Simplify: (64x^5y^9z^8)^3/7
Find the area of the circle with the given radius or diameter. Use = 3.14.
r = 4
A =
50.24 sq. units
100.48 sq. units
25.12 sq. units
Answer:
50.24 square units
Step-by-step explanation:
Hope this helps.
Three cube-shaped boxes are stacked one above the other. The volumes of two of the boxes are 1,331 cubic meters each, and the volume of the third box is 729 cubic meters. What is the height of the stacked boxes in meters?
Answer: The height of the stacked boxes is 31 meters.
Step-by-step explanation:
Since, the Volume of a cube = (side)³
The volume of first box = 1331 cubic meters,
⇒ (side)³ = 1331
⇒
Similarly, the side of second box = 11 meters ( Because, both boxes have the same volume )
Now, the volume of third box = 729 cubic meters
⇒ ⇒ (side)³ = 729
⇒
Thus, the height of the stacked boxes = Side of first box + side of second box + side of third box
= 11 + 11 + 9
= 31 meters.
Zoe is making a quilt using 15 red squares and 30 green squares. Which combination shows the same ratio of red squares to green squares
For how many positive integer values of x is the sum x^2+4x+4 less than 20?
Answer:
2 times
Step-by-step explanation:
Note that since we can only use positive integers for , the minimum will be x = 1. Testing x = 2, we get . Since , we know that only will work, thus, there are positive integer values of such that this function is less than 20.
write a description of the rule (x,y) (x-2,y-7)
The mathematical rule (x,y) to (x-2, y-7) signifies a transformation in the coordinate plane shifting points 2 units to the left and 7 units down. To apply this rule to any point, subtract 2 from the x-coordinate and 7 from the y-coordinate.
Explanation:The rule (x,y) to (x-2,y-7) in Mathematics signifies a specific transformation in a coordinate plane. This is essentially a rule used in graph transformations to shift a point in the coordinate plane. In this specific rule, every point (x, y) is shifted 2 units to the left and 7 units down to get the new point (x-2, y-7). For example, if we take a point, (5,10), applying this rule means we subtract 2 from the x-coordinate and 7 from the y-coordinate resulting in a new point (3,3). Therefore, simplifying this process, to apply the rule (x,y) to (x-2,y-7) to any point, all you need to do is subtract 2 from the x-coordinate and 7 from the y-coordinate of the point.
Learn more about Coordinate Plane Transformations here:https://brainly.com/question/29135202
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Mike deposited $6500 into two saving accounts bearing simple interest. One of the accounts has an interest rate of 3% while the other rate is 6%. If the total interest earned after one year is $225, find the amount deposited into each of the accounts.
Two rockets, A and B, are shot from two different launch pads. The path of rocket A can be represented by the quadratic function A(t) = −(t − 8)2 + 535, where height, A(t), is in meters, and time, t, is in seconds. The path of rocket B is shown below.
This question deals with the physics of projectile motion and rocket trajectories. By analyzing the given equations for acceleration and position over time, we can determine the units of constants and describe the motion of the rockets, emphasizing their parabolic paths.
Explanation:The question at hand involves understanding the motion of two rockets using principles of physics and applying mathematical functions to describe their trajectories. For rocket A, the given quadratic function A(t) = −(t − 8)2 + 535, describes its height as a function of time, indicating a parabolic trajectory, which is typical for projectiles under gravity's influence.
In rocket motion, the acceleration can sometimes be described by an equation of the form a(t) = A - Bt1/2. Here, A and B are constants that determine the rocket's changing acceleration over time. The units of A would be meters per second squared (m/s2), since it represents acceleration, and the units of B would have to be meters per second to the power of five halves (m/s5/2) to ensure the units of time (t) cancel out correctly. When a rocket starts from rest, its velocity changes over time, initially increasing but then possibly decreasing if the acceleration is negative due to the subtraction of the term involving Bt1/2.
If the initial position is set to zero, the rocket's position as a function of time can be found by integrating the velocity function, which is the integral of the acceleration function with respect to time. This integration process accounts for the initial conditions and gives a complete description of the rocket's motion.
In the context of projectile motion, the trajectory is indeed parabolic, represented by the equation y = ax + bx2. To prove this, we use the kinematic equations that separately describe the horizontal and vertical motions (x = Voxt for horizontal and y = Voyt - (1/2)gt2 for vertical motion) and eliminate the time variable to find y as a function of x.
The given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is formed, then use the Law of Sines to solve the triangle, if it is possible, or state that the Law of Sines cannot be used.
B = 137°, c = 9, b = 14
Hector drove 185 miles to a business meeting. His business partner drove 5/4 of this distance to get to the same
meeting. How many miles did the business partner drive?
