Answer:
The zeroes are 2, -2, -6, 5.
Step-by-step explanation:
If 2 of the zeroes are 2 and -2 then (x - 2)(x + 2) is factor of the polynomial.
We can now do long division.
Note (x - 2)(x + 2) = x^2 - 4, so we have:
x^2 - 4 ( x^4 + x^3 - 34x^2 - 4x + 120 ( x^2 + x - 30 <--- Quotient
x^4 - 4x^4
x^3 - 30x^2 - 4x
x^3 -4x
-30x^2 + 120
-30x^2 + 120
x^2 + x - 30 = 0
(x + 6)(x - 5) = 0
x = -6, 5.
Answer:
5 and -6
Step-by-step explanation:
So when a polynomial has zeroes at a, then one of the factors (x-a). This is because in factored form, a polynomial can be written using it's factors as such: [tex]a(x\pm b)(x\pm c)(c \pm d)...[/tex] and so on, with the number of factors depending on the degree. The sign is plus or minus because it can be either, it will depend on the sign of the zero. The reason the zeroes are factors, is because when one of the factors is zero it makes the entire thing zero because multiplying them out will always get 0, if you're multiplying by a zero. Anyways, if you have a factor, you can divide, by those factors. So let's do that.
So you have the two factors (x+2)(x-2). So let's divide by each factor. In this example I'll be using long division. So essentially what long division, is finding how many times the leading coefficient of the dividend (x^4+x^3-34x^2-4x+120) can be divided by the leading coefficient of the divisor ((x-2)(x+2)). And then whatever you get, that will be part of the quotient, then take whatever you got, and multiply it by the divisor and then subtract that product from the dividend and then continue this process until the dividend is equal to 0 or you can't divide any further./
Original equation:
[tex](x+2)\div (x^4+x^3-34x^2-4x+120)[/tex]
Divide the leading coefficients:
[tex]\frac{x^4}{x}=x^{4-1} = x^3[/tex]
The x^3 will be part of the quotient, now multiply this by the divisor
[tex]x^3(x+2) = x^{3+1} + 2x^3 = x^4 + 2x^3[/tex]
Subtract the product from the dividend
[tex](x^4+x^3-34x^2-4x+120) - (x^4+2x^3) = x^4+x^3-34x^2-4x+120 - x^4 - 2x^3[/tex]
Group like terms:
[tex](x^4 - x^4) + (x^3 - 2x^3) -34x^2-4x+120[/tex]
Simplify:
[tex]-x^3 -34x^2-4x+120[/tex]
Divide leading coefficients:
[tex]\frac{-x^3}{x} = -x^{3-1} = -x^2[/tex]
The -x^2 will be part of the quotient, now multiply this by the divisor:
[tex]-x^2(x+2) = -x^{2+1} -2x^2 = -x^3-2x^2[/tex]
Subtract this from the dividend:
[tex](-x^3 -34x^2-4x+120) - (-x^3 - 2x^2) = -x^3 -34x^2-4x+120 + x^3 + 2x^2[/tex]
Group like terms:
[tex](-x^3 + x^3) + (-34x^2 + 2x^2)-4x+120[/tex]
Simplify:
[tex]-32x^2 -4x -120[/tex]
Divide the leading coefficients:
[tex]-\frac{32x^2}{x}=-32x^{2-1} = -32x[/tex]
This will be part of the quotient, now multiply this by the divisor:
[tex]-32x(x+2) = -32x^2 - 64x[/tex]
Subtract this from the dividend
[tex](-32x^2 -4x -120) - (-32x^2-64x) = -32x^2 -4x -120 + 32x^2 + 64x[/tex]
Group like terms:
[tex](-32x^2+32x^2) + (-4x+64x) -120[/tex]
Simplify:
[tex]60x+120[/tex]
Divide the leading coefficients:
[tex]\frac{60x}{x} = 60[/tex]
This will be part of the quotient, multiply it by the divisor:
[tex]60(x+2) = 60x+ 120[/tex]
Subtract this from the dividend:
[tex](60x+120)-( 60x+120) = 0\\[/tex]
Since this comes out perfectly to zero there is no remainder, and this is expected since it's a factor. You now take all the quotients from dividing the leading terms and you get [tex]x^3-x^2-32x+60[/tex]. To keep the original equation you simply multiply it, and you get: [tex](x+2)(x^3-x^2-32x+60)[/tex]. But what we really care about is the x^3-x^2-32x+60. We now divide it by the other factor x-2 using the same process
Original equation:
[tex]x^3-x^2-32x+60[/tex]
Divide leading terms:
[tex]\frac{x^3}{x} = x^2[/tex]
This will be part of the quotient, multiply it by the divisor
[tex]x^2(x-2) = x^3-2x^2[/tex]
Subtract this from the dividend
[tex](x^3-x^2-32x+60) - (x^3 - 2x^2) = x^2-32x+60[/tex]
Dividing leading coefficients:
[tex]\frac{x^2}{x} = x[/tex]
This will be part of the quotient, multiply it by the divisor:
[tex]x(x-2) = x^2-2x[/tex]
Subtract this from the dividend:
[tex](x^2-32x+60) - (x^2-2x) = -30x+60[/tex]
Divide the leading terms:
[tex]\frac{-30x}{x} = -30[/tex]
