To solve this problem, we can use the Greatest Common Factor (GCF) of 10 and 20.
The GCF is the largest number that divides evenly into both 10 and 20. To find the GCF, we can use a factor tree.
We start with 10 and 20 as our starting numbers.
10 = 2 * 5
20 = 2 * 2 * 5
We can see that both 10 and 20 have a factor of 2 and a factor of 5. The Greatest Common Factor between 10 and 20 is 2 * 5, or 10.
Therefore, the greatest number of portions of trail mix Stanley can make is 10.
The perimeter of a rectangular field is 292 m. If the length of the field is 95 m, what is it's width?
The width of the rectangular field is 51 meters
To find the width of the rectangular field, we need to use the formula for the perimeter of a rectangle, which is:
Perimeter = 2 × (length + width)
We are given that the perimeter of the rectangular field is 292 m and the length is 95 m. So, we can plug in these values into the formula and solve for the width:
292 = 2 × (95 + width)
First, we can simplify the right side of the equation:
292 = 190 + 2 × width
Next, we can isolate the variable (width) on one side of the equation by subtracting 190 from both sides:
292 - 190 = 2 × width
102 = 2 × width
Finally, we can solve for the width by dividing both sides by 2:
width = 51 m
Learn more about perimeter here
brainly.com/question/29595517
#SPJ4
first 6 terms of n² + 7
Answer:
8, 11, 16, 23, 32, and 43.
Step-by-step explanation:
When n = 1:
n² + 7 = 1² + 7 = 8
When n = 2:
n² + 7 = 2² + 7 = 11
When n = 3:
n² + 7 = 3² + 7 = 16
When n = 4:
n² + 7 = 4² + 7 = 23
When n = 5:
n² + 7 = 5² + 7 = 32
When n = 6:
n² + 7 = 6² + 7 = 43
Therefore, the first 6 terms of n² + 7 are 8, 11, 16, 23, 32, and 43.
Answer:
When n = 1, n² + 7 = 1² + 7 = 8
When n = 2, n² + 7 = 2² + 7 = 11
When n = 3, n² + 7 = 3² + 7 = 16
When n = 4, n² + 7 = 4² + 7 = 23
When n = 5, n² + 7 = 5² + 7 = 32
When n = 6, n² + 7 = 6² + 7 = 43
The first 6 terms of n² + 7 are 8, 11, 16, 23, 32, and 43.
Step-by-step explanation:
ᓚᘏᗢ
hope u have a good day man
the data in the table shows a sinusoidal relationship between the number of seconds an object has been moving and its velocity v(x), measured in centimeters per second. x 2 4 6 8 10 12 14 16 18 20 22 24 v(x) 34.5 31.3 26.1 20 13.9 8.7 5.2 4 5.2 8.7 13.9 20 what is true of the cosine function that models the data in the table? drag a value into each box to correctly complete the statements.
The period of the cosine function is___ the equation of the midline of the cosinefunction is y=_______The amplitude of the cosine function is
these are the whole statements: Cosine function has a 24-period period. The cosine function's midline has the equation y = 19.25. The cosine function has a 15.25 amplitude.
What does an equation mean?A mathematical equation, such as 6 x 4 = 12 x 2, states that two amounts and values are equal. two. Countable noun. A scenario known as an equation means that two or more components must be taken into account in order to comprehend or understand the overall situation.
Midline = (34.5 Plus 4) / 2 (34.5 + 4) = 19.25 Maximum value plus Minimum value
As a result, the following equation represents the data's model for the midline of a cosine function:
y = 19.25
The biggest deviation from the function's midline is its amplitude in the cosine function. The maximum amount of v(x) was 34.5 cm/s, and the minimum is 4 cm/s, according to the data provided. The cosine function used to model the data has the following amplitude:
Amplitude is calculated as (highest value – minimum values) / 2 (or 34.5 - 4) / 2 (or 15.25).
To know more about equation visit:
https://brainly.com/question/29657983
#SPJ1
3.
If the expression 1/2x
was placed in the form
ax^b
where a and b are real numbers, then which of the
following is equal to a + b ? Show how you arrived at your answer.
