Given the following equation, x^4 -4x^2+10x+13 use synthetic division and show if they are root or not.

Please show steps.

Answer: there were 190 children, 140 parents, and 70 grandparents in attendance at the family reunion.

Step-by-step explanation: Let's denote the number of children, parents, and grandparents as "c", "p", and "g", respectively.

We are given three pieces of information:

The total number of people in attendance is 400:

c + p + g = 400

There were twice as many parents as grandparents:

p = 2g

There were 50 more children than parents:

c = p + 50

We can use this system of equations to solve for the unknown variables.

First, we can use equation (2) to express "p" in terms of "g":

p = 2g

Next, we can substitute this expression for "p" into equation (3) to get:

c = 2g + 50

Now, we can use equations (1) and (4) to eliminate "p" and "c" from the system and express "g" in terms of only known quantities:

c + p + g = 400

2g + 50 + p + g = 400 (substituting c=2g+50)

3g + p = 350 (simplifying)

We can then substitute the expression for "p" from equation (2) into this last equation to obtain:

3g + 2g = 350

Simplifying:

5g = 350

Solving for "g", we get:

g = 70

Now, we can use equation (2) to find "p":

p = 2g = 2(70) = 140

Finally, we can use equation (3) to find "c":

c = 2g + 50 = 2(70) + 50 = 190

Therefore, there were 190 children, 140 parents, and 70 grandparents in attendance at the family reunion.

Answer:

plein-air. Is the correct answer

Claude Monet's Impression: Sunrise (1872) is considered a plein-air painting because it was completed out-of-doors.

The solution to the given inequality is −1.26354284<x<1.75564007 or x>4.50790277.

The given inequality is x³-5x²+10>0.

Solve for x by simplifying both sides of the inequality, then isolating the variable.

Inequality Form: −1.26354284<x<1.75564007 or x>4.50790277

Interval Notation:(−1.26354284,1.75564007)∪(4.50790277,∞)

Therefore, the solution to the given inequality is −1.26354284<x<1.75564007 or x>4.50790277.

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Answer:

To find the derivative of the given function, we will use the product rule and the chain rule of differentiation.

Let u = 4x² and v = (5-7x)^8. Then, we have:

y = u * v

Using the product rule, we have:

y' = u' * v + u * v'

To find u' and v', we use the power rule and the chain rule:

u' = d/dx (4x²) = 8x

v' = d/dx (5-7x)^8 = 8(5-7x)^7 * (-7)

Now, we can substitute these values into the product rule formula:

y' = u' * v + u * v'

= 8x * (5-7x)^8 + 4x² * 8(5-7x)^7 * (-7)

Simplifying this expression, we get:

y' = 8x(5-7x)^7 * (40-56x-28x+49x)

= 8x(5-7x)^7 * (-14x+40)

Therefore, the derivative of the function y = 4x² (5-7x)^8 is y' = 8x(5-7x)^7 * (-14x+40).

the answer is B

B

because the answer B make the most sense to me and hopefully this helps

Pythagoras theorem: In a right triangle, if the hypotenuse, perpendicular, and base are its sides, then as per the theorem, the square of the hypotenuse side is equal to the sum of the square of the base and the square of the perpendicular. Hence, if we know any two sides, then we can easily find the third side of the triangle.

C. 20 ft, 20 ft, 50 ft correct?

The perimeter of the quadrilateral is  b + 2c - 2 inches

To determine the value of the perimeter, we need to know the properties of a quadrilateral.

These properties includes;

The perimeter of a quadrilateral is expressed as;

Perimeter = A + B + C + D

add the values of the sides

Substitute the values, we have;

Perimeter = b + c + b - 2 + c - b

collect the like terms

Perimeter = b + 2c - 2

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The height of the building, found using the equivalent ratios of the corresponding sides of the similar triangles formed by Rob, the building and the shadows is 90 feet

Similar triangles are triangles that have the same shape but may have different sizes.

The length of the shadow cast by the building = 30 feet

Rob's height = 6 feet

The length of Rob's shadow = 2 feet long

The height of the building can be found from the similar right triangles formed by the building and the building's shadow and the triangle formed by Rob and Rob's shadow as follows;

Let h represent the height of the building, we get;

h/30 = 6/2 = 3

h = 30 × 3 = 90

The height of the building is 90 feet tall

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Based on the above, Since Ana bought 3/4 kg of lanzones and 1/2 kg of apples,  Ana bought 1  1/4 kilograms of fruits in all.

