What is the degree of the polynomial function f x 2x3 7x5 − 4x − 12?.

Four rules of multiplication are :

1. 0 × a = 0 , a ∈ R.

2. 1 × a = a  , a ∈ R.

3. -a × -a = + a² , +a × +a = + a²,  , a ∈ R.

4. a × b = b × a, a and b ∈ R.

As given in the question,

Four rules of the multiplication are given by :

1. Zero × any number = 0

0 × a = 0 , a ∈ R.

Example : 0 × 5 = 0

2. One  × any number = Number itself.

1 × a = a  , a ∈ R.

Example : 1 × 5 = 5

3. Multiply two numbers with same sign gives positive negative.

-a × -a = + a , +a × +a = + a,  , a ∈ R.

Example : -2× -2 = 4

3 × 3 = 9

4. Multiplication of two numbers in any order does not affect the result.

a × b = b × a, a and b ∈ R.

Example : 2 × 3 = 3 × 2

Therefore, the four rules of the multiplication are :

1. 0 × a = 0 , a ∈ R.

2. 1 × a = a  , a ∈ R.

3. -a × -a = + a² , +a × +a = + a²,  , a ∈ R.

4. a × b = b × a, a and b ∈ R.

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We would expect about 80 seventh-graders to attend after-school programs.

To estimate the number of seventh-graders attending after-school programs, we can use the proportion of respondents who attend after-school programs from the sample:

28 out of 140 respondents attend after-school programs, which is a proportion of

= 28 / 140

= 0.2.

We can use this proportion to estimate the number of seventh-graders attending after-school programs in the entire population of 400 seventh-graders:

400 * 0.2 = 80

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Answer:

the b part

Step-by-step explanation:

Answer: The y-intercept of y=mx+b is B

Step-by-step explanation:

1. Y is the y-variable

2. Mx is the slope

3. B is the y-intercept.

The pair of expressions 4p + 3c and (c +2p)(2) are not equivalent because they aren't equal.

This is referred to as the expressions that work the same even though they look different.

we were given: 4p + 3c and (c +2p)(2)

: 4p + 3c = (c +2p)(2)

: 4p + 3c = 2c + 4p

They are not equal thereby making them not to be equivalent.

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The full question:

determine whether each pair of expressions are equivalent 4p + 3c and (c +2p)(2)

Answer:

g = -19

Step-by-step explanation:

Given equation,

→ -3g = 57

Now the value of g will be,

→ -3g = 57

→ g = 57/-3

→ g = -(57/3)

→ [ g = -19 ]

Hence, the value of g is -19.

Answer:g=-19 I hope this helps

Step-by-step explanation:

-3g=57

Divide both sides of the equation by -3

-3g divide (-3)=57 divide (-3)

Any expression divided by itself equals 1

g=57 divide (-3) then you do

Dividing a positive and a negative equals a negative: (+) divide(-)=(-)

g=-57 divide 3

Next thing you do is

Calculate the quotient which something like this

g=-19

So you’re answer is g=-19

The measure of the angles are a = 54, b = 54, c = 126, d = 54, e = 126, f = 54, and g = 126 degrees.

It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.

here, we have,

It is given that:

The diagram shows two parallel lines cut by a transversal.

As we know from the definition of the vertically opposite angles:

b = 54 degrees

a + c = 54 + b  (a = c)

2a = 54x2

a = 54 degrees

Since a and g are opposite interior angles, they are congruent, so you proceed with the process as you did for the first and check to see if the angles are acute or obtuse to ensure that the angle measurements are accurate.

Similarly:

b = 54

c = 126

d = 54

e = 126

f = 54

g = 126

Thus, the measure of the angles are a = 54, b = 54, c = 126, d = 54, e = 126, f = 54, and g = 126 degrees.

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The value of g(2) = 36 for the given function.

The given function g is defined by,

[tex]g(x) = 4(3)^{x}[/tex]

Now to find the value of g(2), put x = 2 in the given function we get,

g(2) = 4(3)²

g(2) = 4 × 3 × 3

g(2) = 36

Therefore, the value of g(2) = 36 for the given function.

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Answer:

acute and scalene, remember:

Isoceles: An isosceles triangle is a triangle with two sides of equal length. The two equal sides are called legs and the third side is called the base.

