Answers
A polynomial function of nth degree with given zeros, use the form f(x) = a (x - x1)(x - x2)...(x - xn), which is [tex]f(x) = x^3 - 2x2 - 5x + 6[/tex]
To write a polynomial function of the nth degree with given zeros, you can use the fact that a polynomial function f(x) with zeros at x1, x2, ..., xn can be expressed as:
f(x) = a (x - x1)(x - x2)...(x - xn)
Where 'a' is the leading coefficient, which can be any non-zero real or complex number, and (x - xi) are factors for each zero of the polynomial. If the polynomial is supposed to have a specific coefficient for the highest power term, then 'a' is that coefficient; otherwise, 'a' can be chosen freely to define the polynomial.
To illustrate with an example, if we had a polynomial of degree 3 with zeros at 1, -2, and 3, and we want the leading coefficient to be 1, our polynomial would be:
f(x) = (x - 1)(x + 2)(x - 3)
Expanding this product, we would get:
[tex]f(x) = x^3 - 2x2 - 5x + 6[/tex]
This polynomial of third degree has the specified zeros and a leading coefficient of 1.
Related Questions
Help with algebra 2 please!!!!!!!
Answers
On a scatter plot what does it mean when both variables are increasing
Answers
does anyone know the surface area for this problem. if so i will mark brainliest.
Answers
From the given volume, we know that the ratio is:
[tex]\text {Ratio of yellow eraser to white eraser = } \sqrt[3]{ \dfrac{16}{2} } [/tex]
From the given area, we know that the ratio is:
[tex]\text {Ratio of yellow eraser to white eraser = } \sqrt{ \dfrac{52}{x} } [/tex]
Equate the two ratio and solve for x:
[tex]\sqrt[3]{ \dfrac{16}{2} } = \sqrt{ \dfrac{52}{x} } [/tex]
Cube both sides:
[tex]\dfrac{16}{2} = \bigg(\sqrt{ \dfrac{52}{x} }\bigg)^3[/tex]
Square both sides:
[tex]\bigg(\dfrac{16}{2} \bigg)^2 = \bigg( \dfrac{52}{x} }\bigg)^3[/tex]
Simplify each term:
[tex]\dfrac{16^2}{2^2} = \dfrac{52^3}{x^3} [/tex]
Cross multiply:
[tex]256x^3 = 562432[/tex]
Divide both sides by 256:
[tex] x^3 = 2197[/tex]
Cube root both sides:
[tex] x = 13[/tex]
How many degrees is w?
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w = 180 -38 - 49
w = 93
Answer
w = 93°
Blue marbles, green marbles and red marbles are in a ratio of 5 to 7 to 8 in a box. if the total number of marbles is 240, how many green marbles are in the box?
Answers
= ⁷/₂₀
If there are 240 marbles in the box, then the number of green marbles = (240 × ⁷/₂₀) = 84 marbles
∴ 84 of the marbles in the bag are green.
A ball is thrown upward from the top of a building. The function below shows the height of the ball in relation to sea level, f(t), in feet, at different times, t, in seconds:f(t) = −16t2 + 48t + 100The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is _____feet per second.
Answers
f (t) = -16t2 + 48t + 100
The average rate of change is:
(f (t2) - f (t1)) / (t2 - t1)
We have then:
For t1 = 3:
f (3) = -16 * (3) ^ 2 + 48 * (3) + 100
f (3) = 100
For t2 = 5:
f (5) = -16 * (5) ^ 2 + 48 * (5) + 100
f (5) = -60
Substituting values:
AVR = (-60 - 100) / (5 - 3)
AVR = -80
Answer:
The average rate of change of f (t) from t = 3 seconds to t = 5 seconds is -80 feet per second.
Which of these is an example of continuous random variable
A. Number of flights leaving an airport
B. Distance of a javelin throw
C. Pieces of mail in your mailbox
D. Attendance at a sporting event
Answers
A continuous random variable is a variable that can be any number between the integers not just the integers themselves.
For example, the distance for a javelin throw could be 6.70819203 feet.
However, you would not say that you have 6.70819203 flights, pieces of mail or people at a sporting event.