A student earned 23 out of 30 points on a quiz. What percent of the points did the student earn?
what must be subtracted from 4x4 - 2x3 - 6x2 + x - 5 so that the answer is exactly divisible by x + x - 2
To solve this problem, what we have to do is to divide the whole equation 4 x^4 – 2 x^3 – 6 x^2 + x – 5 with the equation 2 x^2 + x – 1. Whatever remainder we get must be the value that we have to subtract from the main equation 4 x^4 – 2 x^3 – 6 x^2 + x – 5 for it to be exactly divisible by 2 x^2 + x – 1.
By using any method, I used long division we get a remainder of -6.
Therefore we have to subtract -6 from the main equation which results in:
4 x^4 – 2 x^3 – 6 x^2 + x – 5 – (-6) = 4 x^4 – 2 x^3 – 6 x^2 + x + 1
Please help, an explanation would be really helpful too
What is the mean of 82 64 73 91 85
Which is not used to reach a conclusion in a formal proof?
In mathematics especially in verifying certain statements regarding geometry, two column proofs are used. A two-column proof contains a table with a logical series of statements and reasons that reach a conclusion. It is commonly present in geometry. Two column proofs always have two columns: statements and reasons. The other choices don’t fit in the definition of two column proof.
In science, the four ways to incorporate proof into the research paper are:
1. If the research you are investigating has been with other research paper before.
2. There is an experimental proof that the evidence is true.
3. The research published belongs to a reliable source.
4. There are citations of the evidence that you are investigating
Graph the following inequality. Then click to show the correct graph. 3x - 2y ≤ 6
Solution:
The given inequality is :
3 x - 2 y ≤ 6
To draw the graph we will first draw the graph of line : 3 x - 2 y = 6
The graph of this function i.e 3 x - 2 y = 6 will be a straight line.
Then we will check whether origin lies on which side of line .
Put x=0, and y = 0 in the inequality 3 x - 2 y ≤ 6, we obtain
LHS = 0 ≤ 6
It means the line will contain the Origin.
Equation of line in Intercept form is : [tex]\frac{x}{2} -\frac{y}{3}\leq 1[/tex]
given that the two triangles are similar, solve x if AU=20x+108, UB= 273, BC= 703, UV= 444, AV= 372 and AC=589.
A $33$-gon $P_1$ is drawn in the Cartesian plane. The sum of the $x$-coordinates of the $33$ vertices equals $99$. The midpoints of the sides of $P_1$ form a second $33$-gon, $P_2$. Finally, the midpoints of the sides of $P_2$ form a third $33$-gon, $P_3$. Find the sum of the $x$-coordinates of the vertices of $P_3$.
At the fall festival the tennis team is selling hamburgers for $2.00, hotdogs for $1.50, and drinks for $1.00. Half of the money raised will go towards the purchase of team uniforms. If they sell 21 hamburgers, 34 hotdogs, and 65 drinks, how much money will they have to put towards the purchase of uniforms?
What is the standard form of the number shown in this calculator display? The calculator shows three point eight two e positive seven. HURRY ANSWER IMMA FAIL!!! IMMA GIVE 30 POINTS BRUH PLZ AND IF YOU JUST ANSWER IMMA REPORT YOU!!
Answer:38200000 Is the correct answer
Step-by-step explanation:
1.2, 3, 7.5, 18.75, ...
Which formula can be used to describe the sequence?
f(x) = 1.2(2.5)x – 1
f(x) = 2.5(1.2)x – 1
f(x) = 1.2(2.5)x
f(x) = 2.5(1.2)x
It's geometric sequence:
[tex]a_1=1.2,\ a_2=3,\ a_3=7.5,\ a_4=18.75,\ ....[/tex]
Calculate the common ratio:
[tex]r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{3}{1.2}=2.5[/tex]
The explicit formula of geometric sequence:
[tex]a_n=a_1r^{n-1}\to f(x)=a_1r^{x-1}[/tex]
Substitute:
[tex]a_1=1.2,\ r=2.5\\\\f(x)=1.2\left(2.5)^{x-1}[/tex]
Answer: "f(x) = 1.2(2.5)x-1"
Answer:
AStep-by-step explanation:
100% righttt
Janise Smithson invested $4,000 for one year in a CD that earns interest at a rate of 4% compounded monthly. What is the interest earned during the year?
Answer:
$162.97 is the exact answer.
Step-by-step explanation:
Name two fractions that are less than 0.7 ? Plz help
Solve y over negative 6 + 5 = 9. 24 −24 78 −78
[tex] \dfrac{y}{-6}+5=9\ \ \ \ |-5\\\\\dfrac{y}{-6}=4\ \ \ \ |\cdot(-6)\\\\y=-24 [/tex]
If 3 3/4 pounds of candy cost $20.25 how much would 1 pound of candy cost
Determine which system below will produce infinitely many solutions.
