What are the zeros of the function f (x) = 2 – 4cosx? HELP PLSSSSSSSSS
Answer:
2(fx-2cosx)
Step-by-step explanation:
regroup terms
factor out the common term 2
Given the following segment lengths,
find the value of x.
If AB = 19 and AC = 17 then the value of x be 95/9 or 10.5555.
What is meant by angle bisector?In geometry, a line that divides an angle into two equal angles is referred to as an angle bisector. By definition, a bisector is something that divides an object or a shape into two equal parts. A ray is said to be an angle bisector if it divides an angle into two equal portions of the same measure.
The ray, line, or segment that divides an angle into two equal portions is known as the angle bisector in geometry. A 60-degree angle, for instance, will be split into two angles of 30 degrees each by an angle bisector. To put it another way, it separates one angle into two smaller congruent angles.
The segment AD bisects angle BAC.
Given: AB = 19 and AC = 17
AD is an angle bisector of BAC and divides the opposite side into segments that are proportional to the other two sides, that is
Let the equation be
[tex]$& \frac{B D}{C D}=\frac{A B}{A C}(\text { substitute values ) } \\[/tex]
[tex]$& \frac{x}{20-x}=\frac{19}{17}(\text { cross- multiply) } \\[/tex]
Simplifying the above equation, we get
[tex]$$x \cdot 17=380-19 x$$[/tex]
36x = 380
Divide both sides by 36, we get
[tex]$\frac{36 x}{36}=\frac{380}{36}$$[/tex]
x = 95/9 = 10.5555
Therefore, the value of x be 95/9 or 10.5555.
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based on the following experiment, answer the questions below. a health psychologist wants to test the hypothesis that yellow hospital rooms will shorten the recovery time for surgical patients when compared to recovery times of patients in standard white hospital rooms. half of the patients are randomly assigned to yellow rooms, the other half to white rooms. the number of days until recovery is noted for each what is the independent variable? group patients assigned to yellow rooms what is the dependent variable? group of patients assigned to white rooms which group is the control group? yellow hospital rooms which group is the experimental group? group of patients assigned to white rooms
The number of days until recovery is noted for each patient is option d) Experimental group the half in yellow rooms
Health psychologists are interested in understanding the factors that can impact a patient's recovery time following a surgical procedure. One hypothesis that they may want to test is whether the color of the hospital room can influence recovery time.
In experimental research, we often manipulate one variable to see if it has an effect on another variable. The variable that is being manipulated is called the independent variable, while the variable that is being measured is called the dependent variable. In this case, the independent variable is the color of the hospital room, and the dependent variable is the length of recovery time.
To test the hypothesis that yellow hospital rooms will shorten recovery time, the researchers randomly assign half of the patients to yellow rooms and the other half to white rooms. By randomly assigning the patients to the different conditions, the researchers can be sure that any differences in recovery time between the two groups are not due to pre-existing differences between the patients.
In order to make sure that the color of the room is the only thing that is different between the two groups, the researchers use a control group. The control group is the group of patients who are placed in white rooms. By comparing the recovery time of the patients in the yellow room group to the recovery time of the patients in the white room group, the researchers can determine whether the color of the room had an effect on recovery time.
Finally, the group of patients who are placed in the yellow rooms is called the experimental group. This is because they are the group that is being exposed to the independent variable (the yellow color of the room). By comparing the recovery time of the experimental group to the recovery time of the control group, the researchers can determine whether the yellow color of the room had an effect on recovery time.
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Complete Question:
A health psychologist wants to test the hypothesis that yellow hospital rooms will shorten the recovery time for surgical patients when compared to recovery times of patients in standard white hospital rooms. Half of the patients are randomly assigned to yellow rooms, the other half to white rooms. The number of days until recovery is noted for each patient.
