Answers
Okay, here we have this:
Considering the provided points, we are going to write a cubic function with these points as roots, so we have this:
The factored function will be equal to the multiplication of three binomials, where the first term will be x and the second will be each root with an inverse sign. Then we have:
[tex]f(x)=\mleft(x+2\mright)\mleft(x-2\mright)\mleft(x-6\mright)[/tex]Now we are going to operate each term to obtain the expanded function:
[tex]\begin{gathered} f(x)=x^2x+x^2\mleft(-6\mright)-4x-4\mleft(-6\mright) \\ f(x)=x^3-6x^2-4x+24 \end{gathered}[/tex]The last one we write is the function we are looking for and satisfies the requested roots.
Related Questions
rhombus STUV is located at S(-5, 4), T (-1, 5), U(-2, 1), and V(-6, 0). If STUV is translated along the rule (x, y) (x + 7 , y - 8). in which quadrant will the new rhombus be located
Answers
rhombus STUV is located at S(-5, 4), T (-1, 5), U(-2, 1), and V(-6, 0). If STUV is translated along the rule (x, y) (x + 7 , y - 8). in which quadrant will the new rhombus be located
we have that
the rule of the translation is
7 units at right and 8 units down
Verify each ordered pair
S(-5,4) -------> S'(-5+7,4-8) ------> S'(2,-4) (IV quadrant)
T(-1,5) ------> T'(-1+7,5-8) -----> T'(6,-3) (IV quadrant)
U(-2,1) -----> U'(5,-7) (IV quadrant)
V(-6,0) ----> V'(1,-8) (IV quadrant)
therefore
answer is (IV quadrant)John needs 6 cups of ice cream to make 4 servings of milkshake how many servings can John make using 30 cups of ice cream
Answers
To find how many servings John can make we need to write as a relationship, this means that
[tex]\begin{gathered} 6c\Rightarrow4s \\ 30c\Rightarrow? \end{gathered}[/tex]to find the missing value we need to solve the relationship
[tex]\begin{gathered} ?=30c\cdot\frac{4s}{6c} \\ ?=5\cdot4s \\ ?=20s \end{gathered}[/tex]he can make 20 servings with 30 cups of ice cream
you hiked 400 feet up a steep hill that has 25° angle of elevation as shown in the diagram.give each side of an angle measure rounded to the nearest whole number.a =b =m
Answers
Notice that the problem is described by a right angle triangle for which we know the length of the hypotenuse (400 ft), and also know one of the triangle's acute angles (25 degrees)
Base on this knowledge, we can start by finding the other acute angle of the triangle (
This means : 25 + 90 +
Then we can solve for angle
115 +
subtract 115 degrees from both sides to isolate
< B = 180 - 115 = 65
then we have the measure of angle < B = 65 degrees.
Now we can find the value of the side adjacent to the angle 25 degrees by using the cosine trigonometric ratio:
[tex]\begin{gathered} \cos (25)=\frac{adjacent}{\text{hypotenuse}} \\ \cos (25)=\frac{adjacent}{400} \\ \text{adjacent}=400\cdot\cos (25) \\ \text{adjacent}=362.52 \end{gathered}[/tex]Then the side named "b" measures 362.52 ft
We can do something similar to find the measure of side a, but using the trigonometric ratio for the sine function:
[tex]\begin{gathered} \sin (25)=\frac{opposite}{\text{hypotenuse}} \\ \sin (25)=\frac{a}{\text{hypotenuse}} \\ \sin (25)=\frac{a}{400} \\ a\text{ = 400}\cdot\sin (25) \\ a=169.05 \end{gathered}[/tex]Then the measure of side a is 168.05 ft
Now, notice that the problem wants you to round the side measures to the nearest whole number, so you need to type the following:
a = 169 ft
b = 363 ft
angle
For what of 0, in degree, is sin= con 58⁰?
