Solve for x. Type your answer as a number

The rational zeros for the function, f(x) = 2·x³ + 3·x² - 10·x + 7, found using the rational roots theorem are;

-7, -7/2, -1, -1/2, 1/2, 1, 7/2, 7

The rational roots theorem is a theorem in algebra that can be used to find the roots of a polynomial equation. According to the theorem, the rational roots of a polynomial that has integer coefficients have the form p/q, where, p is a factor of the constant term and q is a factor of the leading coefficient.

The rational roots theorem can be used to find the possible rational zeros of a polynomial.

The rational roots theorem states that if a polynomial function has integer coefficients, then any rational zero of the function must have the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient

The specified function, f(x) = 2·x³ + 3·x² - 10·x + 7, the constant term is 7 and the leading coefficient is 2. Therefore, the possible rational zeros of the function are of the form p/q, where p is a factor of 7 and q is a factor of 2.

The factors of 7 are 1, and 7, and the factors of 2 are 1 and 2, Therefore, the possible rational zeros of the functions are;

±1/1, ±7/1, ±1/2, ±7/2

The possible rational zeros of the function f(x) = 2·x³ + 3·x² - 10·x + 7 are;

-7, -7/2, -1, -1/2, 1/2, 7/2, 7

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The approximate value of K of the given quadratic equation is: 16.842

The general expression of a quadratic function is:

ax² + bx + c = 0

The quadratic formula to find the roots is expressed as:

x = [-b ± √(b² - 4ac)]/2a

The product of the 2 roots of the quadratic equation is equal to the constant term.

Let a and b be used to denote the roots of a given quadratic equation.

But according to given condition, one root is equal to the square of the other root. Thus: b = a²

Thus:

a + a² = k

a * a² = 48

a³ = 48

a = 2∛6

Thus:

2∛6 + (2∛6)² = k

k = 16.842

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Answer:

x = 8

Step-by-step explanation:

the angle between the tangent and the radius at the point of contact A is 90°

then Δ ABP is right at A

using Pythagoras' identity in the right triangle

BP² = AP² + AB² , that is

(x + 9)² = x² + 15² ← expand parenthesis on left side using FOIL

x² + 18x + 81 = x² + 225 ( subtract x² from both sides )

18x + 81 = 225 ( subtract 81 from both sides )

18x = 144 ( divide both sides by 18 )

x = 8

Output z obtained as: multiply w with 5 and then subtract 3 from the result: w --> *5 ---> -3 ---> z.

There are only one or two variables in a linear equation.

The given expression is:

z = 5w-3

Here:

Input value : 5w-3

Output value : z

So,

Output z obtained as:

multiply w with 5 and then subtract 3 from the result:

w --> *5 ---> -3 ---> z

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Answer:

X=4

Step-by-step explanation:

First you would simplify the numbers on the right which would give you 168=18x+24x. Since the two numbers have the same variable you can add them which would then give you 168=42x. Lastly you isolate the x by dividing 42 so that x=4.

Answer:

B) a 180° rotation about the origin

Step-by-step explanation:

The trip to the campsite took 2 hours for Sami.

The total time taken by Sami on his journey = 7 hours

Let the time taken by Sami while going from his house to the campsite be 'x' hours

And, the time taken by Sami while coming back from the campsite to his house be 'y' hours

Speed while going from house to campsite = 60 miles per hour

Speed while coming back from campsite to house = 40 miles per hour

Distance from house to campsite and back will be equal as Sami will take the same route.

Let the distance be 'd'.

So, according to the question,
Distance = Speed × Time

We know that,
Time taken while going from house to campsite + Time taken while coming back from campsite = 7 hours

x + y = 7 ...(1)

Distance while going from house to campsite = Distance while coming back from campsited  = 2d ...(2)

Distance = Speed × Timex = d/60 ...(3)

y = d/40 ...(4)

Substituting (2), (3) and (4) in (1), we get,

d/60 + d/40 = 7

Solving the equation, we get d = 120

Therefore, Time taken while going from house to campsite, x = d/60 = 2 hours

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I measured it with a protractor and it is around 135 degrees.