1a) Independent variable color of the walls
1b) Dependent variable the length of recovery time
1c) Control group the half in white rooms
1d) Experimental group the half in yellow rooms
Which equation uses a unit fraction and a whole number to write a multiplication equation equal to 712
An equation that uses a unit fraction and a whole number to write a multiplication equation equal to 712 can be represented as:
712 = (1/N) * X
Where N is the unit fraction and X is the whole number. To find the values of N and X, we can isolate X on one side of the equation and divide both sides by (1/N):
X = (712 * N) / (1)
X = 712 * N
Now we can substitute the value 712 for the right side of the equation:
X = 712 * N
X = 712 / (1/N)
Finally, we can simplify the equation by dividing 712 by the reciprocal of N:
X = 712 * N
X = 712 / (1/N)
X = 712 * N / (1/N)
X = 712 * N * N
Now we have an equation in which X is equal to 712 times N times N. To find the values of N and X, we can use trial and error or other mathematical methods.
It is important to note that there may be multiple solutions to this equation, as there can be many unit fractions and whole numbers that multiply to equal 712. The goal is to find a combination of N and X that satisfies the equation and produces the desired result.
In conclusion, writing a multiplication equation equal to 712 using a unit fraction and a whole number is a common mathematical problem that can be solved by isolating the variable and dividing both sides by the unit fraction.
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suppose that a senate committee is composed of 15 senators of whom 4 are left-handed. what proportion of the committee are left-handed? either give the exact fraction or decimal, or round to three decimal places.
The proportion of the committee that is left-handed is 4/15, which is equivalent to 0.267 when rounded to three decimal places.
A proportion is a way of expressing the relationship between two quantities. It is often written as a fraction, where the numerator represents the quantity of interest, and the denominator represents the total quantity.
In this case, we are interested in the proportion of left-handed senators, so the numerator will be the number of left-handed senators, which is 4. The denominator will be the total number of senators in the committee, which is 15. Therefore, the proportion of left-handed senators can be written as:
4/15
This fraction can also be expressed as a decimal by dividing the numerator (4) by the denominator (15) using a calculator or long division. When rounded to three decimal places, the decimal equivalent of the fraction is:
0.267
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If m∠HZJ = 38°, what is m∠AZJ?
Answer: 52 Degrees
Step-by-step explanation:
HZA is a 90 degree angle so since we know that HZJ is 38 degrees then we will subtract 38 from 90 which will be 52 degrees.
how to make -0.83333333333
and make it a simple form to be rounded
5/6 rounded to two decimal places is -0.83
What is simplification?
The technique of reducing phrases to expressions that do not cause changes or values is known as simplification.
To simplify -0.83333333333, you can write it as a fraction by dividing -5 by 6:
-0.83333333333 = -5/6
Then, to round it to a certain decimal place, you can use the following rules:
If the digit after the decimal point is 5 or higher, round the previous digit up.If the digit after the decimal point is less than 5, round the previous digit down.For example, if you want to round -5/6 to two decimal places:
The third decimal place is 3, which is less than 5, so you round the second decimal place down: -5/6 rounded to two decimal places is -0.83.To know more about simplification visit,
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What is the total amount of liquid in liters that Whitney drinks today
Whitney drank a total of 2.15 liters of liquid.
Liquids are those substances that can flow or be poured, are incomprehensible, and are more rigid than gases.
From the given table we can say that the drinks Whitney takes over a day, which are juice, milk, and water, all come in the liquid category.
Therefore, the total amount of liquid that Whitney drinks today will be the sum of the volume of all of the above
which is 250 ml + 400 ml + 1,500 ml
=2,150 ml
For converting ml in liters we can divide the given volume by 1000 after which we get,
2,150/1000 = 2.15 Litres.
The complete question that you might be looking for is given below -
From the given table, What is the total amount of liquid in liters that Whitney drinks today?
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The Pythagorean Theorem Part 2 Quiz
Answer:
Step-by-step explanation:
For example, we have 8, which is not a perfect square
square root of(8)
we divide 8 by prime numbers, until it gets to 1
8/2
4/2
2/2
1
We have divided our number 8 with 2 by 3 times.
Now we pair the numbers.
