It's Pre-calculus subject

A polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots is P(x)=x²-5x-14

A function is said to as polynomial when a variable in an equation, such as a quadratic equation or cubic equation, etc., has only positive integer exponents or non-negative integer powers. One polynomial with an exponent of 1 is 2x+5, for instance. One that has more than two algebraic terms is referred to as a polynomial expression. Polynomial is a monomial or binomial that is repeatedly added, as the name suggests.

A mathematical expression containing one or more algebraic terms, where each algebraic term is made up of a constant multiplied by one or more variables raised to a nonnegative integral power.

x= -2, x=7

Given,

P(x) = 0

This polynomial function has the roots,

x= -2, x=7

So,

(x+2)(x-7)

We have to multiply both of them we get,

P(x)=(x+2)(x-7)

0=x²-5x-14

x²-5x-14=0

Therefore, P(x)=x²-5x-14 is the polynomial function.

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The value of x from the parallelogram ABCD is 10.

A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.

Given that, ∠A=120-2x, ∠B=70+x, ∠C=105-x² and ∠D=40+4x.

The quadrilateral ABCD is a parallelogram if pairs of consecutive angles are supplementary.

Here, ∠A and ∠D are consecutive angles

Now, 120-2x+40+4x=180

⇒ 160+2x=180

⇒ 2x=20

⇒ x=10

So, ∠A=120-2x=100, ∠B=70+x=80, ∠C=160-6x=100 and ∠D=40+4x=80

Therefore, the value of x is 10.

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"Your question is incomplete, probably the complete question/missing part is:"

The quadrilateral ABCD is a parallelogram if pairs of consecutive angles are supplementary. Given the angle measures, prove that quadrilateral ABCD is a parallelogram by finding the value of x. ∠A=120-2x, ∠B=70+x, ∠C=160-6x and ∠D=40+4x.

The range of the cluster shown in the graph is [1, 6]

What is range of a graph?

The range is all the values of the graph from down to up or on the x-axis.

Solution :

∵ Range is calculated from x-axis

∴ Range  {1,2,3,4,5,6} = 6-1

                                     = 5

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The range of the cluster shown in the graph is [1, 6]

The range is all the values of the graph from down to up or on the x-axis. The possible output values are displayed on the y-axis and make up the range. Remember that the domain and range of the graph could be larger than the visible values if it extends beyond the area that can be seen.

Solution :

∵ Range is calculated from x-axis

∴ Range  {1,2,3,4,5,6} = 6-1

                                    = 5

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The parabola's vertex is (-3/2, -22). Because this is the lowest point on the parabola, the function's minimum value is -22.

To determine the maximum or minimum value of the quadratic function y = 2x² + 12x + 5, you need to find the vertex of the parabola formed by this function.

To find the vertex of the parabola, you can use the formula x = -b / (2a), where x is the x-coordinate of the vertex, a is the coefficient of the x² term, and b is the coefficient of the x term.

In this case, the coefficient of the x² term is 2, and the coefficient of the x term is 12. Therefore, the x-coordinate of the vertex is x = -12 / (2×2) = -6 / 4 = -3/2.

To find the y-coordinate of the vertex, you can substitute the x-coordinate back into the original equation:

y = 2(-3/2)² + 12(-3/2) + 5 = 2(-9/4) + (-18) + 5 = -9 + (-18) + 5 = -22.

Therefore, the vertex of the parabola is (-3/2, -22). This is the lowest point on the parabola, so the minimum value of the function is -22.

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By using the formula for area of rectangle, it can be calculated that-

a) Expression for total area = [tex]6^2 + 2 \times 6 + 24[/tex]

Total area = 72 square inches

b) Length of the figure =  9 inches

Breadth of the figure =  8 inches

What is area of a rectangle?

Area of a rectangle is the total space taken by the rectangle.

If l is the length of the rectangle and b is the breadth of the rectangle, then area of the rectangle is calculated by

Area = l [tex]\times[/tex] b

Side of the square = 6 inches

Area of the square = [tex]6^2[/tex] square inches

Length of white rectangle = 2 inches

Breadth of white rectangle = 6 inches

Area of white rectangle = [tex]2 \times 6 =[/tex] 12 square inches

Area of blue rectangle  = 24 square inches

Total area = [tex]6^2 + 2 \times 6 + 24[/tex] =

                     36 + 12 + 24 =

                     72 sq. inches

b) Let the breadth of the blue rectangle be b inches

Length of the blue rectangle = 2 + 6 = 8 inches

Total area = 8b square inches

By the problem,

[tex]8b = 24 \\b = \frac{24}{8}\\[/tex]

b = 3 inches

Length of the figure = 6 + 3 = 9 inches

Breadth of the figure = 2 + 6 = 8 inches

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The equation of the circle described in the problem is x² + (y - 8)² = 64.

