Problem 1
Answer: The roots are x = 0, x = 2, x = -3
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Explanation:
The term "root" is another way of saying "zeros of a function" or "x intercept".
To find the roots, set each factor equal to zero and solve for x.
x-2 = 0 solves to x = 2, while x+3 = 0 solves to x = -3
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Problem 2
Answer: Roots are x = 1, [tex]x = i\sqrt{5}[/tex] and [tex]x = -i\sqrt{5}[/tex]
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Explanation:
Factor by grouping
x^3 - x^2 + 5x - 5 = 0
(x^3 - x^2) + (5x - 5) = 0
x^2(x - 1) + 5(x - 1) = 0
(x^2 + 5)(x - 1) = 0
x^2 + 5 = 0 solves to the roots [tex]x = i\sqrt{5}[/tex] and [tex]x = -i\sqrt{5}[/tex]
x-1 = 0 solves to x = 1
Note: [tex]i = \sqrt{-1}[/tex]
1) Wat are the real zeros of the function y=x(x-2)(x+3):
Answer: [tex]x_{1} = -3 ; x_{2} = 0; x_{3} =2[/tex]
To find the x-intercept, set y = 0:
x( x -2 ) ( x + 3) = 0
Apply the Zero Product Property:
x - 2 = 0 or x + 3 = 0
x = 2 or x = -3
Find the union of solutions:
x = 0 or x = 2 or x = -3
2) Find all of the solutions of the equation
x^3 -x^2 +5x - 5 = 0
Answer: x = 1 or no real solution
Apply grouping:
[tex](x^{3} -x^{2} ) + *(5x-5)=0[/tex]
Factor out common factor:
[tex]x^{2} (x-1) +5(x-1)=0[/tex]
Factor out --> [tex](x-1)(x^{2} +5) =0[/tex]
Apply zero product property:
[tex]x - 1 =0[/tex] or [tex]x^{2} +5 =0[/tex]
x - 1 = 0
Rearrange variables to the left side of the equation--> x=1 or no real solutions.
Date : . The perimeter of Kite LIKE is 80 cm. The length of LI is 6cm less than Length of IK. Find the length of each side?
Answer:
lK = KE = 23cm
LI = LE = 27cm
Step-by-step explanation:
perimeter of kite LIKE =80cm
If IK=x cm
LI=(x-6) cm
Perimeter =2(a+b)
80 = 2(x+(x-6))
80 = 2(x+x-6)
80 = 2(2x-6)
80/2 = 2x-6
40 = 2x-6
2x = 40+6
2x = 46
x =46/2
x = 23
therefore,IK = 23cm
LI = 23-6 = 27cm
A car travels 14km in 25mins . Find out how far the car can travel in 5 hours if the speed remains the same ?
Answer:
168 km
Step-by-step explanation:
1 hour = 60 minutes
⇒ 5 hours = 5 × 60 = 300 minutes
We have been told the distance that the car traveled in 25 minutes.
Therefore, divide 300 minutes by 25 minutes:
[tex]\implies \sf \dfrac{300}{25}=12[/tex]
So there are 12 'lots' of 25 minutes in 5 hours.
Therefore, to find out how far the car travels in 5 hours, multiply the distance traveled in 14 km by 12:
⇒ total distance = 12 × 14 = 168 km
25min=25/60=5/12h
Speed:-
Distance/time14÷5/1214×12/533.6km/hTotal distance in 5h
5(33.6)168kmWhat is the product
(3a^2b^7)(5a^3b^8)
Answer:
15a^5b^15
Step-by-step explanation:
There's a law of indices which states that when multiplying numbers, if they are the same, the power just add up.
So here 3a^2*5a^3 = 3*5a^2+3, which equals to 15a^5.
As for the b part of the terms, b^7*b^8 = b^7+8, which equals to b^15.
I hope this makes sense.
Answer:
option number 3
Step-by-step explanation:
15a^ 5 b^ 15
Triangle ABC IS an isosceles
Form and solve an equation to find the value of t.