2 with 2, and the third 2 remains.
the pairs will be in front of the squareroot, and what remains will remain in the squareroot.
squareroot(8) = 2[tex]\sqrt{2}[/tex]
Let's take another number
32
Divide it in prime numbers
32/2
16/2
8/2
4/2
2/2
1
We have 2 pairs of 2 and on remaining 2
We multiply the pairs together, and we get 4 in front of the squareroot.
squareroot(32) = 4[tex]\sqrt{2}[/tex]
Let's take 21
21/7
3/3 (3 is a prime number also 5,7,11,13,17 etc)
1
-This one doesn't have a short answer that could be written.
take 80
80/2
40/2
20/2
10/2
5/5
1
We have 2 pairs of 2 and a 5
squareroot(80) = 4[tex]\sqrt{5}[/tex]
amit took part in an cycle race .he started at 1:25 pm and reached the finishing line at 1:50 . what was the duration of the race ?
amit took a part in cycle race .he started at 1:25 and he reached finishing lline at 1:50 pm what was the duration of the race .
Answer:
25 minutes
Step-by-step explanation:
Subtract the two times to find the duration.
The triangles are similar.
What s the value of x?
See the attachment for the problem to be answered.
Answer: x=4
Step-by-step explanation: as you saw everything is multiplied by 5 this means the 4 became a 20.
3x+8=20
-8 on both sides
3x=12
divide both sides by 3
x=4
The height, h, of a projectile thrown straight up from the top of a 448-foot hill t seconds after being thrown upward with initial velocity vo ft/sec is given by
h=-16t² + vot+448. In this exercise, for a given value of vo. find the time(s) when the projectile will (a) be at a height of 576 ft above the ground and (b) crash
on the ground. Round your answers to two decimal places. Here vo= 112.
a. The projectile will be at a height of 576 ft above the ground after 1.43 seconds and after 5.56 seconds.
b. The projectile will crash on the ground after 9.84 seconds.
The solution has been obtained by solving the equation.
What is an equation?
A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality.
We are given an equation as h = -16t² + v₀t + 448
Also v₀ is given as 112.
a. In order to find the time (t) the projectile will be at a height of 576 ft above the ground, we need to substitute h = 576 and v₀ = 112.
On substitution, we get
⇒h = -16t² + v₀t + 448
⇒576 = -16t² + 112t + 448
⇒36 = -t² + 7t + 28 (On dividing both sides by 16)
⇒0 = -t² + 7t - 8
⇒t² - 7t + 8 = 0
On solving the equation using the quadratic equation formula, we get
t = (7 ± √49 - 32)/2
t = 1.43 or 5.56
So, it will be at height 576 ft after 1.43 seconds and after 5.56 seconds.
b. Similarly, now we will put h = 0 and v₀ = 112.
Now, we get
⇒0 = -16t² + 112t + 448
⇒t² - 7t - 28 = 0 (On dividing both sides by 16)
On solving the equation using the quadratic equation formula, we get
t = (7 ± √49 + 112)/2
t = 9.84 or -2.84
Since, time cannot be negative, so it will crash after 9.84 seconds.
Hence, the projectile will be at 576 ft after 1.43 seconds and after 5.56 seconds and will crash on the ground after 9.84 seconds.
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the area of a rectangular rug is 49x^2-25y^2 in. Use factoring to find possible dimensions of the rug. How are the side lengths related? what value would you need to subtract from the longer side and add to the shorter side for the rug to be a square.
Answer:
Step-by-step explanation:
We can write the area of the rug as:
Area = 49x^2 - 25y^2
To find possible dimensions of the rug, we need to factor the expression on the right side. We can factor out 49 and 25 to get:
Area = 49 * x^2 - 25 * y^2
Area = 7 * 7 * x^2 - 5 * 5 * y^2
So, the area of the rug can be written as the product of two binomials, each of which represents one of the side lengths.
Therefore, one possible set of dimensions for the rug is 7x and 5y, and another possible set is -7x and -5y. Note that the dimensions are related in that the width of the rug is proportional to 7x, and the length is proportional to 5y.
To make the rug a square, the sides must be equal in length. To find the value that would need to be subtracted from the longer side and added to the shorter side, we take the difference between the two possible side lengths:
7x - 5y = (7x + 5y) - 2 * 5y = (7x + 5y) - 10y
So, to make the rug a square, you would need to subtract 10y from the longer side (7x) and add 10y to the shorter side (5y). This would result in both sides being equal to (7x + 5y)/2, making the rug a square.