To be able to find out how many kilograms of fruits Ana bought in total, you have to add the amount of lanzones and apples she have.

Ana = 3/4 kg of lanzones

Ana = 1/2 kg of apples

So it will be:

3/4 + 2/4 = 5/4

Therefore, Ana will have bought a total of 5/4 kilograms of fruits.

To convert it to a mixed number, you need to divide the numerator by the denominator:

5 ÷ 4 = 1 remainder 1

So, the mixed fraction will  be 1  1/4 kg.

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See full question below

Ana bought 3/4 kg of lanzones and 1/2 kg of apples. How many kilograms of fruits did she buy in all?​

The number of children, parents, and Grandparents that were in attendance are:

First, we should come up with equations that relate the number of children, parents, and Grandparents, given the information we know. The equations would have C for children, P for parents, and G for grandparents.

Total number of people:

C + P + G = 400

Parents to grandparents:

P = 2G

Children to parents:

C = P + 50

Substituting gives:

( P + 50 ) + P + ( P / 2 ) = 400

P + 50 + P + P / 2 = 400

(5 / 2) P + 50 = 400

(5 / 2 )P = 350

P = 140 parents

The children would be:

C = P + 50

= 140 + 50

= 190 children

The grandparents:

G = P/2

= 140/2

= 70 grandparents

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The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

We have,

Equation of circle: x²+ y² – 2x – 8 = 0

The standard equation of a circle is

x² + y² + 2gx + 2fy + C= 0

where Centre is (-g, -f)

and, radius = √g²+f²-C

from given equation the center is

2gx = -2x

x= -1

and,  2fy = 0

f = 0

So, the Centre = (-(-1), 0) = (1, 0)

Now, r = radius = √g²+f²-C

r= √1²+0²-(-8)

r=√9

r = 3 units

Hence, the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

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Answer: [tex]x_1 = -\frac{3}{2} \\x_2 = \frac{3}{2} \\\\[/tex]

X could equal either -3/2, or 3/2 because x is made into an absolute value

Answer:

[tex]x = 1 \frac{1}{2} \: \\ x = - 1 \frac{1}{2} [/tex]

Step-by-step explanation:

If we're solving for x, then we should divide both sides by 2 and then simplify.

[tex](2 |x| = 3) \div 2[/tex]

[tex] |x| = \frac{3}{2} [/tex]

This gives us the final answer of

[tex]x = ±\frac{3}{2} [/tex]

Which can be simplified into:

[tex]x = 1\frac{1}{2} , \: - 1\frac{1}{2} [/tex]

The standard deviation of the sum S = I + O is [tex]$1,508.48[/tex]. The Option C is correct.

In order to calculate standard deviation of the sum S = I + O on the information given from the question, we can use this formula: "SD(S) = sqrt[SD(I)^2 + SD(O)^2 + 2Cov(I,O)]".

Details:

SD(I) & SD(O) means standard deviations of in-state and out-of-state tuition.

Cov(I,O) means covariance between the two variables.

The two variables I and O are independent

Their covariance is zero

Now, we can solve the S.D. using the formula. The SD(S):

= sqrt[SD(I)^2 + SD(O)^2]

= sqrt[(1003.25)^2 + (1126.50)^2]

= sqrt[1006510.5625 + 1269002.25]

= sqrt[2275512.8125]

= 1508.48029901

= $1508.48

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The probability of passing the quiz by randomly guessing answers is very low, approximately 0.02%.

To pass the quiz with a minimum passing grade of 60%, a person needs to answer at least 12 questions correctly out of the 20 total questions.

If a person is making random guesses for all of the answers, the probability of guessing one question correctly is 1/4, since there are 4 possible answers for each question. The probability of guessing one question incorrectly is 3/4.

Using the binomial probability formula, we can find the probability of passing the quiz by correctly guessing at least 12 questions:

P(X >= 12) = 1 - P(X < 12)

where X is the number of questions answered correctly.