This will be part of the quotient, now multiply it by the divisor:
[tex]-30(x-2) = -30x+60[/tex]
Subtract it from the dividend:
[tex](-30x + 60) - (-30x + 60) = 0[/tex]
Now take all the quotients of the leading terms and you get:
[tex]x^2+x-30[/tex]
Now we can factor this quadratic to get the equation in completely factored form: We're looking for factors that multiply to -30 and add to 1. So we really need to look for factors that have a difference of 1, Or in other words |a-b| = 1. The sign can be determined after we fine the two factors. The factors 5 and 6 have a difference of 1, and since it needs to add to 1, the 5 has to be negative, and the 6 has to be positive.
So we get the factors: [tex](x-5)(x+6)[/tex]. Setting each of them equal to zero gets you:
x-5 = 0
x = 5
x + 6 = 0
x = -6
So the other two zeroes are 5 and -6
A number is equal to the sum of half a second number and 3. The first number is also equal to the sum of one-
quarter of the second number and 5. The situation can be represented by using the graph below, where x
represents the second number.
16-
14-
12
10
8
-22-
8 10 12 14 16 x
Which equations represent the situation?
The equation that represents the situation are x = 1/2 y + 3 and x = 1/4y + 5
System of equation
Let the first number be x and the second number be y. If a number is equal to the sum of half a second number and 3, this is expressed as;
x = 1/2 y + 3
For the second equation;
The first number is equal to the sum of one- quarter of the second number and 5
x = 1/4y + 5
Hence the equation that represents the situation are x = 1/2 y + 3 and x = 1/4y + 5
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Triangles Q R S and T U V are shown. Triangle Q R S is translated across S Q and then is shifted down and to the right to form triangle T U V.
Can a translation and a reflection map TriangleQRS to TriangleTUV? Explain why or why not.
No, the triangles are not congruent.
Yes, a translation mapping vertex Q to vertex T and a reflection across the line containing QS will map
△QRS to △TUV.
No, the triangles are obtuse.
Yes, a translation mapping vertex S to vertex T and a reflection across the line containing RS will map
△QRS to △TUV.
Yes, a translation mapping vertex Q to vertex T and a reflection across the line containing QS will map △QRS to △TUV.
What is translation?A translation is a type of transformation that takes each point in a figure and slides it the same distance in the same direction.
Given:
△QRS and △TUV is translated across SQ and then is shifted down and to the right to form △TUV.
So, translation mapping vertex Q to vertex T is done and a reflection across the line containing QS will map △QRS to △TUV.
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Answer:
B
Step-by-step explanation:
That's what the other person is saying
SM052VGS2E
Consider these four powers.
(-4)⁰
3⁰
10⁰
(3) º
4
What do these powers have in common?
The four powers have zero (0) in common
IndicesFrom the question, we are to determine what the four powers have in common
In the question, we can observe that the four powers have 0 in common.
The value of each of the expressions is 1.
Hence, the four powers have zero (0) in common.
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What is the answer to this pythagoras question?
The length of the segment AB will be equal to 9.848 units.
What is the Pythagorean theorem?It states that in the right-angle triangle the hypotenuse square is equal to the sum of the square of the other two sides.
The length of segment AB will be calculated as:-
Points are A(1,7) and B(10,3)
AB = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
AB = [tex]\sqrt{(10-1)^2+(3-7)^2}[/tex]
AB = √(81+16)
AB = √97
AB = 9.848
Therefore the length of the segment AB will be equal to 9.848 units.
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Which recursive formula can be used to generate the sequence shown, where f(1) = 9.6 and n > 1?
9.6, –4.8, 2.4, –1.2, 0.6, ...
f(n + 1) = (–0.5)f(n)
f(n + 1) = (0.5)f(n)
f(n + 1) = f(0.5n)
f(n + 1) = f(–0.5n)
Answer: f(n + 1) = (–0.5)f(n)
Step-by-step explanation:
This is a geometric series with common ratio -0.5.
