Given:
-5 (multiplicity of 3)
9 (multiplicity of 2)
-2 (multiplicity of 1)
4 (multiplicity of 1)
To make a polynomial with a given zeros and degrees, the first thing we need to do is to get the opposite values of the given zeros and add them to our variable x.
Question 5
What is the equation of the line?
y
1
4X
y = 2x + 2
y= ² x + 2
2
y = 2x - 4
y= ½x−4
-
Answer:
poto
Step-by-step explanation:
The dimensions of a right rectangular prism are 8/5cm, 10/3 cm, and 7/4cm. What is the volume of the prism? A. 25/12cm3 B. 7/3cm3 C. 16/3cm3 D. 28/3cm3
D. 28/3 cm³
1) Given those dimensions, let's plug them into the following formula for the Volume of a Rectangular Prism, and simplify those fractions
8 and 4 by 4: 2, 1
10 and 5 by 5: 2,1
[tex]\begin{gathered} V=w\cdot l\cdot h \\ V=\frac{8}{5}\cdot\frac{10}{3}\cdot\frac{7}{4} \\ V=\frac{2}{1}\cdot\frac{2}{3}\cdot\frac{7}{1} \\ V=\frac{28}{3}\approx9.33cm^3 \end{gathered}[/tex]2) Hence the volume of that Prism is 28/3 cm³
state the possible rational zeros for each function f(x)=3x^3+9x^2-23x+35
Answer is 1
We solve it using the rational zero theorem.
Find the factor (1,2,3,4,5...) that satisfies the given equation, as well as its negatives.
We discover that (-5) satisfies the equation, implying that x+5 is a factor of the equation.
[tex] 3{x}^{3} +9 {x}^{2} - 23x + 35 = 0 \\ put \: x = - 5 \\ 3 ({- 5}^{3}) + 9( { - 5}^{2} ) - 23( - 5) + 35 \\ yes \: we \: get \: 0 \: after \: solving [/tex]
When we divide the equation by x-5, we get a 3x²-6x+7 quotient As there is no remainder, the factors are (x-5) (3x²-6x+7).
We get below after solving 3x²-6x+7.
[tex]x= \frac{(6+ \sqrt (-48))} 6= \frac{1 + 2i \sqrt{3} }{3} [/tex]
[tex]x = \frac{(6 - \sqrt (-48))} 6= \frac{1 + 2i \sqrt{3} }{3}[/tex]
So there is only 1 rational zero and the other 2 zeros are irrational
To get to know more about the rational zero theorem click below
https://brainly.com/question/28828052
A ⊆ B
S (B\A)=28, S(B)=5.S(A). S(A)=?
Answer:
S(A) = 7
Step-by-step explanation:
A ⊆B means A is a proper subset of B. That means all elements of set A are also elements of set B
S(B\A) means the set of all elements of B that are not in set A. This is given as 28
We are also given S(B) = 5.S(A)
Since A is a subset of B, S(B) = set of all elements in A and set of all elements in B but not in A
In other words
S(B) = S(A) + S(B\A)
Since S(B) = 5S(A) we get
5S(A) = S(A) + S(B\A)
5S(A) = S(A) + 28
5S(A) - S(A) = 28
4S(A) = 28
S(A) = 7
x - 3y = 15Use the choices below to determine the type of function above-Quadratic-Exponential-Linear-none of these
In a quadratic equation, the variable x must be raised ti a power of two, this is not our case, since x is not raised to any power.
Linear equations has the form:
y=mx+b, let's arrange our equation to see if we have a linear equation
x-3y=15
by adding 3y in both sides:
x-3y+3y=15+3y
we can cancel 3y in the left side, then we have:
x=15+3y
subtracting 15 from both sides
x-15=3y
dividing by 3 in both sides:
[tex]\frac{3y}{3}=y=\frac{x-15}{3}=\frac{1}{3}x-\frac{15}{3}=\frac{1}{3}x-5[/tex]as we can see, our equation fits into the form of linear equation y=mx+b, where m=1/3 and b= -5
Find the area of the parallelogram in feet. Round to the nearest hundredth if necessary.
