 + 13x — 16 + 6xx = 146 * 14 = 84°
Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
Fred and his workout partner are lifting weights together, doing many sets of each exercise.
On a certain exercise, Fred is using a 19-kilogram bar, increasing the amount of weight he lifts by 4 kilograms on each set. His partner, meanwhile, started out using a 15-kilogram bar and is upping the weight by adding 6 kilograms on every set. Eventually, Fred and his workout partner will be lifting the same amount, and will take turns using the same barbell.
How much weight will they be lifting then? How many sets will they have completed?
The system of equations is:
y = 19 + 4*x
y = 15 + 6x
And the solution is x = 2 and y = 27.
How to write and solve the system of equations?
We know that red is using a 19-kilogram bar, increasing the amount of weight he lifts by 4 kilograms on each set. Then after x sets he will be lifting:
y = 19 + 4*x
kilograms.
And his partner, meanwhile, started out using a 15-kilogram bar and is upping the weight by adding 6 kilograms on every set. Here we can write:
y = 15 + 6x
Then we need to solve the system of equations at:
y = 19 + 4*x
y = 15 + 6x
Using substitution, wecan write:
19 + 4x = 15 + 6x
19 - 15 = 6x - 4x
4 = 2x
4/2 = x
2 = x
They will lift the same weight after 2 sets, and the weight is:
y = 19 + 4*2
y = 19 + 8 = 27
They will be lifting 27 kilograms.
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Write the standard form of the quadratic function that has the indicated vertex and whose graph passes through the given point. Use a graphing utility to verify your result.
Vertex: (3, 1); Point: (5, −7)
The required standard form of the quadratic function that has the indicated vertex and whose graph passes through the given point is y = -2x² + 12x - 17.
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
To find the quadratic function that has the vertex (3, 1) and passes through the point (5, -7), we can use the vertex form of the quadratic function: y = a(x - h)² + k, where (h, k) is the vertex.
First, we substitute the vertex (5, -7) into the vertex form to find a:
y = a(x - 3)² + 1
-7 = a[2]² + 1
a = -2
Since a = -2, the standard form of the quadratic function is:
y = -2x² + bx + c
Substitute the point (5, -7) into the standard form y = -2x² + bx + c to find b and c:
-7 = -2x² + b(5) + c
-7 = -50 + 5b + c
43 = 5b + c - - - - -(1)
Substitute the point (3, 1) into the standard form y = -2x² + bx + c to find b and c:
1 = -18 + b(3) + c
19 =3b + c - - - - -(2)
Solving equations 1 and 2 we get
43 - 19 = 2b
b = 12 and c = -17
Put a,b and c in the standard equation,
y = ax² + bx + c
y = -2x² + 12x - 17
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The average major league baseball team has around 2.5 million people in attendance each year. We-Seat-U sells 60% of the tickets for three of the teams at a charge of $1.50 per ticket. How much does We-Seat-U make per year just from ticket sales of these three teams?
In the diagram shown below,
ABCE is a trapezium,
AD is parallel to BC,
DE=4cm,
Area of ABCE=60cm^2
Area of ABCD=40cm^2
Work out the values of f and g.
You must show all your working
The values for g and f for the length of sides of the trapezium are 8 and 6 respectively.
How to evaluate for the values of g and f for the trapeziumGiven the area of trapezium = 60 cm², then:
1/2 × (g + 4g) × f = 60 cm²
by simplification
f(g + 2) = 60 cm²...(1)
for the area of ABCD = 48 cm², then:
f × g = 48 cm²
f = 48/g...(2)
put 48/g for f in equation (1) to get g;
48/g(g + 2) = 60
60g = 48g + 96 {cross multiplication}
60g - 48g = 96 {collect like terms}
12g = 96
g = 96/11 {divide through by 11}
g = 8
put 8 for g in equation (2) to get f;
f = 48/8
f = 6.
Therefore, the values for g and f for the length of sides of the trapezium are 8 and 6 respectively.
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A farmer takes 250 chickens to be sold at a market. In the first hour he sells 8% of his chickens. In the second hour he sells 10% of those that were left. How many chickens has he sold in total?
Answer:
43 chickens
Step-by-step explanation:
1) 250*8%=20
2) 250-20=230
3) 230*10%=23
4) 20+23=43
PLEASE HELP !!!!!
Function g is graphed here. If function f is the parent exponential function (). what is the equation of transformed function g in terms of f?
Therefore , the solution of the given problem of function comes out to be f(x) = 1.1f(x + 1) is the solution for the graph.
What is function?The study of mathematics includes looking at numbers, their variables, the world around us, buildings, and both real and imagined places. An illustration of the relation between the quantity of inputs and the appropriate outputs for each is called a function. A function, simply described, is a group of inputs who, when combined, provide distinct outputs for each input. Every function has a city, province, or scope—also referred to as a domain—assigned to it. Functions are usually indicated with the letter f. (x). The input contains an x.
