A rock is thrown in the air from the edge of a seaside cliff. Its height in feet is represented by f(x) = –16(x2 – 3x – 18), where x is the number of seconds since the rock was thrown. The height of the rock is 0 feet when it hits the water.How long does it take the rock to hit the water? How many seconds?
The time it takes the rock to hit the water is 6 seconds
Data;
f(x) = -16(x^2 - 3x -18)Time it takes for the rock to hit the ground?To find the time it takes for the rock to hit the ground, we have to use the and assume that the given equation represents the height at which the rock attained.
[tex]f(x) = -16(x^2 - 3x -18)\\0 = -16x^2 + 48x + 288\\16x^2 - 48x - 288 = 0\\x^2 - 3x - 18 = 0[/tex]
Solving the above quadratic equation,
x = - 3 or x = + 6
The time it takes the rock to hit the water is 6 seconds
Learn more on time of flight here;
https://brainly.com/question/1088602
Solve to the equation for y
4x+2y=6
There are 4 seats available at a table in the lunch room of an elementary school, and 12 students are looking for seats. In how many ways can the seats at the table be filled with 4 of these 12 students?
Answer with explanation:
Total number of vacant seats = 4 seat
Number of students Looking for Seats = 12 Student
We have to fill the four Seats and there are 12 students.
First Seat can be filled in 12 ways,11 students are left,So, second seat can be filled in 11 ways ,Now,there are 10 students left ,So, third seat can be filled in 10 ways,Now there are 9 students left,so last seat can be filled in 9 ways.
Total number of ways of filling 4 seats if there are 12 number of students
=12 × 11 × 10 × 9
=132 × 90
= 11880 ways
Or ,you can solve it directly by the concept of Permutation.
Total ways of filling 4 vacant seats if there are 12 students in all
[tex]= _{4}^{12}\textrm{P}=\frac{12!}{(12-4)!}=\frac{12\times 11\times 10\times 9\times 8!}{8!}=12\times 11\times 10\times 9=11880[/tex]
3y-5z=-23
4x+2y+3z=7
-2x-y-z=-3
Solve for each variable, please show work if possible!
explain how you can compare the cost of two items that are different sizes
Answer:
First find the unit price for each. Then compare the unit prices. The item that has the lesser unit cost is the better buy.
Step-by-step explanation:
When comparing the costs of two items that are different sizes, use ratios to make a comparison and consider the unit size.
Explanation:When comparing the costs of two items that are different sizes, you can use ratios to make a comparison. Let's say Item A costs $10 and Item B costs $20. Item A is twice as expensive as Item B. To make the comparison fair, you can also consider the size or quantity of the items. For example, if Item A is twice as expensive but also twice as large as Item B, then the cost per unit size is the same. However, if Item A is half the size of Item B, then Item B is a better deal in terms of size.
If the marginal propensity to consume is 0.8, (a) what is the value of the multiplier?
LeAnn wants to gift wrap a present she got for her little brother. How many square inches of gift wrap will be needed to cover a box that is 4in x 6in x 2in?
A weather forecaster predicts that the temperature in antarctica will decrease 8 degreesf each hour for the next 6 hours how long will it take to go down 36 degrees
Eliza Savage received a statement from her bank showing a checking account balance of $324.18 as of January 18. Her own checkbook shows a balance of $487.38 as of January 29. The bank returned all of the cancelled checks but three. The amounts of these three checks are $15.00, $77.49, and $124.28. How much did Eliza deposit in her account between January 18 and January 29?
A. $197.24 B. $379.97 C. $54.44 D. $201.12
Answer:
b
Step-by-step explanation:
Solve for x.
13(x - 3) = 39
x = 1
x = 4
x = 6
x = 10
How do you solve -3x+d=-9
4.Thirty percent of the liquid evaporated. If 560 milliliters remain, how many milliliters evaporated?
PLEASE HELP ME AND SHOW WORK
Write the polynomial in standard form, then identify its leading coefficient and constant term.
6x^2+2x+11x^3
Standard form: 11x^3+6x^2+2x, can you just show the work for this?
Leading coefficient: 11
Constant term: please show me how to find this
Which linear inequality is represented by the graph
Option B is correct, y≤1/3x-4 is the linear inequality which is represented by the graph
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The equation of line passing through points (3, -3) and (0, -4)
Slope = -4+3/0-3
=1/3
Now let us find y intercept
-4=1/3(0)+b
b=-4
Equation is y=1/3x-4
y≤1/3x-4 is the required inequality of the graph
Hence, y≤1/3x-4 is the linear inequality which is represented by the graph
To learn more on slope of line click:
https://brainly.com/question/16180119
#SPJ7
What is the surface to a rectangular playing surface with 44 feet and 77 feet?
James borrows $300 at an interest rate of 8% and takes 5 years to pay it off. How much does he pay? Question 2 options: $420 $120 $240 $600
In the measurement 0.503 l, which digit is the estimated digit? the 0 immediately to the left of the 3 5 the 0 to the left of the decimal point 3
Answer:
3.
Step-by-step explanation:
We are asked to find the estimated digit in the measurement 0.503 L.
We know that in each measurement the estimated digit is always the last digit.
