Factor 7x3 - 28x2 + 3x - 12

Answer:

5⁄18 < x

Step-by-step explanation:

Start by adding like-terms [⅓ and 2⁄9] with 9 being the Least Common Denominator [LCD]. Since 2⁄9 already has a 9 in the denominator, it does not get touched, so in order to make ⅓ a denominator of 9, we simply multiply both terms by 3, to get 3⁄9. So, adding that to 2⁄9 gives you 5⁄9, also giving you 5⁄9 + x > ⅚. Now, we have to find the LCD again because we have two unlike fractions. Now, our Least Common Denominator is 18, so multiply both terms in ⅚ by 3 [15⁄18] and multiply both terms in 5⁄9 by 2 [10⁄18]. Now you have two like fractions to work with, and you can clearly see that your answer is x > 5⁄18. Although the answer is written in reverse, it is still the same concept.

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Answer:

Problem 3: H. 350 = r * 5

Problem 4: rate of speed = 70 miles per hour

Step-by-step explanation:

Problem 3:

speed = distance/time

Multiply both sides by time.

speed * time = distance/time * time

speed * time = distance

distance = speed * time

distance = 350

speed = r

times = 5

350 = r * 5

Answer: H. 350 = r * 5

Problem 4:

350 = r * 5

Divide both sides by 5.

350/5 = r * 5/5

70 = r

r = 7

rate of speed = 70 miles per hour

Answer:

H. 350 = r*5

Her average rate: 70 miles

Step-by-step explanation:

When finding average rate, you are always either multiplying or dividing so all the choices except for H, won't work.

Also, r represents the rate so its how many miles per hour. So you would multiply the miles per hour by the amount of hours you have.

So r*5.

To find her average you would solve for r in the equation.

So r*5 = 350

You would divide 5 by itself and then by 350, because whatever you do to one side of the equation, you do to the other.

So 5/5 = 1 or just r

350/5 = 70

r = 70

Answer:

Option D 74°

Step-by-step explanation:

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

so

The arcs that the outer angle encompasses are

254° and (360-254)=106°

therefore

∠x=(1/2)[254°-106°]

∠x=(1/2)[148°]

∠x=74°

Answer:

2.94cm^2

Step-by-step explanation:

If you're referring to the mathswatch question, this gets you 2/3 :)

Answer:

(3×20%+2×70%)/3+2=40%

Step-by-step explanation:

Assuming the potions are the same type or do mix then probably the concentration of the potion depends on the type of reaction they have to each other.

Yet we can average the percentage of the active ingredient by the principle mentioned above

Answer:

The final concentration is 40%.

Step-by-step explanation:

Let x the concentration of final solution.

3 liters of solution (1) with 20% concentration is mixed with 2 liters of 70% solution producing (3 + 2) = 5 liters of x% mixture.

Now 3 × (20%) + 2 × (70% = 5 (x%)

3 × 0.2 + 2 × 0.7 = 5 (0.1x)

0.6 + 1.4 = 0.05x

2 = 0.5x

x = 2/0.05

= 40%

The final concentration is 40%.

Answer:

A

Step-by-step explanation:

Work with the two points

Formula

m = (y2 - y1)/(x2 - x1)

Givens

y2 = 3

y1 = 1

x2 = - 2

x1 = - 5

Solution

m = (3 - 1) / (-2 - - 5)

m = 2 / (-2 + 5)

m = 2 / 3

Answer: A

Answer:

[tex]\large\boxed{\text{A.}\,2/3}[/tex]

Step-by-step explanation:

In this question ,we're trying to find the slope with the given points.

We would use the slope-formula to find the slope.

Slope-formula:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

We would plug in the numbers to their right spots in the formula. The second y-coordinate going to y2, the second x coordinate going to x2, and etc.

Your equation should look like this:

[tex]m=\frac{3-1}{-2-(-5)}[/tex]

Now we solve:

[tex]m=\frac{3-1}{-2-(-5)} \\\\m=\frac{2}{-2-(-5)}\\\\\text{Carry the negative over to the 5, turning it to a positive 5}\\\\m=\frac{2}{-2+5}\\\\\text{Add the denominators}\\\\m=\frac{2}{3}[/tex]

When you're done solving, you should get 2/3

This means that the slope is 2/3

Answer:

Step-by-step explanation:

Lets assume that a sphere with greater radius = R = 5cm

And a sphere with smaller radius = r = 4cm

Volume of a sphere = 4/3 π * r³

To find the volume of a sphere with radius 5.

Put the value in the formula.

=4/3π * r³

=4/3π *(5)³

5³ = 5*5*5=125

=4/3π * 125

=4/3 *3.14 *125

=1570/3

=523.3 cm³

Now find the volume of sphere with radius= 4

4/3π*r³

=4/3π * 4³

4³= 4*4*4=64

=4/3*3.14*64

=803.84/3

=267.9cm³

Now to find the space between the spheres subtract the volume of smaller sphere from the volume of larger sphere.

We can write it as:

Space between the spheres = Volume of larger sphere - Volume of smaller sphere

= 523.3 cm³ - 267.9cm³

= 255.4cm³ ....

Answer:

0.19

Step-by-step explanation:

A correlation coefficient is a measure of how well the line of best fit fits the data.  The higher the correlation coefficient, up to 1.0 or -1.0, the better the fit. A positive correlation coefficient means an increasing data set, while a negative correlation coefficient means a decreasing data set.

We can see that this line of best fit is increasing, so our correlation coefficient will be positive.

However we can also see that the points are fairly scattered; this means this is not a very good fit.  This means that 0.19 is the better fit.

Answer:

The answer is

B. x =>z

They all equal the same.

Answer:

[tex]\frac{1}{3}\ in[/tex]

Step-by-step explanation:

we have

[tex]a(n)=9(\frac{1}{3})^{n-1}[/tex]

For n=4

substitute

[tex]a(4)=9(\frac{1}{3})^{4-1}[/tex]

[tex]a(4)=9(\frac{1}{3})^{3}[/tex]

[tex]a(4)=9(\frac{1}{27})[/tex]

[tex]a(4)=\frac{1}{3}\ in[/tex]

Answer:

1/3

Step-by-step explanation:

Answer:

3x-2

Step-by-step explanation:

[tex]9x^{2} -12x+4[/tex] can be factored using the perfect square rule into [tex](3x-2)^{2}[/tex]

and

[tex]9x^{2}-4[/tex] can be factored by using the difference of squares formula into [tex](3x+2)(3x-2)[/tex]

Both can be factored by (3x-2) so it is a common factor.

Hence, there are no common factors between the two equations.

factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder.

given equation is [tex]9x^2-4[/tex]

solving for x,

                     [tex]9x^2=4\\x^2=\frac{9}{4} \\x=\frac{3}{2}, -\frac{3}{2}[/tex]

putting values of x in equation 1,

x = [tex]\frac{3}{2}[/tex],

      [tex]\frac{81}{4}-12.\frac{3}{2}+4\\ \frac{25}{4}[/tex]Therefore, 3/2 is not a common factor

x=[tex]-\frac{3}{2}[/tex],

      [tex]\frac{81}{4}+12.\frac{3}{2}+4\\ \frac{169}{4}[/tex]Therefore, -3/2 is not a common factor

Hence, there are no common factors between the two equations.

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Answer:

7.5 = 2x + 2.1

Step-by-step explanation:

The perimeter of a triangle is the sum of the sides.  In an isosceles triangle, two sides are the same length.  If x is the length of the two sides and y is the length of the third side, then:

P = 2x + y

Given that P = 7.5 and y = 2.1:

7.5 = 2x + 2.1

Answer: The equation that can be used to find the value of x is

2x + 2.1 = 7.5

Step-by-step explanation: An isosceles triangle is a type of triangle which has two of its sides equal to each other. It also has two it's angles (the base angles) equal to each other.

From the question, the given triangle has the shortest side, y to be 2.1 m. This means side y is shorter than the other two sides. Hence, the other two sides must be the sides that are equal to each other. These other two sides are denoted by x ( see the attachment for an illustrative diagram).

The perimeter of a triangle is the sum of all its sides. Therefore, the perimeter (P) of the given triangle is

P = x + x + y

P = 2x + y

From the question, P = 7.5 m

and y = 2.1 m

Hence,

7.5 m = 2x + 2.1 m

2x + 2.1 m = 7.5 m

This equation can be used to find the value of x. The equation can also be written as:

2x = 7.5 m - 2.1m OR

x = (7.5 m - 2.1m) / 2

Answer:

13 slices.

Step-by-step explanation:

To find your total amount of slices at the start, multiply your pizzas by your slices.

[tex]9*8=72[/tex]

Next, find the difference between your total amount of slices and the amount of slices which have been eaten.

[tex]72-59=13[/tex]

13 slices are left.

For this case we have to:

[tex]x <-5:[/tex] Represents the solution of all strict minor numbers to -5.

[tex]x> 5:[/tex] Represents the solution of all strict major numbers to 5.

The global solution is given by the intersection of both sets. The symbol of intersection is denoted as: ∩

If we represent the solution in a numerical line, it gives us empty. do not intersect.

Answeer:

Empty set

Answer:

15 is your answer.

Step-by-step explanation:

Let "a number" = x

"Three times a number increase(d) by 4" = 3x + 4

"...is the same as" = "="

"four times that number decreased by 11" = 4x - 11

Set the equation:

3x + 4 = 4x - 11

Isolate the variable, x. Subtract 4x and 4 from both sides:

3x (-4x) + 4 (-4) = 4x (-4x) - 11 (-4)

3x - 4x = -11 - 4

Simplify. Combine like terms:

-x = -15

Isolate the variable, x. Divide -1 from both sides:

(-x)/-1 = (-15)/-1

x = (-15)/(-1)

x = 15

15 is your answer.

~

Answer:

x ≤-18

Step-by-step explanation:

3-x/2≥12

Subtract 3 from each side

3-3-x/2≥12-3

-x/2≥9

Multiply each side by -2 to clear the fraction.  Remember to flip the inequality since we are multiplying by a negative

-3 * -x/2 ≤ -2 *9

x ≤-18

Answer:

x ≤ - 18

Step-by-step explanation:

Given

3 - [tex]\frac{x}{2}[/tex] ≥ 12

Multiply all terms by 2

6 - x ≥ 24 ( subtract 6 from both sides )

- x ≥ 18

Multiply both sides by - 1, remembering to reverse the sign as a consequence of multiply by a negative quantity.

x ≤ - 18

Answer:

Expressing the distance from the shore by the time needed to reach that distance at an invariable speed of 4.2f/s then f=4.2 p

Answer:

f=4.2p

Step-by-step explanation:

Answer:

330

Step-by-step explanation:

Evaluate the sum of 14 terms and subtract the sum of the first 3 terms

The sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ], so

[tex]S_{14}[/tex] = 7 [ (2 × 6) + (13 × 3)]

                         = 7(12 + 39) = 7 × 51 = 357

[tex]S_{3}[/tex] = 6 + 9 + 12 = 27

Sum of terms from 4 th to 14 th = 357 - 27 = 330

Answer:

The system has no solution

Step-by-step explanation:

we have

y=5x+10 -----> equation C

The slope of the equation C is m=5 and the y-intercept is b=10

y=5x+2 -----> equation D

The slope of the equation C is m=5 and the y-intercept is b=2

Remember that

If two lines are parallel, then their slopes are the same

Equation C and equation D are parallel lines with different y-intercept

therefore

The system has no solution (the lines do not intersect)

Answer:

Step-by-step explanation:

18 - r = 12         subtract 18 from both sides

18 - 18 - r = 12 - 18

-r = -6            change the signs

r = 6

Check

18 - 6 = 12         CORRECT

In the physics context of free fall, it would take an object approximately 7.67 seconds to fall from a 944-foot tower, neglecting air resistance. This is calculated using the formula for distance of a freely falling object s(t)=16t^2.

The question deals with the physics concept of free fall, specifically directed to the time it would take an object to fall from a certain height. Given that the distance s(t) of a freely falling object is given by the equation s(t)=16t^2, we can find the time t for an object to fall from a height of 944 feet, which is the height of the specific tower.

Setting s(t) equal to the height of the tower, we get: 944=16t^2. Solving this equation for t, we'll get the square root of 944/16 which is approximately 7.67 seconds. Therefore, it would take an object about 7.67 seconds to fall to the ground from the top of the 944-foot tower, neglecting air resistance.