How are evidence and counterexamples used in proofs . In a direct proof evidence is used to blank .on the other hand a counterexample is a single example that blank
Evidence is used in proofs to support a claim.
What is an evidence?It should be noted that evidence simply means a claim that's is used to support a proposition that's it's true.
In this case, evidence is used in proofs to support a claim. On the other hand, counterexample is used to disprove a theory.
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30 mi / h = ____ ft / min
a.
2640
c.
880
b.
264
d.
2112
Answer:
A. 2640
Step-by-step explanation:
44 feet per second 30 miles per hour is 2640 feet per minute
can someone help me with this? I’ll mark you brainliest
The point (0, 0) lies in the shaded region and satisfies the solution for the inequality y ≥ 3x - 2
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the inequality y ≥ 3x - 2, since the point (0, 0) lies on the shaded region, hence:
0 ≥ 3(0) - 2
0 ≥ -2
The point (0, 0) satisfies the solution for the inequality y ≥ 3x - 2
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Find the length of the hypotenuse on the following right triangle.
Answer:
Step-by-step explanation:
Miguel plans on retiring in 16 years, and he wants to double his money by that time. He's contacted various banks, looking for a CD that compounds interest monthly, and to calculate what annual interest rate he needs, he is using the rule of 72. (3 points: Part I – 1 point; Part II – 1 point; Part III – 1 point)
Part I: What is the rule of 72? To represent the annual interest rate, use r.
Part II: What equation can Miguel set up to solve for the annual interest rate he needs to double his money by the time he retires?
Part III: What annual interest rate does Miguel need to double his money by the time he retires?
The rule of 72 is a rule of thumb that is used to determine the doubling time for an investment given the annual interest rate.
The equation Miguel needs to set up is r = 72/16.
The interest rate is 4.5%.
What is the rule of 72?
The rule of 72 is used to determine the time it would take an investment to double in value. The doubling time is determined by dividing 72 by the interest rate.
Number of years it would take an investment to double = 72 / interest rate
n = 72 / r
r = 72 / n
72 / 16 = 4.5%
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what is the answer?
please help
Answer:
Slope = 1/3
Step-by-step explanation:
Slope:Pick any two points. (-1,-2) ; (2,-1)[tex]\sf \ x_1=-1 ; \ y_1=-2\\\\ x_2 = 2 ; \ y_2=-1[/tex]
Find the slope using the formula.[tex]\sf \boxed{\bf \ Slope =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf = \dfrac{-1-[-2]}{2-[-1]}\\\\ =\dfrac{-1+2}{2+1}\\\\= \dfrac{1}{3}[/tex]
Need asap pls correct answer
Answer: B. G(x) = (x-5)^2
Step-by-step explanation:
This will shift the graph 5 units right
jacqueline works on math 7/12 hours everyday . how many hours did she work on math after 24 day
Answer:
14
Step-by-step explanation:
24/12=2
(2)7=14 hours
Analyze the diagram below.
Which statements regarding the diagram are correct? Check all that apply.
ST ≅ ST by the reflexive property.
∠RWS ≅ ∠UWT because they are vertical angles.
△RWS ≅ △UWT by AAS.
△RST ≅ △UST by SAS.
∠WTU ≅ ∠WSR because CPCTC.
Based on the relevant congruent theorems, all of the statements are correct except: D. △RST ≅ △UST by SAS.
What is the AAS Congruence Theorem?Two triangles that have two pairs of corresponding congruent angles and a pair of corresponding non-included congruence angles are proven to be congruent by the AAS congruence theorem.
Thus, △RWS ≅ △UWT by AAS because they have two pairs of corresponding congruent angles and a pair of corresponding non-included congruence angles.
△RST cannot be proven to be congruent to △UST by SAS because there is no sufficient information.
Based on the reflexive property, ST ≅ ST. Also, using the CPCTC, all parts of the two congruent triangles are equal, therefore, ∠WTU ≅ ∠WSR.
The only statement that is incorrect is: D. △RST ≅ △UST by SAS.
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Answer:
A, B, C and E
Step-by-step explanation:
For the regular hexagon below, if BC = 9 m and AP = 8 m, find it's area.
A cube shaped suitcase has a length of 3x + 2 units. What is an expression for its area of the
base?