P(X < 12) = sum of the probabilities of getting 0, 1, 2, ..., or 11 questions correct:

P(X < 12) = C(20,0)(1/4)⁰(3/4)²⁰ + C(20,1)(1/4)¹(3/4)¹⁹ + ... + C(20,11)(1/4)¹¹(3/4)⁹

where C(20,0), C(20,1), ..., C(20,11) are the binomial coefficients.

We can use a calculator or a computer to evaluate this sum of probabilities, or we can use a normal approximation to the binomial distribution if we assume that np = 20(1/4) = 5 and n x (1-p) = 20 x (3/4) = 15 are both greater than 10.

Using the normal approximation, we can find the mean and standard deviation of the binomial distribution:

mean = np = 20(1/4) = 5

Standard deviation = √(np(1-p)) = √(20*(1/4) x (3/4)) = √(15/2) = 1.94 (rounded to 2 decimal places)

Then, we can standardize the distribution by subtracting the mean and dividing by the standard deviation:

z = (12 - 5) / 1.94 = 3.61 (rounded to 2 decimal places)

Using a standard normal distribution table or a calculator, we can find the probability of getting a z-score greater than 3.61:

P(Z > 3.61) = 0.0002 (rounded to 4 decimal places)

Therefore, the probability of passing the quiz by randomly guessing answers is very low, approximately 0.02%.

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After 20 years, the initial investment of $650 will have grown to $2,386.10

Now, let's consider the problem at hand: a $650 investment at 6.5% interest compounded continuously for 20 years. To calculate the final amount of the investment, we can use the formula:

A = P[tex]e^{rt}[/tex]

where A is the final amount, P is the initial investment, e is the mathematical constant approximately equal to 2.71828, r is the interest rate (in decimal form), and t is the time (in years).

Plugging in the values given in the problem, we get:

A = 650 x [tex]e^{0.065 \times 20}[/tex]

Simplifying this expression, we get:

A = 650 x [tex]e^{1.3}[/tex]

Using a calculator, we can find that  [tex]e^{1.3}[/tex] is approximately 3.6693. Therefore, the final amount of the investment is:

A = 650 x 3.6693

A = $2,386.10

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The area of the shaded region is  π(R + 3)² - 9π where R is teh radius of the outer circle

The circumference of the inner circle is 18.84 feet

So, we have

2πr = 18.84

Divide by 2π

r = 18.84/2π

Evaluate

r = 3.0

So, the area of the inner circle is

A = πr²

This gives

A = π * 3²

Evaluate

A = 9π

The shaded area is

Area of big - Area of inner circle

So, we have

Shaded area = π(R + 3)² - 9π where R is teh radius of the outer circle

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The solution is the number in polar form 4 - 4i is

4 Root(2) (cos(-45) + i sin(-45)).

We know that,

Polar form of a complex number is r( cos(theta) + i sin(theta) )

r is equal to the total distance created by the rectangular coordinates of the complex number

r = Root(4^2 + (-4)^2) = Root(32) = 4 Root(2)

To find theta, if a > 0, use arctan(b/a), where:

a = the first number

b = the second number

arctan (-4/4) = -45 degrees (-0.7854 radians)

The answer is 4 Root(2) (cos(-45) + i sin(-45))

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complete question;

Express the number in polar form 4 - 4i

Answer:

23 apple pies and 13 cherry pies were sold.

Step-by-step explanation:

Let's use the variables a and c to represent the number of apple and cherry pies sold, respectively.

From the problem, we know that:

The total number of pies sold is 36: a + c = 36

The total revenue from pie sales is $304.00: 7a + 11c = 304

We now have two equations with two unknowns. We can use substitution or elimination to solve for a and c. Here's one way to use substitution:

Solve the first equation for a: a = 36 - c

Substitute a = 36 - c into the second equation: 7(36 - c) + 11c = 304

Simplify: 252 - 7c + 11c = 304

Simplify further: 4c = 52

Solve for c: c = 13

Substitute c = 13 into the first equation to solve for a: a + 13 = 36

Simplify: a = 23

Therefore, 23 apple pies and 13 cherry pies were sold.

Step-by-step explanation:

(20 - m) + 3

that's it. there is not more to it.

