Find the area of the rectangle below (3x-2) (4x-7)
Which represents a quadratic functionWhich represents a quadratic function? f(x) = 2x3 + 2x2 – 4 f(x) = –7x2 – x + 2 f(x) = –3x + 2 f(x) = 0x2 + 3x – 3
Answer:
[tex]f(x) = -7x^2 -x +2[/tex] represents a quadratic function.
Step-by-step explanation:
A polynomial of degree two is called quadratic function,
Also, degree of polynomial is the highest power of its monomial ( individual term with non zero coefficient ),
Since, [tex]f(x) = 2x^3 + 2x^2 -4[/tex] has degree 3,
⇒ [tex]f(x) = 2x^3 + 2x^2 -4[/tex] is not a quadratic function,
[tex]f(x) = -7x^2 -x +2[/tex] has degree 2,
⇒ [tex]f(x) = -7x^2 -x +2[/tex] is a quadratic function,
[tex]f(x) = -3x+2[/tex] has degree 1,
⇒ [tex]f(x) = -3x+2[/tex] is not a quadratic function,
[tex]f(x) = 0x^2 + 3x -3[/tex] has degree 1,
⇒ [tex]f(x) = 0x^2 + 3x -3[/tex] is not a quadratic function,
I am first going to try finding the tangent line at this point:
Take the derivative:
dy/dx = (3x^2 - e^x)/2y
Solve using (0, 1)
dy/dx = (0 - 1)/6 = -1/6
I believe that -1/6 is the slope of the tangent line, so the slope of the normal line should be +6, right?
If BY = 4, YC = 7, XC = 10. Which of the following proportions could be used to solve for AC?
4/7 = 10/AC
7/4 = 10/AC
4/11 = 10/AC
7/11 = 10/AC
Answer:
The correct option is 4.
Step-by-step explanation:
In triangle ABC and XYC,
[tex]\angle BAC=\angle YXC=60^{\circ}[/tex] (Given)
[tex]\angle BCA=\angle YCX[/tex] (Reflexive Property)
By AA rule of similarity,
[tex]\triangle ABC\sim \triangle XYC[/tex]
The corresponding sides of similar triangles are proportional.
Since triangle ABC and XYC, therefore
[tex]\frac{XC}{AC}=\frac{YC}{BC}[/tex]
[tex]\frac{XC}{AC}=\frac{YC}{BY+YC}[/tex]
[tex]\frac{10}{AC}=\frac{7}{4+7}[/tex]
[tex]\frac{10}{AC}=\frac{7}{11}[/tex]
Therefore option 4 is correct.
Find the price per ounce rounded to the nearest cent: 1 lb 10 oz for $10.98.
A.) 0.5
B.) 1.98
C.) 0.42
D.) 0.9
A museum charges a school $200 to hold a trip + $2 entrance fee per person. The students must share the total cost of the trip equally include the entrance feee for 8 teachers. What is the function Y(x) that gives that gives the cost per X person attending the trip?
The endpoints of one diagonal of a rhombus are (-5,2) and (1,6). If the coordinates of the 3rd vertexare (-6,10), what arethe coordinates of the 4th vertex?
A.(2,-2)
B.(-8,0)
C.(4,8)
D.(-9,8)
Answer:
A. (2,-2)
Step-by-step explanation:
That is the right answer. Hope this helps!!!
New York City gift shop sells miniature Statue of Liberty sculptures that are 7.8 inches tall. the scale of the model to the actual statue is 1:232. what is the height of the actual statue to the nearest foot?
Q: what is the complete factorization of the polynomial below x^3+4x^2-x-4?
A. (x+1)(x-1)(x+4)
B. (x-1)(x-1)(x-4)
C. (x+1)(x-1)(x-4)
D. (x-1)(x-1)(x+4)
The solution is Option A.
The factorized form of the polynomial equation A = x³ + 4x² - x - 4 is given by B = ( x + 1 ) ( x - 1 ) ( x + 4 )
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the factorized equation be represented as = B
Now , let the equation be A
The value of A is given by A = x³ + 4x² - x - 4
On simplifying the equation , we get
A = x³ + 4x² - x - 4
Taking x² as the common term in the first two terms of the equation ,
A = x² ( x + 4 ) - x - 4
The equation can be further simplified as
A = x² ( x + 4 ) - ( x + 4 )
Taking ( x + 4 ) as the common term in the first two terms of the equation ,
A = ( x² - 1 ) ( x + 4 )
Now , ( x² - 1 ) can be simplified as ( x + 1 ) ( x - 1 )
So , the value of B is
B = ( x + 1 ) ( x - 1 ) ( x + 4 )
Therefore , the value of B is ( x + 1 ) ( x - 1 ) ( x + 4 )
Hence , the factorized equation is ( x + 1 ) ( x - 1 ) ( x + 4 )
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A bag contains 5 5 green marbles, 10 10 yellow marbles, 4 4 red marbles. two marbles are drawn without replacement which means that once the first marble is selected it is not put bag into the bag. it is not replaced. what is the probability of drawing a green marble then a red marble?
