One number is 32 more than another. Their product is −256.

The roots of the provided polynomial equation of 4 degree are 2,2,1.73,-1.73.

The factor of a polynomial is the terms in linear form, which are, when multiplied together, give the original polynomial equation as a result.\

To find the roots of a polynomial, equate these factors of a polynomial to zero.

The given polynomial equation is,

[tex]x^4+x^2=4x^3-12x+12[/tex]

Take all the terms left side of the equation,

[tex]x^4+x^2-4x^3+12x-12=0\\x^4-4x^3+x^2+12x-12=0[/tex]

The factor form of the polynomial on solving the above equation, we get,

[tex](x-2)(x-2)(x-1.73)(x+1.73)=0[/tex]

Equate all the factors to zero, to find the roots. The roots we get are,

[tex]2,2,1.73,-1.73[/tex]

Hence, the roots of the provided polynomial equation of 4 degree are 2,2,1.73,-1.73.

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Answer:

–1.73, 1.73, 2

Step-by-step explanation:

Answer:

7 inches

Step-by-step explanation:

The surface area of a cube is denoted by: A = 6s², where s is the side length.

Here, we know that A = 294, so plug this into the formula to solve for s:

A = 6s²

294 = 6s²

s² = 49

s = √49 = 7

Thus, the answer is 7 inches.

Answer:

25a^2b^4c^2

Step-by-step explanation:

step 1:

Remove the bracket by multiplying all the power inside the bracket with the power outside the bracket.

5^2a^2b^2x2c^2=25a^2b^4c^2

53x95 = 5035!

hopes this helps! ^^

Answer:

5605

Step-by-step explanation:

I know you're looking for an answer but i'm doing a challenge where i have to answer 10 questions by the end of today, I'm sorry! :(

Using the binomial distribution, it is found that there is a 0.999977 = 99.9977% probability that at least one of them makes a Type I error.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

The probability that at least one commits an error is given by:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{30,0}.(0.3)^{0}.(0.7)^{30} = 0.000023[/tex]

Then:

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.000023 = 0.999977[/tex]

There is a 0.999977 = 99.9977% probability that at least one of them makes a Type I error.

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As x tends to infinity the function [tex]f(x) = \frac{2x}{1-x^{2} }[/tex] approaches zero.

Given function is:

[tex]f(x) = \frac{2x}{1-x^{2} }[/tex]

A function f(x) is a rule which relates two variables where x and y are independent and dependent variables.

Divide the numerator and denominator of the given function by x.

[tex]f(x) = \frac{2}{\frac{1}{x} -x}[/tex]

[tex]\lim_{x \to \infty} f(x) \\\\\lim_{x \to \infty} \frac{2}{\frac{1}{x} -x}[/tex]

As we know that as x approaches the infinity 1/x approaches 0.

So, [tex]\\\\\lim_{x \to \infty} \frac{2}{\frac{1}{x} -x} = \lim_{x \to \infty} \frac{2}{-x}[/tex]

[tex]\lim_{x \to \infty} \frac{-2}{x} =0[/tex]

Therefore, as x tends to infinity the function [tex]f(x) = \frac{2x}{1-x^{2} }[/tex] approaches zero.

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Answer:

Step-by-step explanation:

[tex]\frac{180(n-2)}{n}[/tex] degrees, where n is the number of sides

The measure of an interior angle inside a regular polygon is given by;

[tex]\rm S = (n -2) \times 180[/tex].

An interior angle of a polygon is an angle formed inside the two adjacent sides of a polygon. Or, we can say that the angle measures at the interior part of a polygon are called the interior angle of a polygon.

An Interior Angle is an angle inside a shape.

As per the angle sum theorem, the sum of all the three interior angles of a triangle is 180°.

Multiplying two less than the number of sides times 180° gives us the sum of the interior angles in any polygon.

The measure of an interior angle inside a regular polygon is determined by the following formula;

[tex]\rm S = (n -2) \times 180[/tex]

S = sum of interior angles and n = number of sides of the polygon.