Area of parallelogram = base x height = 5 x 4 = 20 square meter
Now in feet it is 1m = 3.28084 ft
1 square metre= 10.7639111 square ft
20 square meter = 215.2782221 square ft
To the nearest hundredth it is 215.28ft
Evaluate each expression when Y equals 5. 12+4y
please help meYour primary job's gross income is $3,500.00/month, and your second job's realized income is $368.49/month. Deductions are FICA (7.65%), federal tax withholding (10.75%), and state tax withholding (8.35%). How much is the income on your monthly budget?$_______ /month
EXPLANATION
To determine how much is the income, we need to apply the following calculations:
(3500 + 368.49) - ((3500 + 368.49) x (0.0765 + 0.1075 + 0.0835)) = Income
Adding numbers:
(3868.49) - ((3868.49)*(0.2675)
Multiplying numbers:
= (3868.49) - 1034.82
Subtracting numbers:
= 2833.67
In conclusion, the income was $2833.67
Answer:
its $2,932.24
Step-by-step explanation:
The total cost of a purchase of a number ofChromebooks, x can be represented by the functionc(x) = 250x. Which set of numbers best defines thedomain of c(x)? Explain how you know.A: integersB: Positive IntegersC: Rational NumbersD: Positive Rational Numbers
The Answer is Positive Integers (B)
The number of Chromebooks = x
The total cost of purchasing Chromebooks = c(x)
where x is the domain of c(x)
The number of Chromebooks x can be: {0, 1, 2, 3, 4, 5, 6...}. You cannot have numbers like {0.2, 0.5, 3.8 ...} or any other decimal neither can you have surds like:
[tex]\sqrt[]{3},\sqrt[]{8},\sqrt[]{55},\text{ and so on}[/tex]Integers contain numbers like: {... , -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...}
Positive Integer contains numbers like: {1, 2, 3, 4, 5, ...}
Rational Numbers contain numbers like: {-0.2, -0.1, -0.05, -0.005,0.2, 0.1, 0.05, 0.005,...} and also contain numbers like {... , -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...} as in Integers.
Positive rational Numbers are just the positive values of Rational Numbers like: {1, 2, 3, 4, 5, ...} and {0.2, 0.1, 0.05, 0.005,...}
From the information laid out, it is obvious that the only set of values that qualify to be called the domain of c(x) is Positive Integers
The Answer is Positive Integers (B)
What is the value of the coefficient of the 4th term in the expansion of (a + b)^12?A. 220B. 985C. 1320D. 445
Binomial expansion
[tex](a+b)^n=\sum ^n_{k=0}nC_k\cdot a^{n-k}\cdot b^k[/tex]The coefficient of each term is:
[tex]_nC_k[/tex]That is, the number of combinations of k objects from a set with n objects
In the binomial:
[tex](a+b)^{12}[/tex]the value of n is n = 12. In the fourth term, k = 3 (remember that k starts at zero). Therefore, the coefficient of the 4th term is:
[tex]_{12}C_3=\frac{12!}{(12-3)!\cdot3!}=\frac{12!}{9!\cdot3!}=\frac{12\cdot11\cdot10\cdot9!}{9!\cdot3\cdot2\cdot1}=\frac{1320}{6}=220[/tex]Find the range rule for the inverse function y=sin^-1(x). here are my answer options:Interval [1,-1] in quadrants 1 and 4Interval (-pi/2, pi/2) in quadrants I and IIIInterval [0,pi] in quadrants I and IIinterval [-pi/2, pi/2] in quadrants I and IV
The domain of Sine function (sin(x)) is given by
[tex]-\frac{\pi}{2}\le x\le\frac{\pi}{2}[/tex]since the domain of a function is the range of its inverse, therefore, the answer is:
[tex]\begin{gathered} \text{Range of the sine inverse function:} \\ -\frac{\pi}{2}\le y\le\frac{\pi}{2} \end{gathered}[/tex]which corresponds to the interval:
[tex]\lbrack-\frac{\pi}{2},\frac{\pi}{2}\rbrack\text{ In quadrants I and IV}[/tex]In the system below, What will zero out when you add these two equations?
when adds the equations
4x+(-4x)=0
therefore
the answer is the first option
this wont be graded but i need the help with it
Answer:
f(-1) = 0
f(0) = -1
f(1) = 0
Explanation:
Given the below function;
[tex]f(x)=x^2-1[/tex]We're to find the corresponding values of f(x) given different values of x.
