Consider the polynomial P(x)=kx^(3)-4x^(2)+x+4. Find the value of k such that the remainder is -6 when P(x) is divided by x+1. k

Answer:

= -4

Step-by-step explanation:

To solve this expression, we need to perform the division in the correct order, following the rules of mathematical operations. We can simplify the expression as follows:

(-168) ÷ (-14) ÷ (-3) = (-168) ÷ [(-14) x (-3)] [dividing by a negative number is the same as multiplying by its reciprocal]

= (-168) ÷ 42

= -4

Therefore, the quotient of (-168) ÷ (-14) ÷ (-3) is -4.

Answer:

image is blur dear!!!

Step-by-step explanation:

The equation of the parallel line is y = -4x - 23.

To find the equation of the perpendicular line that passes through (-7, 5), we need to first find the slope of the given line y = -4x + 6. The slope of this line is -4. The slope of a perpendicular line is the negative reciprocal of the original slope, so the slope of the perpendicular line is 1/4.

Next, we can use the point-slope form of an equation to find the equation of the perpendicular line:

y - y1 = m(x - x1)

y - 5 = (1/4)(x - (-7))

y - 5 = (1/4)(x + 7)

y = (1/4)x + 9/4 + 5

y = (1/4)x + 29/4

The equation of the perpendicular line is y = (1/4)x + 29/4.

To find the equation of the parallel line that passes through (-7, 5), we can use the same slope as the original line, -4, and the point-slope form of an equation:

y - y1 = m(x - x1)

y - 5 = -4(x - (-7))

y - 5 = -4(x + 7)

y = -4x - 28 + 5

y = -4x - 23

The equation of the parallel line is y = -4x - 23.

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The number is 63. The difference between the digits of a two-digit number is 1.

Number is a mathematical object used to count, measure, and label. Numbers can be represented in a variety of forms, such as numerals, symbols, or words. Numbers are fundamental to mathematics, and all other areas of science and technology. They are used to represent amounts of money, measurements, dates, and amounts of time. Numbers are also used to identify objects and people, and to create equations and formulas. Number is essential for understanding the world around us.

To solve this, the first thing to do is find the sum of the digits. Since the number is one more than five times the sum of its digits, the sum of the digits is (63/5)-1=12.5-1=11.5. This means that the tens digit is 11 and the unit digit is 11 + 1 = 12. Therefore, the two-digit number is 63.

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Answer:

10

Step-by-step explanation:

27-[tex]3x^{3}[/tex]+(4 x [tex]2x^{2}[/tex]) - 6

= 27 - 27 + (4 x 4) - 6

= 0 + 16 - 6

= 10

Answer: 10

Step-by-step explanation:

27 - 3^3 + 4 × 2^2 - 6

= 27 - 27 + 4 × 4 - 6 (since 3^3 = 27 and 2^2 = 4)

= 0 + 16 - 6= 10

Therefore, the simplified value of the expression is 10.

The polynomial  3x³ - 4x² + 9x - 12 as a product of binomials is (3x - 4)(x² + 3).

To rewrite the polynomial 3x³ - 4x² + 9x - 12 as a product of binomials, we need to factor the polynomial. One method to do this is by grouping. Here are the steps:

1. Group the first two terms and the last two terms: (3x³ - 4x²) + (9x - 12)
2. Factor out the common factor from each group: x²(3x - 4) + 3(3x - 4)
3. Notice that (3x - 4) is a common factor in both groups, so we can factor it out: (3x - 4)(x² + 3)
4. Now we have the polynomial rewritten as a product of binomials: (3x - 4)(x² + 3)

Therefore, the polynomial 3x³ - 4x² + 9x - 12 can be rewritten as (3x - 4)(x² + 3).

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Answer:

Step-by-step explanation:

f(x)=x^4−x^2+9

Answer:

Step-by-step explanation:

Assuming that the number of ingredients per pie is constant, we can write an expression for the total number of ingredients and pies baked in the two years as:

Total number of ingredients = (129 x ingredients per pie) + (b x ingredients per pie)

Total number of pies baked = 129 + b

So, if we let "i" represent the number of ingredients per pie, we can write the expression as:

Total number of ingredients = (129 x i) + (b x i)

Total number of pies baked = 129 + b

Note that without knowing the value of "i," we cannot simplify this expression any further.