(1) 1
(2) 3/2
(3) 1/2
(4) -1/2
If the expression 1/2x was placed in the form ax^b where a and b are real numbers, then a + b equal to option (4) -1/2
The given expression is 1/(2x), which can be rewritten as:
1/(2x) = 1/2 × (1/x)
Here, we can see that the expression can be written in the form of ax^b, where a = 1/2 and b = -1.
To see why a = 1/2, notice that 1/2 is the coefficient of (1/x). And to see why b = -1, note that x^(-1) is the exponent on the variable x
So, we have:
1/(2x) = (1/2) × x^(-1)
And, a + b = (1/2) + (-1)
Add the numbers
= -1/2.
Therefore, the correct option is (4) -1/2.
Learn more about exponent here
brainly.com/question/219134
#SPJ4
select all the correct answers. which three pairs of side lengths are possible measurements for the triangle?
The three pairs are (AB = 6, BC = 6) (AB = 4, AC = 4√2) and (BC = 2√2, AC = 4). So, First option, Option 5. and Option 6 are correct answers.
Since we know that,
Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.
The formula for a 30-60-90 triangle is this:
1) Side opposite to 30 will be value a.
2) Side opposite to 60 will be value a√3
3) Hypotenuse will be 2a.
AB is opposite of the angle with 30 degree measurement.
BC is opposite of the angle with 60 degree measurement.
The sides of an isosceles right triangle are in the ratio,
1:1:√2
where √2 is the hypotenuse.
For the example, BC = 2√2, then AC = 2√2 x √2 = 4.
Therefore, the three pairs are;
1. (AB = 6, BC = 6)
5. (AB = 4, AC = 4√2)
6.(BC = 2√2, AC = 4).
To know more about Trigonometry follow;
brainly.com/question/24349828
#SPJ12
The complete question is attached below:
The local hardware store has blue buckets that hold 2 gallons of water and white buckets that hold 5 gallons of water. You bought 7 buckets that can hold 26 gallons of water. How many buckets of each color were purchased?
Answer:
So 3 blue buckets and 4 white buckets were purchased
Step-by-step explanation:
We can solve this by algebra
Let B = number of blue buckets bought
Let W = number of white buckets bought
Total buckets bought:
B + W = 7 (1)
Each blue bucket can hold 2 gallons of water
So B blue buckets can hold 2B gallons of water
Each white bucket can hold 5 gallons of water
So W white buckets can hold 5W gallons of water
Totally they can hold
2B + 5W gallons
We are given that they both can hold 26 gallons of water
So our second equation is
2B + 5W = 26 (2)
By eliminating one of the variable terms we can solve for the other variable term
Let's eliminate the term for variable B
Multiply equation (1) by 2
(1) x 2 ==> 2(B + W) = 2(7)
2B + 2W = 14 (3)
Subtract (3) from (2); B terms are same so they cancel out
(2) - (3):
2B + 5W = 26 [tex]\bold{-}[/tex]
2B + 2W = 14
---------------------
0 + 3W = 12
------------------------
3W = 12
W = 12/3
W = 4
Substitute W= 4 in equation 1
B + W = 7
=> B + 4 = 7
B = 3
So 3 blue buckets and 4 white buckets were purchased
A restaurant owner is buying new tableware for her restaurant. She wants the new pieces to be proportionate, and needs to know the measurements of the different pieces she is buying. The circle-shaped part of the bottom of the glass above has an area of 12.56 in2. What is the radius? Use = 3.14. A. 4 in B. 5 in C. 1 in D. 2 in Reset Submit
The answer is d please
Determine wheter the given vale of the varible is a soultion of the equatiom 9 = 3/4 e e = 12
If e = 12 and the equation is true, then the answer to the equation is 12.
How can you determine a variable's value in an equation?You can solve the equation as before if it has the form axe + b = c, where x is the variable. Addition and subtraction should be "undone" first, followed by multiplication and division.
We insert e = 12 into the equation and check to see if the equation is true to see if the given value of the variable is a solution of the equation 9 = (3/4)e, where e = 12.
9 = (3/4)e
9 = (3/4)(12)
9 = 9
If e = 12 and the equation is true, then the answer to the equation is 12.