Here,
Given:
The parent function f(x) is translated left by one unit and slightly stretched vertically to form g(x).
=>g(x) is:
=> f(x) = 1.1f(x + 1)
Thus , f(x) = 1.1f(x + 1) is the given function which is graphed here.
Therefore , the solution of the given problem of function comes out to be f(x) = 1.1f(x + 1) is the solution for the graph.
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Imagine this:
The altitude of an airplane coming in for a landing is represented by the equation shown below, where y represents the altitude, in feet, of the airplane and x represents the number of minutes the plane has been descending.
y = -10x + 1500
This means y is the altitude with -10ft decent every x minutes when the initial altitude is 1500Ft
Part A: Create a table for the values when x = 0,5,8,10,10
Show your work with the equation used to identify the values you put in the table when X = 0,5,8,10 and 30.
Part B: identify the altitude after 5 minutes and after 30 minutes. use 1-2 sentences to explain the altitude at these two times and describe what is happening to the airplane at these time intervals. Starter: The plane's altitude after 5 minutes would be _________. After 30 minutes, the plane's altitude would be ________.
Then describe if the plane is in the air or on the ground at those times.
The table for the values when x = 0,5,8,10, will be:
x (minutes) y (altitude in feet)
0 1500
5 1450
8 1420
10 1400
30 1200
How to explain the equationAn equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
When x = 0, y will be:
-10x + 1500
= -10(0) + 1500
= 1500
When x = 5 y will be:
= -10(5) + 1500
= 1500 - 50
= 1450
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Use the following information to work out the fraction.
In its simplest form, it is 1/1.
The numerator is even, but the denominator is odd.
The denominator is more than 40 and less than 60.
The fraction cannot be worked out, given the information on the numerator being even and the denominator being odd.
How to work out the fraction ?When fractions are said to be in their simplest forms as 1 / 1, then it means that both the numerator and the denominator are the same. This way, they can divide each other and leave one.
For such a situation to happen, the numbers will have to either both be even numbers, or odd numbers. The numerator cannot be even while the denominator is odd.
This fraction therefore cannot be worked out.
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What is the solution to this equation?
X/4= -12
A. x = -48
OB. x=3
OC. x= -3
OD. x = 48
Answer:
A. x = -48
Step-by-step explanation:
x/4 = -12
x = (-12)(4) = -48
1. Write the following expression without negative
exponents
and without parentheses.
(-6x)-¹
Answer:
[tex]\frac{1}{-6x}[/tex]
Step-by-step explanation:
[tex]\frac{1}{-6x}[/tex] To get a positive exponent, put the expression over 1.
PRE CALC PEOPLE HELP PLSSSSS
Find three additional polar representations of the point (2, 3π/4)
using −2 < < 2.
(r, ) = smallest value?
(r, ) = ?
(r, ) = largest value?
To find three additional polar representations of the point (2, 3π/4), we can add or subtract 2πk to the angle, where k is an integer. Using this method, we get:
(2, -5π/4) - subtract 2π
(2, 11π/4) - add 2π
(2, -3π/4) - subtract 2π
To find the smallest and largest values of the angle, we need to consider the interval −2π < θ < 2π. The given angle of 3π/4 lies in the second quadrant. Adding or subtracting 2π to this angle will give us angles in the third and fourth quadrants. Therefore, the smallest value of the angle is −3π/4, and the largest value is 5π/4. Thus, the polar representations are:
(2, 3π/4)
(2, -5π/4)
(2, 11π/4)
(2, -3π/4)
(2, 5π/4)
Need help on this question!
There are 4 options:
(-7,1)
(-3,-1)
(-1,-3)
(3,3)
Thanks
Answer:
(-1,-3)
Step-by-step explanation:
See the attached worksheet. First step is to apply the transformation. Modifiy the x and y points as per the instructions. The transformed triangle is shown in blue and the coordinates are listed. As the directions indicate, it is slipped down by 2 and to the left by 3 (y-2 and x-3).
Next, convert the x values so that they are reflected across the y axis. The table shows that all x values are the negative of their original values. The reflected triangle is shown in red.
The new point Z is (-1,-3).
1.) The ( ) means that all of the points on the line will satisfy the inequality.
2.) The solution set for the inequality is the entire ( ) shown in the graph
1.) The "(≠)" means that all of the points on the line will satisfy the inequality.
2.) The solution set for the inequality is the entire region (shaded or unshaded portion) shown in the graph. The shaded region represents the set of all points that satisfy the inequality, while the unshaded region represents the set of all points that do not satisfy the inequality.
What is linear inequality?
A linear inequality is an equation that represents a linear relationship between two variables and is used to describe a region of the coordinate plane that satisfies a given set of conditions.