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To determine how long it takes for an object to fall from a 944-foot tower, we use the formula s(t) = 16t^2. Solving for t, we find that it takes approximately 7.68 seconds. Thus, the object hits the ground after 7.68 seconds.

Neglecting air resistance, the distance s(t) in feet traveled by a freely falling object is given by the function s(t)=16t^2, where t is time in seconds. The height of a certain tower is 944 feet. How long would it take an object to fall on the ground from the top of the building?

To solve this problem, we need to determine the time t it takes for the object to hit the ground. Given the height h = 944 feet, we'll use the formula for the distance fallen:

s(t) = 16t^2

We set s(t) equal to the height of the tower:

944 = 16t^2

Next, solve for t:

Divide both sides by 16:

944 / 16 = t^2

t^2 = 59

Take the square root of both sides:

t = √59

t ≈ 7.68 seconds

Therefore, it would take approximately 7.68 seconds for an object to fall to the ground from the top of the building.

Answer:

option C

Step-by-step explanation:

We will call :

A=(-5, -1)    B=(-2, -1)   C=(-3, -4)   D= (-3, -4)

Perimeter= 2*AB+2BC

Where AB= [tex]\sqrt{(-5+2)^{2} +(-1+1)^{2} } = \sqrt{9} =3\\[/tex]

BC =[tex]\sqrt{(-2+3)^{2} +(-1+4)^{2} } = \sqrt{10} =3.16\\[/tex]

So We have:

Perimeter=2*3+2*3.16= 12.32  

Answer:

C.

Step-by-step explanation:

Answer:

0.2237

Step-by-step explanation:

Use the Table of Standard Normal Probabilities for Negative z-scores.

For z= -0.36 NORMSDIST(-0.36)=0.3594 (read value from the table)

For z= -1.10  NORMSDIST(-1.10)=0.1357 (value from the table)

You know P(-1.10<z<-0.36) = 0.3594-0.1357=0.2237

Answer:

Step-by-step explanation:

There are 2 pints in one quart.

93 pints = 93/2 = 46 quarts and 1 pint left over.

Answer:

46.5 quarts

Step-by-step explanation:

There are 2 pints in 1 quart.

Hence,

93 pints     1 quart

------------ * ------------- = 46.5 quarts

      1           2 pints

Answer:

So if y=-4x+2 was changed to y=-4x+5, then the y-intercept would increase by 3.

The y-intercept was (0,2) then it becomes (0,5) in the new line.

Step-by-step explanation:

The slope-intercept form a line is y=mx+b where m is the slope and the y-intercept is b.

Both of these equations given are in this form.

y=-4x+2 when compared to y=mx+b you see that m=-4 and b=2.

Since b=2 then the y-intercept is 2.

y=-4x+5 when compared to y=mx+b you see that m=-4 and b=5.

Since b=5 then the y-intercept is 5.

So if y=-4x+2 was changed to y=-4x+5, then the y-intercept would increase by 3.

Detailed solution to math problems involving functions and mappings.

1. The function represented by the table:

Identify the pattern in the table to determine the function.

The cost increases by $1.95 for every 3 apples, so the function is C(a) = 0.65a (A).

2. Translating a function:

To shift f(x) = x^4 five units right and seven units down, the correct function is g(x) = (x+5)^4 - 7 (D).

3. Mapping the function:

Using the mapping provided, the correct values are: f(5) = 1, f(3) = 0, f(11) = 2, f(21) = 3 (A).

Answer:

I believe it would be B

Step-by-step explanation:

take x and y values and figure it out what it is by itself

Answer:

Step-by-step explanation:

The distributive property: a(b + c) = ab + ac

4(2x - 1) = (4)(2x) + (4)(-1) = 8x - 4

Put x = 6 to the expression:

8(6) - 4 = 48 - 4 = 44

The solution to the given expression is 44.

The distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a given numerical value or factor, the same output would be produced as when each addend is multiplied respectively by the numerical value or factor, and the products are added together.

By applying the distributive property of multiplication to the given expression, we have:

4(2x - 1) = 4(2x) - 4(1)

4(2x - 1) = 8x - 4

when x = 6, we have;

8x - 4

8(6) - 4

48 - 4 = 44.

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