Scalene: A scalene triangle is a triangle with all sides of different lengths. None of its angles are congruent.

Equilateral: An equilateral triangle is a triangle with all three sides of equal length. All three angles are congruent and measure 60 degrees.

The factors for the expression (3x+7)(3x-7)

squared the given 9x² = 3x 49 = 7 if the operation in the first unfactor form is negative the factored form's operation will be positive and negative,  = (3x+7)(3x-7)

The factored form occurs when a quadratic expression is a product of two factors, each of which is a linear expression. By expanding, or multiplying out the factors, an equation in factored form may be restated in standard form.

Several strategies may be used to derive the factored form of a quadratic equation Ax2+Bx+C=0 , A x 2 + B x + C = 0.

Factored form assists us in determining the function's x-intercepts or zeros.

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Answer:

-26

Step-by-step explanation

1) substitute -2 for X

4(-2)(2)-3(-2)-16

2) solve

-8(2)+6-16

-16+6-16

-10-16

-26

The value of function at x= -2 is f(-2) is 54.

In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

We have,

f(x) = 4x² - 3x - 16.

Now, to find the value of f(-2) put the value of x= -2.

so, f(-2)= 4(-2)² - 3(-2) - 16

= 4(16) + 6 - 16

= 64 -10

= 54

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Answer:

39 miles

Step-by-step explanation:

We can start by using algebra to represent the problem in equation form. Let j be the number of miles Jacob ran.

From the information given, we know that:
Adam ran 21.5 miles less than Jacob.
Adam ran 17.5 miles.

We can use these two pieces of information to set up the following equation:
j = 17.5 + 21.5

Now we can solve for j by adding 21.5 to both sides:
j = 39

So Jacob ran 39 miles.

Expression to produce vector b: b = d - c, where d and c add to a. Find d and c using a's components, b is inverse of a.

What is vector ?

Vector is a term that refers colloquially to some quantities that cannot be expressed by a single number, or to elements of some vector spaces.

Suppose vector "a" is given and we want to determine an expression to produce vector "b". To do this, we need to find two vectors, "c" and "d", such that:

a = c + d

where c and d are the vectors that when added together produce vector a. The expression to produce vector b can then be represented as:

b = d - c

The expression can be determined by first finding the components of vector a, and then using these components to determine the components of vectors c and d. For example, if vector a is represented as:

a = <a1, a2, a3>

We can set c and d equal to:

c = <a1/2, a2/2, a3/2>

d = <a1/2, a2/2, a3/2>

So, the expression to produce vector b can be represented as:

b = d - c = <a1/2, a2/2, a3/2> - <a1/2, a2/2, a3/2> = <0, 0, 0>

Expression to produce vector b: b = d - c, where d and c add to a. Find d and c using a's components, b is inverse of a.

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Let's say vector a is represented by the expression (a1, a2), and vector b is represented by the expression (b1, b2).

Then, the expression for the resultant vector (c1, c2) can be calculated as follows:

c1 = a1 + b1

c2 = a2 + b2

So the expression for the resultant vector is (a1 + b1, a2 + b2).

To determine an expression that produces vector b from vector a, you would need to know the relationship between the two vectors. If vector b is a scalar multiple of vector a, the expression for vector b can be represented as:

b = k * a

Where "k" is the scalar factor. If vector b is a vector that is in the opposite direction of vector a, the expression for vector b can be represented as:

b = -1 * a

In this case, the scalar factor is -1.

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The value of x is equal to 3 and the length of VS is 3.5 for the circle Z.

Since ZU and ZV is equal to 8, then QR is equal to ST and the radii ZY and ZW bisect ST and QR respectively.

we shall solve for x in the circle as follows:

QR = ST

4x - 5 = 7

4x = 7 + 5 {add 5 to both sides}

4x = 12

x = 12/4 {divide through by 4}

x = 3

The length VS = 7/2

VS = 3.5

Therefore, the value of x is equal to 3 and the length of VS is 3.5 for the circle Z.

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Answer:

An increase of 20

Step-by-step explanation:

-20 + 20 = 0

The change in temperature in degrees Fahrenheit required is A = 20°F

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The current temperature is -20°F, and we want to know how much it needs to increase to reach 0°F.