I honestly don't know if this is correct but I hope this helps. Feel free to remove my answer if you think this is wrong.

The value of x/y is 35/37. The correct answer is option B).

Let's start by the first right triangle and the inscribed square. We know that the square has side length x and is inscribed in the right triangle with sides 3, 4, and 5, where 5 is the hypotenuse. Since one vertex of the square coincides with the right-angle vertex of the triangle, we have that the side length x of the square is also the length of the altitude from the right angle to the hypotenuse of the triangle. Therefore, we can write:

x = [tex](3*4)/5 = 12/5[/tex]

Now the second right triangle and the inscribed square:

We know that the square has side length y and is inscribed in the right triangle with sides 3, 4, and 5, where 5 is the hypotenuse. Since one side of the square lies on the hypotenuse of the triangle, we have that the sum of the areas of the two smaller squares is equal to the area of the larger square. Therefore, we can write:

[tex]x^{2} + y^{2} = 5^{2} = 25[/tex]

Substituting[tex]$x = {12}/{5}[/tex] gives

[tex](12/5)^{2} + y^{2} = 25[/tex]

Simplifying this equation gives

[tex]y^{2} = 25 - (144/25) = (25^{2} - 144)/25 = 481/25[/tex]

Taking the square root of both sides gives

y = [tex]\sqrt{481}/5[/tex]

Finally, we compute x/y:

x/y = [tex]12*\sqrt{481}/ \sqrt{481}*5[/tex]

x/y = 35/37

The correct option is B)

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--The given question is incomplete, the complete question is

"A square with side length x is inscribed in a right triangle with sides of length 3, 4, and 5 so that one vertex of the square coincides with the right-angle vertex of the triangle. A square with side length y is inscribed in another right triangle with sides of length 3, 4, and 5 so that one side of the square lies on the hypotenuse of the triangle. What is x/y?

(A) 12/13

(B) 35/37

(C) 1

(D) 37/35

(E) 13/12"

Statement to match the given number sentence is The absolute value of -5 is equal to the absolute value of 5.

It is the distance of a number from zero on a number line, and is always positive.

The absolute value of -5 is 5 because -5 is 5 units away from zero on the number line.

Similarly, the absolute value of 5 is 5 because 5 is also 5 units away from zero on the number line.

Therefore, the absolute value of -5 is equal to the absolute value of 5, and the statement for this number sentence is "The absolute value of -5 is equal to the absolute value of 5."

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When AB = AC and A is nonsingular, then the cancellation law holds; is, B = C. The statement is true.

In matrix algebra, the cancellation law is a crucial property to know. It states that if AB = AC, then B = C when A is a nonsingular matrix.

The given statement is true, which means that if AB = AC and A are nonsingular, then B = C. The cancellation law in matrix algebra is a property that helps in solving linear equations involving matrices. It states that if AB = AC and A is a nonsingular matrix, then B = C.

Therefore, we can say that if AB = AC and A is nonsingular, then B = C is true.

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1. Asymptotic slope of the best line for the equation y = 5x⁴ + 3 plotted on a log-log plot is 4. To find this, first note that the dominant term in the equation is 5x⁴. On a log-log plot, the slope corresponds to the exponent of the dominant term. In this case, the exponent is 4.

2. The maximum number of inversions in a list of 100 distinct elements is 4,950. This occurs when the list is sorted in descending order.

To calculate the maximum number of inversions, use the formula n * (n - 1) / 2, where n is the number of elements. In this case, n = 100, so the maximum number of inversions is 100 * 99 / 2 = 4,950.

3. The minimum number of inversions in a list of 100 distinct elements is 0. This occurs when the list is already sorted in ascending order, meaning no inversions are present.

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Answer:

6 + y

Step-by-step explanation:

By BODMAS rule,

1st : Multiply

Then add,

2 + 2 x 2 + y

2 + (2 x 2) + y

= 2 + 4 + y

= 6 + y

The inequality shown by the graph is 4y+3x≤8x+2y+16 (option C).