Answers
Answer: We want to find angle 'theta' for which:
[tex]\sin (\theta)=\cos (58)[/tex]In general, the following is always true:
[tex]\cos (\theta)=\sin (90-\theta)\rightarrow(1)[/tex]Therefore we have the following:
[tex]\cos (58^{\circ})=\sin (90-58)=\sin (32^{\circ})[/tex]Therefore the angles that we were interested in is:
[tex]\theta=32^{\circ}[/tex]
vic sam and li volunteered at a food bank for 52 hours if sam worked 3 fewer hours then vic and 4 fewer then li how many hours did li work?
Answers
Answer:
Li worked for 19 hours.
Explanation:
Let's call x the number of hours that Vic worked, y the number of hours that Sam worked, and z the number of hours that Li worked.
They all work for 52 hours, so:
x + y + z = 52
Sam worked 3 fewer hours than Vic and 4 fewer than Li, so:
y = x - 3 or y + 3 = x
y = z - 4 or y + 4 = z
So, we can replace x and z on the first equation and solve for y as:
(y + 3) + y + (y + 4) = 52
y + 3 + y + y + 4 = 52
3y + 7 = 52
3y + 7 - 7 = 52 - 7
3y = 45
3y/3 = 45/3
y = 15
Then, replacing y by 15, we can calculate the value of x and z as:
x = y + 3
x = 15 + 3
x = 18
z = y + 4
z = 15 + 4
z = 19
Therefore, Li worked for 19 hours.
A company that owed $2,000 paid early and got a $40 discount. What fraction of the amount owed was the discount? (Express As Fraction)
Answers
In order to find the fraction of the amount that the discount represents, we just need to divide the discount amount by the total value:
[tex]\frac{40}{2000}[/tex]Now, to simplify this fraction, we can divide the numerator and denominator by 40:
[tex]\frac{40}{2000}=\frac{40\colon40}{2000\colon40}=\frac{1}{50}[/tex]So the discount is 1/50 of the value paid.
Find the area of the figure. (Sides meet at right angles.)4 m5 m15 m5 m5 m4 m4 m
Answers
The area of the figure will be the area of the rectangle of the top, plus the area of the rectangle of the bottom:
The area of the rectangle of the top is:
[tex]A1=w1\cdot h1=5\cdot4=20m^2[/tex]The area of the rectangle of the bottom is:
[tex]A2=w2\cdot h2=14\cdot4=56m^2[/tex]so, the total area is:
[tex]A=A1+A2=20m^2+56m^2=76m^2[/tex]What is the solution to the inequality -4x < 8?x < -2x > -2x < -24x > -24
Answers
To find:
The solution of the given inequality -4x < 8.
Solution:
Given inequality is -4x < 8. Divide both sides by -4 to isolate x.
If we divide an inequality by a negative number, then the sign of inequality changes to its opposite. So, on dividing the inequality by -4,we get:
[tex]\begin{gathered} -4x<8 \\ \frac{-4x}{-4}<\frac{8}{-4} \\ x>-2 \end{gathered}[/tex]Thus, the answer is x > -2.
Hello do you no how to do Solving Equations Puzzle
Answers
1 - The right and the left side must weight the same, and the weight of both the right and the left side would be 24, therefore each side must weight 12.
2 - Since the heart = 2, and 2*heart + square = 12 , then square = 8
3 - Now, since square = 8 and square + moon = 12, then moon=4
To summarize
heart = 2, square = 8 , moon = 4.
Steven flew from Boston to Orlando with a stop in Atlanta to switch planes. His first flight leftBoston at 12:00 P.M. and was 3 hours and 45 minutes long. Steven was in Atlanta for 2 hours and 30 minutes, and his flight from Atlanta to Orlando was 1 hour and 30 minutes long. Whattime was it when Steven landed in Orlando?
Answers
Answer:
07:45 pm
Explanation:
Steven landed in Orlando after the sum of the following time
3 hours and 45 minutes
2 hours and 30 minutes
1 hour and 30 minutes
If we add the hours and the minutes, we get:
3 hours + 2 hours + 1 hour = 6 hours
45 minutes + 30 minutes + 30 minutes = 105 minutes
But 1 hour = 60 minutes, so
6 hours and 105 minutes = 7 hours and 45 minutes
because
105 - 60 = 45
Since the flight left Boston at 12:00 pm, it was 07:45 pm when Steven landed in Orlando.