On simplifying the equation , we get

We can calculate this by finding the difference between the two temperatures:

0°F - (-20°F) = 0°F + 20°F = 20°F

Hence , the temperature needs to increase by 20°F to reach 0°F

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The height of the rocket 45.161 km.

By adding a and b to h=-b2a, you may determine h, the x-coordinate of the vertex.

Determine k, the vertex's y-coordinate, by calculating k=f(h)=f(b2a).

According to the graph, the velocity first increases for 20 seconds before declining for 120 seconds before changing course.

Thus, it was at its highest peak at t=120 seconds.

Therefore, all that is left to do is figure out the triangle OAB's area at its highest point. This is 2 base + perpendicular = 2 120 * 1000 * 60 km.

The rocket reaches a peak height of 112 feet at a time of 2.48 seconds. The rocket then falls and hits the ground 5.12 seconds after it was launched.

According to the graph, the velocity first increases for 20 seconds before declining for 112 seconds before changing course.

Thus, it was at its highest peak at t = 112  

2.48 seconds.

Therefore, all that is left to do is figure out the triangle OAB's area at its highest point. This is 2 base + perpendicular =  112 * 1000 /2.48 = 45.161 km.

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Answer:

$41.04

Step-by-step explanation:

set up a proportions equation:

[tex]\frac{18.20}{2\frac{1}{3}} =\frac{x}{5\frac{1}{4}}[/tex]

cross multiply and solve for x. this gives you:

x = 41.04

hope this helped, good luck!

The required slope of the curve at the designated point P is 1/4.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,

The slope of the curve at point p is given as
= rise/run

From the graph,
rise = 2 and run = 8
slope of the curve at point P = 2 / 8 = 1/4

Thus, the required slope of the curve at the designated point P is 1/4.

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The value of x using Pythagoras theorem is x = √30.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Using Pythagoras theorem,

⇒ 5² + base² = 8²

⇒ 25 + base² = 64

⇒ base = √64 - 25
⇒ base = √39

In the other triangle,

x² + 3² = 39

⇒ x² = 39 - 9

⇒ x = √30

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Answer:

x = - [tex]\frac{6}{5}[/tex] , x = - 1

Step-by-step explanation:

(x + 1)(5x + 6) = 0 ← in standard form

equate each factor to zero and solve for x

5x + 6 = 0 ( subtract 6 from both sides )

5x = - 6 ( divide both sides by 5 )

x = - [tex]\frac{6}{5}[/tex]

or

x + 1 = 0 ( subtract 1 from both sides )

x = - 1

Gross income means all income you receive in the form of money, goods, property, and services that isn't exempt from tax.

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The number of cans required for John to paint the wall is given by the equation A = 3.375 cans ≈ 4 cans

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the wall be A

Now , the area of wall A = area of rectangle + area of triangle

The side length of the rectangle = 3m

The width of the rectangle = 2 m

The height of the triangle = 1 m

The base of the triangle = 1.5 m

So , the area of the triangle = ( 1/2 ) x 1.5 x 1 = 0.75 m²

Now , the area of the rectangle = length x width

Area of the rectangle = 3 x 2 = 6 m²

So , the area of the figure = 6.75 m²

Now , 11 can of paint covers an area of 22 square meters

So , 1 square meters = 11/22 cans

1 square meters = 1/2 cans

And , the number of cans required for 6.75 m² of area = 6.75 ( 1/2 ) cans

The number of cans required for 6.75 m² of area = 3.375 cans

The number of cans required for 6.75 m² of area = 4 cans

Hence , the number of cans is 4 cans

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The value of variable, x when f(x) = 4 according to the given function expression; f(x) = -x + 3 is; -1.

It follows from the task content that the value of x is to be determined according to the given function expression; f (x) = -x + 3.

Hence, when f (x) = 4, the resulting expression is;

4 = -x + 3

Hence, to determine the value of x, we must solve for x as follows;

4 - 3 = -x

1 = -x

x = -1.

Ultimately, the value of x for which the function instance f(x) = 4 is; x = -1.

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The Chang family has been traveling for 18 hours, thus, t-value is 18.