In mathematics, an inequality is a statement that compares two values, expressing that one value is greater than, less than, or equal to the other. It is represented by symbols such as <, >, ≤, ≥, and ≠. For example, 5 > 3 is an inequality that means "5 is greater than 3", while 2x + 3 ≤ 7x - 2 is an inequality that means "the sum of 2 times x and 3 is less than or equal to 7 times x minus 2". Inequalities are commonly used in algebra, geometry, and real analysis to express relationships between quantities and to find solutions to equations and systems of equations.

To determine the inequality shown by the graph with coordinates (0,8) and (0, 3.25), we need to find the slope-intercept form of the equation for the line passing through these points.

The slope of the line is:

(y2 - y1) / (x2 - x1) = (3.25 - 8) / (0 - 0) = -4.75 / 0 (which is undefined)

Since the line is vertical, its equation is x = 0.

Substituting this into the inequality options, we can see that only option C results in a true statement:

A) 4y+3x≤8x+6y+16 -> 4(8) + 3(0) ≤ 8(0) + 6(8) + 16 -> 32 ≤ 64 (not true)

C) 4y+3x≤8x+2y+16 -> 4(8) + 3(0) ≤ 8(0) + 2(8) + 16 -> 32 ≤ 32 (true)

B) 4y-3x≤5x+2y+16 -> 4(8) - 3(0) ≤ 5(0) + 2(8) + 16 -> 32 ≤ 32 (true)

D) 4y-3x≤8x+2y+16 -> 4(8) - 3(0) ≤ 8(0) + 2(8) + 16 -> 32 ≤ 32 (true)

Therefore, the inequality shown by the graph is 4y+3x≤8x+2y+16 (option C).

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The area of the sector with a central angle of 180° and a diameter of 5.6 cm is approximately 11.8 [tex]cm^2[/tex].

To find the area of a sector, we need to know the central angle and the radius or diameter of the circle that the sector is a part of. In this case, we are given a central angle of 180° and a diameter of 5.6 cm.

Find the radius of the circle is the first step. We can do this by dividing the diameter by 2:

radius = diameter/2 = 5.6/2 = 2.8 cm

Next, we can use the formula for the area of a sector:

Area of sector = (central angle/360°) x π x [tex]radius^2[/tex]

Plugging in the given values, we get:

Area of sector = [tex](180/360) * \pi * (2.8)^2[/tex]

= [tex](1/2) * 3.14 * 2.8^2[/tex]

= [tex]11.77 cm^2[/tex]

Rounding to the nearest tenth, we get:

Area of sector ≈ 11.8 [tex]cm^2[/tex]

Therefore, the area of the sector is approximately 11.8 [tex]cm^2[/tex].

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To simplify this expression, we can use the rule of exponents that states when dividing two powers with the same base, we can subtract their exponents. Therefore:

6^8/6^4 = 6^(8-4) = 6^4

So the expression 6^8/6^4 can be simplified as a single power of 6, which is 6^4.

The appropriate z-value to use in the situation given in the question is 1.28.

Given,Total number of adults in the sample = 2092

Number of adults using the internet = 1318

Number of internet users who expect businesses to have websites that give product information = 1041

Probability of internet users who expect businesses to have websites that give product information as per the teacher's statement = 80% = 0.8

To find the appropriate z-value to use in this situation, we need to calculate the standard error of proportion, which is given by:

SEp = √[p(1-p)/n]

where p is the proportion of internet users who expect businesses to have websites that give product information and n is the sample size.

Substituting the given values in the formula,

SEp = √[(1041/1318)(1-1041/1318)/1318]SEp = 0.019

z-value is given by:

z = (p - P)/SEp

where P is the proportion of internet users who expect businesses to have websites that give product information as per the teacher's statement.

Substituting the given values in the formula,

z = (0.8 - 1041/1318)/0.019

z = - 1.28

The appropriate z-value to use in this situation is -1.28.

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The function [tex]f(x) = 648 × { (\frac{1}{3} )}^{x} [/tex] represents the same relationship.

Here given a function f(x)

When x= 0,1,2,3,4 the value of f(x) will be 648,216,72,24,8 respectively.