To determine the value of f(x) for each value of x, all we need to do is to substitute the said value of x into the function and solve for f(x).
When x = -1, let's go ahead and find f(-1);
[tex]f(-1)=(-1)^2-1=1-1=0[/tex]When x = 0, let's solve for f(0);
[tex]f(0)=(0)^2-1=0-1=-1[/tex]When x = 1, let's solve for f(1);
[tex]f(1)=(1)^2-1=1-1=0[/tex]Evaluate the following product. Leave your answer in scientific notation.(3.6 x 10-4)(5.9 x 10-9)
Given:
[tex](3.6\times10^{-4})(5.9\times10^{-9})[/tex][tex]\begin{gathered} (3.6\times10^{-4})(5.9\times10^{-9})=21.24\times10^{-13} \\ =2.124\times10^{-12} \end{gathered}[/tex]Use the given conditions to write an equation for the line in point-slope form and slope-intercept form Passing through (-2,4) and parallel to the line whose equation is x-3y = 7
The equation for the line is:
3y - x = 14
Explanation:Given the line:
x - 3y = 7
This line can be written as:
y = (1/3)x - 7/3
The slope is 1/3
The y-intercept is -7/3
A line parallel to this has the same slope but different y-intercept, written as:
y = (1/3)x + b
Using the given point (-2, 4), with x = -2 and y = 4, we can obtain the value of b
4 = (1/3)(-2) + b
b = 4 + 2/3
= 14/3
Therefore, the line is:
y = (1/3)x + (14/3)
or
3y - x = 14
You make seven dollars and 3/4 per hour if you made 248 last week dollars how many hours did you work
Answer:
Step-by-step explanation:
248/7.25= 34.21
The Cat is a high-speed catamaran auto ferry that operates between City A and City B. The Cat can make the trip in about 2 hours at a speed of 59 mph. About howfar apart are City A and City B?What is the distance between City A and City B?The distance between City A and City B is
The Cat can travel 59 miles in 1 hour. If the trip lasts 2 hours, then to find the distance between city A and B we can use the next proportion:
[tex]\frac{59\text{ miles}}{x\text{ miles}}=\frac{1\text{ hour}}{2\text{ hours}}[/tex]Solving for x:
[tex]\begin{gathered} 59\cdot2=1\cdot x \\ 118\text{ miles = x} \end{gathered}[/tex]The distance between City A and City B is 118 miles
determine if the sequence converges or diverges 8, 108, 208, 308, 408
Hello there. To solve this question, we'll have to remember some properties about convergence of sequences.
Given the following sequence:
[tex]\mleft\lbrace a_1,a_2,\ldots,a_n\mright\rbrace[/tex]If it is a finite sequence, then it converges to its last term, that is the lim sup (or greatest term of the sequence).
If it is infinite, then the sequence only converges if this limit exists and is equal to zero, that is:
[tex]\lim _{n\rightarrow\infty}a_n=0[/tex]With this, we'll be able to determine whether the following sequence is convergent or not:
[tex]S=\mleft\lbrace8,108,208,308,408\mright\rbrace[/tex]Since it is a finite sequence, we already know it converges.
The lim sup of this sequence is its largest term, in this case, 408, and we write:
[tex]\limsup S=408[/tex]If it was an infinite sequence, on the other hand, we would have to determine the general term a_n and see if the limit is equal to zero.
Notice that there is a pattern between the values: the difference between two consecutive numbers is equal to 100.
In other words, it is an arithmetic progression with ratio equal to 100.