Hello! I need some help with this homework question, please? The question is posted in the image below. Q21
Answers
To find the zeros of the polynomial given, we will first have to find some simpler zeros first then factor the polynomial so we can use the quadratic equation.
Since we can assume this question is to be solved without external tools, it is likely that two of the roots are simple ones.
So, we can try to use the rational root theorem to find these simpler ones.
Since the leading coefficient is 1 and the constant term is -18, if there are rational roots, they can be written as a fraction of a factor of -18 divided by a factor of 1.
The only factor of 1 is 1, so we now that if there are rational roots, they have to have denominator equal to 1.
The factors of 18 are 1, 2, 3, 6, 9 and 18.
Also, we have to consider the possibilities of positive and negative.
It is easier to test the lower ones, so let's start by testing 1/1 and -1/1. For either to be a zero, the polynomial has to result in 0:
[tex]\begin{gathered} x^4+x^3+7x^2+9x-18 \\ x=1 \\ 1^4+1^3+7\cdot1^2+9\cdot1-18=1+1+7+9-18=18-18=0 \end{gathered}[/tex]So, x = 1 is a zero of the polynomial.
[tex]\begin{gathered} x^4+x^3+7x^2+9x-18 \\ x=-1 \\ (-1)^4+(-1)^3+7(-1)^2+9(-1)-18=1-1+7-9-18=-2-18=-20 \end{gathered}[/tex]So, x = -1 is not a zero.
Now, let's try the next factor, 2/1 and -2/1:
[tex]\begin{gathered} x^4+x^3+7x^2+9x-18 \\ x=2 \\ 2^4+2^3+7\cdot2^2+9\cdot2-18=16+8+28+18-18=52 \end{gathered}[/tex]So, x = 2 is not a zero.
[tex]\begin{gathered} x^4+x^3+7x^2+9x-18 \\ x=-2 \\ (-2)^4+(-2)^3+7(-2)^2+9(-2)-18=16-8+28-18-18=8+10-18=0 \end{gathered}[/tex]So, x = -2 is also a zero of the polynomial.
We could continue, by we only need 2 zeros, so this is enough.
Now we know x = 1 and x = -2 are zeros of the polynomial, we can use synthetic division to factor the polynomial:
1 | 1 1 7 9 -18
| 1 2 9 18
| 1 2 9 18 0
Using the last line, we have that the remainder is 0 and the quotient is:
[tex]x^3+2x^2+9x+18[/tex]So, we have that:
[tex]x^4+x^3+7x^2+9x-18=(x-1)(x^3+2x^2+9x+18)[/tex]Now, we can use synthetic division again on the quotient, but now use the other zero, x = -2:
-2 | 1 2 9 18
| -2 0 -18
| 1 0 9 0
Since x = -2 is a zero, we also got a remainder of 0, and the quotient is:
[tex]\begin{gathered} x^2+0x+9 \\ x^2+9 \end{gathered}[/tex]So, we can rewrite the polynomial as:
[tex]x^4+x^3+7x^2+9x-18=(x-1)(x+2)(x^2+9)[/tex]Now, we can just find the zeros of the remainer factor, x² + 9, so:
[tex]\begin{gathered} x^2+9=0 \\ x^2=-9 \\ x=\pm\sqrt[]{-9} \\ x=\pm\sqrt[]{9}\sqrt[]{-1} \\ x=\pm3i \end{gathered}[/tex]This means that the complex zeros of the given polynomial are:
[tex]\begin{gathered} x=1 \\ x=-2 \\ x=3i \\ x=-3i \end{gathered}[/tex]And the factored usinf complex factors is:
[tex]x^4+x^3+7x^2+9x-18=(x-1)(x+2)(x-3i)(x+3i)[/tex]
3. Given the degree and zeros of a polynomial function, identify the missing zero and then find the standard form of the polynomial.
