The binomial expansion 625x4 – 7,500x3 + 33,750x2 – 67,500x + 50,625 can be expressed as (ax + b)4. What is the value of b?
A. –15
B. –5
C. 5
D. 15
Answers
Answer:
Step-by-step explanation:
The value of b according to the binomial expansion expressed in the form, (ax + b)⁴ is; b = 15.
The binomial expansion given is;
625x4 – 7,500x3 + 33,750x2 – 67,500x + 50,625.
While expressing the binomial expansion in the form; (ax + b)⁴;
The value of b can be evaluated as follows;
b⁴ = 50,625In essence, the quartic root of 50625 is the value of b as follows;
\(b = \sqrt[4]{50625} \)
b = 15. OR. b = -15
However, more convincingly, the value of b is; Choice D: 15
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An object was launched off the top of a building. The function f(x)=-16x^2+16x+672 represents the height of the object above the ground, in feet, x seconds after being launched. Find and interpret the given function values and determine an appropriate domain for the function.
Answers
Answer:
6x2 + 16x = 672
Reorder the terms:
16x + 16x2 = 672
Solving
16x + 16x2 = 672
Solving for variable 'x'.
Reorder the terms:
-672 + 16x + 16x2 = 672 + -672
Combine like terms: 672 + -672 = 0
-672 + 16x + 16x2 = 0
Factor out the Greatest Common Factor (GCF), '16'.
16(-42 + x + x2) = 0
Factor a trinomial.
16((-7 + -1x)(6 + -1x)) = 0
Ignore the factor 16.
Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:
Simplifying
-7 + -1x = 0
Solving
-7 + -1x = 0
Move all terms containing x to the left, all other terms to the right.
Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7
Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7
Combine like terms: 0 + 7 = 7
-1x = 7
Divide each side by '-1'.
x = -7
Simplifying
x = -7
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:
Simplifying
6 + -1x = 0
Solving
6 + -1x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6
Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6
Combine like terms: 0 + -6 = -6
-1x = -6
Divide each side by '-1'.
x = 6
Simplifying
x = 6
Solution
x = {-7, 6}
Step-by-step explanation:
The given quadratic function models the projectile of the object as it is
launched off the top of the building.
The interpretation of the function values are;
The maximum height reached by the object is 676 feetThe height of the building is 672 feetTime of flight of the object is 7 secondsThe appropriate domain is 0 ≤ x ≤ 7
Reasons:
The given function for the height of the object is f(x) = -16·x² + 16·x + 672
The domain is given by the values of x for which the value of y ≥ 0
Therefore, when -16·x² + 16·x + 672 = 0, we get;
-16·x² + 16·x + 672 = 0
16·(-x² + x + 42) = 0
-x² + x + 42 = 0
x² - x - 42 = 0
(x - 7)·(x + 6) = 0
x = 7, or x = -6
The minimum value of time, x is 0, which is the x-value at the top of the
building, and when x = 7, the object is on the ground.
Therefore;
The appropriate domain is 0 ≤ x ≤ 7The maximum value of f(x) = a·x² + b·x + c, is given at \(x = -\dfrac{b}{2 \cdot a}\)
Therefore;
We have;
\(x = -\dfrac{16}{2 \times (-16)} = \dfrac{1}{2}\)
Which gives;
\(f \left(\frac{1}{2} \right) = -16 \times \left(\dfrac{1}{2} \right)^2 + 16 \times \left(\dfrac{1}{2} \right)+ 672 = 676\)
The maximum height reached by the object, \(f\left(\frac{1}{2} \right)\) = 676 feetThe height of the building is given when the time, x = 0, as follows;
Height of building, f(0) = -16 × 0² + 16 × 0 + 672 = 672
The height of the building, f(0) = 672 feetLearn more here;
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Members of some species will sound warning calls when they notice predators even though this increases the likelihood the predator will find the individual that provided the alarm. The evolution of such behaviors provides evidence for which hypothesis
Answers
The evolution of warning calls by some species, despite increasing the risk to the individual providing the alarm, provides evidence for the "kin selection" hypothesis.
The behavior of sounding warning calls, despite the potential risk it poses to the individual, can be understood through the concept of kin selection. According to this hypothesis, individuals are more likely to engage in behaviors that benefit their genetic relatives, even if it comes at a cost to themselves. By sounding the alarm, the individual may attract the predator's attention, increasing their own risk of predation.
However, this behavior benefits their relatives who share similar genes, as they have a higher chance of surviving the predator's attack. Over time, this selfless behavior can be favored by natural selection, as it promotes the survival and reproductive success of genetically related individuals. Thus, the evolution of warning calls despite the increased risk supports the kin selection hypothesis.
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If the velocity of an orbiting body were increased, its orbital path would change
into a parabola or hyperbola. If this were to happen, what would happen to the
object and its gravitational pull of the Sun?
Answers
The gravitational pull of the Sun on the object would decrease as the distance between them increased.
What is the gravitational pull?If the velocity of an orbiting body were increased, its orbital path would change from an elliptical orbit to a parabolic or hyperbolic orbit, depending on the extent of the increase in velocity.
The amount of gravitational pull on the object would decrease as the distance between the object and the Sun increased. This is because gravitational force decreases with distance according to the inverse-square law.
In summary, if the velocity of an orbiting body were increased to the point where its orbital path changed into a parabolic or hyperbolic orbit, the object would eventually escape the Sun's gravitational pull and move away from it in a straight line.
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Find the slope of the line between the two points.
Answers
The slope of the line between the two points is - 2 / 3.
How to find the slope of a line?The slope of a line is the change in y coordinate with respect to the change in x coordinate.
The slope of a line is rise over run.
The slope of a line can be express as follows:
slope = y₂ - y₁ / x₂ - x₁
using two coordinates (3, 1)(0, 3)
where
x₁ = 3
x₂ = 0
y₁ = 1
y₂ = 3
Therefore,
slope = 3 - 1 / 0 - 3
slope = 2 / -3
slope = - 2 /3
Therefore, the slope of the line is - 2 / 3.
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-3(3-10x) could you answer it quickly for me? please and thank you
It's distribute property.
Answers
Answer:
-9+30x
Step-by-step explanation:
-3 x 3 is -9
-3 x -10x is 30x
Answer:
-9 + 30x
Step-by-step explanation:
Like you mentioned, to solve this expression we need to use the distributive property...
We have to distribute -3 to 3 and -10x.
When multiplying negative and positive numbers it is important to know that...
-negative times negative equal positive
-negative times positive equal negative
-3 · 3 = -9
-3 · -10x = 30x
Therefore the answer is -9 + 30x
Hope this helps! Let me know if you have any further questions :D
The probability that a marksman will hit a target each time he shoots is 0. 89. If he fires 15 times, what is the probability that he hits the target at most 13 times?.
Answers
The probability that marksman will hits the target at most 13 times is 27.92%.
Explain the term binomial distribution?Let X be the quantity of times that target is hit and be a random variable. 15 rounds are fired, hence the number of trials ("n") is equal to 10 as a result. In a binomial distribution, "p" denotes the likelihood of success, and "q" is the likelihood of failure (where q = 1 - p). Since there is a 0.89 chance of striking the target, p = 0.89 and q = 0.11.The number of successes ("x") is the probability mass function for such binomial distribution.
P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ
We are interested in the likelihood that the target will be struck exactly five times, therefore the desired number of successes is five (i.e., x = 13).
P(X = 13) = ¹⁵C₁₃. (0.89)¹³ (0.11)²
P(X = 13) = 0.2792
P(X = 13) = 27.92%
Thus, the probability that marksman will hits the target at most 13 times is 27.92%.
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If the parent function f(x) =|x| is transformed to h(x)=|x|+2 what transformation occurs from f(x) to h(x)? How are the vertex and range of u(x) affected?
Answers
The transformation is shift 2 units up
This will add 2 to each y output in the range.
The old range was \(\text{y} \ge 0\) and it updates to \(\text{y} \ge 2\)
The graph is shown below. I used GeoGebra, but Desmos is another good option.
que es la radicasion
Answers
Answer:
un lugar, típicamente uno que ha estado previamente deshabitado, donde la gente establece una comunidad.
The midpoint of CD is M=(2, -1). One endpoint is C=(-3,-3). Find the coordinates of the other endpoint, D. D (?, ?) M (2,-1) C (-3,-3) D = (-7, -1) Find an ordered pair (x, y) that is a solution to the equation. -x+5y=2
Answers
The ordered pair (x, y) that is a solution to the equation -x + 5y = 2 is (0, 2/5).
To find the coordinates of the other endpoint D given that the midpoint of CD is M(2, -1) and one endpoint is C(-3, -3), we can use the midpoint formula:
Midpoint formula:
The coordinates of the midpoint between two points (x₁, y₁) and (x₂, y₂) are given by ((x₁ + x₂) / 2, (y₁ + y₂) / 2).
Using the given information, we can substitute the known values into the midpoint formula and solve for the coordinates of D:
M(2, -1) = ((-3 + x₂) / 2, (-3 + y₂) / 2)
Simplifying the equation:
2 = (-3 + x₂) / 2
-1 = (-3 + y₂) / 2
To solve for x₂:
4 = -3 + x₂
x₂ = -3 + 4
x₂ = 1
To solve for y₂:
-2 = -3 + y₂
y₂ = -3 - 2
y₂ = -5
Therefore, the coordinates of the other endpoint D are D(1, -5).
To find an ordered pair (x, y) that is a solution to the equation -x + 5y = 2, we can choose any value for either x or y and solve for the other variable. Let's choose x = 0:
-0 + 5y = 2
5y = 2
y = 2/5
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PLEASE HELP ME I WILL MARK BRAINLIEST (ITS DUE IN A HOUR)
Answers
its b/13=5 and then to solve you multiply both sides by 13 to get b=65
so 65 bean bags
A store receives `12` boxes that contain many different numbers of lemons. They weigh each box and then count the lemons. The data is in the scatter plot. A new box weighs `30` pounds. Approximately how many lemons are in the box?
answer - UR MOTHERRRRR
Answers
Answer:
12*30 is the answer
if u multiply it
Determine which of the lines,if any are parallel. Explain
Answers
For line a:
Take two points on the line…
(x1,y1) => (0,3)
(x2,y2) => (-3,1)
m=(1-3)/(-3-0) = 2/3
For line b:
Take two points on the line…
(x1,y1) => (3,2)
(x2,y2) => (0,0)
m=(0-2)/(0-3) =2/3
For line c:
Take two points on the line…
(x1,y1) => (3,0)
(x2,y2) => (-2,-3)
m=(-3-0)/(-2-3) =3/5
Based off the information above, only lines a and b are parallel.
Help me please!!! !!!
Answers
To solve this problem, we need to calculate the volume of water in Container A, the volume of Container B, and subtract the volume of water from Container B from the volume of Container A.
The volume of water in Container A can be found using the formula for the volume of a cylinder:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
For Container A, we have:
V(A) = π(6^2)(15)
V(A) = 1,620π
The volume of Container B can be found using the same formula:
V(B) = π(7^2)(8)
V(B) = 1,232π
After pumping the water from Container A into Container B, Container B is completely full, which means its volume is equal to the volume of the water from Container A.
So, the volume of water in Container A is:
V(water) = V(B)
V(water) = 1,232π
To find the volume of the empty space inside Container A, we need to subtract the volume of water in Container A from the total volume of Container A:
V(empty space) = V(A) - V(water)
V(empty space) = 1,620π - 1,232π
V(empty space) = 388π
V(empty space) ≈ 1,219.8 cubic feet
Therefore, the volume of the empty space inside Container A is approximately 1,219.8 cubic feet (rounded to the nearest tenth of a cubic foot).
Hope you understood it...
Label the net for the cylinder. Then find the surface area of the cylinder. Give your answer in terms of π and as a decimal number rounded to the nearest tenth.
Answers
The surface area of the cylinder is approximately 94.2 ft².
What is surface area?Surface area refers to the total area of the external or outer part of an object. It is the sum of the areas of all the individual surfaces or faces of the object. Surface area is typically measured in square units, such as square inches (in²), square feet (ft²), or square meters (m²), depending on the unit of measurement used.
According to the given information:
The surface area of a cylinder is the sum of the lateral surface area (the curved surface) and the area of the two circular bases.
The formula for the lateral surface area of a cylinder is given:
Lateral Surface Area = 2πrh
where r is the radius of the cylinder and h is the height of the cylinder.
Plugging in the given values for the radius (r = 3 ft) and height (h = 2 ft), we can calculate the lateral surface area:
Lateral Surface Area = 2π * 3 * 2 = 12π ft²
The formula for the area of a circle (which represents the bases of the cylinder) is given:
Circle Area = πr²
Plugging in the given value for the radius (r = 3 ft), we can calculate the area of each circular base:
Circle Area = π * 3² = 9π ft²
Since there are two bases in a cylinder, we multiply this by 2 to account for both bases:
2 * Circle Area = 2 * 9π = 18π ft²
Now, we can add the lateral surface area and the area of the two bases to find the total surface area of the cylinder:
Total Surface Area = Lateral Surface Area + 2 * Circle Area
= 12π + 18π
= 30π ft²
As a decimal rounded to the nearest tenth, the surface area of the cylinder is approximately 94.2 ft²
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Simplify the following Boolean function using Boolean Algebra rule. F = xy'z' + xy'z + w'xy + w'x'y' + w'xy
Answers
When the above is simplified using Boolean Algebra, we have F = x' + y' + w'xy.
What is the explanation for the above ?
We can simplify the Boolean function F = xy'z' + xy'z+ w'xy + w'x'y' + w'xy using the following Boolean Algebra rules.
Absorption - x + xy = x
Commutativity - xy = yx
Associativity - x(yz) = (xy)z
Distributivity - x(y + z) = xy + xz
Using the above , we have
F = xy'z' + xy'z+ w'xy + w'x'y' + w'xy
= xy'(z + z') + w'xy(x + x')
= xy' + w'xy
= (x' + y)(x' + y') + w'xy
= x' + y' + w'xy
This means that the simplified expression is F = x' + y' + w'xy.
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Find the discounted price of each item.
prescription glasses: $149
discount: 20%
Answers
Answer:
$119.2
Step-by-step explanation:
Answer:
119.2
Step-by-step explanation:
149 x 0.2 = 29.8
Then 149 - 29.8 = 199.2
Please answer this question now
Answers
Answer:
39°Step-by-step explanation:
A radius to the tangent point always forms a right angle with the tangent:
m∠XWY = 90°
So:
90° + 58° + x - 7° = 180°
141° + x = 180°
x = 39°
What is the evidence that the energy of the spring is higher when you stretch or compress it?
Answers
Answer: When a spring is compressed or stretched, it will try to restore its equilibrium position by exerting a force equal and opposite to the external force. So the external work done by us in compression as well as stretching will store in the spring as potential energy
Answer: Energy of the spring is equal when compressed as when stretched.
Step-by-step explanation: Potential Energy (PE) of the spring is highest at both compression and when stretched. During this time, the Kinetic Energy (KE) is zero. When the spring is at rest, KE is highest and PE is zero.
The graph shows the distance a car traveled, y, in x hours: A coordinate plane graph is shown. The x-axis is labeled time in hours, and the y-axis is labeled distance in miles. The line passes through the points 1 comma 35, 2 comma 70, and 3 comma 105. What is the rise-over-run value for the relationship represented in the graph? (4 points)
Answers
SOLUTION
From the graph,
\(\begin{gathered} \text{Rise}=\text{Distance(mi)}=y-\text{values} \\ \text{Run}=\text{Time(hr)}=x-\text{values} \end{gathered}\)To obtain the rise-over-run value, we will pick any two points on the graph and solve for the slope.
\(\begin{gathered} (x_1,y_1)=(1,35) \\ (x_2,y_2)=(2,70) \end{gathered}\)The formula for the slope(m) between two points is,
\(m=\frac{y_2-y_1}{x_2-x_1}\)Therefore,
\(\begin{gathered} m=\frac{70-35}{2-1}=\frac{35}{1}=35 \\ \therefore m=35 \end{gathered}\)Hence, the rise-over-run value is 35 (OPTION 3).
Simplify and write your answer in the form a+bi.
10/1+2i (this is a fraction)
Answers:
A. 10-20i/5
B. 2-4i
C. 1-2i
D. 10+5i
Answers
\(\dfrac{10}{1+2i}\\\\\\=\dfrac{10(1-2i)}{(1+2i)(1-2i)}\\\\\\=\dfrac{10-20i}{1 - (2i)^2}\\\\\\=\dfrac{10-20i}{1+4}~~~~~;[i^2 =-1]\\\\\\=\dfrac{10-20i}5\\\\=\dfrac{10}5 - \dfrac{20i}5\\\\=2-4i\)
Can someone help me on this question? The question is down below...
Answers
Answer:12m
Step-by-step explanation:
Because you are given that this is a right angled triangle, you can apply the pythagoras theorem where a^2 = b^2 + c^2
15^2 = 9^2 + x^2
225-81 = x^2
144 = x^2
x = 12m
Quadrilateral XENA is a parallelogram. T is the point of intersection of the diagonals. For each situation, write an equation and solve for y.
Answers
Answer:
b
Step-by-step explanation:
just took the test yyyyyyyyyyyyyyyyyyyyyyyyy
can u just tell me where to put it instead of pics cause i cant see pics like 4 and 3 up sum like that please
Answers
Answer:
(1.5, 0)
(0, 1)
Add a point in the graph where 1 is (plot it in the line that is vertical) then from that point go down 2 and to the right 3 then just continue doing that
Explanation:
Hope this helped if u have any questions feel free to ask :)
Please help me on 22 and 28 please. Thank you.
Answers
Answer:
Step-by-step explanation:
T/F : Regression analysis uses all data points, not just the highest and lowest volume data points.
Answers
True. Regression analysis involves analyzing the relationship between two variables, typically by using all available data points.
Ignoring certain data points, such as the highest and lowest volume data points, can skew the results and lead to inaccurate conclusions. Therefore, it is important to use all available data points in regression analysis to ensure that the relationship between the variables is accurately represented.
True: Regression analysis uses all data points, not just the highest and lowest volume data points. It is a statistical method for analyzing the relationship between a dependent variable and one or more independent variables. By including all data points, regression analysis can identify patterns and trends, providing a more accurate representation of the data. This allows for better predictions and insights into the relationships between variables. Excluding some data points, such as only using the highest and lowest volume data points, would limit the analysis and potentially lead to inaccurate results.
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The time constant of RC circuit is the time in which the current decreases to _____ of its initia value
a. 1/10
b. ½
c. 1/√2
d. 1/╥
e. 1/e
Answers
The correct solution to this problem is option e. 1/e. We can find it in the following manner.
The time constant of an RC circuit is the time in which the current decreases to 1/e (approximately 0.368) of its initial value.
This can be derived from the equation for the current in an RC circuit:
\(I=10 * e^({-t/RC} )\)
where I is current at time t, I0 is the initial current, R is the resistance, C is the capacitance, and e is the mathematical constant approximately equal to 2.71828.
To find the time constant, we set the exponent to -1:
\(e^({-t/RC} ) = 1 /e\)
Solving for t/RC, we get:
t/RC = 1
Therefore, the time constant is equal to RC, and the current decreases to 1/e of its initial value in one time constant.
So the answer is e. 1/e.
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what are the coordinates of a’?
Answers
Answer:
(1,3)
Step-by-step explanation:
You are at (-3,5). Ordered pairs are written (x,y) The x tells you how far right or left you are from the origin (0,0) and the y tells you how high above or below You are from the origin (0,0).
(-3+ 4,5 -2) We are 3 unit to the right of (0,0) to begin with and the directions tell us to go 4 more units right. We will now be 1 units to the right of zero. We started at 5 units above zero, the directions tells us to move two units down. That would be at 3.
So, our new order pair will be (1.3)
PLZ HELP im am stupid
Answers
Answer:
x = 17
Step-by-step explanation:
The two indicated angles are corresponding and congruent, thus
11x - 31 = 8x + 20 ( subtract 8x from both sides )
3x - 31 = 20 ( add 31 to both sides )
3x = 51 ( divide both sides by 3 )
x = 17
Answer:
the answer is number 4 17
Step-by-step explanation:
Jaxon must sell at least 49 rolls of wrapping paper to support the robotics club fundraiser. He has already sold 24 rolls of wrapping paper. Which inequality best represents the number of rolls of wrapping paper Jaxon still needs to sell?
A. x + 24 > 49
B. x + 24 ≤ 49
C. x + 24 < 49
D. x + 24 ≥ 49
Answers
Answer:
D. x + 24 ≥ 49
Step-by-step explanation:
He has already sold 24 rolls, and will sell more x.
So, the total number of rolls that he will sell is:
\(T = 24 + x\)
Jaxon must sell at least 49 rolls of wrapping paper to support the robotics club fundraiser.
This means that:
\(T \geq 49\)
\(24 + x \geq 49\)
The correct answer is given by option D.
How many square units are in a feet?
Answers
According to different units 1 sqaure foot value will be change like
1 square foot (ft²) = 0.09290304 square meters (m²)
What is square foot let's understand?
The square foot is an area measurement unit that is used in both the United States and the United Kingdom. It is also used in Bangladesh, India, Nepal, Pakistan, Ghana, Liberia, Malaysia, Myanmar, Singapore, and Hong Kong to a lesser extent. It is described as the surface of a square with 1-foot sides.
1 square foot (ft²) = 0.09290304 square meters (m²)
1 square foot (ft²) = 144.0000002229 square inches (in²)
1 square foot (ft²) = 0.111111106982 square yards (yd²)
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