To know more about equation visit:-
https://brainly.com/question/29538993
#SPJ1
Name the shape that will result from connecting the points (-4, 1) , (-4, -4) , (0, 3) , and (0, 6) .
A: Square
B: Rectangle
C: Trapezoid
D: Parallelogram
The shape that results from connecting the points (-4, 1), (-4, -4), (0, 3), and (0, 6) is a trapezoid.
What is a trapezoid?A trapezoid is a geometric form that has four sides, two of which are parallel and two of which are nonparallel (or skew lines). A trapezoid is also known as a trapezium (UK) or a trapeze (US).
The trapezoid's parallel sides are known as the bases, and the two nonparallel sides are known as the legs or lateral sides. The trapezoid is also sometimes referred to as the irregular quadrilateral.
How to identify a trapezoid?A quadrilateral is a shape that has four sides, four vertices, and four angles. The following are the characteristics of a trapezoid:
It has four sidesIt has two parallel sides and two nonparallel sidesIt has two opposite sides that are parallel to one another and two other sides that are not parallelIt has two acute angles and two obtuse anglesIt has diagonals that intersect at a midpointThe formula for the area of a trapezoid is as follows:
Area of a trapezoid = [ (base 1 + base 2) / 2 ] x height
To know more about the "trapezoid": https://brainly.com/question/1463152
#SPJ11
Pls Help very Confused
Answer: x=1
Step-by-step explanation:
Vertical angles mean they are equal to each other. So first you would set the two equations equal to each other.
7x+26=4x+29
Then subtract 4x from both sides.
7x+26−4x=29
combine 7x and −4x to get 3x.
3x+26=29
Then subtract 26 from both sides.
3x=29−26
subtract 26 from 29 to get 3.
3x=3
Lastly divide both sides by 3.
3/3x=3/3
Divide 3 by 3 to get 1.
x=1
The ratio of the sines of any two angles in a triangle equals the ratio of the lengths of their opposite sides. Justify your answer.
Answer: This statement is known as the Law of Sines and can be proven using trigonometry and the properties of similar triangles.
Consider a triangle ABC with sides of lengths a, b, and c opposite to the angles A, B, and C respectively. Let's draw an altitude from vertex A to side BC, splitting side BC into two segments: BD of length x and CD of length c-x.
Using the Pythagorean theorem, we can write:
a^2 = x^2 + h^2 (1)
b^2 = (c-x)^2 + h^2 (2)
where h is the length of the altitude from A to BC.
Dividing equation (1) by sin^2(A) and equation (2) by sin^2(B), we get:
a^2 / sin^2(A) = x^2 / sin^2(A) + h^2 / sin^2(A)
b^2 / sin^2(B) = (c-x)^2 / sin^2(B) + h^2 / sin^2(B)
Since angles A and B are complementary (i.e. A + B = 90 degrees), we have sin(A) = cos(B) and sin(B) = cos(A). Substituting these identities and rearranging the equations, we get:
a^2 / sin(A) = x / cos(B) + h / sin(B)
b^2 / sin(B) = (c-x) / cos(A) + h / sin(A)
Multiplying both equations by sin(A)sin(B), we obtain:
a^2 sin(B) = x sin(A) cos(B) + h sin(A)
b^2 sin(A) = (c-x) sin(B) cos(A) + h sin(B)
Now, we use the fact that h = a sin(B) = b sin(A), which follows from the definition of sine as opposite/hypotenuse. Substituting this into the above equations and simplifying, we get:
a / sin(A) = 2R
b / sin(B) = 2R
c / sin(C) = 2R
where R = a/(2sin(A)) = b/(2sin(B)) = c/(2sin(C)) is the radius of the circumcircle of triangle ABC. This is the Law of Sines in its usual form.
From this, we can see that the ratio of the sines of any two angles in a triangle equals the ratio of the lengths of their opposite sides, as required.
Step-by-step explanation:
on jerry's text messaging phone plan, he paid $0.60 for every 30 messages he sent. what is the his cost per message?