40 cm
2t + 5 cm
3t - 8 cm
Answer:
Step-by-step explanation:
The lengths of the sides of a triangle are 3t, 5t - 12, and t + 20 . a. Find the value(s) of that t make the triangle isosceles. b. Does any value of make the triangle equilateral?
As you can see, I have my subsidies trying out and, like, a lot of time president focused on assessing. Okay, so we need to figure out what seat for the size that we're giving you could put them in any order you want. So we're gonna try this order for us, and then we're gonna try. So we're gonna do you know that the inside of the a softly triangle in this out of this triangle are equal to each other. And when you add them together, there has to be greeted with this out of this. Had a trying. So we're first gonna do three t is equal to five t oneness. Well, arguments of drugs five from both sides fascinate this negative to t is equal to negative. After this, we could divide negative to on both sides to find out what see is to get T bites so tracked, divided by negative tune. And then we're gonna do t is equal to negative 12 of our negative to 6 36 So we're going to check our solution by plugging in six. So when we plug six into this equation, we're gonna gate 18 3 times six is 18. And when we plug six into this equation, we're gonna get five times six, which is dirty five times six is 30 and you're going to subtract. Told him 30 that gave to. And then we're gonna put 6 40 and we're gonna add it to Tony, which is 26. And then after this, we're gonna add these two 18 18 to figure it out if it's hired into 6 18 plus 18 is 36. So it's harder 26 c is equal to is equal to six. Like I said before, this is not the only order because switch up the sides with them in different places. So I'm gonna take away this side. I took a week this, and I'm gonna put I want to take with this ad too, and I'm in. I'm gonna put t this 20 this side and five C minus. Whoa, This Okay, so we're gonna do the same thing we did over here. We're gonna do three t is equal to C plus 25 because these two sides great. See? Do you see before? See e waas 20 first. We're going to subtract C from both sides we're gonna get to t is equal to finding. And then we're gonna divide to from both sides to get by itself. And, uh, an anti is equal to 10 because 20 the bottom right to it. So we also know that he gave me 10. So we're gonna plug 10 in today, San plus 10 times their times three is equal to this is dirty. And we also know we're gonna put 10 for this side. A tent was 20 is dirty also, it's an end times what? It's 50 When you subtract well, you get 36. No, you get 30 feet, you get 38 when you add 30 plus dirty is 60. So this works. So t is also equal to 10 and we're gonna switch up the order again. This sound this one, I believe this one. And also as you know, we're switching at the side, trying all the possible leads with right. Let's go drop this trying. So this side now will be treaty. And this I will be five c minus slow. We're gonna go. We're gonna do five minutes. 12 is equal to 10 is equal city plus 20 because we know these two sides has equal five feet on its 12. I just love equal See loose. Okay, As you can see, we're going to subtract, see from both sides. And I was going to or C and I'm going to do two steps at a time for gonna actual on this side to everything this tool to get rice on one side of the equation. So I'm gonna add so so both side, and it's gonna before C is equal to dirty, too. We're gonna divide both sides by four to get see bites. So four divided by 36 is line for teeth equal to nine. We're gonna plug that incident equation tee. Times five is nine times five is 45. We're gonna subject for from him that is equal to 32. 33 and then we're gonna do nine waas 20. So amid a misty 2012 is actually 32. So these so t is actually equal to eight because three times 32 divided by four is eight. And we're gonna redo this one because so eight times five is 40 eight times five is sporting. And when we take away Whoa. 40 minus 12 is 28 is doing a So we're gonna do and we're gonna put in April. See here too. This is gonna be a plus 20 which is 28. We're gonna plug in eight for decide eight times three is 24 24. And as you see, this is obviously lower. It's gonna be lowered, indecent. Act together. So, you know, seek and also equal to eight. So for the sausages triangle there. Three possible answers for teeth, depending on how you put the sides which side before, which in just it depend on how you put your sides for the collateral. We know that all of the size has to equal to one thing. And from this, the signs don't equal the same thing One of them is You could get two of them to equal to each other so you can get rid of the size to be able to the same thing. So for the equilateral triangle, it's not possible. So not
