Find the missing side
Please help with

c=25/9 for the given condition of the bionomial.

We can solve this problem by using the technique of completing the square.

First, let's assume that [tex]9x^2 + 10x + c[/tex] is equal to the square of a binomial:

[tex](3x + b)^2 = 9x^2 + 6bx + b^2[/tex]

If we compare the above expression with [tex]9x^2 + 10x + c[/tex], we can see that:

6bx = 10x, which implies that b = 5/3

b^2 = c, which implies that [tex]c = (5/3)^2 = 25/9[/tex]

Therefore, c = 25/9 is the constant that satisfies the condition

[tex]9x^2 + 10x + c[/tex] is equal to the square of a binomial.

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The solution set of f(x) > 0 is x ∈ (-2, 8).

To find the solution set of f(x) > 0, we need to first determine the critical values of x where f(x) changes sign.

Let's start by finding the domain of the function:

x² - 6x - 16 ≠ 0

We can solve for x by using the quadratic formula:

x = [6 ± √(6² + 4(16))]/2 = [6 ± √52]/2 = 3 ± √13

So the domain of f(x) is (-∞, 3 - √13) U (3 + √13, ∞).

Now let's factor the numerator and denominator of f(x):

f(x) = (x + 10)/[(x - 8)(x + 2)]

The critical points occur where the numerator or denominator of f(x) changes sign.

The numerator changes sign at x = -10, and the denominator changes sign at x = -2 and x = 8.

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Answer:

  7²

Step-by-step explanation:

You want to know what 7×7 is when it is written using an exponent.

At its most basic, an exponent signifies repeated multiplication. It represents the number of times a value appears as a factor in the product.

The expression 7×7 has 7 as a factor 2 times. It can be written as 7 with an exponent of 2.

  7×7 = 7²

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Answer: b, c, d,

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The polar coordinates of the point (17,0) are (r,θ) = (17,0). This means that the point is located on the positive x-axis, at a distance of 17 units from the origin.

To find the polar coordinates of a point given in rectangular coordinates, we need to use the following formulas:

r = √(x² + y²)

θ = tan⁻¹(y/x)

where r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin and the point.

In this case, the point is (17,0), so x = 17 and y = 0. Using the formulas above, we get:

r = √(17² + 0²) = 17θ = tan⁻¹(0/17) = 0

In polar coordinates, a point is represented by an ordered pair (r,θ), where r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin and the point, measured in radians.

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The calculated measure of the arc XYZ is 83 degrees

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

The circle

The angles created by secants and tangents that intersect outside a circle, which states that

The size of the angle formed by these two lines is equivalent to half the numerical difference between the measures of the arcs that they cut out from the circle.

So, we have

XYY = 1/2 * (166 - 0)

Evaluate

XYY = 83

Hence, the measure of the angle is 83 degrees

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a. 4. b > 0

If b is positive, then we know it will be greater than 0.

b. 1. s ≤ 0

If s is nonpositive, this means it is negative or 0. We will use a less than or equal to symbol.

c.  3. w ≥ -8

If w is greater than or equal to -8, we will use a greater than or equal to symbol.

It can be found by graphing the points given and sketching the parabola. Another point on the graph is (-1, 9) that passes through them. You can move over and up from the vertex and do the same on the opposite side of the line x = -1.

In Mathematics and Geometry, the vertex form of a quadratic function is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

Based on the information provided, the vertex is located at point (2, 0), and this ultimately implies that the axis is represented by the vertical line x = 2 that passes through the vertex.

Additionally, the parabola would be bilaterally symmetric about the above axis, and the mirror image of the point (5, 9) would also be on this parabola.

Therefore, the mirror image would have the same y-coordinate of 9 while the x-coordinate is given by:

x = 2 - (5 -2)

x = -1.

In conclusion, the required point is (-1, 9).

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Complete Question:

The graph of a quadratic function has a vertex (2, 0). One point on the graph is (5, 9). Explain how to find another point on the graph. It can be found by graphing the points given and sketching the parabola. Another point on the graph is (-1, _) that passes through them. You can move over and up from the vertex and do the same on the opposite side of the line x=

The measure of the angle that turns through 3/10 of the circle is 108 degrees.

An angle is a geometric figure that is formed by two rays that share a common endpoint, which is called the vertex of the angle. The rays are referred to as the sides or legs of the angle. Angles are typically measured in degrees, with a full circle measuring 360 degrees.