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HELP WHAT IS THE VALUE OF TAN A
Answer: 4 / 3
Step-by-step explanation:
Soh Cah Toa
In this case, we'll use Toa
Tangent = Opposite / Adjacent
Tan A = 40 (opposite) / 30 (adjacent)
Tan A = 40 / 30 = 4 / 3 (simplified)
Evaluate the expression.
5
−
3
=
Value of expression 5 - 3 is 2
Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
Given expression,
5 - 3 = ?
we need the difference of 5 and 3
5 - 3 = 2
Hence, 2 is value of expression 5 - 3
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Over spring break, you are going to volunteer and paint 30
houses. You will need 8 gallons of paint for each home. You
receive two donations of paint, each with 15 containers, and
will purchase the required remaining paint.
If each container holds 5 gallons of paint, how many
containers do you need to buy?
Answer:
33 containers
Step-by-step explanation:
total gallons needed=8×30=240
gallons in 15 containers=15×5=75
gallons needed=240-75=165
no. of containers needed to buy=165÷5=33
HELLLPPP ILL MARK BRAINLIEST
Answer:
Below
Step-by-step explanation:
2/3 x = 9 - 2(-1/3 x +3 ) Expand the parentheses
2/3 x = 9 - -2/3x -6 simplify the R side a bit
2/3 x = 9 + 2/3x - 6
2/3 x = 3 + 2/3 x subtract 2/3 x from both sides
0 = 3 <===== obvously not true, NO SOLUTION
BROTHERS AND SISTERS, PLS HELP, REALLY NEED HELP!!!!!!!!
The functions that we have are;
1) y = 2.2x + 104
2) y =5.06e^-0.011t
3) The dependent variable is the number of organisms while the independent variable is the time in years.
4) This is an exponential decay
5) The decay rate is 1.1%
What is an equation?We know that an equation is often used to show a function. The equation is a mathematical rule that is used to express the particular situation that we have.
In the case of the problems that we have here, there is a mathematical function that can be used in the representation of each of the cases that have been shown as we can see above.
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You are tiling a floor with parallelogram shaped tiles. If one angle of the
parallelogram is 48 degrees, what are all the other angles?
The provided parallelogram has angles of 45 degrees and 45 degrees, as well as 48 degrees and 48 degrees.
What is parallelogram?A parallelogram is a basic quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposing or facing sides are of equal length, and its opposite angles are of equal measure. A parallelogram is a quadrilateral with opposing sides that are parallel and equal. It has equal interior opposite angles. In addition, the angles on the same side of the transversal add up to 180 degrees or are additive to each other.
Here,
A parallelogram has two pairs of opposite angles that are equal.
Since one angle of the parallelogram is 48 degrees, its opposite angle must also be 48 degrees.
The other two angles must add up to 90 degrees (since they form a right angle), so they must each be equal to 180 - 90 = 90 degrees / 2 = 45 degrees.
So, the other angles of the parallelogram are 45 degrees and 45 degrees.
The angles of given parallelogram are 45 degrees and 45 degrees as well as 48 degrees and 48 degrees.
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we are interested in testing to see if the variance of a population is less than 7. the correct null hypothesis is
The test is determined whether the population variance is less than 7.
The hypothesis formulation-
‘H0: σ² ≥ 7’
‘H1: σ² < 7’
Now let us solve this question options-wise:
Option a is incorrect because we should always contain the ‘=’ or ‘≥’ or ‘≤’ sign, and in the null hypothesis, and also this option denotes the standard deviation, not the variance.
Option b is correct because it contains a ‘≥’ sign and it is the right complement to the alternative hypothesis.
Option c is incorrect because it measures the standard deviation instead of the variance.
Option d is incorrect because it has the lower limit of the variance as 49 instead of 7
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full question:
We are interested in testing to see if the variance of a population is less than 7. The correct null hypothesis is
a. σ< 7.
b.σ^2≥7.
c. σ< 49.
d.σ^2≥ 49
a) complete the table of values for y = 2x^2 + x
b) Which of the three curves drean matches the graph of y = 2x^2 + x
Answer:
a)
x y
-2 6
-1 1
0 0
1 3
2 10
b) Curve B matches all the values.
Step-by-step explanation:
See attached worksheet.
a) Enter the x values into the equation to find the corresponding values of y.
b) Mark these x,y values on the graph to identify the curve that matches all points. That is curve B.
Jason purchased a car $22,995. According to his research, this make and model of a car loses all of it's marketable value after 9 years. If this car depreciates in a straight line form, what are the coordinates of the intercepts of the depreciation equation?
The coordinates of the intercepts of the depreciation equation are (9, 0) and (0, 22,995).
What are Intercepts?The x intercept is the x coordinate of a point where the line touches the X axis.
The y intercept is the y coordinate of a point where the line touches the Y axis.
Here, there are two variables.