What is the equation of a circle?

The general equation of any type of circle is represented by: x2 + y2 + 2gx + 2fy + c = 0, for all values of g, f, and c.

The general equation of a circle is (x – h)2 + (y – k)2 = r2, where (h, k) represents the location of the circle's center, and r represents the length of its radius.

The standard form equation of a circle with center at (h, k) and radius r is given by:

(x - h)² + (y - k)² = r²

Substituting the given values into this equation, we get:

(x - 0)² + (y - 8)² = (8)²

Simplifying this equation gives:

x² + (y - 8)² = 64

Hence, This is the equation of the circle described in the problem.

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The total commission that's earned will be $360.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

In this case, an employee who earns $12/hour, worked 37 hours this week, is paid a commission of $40 for each sale, and makes 9 sales during the same week. Employees receive commission, also referred to as a sales commission, based on the sales they generate. A sales commission is a payment made to an employee after they successfully complete a task, typically selling a predetermined volume of goods or services. Sales commissions are a common incentive used by employers to boost employee productivity. A commission can be paid instead of or in addition to a salary.

The total commissions will be:

= Amount of commission × Number of sales

= $40 × 9

= $360

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The graph of the odd-degree polynomial reaches positive and negative infinity.

A polynomial function's final behavior is how its graph behaves as x gets closer to positive or negative infinity.

The graph's final behavior is determined by a polynomial function's degree and leading coefficient.

The given polynomial is shifted towards the left it reaches negative infinity quicker than positive infinity.

Also, the graph of the polynomial is of odd degree as it is symmetric about the origin shifted towards left.

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The expression that shows how many charms Jenny's older sister has is

c + 5.

What are algebraic expressions?

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.).

Expressions are made up of terms.

According to the given question:

Jenny has c charms on her bracelet.

Her older sister has 5 more charms than Jenny.

To write an expression that shows the number of charms her older sister has. we simply add 5 extra charms to the number of charms Jenny has

Therefore, Jenny's older sister has c + 5 charms.

In this expression c represents the number of charms Jenny has.

The complete question is as follows:

Jenny has c charms on her bracelet. Her older sister has 5 more charms than Jenny. Write an expression that shows how many charms her older sister has.

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Answer:

unexplainable

Step-by-step explanation:

does not make since

Answer:

To express a number in scientific notation, you need to write it as a number between 1 and 10, multiplied by a power of 10.

In this case, 367 can be written as 3.67 x 100, and 10-3 can be written as 0.001.

Therefore, 367 x 10-3 can be expressed in scientific notation as:

3.67 x 0.001 = 0.00367

This can also be written as 3.67 x 10^-3. The ^ symbol indicates an exponent, and in this case, it means that the base number (3.67) is multiplied by 10 to the power of -3.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer 2

You would divide 7 by 3.5 and you get 2 If the equation was what times 3.5 =7  

Your knowledge of the percentage 47.728 is already complete.4772.8% is the percentage equivalent of 47 7 2 8.

To compute 47.728 as a percentage of a given number x, divide 47.728 by x and multiply the result by 100.

For instance, the ratio of 47.728 to 10 is equal to (47.728 / 10) times 100%, or 477.28%.

Use the decimals to percents converter found below at your convenience.

Place your value in the "% of" area after entering 47.728 in the number field.

Press reset first if you want to restart.

At this point, an automatic conversion to 47.728 in percent will take place.

The answer has been rounded to ten decimal places, as you can see.

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The polygon ABCD is transformed 4 units to the left after being reflected across the x-axis.

The transformation of a function may involve any change.

Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.

Reflect the polygon ABCD across the x-axis as;

A(x, y) → A'(x, -y) (x, -y) (x, -y)

According to this rule, A's coordinates are

A(1, -5) →  A'(1, 5) (1, 5) (1, 5)

ABCD is shifted 4 units further to the left.