Answer:

see explanation

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

4x + 21 + x - 10 + 2x + 8 = 180

7x + 19 = 180 ( subtract 19 from both sides )

7x = 161 ( divide both sides by 7 )

x = 23

Then angles in triangle are

4x + 21 = 4(23) + 21 = 92 + 21 = 113°

x - 10 = 23 - 10 = 13°

7x + 8 = 7(23) + 8 = 161 + 8 = 169°

the only 2 possible angle measures are A and E

The exponential function showing the relationship between y and t is y = 41,000 x (1.07)^t

From the question, we have the following parameters that can be used in our computation:

Initial value, a = 41,000

Rate = 7% increment

The exponential function for the college enrollment y of the college, in dollars, after t years can be expressed as:

y = a(1 + r)^t

Substitute the known values in the above equation, so, we have the following representation

y = 41,000 x (1 + 7%)^t

Evaluate

y = 41,000 x (1.07)^t

Where 1.07 is the factor by which the college enrolment increases

Hence, the function is y = 41,000 x (1.07)^t

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The relationship between ∠8 and ∠4 include the following: A. corresponding angles.

In Mathematics, corresponding angles can be defined as a postulate (theorem) which states that corresponding angles are always congruent when the transversal intersects two (2) parallel lines. This ultimately implies that, the corresponding angles will be always equal (congruent) when a transversal intersects two (2) parallel lines.

By applying corresponding angles theorem to lines l and m, we have the following:

8 ≅ ∠4

3 ≅ ∠7

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The restriction on the variablex is that it must be greater than or equal to 1/3. If x is less than 1/3, the expression √6x-2 will not be a real number.

The restrictions on the variablex in the expression √6x-2 are determined by the fact that the square root of a negative number is not a real number. Therefore, the expression under the square root must be greater than or equal to zero. This gives us the following inequality:

6x-2 ≥ 0

Solving for x, we get:

6x ≥ 2

x ≥ 2/6

x ≥ 1/3

So the restriction on the variablex is that it must be greater than or equal to 1/3. If x is less than 1/3, the expression √6x-2 will not be a real number.

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There are no values of x that satisfy the equation -6-(4x)/(x+2)=(8)/(x+2).

To find the values of x for the equation -6-(4x)/(x+2)=(8)/(x+2), we need to follow the following steps:

Multiply both sides of the equation by (x+2) to eliminate the fractions:
(x+2)(-6-(4x)/(x+2))=(x+2)(8)/(x+2)

Simplify the equation:
-6(x+2)-4x=8

Distribute the -6:
-6x-12-4x=8

Combine like terms:
-10x-12=8

Add 12 to both sides:
-10x=20

Divide both sides by -10:
x=-2

However, we need to check our answer to make sure it does not result in a zero denominator in the original equation. If we plug in x=-2 into the original equation, we get a zero denominator, which is not allowed. Therefore, there are no values of x that satisfy the equation.

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Answer:

-2

Step-by-step explanation:

[tex]m=\frac{4-(-8)}{-4-2} \\m=\frac{4+(+8)}{-4-2} \\m=\frac{12}{-6} \\m=\frac{2}{-1} \\m=-2[/tex]

The given trinomial x^(2)+12x+35 is factorable. It's factors would be (x+7)(x+5).

To factor this trinomial, we need to find two numbers that multiply to 35 and add to 12. The two numbers that satisfy this condition are 7 and 5. Therefore, we can factor the trinomial as follows:

x^(2)+12x+35 = (x+7)(x+5)

So, the factored form of the given trinomial is (x+7)(x+5).

Therefore, the answer is (x+7)(x+5).

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It is not possible to use Cramer's Rule to solve the system of equations you provided. This is because Cramer's Rule can only be applied to systems of linear equations that have the same number of equations as there are unknowns.

In the system you provided, there are four equations but only two unknowns. This means that Cramer's Rule cannot be applied.

Instead, you can use other methods such as substitution or elimination to solve the system. However, it is important to note that with more equations than unknowns, it is possible that there may be no solution or an infinite number of solutions.

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The polygons are classified as :-

1.CONVEX

2.CONCAVE

3.CONCAVE

4.REGULAR

5.CONCAVE

6.IRREGULAR

A polygon is a geometrical figure, with finite sides and angles, they can be regular and irregular.