Degree: 3; zero: 9, 8 - i
The missing zero is:
+
i
The expanded polynomial is:
x3 +
x2 +
x +
Answers
The equation of the polynomial equation in standard form is P(x) = x³ - 25x²+ 209x - 585
How to determine the polynomial expression in standard form?The given parameters are
Degree = 3
Zero = 9, 8 - i
There are complex numbers in the above zeros
This means that, the other zeros are
Zeros = 8 + i
The equation of the polynomial is then calculated as
P(x) = (x - zero)^multiplicity
So, we have
P(x) = (x - 9) * (x - (8 - i)) * (x - (8 + i))
This gives
P(x) = (x - 9) * (x - 8 + i) * (x - 8 - i)
Evaluate the products
P(x) = (x - 9) * (x² - 8x - ix -8x + 64 + 8i + ix - 8i + 1)
Evaluate the like terms
P(x) = (x - 9) * (x² - 16x + 65)
Express in standard form
P(x) = x³ - 16x² + 65x - 9x² + 144x - 585
Evaluate the like terms
P(x) = x³ - 25x²+ 209x - 585
Hence, the equation is P(x) = x³ - 25x²+ 209x - 585
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GraphON4andon the number line to show how each fraction relates to 1.Click each dot on the image to select an answer.十+01Compare.our24.36Eng
Answers
2/6 = 1/3 = 0.3333
0.333 is less than 1 so it should be on the left side of the graph.
4/3 = 1.333
1.333 is greater than 1 so it should be on the right side of the graph .
So the bigger dot on the left hand side which is before 1 should be 2/6 while the smaller dot on the right hand side which is after 1 should be 4/3 .
The perimeter of a geometric figure is the sum of the lengths of its sides. If the perimeter of the pentagon to the right (five-sided figure) is 80 meters, find the length of each side.
Answers
Answer:
16 m
Step-by-step explanation:
If the perimeter of an equilateral pentagon is 80 m and it has five sides, the length of each side must be 16 m:
[tex]x=\frac{80}{5}[/tex]
[tex]x=16[/tex]
Therefore, if each side is 16 m in length, 2½ sides must equal 40 m:
[tex]2.5x=2.5(16)[/tex]
[tex]2.5x=40[/tex]
-7(w— 4) + Зw – 27Simplify it help ASAP
Answers
-7(w - 4) + 3w - 27
Expand
-7w + 28 + 3w - 27
Simplify like terms
-7w + 3w + 28 - 27
Result
-4w + 1
Which of the following graphs represents the equation 2x - 8y = 32?
Answers
Answer:
C
Step-by-step explanation:
2x-8y = 32
2/2 x - 8/2 y = 32/2
x - 4y = 16
if x = 0
-4y = 16
-4/-4 y = 16/-4
y = -4
If x = 16
16-4y = 16
-4y = 0
-4/-4 y = 0/-4
y = 0
Find the area of triangle ABC.A = 37.2°, b = 10.1 in., c = 6.2 in.A. 19 in²B. 20 in²C. 17 in²D. 18 in²
Answers
Given:
A = 37.2°
b = 10.1 in
c = 6.2 in
Let's find the area of the traingle.
To find the area, apply the formula below:
[tex]\text{Area}=\frac{1}{2}\ast b\ast c\ast\sin A[/tex]Hence, we have:
[tex]Area=\frac{1}{2}\ast10.1\ast6.2\ast\sin 37.2[/tex]Solving further:
[tex]\begin{gathered} \text{Area}=\frac{1}{2}\ast10.1\ast6.2\ast0.605 \\ \\ \text{Area}=18.9\text{ }\approx19in^2 \end{gathered}[/tex]Therefore, the area of triangle ABC is 19 square inches
ANSWER:
A. 19 in²
which of the triangles cannot be proved congruent? so a different tutor gave me the answer which is D. But he told me to ask another tutor to tell me how to type out how I got the answer.
Answers
The triangles that cannot be proved congruent are the triangles in option D. We are not told that the other side is congruent to the corresponding side of the other triangle.
To prove they are congruent, we need to know the other side is congruent and prove this using the SSS postulate.
In the other cases, we can be proved they are congruent by:
• Case A ---> SAS postulate.
,• Case B ---> ASA postulate.
,• Case C ---> SSS postulate (the triangles share a common side)
In summary, we only have that the triangles in D cannot be proved congruent since we have two corresponding congruent sides, and one angle (vertical angle) to be congruent corresponding parts. It would be an SSA method. However, this method is not Universal, and it is not enough to demonstrate they are congruent.
an architect wants to create a rectangular sun porch in a house. he wants it to have a total area of 92 square feet, and it should be 12 feet longer than it is wide. what dimensions should he use for the sun porch? round to the nearest hundredth of a foot
Answers
we can write 2 equations
[tex]\begin{gathered} x\times y=92 \\ \end{gathered}[/tex][tex]x+12=y[/tex]where x is the wide and y the long
we can replace y=x+12 from the second equation on the first
[tex]x\times(x+12)=92[/tex]and solve x
[tex]\begin{gathered} x^2+12x=92 \\ x^2+12x-92=0 \end{gathered}[/tex]factor ussing
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where a is 1, b is 12 and c -92
replacing
[tex]\begin{gathered} x=\frac{-(12)\pm\sqrt[]{12^2-4(1)(-92)}}{2(1)} \\ \\ x=\frac{-12\pm16\sqrt[]{2}}{2} \\ \\ x=-6\pm8\sqrt[]{2} \end{gathered}[/tex]the two solutions are
[tex]\begin{gathered} x_1=5.31 \\ x_2=-17.31 \end{gathered}[/tex]the solution must be positive because it is a measure
so x=5.31feet
now we can replace the value of x on any equation to solve y(I will replace on the second equation)
[tex]\begin{gathered} x+12=y \\ 5.31+12=y \\ y=17.31 \end{gathered}[/tex]so the measurements are x=5.31 and y=17.31
21/8 and 7/8 in a mixed number
Answers
EXPLANATION:
To convert a fraction to a mixed number we must follow the following steps:
1.First we divide the numerator by the denominator.
2.The quotient becomes the integer part.
3.The remainder that the division gives, becomes the new numerator, and the quotient becomes the whole part, the denominator if it remains the same.
The exercise is as follows: 21/8
Now since 7/8 is a proper fraction, that is to say that its numerator is less than the denominator, it cannot be converted into a mixed fraction.
Given g(x) =9x^2-18x+11, for what value (s) is g(x) =23
Answers
The values of x for which g(x) = 23 are x = 2.53 and x = -0.53
Determining the values of x for which g(x) = 23From the question, we are to determine the value(s) for which g(x) = 23
From the given information,
The function is
g(x) = 9x² - 18x + 11
Now, we will substitute g(x) = 23
That is,
23 = 9x² - 18x + 11
Rearranging
9x² - 18x + 11 - 23 = 0
9x² - 18x - 12 = 0
Divide through by 3
3x² - 6x - 4 = 0
Now, solve the quadratic equation
3x² - 6x - 4 = 0
Using the general formula,
x = [-b±√(b²-4ac)]/2a
a = 3, b = -6, c = -4
x = [-(-6)±√((-6)²-4(3)(-4))]/2(3)
x = [6±√(36 + 48)]/6
x = [6±√(84)]/6
x = [6 ± 9.17]/6
x = [6 + 9.17]/6 OR x = [6 - 9.17]/6
x = 15.17/6 OR x = -3.17/6
x = 2.53 OR x = -0.53
Hence, the values of x are x = 2.53 and x = -0.53
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1. Jeremy is going to show off his skateboarding skills. He has a ramp that must beset up torise from the ground at a 30° angle. If the height from the ground to the platform is 8 feet,how far is the end of the ramp to the base of the platform? How long is the ramp up to thetop of the platform?
Answers
this is a question that involves angle of elevation and right angled triangles.
first, a diagram deoicting the scenerio is drawn below;
using the SOHCAHTOA rule for right angled triangles, we would name he distance of the ramp to the platform; x
y is length of the ramp up to the platform (the side opposite the right angle), H
8ft is the height from the ground to the platform ( the distance of the side opposite the angle), O
x is the length of the end of the ramp to the base of the platform( is the adjacent) A
THEREFORE, we will be applying TOA
[tex]\begin{gathered} \tan \theta=\text{ opposite/adjacent} \\ \cos 30=\frac{O}{A} \\ \cos 30=\frac{8}{X} \\ 0.8660=\frac{8}{x} \\ x=\frac{8}{0.8660} \\ x=9.24ft \end{gathered}[/tex]the end of the ramp is 9.24ft from the base of the platform
[tex]\begin{gathered} \sin 30=\frac{posite}{\text{hypotenuse}} \\ \sin 30=\frac{8}{y} \\ 0.5=\frac{8}{y} \\ y=\frac{8}{0.5} \\ y=\text{ 16ft} \end{gathered}[/tex]the ramp is 16ft long up to the top of the platform
1/2=_/12Find the answer for the blank space
Answers
We have to fill the blank to have an equivalent fraction:
[tex]\begin{gathered} \frac{1}{2}=\frac{x}{12} \\ \frac{1}{2}\cdot12=x \\ x=6 \end{gathered}[/tex]Answer: 6
what does the "The probability of a correct inference:" means in this question and how can i solve it
Answers
The probability that the test-taker doesn't use drugs is the ratio of the number of people who take drugs to the total number of people. Hence the probability that the test-taker doesn't take drug is
= 194/450
= 0.4311
2.
Which expressions are equivalent to the one below? Check all that apply. 9x 36* D A Св. х5 B. | * c. c. 36 D D. 9.9X+1 36 DE E. LASSE F. 9.9x-1
Answers
To answer this question we will use the following properties of exponents:
[tex]\begin{gathered} (\frac{a}{b})^x=\frac{a^x}{b^x}, \\ a^x*a^y=a^{x+y}. \end{gathered}[/tex]Now, notice that:
[tex]9=\frac{36}{4}.[/tex]Therefore:
[tex]9^x=(\frac{36}{4})^x.[/tex]Using the first property we get that:
[tex]9^x=\frac{36^x}{4^x}.[/tex]Now, notice that x=1+x-1, then:
[tex]9^x=9^{1+x-1}=9*9^{x-1}.[/tex]Answer: Options A, E, and F.
confused on perimeter
Answers
The area will be, the area of the small square plus the area of the parallelogram plus the area of the rectangle.
The area of the square:
[tex]As=l\cdot l=2\cdot2=4in^2[/tex]The area of the parallelogram:
[tex]Ap=B\cdot H=5\cdot3=15in^2[/tex]The area of the rectangle:
[tex]Ar=l\cdot w=5\cdot2=10in^2[/tex]Therefore:
[tex]\begin{gathered} A=As+Ap+Ar \\ A=4in^2+15in^2+10in^2 \\ A=29in^2 \end{gathered}[/tex]the question is "Which of the following has a value of 18?"
Answers
First Quartile is = 6
Median = 15
Range = 30 - 0
=30
Third Quatile = 24
Consider the equation and the following ordered pairs: (4, y) and (x, 1).y = 2x-5Step 2 of 2: Plot the resulting set of ordered pairs using your answers from Step 1.(the ordered pairs from the last problem are (4,3) (3,1))
Answers
In order to plot an ordered pair into the cartesian plane, we need to use the first coordinate in the x-axis and the second coordinate in the y-axis.
Then, we draw the point that has these coordinates in the plane.
For example, plotting the point (2, 3), we have:
Now, plotting the points (4, 3) and (3, 1) in the plane, we have:
are two figures congruent if they have the same size and shape true or false
Answers
From congruence triangles, it is possible to see ED is congruent to DS because they are in the same line.
Answer: DS
i am not sure what I am doing wrong here
Answers
We know that segment RS is a diameter of the circle, this means that arcs RS an RST measure 180°. Now that we know that an using the ratio for arcs RT and TS given we have:
[tex]\begin{gathered} RT+5RT=180 \\ 6RT=180 \\ RT=\frac{180}{6} \\ RT=30 \end{gathered}[/tex]Now, we know that an angle inscribed in a circle is half its intercepted arc, then we have:
[tex]m\angle RST=\frac{30}{5}=15[/tex]Therefore, we have that arc RT is 30° and angle RST is 15°