What is the factorization of 3x^2-8x+5

Answer:

The volume of a cube whose total surface area is 150 sq. ft. is 125 cubic feet.

Step-by-step explanation:

Set up an equation that shows the relation between the side length L of the cube and its surface S:

[tex]S = 6\cdot L^2\\150 = 6\cdot L^2\implies\\|L| = \sqrt{\frac{150}{6}}= 5[/tex]

The side length of a cube with an area of 150 sq. ft is 5 ft. Now we can easily calculate the volume V:

[tex]V = L^3 = 5^3 = 125[/tex]

The volume of a cube whose total surface area is 150 sq. ft. is 125 cubic feet.

The volume of a cube with a total surface area of 150 square feet is 125 cubic feet. This is found by first dividing the total surface area by 6 to find the area of one face, then taking the square root to find the length of one side, and finally cubing this length.

To find the volume of a cube when you know the total surface area, you begin by realizing that a cube has six identical faces. Hence, the surface area of one face is the total surface area divided by 6. In this case, 150 square feet divided by 6 equals 25 square feet. This is the area of one face. Because this is a cube, the length, width, and height are equal, so the square root of 25 (which is 5) would give us the length of one side.

Now, the volume of a cube is the side length cubed. Hence, in this case, the volume would be 5 feet (the length of a side) cubed, or 5 * 5 * 5, which equals 125 cubic feet.

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Answer:

10

Step-by-step explanation:

let's call the difference in each term d so the sequence would look like

3,(3+d),(3+2d),(3+3d),(3+4d)

notice how in this sequence that (3+4d) is the fifth term so it must equal 31

3+4d=31

4d=28

d=7

now plug this into the second term

(3+(7))

and we see that the second term is 10

The value of the second term will be 10.

Since the arithmetic sequence has a first term of 3 and the fifth term of 31, this can be represented thus:

First term = a = 3

Fifth term = a + 4d = 31.

Substitute the value of a into the second equation.

a + 4d = 31

3 + 4d = 31

4d = 31 - 3

4d = 28.

d = 28/4

d = 7

Therefore, the value of the second term will be:

= a + d

= 3 + 7

= 10

The value of the second term will be 10.

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Answer:

40 yards

Step-by-step explanation:

8×5≈40

1/3+3/4=4/12+9/12=13/12=1 and 1/12. (1 1/12)

5/6+2/3=5/6+4/6=9/6=3/2 or 1.5 or 1 and 1/2.

Answer:

1.75 %  

Step-by-step explanation:

The formula for the future value (FV) of an investment is

FV =PV(1 + r/n)^nt

If the interest is calculated once a year, n = 1, and the formula reduces to

     FV = PV(1 +r)^t

5550 = 5000(1 + r)⁶     Divide both sides by 5000

 1.110 = (1+r)^6              Take the sixth root of each side

 1 + r = 1.0175               Subtract 1 from each side

      r = 0.0175               Convert to percent

     r = 1.75 %

The interest rate is 1.75 %.

Answer:

3B

Step-by-step explanation:

The greatest common factor is the greatest number that will divide two values. We have two values 3B and 30B. Each has numbers which multiply together to give the number. We need to find the highest value or most in common they share. Each has the factors:

3B: 1,3,B

30B: 1, 3, 5, 6, 10, B

Both have 3 and B has factors. Our GCF is these two factors.

Answer:  5/8 × 24 = 15

Answer:

a=48

b=-192

c=84

Step-by-step explanation:

figure it out yourself :3 jk Idrk

Answer:

see explanation

Step-by-step explanation:

given (4x - 2) × 6(2x + 7), then

= 6(4x - 2)(2x + 7) ← expand factors using FOIL

= 6(8x² + 28x - 4x - 14)

= 6(8x² + 24x - 14) ← distribute

= 48x² + 144x - 84 ← in standard form

with a = 48, b= - 144, c = - 84

Answer:

Domain is all real numbers

Range is

[tex]y\le 12.95[/tex]

Step-by-step explanation:

The given function is

[tex]f(d)=-0.6d^2+5.4d+0.8[/tex]

This is a maximum quadratic function therefore the domain is all real numbers.

Let us complete the square to find the vertex.