This means that we can use the following formula:
[tex]a_n=a_1+(n-1)\cdot r[/tex]Where a_1 = 8 and r = 100, therefore:
[tex]\begin{gathered} a_n=8+(n-1)\cdot100 \\ a_n=8+100n-100 \\ a_n=100n-92 \end{gathered}[/tex]And taking the limit as it goes to infinity, we have that:
[tex]\lim _{n\to\infty}a_n=\lim _{n\to\infty}100n-92=\infty[/tex]That is, the limit is not zero (not even a real number), so the sequence would not converge.
Find the area of the window. Round to the nearest tenth
Hello there. To solve this question, we'll have to remember some properties about finding the area of polygons.
First, notice the area of this window is a merge of the areas of a rectangle, with length 5 dm and width 12 dm, and a semicircle with diameter 5 dm (since its bottom is parallel to the rectangle).
In this case, remember the formulas for:
Area of a rectangle
Area of a semicircle (diameter)
Therefore the area of the window will be given by:
Using 3.14 as an approximation for pi, we have:
[tex]A\approx69.8dm^2[/tex]This is the area of the window we've been looking for.
Total Area of window = 69.81 dm²
Firstly, we need to notice the area of this window is a combination of the areas of a rectangle, with a length of 5 dm and width of 12 dm, and a semicircle with a diameter of 5 dm.
Thus, Total Area = The Area of the rectangle + The Area of Semi circle.
Formulas :
Area of Rectangle = length * breadth Area of a semicircle = PI * (radius)* (radius)Therefore the Area of the Window will be given by:
Using PI = 3.14,
Total Area = ( 5 dm * 12 dm ) + ( 3.14 * 2.5 * 2.5 )/2
= 60 + 9.81 = 69.81 dm²
Therefore Area of the window is 69.81 dm².
Know more about the Area of the Rectangle: https://brainly.com/question/2607596
#1 What is the equation of the line that passes through the point (1, 6) with a slope of -5? Write the equation in point-slope form.
Point-slope form:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line. Replacing with m = -5 and point (1, 6) we get:
y - 6 = -5(x - 1)
For the following inequality, write the solution set in set-builder and interval notation, and graph the solution seton a number line.Set-builder notation: {x||Interval notation:Graph the solution set:
We have a inequality defined as:
[tex]x\leq\frac{2}{3}[/tex]We have to express it in set-builder notation.
We can do it directly as:
[tex]\lbrace x|x\leq2\/3\rbrace[/tex]If we have to express it in interval notation we can express all the values of x that are equal to or less than 2/3 as:
[tex]x\in(-\infty,2\/3][/tex]Finally we can graph this in a number line as:
Answer:
Set-builder notation: { x | x ≤ 2/3 }
Interval notation: (-∞, 2/3]
Number line: picture in the answer
Find the lateral surface area and volume of the cylinder shown in the picture and round answer to nearest whole number as needed
We will solve as follows:
In order to determie the lateral surface area and also the volume for the circular cylinder we operate as follows:
*Lateral surface area: We will determine the lateral surface area, this is the product of the circumference times the height:
[tex]A=C\cdot h[/tex]Then:
[tex]A=(2\pi r)\cdot h\Rightarrow A=2\pi(2)(15)[/tex][tex]\Rightarrow A=60\pi\Rightarrow A=188.4955592[/tex][tex]\Rightarrow A\approx188[/tex]So, the lateral surface area is approximately 188 square inches.
*Volume: We have that the volume for a circular cylinder is give by:
[tex]V=\pi r^2h[/tex]Then:
[tex]V=\pi(2)^2(15)\Rightarrow V=60\pi[/tex][tex]\Rightarrow V\approx188[/tex]So, the volume of the cylinder is approxiately 188 cubic inches.
How can I get to know the equation of a straight line when I have the two points?
ANSWER
[tex]y=5x-6[/tex]EXPLANATION
Let the two points be (2, 4) and (3, 9).