Answer:
$0.02
Step-by-step explanation:
0.60/30
20 people ride the bus, 80 people ride motorbikes, 65 people drive vans, and 215 people drive cars. Based on the data, how many would you expect to use motorbikes if you asked 800 people? how many people ride motorbikes
Exponential for (0,35), (1,50), (2,100), (3,200), (4,400)
The exponential equation that fits the data points (0,35), (1,50), (2,100), (3,200), and (4,400) is y = 35 * (10/7)^x.
To find an exponential equation that fits the given data points, we can use the general form of an exponential equation:
y = a * b^x
where y is the dependent variable (in this case, the second coordinate of each data point), x is the independent variable (the first coordinate of each data point), a is the initial value of y when x is 0, and b is the growth factor.
Using the given data points, we can create a system of equations:
35 = a * b^0
50 = a * b^1
100 = a * b^2
200 = a * b^3
400 = a * b^4
The first equation tells us that a = 35, since any number raised to the power of 0 is 1. We can then divide the second equation by the first equation to get:
50/35 = b^1
Simplifying, we get:
10/7 = b
We can now substitute a = 35 and b = 10/7 into the remaining equations and solve for y:
y = 35 * (10/7)^x
This is the exponential equation that fits the given data points. We can use it to find the value of y for any value of x. This equation gives us a way to predict the value of y for any value of x.
To learn more about exponential click on,
https://brainly.com/question/11776332
#SPJ4
if terri were to paint her living room alone, it would take 3 hours. her sister angela could do the job in 4 hours. how many hours would it take them working together?
The time in hours which it will take them for working together for terri is about 1.71 hours.
What is the time in hours?Inverse Proportion: When two quantities are related in such a way that the product of one quantity with the reciprocal of the other quantity remains constant, it is said to be in inverse proportion.
Let's calculate their working rate:
Terri takes 3 hours to complete the painting of her living room, so she can paint her living room in [tex]\frac{1}{3} hours[/tex]
Angela takes 4 hours to complete the painting of the living room, so she can paint her living room in [tex]\frac{1}{4} hours[/tex]
If both work together, then the time taken to complete the work will be less than the time taken by each of them individually.
To find the time taken by both working together, we will add their rates.
Terri's work rate = [tex]\frac{1}{3} hours[/tex]
Angela's work rate = [tex]\frac{1}{4} hours[/tex]
Work rate when working together = Terri's rate + Angela's rate= [tex]\frac{1}{3} + \frac{1}{4} = \frac{7}{12}[/tex]
Thus, both will take [tex]\frac{12}{7} = 1.71 hours[/tex] approximately to complete the painting of the living room when they work together.
Therefore, the time in hours is about 1.71 hours.
Learn more about Working rate here:
https://brainly.com/question/29071883
#SPJ11
Calculate Suppose that on each of the
4,500 dives Alvin has made, a new pilot and two new scientists were on board.
How many scientists have seen the
deep ocean through Alvin's windows? How
many people, in total, traveled in Alvin?
The calculation shows that 9,000 scientists have seen the deep ocean through Alvin's windows; and
a total of 13,500 people have traveled in Alvin over the course of its 4,500 dives.
What is the explanation for the above calculation?1) If on each of the 4,500 dives Alvin carried a new pilot and two new scientists, then the total number of scientists who have seen the deep ocean through Alvin's windows is:
4,500 dives x 2 scientists per dive = 9,000 scientists
Therefore, 9,000 scientists have seen the deep ocean through Alvin's windows.
2) To calculate the total number of people who traveled in Alvin, we can add the number of pilots and scientists on each dive and multiply by the number of dives:
4,500 dives x (1 pilot + 2 scientists)
= 4,500 x 3
= 13,500 people
Therefore, a total of 13,500 people have traveled in Alvin over the course of its 4,500 dives.
Learn more about calculation:
https://brainly.com/question/30781060
#SPJ1
mrs. jeffers started the school year with 22 students. during the school year, another s students joined her class. write an expression that shows the number of students at the end of the year.
At the end of the year, the expression that shows the total number of students is [tex]22+s[/tex]
What is an expression?An expression is a mathematical phrase that can contain numbers, variables, and operators. It doesn't contain an equal sign (=) or a value.
Mrs. Jeffers started the school year with 22 students. During the school year, another s student joined her class.