Answer:
[tex]\huge\boxed{\sf 9x^2+12x+4 \ units^2}[/tex]
Step-by-step explanation:
Given that,
Length of cube = l = 3x + 2 units
Base Area:[tex]= l \times l\\\\= (3x+2)(3x+2)\\\\= 3x(3x+2)+2(3x+2)\\\\= 9x^2+6x+6x+4\\\\= 9x^2+12x+4 \ units^2\\\\\rule[225]{225}{2}[/tex]
Find the length of line segments (4,6) and (5,2)
Answer: [tex]\displaystyle d=\sqrt{1 7}\;\text{or about 4.123 units}[/tex]
Step-by-step explanation:
We can use the distance formula to solve. Let (4, 6) be point one and (5, 2) be point two.
[tex]\displaystyle d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2}[/tex]
[tex]\displaystyle d=\sqrt{(5-4)^2 +(2-6)^2}[/tex]
[tex]\displaystyle d=\sqrt{(1)^2 +(-4)^2}[/tex]
[tex]\displaystyle d=\sqrt{1 +16}[/tex]
[tex]\displaystyle d=\sqrt{1 7}[/tex]
answer pleaseeeeeeeeeeeeeee
Answer:
A. Square
Step-by-step explanation:
Hope this helps!
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What is the value of this subject when a =2 and b= -3?
a^3-b^3/5
Answer:
7
Step-by-step explanation:
a^3 = 2^3 = 8
b^3 = -3^3 = -27
(8 - (-27))/5= (8+27)/5 =35/5=7
Which rectangular equation represents the parametric equations x = t²-4 and y = 2t?
Oy = 2(x² + 4)
* y = 2(x² - 4)
Oy = 2√x+4
O y = 2√√x-4
Answer:
[tex]\displaystyle{y=2\sqrt{x+4}}[/tex]
Step-by-step explanation:
We are given parametric equations of:
[tex]\displaystyle{x=t^2-4}[/tex] and [tex]\displaystyle{y=2t}[/tex]
Isolate t-variable in [tex]\displaystyle{x=t^2-4}[/tex] first by adding both sides by 4:
[tex]\displaystyle{x+4=t^2-4+4}\\\\\displaystyle{x+4=t^2}[/tex]
Square root both sides then write plus-minus:
[tex]\displaystyle{\sqrt{x+4}=\sqrt{t^2}}\\\\\displaystyle{t=\pm \sqrt{x+4}}[/tex]
Since the choice determines y-term as a function and only positive t-value exists, substitute only [tex]\displaystyle{t=\sqrt{x+4}}[/tex] in [tex]\displaystyle{y=2t}[/tex].
Therefore, the answer is [tex]\displaystyle{y=2\sqrt{x+4}}[/tex]
Answer:
c
Step-by-step explanation:
-80 +77 show work ...........
Answer:
157
Step-by-step explanation:
-80 is a negative number. 77 is a even number. Since your adding a negative number with a even number. You answer will be even.
-80
+70
———
157
I hope I’ve helped you here’s a link to help you https://www.purplemath.com/modules/negative2.htm
What is the least amount of integers you must pick in order to be sure that at least two of them have the same remainder when divided by 15
There are exactly 15 remainders modulo 15 and they are 0,1,2,…,14.
It is given that at least two of them should have the same remainder when divided by 15.
Division algorithm.
Let aa be an integer and d a positive integer. Then there are unique integers q and r with [tex]0\leq r < d[/tex] such that [tex]a=dq+r[/tex]
q is called the quotient and r is called the remainder
q=a div d
r=a mod d
Pigeonhole principle If k is a positive integer and k+1or more objects are placed into k boxes, then there is at least one box containing two or more objects.
Hence, there are exactly 15 remainders modulo 15 and they are 0,1,2,…,14.
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Lee is staying at a hotel. The cost of the first night is $240. The cost for each night after that is $210. Let y represent the total cost of staying at the hotel for x nights. Which type of sequence does the situation represent
A) The situation represents an arithmetic sequence because the successive y-values have a common difference of 210.
F(1) = 240 +210
F(2) = 240 +2(210)
F(3) = 240+3(210)
.
.
.
.
F(x)= 240 +210x.
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Find ST. Help me please. Thank you :)
The value of ST is 3
How to solve for ST?The given parameters are:
RT = 8
RS = 5
To calculate ST, we make use of the following straight line theorem
RT = RS + ST
This gives
8 = 5 + ST
Subtract 5 from both sides
ST = 3
Hence, the value of ST is 3
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Jon, Dave, and Kevin collected rocks at the beach. Each boy collected 25 rocks. How many rocks did the boys collect in all?
By taking the product between the number of boys and the number of rocks that each gets, we conclude that they collected 75 rocks.
