which property is illustrated by the following statement 4.8 + k = k + 4.8

The values of a and b using the factor theorem for the polynomial f(x), we set f(1) and f(-1) equal to zero. Solving the resulting system of equations, we find that a = 12 and b = -1.

To find the values of a and b using the factor theorem, we need to use the given factors (x - 1) and (x + 1) and the fact that they are roots of the polynomial f(x).
The factor theorem states that if (x - c) is a factor of a polynomial, then f(c) = 0. Therefore, we can set x = 1 and x = -1 in the polynomial f(x) to get two equations.
First, let's substitute x = 1 into f(x):
f(1) = (1)^3 + a(1)^2 + b(1) - 12
f(1) = 1 + a + b - 12
Next, let's substitute x = -1 into f(x):
f(-1) = (-1)^3 + a(-1)^2 + b(-1) - 12
f(-1) = -1 + a - b - 12
Since (x - 1) and (x + 1) are factors, f(1) and f(-1) must equal zero. Therefore, we can set the two equations equal to zero and solve for a and b:
1 + a + b - 12 = 0
-1 + a - b - 12 = 0
Rearraning the equations, we have:
a + b = 11
a - b = 13
Now, we can solve this system of equations. Adding the two equations, we get:
2a = 24
a = 12
Substituting the value of a into one of the equations, we find:
12 - b = 13
b = -1
Therefore, the values of a and b are 12 and -1 respectively.

For more such questions on polynomial

https://brainly.com/question/1496352

#SPJ8

Answer:

40 is surface the answer of I think about it but I will solve the sum and will give the ans

Answer:

3:7

Step-by-step explanation:

Let x = pounds of the $10 rice in the mixture

Let y = pounds of the $30 rice in the mixture

Total cost of the $10 rice = 10x

Total cost of the $30 rice = 30y

(10x + 30y) / (x + y) = 24

Solve this equation for y/x:

10x + 30y = 24(x + y)

10x + 30y = 24x + 24y

30y - 24y = 24x - 10x

6y = 14x

y/x = 6/14  simplify the fraction

y/x = 3/7

So, the ratio of the two different types of rice (y:x) is 3:7, meaning a pound of the rice mixture has 3 parts of the $30 rice to 7 parts of the $10 rice.

Answer:

Closet #1.

Step-by-step explanation:

Closet #1 is 4x5x8, right? so, 4x5=20, and 20x8=160 feet. Closet #2 is 6x3x8, and 6x3 is 18. That's already less than 20 even before we multiply by 8. So, the answer to your question is Closet #1.

Answer:

Answer: The first closet is larger.

Step-by-step explanation:

Closet #1

V = l × w × h

V = 4 ft. × 5 ft. × 8 ft.

V = 160 cu. ft.

Closet #2

V = l × w × h

V = 6 ft. × 3 ft. × 8 ft.

V = 144 cu. ft.

Compare the size of the closets

160 cu. ft. > 144 cu. ft.

Answer: The first closet is larger.

Answer:

25

Step-by-step explanation:

First I would divide 15 by 3 which would get me 5 then i would multiply it by 5 to get the answer of 25.

Answer: 22 hours

Step-by-step explanation: 26400/20 is 1320 and 1320/60 is 22

Answer:

Option 2.

Step-by-step explanation:

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.

Domain: \((- \infty} ,0)\) ∪ \((0, \infty} )\)

Range: \((- \infty} ,0)\)∪\((0, \infty} )\)

Answer:

Rachel has 27

Hong has 51

Manuel has 17

Step-by-step explanation:

Let R represent Rachel, H represent Hong, and M represent Manuel.

They combined have a total of 95. Thus:

\(R+H+M=95\)

Hong has 3 times what Manuel has. Therefore:

\(H=3M\)

Rachel has 10 more than Manuel. Therefore:

\(R=10+M\)

Substitute:

\(R+H+M=95\\(10+M)+(3M)+M=95\)

Combine like terms:

\(5M+10=95\)

Subtract 10 from both sides:

\(5M=85\)

Divide by 5:

\(M=17\)

Therefore, Manuel has 17.

Now, find Rachel and Hong's money.

\(H=3M\\H=3(17)=51\)

So, Hong has 51.

And for Rachel:

\(R=10+M\\R=10+17=27\)

Rachel has 27.

Answer:

7250%

Step-by-step explanation:

To express 72 1/2 as a percentage, you need to convert it to a decimal first and then multiply by 100.