Angles can be classified based on their degree of measurement: acute angles are less than 90 degrees, right angles are exactly 90 degrees, obtuse angles are greater than 90 degrees but less than 180 degrees, and straight angles are exactly 180 degrees.

Since a full circle has 360 degrees, 3/10 of the circle can be represented as:

(3/10) x 360 degrees = 108 degrees

Therefore, the measure of the angle that turns through 3/10 of the circle is 108 degrees.

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The complete question is :

The angle turns through 3/10 of the circle. What is the measure of the angle?

Answer: The first number is the X-axis and the second is the Y-axis.

Step-by-step explanation:

5, 1, 4, and 2 belong in X. 35, 7, 28, and 14 belong in Y.

The rule is that X always goes first the Y goes after.

Answer:

y=(x+8)^2/6 - 5/2

Step-by-step explanation:

Khan Academy

After making six monthly payments on her car loan, Ms. Hughes's savings account balance will decrease by $1,470.

To find the change in Ms. Hughes's savings account balance each month due to her car payment, we can divide the total change in balance for the year ($-2,940) by the number of months in a year (12):

Change in savings account balance each month = $2,940 / 12 = -$245

So, Ms. Hughes's savings account balance decreases by $245 each month due to her car payment.

To find the total change in Ms. Hughes's savings account balance after making six monthly payments on her car loan, we can multiply the change in savings account balance each month by the number of months (6):

Total change in savings account balance after six monthly payments = -$245 * 6 = -$1,470

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The three numbers are 10, 20, and 40.'

Let's assign variables to each number:

According to the problem, the sum of these three numbers is 70:

x + y + z = 70

Now, we can substitute the expressions for y and z in terms of x:

x + 2x + 2(2x) = 70

Combine the terms:

x + 2x + 4x = 70

7x = 70

Now, divide by 7 to find the value of x:

x = 70 / 7

x = 10

Now that we have the value of x, we can find the values of y and z:

y = 2x = 2(10) = 20

z = 2y = 2(20) = 40

So, the three numbers are 10, 20, and 40.

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The question in English is

The sum of 3 numbers is 70, the second number is twice the first and the third is twice the second.

2. The total dollar amount for each cash dividend is $23,700.

 1. Calculation of outstanding common shares on each cash dividend date:

2.

Calculation of total dollar amount for each cash dividend:

Therefore, the total dollar amount for each cash dividend is $23,700.

3.

Calculation of the capitalization of retained earnings for the stock dividend:

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The equity sections from Atticus Group’s 2016 and 2017 year-end balance sheets follow Stockholders’ Equity (December 31, 2016)

Common stock—$4 par value, 100,000 shares

authorized, 40,000 shares issued and outstanding . .. . . . . . . . . . $160,000

Paid-in capital in excess of par value, common stock .. . . . . . . . . . . . . . . . 120,000

Retained earnings .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320,000

Total stockholders’ equity .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $600,000

Stockholders’ Equity (December 31, 2017)

Common stock—$4 par value, 100,000 shares

authorized, 47,400 shares issued, 3,000 shares in treasury . .. . . . . . . $189,600

Paid-in capital in excess of par value, common stock . . . . . .. . . . . . . . . . . . 179,200

Retained earnings ($30,000 restricted by treasury stock) .. . . . . . . . . . . . . 400,000

768,800

Less cost of treasury stock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (30,000)

Total stockholders’ equity . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . $738,800

The following transactions and events affected its equity during year 2017.

Jan. 5 Declared a $0.50 per share cash dividend, date of record January 10.

Mar. 20 Purchased treasury stock for cash.

Apr. 5 Declared a $0.50 per share cash dividend, date of record April 10.

July 5 Declared a $0.50 per share cash dividend, date of record July 10.

July 31 Declared a 20% stock dividend when the stock’s market value was $12 per share.

Aug. 14 Issued the stock dividend that was declared on July 31.

Oct. 5 Declared a $0.50 per share cash dividend, date of record October 10.

Required

1. How many common shares are outstanding on each cash dividend date?

2. What is the total dollar amount for each of the four cash dividends?

3. What is the amount of the capitalization of retained earnings for the stock dividend?

The missing values of function rule, Y for corresponding value of X= (-4 ) and (-2) will be 9 and 3 respectively.

                                              [tex]X|-4 |- 2|\\ Y|\quad9\; | \quad3\;|[/tex]

Now for the given fucntion ,

By substituting the values of x into the equation [tex]y = -3x - 3[/tex] and solving for y, we can determine the values of y for [tex]x = -4\; and -2[/tex].