The B. distance of a javelin throw is an example of a continuous random variable.
Explanation:A continuous random variable is a variable that can take any value within a specified range, often associated with measurements and quantities. Unlike discrete variables, it can assume an infinite number of values, typically represented by intervals on the real number line.
Out of the given options, the distance of a javelin throw is an example of a continuous random variable. A continuous random variable is one that can take on any value within a given range. In the case of a javelin throw, the distance can be any real number value within a certain range, such as 0 to infinity. This is in contrast to the other options, which are discrete random variables that can only take on specific whole number values.
Solve system by elimination
y=x^2
y=x+2
SHOW YOUR WORK
Answers
y=x²----> equation 1
y=x+2-----> equation 2
multiply equation 1 by -1
-y=-x²
add equation 1 and equation 2
-y=-x²
y=x+2
------------
0=-x²+x+2-------------> -x²+x+2=0-----> x²-x-2=0
Group terms that contain the same variable, and move the constant to the opposite side of the equation
(x²-x)=2Complete the square. Remember to balance the equation by adding the same constants to each side
(x²-x+0.5²)=2+0.5²
Rewrite as perfect squares
(x-0.5)²=2+0.5²(x-0.5)²=2.25-----> (x-0.5)=(+/-)√2.25-----> (x-0.5)=(+/-)1.5
x1=1.5+0.5-----> x1=2
x2=-1.5+0.5---- > x2=-1
for x=2
y=x²----> y=2²----> y=4
the point is (2,4)
for x=-1
y=x²----> y=(-1)²---> y=1
the point is (-1,1)
the answer is
the solution of the system are the points
(2,4) and (-1,1)
Write the inverse function for the function, ƒ(x) = x + 4. Then, find the value of ƒ -1(4). Type your answers in the box.
ƒ -1(x) = _________ x ___________ ______
ƒ -1(4) = _____________
Answers
Answer: The required values are
[tex]f^{-1}(x)=x-4~~~~~~~~\textup{and}~~~~~~~~~f^{-1}(4)=0.[/tex]
Step-by-step explanation: We are given the following function f(x) :
[tex]f(x)=x+4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We are to find the values of [tex]f^{-1}(x)[/tex] and [tex]f^{-1}(4).[/tex]
Let us consider that
[tex]y=f(x)~~~~~~~~\Rightarrow x=f^{-1}(y).[/tex]
So, from equation (i), we get
[tex]f(x)=x+4\\\\\Rightarrow y=f^{-1}(y)+4\\\\\Rightarrow f^{-1}(y)=y-4\\\\\Rightarrow f^{-1}(x)=x-4.[/tex]
Substituting x = 4 in the above equation, we get
[tex]f^{-1}(4)=4-4=0\\\\\Rightarrow f^{-1}(4)=0.[/tex]
Thus, the required values are
[tex]f^{-1}(x)=x-4~~~~~~~~\textup{and}~~~~~~~~~f^{-1}(4)=0.[/tex]
i really need help. please help
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4^−x and y = 8^(−x−1) intersect are the solutions of the equation 4^−x = 8^(−x−1). (4 points)
Part B: Make tables to find the solution to 4^−x = 8^(−x−1). Take the integer values of x between −3 and 3. (4 points)
Part C: How can you solve the equation 4^−x = 8^(−x−1) graphically? (2 points)
Answers
The answer to B is forming a table. This is quite easier than you think :D.
Start with x on one side (3) and go all the way down to -3 like this:
(x) 4^-x 8^-x-1
-3 64 (Do the same with this)
-2 16
-1 4
0 1
1 1/4
2 .0625
3 .015625
So basically you just fill in the x variable with every number between 3 and -3. After that, it's just a bit of math and you've done it!
C is a bit misguided. I think it would be quite simple to just use a graphing calculator, but you would have to actually input all the x and y values from the table. After that, you will have a graph.
I hope I helped! Good luck and good day!
Given that the two triangles shown are congruent, explain one way to verify that the corresponding angles of the two triangles are congruent.