if trapezium of area 140 cm horsepower sides 10 cm apart and one of them decides is 16 cm longfind the area find the length of the sother side
Given :
Area of the trapezium is 140 cm².Its height is 10 cm.One of the parallel side is 16 cm.To Find :
The other parallel side.Solution :
Let the other parallel side be xWe know that,
[tex]{ \qquad \: \pmb{ \dfrac{1}{2} \times (sum \: of \: the \: parallel \: sides) \times height} = \pmb{Area_{(trapezium)}}}[/tex]
Now, Substituting the given values in the formula :
[tex]\qquad { \dashrightarrow \: { \sf{ \dfrac{1}{2} \times (16 + x)\: \times 10 \: = {140}}}}[/tex]
[tex]\qquad { \dashrightarrow \: { \sf{ 5 \times (16 + x)\ \: = {140}}}}[/tex]
[tex]\qquad { \dashrightarrow \: { \sf{ 80 + 5x = {140}}}}[/tex]
[tex]\qquad { \dashrightarrow \: { \sf{ 5x = {140 - 80}}}}[/tex]
[tex]\qquad { \dashrightarrow \: { \sf{ 5x = {60}}}}[/tex]
[tex]\qquad { \dashrightarrow \: { \sf{ x = { \dfrac{60}{5} }}}}[/tex]
[tex]\qquad { \dashrightarrow \: { \pmb{ x = { 12 }}}}[/tex]
Therefore,
The other parallel side of the trapezium is 12 cm.Can you help answer this question.
Answer: Top right
Step-by-step explanation:
This is substituting into point-slope form.
Write and solve a proportion to answer the question.
48 is what percent of 160?
show steps to get brainliest
Answer:
76.8% or 77%
Step-by-step explanation:
first you would want to multiply 48*160=7680 then you would want to divide by 100 to get it down to a reasonable number, or another way to do it would be to divide 48first by 10 to get it to a decimal and out of the precents, then multiply that by 160 which would give the same answer.
Part A
The first part of Ray and Kelsey's roller coaster is a curved pattern that can be represented by a polynomial function.
Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has 4 intercepts. Kelsey argues the function can have as many as 3 zeros only. Is there a way for the both of them to be correct? Explain your answer.
Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.
g(x) = x3 − x2 − 4x + 4
g(x) = x3 + 2x2 − 9x − 18
g(x) = x3 − 3x2 − 4x + 12
g(x) = x3 + 2x2 − 25x − 50
g(x) = 2x3 + 14x2 − 2x − 14
Create a graph of the polynomial function you selected from Question 2.
Part B
The second part of the new coaster is a parabola.
Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = ax2 + bx + c. Describe the direction of the parabola and determine the y-intercept and zeros.
The safety inspector notes that Ray also needs to plan for a vertical ladder through the center of the coaster's parabolic shape for access to the coaster to perform safety repairs. Find the vertex and the equation for the axis of symmetry of the parabola, showing your work, so Ray can include it in his coaster plan.
Create a graph of the polynomial function you created in Question 4.
Part C
Now that the curve pieces are determined, use those pieces as sections of a complete coaster. By hand or by using a drawing program, sketch a design of Ray and Kelsey's coaster that includes the shape of the g(x) and f(x) functions that you chose in the Parts A and B. You do not have to include the coordinate plane. You may arrange the functions in any order you choose, but label each section of the graph with the corresponding function for your instructor to view.
Part D
Create an ad campaign to promote Ray and Kelsey's roller coaster. It can be a 15-second advertisement for television or radio, an interview for a magazine or news report, or a song, poem, or slideshow presentation for a company. These are just examples; you are not limited to how you prepare your advertisement, so be creative. Make sure to include a script of what each of you will say if you are preparing an interview or a report. The purpose of this ad is to get everyone excited about the roller coaster.