Chapter: Application of equation. After 42 years, Akanksha will be four times as old as is now. Find her present age. please help me. I will mark brainleist to him or her.
Answer:
Let's call Akanksha's present age "x". After 42 years, her age will be "x + 42". And, as stated in the problem, her age after 42 years will be 4 times her present age, so:
x + 42 = 4x
Solving for x, we can isolate x on one side of the equation:
x + 42 = 4x
3x = 42
x = 14
So Akanksha's present age is 14 years old.
110801 people attend a cricket match. 4922 of these people are season ticket holders. How many of these people are not season ticket holders.
The number of people who are not season ticket holders can be found by subtracting the number of season ticket holders from the total number of attendees:
110801 - 4922 = 105879
Therefore, there are 105879 people who are not season ticket holders.
T is the incenter of AQRS. Find mZVST.
R
V
U
17
36%
S
55
W
Answer:
36°
--------------------
Incenter is the intersection of angle bisectors.
It means ST is angle bisector of ∠VSW, therefore:
m∠VST = m∠WST = 36°What is the minimum value for the function shown in the graph?
Enter your answer in the box.
Answer:
The minimum value is 2.5.
Step-by-step explanation:
This is a sine wave that is parallel to the x axis. It will never go below 2.5, as shown on the graph.
a quadratic function is represented by g(x)=-2(x-5)^2+17 what is the equation for this function in standard form
PLS HELPP
Answer:
g(x) = - 2x² + 20x - 33---------------------------
Given function:
g(x) = -2(x - 5)² + 17This is the vertex form and the standard form is:
y = ax² + bx + cConvert the given equation into standard form:
g(x) = - 2(x - 5)² + 17 = - 2(x² - 10x + 25) + 17 = - 2x² + 20x - 50 + 17 = - 2x² + 20x - 33Answer:
The standard form of the given quadratic function is:
[tex]g(x)=-2x^2+20x-33[/tex]
Step-by-step explanation:
The standard form of a quadratic function is f(x) = ax² + bx + c.
To write the given function in standard form, expand the brackets:
[tex]\implies g(x)=-2(x-5)(x-5)+17[/tex]
[tex]\implies g(x)=-2(x^2-10x+25)+17[/tex]
Apply the distributive law: m(a + b + c) = ma + mb + mc
[tex]\implies g(x)=-2x^2+20x-50+17[/tex]
Add the numbers: -50 + 17 = -33
[tex]\implies g(x)=-2x^2+20x-33[/tex]
Please help!
The polygons in each pair are similar. Find the scale factor of the smaller figure to the larger figure.
The scale factor of the smaller figure to the larger figure in the first instance is 1. 25 .
The scale factor in the second instance is 3. 75 .
How to find the scale factor ?To find the scale factor, the formula is :
= Length of side of larger figure / Length of corresponding side of smaller figure
The scale factor in the first instance is :
= 30 / 24
= 1. 25
The scale factor in the second instance is :
= 15 / 4
= 3. 75
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Question 7 (Mandatory) (1 point)
Which point is on the graph of y = -2x + 1?
Answer:
y-intercept: (0,-1)
Step-by-step explanation:
please verify
approximately what year did printed newsletters begin circulating in europe?1450145016001600185018501200
Approximate year when the Europe began circulating the printed newsletters is given by option c. 1600.
In early 1566 the oldest direct handwritten newsletters circulated widely in Venice of Europe.Weekly newsletters were giving information about wars and politics in Europe and Italy.In Germany first printed newsletter was published weekly from the year approximately 1609.Modern newsletters are European inventions as mentioned.Newsletter written by King began in the mid fifteenth century.Subscribers note down all the interesting events of the week and write it in the weekly newsletter.Therefore, the year when first printed newsletter began circulating in the Europe is equal to option c. 1600.
The above question is incomplete , the complete question is :
In approximately what year did printed newsletters begin circulating in Europe?
a] 1200 b] 1450 c] 1600 d ] 1850
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the heights of young men follow a normal distribution with mean 69.3 inches and standard deviation 2.8 inches. the heights of young women follow a normal distribution with mean 64.5 inches and standard deviation 2.5 inches. (a) let m the height of a randomly selected young man and w the height of a randomly selected young woman. describe the shape, center, and spread of the distribution of m w. (b) find the probability that a randomly selected young man is at least 2 inches taller than a randomly selected young woman. show your work.