Now apply to the translation:

A"(x - 4, y) = A'(x, y) (x - 4, y)

A'(1, 5) → A"(1 - 4, 5) (1 - 4, 5) (1 - 4, 5)

→ A"(-3, 5) (-3, 5) (-3, 5)

Thus Polygon ABCD will eventually overlap Polygon A'B'C'D' through a series of transformations.

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what are we supposed to be solving

Answer:

Step-by-step explanation:

duh

The value of slope for line equation 1 is -5/2. The value of slope for line equation 2 is 5/3.

A line's steepness may be determined by looking at its slope. Slope is computed mathematically as "rise over run" (change in y divided by change in x). The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b). For instance, the slope and y-intercept of the equation y = 3x - 7 are 3 and 0, respectively.

Here,

y=mx+c

where m is slope.

line equation 1,

y=-5/2x-5

m=-5/2

line equation 2,

y=5/3x

m=5/3

For line equation 1, the slope is equal to -5/2. For line equation 2, the slope is equal to 5/3.

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Answer:

Vhc = 401.92 cm3

Step-by-step explanation:

Vcylender = Pi*r2*h

Vhalfcyldr = (Pi*r2*h)/2

then

h= 16cm

r = 8cm/2 = 4cm

then

Vhalfcylinder = ((3.14)*(4)2*16) / 2

Vhc = 401.92 cm3

Answer:

$27

Step-by-step explanation:

Simple interest is a way of calculating the interest charge on a loan or investment. It is calculated by multiplying the principal amount by the interest rate and the time period. In your example, the simple interest calculation would be $225 * 6% * 2 years = $27.

Answer:

Simple interest is a type of interest that is calculated only on the principal amount of a loan or investment, without taking into account any additional interest that has been earned on the principal. To calculate simple interest, you multiply the principal amount by the interest rate and the length of time the interest is being applied. For example, if you have a principal of $225, an interest rate of 6%, and a time of 2 years, the simple interest would be calculated as follows:

$225 x 6% x 2 years = $27.

In this case, the simple interest on the $225 principal would be $27. This means that after 2 years, you would owe $252 in total, including the original principal and the interest that has been earned on it. Simple interest is typically used for short-term loans or investments, where the interest is paid or earned at regular intervals, such as monthly or annually.

An expression that represents the ADDITION of the two number lines is: B. -10x - 5x + 30x.

Each segment equals 5x and the first arrow is 30x long.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

Based on the number line shown above, we can reasonably infer and logically deduce that each of its segment is equal to 5x with the longest arrow measuring 30x on the number line.

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Answer:

66 [tex]cm^{2}[/tex]

Step-by-step explanation:

Front: 6 x 5 = 30

Back:  6 x 4 = 24

Left side: 1/2 (3 x 4) =6

Right side: 1/2 ( 3 x 4) 6

Add

30 + 24 + 6 + 6 = 66

The monthly payment will be $161.20.The total amount paid over the term of the loan is $38,688 and 58.2% is paid toward the principal while 41.8% is paid toward interest.

Compound interest is applicable when there will be a change in principal amount after the given time period.

For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount.

As per the given,

Principle amount P = ​$25,000

APR = 9% = 0.09

Time period T = 20 years

a) Monthly payment will be given as,

⇒ P(r/12)/(1 -(1 +r/12)^(-12t))

⇒ 22500·(0.06/12)/(1 -(1 +0.06/12)^(-12·20))

⇒ $161.20

b) After 20 years the amount as,

$161.20 x 240 = $38,688

c) (22500/38688)·100% = 58.2% is paid toward principal

The remaining amount, 41.8% is paid toward interest.

Hence "The monthly payment will be $161.20.The total amount paid over the term of the loan is $38,688 and 58.2% is paid toward the principal while 41.8% is paid toward interest".

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The true statement about n is (a) The value of n is 1/5 because (⁵√2)⁵ = 2¹ and (2¹/⁵)⁵ = 1, so ⁵√2 = 2¹/⁵

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

Expression =  ⁵√2

Also from the question, we understand that the expression is to be expressed as

2ⁿ

This means that

⁵√2 = 2ⁿ

Re-express ⁵√2 using the law of indices

2ⁿ = 2¹/⁵

By comparison, we have

n = 1/5

This means that the value of n is 1/5

Hence, the true statement is (a)

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Answer:

1236

Step-by-step explanation:

The wheel will travel 904.32 inch when it take 4 rotation

How do you calculate distance using radius and revolutions?