Answer:
Tell a Small question i cant read it tho
Step-by-step explanation:
Answer:
i am doing the same thing lol basically the farthest i got was
Step-by-step explanation:
1. They both cannot be correct because a three-degree polynomial can only have 3 maxium terms.
2. i chose g(x) = (x + 2)(x − 1)(x − 2)
3. the graph is the first one shown
PLEASE HELPPP kahsjahsjad I need help
Answer:
[tex]166\frac{2}{3} *x=y[/tex]
Step-by-step explanation:
[tex]\frac{500}{3} =166\frac{2}{3}[/tex]
Therefore, [tex]166\frac{2}{3} *x=y[/tex]
Express the equation 8x + 3y - 24 = 0 in slope intercept form ?
Subtract - 7x – 9 from -4.2 + 3x – 5
Answer:
−4x^2 + 10x+ 4
Step-by-step explanation:
that is the simplifyed version of the expression
Answer: The answer is −4x−9.8
Step-by-step explanation:
−7x−9−−4.2+3x−5
The opposite of −4.2 is 4.2.
−7x−9+4.2+3x−5
Add −9 and 4.2 to get −4.8.
−7x−4.8+3x−5
Combine −7x and 3x to get −4x.
−4x−4.8−5
Subtract 5 from −4.8 to get −9.8.
−4x−9.8
Ps: I hope this is correct, hope it helps also have a great day.
sue gets 4 texts every 10 minutes. how many texts does she get in a week.
Answer:
4032
Step-by-step explanation:
1 day is 1440 min
1440 divided by 10 = 144
144 times 4 = 576
576 times 7 (because there are 7 days in a week) = 4032
*I may be wrong if so im sorry*
Possible
C_m_i_a_i_n_
Theoreticali
E_p_r_m_n_a_
What is the missing letters in Maths for Probability - Listing Outcomes?
Answer:
Last one is EXPERIMENTAL
Step-by-step explanation:
Hope it helps!!!
He wins 5 games out of every 13 games. If he plays 78 games, how many would we expect him to win?
- - - - - - - - - - - - - - - - - - - - - - - - - - -
If 'he' wins 5 out of 13 games, that's an immediate ratio of 5:13.
- - - - - - - - - - - - - - - - - - - - - - - - - - -
Let's call him Max :)
Okay, now for the math.
I'm going to try a number line- but first, we have to know how many times 13 goes into 78.
- - - - - - - - - - - - - - - - - - - - - - - - - - -
78 / 13 = 6
So now we multiply the ratio (5:13) by six...
30:78
That's the answer!
- - - - - - - - - - - - - - - - - - - - - - - - - - -
Good luck!
~pinetree
You need to download 3 games for your math class. Each game is the same price. Since this is your first time downloading a game from the site, you are also charged a one-time $0.50 access fee. You are charged a total of $4.35. What is the cost of each game? Show your work and round your answer to the nearest cent.
pls show your work
Answer:
each game cost 1.28
Step-by-step explanation:
4.35- 0.50
3.85
3.85/3 = 1.283 rounded to 1.28
Use synthetic division to find the result when 4x^4 + 11x^3 + 17x^2 + x-9 is divided by x + 1.
Answer:
4x^3-26x^2+15x-3
Step-by-step explanation:
STEP 1:
Simplify 3/1
The equation at the end of step 1:
(4•(x3)-(26•(x2)+15x)-3
STEP 2:
The equation at the end of step 2:
(4 • (x3) - (2•13x2)+ 15x) - 3
STEP 3:
The equation at the end of step 3:
(22x3 - (2•13x2)+ 15x) - 3
STEP 4:
Checking for a perfect cube
4.1 4x3-26x2+15x-3 is not a perfect cube
Trying to factor by pulling out :
4.2 Factoring: 4x3-26x2+15x-3
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 15x-3
Group 2: 4x3-26x2
Pull out from each group separately :
Group 1: (5x-1) • (3)
Group 2: (2x-13) • (2x2)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
Polynomial Roots Calculator :
4.3 Find roots (zeroes) of : F(x) = 4x3-26x2+15x-3
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above-mentioned tools. It would only find Rational Roots that are numbers x which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 4 and the Trailing Constant is -3.
The factor(s) are:
of the Leading Coefficient: 1,2,4
of the Trailing Constant: 1,3
Let us test...
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -48.00
-1 2 -0.50 -17.50
-1 4 -0.25 -8.44
-3 1 -3.00 -390.00
-3 2 -1.50 -97.50
-3 4 -0.75 -30.56
1 1 1.00 -10.00
1 2 0.50 -1.50
1 4 0.25 -0.81
3 1 3.00 -84.00
3 2 1.50 -25.50
3 4 0.75 -4.69
Polynomial Roots Calculator found no rational roots
Final result :
4x3 - 26x2 + 15x - 3
A square has a perimeter of 16 units and an area of 16 square units. What is the side length of the square? Show your work.
Answer:
4 units
Step-by-step explanation:
according to question:
perimeter of square = 16 units
4a = 16
where a is the side length
a = 16/4
= 4 units
Step-by-step explanation:
that r = P/(2π) so A = π(P/(2π))2 = P2/(4π). Any positive area less than this is also possible. So in this problem the largest area possible is (16 in.)2/(4π) = 64/π sq.
a) 4/15 + 2/5
its urgent pls
Answer:
10/15, or 2/3
Step-by-step explanation:
To get common denominator multiply 2/5 by three: 6/15
4/15 + 6/15 = 10/15
divide by 5: 2/3
Hey there!
4/15 + 2/5
≈ 4/15 + 6/15
≈ 4 + 6 / 15 - 0
≈ 10 / 15
≈ 10 ÷ 5 / 15 ÷ 5
≈ 2/3
Therefore, your answer is: 2/3
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Which radian measure is equivalent to −15°?
−9π/20
−20π/9
−12π
−π/12
Answer:
-π/12
Step-by-step explanation:
1) -15 * π/180 =
2) = -π/12
Answer:
D
explanation:
I took the quiz
i really need help
[tex]3\pi +\frac{2\pi }{3}[/tex] ?
Answer:
Image attached below with answer in decimal form and fraction form
Pls help me identify the angle
Answer:
x=45°
Step-by-step explanation:
By linear pair property
[tex]x+135=180[/tex]
[tex]x=180-135[/tex]
[tex]x=45^o[/tex]
~
Tell whether the statement is always, sometimes, or never true. Explain.
The LCD of two rational expressions will have a degree greater than or equal to that of the denominator with the higher degree
The LCD of two rational expressions will have a degree greater than or equal to that of the denominator with the higher degree,
What is least common denominator (LCD)?
The least common denominator (LCD) of two rational expressions is the least common multiple (LCM) of the denominators. When adding or subtracting two rational expressions, the LCD is first determined before computation.
The LCD of two rational expressions will have a degree greater than or equal to that of the denominator with the higher degree,
Find out more on LCD at: https://brainly.com/question/24368819
dont understand this pls help
True or false?
The point (-9, 7) is a reflection of (9, 7) over the y-axis
(will give brainleist)
Answer:
true, because in a point it is (x,y) which the x moves left and right and the y moves up and down and the y axis goes straight up and down in the middle of the graph so the x would reflect from -9 to 9 because it is going across the y axis going up and down.
Step-by-step explanation:
take advantage of free food, in this case free answers.
I need Help Plssss!!!♥
Step-by-step explanation:
such a rectangular prism is in that sense like a cube (or die) : it has 6 sides or surface areas. top, down, front, back, left, right.
to get the total surface area we need to calculate each individual side area and sum all 6 of them up.
since it is a rectangular shape, there are 3 pairs of equal side areas, so, we really need to calculate only 3 different ones :
front and back : each is
10×9 = 90 in², both together are 180 in²
left and right : each is
8×9 = 72 in², both together are 144 in²
top and bottom : each is
10×8 = 80 in², both together are 160 in²
the total surface area of the prism is
180 + 144 + 160 = 484 in²
ASAP help plsss!!