Regular Polygon

A regular polygon is that which has all its sides and angles equal, for example an equilateral triangle and a square.

Irregular Polygon

A irregular polygon is that which has all its sides and angles unequal,

For example, a scalene triangle, a rectangle, a kite, etc.

Convex Polygon

A Convex polygon is that which has all its angles less than 180 degrees,

Concave Polygon

A Concave polygon is that which has its angles greater than 180 degrees,

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The complete question attached

The final response is:
−8x^3+6x^2−9x+4 / x−2 = -8x^2 - 10x - 29 + (62/(x-2))

The synthetic division of −8x^3+6x^2−9x+4 / x−2 can be performed as follows:

Step 1: Write the coefficients of the dividend in a row: -8, 6, -9, 4

Step 2: Write the divisor in the form x-a, in this case x-2, so a=2

Step 3: Bring down the first coefficient, -8, to the bottom row

Step 4: Multiply the first number in the bottom row, -8, by a, 2, and write the result, -16, in the next column

Step 5: Add the numbers in the second column, 6 and -16, to get -10, and write the result in the bottom row

Step 6: Repeat steps 4 and 5 with the new number in the bottom row, -10, until all columns have been completed

Step 7: The last number in the bottom row is the remainder, and the other numbers in the bottom row are the coefficients of the quotient

The synthetic division table looks like this:

| 2 |  |   |   |   |
|---|---|---|---|---|
|-8 | 6 | -9| 4 |   |
|   |-16|-20| 58|   |
|---|---|---|---|---|
|-8 |-10|-29| 62|   |

The quotient is -8x^2 - 10x - 29 with a remainder of 62.

So the final response is:
−8x^3+6x^2−9x+4 / x−2 = -8x^2 - 10x - 29 + (62/(x-2))

I hope this synthetic division explanation was helpful!

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vector u can be written as a linear combination of the vectors in set S with the scalars a = 1 and b = 0.

To write vector u as a linear combination of the vectors in set S, we need to find scalars a and b such that:

u = a[1] + b[0]

Substituting the values of vector u and the vectors in set S into this equation, we get:

[1] = a[1] + b[0]

This equation can be simplified to:

[1] = [a] + [0]

Since the scalar b is being multiplied by the zero vector, it will always equal the zero vector, and can therefore be eliminated from the equation. This leaves us with:

[1] = [a]

We can see that the scalar a must equal 1 in order for this equation to be true. Therefore, vector u can be written as a linear combination of the vectors in set S as follows:

u = 1[1] + 0[0]

In conclusion, vector u can be written as a linear combination of the vectors in set S with the scalars a = 1 and b = 0.

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The standard equation of this ellipse is x²/144 + y²/80 = 1.

The standard equation of an ellipse is (x-h)²/a² + (y-k)²/b² = 1, where (h,k) is the center of the ellipse, a is the semi-major axis, and b is the semi-minor axis.

In this case, the center of the ellipse is (0,0) since the vertices and foci are both on the y-axis. The distance between the vertices is 24 (12 - (-12)), so the semi-major axis is 12. The distance between the foci is 16 (8 - (-8)), so the distance between the center and each focus is 8. Using the formula c² = a² - b², where c is the distance between the center and each focus, we can solve for b:

c² = a² - b²
8² = 12² - b²
64 = 144 - b²
b² = 80

So the equation of the ellipse is (x-0)²/12² + (y-0)²/80 = 1, or x²/144 + y²/80 = 1.

You keep getting (x²)/80 + (y²)/144 because you are switching the values of a and b. The semi-major axis should be in the denominator of the x term, and the semi-minor axis should be in the denominator of the y term.

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Answer:

Step-by-step explanation:

Given: [tex]f(x)=x^{2} -3x - 8[/tex]

To find:

a) f(8)

To find f(8), replace x with 8 in f(x)

[tex]f(8) = 8^{2} -3(8) -8 = 32[/tex]

b)  f(x+9)

To find f(x+9), replace x with x +9 in f(x)

[tex]f(x+9) = (x +9)^{2} -3(x +9) -8 = x^{2} +18x+81-3x-27-8=x^{2} +15x+46[/tex]

c) f(-x)

To find f(-x), replace x with -x in f(x)

[tex]f(x)=(-x)^{2} -3(-x) - 8 =x^{2} +3x-8[/tex]

This is how we simplify these expressions.