[tex]f(d)=-0.6(d^2-9d)+0.8[/tex]

[tex]f(d)=-0.6(d^2+9d)+-0.6(\frac{9}{2})^2- -0.6(\frac{9}{2})^2+ 0.8[/tex]

[tex]f(d)=-0.6(d-\frac{9}{2})^2+\frac{243}{20}+ 0.8[/tex]

[tex]f(d)=-0.6(d-\frac{9}{2})^2+\frac{259}{20}[/tex]

Therefore the range is

[tex]y\le \frac{259}{20}[/tex]

[tex]y\le 12.95[/tex]

See graph

Answer:

Domain:

[tex][0,9.146][/tex]

Range:

[tex][0,12.95][/tex]

Step-by-step explanation:

we are given

a baseball follows the path graphed by the quadratic function

[tex]f(d)=-0.6d^2+5.4d+0.8[/tex]

where

d is the horizontal distance the ball traveled in yards

ƒ(d) is the height, in yards, of the ball at d horizontal yards

Domain:

we know that domain is all possible values of x for which any function is defined

So, for finding domain , we will take smallest x-value to largest x-value

so, we can set f(d)=0 and find zeros

[tex]-0.6d^2+5.4d+0.8=0[/tex]

we can use quadratic formula

[tex]d=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]d=\frac{-54\pm \sqrt{54^2-4\left(-6\right)8}}{2\left(-6\right)}[/tex]

[tex]d=-\frac{\sqrt{777}-27}{6},\:d=\frac{27+\sqrt{777}}{6}[/tex]

[tex]d=-0.14579,d=9.146[/tex]

we know that d is a horizontal distance

and distance can never be negative

so, domain will be

[tex][0,9.146][/tex]

Range:

Since, this is quadratic equation

so, it is also equation of parabola

so, firstly we will find vertex of parabola

Suppose, we have

[tex]ax^2+bx+c=0[/tex]

Vertex is

[tex]x=\frac{-b}{2a}[/tex]

so, we can compare

a=-0.6

b=5.4

c=0.8

now, we can find vertex

[tex]x=\frac{-5.4}{2\times -0.6}[/tex]

[tex]d=4.5[/tex]

now, we can find y-value

[tex]f(4.5)=-0.6(4.5)^2+5.4(4.5)+0.8[/tex]

[tex]f(4.5)=12.95[/tex]

we can see

that leading coefficient is -0.6

which is negative

so, parabola opens downward

so, range will be

[tex][0,12.95][/tex]

Answer:

The ratio of the white fabric to the colored fabric is [tex]\frac{20}{9}[/tex] in its simplest form

Step-by-step explanation:

The ratio indicates how many times one number contains another

The ratio can be written as:

The two terms of the ratio must have the same units

∵ Sarah uses 9 mm of colored fabric to make her curtains

∵ She also uses 2 cm of of white fabric

- To express the amount of white fabric to colored fabric as a ratio

   you must change the centimeter to millimeter because the

   terms of ratio must have the same unit

∵ 1 centimeter = 10 millimeters

∴ 2 centimeters = 2 × 10 = 20 millimeters

∴ She uses 20 millimeters of the white fabric

Now write the ratio between the white fabric and the colored fabric

→  White    :    colored

→  20          :    9

∵ 20 and 9 do not have a common factor

∴ The simplest form of the ratio is 20 : 9

The ratio of the white fabric to the colored fabric is [tex]\frac{20}{9}[/tex] in its simplest form

Sarah uses 2 cm of white fabric for every 9 mm of coloured fabric. After converting to the same unit (centimeters), the simplest form of the ratio of white fabric to coloured fabric is approximately 2.22:1.

To determine the ratio of the amount of white fabric to coloured fabric Sarah needs for her curtains in its simplest form, we first need to ensure that both fabrics are expressed in the same units. The question states Sarah uses 9 mm of coloured fabric and 2 cm of white fabric. Since there are 10 mm in a cm, 9 mm of coloured fabric can be converted to 0.9 cm.