Hint: To calculate the wheel's circumference, use the formula 2πr, where r is the radius and π=3.14 , to first determine the distance covered in one revolution. To determine the distance traveled, multiply the distance covered in one revolution by 200. In the end, multiply it by 100 to get the distance in meters.

In mathematics, what is the circumference?

The distance between the center of the sphere and any plane passing through it is known as the circumference. Any large circle that passes through a point known as a pole is called a meridian.

The circle's circumference must be known in order to compute the distance covered during one rotation. C=2πr is the formula for the circumference.

The radius, designated as r, is 36 inches. As a result, C=2π36 = 72π. The distance covered in one rotation is 226.08 inches because (pi) =3.14159, C=226.08 inches. So when we rotate this 4 times the it travels 226.08 * 4 = 904.32 inch

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Answer:

the functions domain is;  x < -19 or x > -19

x= -19

Sorry otherwise im not sure what you need here :P

Answer:

Step-by-step explanation:

The area of each triangle is one-half the area of the rectangle. So, the area A of a triangle is given by the formula A=12bh where b is the base and h is the height of the triangle.

The solutions for the given equation are x=-3 and x=1.

The given equation is (x + 1)² - 4(x + 1) + 2 = 0.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

(x + 1)² - 4(x + 1) + 2 = 0

⇒ (x + 1)² - 4(x + 1)=-2

⇒ (x+1)[(x+1)-4]=-2

⇒ x+1=-2, (x+1)-4=-2

⇒ x=-2-1, x+1=-2+4

⇒ x=-3, x+1=2

⇒ x=-3, x=1

Therefore, the solutions for the given equation are x=-3 and x=1.

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The probability that the Yankees will lose when they score 5 or more runs is equal to 0.2766.

What is Conditional Probability?

From the question, we know that the probability that the Yankees will win a game is 0.53.

[tex]\implies P(W)=0.53[/tex]

Also, then the probability that the Yankees will lose a game is given as,

[tex]P(L)=1-P(W)\\\implies P(L)=1-0.53\\\implies P(L)=0.47[/tex]

It is also given that, the probability that the Yankees will score 5 or more runs is 0.48.

[tex]\implies P(A)=0.48[/tex]  -----(1)

So, the probability that the Yankees will score less than 5 runs is,

[tex]P(S)=1-P(A)\\\implies P(S)=1-0.5\\\implies P(S)=0.5[/tex]------(2)

We also know the probability that the Yankees will win and score 5 or more runs is 0.42.

[tex]\implies P(B)=0.42[/tex]

Also, then the probability that the Yankees will lose or score less than 5 runs is given as,

[tex]P(C)=1-P(B)\\\implies P(C)=1-0.42\\\implies P(C)=0.58[/tex]

Next, the probability that the Yankees will lose and score less than 5 runs is,

[tex]P(D)=0.42+0.5-0.58\\\implies P(D)=0.34[/tex]

Now, the required probability is the probability that the Yankees will lose and score 5 or more runs.

It can be calculated using the conditional probability formula, [tex]P(M/N)=\frac{P(M\cap N)}{P(N)}[/tex]

So, the required probability  that the Yankees will lose and score 5 or more runs is given as,

P(they score 5 or more runs / probability that they lose game) = P(they lose and score 5 or more runs) / P(they lose the game)

[tex]\implies P(E)=\frac{0.47-0.38}{0.47} \\\implies P(E)=0.2766[/tex]

Therefore, the probability that the Yankees will lose when they score 5 or more runs is equal to 0.2766.

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A graph of the two (2) points (-0.5, 0) and (9, 0) that represent the distance which this object would travel in different amounts of time at that rate is shown in the image attached below.

Mathematically, a linear function is sometimes referred to as the slope-intercept form of a straight line and it can be modeled (represented) by this mathematical expression;

d = mt + b

Where:

Therefore, the required linear function that relates the distance (d) and speed (s) at time (t) seconds is given by this mathematical expression;

d(t) = 18t + 9

For instance when time (t) = -0.5 seconds, the distance traveled by this object placed on a conveyor belt is given by;

d(t) = 18t + 9

d(-0.5) = 18(-0.5) + 9

d(-0.5) = -9 + 9

d(-0.5) = 0 feet.

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