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Answer:

height: 125m; distance: 500m

Step-by-step explanation:

x = 250

f(x) = x − 0.002x2

f(x) = 250 − 0.002(250 )2

= 250 − 0.002(62,500)

= 250 − 125

= 125

250 times 2 = 500

[tex]\\ \rm\rightarrowtail y=x-0.002x^2[/tex]

So

[tex]\\ \rm\rightarrowtail y=250-0.002(250)^2[/tex]

[tex]\\ \rm\rightarrowtail y=250-0.002(62500)[/tex]

[tex]\\ \rm\rightarrowtail y=250-125[/tex]

[tex]\\ \rm\rightarrowtail y=125m[/tex]

Distance:-

Equation of a Circle: (x - h)^2 + (y - k)^2 = r^2

---Center = (h, k)

---Radius = r (this value will need to be squared in the final answer)

Center = (-3, -6)

---h = -3

---k = -6

Radius = 4

Equation: (x + 3)^2 + (y + 6)^2 = 16

Correct Answer: A

Hope this helps!

Answer:

[tex]\boxed{\sf{x=7 \quad y=2}}[/tex]

Step-by-step explanation:

To solve this problem, isolate it on one side of the equation.

x-3y=1: x=1+3y

x=1+3y

Substitute.

x=1+3y= 3(1+3y)-5y=11

Solve.

3+4y=11

Subtract by 3 from both sides.

3+4y-3=11-3

Solve.

11-3=8

Rewrite the problem down.

4y=8

Divide by 4 from both sides.

4y/4=8/4

Solve.

8/4=2

y=2

x=1+3y

x=1+3*2

Solve.

PEMDAS stands for:

1+3*2

Multiply.

3*2=6

Add.

1+6=7

x=7

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

the answer to your question is B

The equation to solve for the width of a rectangular frame that has a total area of 140 square inches is 4x²+32x-80=0.

The area of the rectangle is the product of its length and its breadth.

As it is given that the length of the rectangular frame is (2x+10), while the width of the rectangular frame is (2x+6). Also, it is mentioned that the area of the rectangular frame is 140 in².

Now we know the area is the product of length and breadth, therefore,

[tex]\rm \text{Area of rectangle} = length \times breadth[/tex]

[tex]140 = (2x+10)(2x+6)\\\\140 = 4x^2 + 12x + 20x + 60\\\\0=-140+4x^2 + 12x + 20x + 60\\\\4x^2 + 32 x -80=0[/tex]

Hence, the equation to solve for the width of a rectangular frame that has a total area of 140 square inches is 4x²+32x-80=0.

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Answer:

A.)  4x2 + 32x − 80 = 0

Step-by-step explanation:

Just took the test

Answer:

200/7

Step-by-step explanation:

(2 meters)/(7 centimeters) or (2m/7cm)

1 meter = 100 cm

(2m/7cm)*(100cm/1m) = 200/7 (or   28.57) scale factor.

Answer:

C or D Both basically

Step-by-step explanation:I read them

Answer:

398

Step-by-step explanation:

3582 / 9 = 398

Answer: x = 5, y = 7

Step-by-step explanation:

1. First, put the variables together/rearrange:

y - x = 2 & 5x - 4y = -3

2. Cancel out variable x by multiply the first equation by 5:

5y - 5x = 10 & 5x - 4y = -3

3. Add equations:

y = 7

4. Then determine x by plugging y back into the first equation y = x + 2:

x = 5

Answer:

5/6

Step-by-step explanation:

it comes out originally like 10/12 but if your simplify it it's 5/6

Answer:5/6

Step-by-step explanation: 12-2 =10 so 10/12 which simplifies to 5/6

Answer:

<1 and <2

Step-by-step explanation:

Complementary angles are two angles which their measure add up to 90 degrees.

There are only one angle pair that meet this requirement:

angle 2 and angle 1

The trigonometry identity sin(x + y) = sinx cosy + cosx siny.

sin(x + y) is one of the identities in trigonometry for compound angles.

The angle (x + y) represents the compound angles.

sin(x + y) = sinx cosy + cosx siny

To prove sin(x + y) = sinx cosy + cosx siny

Consider OX as a rotating line anti-clockwise. Let angle XOY = a

the making of an acute angle b the rotation in the same direction is

angleYOZ = b , angle XOZ = a + b

From triangle PTR,

∠TPR = 90 - ∠PRT , ∠ROX = a

From the right-angled triangle PQO

sin(a + b) = PQ/OP

= (PT + TQ) / OP

= PT/OP + TQ/OP

= PT/PR × PR/OP + RS/OR × OR/OP

= cos (∠TPR ) sinb + sina cosb

= sina cosb + cosa sinb

if we replace a=x and b=y

Therefore, sin(x + y) = sinx cosy + cosx siny.

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Answer:

cars value decreases in value exponentially

Step-by-step explanation:

cant really read it but say that the cars value decreases in value exponentially and compare that to however the other cars decrease in value over time

The translation of points A(2, 3), B(–1, –4), and C(2, –2), 1 unit left and 4 units down gives A'(1, -1), B'(-2, -8) and C'(1, -6)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, reflection and dilation.

Given the points A(2, 3), B(–1, –4), and C(2, –2), the translation 1 unit left and 4 units down gives:

A'(1, -1), B'(-2, -8) and C'(1, -6)

The translation of points A(2, 3), B(–1, –4), and C(2, –2), 1 unit left and 4 units down gives A'(1, -1), B'(-2, -8) and C'(1, -6)

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Answer:

24

Step-by-step explanation:

I did this question before.

Answer:

4.5^5

Step-by-step explanation:

Answer:

(4.5)^5

Step-by-step explanation:

Answer:

Let a = side length of a cube

Let S = surface area of a cube

Area of a square = a²

Since a cube has 6 square sides:  S = 6a²

To make a the subject:

S = 6a²

Divide both sides by 6:

[tex]\sf \implies \dfrac{S}{6}=a^2[/tex]

Square root both sides:

[tex]\sf \implies a=\sqrt{\dfrac{S}{6}}[/tex]

(positive square root only as distance is positive)

-----------------------------------------------------------------------------------------------

[tex]\sf x=-3-\sqrt{2} \implies (x+[3+\sqrt{2}])=0[/tex]

[tex]\sf x=-3+\sqrt{2} \implies (x+[3-\sqrt{2}])=0[/tex]

Therefore,

[tex]\sf y=a(x+[3+\sqrt{2}]) (x+[3-\sqrt{2}])[/tex]  for some constant a

Given the y-intercept is at (0, -5)

[tex]\sf \implies a(0+3+\sqrt{2}) (0+3-\sqrt{2})=-5[/tex]

[tex]\sf \implies a(3+\sqrt{2}) (3-\sqrt{2})=-5[/tex]

[tex]\sf \implies a(9-2)=-5[/tex]

[tex]\sf \implies 7a=-5[/tex]

[tex]\sf \implies a=-\dfrac57[/tex]

Substituting found value of a into the equation and simplifying:

[tex]\sf y=-\dfrac57(x+[3+\sqrt{2}]) (x+[3-\sqrt{2}])[/tex]

[tex]\sf \implies y=-\dfrac57(x^2+6x+7)[/tex]

[tex]\sf \implies y=-\dfrac57x^2-\dfrac{30}{7}x-5[/tex]

The required equation f(10) = 13.52 mg remains.

We have given that ,

m is the initial mass and h is the half-life in years. cobalt-60 has a half-life of about 5.3 years. which equation gives the mass of a 50 mg cobalt-60

The amount of a radioactive substance remaining after t years is given by the function  

[tex]f(t)=m(0.5)^{t/h}[/tex]............ (1),

where m = initial mass and h= half-life in years.

Now, for Cobalt-60, h = 5.3 years, m = 50 mg and t = 10 years,

then from equation (1) we get,

[tex]f(10)=50(0.5)^{10/5.3}[/tex]

Therefore  the required equation  f(10) = 13.52 mg .

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Answer:

The required equation f(10) = 13.52 mg remains.

We have given that ,

m is the initial mass and h is the half-life in years. cobalt-60 has a half-life of about 5.3 years. which equation gives the mass of a 50 mg cobalt-60

What is the fromula for he amount of a radioactive substance remaining after t years?

The amount of a radioactive substance remaining after t years is given by the function  

............ (1),

where m = initial mass and h= half-life in years.

Now, for Cobalt-60, h = 5.3 years, m = 50 mg and t = 10 years,

then from equation (1) we get,

Therefore  the required equation  f(10) = 13.52 mg .

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first add the ratio numbers which is 12

[tex] \frac{2}{12} \times 6000 = 1000[/tex]

then divide 1000 with 175

=5.71

5.71×2.25

=12.85 ruro