Now, with both fabric measurements in centimeters, we can write the ratio of white fabric to coloured fabric: 2 cm of white fabric to 0.9 cm of coloured fabric. To find the simplest form of this ratio, we divide both sides by 0.9:

The simplest form of the ratio is therefore 2.2222...:1, which can be rounded and written as approximately 2.22:1, white to coloured fabric.

Rounding 125.3546 to 1 decimal place involves looking at the second decimal digit (5) and rounding up, resulting in 125.4.

We look at the second decimal digit, which is a 5. Since it is 5 or more, we round the first decimal place up. Therefore, 125.3546 rounded to 1 decimal place is 125.4.

15) Yes, it is a function.

16)

A f(-4)=2

B F(3)= something around -1.75

C f(-5)=0

D f(-2)=4

E f(0)=0

F) -2

17)2(2a+5)=4a+10

a(a+5)=a^2+5a

18) 1

Answer:

t≤ 2

Step-by-step explanation:

The temperature must be 2F or less

t <=2

t≤ 2

Answer:

no

Step-by-step explanation:

since the y=mx+b format is used here, your b is -5. for this to be correct, your y-int needs to be on -5, not -2 as you have it. Other than that, i believe you are correct

Answer:

no

Step-by-step explanation:

the point has to be on the 5

Answer:

The solution to the equation is:

Option c. b=0 and b=4

Step-by-step explanation:

5 / (3b^3-2b^2-5) = 2 / (b^3-2)

Cross multiplication:

5(b^3-2)=2(3b^3-2b^2-5)

Applying distributive property both sides of the equation to eliminate the parentheses:

5(b^3)-5(2)=2(3b^3)-2(2b^2)-2(5)

Multiplying:

5b^3-10=6b^3-4b^2-10

Passing all the terms to the right side of the equation: Subtracting 5b^3 and adding 6 both sides of the equation:

5b^3-10-5b^3+10=6b^3-4b^2-10-5b^3+10

Adding like terms:

0=b^3-4b^2

b^3-4b^2=0

Getting common factor b^2 on the left side of the equation:

b^2 (b^3/b^2-4b^2/b^2)=0

b^2 (b-4) = 0

Two solutions:

(1) b^2=0

Solving for b: Square root both sides of the equation:

sqrt(b^2)=sqrt(0)

Square root:

b=0

(2) b-4=0

Solving for b: Adding 4 both sides of the equation:

b-4+4=0+4

Adding like terms:

b=4

The solution of the equation is: b=0 and b=4 (Option c)

Final answer:

To solve the equation, we can use the quadratic formula and find the solutions for b.

Explanation:

To solve the equation 5/3b^3 - 2b^2 - 5 = 2/b^3 - 2, we need to find the values of b that satisfy the equation. To do this, we can cross-multiply and rearrange the equation to get a quadratic equation in terms of b. Using the quadratic formula, which states that b = (-b ± √(b^2 - 4ac)) / 2a, we can find the solutions for b.

Substituting the values a = 5/3, b = -2, and c = -7 into the quadratic formula, we obtain the solutions b = -4 and b = 0.

Therefore, the solution to the equation 5/3b^3 - 2b^2 - 5 = 2/b^3 - 2 is b = -4 and b = 0.

[tex]|x|- 7 = 8\\\\|x|=15\\\\x=-15 \vee x=15[/tex]

Answer:

x = –15 or 15

Step-by-step explanation:

|x| – 7 = 8

We need to isolate the absolute value.

Add 7 to each side

|x| – 7+7 = 8+7

|x|  = 15  

Now to get rid of the absolute values, we take what is inside the absolute values and set it equal to the right hand side.  Remember we set it equal to the positive amount and the negative amount.

x=+15 and x=-15

Answer:

Option 4

Step-by-step explanation:

Firstly, we need to make the two x's or the two y numbers the same. Lets multiply the second equation by 2:

(2x + 3y = 5 ) * 2 =

4x + 6y = 10

Now, subtract the second equation from the first one:

(4x - y = -11) - (4x + 6y = 10)

4x - 4x = 0

-y - 6y = -7y

-11 - 10 = -21

-7y = -21

Divide both sides by -7:

y = 3

Plug 3 into the first equation as y:

4x - 3 = -11

4x = -11 + 3

4x = -8

x = -2

So x = -2 and y = 3. We need to find one of the options that equals this.