The algebra expression can be expressed as: 3 + (20 - m)

Algebraic word problems are defined as questions that require translating sentences to equations, and then solving those equations. The equations we need to write will only involve basic arithmetic operations. and a single variable. Normally, the variable represents an unknown quantity in a real-life scenario.

We are told that 3 more than the difference of 20 and a number m.

This can be expressed as:

3 + (20 - m)

That is the literal expression of the algebra word problem.

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The roots of equation are 2 , -2, 3i, 1/5 and -5.

We have,

([tex]x^4[/tex] + 5x² -36)(2x² + 9x-5)=0

Now, factories each equation as

([tex]x^4[/tex] + 5x² -36)

= ([tex]x^4[/tex] + 9x² - 4x² -36)

= x²(x² + 9) - 4(x² + 9)

= (x² - 4)(x² + 9)

= (x-2)(x+2)(x²+9)

and, 2x² + 9x-5

= 2x² + 10x - x -5

= 2x(x+5)- (x+5)

= (2x -1)(x+5)

So, the factored form is (x-2)(x+2)(x²+9) (2x -1)(x+5)

and, the roots of equation are 2 , -2, 3i, 1/5 and -5.

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Answer:

Charles Baudelaire recommended that artists paint scenes of modern life.

Charles Baudelaire was the one who recommended that artists paint scenes of modern life.

The quadratic regression equation for the data is given as follows:

y = 2.4x² - 14.4x + 46.8.

To find the quadratic regression equation, we need to insert the points (x,y) into a quadratic regression calculator.

The points for this problem are taken from the table, as follows:

(1, 35), (2, 27), (3, 24), (4, 28), (5, 33).

Inserting these points into a calculator, the equation is given as follows:

y = 2.4x² - 14.4x + 46.8.

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Answer:

Regarding the conjecture of Serena and Jack:

Serena suggests that they can use the graph of the first rocket and shift it to find the graphs for the other two rockets. This means that the paths of the rockets are similar, and the only difference is the time of launch. Jack suggests that they need to recalculate the graphs for the other two rockets, which means that the paths of the rockets are different.

In this scenario, Serena is correct. Since the rockets are identical, they will follow the same path, but with a different time of launch. Thus, they can use the graph of the first rocket and shift it to the right to get the graph of the second rocket and shift it further to the right and up to get the graph of the third rocket.

Analyzing the equation:

The equation for the first rocket's path is h(t) = -6(t-3.7)^2 + 82.14. Assuming that the graph is a transformation from f(t) = -6t^2, the term -3.7 shifts the graph horizontally to the right by 3.7 seconds. This means that the first rocket was launched 3.7 seconds before the time t in the equation. The value t = 3.7 represents the time when the first rocket was launched.

The term 82.14 shifts the graph vertically up by 82.14 feet. This means that the initial height of the rocket is 82.14 feet above the ground. Therefore, the value h(t) = 82.14 represents the initial height of the rocket.

Equation of the second rocket:

The second rocket is launched 3 seconds after the first rocket. This means that the graph of the second rocket is a horizontal shift of the first rocket's graph by 3 seconds. Therefore, the equation of the second rocket is:

h(t) = -6(t-6.7)^2 + 82.14

This is because the launch time of the second rocket is t = 6.7 seconds (which is 3 seconds after the first rocket's launch).

Description of the third rocket's graph:

The third rocket is launched 3 seconds after the second rocket and from a 20-foot-tall platform. This means that the graph of the third rocket is a horizontal shift of the second rocket's graph by 3 seconds and a vertical shift upwards by 20 feet. Therefore, the equation of the third rocket is:

h(t) = -6(t-9.7)^2 + 102.14

This is because the launch time of the third rocket is t = 9.7 seconds (which is 3 seconds after the second rocket's launch).

Answers to the questions:

a. The third rocket is launched at approximately t = 9.7 seconds.

b. The first rocket lands when h(t) = 0. Solving -6(t-3.7)^2 + 82.14 = 0 gives t = 5.16 seconds (approximate).

c. The approximate interval during which all three rockets are in the air is from t = 6.7 seconds (when the second rocket is launched) to t = 14.46 seconds (when the first rocket lands).

The coordinates of Y' are (6, 4) and the coordinates of Z' are (5, -1).

Here, we have,

To find the coordinates of Y' and Z', we need to apply the same translation that maps X to X'.