How many rocks did the boys collect in all?
We know that there are 3 boys, and each boy collected 25 rocks.
If we take the product between the number of boys and the number of rocks that each boy collected, we get:
R = 3*25 rocks = 75 rocks.
We conclude that the boys collected 75 rocks in total.
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(Round answers to
the nearest hundredth.)
Answer:
28.31
Step-by-step explanation:
So in this case you're going to need to use the law of sines which essentially states that: [tex]\frac{a}{sinA}=\frac{b}{sinB}[/tex] which should apply to any of the sides. the lowercase a and b are the opposite sides of the angles A and B. In this example the angle A is given and C is given, but not in the text. Since you have the right angle thing in the diagram, angle C is a right angle (90 degrees).
Given information:
[tex]\angle A = 32\\a=15\\\angle C = 90 \text{(the right angle symbol in the diagram of the triangle)}[/tex]
Law of sines equation:
[tex]\frac{a}{sinA}=\frac{b}{sinB} \text{ can be applied to any two sides }[/tex]
Plug in known information:
[tex]\frac{15}{sin(32)}=\frac{c}{sin (90)}[/tex]
since sin(90) = 1, simplify the fraction
[tex]\frac{15}{sin(32)} = c[/tex]
Calculate sin(32)
[tex]\frac{15}{0.530}\approx c[/tex]
Divide
[tex]28.306\approx c[/tex]
If you haven't learned law of sines yet and don't quite understand why it works you can also use the definition of tan to find what b equals and then use the Pythagorean Theorem to solve for c
tan is defined as: [tex]\frac{opposite}{adjacent}[/tex]
[tex]tan(32)=\frac{15}{b}[/tex]
now multiply both sides by b
[tex]b * tan(32)=15[/tex]
Divide both sides by tan 32
[tex]b = \frac{15}{tan(32)}[/tex]
[tex]b\approx 24.005[/tex]
Now use the Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex]
[tex](24.005)^2+15^2=c^2\\[/tex]
Square known values
[tex]576.241+225=c^2[/tex]
Add the values
[tex]801.241 = c^2[/tex]
take the square root of both sides
[tex]28.306\approx c[/tex]
Rounding to the nearest hundredth gives you 28.31
2x - 5y = 2
3x + 2y = -16
Answer:
(-4,-2)
Step-by-step explanation:
Isolate x:
2x - 5y = 2
2x = 5y + 2
x = 5/2y + 1
Substitute and solve for y:
3(5/2y + 1) + 2y = -16
15/2y + 3 + 2y = -16
7.5y + 2y = -16 - 3
9.5y = -19
y = -2
Substitute and solve for x:
2x - 5y = 2
2x - 5(-2) = 2
2x + 10 = 2
2x = -8
x = -4
The values of x and y vary directly and one pair of values are given. Write an equation that relates x and y.
x=2, y=5
The equation that relates x and y is y = 2.5x.
How to solve variation?
The values of x and y vary directly. Therefore,
y α x
where
x and y are the variable.Hence,
y = kx
where
k = constant of proportionality.Therefore,
x = 2
y = 5
5 = 2k
k = 5 / 2
k = 2.5
Hence, the equation that relates x and y are as follows;
y = 2.5x
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help me please i dont understand
20 points
Answer:
50 [tex]cm^{2}[/tex]
Step-by-step explanation:
Area of a trapezoid: [tex]\frac{a+b}{2} h[/tex]
[tex]\frac{a+b}{2} h[/tex]
= [tex]\frac{14+6}{2} (5)[/tex]
= [tex]\frac{20}{2} (5)[/tex]
= [tex]10(5)[/tex]
= 50 sq. cm
Betty and Jane have the same number of coins. Betty
sorts her coins in groups of 6, with no coins left over.
Jane sorts her coins in groups of 8, with no coins left
over. What is the least possible number of coins that each
of them has?
Using the least common multiple, it is found that the least possible number of coins that each of them has is of 24.
What is the least possible number of coins that they have?They have the same number of coins, with Betty sorting the coins in groups of 6 and Jane sorting the coins in groups of 8, and none of them having coins remaining.
Thus, the least possible number of coins they have is the least common multiple of 6 and 8, found factoring both these numbers into prime factors, as is done below:
6 - 8|2
3 - 4|2
3 - 2|2
3 - 1|3
1
Hence the least common multiple of 6 and 8 is given by:
lcm(6,8) = 2 x 2 x 2 x 3 = 2³ x 3 = 24.
Thus, it is found that the least possible number of coins that each of them has is of 24.
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