72 1/2 is equivalent to 72.5 as a decimal.

To convert it to a percentage:

72.5 * 100 = 7250

Therefore, 72 1/2 is equal to 7250% when expressed as a percentage.

let me know it is helpful for you or not

Answer: 36 yards; 144 inches

Step-by-step explanation: there are 3 yards in a foot and 12 inches in a foot. 12x3 = 36 and 12x12 = 144

Given:

The sum of the two roots is 12.

One root is 5.

To find the other root and the quadratic equation:

Since the sum of the two roots is 12 and one root is 5.

So, the other root is 7.

Next, the quadratic equation becomes,

Hence, the quadratic equation is,

Answer:

Function, function

Step-by-step explanation:

Each input corresponds to one output. Thus, by the definition of a function, both graphs represent functions

Answer:

53\(x_{123}\) == 134 cf

Step-by-step explanation:

A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a​

The height of the building is approximately 78.63 meters.

The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.

Therefore, the height of the building is approximately 78.63 meters.

For more such questions on height, click on:

https://brainly.com/question/28122539

#SPJ8

The equation that describes the diagram could be; 5 + 9 = 14

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Since Adding a negative number is the same as subtracting a positive number just as subtracting a negative number is the same as adding a positive.

The equation becomes as

5 + 9 = 14

Learn more about equations here;

https://brainly.com/question/25180086

#SPJ1

Answer:

6 bags.

Step-by-step explanation:

Subtract 38 from 75 to represent the remaining amount of Matthew's money.

\(75-38=37.\)

Matthew has $37 left over from buying flowers.

Divide 37 by 6 to represent how many bags of soil he can buy.

\(37\div6=6\frac{1}{6}\)

Matthew can only buy 6 bags of soil, 1/6 isn't included because you can't buy a fraction of a bag.

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.

To know more about circle, visit:

https://brainly.com/question/29142813

#SPJ1

The complete question is :

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

Answer:

the agv speed is 223

Step-by-step explanation:

Answer:

51.42 avg mph

Step-by-step explanation:

45+45 = 90 miles total for 1 3/4 hours

90/.75 = 51.42 avg mph

Answer:

The chance of rolling a number greater than 4 (a 5 and 6) is 2/6 = 1/3 after simplification. The probability it WON'T happen is 1 - 1/3 = 2/3.

The ratio of against to for is 2/3:1/3

You can further simplify this ratio by multiplying each side by 3 and yielding

2:1.

The chance of it not happening is twice as likely as it is to roll a number greater than 4

The area of a circle is just one which is

where is r= radius

Alternatively , we can express it in form of diameter

in that case, Area of a circle is

The surface areas are 110 in², 87.6 mm² and 49 m².

Given that are solid figure, we need to find the surface area of them,

1) Triangular prism = perimeter × length + 2 × base area

= (5 + 5 + 6) × 5 + 2(3×5) = 110 in²

2) Triangular pyramid = base area + perimeter × slant height / 2

= 1/2 × 5.2 × 6 + 3 × 6 × 8/2

= 87.6 mm²

3) Cube = 4side²

= 4 × (3 1/2)²

= 4 × 3.5²

= 49 m²

Hence the surface areas are 110 in², 87.6 mm² and 49 m².

Learn more about surface areas click;

https://brainly.com/question/29298005

#SPJ1

Punto:

Línea:

Plano:

Superficie:

El punto es una entidad que tiene una posición, pero no tiene dimensiones (largo, ancho o alto). Por lo tanto, es de dimensión cero, es decir, adimensional. Contiene el significado de lugar, de existencia, pero no tiene elementos mensurables, es decir, no se puede medir.

En contextos geométricos, una línea es un cuerpo unidimensional de forma y longitud arbitrarias. Todos los objetos unidimensionales, como cuerdas, líneas rectas, mitades y perímetros, son líneas. Se cree que una línea se forma cuando un punto de dimensión cero se mueve en el espacio y forma una línea infinita de múltiples puntos.

Intuitivamente, el concepto de plano se puede describir como una superficie perfectamente recta (es decir, sin curvatura ni cavidad) y lisa, que tiene volumen cero y ocupa solo las dos dimensiones del espacio tridimensional.

La superficie de un objeto se refiere a una superficie bidimensional, que separa el objeto de otros objetos y del entorno. En topología, la superficie es una dimensión bidimensional.

Aprenda más sobre geometría en https://brainly.com/question/4637858

Answer:

i believe the answer that you picked is right ....i think ^^