The function that represents the same relationship as the table is [tex]f(x) = 648 × { (\frac{1}{3} )}^{x} [/tex]

We can see that each successive value of f(x) is one-third of the previous value. So, we know that the function is of the form [tex]f(x) = a { (\frac{1}{3} )}^{x} [/tex] for some constant a.

To find the value of a, we can use the fact that f(0) = 648.

Substituting x = 0 into the equation gives f(0) = a(1/3)⁰ = a = 648

So, the function is [tex]f(x) = 648 × { (\frac{1}{3} )}^{x} [/tex]

Therefore, the correct answer is [tex]f(x) = 648 × { (\frac{1}{3} )}^{x} [/tex]

So, option D is the correct option.

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Since Ruby has 3 cups of sugar left, she has enough sugar to make the 45 cupcakes she wants

If Ruby needs 2 cups of sugar to make 45 cupcakes, then we can calculate how much sugar she needs for one cupcake by dividing 2 cups of sugar by 45 cupcakes:

2 cups of sugar / 45 cupcakes = 0.0444 cups of sugar per cupcake (rounded to 4 decimal places)

To make 45 cupcakes, Ruby would need:

45 cupcakes x 0.0444 cups of sugar per cupcake = 1.998 cups of sugar (rounded to 3 decimal places)

Since Ruby has 3 cups of sugar left, she has enough sugar to make the 45 cupcakes she wants (3 cups of sugar > 1.998 cups of sugar needed for 45 cupcakes).

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Ruby wants to make 45 cupcakes.

Use your answer to b) to work out fi she has enough sugar left.

Ruby needs 2 cups of sugar to make 45 cupcakes, and she has 3 cups of sugar left.

Answer:

70

Step-by-step explanation:

Ill give it to you if you really need it its gonna take a while to explain

:)

Answer:

(v+8) x (v+9)

We can multiply v into the other two terms in the second bracket, then we can do the same with 8.

(v*v + v*9) + (8*v + 8*9)

v² + 9v + 8v + 72

v² + 17v + 72.

The value of length of side of triangle AD using the angle bisector theorem is obtained as: AD = 4.68.

Angles are measurements created by joining two lines, also known as the vertex. Geometric forms such as triangles but also rectangles contain internal angles produced by their sides.

Using the angle bisector theorem in the given triangles:

The ratios of the sides will be equal.

AB / BC = AD / DC

AB = 9 ; BC = 11.7 AD = 3.6

Put the values.

9/11.7 = 3.6 / AD

AD = 3.6*11.7 / 9

AD = 4.68

Thus, the value of length of side of triangle AD using the angle bisector theorem is obtained as: AD = 4.68.

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The equation of the polynomial using finite difference is y = 18x^3 - 126x^2 + 269x - 163 and other solutions are shown below

To find the equation of the polynomial table using finite difference, we need to calculate the differences.

The differences are obtained by subtracting each value of y from the next value of y and this is repeated for the differences

So, we have

x   1   2   3   4   5

y  -2  15  -4  49  282

1st 17 -19  53 233

2nd -36 72 180

3rd 108 108

Since the third differences are all the same, this indicates that the original data can be represented by a cubic polynomial.

We can use the formula for a cubic polynomial:

y = ax^3 + bx^2 + cx + d

Using the table of values, we have:

a + b + c + d = -2

8a + 4b + 2c + d = 15

27a + 9b + 3c + d = -4

64a + 16b + 4c + d = 49

Using a graphing calculator, we have

a = 18, b = -126, c = 269 and d = -163

So, we have

y = 18x^3 - 126x^2 + 269x - 163

We can use the formula for a cubic polynomial:

y = a(x - x1)(x - x2)(x - x3)

Using the ordered pairs, we have:

y = a(x + 3)(x + 1)(x - 2)

At (0, -12), we have

a(0 + 3)(0 + 1)(0 - 2) = -12

a = 2

So, we have

y = 2(x + 3)(x + 1)(x - 2)

Expand

y = 2x^3 + 4x^2 - 10x - 12

We can use the formula for a cubic polynomial:

y = a(x - x1)(x - x2)(x - x3)

Using the ordered pairs, we have:

y = a(x + 10)(x + 5)(x - 4)

At (-8, -2), we have

a(-8 + 10)(-8 + 5)(-8 - 4) = -2

a = -1/36

So, we have

y = -1/36(x + 10)(x + 5)(x - 4)

Expand

[tex]y = -\frac{x^3}{36}-\frac{11x^2}{36}+\frac{10x}{36}+\frac{200}{36}[/tex]

We have

g(x) = -9x^5 + 3x^4 + x^2 - 7

g(x) is a polynomial function of odd degree (5), so it will have at least one real root.