-4x - 9y = -21

-10y = -30

40x - 90y = -210

-90y = -270

40x - 0 = 40x

-90y - - 90y = -90 + 90 = 0y

-210 - -270 = -210 + 270 = 60

40x = 60

x = 1.5

We already know this isn't equivalent because the x value is not the x value of the given equation.

4x + 3y = 5

2y = -6

_______

8x + 6y = 10

6y = -18

8x - 0 = 8x

6y - 6y = 0

10 - -18 = 10 + 18 = 28

8x = 28

x = 3.5

So we know this isn't equivalent because again, the x value isn't the same as the given equation.

7x - 3y = -11

9x = -6

-----------

63x - 27y = -99

63x = -42

----------------

63x - 63x = 0

-27y - 0 = -27y

-99 - - 42 = -99 + 42 = -57

-27y = -57

-9y = -19

9y = 19

y = 19/9

So we know this one isn't equivalent as the y value isn't the same as the given equation.

12x - 3y = -33

14x = -28

x = -28/14 = -2

12(-2) - 3y = -33

-24 - 3y = -33

-3y = -33 + 24

-3y = -9

y = 9/3

y = 3

So x = -2 and y = -3 which is the same as the first equation.

Final answer:

Option 4 is the correct equivalent system for the given linear equations because you can derive the system in Option 4 by multiplying the original system's equations by constants and rearranging them.

Explanation:

We are given the system of linear equations:

To find an equivalent system, each equation from the new system should be derivable from the original system. A common method is to multiply one or both of the original equations by a constant to see if it matches one of the offered options.

Option 4 is the correct choice. Multiplying the first original equation by 3, we get:

And multiplying the second original equation by 7 and rearranging yields:

The other options cannot be derived from the original system through multiplication or other allowed operations, hence they are not equivalent.

Answer:

5

Step-by-step explanation:

The degree of a polynomial is found by identifying the term with the largest exponent. The degree of a term is found by adding all the exponents of the variables of that term.

For example: [tex]3x^{2} yx^{3}[/tex]

The degree of this term is found by adding all the exponents: 2+1+3=6

In the case of a polynomial, it meets the largest degree term

For example: [tex]2x^{2} y+5x^{2} y^{2} z-8x^{4}[/tex]

If we add the exponents of each term, we will have the term with the greatest degree :   5

The degree of the polynomial, [tex]x^5-4x+2[/tex] is 5.

The degree of a polynomial can be defined as the largest exponents on any of the variables of a polynomial of the largest sum of exponents, if any of it's term has multiple variables.

Thus: The largest exponent in [tex]x^5-4x+2[/tex] is 5.

Therefore, the degree of the polynomial, [tex]x^5-4x+2[/tex] is 5.

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Answer:

2a+b+(-b)=2a+0

Step-by-step explanation:

Additive inverse

x+ -x =0

Answer:

a would be the answer

Step-by-step explanation: the whole point of additive inverse is to add a negative number. So putting parenthesis around the negative number and then adding it to another number, would be correct. In my opinion it also looks easier to do.

Answer:

(- 25, 81) does not lie on the line

Step-by-step explanation:

We can use the slope m to determine if (- 25, 81) lies on the line or not

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (2, 0)

m = [tex]\frac{0-4}{2-0}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2

now if (- 25, 81) lies on the line then the slope between (- 25, 81) and either of the 2 points on the line should equal - 2

(x₁, y₁ ) = (- 25, 81) and (x₂, y₂ ) = (2, 0)

m = [tex]\frac{0-81}{2+25}[/tex] = [tex]\frac{-81}{27}[/tex] = - 3

The slopes are not equal hence (-25, 81) does not lie on the line

[tex]\text{Step 1:}\\\\\text{Find the equation of the line passing through the points}\\\\\text{The slope-intercept form:}\ y=mx+b\\\\m-slope\\b-y-intercept\to(0,\ b).\\\\\text{We have the points:}\\(0,\ 4)-y-intercept\to b=4\\(2,\ 0)-x-intercept\\\\\text{Therefore we have the equation:}\ y=mx+4.\\\\\text{The formula of a slope}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{put the coordinates of the points:}\\\\m=\dfrac{0-4}{2-0}=\dfrac{-4}{2}=-2\\\\\text{Therefore we have}\ \boxed{y=-2x+4}[/tex]