12 blue whales will weigh [tex]\( 2.16 \times 10^{7} \mathrm{~kg} \)[/tex].

The weight of 12 blue whales will be the product of the weight of a single blue whale and the number of blue whales. To find the product, we simply multiply the weight of a single blue whale by the number of blue whales.

So, the weight of 12 blue whales will be:

[tex]\( 1.8 \times 10^{6} \mathrm{~kg} \) × 12 = \( 2.16 \times 10^{7} \mathrm{~kg} \)[/tex]

Therefore, 12 blue whales will weigh [tex]\( 2.16 \times 10^{7} \mathrm{~kg} \)[/tex]

Multiplication refers to binary operations in which different numerical sets are established. In mathematics the process of multiplication is elementary in several operations, it is also accompanied by addition, subtraction and division. Multiplication is the opposite of division.

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Answer:

0.33

Step-by-step explanation:

5.11-3.79= total for 4 postcards

then answer divided by 4 postcards

Answer:

2080cm^3

Step-by-step explanation:

V(t)=S ert-W/r

a. The rate at which the account changes (dt/dV) is equal to the interest rate (r) times the value of the account (V) minus the amount withdrawn (W). This can be written mathematically as dt/dV=rV-W. This is a separable differential equation, which can be solved by integrating both sides of the equation with respect to time. The solution is V(t)=S ert-W/r.

b. The value of the Jones' account at the end of 10 years can be found using the solution V(t) from part a: V(10)=500,000 e5%x10-50,000/5% = $387,468.51.

c. To keep their account unchanged at $500,000, the Jones' must withdraw an annual amount W such that V(t)=500,000. From the solution V(t)=S ert-W/r, we can solve for W: W = 500,000e5%x10 - 500,000/5% = $47,613.30.

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Tower B is 2.34 miles far from the point on the road closest to the fire.

The point on the road closest to the fire can be found by drawing a line perpendicular to the road that passes through the fire location. Let x be the distance from tower B to this point. Then, using trigonometry, we can find that the distance from tower A to the fire location is x/tan(22) and the distance from tower B to the fire location is (5 - x)/tan(37). Since the fire location is the same from both towers, these distances must be equal, so we can set up the equation x/tan(22) = (5 - x)/tan(37) and solve for x, which is approximately 2.34 miles.

To sketch the fire location, draw a straight road with two fire towers located 5 miles apart. From tower A, draw a line at an angle of 22 degrees towards the north side of the road to represent the direction of the fire location. From tower B, draw a line at an angle of 37 degrees towards the same side of the road. The point where these two lines intersect represents the location of the fire. Draw a line perpendicular to the road passing through this point to find the closest point on the road to the fire.

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The graph of the quadratic function is on the image at the end.

Here we have the quadratic function:

f(x) = (x + 1)*(x - 5)

To graph this, we need to find some points of the parabola and then connect them.

So let's evaluate the function.

if x = -1

f(-1) = (-1 + 1)*(-1 - 5) = 0

if x = 0

f(0) =  (0 + 1)*(0 - 5) = -5

if x = 1

f(1) =  (1 + 1)*(1 - 5) = 2*-4 = -8

if x = 5 then:

f(5) =   (5 + 1)*(5 - 5) = 0

So we have the points (-1, 0), (0, -5), (1, -8) and (5, 0).

With these we can graph the parabola (you can try to find more points to get a better graph).

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Jill played for 10 mins. 25+15=40 50-40=10

The linear speed of the circle is 2.125 cm/s and the angular speed of the circle is 0.1012 rad/s.

The linear speed of the circle can be found by calculating the length of the arc traveled in 25 seconds. The length of an arc is given by the formula L = rθ, where r is the radius of the circle and θ is the central angle in radians. Converting the given angle from degrees to radians, we have:

θ = 145 degrees * π/180 = 2.53 radians

Substituting the values into the formula, we get:

L = 21 cm * 2.53 = 53.13 cm

Therefore, the linear speed of the circle is:

v = L/t = 53.13 cm/25 s = 2.125 cm/s

The angular speed of the circle can be found by dividing the central angle by the time taken to travel that angle. Therefore, the angular speed of the circle is:

ω = θ/t = 2.53 radians/25 s = 0.1012 rad/s

Hence, the linear speed of the circle is 2.125 cm/s and the angular speed of the circle is 0.1012 rad/s.

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