[tex]For \;x = -4:\\y = -3(-4) - 3\\y = 12 - 3\\y = 9[/tex]

Hence, for x =(-4), y= 9

[tex]For\; x = -2:\\y = -3(-2) - 3\\y = 6 - 3\\y = 3[/tex]

Hence, for x =( -2), y = 3

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Correct Question:Fill in the table using this function rule. y = - 3x-3

[tex]X|-4 |- 2|\\ Y|\quad?\; | \quad?\;|[/tex]

The answer for given polynomial is 4,1,-1.

A polynomial is made up of two terms, namely Poly (which means "many") and Nominal (which means "terms."). An expression that consists of variables, constants, and exponents and that is combined using mathematical operations such as addition, subtraction, multiplication, and division (no division operation by a variable) is referred to as a polynomial. The expression is divided into three categories: monomial, binomial, and trinomial depending on how many terms are included in it.

The zeros of a function are the values of its variables that meet the equation and result in the function's value being equal to 0. The zeros of a function can be represented graphically as the x-coordinates (or x-intercepts) where the graph intersects the x-axis. The discriminant formula allows us to identify whether the zeros of a quadratic function are real, complex, or repeating. As a result, when a function f(x) = 0, its zeros are x values. Therefore, if f(a) = 0, then 'a' is a zero of f(x).

according to question,

(((([tex]x^{4}[/tex])-(3•(x³)))-5x²)+3x)+4  = 0

 (((([tex]x^{4}[/tex]) -  3x³) -  5x²) +  3x) +  4  = 0

Polynomial Long Division

Dividing :  x4-3x3-5x2+3x+4

                             ("Dividend")

By         :    x-4    ("Divisor")

dividend     x4  -  3x3  -  5x2  +  3x  +  4

- divisor  * x3     x4  -  4x3            

remainder         x3  -  5x2  +  3x  +  4

- divisor  * x2         x3  -  4x2        

remainder          -  x2  +  3x  +  4

- divisor  * -x1          -  x2  +  4x    

remainder              -  x  +  4

- divisor  * -x0              -  x  +  4

remainder                    0

Quotient :  x3+x2-x-1  Remainder:  0

the answer for the given polynomial by hit and trial method is 4,1,-1.

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The zeros of the polynomial is -1 , 1 and 4.

what is polynomial?

A polynomial is made up of two terms, namely Poly (which means "many") and Nominal (which means "terms."). An expression that consists of variables, constants, and exponents and that is combined using mathematical operations such as addition, subtraction, multiplication, and division (no division operation by a variable) is referred to as a polynomial. The expression is divided into three categories: monomial, binomial, and trinomial depending on how many terms are included in it.

Here the given polynomial is g(x) = [tex]x^4-3x^3-5x^2+3x+4[/tex]

To find zeros , take g(x) = 0 then

=> [tex]0=x^4-3x^3-5x^2+3x+4[/tex]

=> [tex]-x^4+3x^3+5x^2-3x-4=0\\[/tex]

=> [tex]-x^4+x^3+2x^3-2x^2+7x^2-7x+4x-4=0[/tex]

=> [tex]-x^3(x-1)+2x^2(x-1)+7x(x-1)+4(x-1)=0[/tex]

=> [tex]-(x-1)(x^3-2x^2-7x-4)=0[/tex]

=> [tex]-(x-1)(x^3+x^2-3x^2-3x-4x-4)=0[/tex]

=> [tex]-(x-1)(x^2(x+1)-3x(x+1)-4(x+1)=0[/tex]

=> [tex]-(x-1)(x+1)(x^2-3x-4)=0[/tex]

=> [tex]-(x-1)(x+1)(x^2+x-4x-4)=0[/tex]

=> -(x-1)(x+1)(x+1)(x-4)=0

=> x-1=0 , x+1=0 , x-4=0

=> x = -1,1,4

Hence the zeros of the polynomial is -1 , 1 and 4.

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Answer:

a) x < 0 excluding zero.

b) y ≥ 0

Step-by-step explanation:

a)

"x is negative": This means that x is less than zero. Negative numbers are any numbers less than zero, so this statement implies that x is a negative number. For example, x could be -1, -2, -3, and so on.

so answer is x < 0 excluding zero.

The inequality that expresses the statement "x is less than 0" using the expression "5a^2" would be:

5a^2 > 0 and x < 0

Here, the expression "5a^2 > 0" means that the value of "5a^2" is positive for any non-zero value of "a". Therefore, the expression "5a^2 > 0" is true for all non-zero values of "a". The inequality "x < 0" means that "x" is negative, or less than zero.

