Multiple the polynomial by the monomial. (Simplify answer) 8r(2r^2 - 6r + 2)

Answer:

Below

Step-by-step explanation:

Pop = 1000 ( y)^t       when t = 3

 216 = 1000 ( y)^3

216/1000 = y^3

  y = cubrt(216/1000) =  .6

so the equation becomes

 P(t) = 1000 ( .6^t)     where t is # years past 2004

Answer:

100

Step-by-step explanation:diego died

Answer:

the way in which factors are grouped in a multiplication problem does not change the product.

Step-by-step explanation:

For the given function C(x) = 0.37 + (x - 1)0.11 the cost of mailing a 1.6-ounce letter is $0.436

The term function in math is defined as a relation between a set of inputs having one output each.

Here we have given that certain mailing service's first class mail rates are $0.37 for the first ounce and $0.11 for each additional ounce or fraction thereof up to 3.5 ounces.

Let us consider that the term C refers that cost in dollars of a first class mailing and x refers the weight in ounces.

The the function for the given situation is written as,

=> C(x) = 0.37 + (x - 1)0.11

Here we have given that we need to find the cost of mailing a 1.6-ounce letter which defines that the value of x is 1.6, then the cost is calculated as,

=> C(x) = 0.37 + (1.6 - 1) 0.11

=> C(x) = 0.37 + 0.066

=> C(x) = 0.436.

Complete Question:

A certain mailing service's first class mail rates are $0.37 for the first ounce and $0.11 for each additional ounce or fraction thereof up to 3.5 ounces. Find the function of the situation and the cost of mailing a 1.6-ounce letter.

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Answer:

2

Step-by-step explanation:

f(x) = 2^(x+3)      

f(-2) = put in -2 where x is

      = 2 ^(-2+3) = 2^1 = 2  

Answer:

\(p(x)=-5(x-12)^2+405\)

Step-by-step explanation:

Hi there!

Vertex form: \(f(x)=a(x-h)^2+k\)

\(p(x)=-5x^2+120x-315\)

Factor out -5 from the first two terms

\(p(x)=-5(x^2-24x)-315\)

Complete the square by adding \((\frac{24}{2} )^2\) (the square of half of the x-coefficient)

\(p(x)=-5(x^2-24x+(\frac{24}{2} )^2)-315-(-5)(\frac{24}{2} )^2\)

We're subtracting \((-5)(\frac{24}{2} )^2\) because we need to keep the equation balanced and we can't just add new values.

Complete the square

\(p(x)=-5(x-(\frac{24}{2} ))^2-315-(-5)(\frac{24}{2} )^2\)

Simplify

\(p(x)=-5(x-12)^2-315+720\\p(x)=-5(x-12)^2+405\)

Summary:

I hope this helps!

Answer:

6610

Step-by-step explanation:

We have tan(X) = opposite/ adjacent

tan(QBP) = PQ/BQ

tan(35) = PQ/BQ    ---eq(1)

tan(QAP) = PQ/AQ

tan(20) = \(\frac{PQ}{AB +BQ}\)

\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)

230*tan(20) + PQ*tan(20)*tan(35) = PQ

⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)

⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]

\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)

\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)

PQ = 110.4

≈110

Height above sea level = 6500 + PQ

6500 + 110

= 6610

Answer:

3x)^3=3^3*x^3=27x^3

Step-by-step explanation:

hope i was right let me know if i was wrong!

Answer: Let's call the width of the rectangular playing field "w" and the length "l". From the problem, we know that:

l = 3w + 4 (the length is 4 yards longer than triple the width)

We also know that the perimeter of a rectangle is the sum of the lengths of all four sides, so:

P = 2l + 2w

We are given that the perimeter is 416 yards, so we can substitute that into the perimeter equation:

416 = 2(3w + 4) + 2w

Simplifying and solving for w:

16 = 6w + 8

8 = 6w

w = 8/6 = 4/3

We can now substitute that back into the equation for the length:

l = 3w + 4

l = 3(4/3) + 4

l = 4 + 4

l = 8

So the dimensions of the rectangular playing field are 4/3 yards wide and 8 yards long.

Step-by-step explanation:

I need to deposit $1558.41 to have $2000 in the account in 5 years.

What is compound interest?

The interest charged on a debt or deposit is known as compound interest. It is the idea that we use the most regularly. Compound interest is calculated for a sum based on both the principal and cumulative interest.

    ∴ Compound interest = P(1 + \(\frac{r}{100*12}\))ⁿ  (∵ for monthly interest)

        P = Principal

        r = rate of interest per month

        n = number of months

Given:

r = 5% per month

n = 5 years = 5*12 = 60 months

  CI = P (1+5/(12 * 100))⁶⁰

2000 = P(1.0041)⁶⁰

2000 = P(1.2834)

      P = 1558.41

Therefore, the amount required to deposit is 1558.41 dollars to get 2000 dollars after 5 years with 5 percent interest per month.

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a) The bill before the tax is of: $74.

b) The tip would be of: $16.28.

c) The total bill would be of: $94.72.

The amounts are obtained applying the proportions in the context of the problem.

Considering the tax, 100 + 6 = 106% of the bill is of $78.44, hence the bill before tax is obtained as follows:

1.06x = 78.44

x = 78.44/1.06

x = $74.

A 22% tip of this bill would have a value of:

0.22 x 74 = $16.28.

Hence the total bill would be of:

78.44 + 16.28 = $94.72.

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The relation that can not be supported by the evidence in the image is option B

Corresponding angles are those that are located on the same side of the transversal and in identical relative positions to the parallel lines. Angles that correspond to one another have the same measure.

Alternate interior angles are those that are located on the transverse and within the area between the parallel lines, respectively. Congruent alternate interior angles exist.

Alternate external angles are those that are outside of the space between the parallel lines and on the opposing sides of the transversal. Congruent external angles exist between the two.

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Answer:

place value of 3 in 783.97 is 3

Step-by-step explanation:

Answer:

Units

Step-by-step explanation:

The units start counting from 3 because after the point that is the 9 start counting tenth

Answer:

Step-by-step explanation:

a) if she had 16 m of fencing

all possible outcomes

4 by 4

2 by 6  

1 by 7

the greatest should be 4 by4

b) she could alter it to 2 by 6

Answer:

slope intercept form: y= -6x+3

point slope form: y-0= -6(x -1/2)

Step-by-step explanation:

point slope form: y - y1 = m(x - x1)

substitute the values  y-0=-6(x-1/2)

slope intercept form:

find the slope using two given points

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

= (3 - 0) / (0 - 1/2)

= 3 / (-1/2)

= -6

substitute into equation

y= -6x+3

Step-by-step explanation:

0.4t = 10.4 -19.6

0.4t= -9.2

t = -9.2/0.4

t = -23

Answer:

Step-by-step explanation:

\( 0.4t+19.6=-10.4\\\\\\0.4t=-10.4-19.6\\\\\\0.4t=-30\\\\\\t=-\dfrac{30}{0.4}\\\\\\t=-75\)

Answer:

f(x) = 3x + 2

x = 3f-1(x) + 2

x - 2 = 3f-1(x)

(x - 2)/3 = f-1(x)

(14 - 2)/3 = f-1(14)

12/3 = f-1(14)

4 = f-1(14)  

f(f-1(14)) = f(4)

f(4) = 3(4) + 2

f(4) = 12 + 2

f(4) = 14

A function and its inverse are inverse operations, like addition and subtraction. They undo each other.

f(f-1(x) = x

Step-by-step explanation:

Answer:

Complementary angles

Step-by-step explanation:  Two angles that = 90 degrees is the definition or complementary.  Supplementary is 180 degrees.  Vertical is just a straight angle.  The reason why it isn't a right angle is because a right angle is one individual angle not 2 or more equaling 90 degrees.

Answer: 5 second on the way down

Step-by-step explanation: i hope this helps plz tell me if its wrong so i can fix it

The original dimensions of the piece of metal were 15 inches by 20 inches.

To solve this problem, we can use the given information to set up an equation. Let's assume that the width of the rectangular piece of metal is x inches. According to the problem, the length of the piece of metal is 5 inches longer than its width, so the length would be (x+5) inches.

When squares with sides 1 inch long are cut from the four corners, the width and length of the resulting box will be reduced by 2 inches each. Therefore, the width of the box will be (x-2) inches and the length will be ((x+5)-2) inches, which simplifies to (x+3) inches.

The height of the box will be 1 inch since the flaps are folded upward.
Now, let's calculate the volume of the box using the formula Volume = length * width * height.

Substituting the values, we have:

234 = (x+3)(x-2)(1)

Simplifying the equation, we get:

234 = x^2 + x - 6

Rearranging the equation, we have:

x^2 + x - 240 = 0

Now, we can solve this quadratic equation either by factoring or by using the quadratic formula. Let's use factoring to find the values of x.

Factoring the equation, we have:
(x+16)(x-15) = 0
Setting each factor equal to zero, we get:
x+16 = 0 or x-15 = 0
Solving for x, we have:
x = -16 or x = 15
Since the width cannot be negative, we take x = 15 as the valid solution.
Therefore, the original dimensions of the piece of metal were 15 inches in width and (15+5) = 20 inches in length.

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The required present value needed now to get $700 after 4 years at 11% compounded monthly is $451.73.

To find the present value of $600 after 4 years at 7% compounded monthly, we can use the formula for compound interest:

Compound Interest =P(1+r/n)^rt

Substituting the given values, we get:

Compound Interest =600 (1+7/n)^4

Simplifying this equation, we get

P = 600 / 1.487

P = 451.73

Therefore, the present value needed now to get $600 after 4 years at 7% compounded monthly is $451.73.

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Answer:

9:8

Step-by-step explanation:

We know that 72:64

If you multiply 9 by 8 you get 72, so you know that the answer will have to be simplified by 8.

64/8 = 8

Therefore your answer for this will be 9:8

The following statements are true or show through counterexamples that they are false:

An example of network graph

shortest path between s and t is with a distance of 5

(1+1+1+2) =5

The maximum value of cy occurs at (s,a) arc, but this is not a vital arc as deletion of (s,a) does not increase the shortest distance.

Arc (d,f) is a most vital arc with cost 2 . (d,f) ∈ shortest path. There exists another most vital arc (f,t) with cost of 2

Let s→t be any shortest path where (u,v) ∉ s→t .

The cost of (u,v) is C(u,v)

If we delete always can find path which is considered shortest.

Arc (d,f) is a most vital arc with cost 2 . (d,f) ∈ shortest path. There exists another most vital arc (f,t) with cost of 2

Arcs (d,s) , (f,t) are most vital areas .

If any of these two arcs is deleted the shortest distance will increase by 1

The new shortest parth s→c→d→e→f

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The simplified expression for \($(27^{\frac{1}{2} }) ^{\frac{2}{3} }\) is equal to 3.

We can write the simplified form of the given expression using the exponent rule as -

{aˣ/aⁿ} = {aˣ a⁻ⁿ} = {aˣ ⁻ ⁿ}

Given is the expression as -

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} }\)

We can simplify the expression as -

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = (27)^{\frac{1}{2} \times \frac{2}{3} }\)

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = 27^{\frac{1}{3} }\)

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = (3)^{3}^{\frac{1}{3} }\)

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = 3\)

Therefore, the simplified expression for \($(27^{\frac{1}{2} }) ^{\frac{2}{3} }\) is equal to 3.

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Answer:

20 blogs

Step-by-step explanation:

Step 1:  Determine the proportion of pop culture blogs:

First, we need to determine the proportion of pop culture blogs already written.  We can do this by dividing the number of pop culture blogs already written by the total number of blogs written:

The proportion of pop culture bloggers = Number of pop culture bloggers / Total number of bloggers

Proportion =  26 / (20 + 26 + 7 + 12)

Proportion = 26 / 65

Proportion = 0.4

Step 2:  Multiply the proportion of pop culture blogs by the number of upcoming blogs:

To determine the expected number of pop culture blogs that will be written given the data, we can multiply the proportion of pop culture blogs already written by the number of upcoming blogs:

Expected number of pop culture blogs = proportion of pop culture blogs *  number of upcoming blogs

Expected number = 0.4 * 50

Expected number = 20

Thus, you should expect 20 pop culture blogs to be written given the data.

y=0.002x² +0.15x + 2 and y=x set best models the point of intersection of the arrow and the target because it accounts for the fact that the arrow is travelling in a parabolic arc, while the target is located on a straight line.

A parabolic arc is defined by its vertex, focus, and directrix. The arc can be used to describe the trajectory of a projectile, the shape of a satellite dish, or the shape of some suspension bridges.

The equation y=0.002x² +0.15x + 2 models the parabolic arc of the arrow's trajectory and the equation y=x models the straight line of the target.

This equation set is the only one that correctly models both the parabolic arc of the arrow and the straight line of the target.

To better understand why this equation set is the correct answer, let's look at the other equation sets.

The equation set y=-0.002x²+0.15x+2 and y=-x does not work because the equations do not model a parabolic arc and a straight line, respectively.

The equation set y=0.002x²+0.15x + 2 and y=0,2x does not work because the second equation, y=0.2x, does not model a straight line, but rather a line with a slope of 0.2.

Finally, the equation set y=-0.002x² +0.15x+2 and y = 0.2x does not work because the first equation, y=-0.002x² +0.15x+2, does not model a parabolic arc.

Therefore, the equation set y=0.002x² +0.15x + 2 and y=x is the correct answer because it is the only equation set that accurately models both the parabolic arc of the arrow and the straight line of the target.

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Answer: We have f(x)=3x⁵+6x²-5 and g(x)= 2x⁴+7x²-x+16

                        (f-g)(x)= 3x⁵-2x⁴-x²+x-21

Step-by-step explanation:

Here we have,

Given : f(x)=3x⁵+6x²-5 and g(x)= 2x⁴+7x²-x+16

We know,

(f-g)(x)= f(x)-g(x)

= (3x⁵+6x²-5 ) - ( 2x⁴+7x²-x+16)

On subtracting g(x) from f(x) we get,

(f-g)(x)= (3x⁵+6x²-5  - 2x⁴-7x²+x-16)

On simplify,

 (f-g)(x) =3x⁵-2x⁴-x²+x-21

Hence,

(f-g)(x) = f(x) - g(x) = 3x⁵-2x⁴-x²+x-21

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