The general form of the equation of a straight line is given by:
[tex]y=mx+b[/tex]where m = slope
b = y-intercept
First, we have to find the slope of the line using the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1, y1) and (x2, y2) are the two points that the line passes through
Therefore, the slope of the line is:
[tex]\begin{gathered} m=\frac{9-4}{3-2}=\frac{5}{1} \\ m=5 \end{gathered}[/tex]Now, we find the equation of the line using the point-slope method:
[tex]y-y_1=m(x-x_1)[/tex]Therefore, the equation of the line is:
[tex]\begin{gathered} y-4=5(x-2) \\ y-4=5x-10 \\ y=5x-10+4 \\ y=5x-6 \end{gathered}[/tex]NEED HELP !!!!!!!!!!! TYYY
Answer:
The equation is T=$2256-($40/week)*t. The money left after 8 weeks is $1936
Step-by-step explanation:
The amount Jack will have left (T) is the difference of his initial savings ($2256) and the amount he will spend after w weeks ($40/week)w:
a) T = $2256 - ($40/week)*t, where t is in weeks
b) T = $2256 - ($40/week)*(8 weeks), where t is 8 weeks
T = $1936
graph the equation x + 4y equals negative 6 but plotting points
In order to graph the equation, we need to find two points that are solution of the equation, then we plot the points and the line that passes through both points.
To find the points, we can choose values for x and then calculate the correspoding values of y.
For x = -2 and x = 2, we have:
[tex]\begin{gathered} x=-2\colon \\ -2+4y=-6 \\ 4y=-6+2 \\ 4y=-4 \\ y=-1 \\ \\ x=2\colon \\ 2+4y=-6 \\ 4y=-8 \\ y=-2 \end{gathered}[/tex]So we have the points (-2, -1) and (2, -2). Graphing the points and the line, we have:
The San Diego Clippers won 6 of their first 9 games how many games will they win in 15 games
win / total = 6 /9
For 15 games:
x / 15
Where x is the number of wins in 15 games.
[tex]\frac{6}{9}=\frac{x}{15}[/tex]Cross multiply:
[tex]6\cdot15=9x[/tex][tex]90=9x[/tex]Divide both sides by 9
[tex]\frac{90}{9}=\frac{9x}{9}[/tex][tex]x=10[/tex]They will win 10 games.
Segment LC= segment JB= Angle K= triangle MLC= angle M= triangle KBJ=
Given that triangle LMC is congruent to triangle BJK
To Determine: The segment that is congruent to segment LC
Solution:
If triangle LMC is congruent to triangle BJK, then it follows that
[tex]\begin{gathered} \Delta LMC\cong\Delta BJK \\ \text{Then,} \\ \angle LM\cong\angle BJ \\ \angle MC\cong\angle JK \\ \angle LC\cong\angle BK \end{gathered}[/tex]Hence, segment ∠LC ≅ segment ∠BK
What is the value of 4(x − 2)(x − 3) + 7(x-2)(x - 5) - 6(x - 3)(x - 5) when * = 5?
Answer:
24
Step-by-step explanation:
Substitute 5 for x.
4(5-2)(5-3) + 7(5-2)(5-5) - 6(5-3)(5-5)
Simplify data inside of parenthesis.
4(3)(2) + 7(3)(0) - 6(2)(0)
Because anything multiplied by 0 is 0, you can cancel out the last 2 terms.
Remaining term.
4(3)(2)
Solve: 12*2
24
11. Which of the following answers represents a correct way to set up and solve for y? D (4y - 4) ° 3y (x - 5) 128 A B. O - X-5 + 128 = 180 ТС O 4y - 4 + 3y +128 = 180 4y - 4 + 3y = 128 4y - 4 + 3y = 180
We will have that the solution is given by:
[tex](4y-4)+128+3y=180[/tex]So, the answer is option 2.
***
if the vertical height of the roller coaster below is 315 feet, find d to the nearest foot.
we have that
cos(47)=315/d -----> by adjacent side divided by the hypotenuse
solve for d
d=315/cos(47)
d=462 feet
therefore
answer is option B