We can see that the first digit in the given measurement is 5, the second digit is 0 and the last digit is 3.
Since the last digit is in our given measurement 3, therefore, the estimated digit is 3.
) compute $x+y$ and $\sqrt{x^2+y^2}$ when $x=5$ and $y=12.$
b.when is \[x+y=\sqrt{x^2+y^2}?\]when is
The domain for f(x) and g(x) is the set of all real numbers. Let f(x) = 3x + 8 and g(x) = x2. Find (f • g)(x).
A. x2 − 3x − 8
B. 3x2 + 8
C. 3x3 + 3x2 + 8
D. 3x3 + 8x2
In how many ways can you place 8 rooks on a 8x8 chessboard so that no row or column contains more than one rook if
82=6482=64choices for that.
Now, for the second one, we can't be in the row or column of that first one, so leaving us with 72=4972=49 choices.
Then so on, we have 62=3662=36 for the third one, 2525 for the fourth one, and so on ……
But, however, we have to remember the rooks are not labeled, thus it doesn't matter specifically about a specific rook's position.
Thus, we have a total of (8!)28!=40320(8!)28!=40320 ways.
What is the best answer???
What method can be used to write the equation of a line in slope-intercept form given two points?
To write the equation of a line in slope-intercept form given two points, calculate the slope from the points, use one point and the slope to find the y-intercept, then write the equation as y = mx + b.
Explanation:To write the equation of a line in slope-intercept form, given two points, follow these steps:
Calculate the slope (m) using the formula m = (Y2 - Y1) / (X2 - X1), where (X1, Y1) and (X2, Y2) are the coordinates of the two given points.Once you have the slope, choose one of the two points to substitute into the slope-intercept form equation, y = mx + b, along with the slope you calculated. This will allow you to solve for the y-intercept (b).With both the slope and y-intercept, you can write the final equation of the line: y = mx + b.For example, if the two points given are (1, 3) and (4, 11), the slope would be (11 - 3) / (4 - 1) = 8 / 3. Then choosing the point (1, 3), we would substitute to find the y-intercept: 3 = (8/3)(1) + b, resulting in b = 3 - 8/3 = 1/3. So the equation of the line is y = (8/3)x + 1/3.
5/6 is equivalent to a percent that is larger than 100%. True False
What is the center point of a data set when all of the values are listed in order?
the mean
the median
the mode
the range
log(w^2+21)=log(10w)
[tex]\[ w = 7 \][/tex]
Explanation:The given equation is [tex]\(\log(w^2+21)=\log(10w)\)[/tex]. To find the solution, we can set the arguments of the logarithms equal to each other, giving [tex]\(w^2 + 21 = 10w\)[/tex].
Rearranging, we get a quadratic equation [tex]\(w^2 - 10w + 21 = 0\).[/tex] Factoring or using the quadratic formula yields the solutions
However, we need to check for extraneous solutions. Substituting [tex]\(w = 3\)[/tex] back into the original equation results in taking the logarithm of a negative number, which is undefined in the real number system. Therefore, [tex]\(w = 3\)[/tex] is extraneous, and the valid solution is [tex]\(w = 7\).[/tex]
In the detailed explanation, we used the property of logarithms that states [tex]\(\log(a) = \log(b)\)[/tex] implies [tex]\(a = b\)[/tex]. By setting the arguments of the logarithms equal to each other, we obtained a quadratic equation.
Factoring or applying the quadratic formula allowed us to find the solutions. However, we must always check for extraneous solutions by substituting them back into the original equation and ensuring the logarithms are defined for the real number system.
In this case, only [tex]\(w = 7\)[/tex] satisfies the equation without resulting in undefined logarithms.
m is the set of integers that are greater than -1 and less than 4
Which statement is true about this argument?
Premises:
If a parallelogram has a right angle, then it is a rectangle.
Parallelogram PQRS has a right angle.
Conclusion:
Parallelogram PQRS is a rectangle.
The argument is not valid because the conclusion does not follow from the premises.
The argument is valid by the law of syllogism.
The argument is not valid because the premises are not true.
The argument is valid by the law of detachment.
The argument is valid by the law of detachment.
Answer:
The argument is valid by the law of detachment.
Step-by-step explanation:
We first verify that the first statement, "if p, then q" is correct. If a parallelogram has a right angle, this means that the angle opposite that angle must also be right; this is because the opposite angles of a parallelogram are congruent.
This also means that the adjacent angle to this right angle must also be right; this is because the adjacent angles in a parallelogram are supplementary.
Thus "if p, then q" is true.
The law of detachment states that if I have two statements, one of the form "if p, then q" and the other "p", then the conclusion, "q," is valid.
A rectangle has an area of 126 m2 and a width of 7 m. What is its length?
Find the maximum rate of change of f(xy)=ln(x2+y2) at the point (-1, -5) and the direction in which it occurs.
Rank and alice are penguins. at birth, frank's beak was 1.95 inches long, while alice's was 1.50 inches long. homework help ✎ frank's beak grows by 0.25 inches per year and alice's grows by 0.40 inches per year. write an equation to represent the length of each penguin's beak in x years. how old will they be when their beaks are the same length?