−6x + 3y = 18
4x − 3y = 6
2x + 4y = 24
6x + 12y = 36
3x − y = 14
−9x + 3y = −42
5x + 2y = 13
−x + 4y = −6
Answer:
The answer is C
[tex]3x-y=14\\-9x+3y=-42[/tex]
Step-by-step explanation:
In order to determine the system, we have to know the condition to produce infinitely solutions. A solution of a system is the coordinate (x,y) which is common between two lines ( in a 2D plane). A system does not have solution when the lines do not intercept each other, that it means, they are parallele. When two lines are coincident in all points, there are infinitely solutions.
I have attached an image that shows different systems of two lines.
So, to find the system, we have to find two equal equation. If we multiply by 3 the third system:
[tex]3x-y=14\\-9x+3y=-42\\\\(-3)*(3x-y)=(-3)*14\\(1)*(-9x+3y)=(1)*-42\\\\-9x+3y=-42\\-9x+3y=-42[/tex]
This system has infinitely solutions.
From a group of 7 candidates, a committee of 6 people is selected. In how many different ways can the committee be selected?
C(n,r)=C(7,6)
=7!(6!(7−6)!)Final answer:
There are 7 different ways to select a committee of 6 people from a group of 7 candidates, calculated using the combinations formula C(7, 6) = 7! / (6! * (7 - 6)!) = 7.
Explanation:
The question is asking to determine the number of different ways a committee can be selected from a group of candidates, which is a common problem in combinatorics, a branch of mathematics. To find the number of different ways a committee of 6 people can be selected from a group of 7 candidates, you can use combinations. Since the order in which the committee is chosen does not matter, you calculate combinations and not permutations. The formula for combinations is:
C(n, k) = n! / (k! * (n - k)!)
Applying the formula:
C(7, 6) = 7! / (6! * (7 - 6)!) = 7 / 1 = 7
Therefore, there are 7 different ways to select a committee of 6 people from a group of 7 candidates.
An image point after a 180° rotation is Z'(3, 7). What were the coordinates of the pre-image point?
Z(-3, -7)
Z(7, 3)
Z(-7, -3)
Z(7, -3)
A ball is thrown vertically upward from the top of a 100-foot tower, with an initial velocity of 20 ft/sec. Its position function is s(t) = –16t2 + 20t + 100. What is its velocity in ft/sec when t = 1 second? (This is Calculus, involving limits, please help and explain, because I mostly just need to know how to do this. :) )
Final answer:
The velocity of the ball at t = 1 second is found by taking the derivative of the position function s(t) and evaluating it at t = 1. The derived velocity function is v(t) = -32t + 20, and the velocity at t = 1 second is 8 ft/sec.
Explanation:
The student wants to find the velocity of a ball at t = 1 second when thrown vertically upward from the top of a 100-foot tower with an initial velocity of 20 ft/sec. The position function given is [tex]s(t) = -16t^2 + 20t + 100[/tex]. To find velocity, we need to take the derivative of the position function with respect to time, which represents the velocity function v(t).
The derivative of the position function is:
v(t) = −32t + 20.
To find the velocity at t = 1 second, substitute 1 for t:
v(1) = −32×1 + 20 = −12 + 20 = 8 ft/sec.
Therefore, the velocity of the ball at t = 1 second is 8 ft/sec.
what are all the exact solutions of 2sec^2x-tan^4x=-1 ?
Answer:
A
Step-by-step explanation:
on Edge
To find the exact solutions of the given equation 2sec^2x-tan^4x=-1, we can simplify the equation using trigonometric identities and solve for tanx. The solutions are x = pi/3 + n*pi for tanx = sqrt(3), and x = -pi/4 + n*pi for tanx = -1.
Explanation:The given equation is 2sec^2x-tan^4x=-1. To solve this equation, we need to simplify the trigonometric terms using known identities. The identity sec^2x = 1 + tan^2x can be used here. Substituting this identity into the equation gives us 2(1 + tan^2x) - tan^4x = -1. Simplifying further, we have 2 + 2tan^2x - tan^4x = -1. Rearranging the terms, we get tan^4x - 2tan^2x - 3 = 0.
Now, let's substitute tan^2x with u, giving us the equation u^2 - 2u - 3 = 0. This is a quadratic equation that can be factored as (u - 3)(u + 1) = 0. Solving for u, we have u = 3 or u = -1. Substituting back tan^2x for u, we get tan^2x = 3 or tan^2x = -1. Taking the square root of both sides, we have tanx = sqrt(3) or tanx = -1.
Finally, to find the exact solutions of x, we need to consider the periodic nature of trigonometric functions. Since tanx repeats every pi radians, the solutions are x = pi/3 + n*pi, where n is an integer, for tanx = sqrt(3), and x = -pi/4 + n*pi, for tanx = -1.