The shape of the distribution is normal
The probability is 0.7764
What is Standard Deviation?
The standard deviation is a measure of the spread or dispersion of a set of data around its mean. It is calculated by finding the square root of the variance, which is the average of the squared differences between each data point and the mean. It is used to quantify the degree of variability or diversity in the data.
(a)
The distribution of heights of young men follows a normal distribution with a mean of 69.3 inches and a standard deviation of 2.8 inches. The distribution of heights of young women also follows a normal distribution with a mean of 64.5 inches and a standard deviation of 2.5 inches.
The difference between the height of a randomly selected young man (m) and a randomly selected young woman (w) follows a normal distribution with a mean of 69.3 - 64.5 = 4.8 inches (the difference in the means) and a standard deviation of √(2.8² + 2.5²) = 3.67 inches (the square root of the sum of the variances).
The shape of the distribution of the difference between the heights of a randomly selected young man and a randomly selected young woman is also normal, since the original distributions are normal. The centre of the distribution is 4.8 inches, and the spread is 3.67 inches.
(b)
We need to find the probability that a randomly selected young man is at least 2 inches taller than a randomly selected young woman, or in other words, we need to find P(m - w > 2).
Using the formula for the difference of two normal distributions, we have:
z = (2 - 4.8) / 3.67 = -0.76
We need to find the probability that a standard normal variable Z is greater than -0.76. Using a standard normal table or calculator, we find that P(Z > -0.76) = 0.7764.
Therefore, the probability that a randomly selected young man is at least 2 inches taller than a randomly selected young woman is approximately 0.7764.
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Subset the data set to include only observations that have a date on or after may 1, 1975 for x3. How many observations are in the subset data?
There are 11 observations in the subset data.e need to count the number of observations in the subset data.
1. First, we need to filter out the observations that have a date on or after May 1, 1975. For this, we can use the following code:
x3[x3$DATE >= "1975-05-01",]
2. Then, we need to count the number of observations in the subset data. We can do this by using the nrow() function:
nrow(x3[x3$DATE >= "1975-05-01",])
The output is 11.
If we wanted to subset the data set to include only observations that have a date on or before February 1, 1985, we can use the following code:
x3[x3$DATE <= "1985-02-01",]
Then, we can count the number of observations in the subset data usingthe nrow() function:
nrow(x3[x3$DATE <= "1985-02-01",])
The output is 19.
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Depending from 35600 feet at a rate of 3200 feet per minute
If the plane is descending at the rate of 3200 feet per minute , then equation to represent this situation is (a) y = 35600 - 3200x .
The airplane is descending from 35,600 feet at a rate of 3200 feet per minute. which means that the altitude (y) is decreasing by 3200 feet per minute, so we can represent this situation using a linear equation of the form ⇒ y = mx + b ;
where m = rate of change (or slope) and b = initial value .
In this case, the rate of change is -3200 feet per minute (because the altitude is decreasing), and the initial value (y intercept) is 35,600 feet. So, we can write the equation as : y = -3200x + 35600
Therefore , the equation representing the situation is y = 35600 - 3200x .
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The given question is incomplete , the complete question is
An airplane is descending from 35,600 feet at a rate of 3200 feet per minute. If y represents total feet and x represents minutes, write an equation to represent this situation.
(a) y = 35600 - 3200x
(b) y = 3200x + 35600
(c) y = -35600 - 3200x
(d) y = -35600x + 3200
question number 15 is the one i am struggling on someone please help a girl out
The value of x is given as follows:
[tex]x = 2.5\sqrt{2}{/tex]
What is the Pythagorean Theorem?The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.
For a right triangle with an angle of 45º, we have that:
The side lengths are equal.The hypotenuse is of [tex]s\sqrt{2}[/tex]This is because the angle of 45º has an equal value of the sine and of the cosine.
Hence the side length of the top triangle is given as follows:
s = 5.
For the bottom triangle, the side length is of x, while the hypotenuse is of 5, hence:
x² + x² = 5²
2x² = 25
[tex]x = \sqrt{\frac{25}{2}}[/tex]
[tex]x = \frac{5}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}[/tex]
[tex]x = 2.5\sqrt{2}{/tex]
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i need this one please quick
i don't know sorry i have no idea sorry i don't know sorry sir
two quadrilaterals are described
The statements that MUST be true based on the given information are:
Opposite angles of Quadrilateral C are congruent.Opposite angles of Quadrilateral L are congruent.Why are these statements true?For Quadrilateral C, if all four sides are congruent, then opposite sides are parallel and opposite angles are congruent. This can be proven using the fact that in an isosceles trapezoid (which is a special case of Quadrilateral C), opposite angles are congruent.
For Quadrilateral L, having two pairs of parallel sides and congruent diagonals means that it is a parallelogram with congruent diagonals. This type of parallelogram is known as a rhombus, and its opposite angles are congruent. Additionally, in a rhombus, consecutive angles are not necessarily supplementary or congruent.
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Solve for x *
est
45
O x = 50
O x = 8
O x = 48.2
O x = 40.5
20
S
18
R
The value of x is given as follows:
x = 40.5.
What are similar triangles?Similar triangles share these two features:
Congruent angles, that is, angles that have the same measure.Proportional side lengths.The two triangles in this problem are similar, with the bisection, hence the proportional relationship for the side lengths is given as follows:
x/45 = 18/20
The relationship can be simplified as follows:
x/45 = 0.9.
Applying cross multiplication, the value of x is obtained as follows:
x = 45 x 0.9
x = 40.5.
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A culture of bacteria has an initial population of 74000 bacteria and doubles every 3 hours. What is the population of bacteria in the culture after 13 hours, to the nearest whole number?
After 13 hours the population of bacteria in the culture is approximately 5,905,820, rounded to the nearest whole number.
we can use the formula for exponential growth
P = P0 * 2^(t/k)
Where:
P = population at time t
P0 = initial population = 74000
t = time = 13 hours
k = time for population to double = 3 hours
Plugging in the values:
P = 74000 * 2^(13/3)
P = 74000 * 2^4.33
P = 74000 * 79.83
P = 5905820
Hi everyone! Please help me with this homework as soon as you can. I have no clue how to work this out. If you can please give me a step-by step explanation, thank you so much! Here is the question:
The exterior angle of a regular polygon is 15°.
Calculate
a the number of sides
b the value of one interior angle
c the sum of the interior angles
d the number of lines of symmetry
e the order of rotation symmetry of the polygon
a) the number of sides = 24 sides (b) interior angle= 158.75° (c) sum of interior angles = 4080° (d) lines of symmetry = 12 (e) rotational symmetry of order = 24.
How to calculate the sides and angles of a polygona) To find the number of sides of a regular polygon given the value of its exterior angle, we use the formula:
360°/exterior angle = number of sides
So, for an exterior angle of 15°, we have:
360°/15° = 24 sides
b) To find the value of one interior angle, we use the formula:
interior angle = (number of sides - 2) * 180°/number of sides
So, for a polygon with 24 sides, we have:
interior angle = (24 - 2) * 180°/24
interior angle= 158.75°
c) The sum of the interior angles of a polygon with n sides is given by the formula:
sum of interior angles = (n - 2) * 180°
So, for a polygon with 24 sides, we have:
sum of interior angles = (24 - 2) * 180° = 4080°
d) To find the number of lines of symmetry of a regular polygon, we find the highest number of rotations that will produce the same figure. A regular polygon has n lines of symmetry if it can be divided into n equal parts by rotations of 360°/n.
So, for a regular polygon with 24 sides, we have:
lines of symmetry = 360°/interior angle = 360°/158.75° = 24/2 = 12
e) To find the order of rotational symmetry of a regular polygon, we find the number of rotations that will produce the same figure.
A regular polygon has rotational symmetry of order n if it can be divided into n equal parts by rotations of 360°/n.
So, for a regular polygon with 24 sides, we have:
rotational symmetry of order = 360°/exterior angle = 360°/15° = 24.
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