[tex]\text{Step 2:}\\\\\text{Put the coordinates of the point (-25, 81) to the equation of a line}\\\text{and check equality}\\\\y=-2x+4,\ x=-25,\ y=81\\\\-2x+4\to-2(-25)+4=50+4=54\neq81[/tex]

Answer:

(x + 3)² + (y+ 2)² = 1²

Step-by-step explanation:

The standard form for the equation of a circle with centre (a, b) and radius r is

(x - a)² + (y - b)² = r²

x² + 6x + y² + 4y + 12 =  0

Step 1. Subtract the constant from each side

x² + 6x +           y² + 4y        = -12

Step 2. Complete the squares for x and y

Square half the coefficients of x and y

(x² + 6x + 3²) + (y² + 4y + 2²) = -12 + 3² + 2²

Step 3. Write the lhs as squares of binomials

(x + 3)² + (y+ 2)² = -12 + 3² + 2²

Step 4. Convert the rhs to a square

(x + 3)² + (y+ 2)² = -12 + 9 + 4

(x + 3)² + (y+ 2)² = 1

(x + 3)² + (y+ 2)² = 1²

The graph below shows that this is the equation for a circle with

centre (-3, -2) and radius 1.

The center and radius of the given circle are respectively; (-3, -2) and 1

The standard form for the equation of a circle with it's centre coordinate (a, b) and radius r is given as;

(x - a)² + (y - b)² = r²

Now, we are given the circle equation to be; x² + 6x + y² + 4y + 12 =  0

Let us subtract 12 from both sides to leave only the variables on the left side;

x² + 6x + y² + 4y + 12 - 12 =  0 - 12

x² + 6x + y² + 4y = -12

Now let us complete the squares for variable x and y;

Square half the coefficients of x and y and add to both the x, y and constant to get;

(x² + 6x + 3²) + (y² + 4y + 2²) = -12 + 3² + 2²

(x² + 6x + 3²) + (y² + 4y + 2²) = -12 + 9 + 4

(x² + 6x + 3²) + (y² + 4y + 2²) = 1

Write the left hand side as squares of binomial to get;

(x + 3)² + (y+ 2)² = 1

This can be also written as;

(x + 3)² + (y+ 2)² = 1²

Thus, from the general standard form of equation of a circle, we can say that;

centre is at (-3, -2) and radius is 1.

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Answer:

654

Step-by-step explanation:

The graphs of lines in the form y=mx always pass through the origin (0, 0). These graphs only differ in the rate of decrease or increase of the lines.

In Mathematics and Geometry, a proportional relationship is a type of relationship that produces equivalent ratios and it can be represented by the following mathematical equation:

y = mx

Where:

Generally speaking, the characteristics for a graph that shows a proportional relationship or an equation in y = mx form include the following:

In conclusion, the difference between the graphs of the form y = mx is the rate of decrease or increase of the lines.

Complete Question:

What do the graphs of lines in the form y=mx have in common? How might they differ?

Need more info:

Can you give me more info so I can help you better?

[tex]42=2\cdot21=\boxed2\cdot3\cdot\boxed7\\\\56=2\cdot28=2\cdot2\cdot14=\boxed2\cdot2\cdot2\cdot\boxed7\\\\Answer:\ GCF(42,\ 56)=\boxed2\cdot\boxed7=14[/tex]

Answer:

1. (2.923)   2.  i don't know what they are asking for but i believe it is the mean so add all of the data up and divide by how many data pieces there are ( there are seven

Answer:

$0.79 x 3.7 would give you 2.923 but since its money it would be $2.92 and 2) im not sure how there the same question if one is dealing with weather and the other with money, Im sorry

Answer:

-3

Step-by-step explanation:

2(x-6)= 6(x)

2x-12= 6x

-12=4x

x= -3

Answer: -3

Step-by-step explanation:

2(n - 6) = 6n

2n - 12 = 6n

-2n       -2n          

     -12  = 4n

      ÷4   ÷4  

       -3 = n