A) reflect triangle 1 across the y-axis
B) reflect triangle 2 across the y-axis
C) rotate triangle 2 counter-clockwise 90° about the origin
D) reflect triangle 2 across the y axis and rotate 90° about the origin at
Answers
C) rotate triangle 2 counter-clockwise 90° about the origin
Answer:
The correct option is C.
Step-by-step explanation:
From the given graph it is noticed that the vertices of triangle 1 are P'(-2,2), Q'(-4,4) and R'(-2,4). The vertices of triangle 2 are P(2,2), Q(4,4) and R(4,2).
If a figure rotated counter-clockwise 90° about the origin, then
[tex](x,y)\rightarrow (-y,x)[/tex]
If we rotate triangle 2 counter-clockwise 90° about the origin, then[
[tex]P(2,2)\rightarrow P'(-2,2)[/tex]
[tex]Q(4,4)\rightarrow Q'(-4,4)[/tex]
[tex]R(4,2)\rightarrow R'(-2,4)[/tex]
If we rotate triangle 2 counterclockwise, then we get the triangle 1.
Therefore the correct option is C.
divide r+5/ r^2+5r-14 by r^2+4-21/r-2
Answers
The first thing we are going to do is factor the denominator of the first fraction and the denominator of the second one:
- For our first fraction:
[tex]r^2+5r-14=(r+7)(r-2)[/tex]
Now we can rewrite our first fraction:
[tex]\frac{r+5}{r^2+5r-14} = \frac{r+5}{(r+7)(r-2)} [/tex]
- For our second fraction:
[tex]r^2+4r-21=(r+7)(r-3)[/tex]
Now we can rewrite our second fraction:
[tex] \frac{r^2+4r-21}{r-2} = \frac{(r+7)(r-3)}{r-2} [/tex]
Last but not least, we can express our division as a fraction and simplify:
[tex] \frac{\frac{r+5}{(r+7)(r-2)}}{ \frac{(r+7)(r-3)}{r-2}} = \frac{(r+5)(r-2)}{(r+7)(r-2)(r+7)(r-3)} = \frac{r+5}{(r+7)^2(r-3)} [/tex]
We can conclude that the result of dividing r+5/ r^2+5r-14 by r^2+4r-21/r-2 is: [tex] \frac{r+5}{(r+7)^2(r-3)} [/tex]
find the greatest common factor 9x^2a + 9xa^2
Answers
9x^2a+9xa^2
factor out 9 we get:
9(x^2a+xa^2)
=factoring out x we get
9x(xa+a^2)
factoring out a we get
9ax(x+a)
therefore the GCF is 9ax
Factor this trinomial completely.
–6x2 + 26x + 20
A. –6x2 + 26x + 20
–2(3x2 – 13x – 10)
–2(3x + 2)(x – 5)
B. –6x2 + 26x + 20
–2(3x2 + 11x + 10)
–2(3x + 5)(x + 2)
C. –6x2 + 26x + 20
–2(3x2 – 13x – 10)
–2(3x – 10)(x + 1)
D. –6x2 + 26x + 20
–2(3x2 – 13x + 10)
–2(3x – 5)(x – 2)
Answers
6x² + 26x + 20
6x² + 6x + 20x + 20
6x(x + 1) + 20(x + 1)
(6x + 20)(x + 1)
2(3x + 10)(x + 1)
2(3x + 10)(x + 1) is your answer.
First, factor out -2 from the trinomial, and then factor the resulting quadratic expression by grouping. The correct factored form is -2(3x + 2)(x - 5).
To factor the trinomial “6x² + 26x + 20 completely, follow these steps:
First, factor out the greatest common factor, which is -2:“6x² + 26x + 20 = –2(3x² – 13x – 10).Next, factor the quadratic expression inside the parentheses:
3x² – 13x – 10.
We need to find two numbers that multiply to (3 × -10 = -30) and add up to -13. Those numbers are -15 and 2.Rewrite the quadratic equation using these numbers:
3x² – 15x + 2x – 10.Now, factor by grouping:
3x(x – 5) + 2(x – 5) = (3x + 2)(x – 5).Combining everything, we get:
–2(3x + 2)(x – 5).
Therefore, the correct factored form is (Option A) “2(3x + 2)(x – 5).