A significant t-score, also known as a t-value, implies that the groups are distinct, whereas a small t-score suggests that the groups are similar. Degrees of freedom are the values in a study that are open to change and are crucial for determining the significance and reliability of the null hypothesis.

D(t) = 2,280 - 60t

D(t) = 1,200; find t.

D(t) = 2,280 - 60t

1200 = 2280 - 60t

From both sides of the equation, deduct 2280.

1200 - 2,280 = 2280 - 60t - 2,280

- 1080 = - 60t

multiplied by -60 on both sides

- 1080 / -60 = - 60t / -60

18 = t

t = 18

The Chang family had travelled for 18 hours, according to this.

The Chang family has been traveling for 18 hours, t = 18.

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The complete question is,

Having just returned from a cross-country road vacation, the Chang family is traveling back home. They can visualize their distance from home in miles after t hours of travel by using the function D(t) = 2,280 - 60t during the journey. If D(t) = 1,200, what does t represent? That value stands for what?

A.t = 20; the Chang family has been traveling for 20 hours.

B. t = 20, meaning the Chang family will need to travel 20 more hours to reach home.

The Chang family has been traveling for 18 hours, thus c. t = 18.

The Chang family must go home for an additional 18 hours using the formula D. t = 18.

Answer: A. 9/19

Step-by-step explanation:

20 + 18(amount of cookies) = 38

there are 18 chocolate chip cookies, so it's an 18/38 chance it's a chocolate chip cookie that broke, but 18/38 can be simplified.

18 divided by 2 is 9 and 38 divided by 2 is 19

so 9/19

The original dimensions of the garden are 12 ft by 16 ft.

Width: x + 4 (not 2 because the width has two ends)

Length: x + 8 (same reason; this is x + 4 + 4)

The area of the garden and the border combined is 320 sq. ft.

The dimensions of the garden with the border around it are (x + 4) and (x + 8).

A (rectangle) = lw

A (garden with border) = lw

320 sq. ft. = (x + 4) (x + 8)

320 sq. ft. = x2 + 12x + 32

Transpose 320 to the right side of the equation.

0 = x2 + 12x + 32 - 320

0 = x2 + 12x - 288

Factor out.

0 = (x + 24) (x - 12)

One or both of the amounts are equal to zero when the product of two values is zero.

Equate the factors to 0.

x + 24 = 0 x - 12 = 0

x = - 24 x = 12

Since we cannit have a negative measure of distance, x = 12.

Find the original dimensions of the garden.

The original dimensions of the garden (without the border) are x and x + 4.

Width = x = 12

Length = x + 4 = 12 + 4 = 16

The original dimensions of the garden are 12 ft by 16 ft.

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The volume of cylinder = 15,869.56 mm.

The formula for determining a cylinder's volume is the base area times the height. Volume of a cylinder is r2h cubic units.

To calculate a box's volume, you need to know its height, width, and depth. The volume can be calculated by multiplying these three dimensions.

Assume for the moment that the spherical discs are stacked h levels high. The volume of the cylinder will now be calculated by multiplying the discs' base areas by their heights, "h". Therefore, r2h is used to represent the volume of a cylinder with base radius r and height h. The amount of material required to fill an object can be calculated using the volume of the object.

We know that the volume of cylinder = πr²h

Given,

height = 14 mm

radius = 19 mm

V = π × 19 × 19 × 14

⇒  V = 15,869.56 mm

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Step-by-step explanation:

x1, y1 = (-5,-2)

slope,m = -6/5

general equation, y= MX + C

(y-y1)/(x-x1)=m

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

5y+10=-6x-30

5y=-6x-40

y=-(6x/5) - 8

Answer:  u = sr/qut

Step-by-step explanation:

Given the equation sr = qut, we can solve for u by isolating it on one side of the equation. To do this, we divide both sides by qut. This gives us sr/qut = u. This means that u can be represented in terms of q, r, s, and t as sr/qut. This is the final result.

.........

Given the equation sr = qut, we can solve for u in terms of q, r, s, and t by isolating u on one side of the equation.

To do this, we can divide both sides of the equation by (qut)

sr/qut = u

Then we have u = sr/qut

So, u is expressed in terms of q, r, s, and t as u = sr/qut

Step-by-step explanation:

-8(-5/8x + y = -1/4)

5x - 8y = 2 is the standard form