Is the following graph proportional? How do you know?
Answer:
it’s is because it’s linear and going up
Step-by-step explanation:
what is A sq divied by B sq
Answer: (a + b)2 = a2 + b2 + 2(a - b)2 = a2 + b2 - 2ab a2 - b2 = (a + b) (a - b) (x + a) (x + b) = x2 + x (a + b) + ab (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
(a + b)3 = a3 + b3 + 3ab(a + b) (a - b)3 = a3 - b3 - 3ab(a - b) a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca)
Step-by-step explanation:
Michael has x dollars saved. John has $18 more than Michael. Their friend Ian has $2 less than two-
thirds that Michael has. The total amount of money they have is $272. How much does Michael
have?
Answer:
$96
Step-by-step explanation:
Micheal's money = x
John's money = y
Ian's money = z
x + 18 = y
2/3x - 2 = z
x + y + z = $272
rearrange the equations we have:
2/3x = z + 2
x = 3/2(z + 2)
x = y - 18
Substitute y - 18 into x values:
3/2(z + 2) = y - 18
y - 18 + y + z = 272 --> 2y - 18 + z = 272
Solve for y:
Firstly rearrange
2y - 18 + z = 272 --> z = 272 + 18 - 2y, which simplifies to z = 290 - 2y
substitute into the formula:
3/2((290 - 2y) + 2) = y - 18
3/2(292 - 2y) = y - 18
438 - 3y = y - 18
4y = 456
y = $114
Substitute back into the formula to find z:
z = 290 - 2(114)
z = 290 - 228
z = $62
Put all of this back into one of the original formulas to find x:
x + y + z = 272
x + 114 + 62 = 272
x + 176 = 272
x = $96
Total amount = $272
Now, ATQ[tex] \tt \nrightarrow \: x + 18 + x + 2 - \frac{2}{3} x = 272[/tex]
[tex] \tt \nrightarrow \: 2x + 20- \frac{2}{3} x = 272[/tex]
[tex] \tt \nrightarrow \: 6x + 60 - 2x = 816[/tex]
[tex] \tt \nrightarrow \: 4x + 60 = 816[/tex]
[tex] \tt \nrightarrow \: 4x = 816 - 60[/tex]
[tex] \tt \nrightarrow \: 4x = 756[/tex]
[tex] \tt \nrightarrow \: x = 189[/tex]
➪ Thus, Michael has $189...~
Chang buys candy that costs 4$ per pound. He will buy at least 11 pounds of candy. What are the possible amounts he will spend on candy? Use c for the amount Chang will spend on candy. Wright your answer as an inequality solved for c
Answer:
Chang will spend $44 on 11 pounds of candy. The possible amounts he will spend is $44.
Step-by-step explanation:
Multiply4x11=44 which is the answer and if you contract it it will make 44 pounds and 44 pounds is 176 so $176 is he had 44 pounds but he only has 11 so
Answer:$44
π + 3.14 × π + 3.14 ÷ 3.14 answers it if you want to also it pie
Answer:
14.006
Step-by-step explanation:
π + 3.14 × π + 3.14 ÷ 3.14
14.00619358
Rounded -
14.006
Let's see
We know π approximately. 3.14[tex]\\ \rm\rightarrowtail \dfrac{\pi\pi(3.14)(3.14)}{3.14}[/tex]
[tex]\\ \rm\rightarrowtail \pi\pi(3.14)[/tex]
[tex]\\ \rm\rightarrowtail \pi^2(\pi)[/tex]
[tex]\\ \rm\rightarrowtail \pi^3[/tex]
which equation in standard form has a graph that passes through the point (-4, 2) and has a slope of 9/2
9x - 2y = -10 is the answer but why?
Answer:
-40
Explanation:
Hope it helps