The independent variable x is the number of years.
The dependent variable y is the value of the car.
x intercept is the year when the value of the car is 0.
Given that, model of a car loses all of it's marketable value after 9 years.
x intercept = 9
y intercept is the value of the car in the 0th year.
Initial value of the car = $22,995
y intercept = 22,995
Hence the intercepts are (9, 0) and (0, 22,995).
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А. B. Males Females Based on the information above, which statement is true? C. female students The number of male students in School A and School B are equal The number of male students in School B is less than the number of male students in School A The number of female students in School A is more than the number of male students
Based on the information below, a statement which is true include the following: C. the number of female students in School A is more than the number of male students in School B.
What is a pie chart?In Mathematics, a pie chart is sometimes referred to as a circle graph and it can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors or sections.
By critically observing the pie chart shown in the image attached below, we can reasonably infer and logically deduce that the total number of male students in School A is less than the total number of female students in School B.
In conclusion, School A has more female students than male students.
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At the Piedmont Middle School baseball game last Friday, the Piedmont Ravens hit 3 times as many foul balls as the other team, the Rossville Crows.
Step-by-step explanation:
jaubslsjsolqmaiBaokmaalo
In Youngtown, the population reached 4420 people in 1993. In 1998, there were 5600 residents. What was the population in the year 2000?
6062
6068
6058
6072
NEED HELP ASAP
Answer:
6,072
Step-by-step explanation:
5,600 - 4,420 = 1,180
They gained 1,180 people over 5 years. Now we need to find how many people they gain every year (roughly).
Since it's 5 years, we are going to divide.
1,180 / 5 = 236
They gained 236 people over 1 year. Since 1998 is two years is before 2000, we're going to multiply 236 by 2.
236 x 2 = 472
Now we add this to the 1998 population.
5,600 + 472 - 6,072
The population in the year 2,000 is 6,072
Consider the error formulas.
|E| ≤
(b − a)3
12n2
[max |f ''(x)|], a ≤ x ≤ b
Trapezoidal Rule
|E| ≤
(b − a)5
180n4
[max |f (4)(x)|], a ≤ x ≤ b
Simpson's Rule
Use these to estimate the errors in approximating the integral, with n = 4, using the Trapezoidal Rule and Simpson's Rule.
6 1 (x − 1)2 dx 2
Trapezoidal Rule: [tex](b-a)^3 / 96n^2,[/tex] Simpson's Rule: [tex](b-a)^5 / 2880n^4\\[/tex]. Both approximations have error of 0.0208.
For the Trapezoidal Rule, the formula for estimating the error is |E| ≤ (b − a)3/12n2[max |f ''(x)|], a ≤ x ≤ b. In this case, the integral is from x=1 to x=3, so b-a = 2. Plugging in all the values, we get [tex]|E| ≤ 2^3/12(4)^2(2)[/tex] or |E| ≤ 0.0208. For the Simpson's Rule, the formula for estimating the error is |E| ≤ (b − a)5/180n4[max |f (4)(x)|], a ≤ x ≤ b. Again, b-a = 2. Plugging in all the values, we get[tex]|E| ≤ 2^5/180(4)^4(2)[/tex] or |E| ≤ 0.0208. Therefore, the error in approximating the integral with n = 4, using the Trapezoidal Rule and Simpson's Rule, is 0.0208.
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What is the image of point (4,5) after a rotation of 90 counterclockwise about the origin
Answer: ez ahh question, the answer is (4,-5)
Step-by-step explanation:
focus (4,-3) directrix y=-3 what’s the equation for the parabola
The equation of the parabola is x² - 8x + 16 = 0
What is the equation of the parabolaTo find the equation of the parabola with focus (4, -3) and directrix y = -3, we can use the definition of a parabola.
A parabola is the set of all points that are equidistant to the focus and the directrix.
The distance from a point (x, y) to the directrix y = -3 is simply the vertical distance between the point and the line, which is |y - (-3)| = |y + 3|.
The distance from a point (x, y) to the focus (4, -3) can be found using the distance formula:
d = √[(x - 4)² + (y + 3)²]
Since the point is equidistant to the focus and the directrix, we have:
d = |y + 3|
Squaring both sides, we get:
(x - 4)² + (y + 3)² = (y + 3)²
Simplifying, we get:
(x - 4)² = 0
Thus, the equation of the parabola is simply:
x² - 4x - 4x + 16 = 0
x² - 8x + 16 = 0
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Express the product shown as a fraction in simplest form: -2/5 . 2/5
The simplified product of - (2/5).(2/5) is equal to - 4/25.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
A product of two fractions - 2/5 and 2/5 is given.
We know in the product of fractions numerator is multiplied by the numerator and the denominator is multiplied by the denominator.
Therefore, - (2/5).(2/5).
= - (2×2)/(5×5).
= - 4/25.
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