What is the value of x?
a. 6
b. 6√3
c. 12
d. 12√3
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A field goal post in football is 3.33 yards above the ground. If a football player kicks the ball at a 10 degree square angle in a straight line toward the goal post what is the distance away in yards where the ball barely goes over the goal post
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because tan(10)=opposite/adjacent=3.33/x and x is distance
x=3.33/tan(10)=18.9 yd
A bowl contains 24 marbles consisting of 6 white marbles, 8 blue marbles, 7 black marbles, 3 red marbles. What is the probability of drawing a red marble?
a. 6/24B.5/25C.1/8D.7/8
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Given y = 4x + 3, what effect does changing the equation to y = 2x + 3 have on the slope?
Answers
Hope this helps!
can I get a brainleist pls!
Changing the slope of the equation from 4 to 2 reduces the steepness of the line in the graph, with the y-intercept remaining constant at 3.
Explanation:The student asked about the effect on the slope of the linear equation when changing from y = 4x + 3 to y = 2x + 3. The slope of the first equation is 4, which can be seen from the coefficient of x, indicating a rise of 4 on the vertical axis for every increase of 1 on the horizontal axis. When the equation changes to y = 2x + 3, the slope is reduced to 2, which means there is a rise of 2 on the vertical axis for every increase of 1 on the horizontal axis. This change in the slope would cause the line to rotate clockwise when graphed on a coordinate plane. The y-intercept remains the same at 3 since it is unchanged in both equations. Therefore, changing the equation has the effect of decreasing the steepness of the line, but the location where the line crosses the y-axis does not change.
Rewrite with only sin x and cos x. Sin2x-cos2x
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So sin2x-cos2x = 2sinxcosx - ([tex]cos^{2} x - sin^{2} x[/tex]) in terms of sinx and cosx
describe the steps you would use to solve the following inequality
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[tex] \frac{x + 1}{2x - 3} > 2 \\ x + 1 > 2(2x - 3) \\ x + 1 > 4x - 6 \\ - 3x + 1 > - 6 \\ - 3x > - 7x \\ x < \frac{7}{3} [/tex]
Answer:
Rewrite the inequality so there is a single rational expression on one side, and 0 on the other.
Combine under a common denominator.
Test points in the critical regions.
Construct the solution.
Step-by-step explanation:
Answer Above
Troy has a box of 600 tiny blocks. Each block is a cube with dimensions of 1 cm x 1cm x 1cm. The blocks are arranged in the box in rows and layers so that there are no gaps. Which could be the dimensions of the box?
a. 5 cm x 10 cm x 12 cm
b. 5 cm x 10 cm x 10 cm
c. 10 cm x 10 cm x 12 cm
d. 200 cm x 200 cm x 200 cm
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If the ratio of the radii of two spheres is 8:9, what is the ratio of the volumes of the two speheres
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A------------> smaller sphere
B----------> larger sphere
radius of sphere A-------> rA
radius of sphere B----> rB
we know that
rA/rB=8/9
the scale factor is equal to 8/9
volume smaller sphere A=[scale factor]³*volume larger sphere B
volume smaller sphere A/volume larger sphere B=[scale factor]³
volume smaller sphere A/volume larger sphere B=[8/9]³----> 512/729
the answer is
512/729
The shorter leg of a right triangle is 7 inches shorter than the longer leg. The hypotenuse is 17 inches longer than the longer leg. Find the side lengths of the triangle.
Answers
Or round them all up.
a² + b² = c²
c² - a² = b²
17² - 7² = x² ↓
289 - 49 = √240
√240 = 15.49193338482967 (rounded 15.49 or 15.5)
Hope this helps,
♥A.W.E.S.W.A.N.♥
On a map, 1 inch equals 9.2 miles. two houses are 3.5 inches apart on the map. what is the actual distance between the houses? use pencil and paper. show how you can represent the scale with two different ratios. what ratio is more helpful for solving the problem? explain.
Answers
The actual distance between the houses is 18.9 miles.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Multiplication is the mathematical operation that is used to determine the product of two or more numbers.
Given that On a map, 1 inch equals 9.2 miles. Two houses are 3.5 inches apart on the map.
To find the actual distance between the houses.
Given that,
1 inch = 9.2 miles
Therefore,
∴ we get
3.5 inches = 3.5 × 9.2 miles
= 13.8 miles
The actual distance is 13.8 miles.
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Final answer:
To find the actual distance between the houses, we can set up a proportion using the given map scale. The actual distance between the houses is 32.2 miles. Using the ratio 1 inch/9.2 miles = 3.5 inches/x is more helpful in solving the problem.
Explanation:
To find the actual distance between the houses, we need to use the scale of 1 inch equals 9.2 miles. We are given that the two houses are 3.5 inches apart on the map.
First, we can set up a proportion to find the actual distance:
1 inch / 9.2 miles = 3.5 inches / x
Cross-multiplying, we have:
1x = 3.5 * 9.2 miles
Simplifying, we get:
x = 32.2 miles
The actual distance between the houses is 32.2 miles.
To represent the scale with two different ratios, we can use the proportion:
1 inch / 9.2 miles = 3.5 inches / x
This ratio is more helpful for solving the problem as it allows us to directly calculate the actual distance using the given map distance and the scale ratio.
SOLVE FOR X one question 20 points
Answers
a^2 + b^2 = c^2 (c^2 is the hypertenuse)
The equation will look like this:
14^2 + 14^2 = x^2
196 + 196 = x^2
x^2 = 392
So the answer is the square root of 392:
14[tex] \sqrt{2} [/tex]
If you want a decimal form:
14 * 1.414 = 19.796
Answer:
ANSWER IS
Step-by-step explanation:
Write an algebraic expression for the verbal description. the distance a car travels in t hours at a rate of 50 miles per hour
Answers
d=50t
Where; d is the distance covered in miles
t is the time taken in hours
The algebraic expression is D = 50t where D is the distance covered in miles and t is the time taken in hours.
What is the distance?Distance is defined as the product of speed and time.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
The operator that performs the arithmetic operations is called arithmetic operator.
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
/ Division operation: Divides left-hand operand by right-hand operand
For example 4/2 = 2
Given that the distance a car travels in t hours at a rate of 50 miles per hour
Let the distance covered in miles = D
And t is the time taken in hours
Since distance is defined as the multiplication of speed and time.
So an algebraic expression for the verbal description as
⇒ D = 50t
Hence, the algebraic expression is D = 50t where D is the distance covered in miles and t is the time taken in hours.
Learn more about Arithmetic operations here:
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Use the given graph to determine the limit, if it exists.
Find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x.
Answers
As the value of x approaches 2 from the positive side i.e. the right hand side, the value of function approaches -4
Since the Right hand limit and the Left hand limit as x approaches 2 are not the same, the limit does not exist at x = 2
The population of a city is 578,992. The land area of the city is 67.2 mi². What is the population density of the city? Enter your answer in the box. Round your answer to the nearest whole number.
Answers
Population Density = Number of People / Land Area.
then
Number of People=578,992
Land Area=67.2 mi²
so
Population Density =578,992/67.2-----> 8615.95 people/mi²
the answer is
8616 people/mi²
Just took the K12 test and the correct answer is 8616 people/mi²
(please give the other person brainliest-thanks!!!)
What is the best estimate of the mean price of all the sunglasses on the rack?
Answers
.
(12 +12 +14 +15 +18 +20 +20 +25)/8 = 136/8 = 17
The best estimate of the mean of the population is
$17
The product of a number (n) and 12 is 64. Which equation shows this relationship
12+n=64
64n=12
12n=64
64-n=12
Answers
The equation that shows the relationship between the number (n) and 12 being multiplied to equal 64 is 12n = 64, the correct option is C.
In this equation, the variable n represents the number we are trying to find. The equation states that when we multiply 12 and n together, the result is 64.
To solve this equation and find the value of n, we divide both sides of the equation by 12:
(12n)/12 = 64/12
n = 64/12
Which can be further simplified to:
n = 16/3
Therefore, the equation that represents the relationship between the number (n) and 12 being multiplied to equal 64 is 12n = 64.
Learn more about equations here;
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