So, combining the two expressions, we get the inequality:

5a^2 > 0 and x < 0

b)

The statement "y is nonnegative" means that y is greater than or equal to zero. Therefore, the valid options for y are:

Therefore, the valid option for y is y ≥ 0.

As the given statement "y is nonnegative" cannot be expressed as an inequality involving the expression "5a^2". The expression "5a^2" is a polynomial in the variable "a", and it is not related to the variable "y" in the statement.

The inequality that expresses the statements "x is less than 0" and "y is non-negative" using the expression "5a^2" would be:

5a^2 > 0 and y ≥ 0 and x < 0

Here, the expression "5a^2 > 0" means that the value of "5a^2" is positive for any non-zero value of "a". Therefore, the expression "5a^2 > 0" is true for all non-zero values of "a".

The inequality "y ≥ 0" means that "y" is non-negative, or greater than or equal to zero.

The inequality "x < 0" means that "x" is negative, or less than zero.

So, combining the three expressions, we get the inequality:

5a^2 > 0 and y ≥ 0 and x < 0

I hope this helps!

The given system of equations can be written as a vector equation [tex]7x^1+x^2-3x^3[/tex] = 7 and as a matrix equation = , where A = [7 1 -3 3 2 2] and B = [7 0].

An equation is a mathematical statement that expresses the equality of two expressions. It usually consists of two expressions separated by an equals sign (=). The expressions may contain numbers, variables, and operations, such as addition, subtraction, multiplication, and division. The solution of an equation is the value of the variable that makes the equation true.

Vector equation:

[tex](7x^1+x^2-3x^3)=7[/tex]

Part 2

Write the system as a matrix equation. Select the correct choice below and fill in any answer boxes to complete your choice.

Matrix equation:

=

A =

[7 1 -3

3 2 2]

B =

[7

0]

Conclusion:

The given system of equations can be written as a vector equation [tex](7x^1+x^2-3x^3)[/tex] = 7 and as a matrix equation = , where A = [7 1 -3 3 2 2] and B = [7 0].

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Answer:0.125

Step-by-step explanation:

Answer: D

Step-by-step explanation:

Hence, a person on a 2000 calorie diet  should eat more calories approximate ratio of 200-300 calories from  vegetables and 900-1300 calories from carbohydrates.

A calorie is a measurement,  just like a teaspoon or an inch.  Calories are the amount of energy released when your body breaks down (digests and absorbs) food.  The more calories a food has, the more energy it can provide to your body

The  number of calories a person  should consume from vegetables versus carbohydrates depends on various factors  such as age, gender, activity level, body composition, and overall health status. However, in general, it is recommended that a person on a  2000 calorie diet should  consume more calories from vegetables than from carbohydrates.

The United States Department of Agriculture (USDA) recommends  that adults consume 2.5 to 3 cups of vegetables per day, depending on their age, gender, and level  of physical activity. On a 2000 calorie diet, this would amount to approximately 200-300  calories from vegetables.

For carbohydrates, the recommended  intake varies depending on the individual's energy needs,  but it generally accounts for 45-65% of their total calorie intake. This  equates to 900-1300 calories from carbohydrates on a 2000 calorie diet.

Therefore, a person on a 2000 calorie diet  should eat more calories  from vegetables than from carbohydrates, with an approximate ratio of 200-300 calories from  vegetables and 900-1300 calories from carbohydrates.

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Answer:

12 = constant

5x = coefficient

Step-by-step explanation:

12 is a constant because it can not be changed.

5 is a coefficient because it can changed by the variable (x)

Answer:

the area is 49m² this because for area you have to mutiple

Step-by-step explanation:

7×7=49

The circumference of a circle whose area is 20π cm² in terms of pi is 8.94π centimeters.

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The area of a circle is expressed mathematically as;

[tex]\text{A} = \pi \text{r}^2[/tex]

The circumference of a circle is expressed mathematically as;

[tex]\text{C} = 2\pi \text{r}[/tex]

Given that the area of the circle is 20π cm², we determine the radius of the circle.

[tex]\text{A} = \pi \text{r}^2[/tex]

[tex]20\pi \ \text{cm}^2 = \pi \times \text{r}^2[/tex]

[tex]\text{r}^2= \dfrac{ 20\pi \ \text{cm}^2}{\pi }[/tex]

[tex]\text{r}^2 = 20 \ \text{cm}^2[/tex]

[tex]\text{r} = \sqrt{20 \ \text{cm}^2}[/tex]

[tex]\text{r} = 4.47 \ \text{cm}[/tex]

Now, we determine the circumference of the circle.

[tex]\text{C} = 2\pi \text{r}[/tex]

[tex]\text{C} = 2 \times \pi \times 4.47 \ \text{cm}[/tex]

[tex]\text{C} = 8.94 \ \text{cm}\times\pi[/tex]

[tex]\text{C} = 8.94\pi[/tex]

Therefore, the circumference of the circle is 8.94π centimeters.

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Answer:

13

Step-by-step explanation:

By counting the amount of dots there is on the graph you would end up with 13 trees.

The probability that all 3 children will be born with the disease is approximately 0.195 or 19.5%.

We have,

Assuming that the probability of a child being born with the disease is independent of whether or not their siblings are born with the disease, we can use the multiplication rule of probability:

P(all 3 children have the disease)

= P(first child has the disease) x P(second child has the disease) x P(third child has the disease)

Since each child has a 57% chance of being born with the disease:

P(all 3 children have the disease)

= 0.57 x 0.57 x 0.57

Now,

P(all 3 children have the disease)

= 0.195

Therefore,

The probability that all 3 children will be born with the disease is approximately 0.195 or 19.5%.

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Mrs. Jenkins could divide each cookie into six equal pieces, giving each son six pieces of cookies, which would add up to 10 cookies in total.

How to solve the question?

If Mrs. Jenkins gifts 10 cookies to her six sons, the number of cookies each son should get can be found by dividing the total number of cookies by the number of sons.

So, if we divide 10 cookies equally among six sons, we get:

10 / 6 = 1.6667

This means that each son should get approximately 1.67 cookies. However, since it is not possible to divide a cookie into fractions, the actual number of cookies each son would get may vary.

To distribute the cookies equally, Mrs. Jenkins can either give each son one cookie and then divide the remaining four cookies equally among the six sons. This would give each son one cookie and each son would get an additional 4/6 or 0.67 cookies.

Alternatively, Mrs. Jenkins could divide each cookie into six equal pieces, giving each son six pieces of cookies, which would add up to 10 cookies in total.

In any case, the important thing is to ensure that each son receives an equal share of the cookies.

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YOUR COMPLETE QUESTION IS :-

Mrs. Jenkins gifts 10 cookies to her six sons if they share the cookies equally how many cookies should each son get

The wi-fi router shall not be strong enough to cover the area of the house.

According to the statement, we must determine if a wi-fi router can cover all the area of a house, described by a rectangle. The area formula of rectangle is introduced below:

A = b · h

Where:

Now we proceed to determine the area of the house:

A = (50 ft) · (50 ft)

A = 2500 ft²

The wi-fi router shall not cover the entire area of the house.

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The expressions that are equivalent to 6x²y + 2xy⁵; are 2(3x²y + xy⁵), 2xy(3x + y⁴), xy(6x + 2y⁴) and 4xy(3/2x + 1/2y⁴). So, the correct options are a, b, e and g.

Algebra is known to be a branch of mathematics in which problems are represented as mathematical expressions using letters or variables (x, y, z, etc.) to represent unknown values ​​that may change. The purpose of algebra is to understand what the unknown values ​​are in order to find solutions to problems. The degree of an algebraic equation is the largest power that exists for the variables in the equation. Algebraic equations can be classified by degree as follows:

Equation A: 2(3x²y + xy⁵) = 6x²y + 2xy⁵

Equation B: 2xy(3x + y⁴) = 6x²y + 2xy⁵

Equation C: 2x²y(6 + 5y) = 12x²y + 10x²y²

Equation D: 6x²y.2xy⁵

Equation E: xy(6x + 2y⁴) = 6x²y + 2xy⁵

Equation F: 2y(3x + xy⁴)⁰ = 2y

Equation G: 4xy(3/2x + 1/2y⁴) = 6xy + 2xy⁵

Hence, Equation A, B, E and G are the equations found equivalent to the given equation, 6x²y + 2xy⁵.

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1. The value of Angle STR is 19°

2. The value of arc ST is 134°

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.

Part of circle theorem states that: The angle in the same segment are equal.

1. Therefore the value of angle STR is calculated as;

= 180- ( 90+71)

= 180- 161

= 19°

2. The value of arc ST is calculated as;

Since arc SR = QR = 46°

representing the value of arc ST by x

therefore,

46+46+x+x = 360

92 +2x = 360

2x = 360-92

2x = 268

divide both sides by 2

x = 268/2

x = 134°

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