The expression that shows the number of students at the end of the year is.[tex]22+s[/tex]
The symbol "+" is an operator that stands for addition, and "s" is a variable that represents the number of students who joined the class.
Learn more about expression here:
brainly.com/question/1859113
#SPJ11
Marisa bought a car for $9,632. She paid $2,000 down. She will pay the remainder
in 24 monthly payments. How much will she pay each month?
Explain your answer.
Answer: $318/mo
Step-by-step explanation:
First, we get the remainder, which is the difference between $9, 632 and $2,000. That gives us $7, 632.
Then, since we know she will pay in 24 months, we assume she pays the same amount each month and divide $7, 632 by 24 = $318/mo
The 17 cows on the farm produced 209 & and 780 ml of milk this morning. How much milk did each cow produce today on average?
Therefore, on average, each cow produced 169.41 ml of milk today.
What is average?The average, also known as the arithmetic mean, is a statistical measure that is calculated by adding together a set of numbers and then dividing the sum by the total number of values in the set. The result is a single value that represents the central tendency of the data set.
Given by the question.
To find the average amount of milk produced by each cow, we need to divide the total amount of milk by the number of cows.
Average milk produced by each cow = (Total milk produced)/ (Number of cows)
Total milk produced = 2090 ml + 780 ml = 2870 ml
Number of cows = 17
Therefore,
Average milk produced by each cow = 2870 ml/17
= 169.41 ml
To learn more about measure:
https://brainly.com/question/4725561
#SPJ1
Two balls are pulled one after another, without replacement, from the box containing three black, five yellow, and seven red balls. What is the probability that the 1st ball is yellow, if the 2nd ball is black? (Hint: use common fractions during your calculations and round only your final answer to 2 places after the decimal point). A. 0.21 B. 0.36 C. 0.42 D. None of the above
The probability that the first ball is yellow if the second ball is black is 1/14. The correct option is D.
What is the probability?The given question is a classic example of dependent events in probability. As the balls are drawn without replacement, the second event's outcome will depend on the outcome of the first event.
Probability = Number of favorable events/ Total number of events
The probability of the first ball being yellow is [tex](5/15)[/tex], while the probability of the second ball being black is [tex](3/14)[/tex].
Mathematically represented as P(Yellow ball on the first draw) = P(Yellow ball) = [tex]5/15[/tex]
P(Blackball on second draw given Yellow ball on the first draw) = P(Blackball | Yellow ball) = [tex]3/14[/tex]
As both the events are dependent, we need to find the joint probability of both the events, which can be calculated as P(Yellow ball on the first draw and Blackball on the second draw) = P(Yellow ball) × P(Blackball | Yellow ball)
P (Yellow ball on the first draw and blackball on second draw) = [tex](5/15) × (3/14) = 3/42 = 1/14.[/tex]
Therefore, the correct option is D.
Learn more about probability here:
https://brainly.com/question/30034780
#SPJ11
how to calculate the product of two random variable that follows normal distribution with mean 0 and variance 1
To calculate the product of two random variables that follows the normal distribution with mean 0 and variance 1 by using the covariance formula
Cov(X, Y) = E[XY] - E[X]E[Y] = E[XY] - 0 = E[XY]
Given that two random variables follow a normal distribution with mean 0 and variance 1.
Let X and Y be two independent normal random variables such that X ~ N(0,1) and Y ~ N(0,1)
Now, The expected value of the product of two random variables is given by;
E[XY] = E[X]E[Y] + Cov(X,Y)
Where E[X] and E[Y] are the means of the two random variables X and Y respectively.
Cov(X, Y) is the covariance between the two random variables, which can be calculated using the formula;
Cov(X,Y) = E[XY] - E[X]E[Y]
Now, E[X] = E[Y] = 0 as both have a mean of 0.
Cov(X, Y) = E[XY] - E[X]E[Y]
⇒ E[XY] = the expected value of the product of X and Y.
As X and Y are independent, their covariance will be zero, which implies;
Cov(X, Y) = E[XY] - E[X]E[Y] = E[XY] - 0 = E[XY]
Thus, we can calculate the product of two random variables that follow a normal distribution with mean 0 and variance 1 using the above formula for covariance.
To know more about the "covariance": https://brainly.com/question/21287720
#SPJ11
Let Y be a binomial random variable with n trials and probability of success given by p. Use the method of moment-generating functions to show that U = n - Y is a binomial random variable with n trials and probability of success given by 1 - p.
U is a binomial random variable with n trials and probability of success given by 1 - p.
As Y is a binomial random variable with n trials and probability of success given by p. Using the moment-generating functions method, it can be shown that U = n - Y is a binomial random variable with n trials and probability of success given by 1 - p. The binomial distribution is described by two parameters: n, which is the number of trials, and p, which is the probability of success in any given trial. If a binomial random variable is denoted by Y, then:[tex]P(Y = k) = \binom{n}{k}p^{k}(1 - p)^{n-k}[/tex]
The method of generating moments can be used to show that U = n - Y is a binomial random variable with n trials and probability of success given by 1 - p. The moment-generating function of a binomial random variable is given by: [tex]M_{y}(t) = [1 - p + pe^{t}]^{n}[/tex]
The moment-generating function for U is: [tex]M_{u}(t) = E(e^{tu}) = E(e^{t(n-y)})[/tex]
Using the definition of moment-generating functions, we can write: [tex]M_{u}(t) = E(e^{t(n-y)})$$$$= \sum_{y=0}^{n} e^{t(n-y)} \binom{n}{y} p^{y} (1-p)^{n-y}[/tex]
Taking the summation of the above expression: [tex]= \sum_{y=0}^{n} e^{tn} e^{-ty} \binom{n}{y} p^{y} (1-p)^{n-y}$$$$= e^{tn} \sum_{y=0}^{n} \binom{n}{y} (pe^{-t})^{y} [(1-p)^{n-y}]^{1}$$$$= e^{tn} (pe^{-t} + 1 - p)^{n}[/tex]
Comparing this expression with the moment-generating function for a binomial random variable, we can say that U is a binomial random variable with n trials and probability of success given by 1 - p.
To learn more about "Binomial random variable": brainly.com/question/30657837
#SPJ11
Rewrite the following expression using the division symbol and as a fraction: The quotient of m and 11.
Answer:
[tex]\frac{m}{11}[/tex]
Step-by-step explanation:
To write the given expression as a fraction, put m in the numerator and 11 in the denominator as shown: [tex]\frac{m}{11}[/tex]
This would be the quotient of m and 11 expressed as a fraction!
#Keep learning
There are 58 students enrolled in an art class. The day before the class begins 10.3% of the students cancel. How many students actually attend the art class
The total number of students which attend the art class is 52 which is 89.75 of the total enrolled students that is 58.
Explain about the percentage of number?A Latin word with the meaning "out of one hundred" is percentage.
Working with parts of 100 is much easier than working with thirds, twelfths, and other fractions, especially since many fractions lack a consistent (non-recurring) decimal equivalent.
Significantly, this also makes comparing percentages more simpler than comparing fractions with various denominators. This contributes to the widespread usage of the metric measuring system and decimal currencies.
Total students enrolled for art class = 58
Percentage of cancelled students = 10.3%
Then, Percentage of non-cancelled students = 100 - 10.3 = 89.7%
So,
Attended students = 89.7% of 58.
= 89.7*58 / 100
= 52.06
= 52 (approx)
Thus, the total number of students which attend the art class is 52 which is 89.75 of the total enrolled students that is 58.
Know more about the percentage of number
https://brainly.com/question/26511030
#SPJ1
Unit 7 polygons and quadrilaterals
Homework 7 trapezoids
** this is a 2-page document **
Directions: if each quadrilateral below is a trapezoid, find the missing measures
The value of ML in the given quadrilateral which is a trapezoid is 58 units.
What is a trapezoid?A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.
Trapezoids are defined differently by different people. A trapezoid can have one and only one pair of parallel sides, according to one school of mathematics, whereas another contends that a trapezoid can have several pairs of parallel sides. If we take into account the second definition, then a parallelogram is also a trapezoid under that definition.
We know that, A median on a trapezoid will be parallel to the bases, with a length equal to the sum of the bases divide by 2.
Thus,
45 = 3x + 11 + 10x - 12 / 2
45 = 13x - 1/ 2
90 = 13x - 1
91 = 13x
x = 7
Substitute the value of x in ML:
ML = 10x - 12
ML = 10(7) - 12
ML = 70 - 12
ML = 58
Hence, the value of ML in the given quadrilateral which is a trapezoid is 58 units.
Learn more about trapezoid here:
https://brainly.com/question/22227061
#SPJ1
A function is shown in the box. What is the value of this function for f(-8)?
(Write the answer as an improper fraction in lowest terms.)
Answer:
f(x) = (5/6)x - (1/4)
f(-8) = (5/6)(-8) - (1/4)
f(-8) = (5/3)(-4) - (1/4)
f(-8) = (-20/3) - (1/4)
f(-8) = (-80-3)/12
f(-8) = -83/12
A hawk flying at 19 m/s at an altitude of 228 m accidentally drops its prey. The parabolic trajectory of the falling prey is described by the equation y = 228 − x^2/57 until it hits the ground, where y is its height above the ground and x is its horizontal distance traveled in meters. Calculate the distance traveled by the prey from the time it is dropped until the time it hits the ground. Express your answer correct to the nearest tenth of a meter.
The parabolic trajectory of the falling prey can be described by the equation y = 228 – x2/57, where y is the height above the ground and x is the horizontal distance traveled in meters. In this case, the prey was dropped at a height of 228 m and flying at 19 m/s. To calculate the total distance traveled by the prey, we can use the equation for the parabola to solve for x.
We can rearrange the equation y = 228 – x2/57 to solve for x, which gives us[tex]x = √(57*(228 – y))[/tex]. When the prey hits the ground, the height (y) is 0. Plugging this into the equation for x, we can calculate that the total distance traveled by the prey is[tex]x = √(57*(228 - 0)) = √(57*228) = 84.9 m.\\[/tex] Expressing this answer to the nearest tenth of a meter gives us the final answer of 84.9 m.
for such more questions on parabolic trajectory
https://brainly.com/question/13244761
#SPJ11
if there are m ways of doing one thing and n ways of doing another, how many ways are there to do both? for example, if a toy comes in m colors and n sizes, how many different toys can there be
The number of ways of doing both things is N = m × n
How to find the number of ways of doing both things?Since there are m ways of doing one thing and n ways of doing another, to find how many ways are there to do both, we proceed as follows.
Since there are m ways of doing one thing and n ways of doing another, to find the number of many ways to do both things,we multiply both numbers together.
So, then number of ways of doing both things is N = m × n
So, there are m × n ways of doing both things
Learn more about number of ways of doing things here:
brainly.com/question/29594894
#SPJ1
Write the definition of each word
1. An acute angle is οne that is less than 90 degrees.
What is an acute angle ?An angle smaller than the right angle is called an acute angle. In οther wοrds, the angle which is less than 90 degrees fοrms an acute angle. The pοlygοns such as triangle, parallelοgram, trapezοid, etc. cοnsist οf at least οne acute angle
2. Obtuse angle: A measurement οf an angle that is greater than 90 degrees but less than 180 degrees.
3. A right angle is οne that is exactly 90 degrees.
4. A straight angle is οne that is exactly 180 degrees in length.
5. Adjacent angles are twο angles that share a cοmmοn vertex and a cοmmοn side.
6. A pair οf nοn-adjacent angles fοrmed by the intersectiοn οf twο lines are knοwn as vertical angles. They are οf equal size.
7. Cοmplementary angles are defined as twο angles that add up tο 90 degrees.
8. Twο angles that add up tο 180 degrees are referred tο as supplementary angles.
9. Angles with the same measure are said tο be cοngruent.
10. A linear pair is twο adjacent angles that fοrm a straight line and add up tο 180 degrees.
To know more about Angle visit:
brainly.com/question/13954458
#SPJ1
x = -3y - 17 2x + 3y = -7
Answer:
x = 10
y = -9
Step-by-step explanation:
x = -3y - 17
2x + 3y = -7
Plug in x
2 (-3y - 17) + 3y = -7
-6y - 34 + 3y = -7
-3y = 27
y = -9
Plug in the value you got for y back into the equation to find the x value
x = -3(-9) - 17
x = 10