Also, the leading coefficient is negative;

So, g(x) has at least one root in the interval (-∞, ∞).

Since g(0) = -7 < 0 and g(1) = -12 < 0, and g(x) is continuous, there exists a root of g(x) in the interval (0, 1).

Similarly, since g(-1) = 6 > 0 and g(-2) = 333 > 0, there exists a root of g(x) in the interval (-2, -1).

Since g(x) is a polynomial of odd degree, it cannot have an even number of real roots.

Therefore, g(x) has exactly one real root.

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Answer:simpler interest is 109.92.  Annual compounded interest is 111.98

Step-by-step explanation:

Answer: $209.2

Step-by-step explanation:
hey! i'm gonna try to make this as simple as possible;
with simple interest, the formula to this is I = PRT (Interest = Principle x Rate x Time).
we're going to take the $89 , 4.7% simple interest and the 5 years together into the same sentence like the formula.
89 (Principle, the money) x 4.7% (Interest rate)  x 5 (Time). we'll narrow down the decimal by moving the decimal forward once so we get a decimal of .47 / 0.47.
back to the equation, it is now 89 x .47 x 5. multiply all those and you'll get a sum of 209.15! by the end of the five years, patricia will have $209.15. to the nearest penny, she will have $209.2. (5 or more, it goes to the next number. 4 or less, it stays in the same place.)
hope this helped :)

The required 95% confidence interval representing the true population mean falls within the given interval, based on the given sample mean is  equals to (233.00, 271.90).

Use the t-distribution,

To construct a confidence interval for the population mean,

The sample size is relatively small (n = 64)

And the population standard deviation is unknown.

The formula for the confidence interval is,

[tex]\bar{x}[/tex] ± tα/2 × (s/√n)

where [tex]\bar{x}[/tex] is the sample mean,

s is the sample standard deviation,

n is the sample size,

And tα/2 is the critical value of the t-distribution with (n-1) degrees of freedom, corresponding to the desired confidence level.

For a 95% confidence interval, the critical value of the t-distribution with 63 degrees of freedom is approximately 1.998.

Plugging in the given values, we get,

252.45 ± 1.998 × 74.50/√64)

Simplifying we get,

252.45 ± 19.45

This implies,

The 95% confidence interval for the mean amount spent per day by a family of four visiting Niagara Falls is (233.00, 271.90)

Therefore, 95% confidence interval that the true population mean falls within this interval, based on the given sample is  (233.00, 271.90).

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The above question is incomplete , the complete question is:

A survey conducted by the American automobile association showed that a family of four spends an average of $215.60 per day while on vacation. suppose a sample of 64 families of four vacationing at Niagara falls resulted in a sample mean of $252.45 per day and a sample standard deviation of $74.50.

a. Develop a 95% confidence interval estimate of the mean amount spent per day by a family of four visiting Niagara Falls (to 2 decimals).

The answers that describe the polygon ABCD if measure A is congruent to measure B, and measure C is congruent to measure D, and segment AB is parallel to segment CD are;

A. Parallelogram

B. Quadrilateral

C. Rectangle

D. Rhombus

E. Square

In Mathematics, a parallelogram simply refers to a four-sided geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that is composed of two (2) equal and parallel opposite sides.

In Mathematics and Geometry, a rhombus is a type of quadrilateral that is composed of four (4) equal sides and opposite interior angles that are congruent (equal).

In conclusion, a square, parallelogram, rectangle, rhombus, and quadrilateral satisfies the given conditions.

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Answer:

36

Step-by-step explanation: