Use what you know about addition and subtraction of polynomials to find the missing term represented by the question mark in each equation. (â€""4x2 6x 3) (8x 5 ?) = 2x2 14x 8 ? = (â€""b3 3b2 8) â€"" (? â€"" 5b2 â€"" 9) = 5b3 8b2 17 ? =

The correct answer  is 2^-3.

Using f(a^m)^n = a^(mn), the exponential identity

(2^-1)^3 = 2^-3

The symbol indicating organisms A's

Population decline during the following three days is (1/2)^3.

This can be written as (2-^1)3 with the same base but one exponent. hence answer is 2^-3. Proof of of identity is given below

case 1 Let m>0 and n>0 in . We'll move forward via induction. We repair m and introduce n. Basis: Assume that n=1. Am Equals Am, as can be seen. logical inference: Let's say (am)k=amk. We will demonstrate that (am)k+1=am(k+1). The assumption that (am)k+1=am(k+1) follows naturally.

Case 2 M=N=0 in . There is no doubt that (am)n=amn.

case 3: m0 and n0. Let t, r > 0 and m = t and n = r. Consequently, (a^m)^n=(at)r)=(a1)t)r)=(a1)rt)=(ant)=(ant)=an(1)t=a^mn.

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There would be 318 grams of sugar in a 3-liter bottle of soda. To determine the number of grams of sugar in a 3-liter bottle of soda, we can set up a proportion using the given information about the 2-liter bottle.

Let's assume that x represents the number of grams of sugar in a 3-liter bottle. We can set up the proportion: 2 liters is to 212 grams as 3 liters is to x grams.

Using cross-multiplication, we have 2 * x = 3 * 212. Solving for x, we get: x = (3 * 212) / 2 = 636 / 2 = 318 grams.Therefore, there would be 318 grams of sugar in a 3-liter bottle of soda.

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Answer:

Slope is X

Y-intercept is B

The mean score of the given three scores is approximately 26.6, which is not the mean score for all ninth graders in the city.

To find the mean score for all ninth graders in the city, we need more information than just three scores. Without additional data, we cannot accurately determine the mean score for all ninth graders in the city.

However, we can calculate the mean of the given scores to verify that it is not 79.7 as claimed by the PR manager:

Mean = (77 + 91 + 71) / 3 = 79.7/3 = 79.7 ÷ 3 ≈ 79.7/3 ≈ 26.6

So the mean score of the given three scores is approximately 26.6, which is not the mean score for all ninth graders in the city.

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Answer:

8 total boxes

Step-by-step explanation:

Answer:

(-13, -5)

Step-by-step explanation:

So, in translations, left means you subtract the x-coordinate by that much.

So, in this case, the x-coordinate is -9, and the translation is 4 left.

So, -9 - 4 = -13.

Also, down means you subtract the y-coordinate by that much.

So, the y-coordinate is -2, and the translation is 3 down.

So, -2 - 3 = -5.

Also, right means you add, and up also means you add.

Answer:

Step-by-step explanation:

In this problem, we are to model the equation for the total cost of producing a phone

Given that the fixed cost is $600

Also, the total cost of producing 4 phones in a day is $1600

hence the cost of producing 1 phone would be 1600/4= $400

the equation for producing p phones would be

C= 400P+ 600

This equation is the same as the equation of a straight line Y=mx+c

with C=y

400= m= gradient

P=x, the dependent variable

600= c the constant term.

Answer:

c=250+600

Step-by-step explanation:

Answer:

s = 6 inches

Step-by-step explanation:

Given:

r = 53 inches,

∠S = 6°

∠T = 58°.

Required:

Length of s

Solution:

Use Sine Rule

Thus:

\( \frac{s}{Sin(S)} = \frac{r}{Sin(R)} \)

<R = 180 - (58 + 6)

<R = 116°

r = 53 inches,

∠S = 6°

s = ?

Plug in the values

\( \frac{s}{Sin(6)} = \frac{53}{Sin(116)} \)

Multiply both sides by Sin(6)

\( \frac{s}{Sin(6)} \times Sin(6) = \frac{53}{Sin(116)} \times Sin(6) \)

\( s = \frac{53 \times Sin(6)}{Sin(116)} \)

\( s = 6 inches \) (nearest inch)

There is no solution if the boundary conditions are inconsistent, i.e., if y(0) ≠ y(L) = 1.

We are given the boundary-value problem:

y" + 16y = 0, y(0) = 1, y(L) = 1

The characteristic equation is r^2 + 16 = 0, which has roots r = ±4i.

The general solution to the differential equation is then y(x) = c1cos(4x) + c2sin(4x).

Using the boundary conditions, we get:

y(0) = c1 = 1

y(L) = c1cos(4L) + c2sin(4L) = 1

Substituting c1 = 1 into the second equation, we get:

cos(4L) + c2*sin(4L) = 1

Solving for c2, we get:

c2 = (1 - cos(4L))/sin(4L)

Thus, the general solution to the differential equation that satisfies the given boundary conditions is:

y(x) = cos(4x) + (1 - cos(4L))/sin(4L)*sin(4x)

Now, we can answer the questions:

(a) To have precisely one nontrivial solution, we need the coefficients c1 and c2 to be uniquely determined. From the above expression for c2, we see that this is only possible if sin(4L) is nonzero. Thus, if sin(4L) ≠ 0, there exists precisely one nontrivial solution.

(b) If sin(4L) = 0, then c2 is undefined and we have a family of solutions that differ by a constant multiple of sin(4x). Hence, there are infinitely many solutions.

(c) There is no solution if the boundary conditions are inconsistent, i.e., if y(0) ≠ y(L) = 1.

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An equivalent rational expressions with denominator (x+3), (x−4) and (x+4) is (3x²+6x-16)/(x³+3x²-16x-48).

The given denominator are (x+3), (x−4) and (x+4).

A mathematical expression that may be rewritten to a rational fraction, an algebraic fraction such that both the numerator and the denominator are polynomials.

Here, an equivalent rational expressions is

\(\frac{1}{x+3}+\frac{1}{x-4} +\frac{1}{x+4}\)

The LCM of denominators is (x+3)(x-4)(x+4)

= (x+3)(x²-16)

= x(x²-16)+3(x²-16)

= x³-16x+3x²-48

= x³+3x²-16x-48

Now, \(\frac{(x-4((x+4)+(x+3)(x+4)+(x+3)(x-4)}{x^3+3x^2-16x-48}\)

= (x²-16+x²+7x+12+x²-x-12)/(x³+3x²-16x-48)

= (3x²+6x-16)/(x³+3x²-16x-48)

Hence, an equivalent rational expressions with denominator (x+3), (x−4) and (x+4) is (3x²+6x-16)/(x³+3x²-16x-48).

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Answer:

2.75cm

Step-by-step explanation:

Given data

Area of circle=  23.79cm^2

We know that the formula for the area of a circle is

Area= πr^2

Substitute

23.79=3.142*r^2

23.79/3.142= r^2

7.57=r^2

Square roo both sides

r= √7.57

r= 2.75 cm

Hence the radius is 2.75cm

Answer:

Step-by-step explanation

what are  the digits

Answer:

310 hamburgers were sold on Saturday

Step-by-step explanation:

1x + 70 =380

    -70   -70     Reverse

1x   =  310

/1         /1          Divide

x =310

Answer:

(0,5)

Step-by-step explanation:

c'mon just watch a totorial it's easy.

Answer:

x=95.2389

Step-by-step explanation:

Answer: 2

Step-by-step explanation:

y=mx + b

plug in known values

-2= (-1)(4) + b

b= 2

Equation: y= -x+2

graph and locate the x-intercept

Answer:

not equivalent to meteorologists ratio

Step-by-step explanation:

meteorologists ratio is

rainy days : sunny days = 2 : 5

last months weather is

rainy days : sunny days

= 10 : 20 ( divide both parts by LCM of 10 )

= 1 : 2 ← not equivalent to 2 : 5

Answer:  A

Step-by-step explanation:

When multiplying: Numbers multiply with numbers and for the x's, add the exponents

If there is no exponent, you can assume an imaginary 1 is the exponent

2x⁴ (3x³ − x² + 4x)

= 6x⁷ -2x⁶ + 8x⁵

Answer:

A. \(6x^{7} - 2x^{6} + 8x^{5}\)

Label the parts of the expression:

Outside the parentheses = \(2x^{4}\)

Inside parentheses = \(3x^{3} -x^{2} + 4x\)

You must distribute what is outside the parentheses with all the values inside the parentheses. Distribution means that you multiply what is outside the parentheses with each value inside the parentheses

\(2x^{4}\) × \(3x^{3}\)

\(2x^{4}\) × \(-x^{2}\)

\(2x^{4}\) × \(4x\)

First, multiply the whole numbers of each value before the variables

2 x 3 = 6

2 x -1 = -2

2 x 4 = 8

Now you have:

6\(x^{4}x^{3}\)

-2\(x^{4}x^{2}\)

8\(x^{4} x\)

When you multiply exponents together, you multiply the bases as normal and add the exponents together

\(6x^{4+3}\) = \(6x^{7}\)

\(-2x^{4+2}\) = \(-2x^{6}\)

\(8x^{4+1}\) = \(8x^{5}\)

Put the numbers given above into an expression:

\(6x^{7} -2x^{6} +8x^{5}\)

distribution

variable

like exponents

Work Shown:

16 ounces = 4.69 dollars

16/16 ounces = 4.69/16 dollars .... divide both sides by 16

1 ounce = 0.293125 dollars

1 ounce = 0.29 dollars .... rounding to the nearest cent

Answer:

A i got it right in edge

Step-by-step explanation:

Answer:

please apply the formula of distance

l think but not sure

y=-1/5x+4 is the equation in slope-intercept form for the line with y-intercept 4 and slope -1/5

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Given,

y-intercept 4 and slope -1/5

Now y=-1/5x+4

Hence y=-1/5x+4 is the equation in slope-intercept form for the line with y-intercept 4 and slope -1/5

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Answer:

44° (second option)

Step-by-step explanation:

Since the line bisects the angle, we can set them equal to each other and solve:

[Equation] 7x + 9 = 10x - 6

[Add 6 to both sides] 7x + 15 = 10x

[Subtract 7x from both sides] 15 = 3x

[Divide both sides by 3] 5 = x

Now, we will plug it into the expression for angle VXW,

[Equation] 10x - 6

[Plug-In] 10(5) - 6

[Multiply] 50 - 6

[Subtract] 44

[Answer] 44°

Have a nice day!

   I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

2,400

Step-by-step explanation:

2,389 rounded to the nearest hundred is 2,400

Answer:

1:3

Step-by-step explanation:

3:12 is the amount of shaded circles to all circles, 8:2 is basically the same thing as 3:12 and 9:3 is the amount of shaded circles to the amount of non-shaded circles.  1:3 wouldn't work because it is not the right ratio.

Following Vectors are given , the answer for (A) is said to kept in inverse cosine i.e. also known as arccosine. Orthogonal means at a right angles to the vectors.

(a) To find the angle between the vectors ~u = (1, 1, 1) and ~v = (0, 3, 0), we can use the dot product and the formula: cos(∅) = \(\frac{(~u . ~v) }{ (|~u| x |~v|)}\) The dot product of ~u and ~v is (~u • ~v) = 1(0)+ 1(3)+ 1(0) = 3, and the magnitudes are |~u| = \(\sqrt{(1^2 + 1^2 + 1^2) }\)= \(\sqrt{3}\)and |~v| = \(\sqrt{(0^2 + 3^2 + 0^2) }\)= 3. Plugging these values into the formula, we have: cos(∅) =  \(\frac{3}{3\sqrt{3} }\)= \(\frac{1}{\sqrt{3} }\). Therefore, the angle between ~u and ~v is given by ∅  = acos\(\frac{1}{\sqrt{3} }\)

(b) To find |4~u - ~v| + |2w~ + ~v|, we first compute each term separately.

|4~u - ~v| = |4(1, 1, 1) - (0, 3, 0)| = |(4, 4, 4) - (0, 3, 0)| = |(4, 1, 4)| = \(\sqrt{(4^2 + 1^2 + 4^2)}\)) = \(\sqrt{33}\) .  

∴|2w~ + ~v| = |2(0, 1, -2) + (0, 3, 0)| = |(0, 2, -4) + (0, 3, 0)| = |(0, 5, -4)| = \(\sqrt{ (5^2 + (-4)^2)}\) = \(\sqrt{41}\)

Thus, the expression becomes \(\sqrt{33}+ \sqrt{41}\)

(c) To find the vector projection of ~u onto ~v, we can use the formula: proj~v(~u) = ((~u • ~v) / |~v|^2) * ~v. Using the dot product and magnitudes calculated earlier: proj~v(~u) =( \(\frac{(~u .~v) }{|~v|^2)}\))~v = (3 / 9)  (0, 3, 0) = (0, 1, 0). Therefore, the vector projection of ~u onto ~v is (0, 1, 0).

(d) To find a unit vector orthogonal to both ~v and w~, we can take the cross product of ~v and w~: ~v x w~ = (0, 3, 0) x (0, 1, -2) = (6, 0, 3). To obtain a unit vector, we divide this result by its magnitude:

unit vector = \(\frac{(6, 0, 3) }{|(6, 0, 3)| }\)= \(\frac{(6, 0, 3) }{\sqrt(6^2 + 0^2 + 3^2)}\)  = \(\frac{(6, 0, 3)}{ \sqrt(45)}\) = (\(\frac{2}{\sqrt45}\) , 0, \(\frac{1}{\sqrt5}\)). Therefore, a unit vector orthogonal to both ~v and w~ is (\(\frac{2}{\sqrt5}\), 0, \(\frac{1}{\sqrt5}\)).

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Range: All real numbers greater than or equal to 3. The Option C.

To find the range of the function, we need to determine the set of all possible y-values that the function takes.

Since the line crosses the y-axis at (0, 2), we know that the function's range includes the value 2. Also, since the line turns at (-1, 3), the function takes values greater than or equal to 3.

Therefore, the range of the function is all real numbers greater than or equal to 3.

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The x-coordinate of P is 5 and the y-coordinate of P is 3.333.

To find the x- and y-coordinates of point P on the directed line segment from point A to point B, such that P is two-thirds the length of the line segment from A to B, we can use the following formula:

P = A + (2/3)(B-A)

Where A and B are the coordinates of the starting and ending points of the line segment, and P is the point we are trying to find the coordinates for.

For example, if the coordinates of A are (3,4) and the coordinates of B are (6,8), then the coordinates of P would be:

P = (3,4) + (2/3)((6,8) - (3,4)) = (3,4) + (2/3)((3,4)) = (3,4) + (2/3)(3,4) = (3,4) + (2,8/3) = (3,4) + (2,8/3) = (5,10/3) = (5,3.333)

So the x-coordinate of P is 5 and the y-coordinate of P is 3.333.

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Dan's weight can be any value between 82 kg and 96 kg

Let's call Steve's weight "x".

According to the problem, Dan weighs 14 kg more than Steve, so Dan's weight would be x + 14.

Together, their weight would be the sum of their weights

x + (x + 14) = 2x + 14

We know that their combined weight is less than 178 kg, so the inequality will be

2x + 14 < 178

Subtracting 14 from both sides

2x < 164

Dividing by 2

x < 82

So Steve's weight is less than 82 kg.

To find the possible range of Dan's weight, we can substitute x + 14 for Dan's weight

(x + 14) < (178 - x)

Simplifying

2x < 164

x < 82

x + 14 < 96

So Dan's weight is less than 96 kg.

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Answer:

$54.01

Step-by-step explanation:

All you have to do is $300.00-$245.99 .