We know that the vector that connects X to X' is (3 - (-1), 1 - 0) = (4, 1).

So, to translate Y to Y', we add the vector (4, 1) to the coordinates of Y:

Y' = Y + (4, 1)

= (2, 3) + (4, 1)

= (6, 4)

Similarly, to translate Z to Z', we add the vector (4, 1) to the coordinates of Z:

Z' = Z + (4, 1)

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

= (5, -1)

Therefore, the coordinates of Y' are (6, 4) and the coordinates of Z' are (5, -1).

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Option A correctly matches the data set.

First, by looking at the numbers and description of the numbers; I notice that it starts at 10, ending at 48.

Second, I see that the first quartile (Q1) is 20, eliminating option D

Third, I see the third quartile (Q3) is 45, eliminating option C.

Lastly, I look at the median (Q2) is 30, eliminating option B.

Since I have eliminated option B, C, and D; only option A remains.

—————

Please remember to revise this and make it in your own words if you want! I hope this helps you. -Doodle

—————

Answer:

There are 300 students at East High School.

Step-by-step explanation:

East High School has 1/10 as many students as West High School, which means that the number of students at East High School is equal to 1/10 of the number of students at West High School.

To find out how many students are at East High School, we can multiply the number of students at West High School by 1/10:

East High School = West High School x 1/10East High School = 3000 x 1/10East High School = 300

Therefore, there are 300 students at East High School.

Answer:

East High School has 1/10 × 3,000 = 300 students.

The complete proof to show that ∠HIJ ≅ ∠EFG is:

Statement                                         Reason

FG ⊥ EF                                             Given

HI ⊥ IJ                                                Given

m ∠EFG = 90°                                    Definition of perpendicular lines  

m ∠HIJ = 90°                                     Definition of perpendicular lines

∠HIJ ≅ ∠EFG                                    Substitution property

From the question, we to prove that the given angles are congruent.

The given angles are ∠HIJ and ∠EFG

To prove that angle HIJ is congruent to angle EFG we will complete the given table.

The given table is

Statement                                         Reason

FG ⊥ EF                                             Given

HI ⊥ IJ                                                Given

m ∠EFG = 90°                                    Definition of perpendicular lines  

m ∠HIJ = 90°                                     Definition of perpendicular lines

Now, we will complete the proof by adding the last statement and its reason

Statement                                         Reason

FG ⊥ EF                                             Given

HI ⊥ IJ                                                Given

m ∠EFG = 90°                                    Definition of perpendicular lines  

m ∠HIJ = 90°                                     Definition of perpendicular lines

∠HIJ ≅ ∠EFG                                    Substitution property

Hence,

We have completed the proof by using the substitution property

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For each relation, we would determine whether or not it is a function as follows;

Relation 1 is: B. not a function

Relation 2 is: A. function.

Relation 3 is: B. not a function

Relation 4 is: A. a function.

In Mathematics and Geometry, a function is generally used for uniquely mapping an independent value (domain or input variable) to a dependent value (range or output variable).

This ultimately implies that, an independent value (domain) represents the value on the x-coordinate of a cartesian coordinate while a dependent value (range) represents the value on the y-coordinate of a cartesian coordinate.

Based on relations 1 and 3, we can logically deduce that they do not represent a function because their independent value (domain) has more than one dependent value (range).

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The area of the sidewalk is 264 sq. m.

A circle is a figure that is bounded by curved line called its circumference. Its area is the amount of space that he circle will cover on a 2 dimensional plane. It can be determined by:

area of a circle = πr^2

where r is the radius of the circle.

In the given question,

area of the circular flower = πr^2

   r = d/2 (d is the diameter)

      = 17/ 2

r = 8.5 m

area of the circular flower = 3.14*(8.5)^2

                                           = 226.865 sq. m

area of the circular flower with sidewalk = πr^2

d = 4 + 17 + 4 = 25 m

so that,

r = 25/ 2 = 12.5 m

area of the circular flower with sidewalk = 3.14*(12.5)^2

                                              = 490.625 sq. m

Area of the sidewalk = area of the circular flower with sidewalk - area of the circular flower

                                  = 490.625 - 226.865

                                  = 263.76 sq. m

The area of the sidewalk is 264 sq. m.

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