Techechtium-99m has a half-life of 6 hours. If 1000mg is in use, in how many hours will 62.5mg remain?
Techechtium-99m has a half-life of 6 hours. It will take 96 hours for 62.5 mg of Techechtium-99m to remain from an initial amount of 1000mg.
Explanation:To determine how many hours it will take for 62.5 mg of Techechtium-99m to remain from an initial amount of 1000mg, we can use the concept of half-life.
Techechtium-99m has a half-life of 6 hours, which means that after every 6 hours, half of the initial amount will decay.
So, to find the number of half-lives required to reach 62.5 mg, we can divide the initial amount by the remaining amount:
1000mg / 62.5mg = 16.
Since each half-life is 6 hours, we can multiply the number of half-lives by 6 to find the total number of hours:
16 x 6 = 96.
Therefore, it will take 96 hours for 62.5 mg of Techechtium-99m to remain from an initial amount of 1000mg.
The dot product of u with itself is 12. what is the magnitude of u?
Answer: The magnitude of the vector u is √12 units.
Step-by-step explanation: Given that the dot product of a vector u with itself is 12.
We are to find the magnitude of the vector u.
Let <a, b> represents the vector u.
That is, u = <a, b>
Then, according to the given information, we have
[tex]u.u=12\\\\\Rightarrow <a, b>.<a, b>=12\\\\\Rightarrow a^2+b^2=12\\\\\Rightarrow \sqrt{a^2+b^2}=\sqrt{12}\\\\\Rightarrow |u|=\sqrt{12}.[/tex]
Thus, the magnitude of the vector u is √12 units.
How to find all values of x where the tangent line is horizontal?
To find x-values where a function's tangent line is horizontal, find the derivative, set it to zero, and solve for x considering any function's restriction.
Explanation:To find all the values of x where the tangent line is horizontal, we need to understand that these are the points where the derivative of the function is zero. This is because the derivative of a function at a point gives us the slope of the tangent line at that point. And, for a line to be horizontal, its slope needs to be zero.
So, to find these values:
Find the derivative of the given function. Set this derivative equal to zero.Solve the equation for x.The solutions will give you the x-values where the tangent line is horizontal. Do note that you need to be aware of the domain and any restrictions of the original function to have valid solutions.
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Solve the inequality. Graph the solution set.
2r−9≤−6
Suppose two fair six-sided dice are rolled. what is the probability that they will both come up with the same number?
The base of a triangle is 15 centimeters and its height is 6 centimeters. What is the area of the triangle?
a.21 cm2
b.45 cm2
c.90 cm2
d.180 cm2 Submit
An item that originally cost $100 is decreased by 8%. The reduced price is then increased by 8%.
The resulting price is _____.
Answer:
The resulting price is $99.36.
Step-by-step explanation:
Original cost of the item = $100
The decrease percentage is 8% or 0.08
So, the reduced price becomes :
[tex]100-(0.08\times100)=92[/tex] dollars
Now again the reduced price is increased by 8%.
So, multiplying the reduced price by 8% and adding it again we get;
[tex]92+(0.08\times92)[/tex] =$99.36
So, the resulting price is $99.36.
What is the measure of the angle?
Haley measured the distances between her house and two of her friends' houses. ellen's house is 1.41 miles away from haley's, and dirk's house is 6,547 feet away from haley's. whose house is farther away from haley's, and how many feet farther away is it, to the nearest whole foot?
Answer: Ellen's house is farther away by 898 feet.
Step-by-step explanation:
Given: The distance between Haley's house and Ellen's house = 1.41 miles
We know that 1 mile = 5,280 feet
Then, [tex]1.41\text{ miles}=1.41\times5,280\text{ feet}=7,444.8\text{ feet}[/tex]
The distance between Haley's house and Dirk's house = 6,547 feet
Clearly, 6,547<7,444.8
And [tex]7444.8-6547= 897.8\approx898[/tex]
Therefore, Ellen's house is farther away by 898 feet.
(need help!) A dart is thrown at the board shown. It hits the board at a random point. Find the probability that it will land in the unshaded region. Round to the nearest percent.
20%
33%
17%
25%
[tex] |\Omega|=360\\
|A|=120\\\\
P(A)=\dfrac{120}{360}=\dfrac{1}{3}\approx33\% [/tex]
a garden patio is covered with grey slabs and yellow slabs. 1/5 is grey. 1/4 is yellow. there’s 55 slabs in total. what is the number of yellow slabs
Answer:
44
Step-by-step explanation:
1:4
4+1=5
55/5=11
11*4=44
the answer is 44
n circle A shown below, m Arc BC is 61° and m Arc EF is 76°: Points B, C, E, F lie on Circle A. Lines BE and CF pass through point D creating angle EDF. Measure of arc BC is 61 degrees and What is m∠FDE?
Answer:
The correct answer is 68.5°
The calculated result of the angle FDE is 68.5°. Whenever two chords cut across a circle, the resulting angle is equivalent to half of the sum of the measurements of the arc the angle intersects and that which the angle vertical to the first angle intercepts.
m<FDE = 1/2( Arc BC + Arc 76)
m<FDE = 1/2 (61° + 76°)
m<FDE = 137/2 = 68.5°
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The measure of an angle is two times the measure of a supplementary angle. what is the measure of each angle
Answer:
60 and 120 have a good day!
Step-by-step explanation:
Wai recorded the length of each wire needed for a science project. What is the total length of wire needed?
Answer:
14 5/8
Step-by-step explanation:
multiply each number by it's frequency the product is the total value .
what is the following product 3 sqrt 2(5 sqrt 6-7 sqrt 3)
Answer:
[tex](30\sqrt{3}-21\sqrt{6})[/tex]
Step-by-step explanation:
We have to find the product of the expressions.
[tex]3\sqrt{2}(5\sqrt{6}-7\sqrt{3})\\[/tex]
= [tex]3\sqrt{2}\times 5\sqrt{6}-7\sqrt{3}\times 3\sqrt{2}[/tex] ( By distributive rule)
= [tex]3\times 5(\sqrt{2})(\sqrt{6})-7\times 3(\sqrt{3})(\sqrt{2})[/tex]
= [tex]15\sqrt{12}-21\sqrt{6}[/tex]
= [tex]15\sqrt{4\times 3}-21\sqrt{6}[/tex]
= [tex]30\sqrt{3}-21\sqrt{6}[/tex]
= [tex](30\sqrt{3}-21\sqrt{6})[/tex]
Help me please.
Luke Skywalker's height is 68 inches. The mean height for all Jedi is 66.5 inches and the standard deviation of the Jedi heights is 2.4 inches. What is the z score for Luke Skywalker's height?
Round to the nearest thousandth
The z-score for Luke Skywalker's height is 0.625, indicating that his height is 0.625 standard deviations above the mean.
Z-score Formula: The z-score for Luke Skywalker's height can be calculated using the formula: z = (x - μ) / σ, where x is the individual's height, μ is the mean height, and σ is the standard deviation.
Plugging in the values, we get z = (68 - 66.5) / 2.4 = 0.625 (rounded to the nearest thousandth).
Which sequence is modeled by the graph below? Coordinates are 1,1 2,2 3,4 4,8
jen is thinking of a number. the product of this number and 3.4 is 176.8. find jens number.
Find the dot product, a • b. a = 6i + 5j, b = -5i + 4j
Answer:
-10
Step-by-step explanation:
took the test
There is an expression some people use that says, “What you put into it is what you get out of it.” People might use this expression to describe your skills at a sport or activity and how that relates to the amount of time and effort you spend practicing that activity. Does this expression apply to functions? How? Give an example to support your answer.
The phrase 'What you put into it is what you get out of it' applies to functions in mathematics, where given an value x (input) into a function, you get an output y. It also applies to real life examples, like sports practice, where your input of time and effort has a corresponding output of skill level.
Explanation:Yes, the expression “What you put into it is what you get out of it” can be applied in mathematics, particularly to functions. In mathematical context, this statement represents the fundamental concept of a function, where an input (what you put into it) mapped to an output (what you get out of it). For example, consider a linear function y = 2x + 3. The value of y (output) depends on the value chosen for x (input). Thus, if x = 2 (input), y = 7 (output). The output here is a result of the input 'fed' into the function.
The same idea can be extrapolated to functions in everyday life, such as practicing a sport. The input to the 'function' is the time and effort you put in, and the output is the proficiency you achieve. As with mathematical functions, each 'input' in life tends to have a corresponding 'output', reinforcing the idea of causes having effects.
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The expression 'What you put into it is what you get out of it' applies to functions such that what you put into the function (input) directly influences what you get out of the function (output).
Explanation:Yes, the expression 'What you put into it is what you get out of it' can indeed be applied to the concept of functions in mathematics. A function is a special relation from a set of inputs to a set of possible outputs where each input is related to exactly one output. The input you 'put into' a function is the independent variable and the output or 'what you get out of' the function is the dependent variable.
As an example, consider an equation of a function like y = 2x. Here, 'x' represents the inputs and 'y' the outputs. If you 'put into' this function x = 3 (input), you 'get out of' the function y = 6 (output). Thus, what you 'put into' the function (input) directly influences what you 'get out of' the function (output), demonstrating the principle of 'What you put into it is what you get out of it'
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