Find two positive numbers such that the sum of one and the square of the other is 200 and whose product is a maximum.

A number system is defined as a system of writing to express numbers. between 9 and 10  positive integers is the square root of 85 is there.

A number system is defined as a system of writing to express numbers.

We need to find the two consecutive positive integers  which have square root of 85 in between.

Firstly we need to know meaning of consecutive numbers.

Numbers which follow each other continuously in the order from smallest to largest are consecutive numbers.

Let us take some perfect square numbers

1,4,16,25,36,49,64,81,100

We know that square root of 81 is 9

square root of 100 is 10

square root of 85 is in between 9 and 10

Hence between 9 and 10  positive integers is the square root of 85 is there.

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Final answer:

The range of the given function is {3, 5, 7}.

Explanation:

The range of a function refers to the set of all possible output values (y-values) it can produce. Given the function represented by the set of ordered pairs {(-4,3), (-1,3), (0,3), (1,5), (3,7)}, to determine its range, we look at the second elements in each ordered pair since they correspond to the y-values produced by the function.

The y-values in the given set are 3, 3, 3, 5, and 7. Even though the value 3 is repeated, it is only counted once in the range. Thus, the range of this function is the set {3, 5, 7}.

Remember, the range includes all unique y-values that the function outputs. This set contains the different y-values that the function produces according to the given ordered pairs, which means these are the possible values that we can get as outputs from this function.

Answer:

Amanda's method is linear because the number of minutes increased by an equal number every week.Step-by-step explanation:I took the test and got it right.

Amanda          

Billy1st week       10                   52nd week      20                  10 3rd week       30                  204th week       40                  40A)

Amanda's method is linear because the number of minutes increased by an equal number every week.common difference is 10.1st week      0 + 10 = 102nd week   10 + 10 = 203rd week    20 + 10 = 304th week    30 + 10 = 40Billy's method is exponential:5(2)^x1st week   5(2⁰) = 5(1) = 52nd week  5(2¹) = 5(2) = 103rd week   5(2²) = 5(4) = 204th week   5(2³) = 5(8) = 40Mark

To solve for the length and width of the rectangle, equations were set up based on the given perimeter and the relation between length and width. The width was found to be 8 cm, and substituting this into the length formula gave a length of 19 cm.

The question concerns finding the length and width of a rectangle given that the length is 5 cm less than three times the width and the perimeter is 54 cm. To solve this, let's denote the width of the rectangle as 'w' and the length as 'l'. The relationship between the length and width can be expressed as 'l = 3w - 5 cm'. The perimeter (P) of a rectangle is given by P = 2l + 2w, and substituting our expressions in terms of 'w' into the formula gives us 2(3w - 5) + 2w = 54. Simplifying and solving for 'w' gives us the width. Subsequently, we can substitute this width into the equation for length to find 'l'.

So, let's start by setting up the equation:
2(3w - 5) + 2w = 54
6w - 10 + 2w = 54
8w - 10 = 54
8w = 64
w = 8 cm

Now we substitute w = 8 cm into the length formula:
l = 3(8) - 5
l = 24 - 5
l = 19 cm

Therefore, the width of the rectangle is 8 cm and the length is 19 cm.

Answer:

it would cancel eachother out so infinite

Step-by-step explanation:

For the parent function y = f(x), the vertical stretching or compression of the function is a f(x). 

If | a | < 1 (a fraction between 0 and 1), then the graph is compressed vertically by a factor of a units.
If | a | > 1, then the graph is stretched vertically by a factor of a units.

For values of a that are negative, then the vertical compression or vertical stretching of the graph is followed by a reflection across the x-axis.

Yes,  Y = 0.3x^2 is correct!!

Answer: The answer is (C) 120 sq. units.

Step-by-step explanation: We are given to find the area of a trapezoid with bases of lengths 8 units and 16 units and height of 10 units.

We know that the area of the trapezoid with 'a' and 'b' as lengths of the bases and height 'h' is given by

[tex]A=\dfrac{1}{2}(a+b)h.[/tex]

Here, a = 8 units, B = 16 units and h = 10 units.

Therefore, the area of the given trapezoid will be

[tex]a\\\\=\dfrac{1}{2}(a+b)h\\\\=\dfrac{1}{2}\times(8+16)\times 10\\\\=24\times 5\\\\=120~\textup{sq. units.}[/tex]

Thus, the correct option is (C).

Answer:

If an organism had 200 atoms of carbon-14 at death, how many atoms will be present after 14,325 years? Round the answer to the nearest hundredth.

35.36

atoms

The linear function models the scenario is g(x) = 2.5x + 25 if He receives a base pay plus an additional amount per newspaper delivered option (C) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

Pedro works as a newspaper deliverer. He receives a base pay plus an additional amount per newspaper delivered.

x = the number of newspapers Pedro delivers

y =  the earnings he receives in dollars.

From the data given the linear function can be framed as follows:

y = mx + b

Plug x = 5

y = 37.50

37.50 = 5m + b ...(I)

Plug x = 20, and y = 75

75 = 20m + b ...(II)

After solving equation (I) and equation (II):

m = 2.5

b = 25

y = 2.5x + 25

Replace y with g(x)

g(x) = 2.5x + 25

Thus, the linear function models the scenario is g(x) = 2.5x + 25 if He receives a base pay plus an additional amount per newspaper delivered option (C) is correct.

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Answer:

Option C

The area of the doghouse is [tex]66.5\ ft^{2}[/tex]

Step-by-step explanation:

we know that

The area of trapezoid is equal to

[tex]A=\frac{1}{2}(b1+b2)h[/tex]

where

b1,b2 are the parallel bases of trapezoid

h is the height of trapezoid

in this problem we have

[tex]b1=7\ ft[/tex]

[tex]b2=7+5=12\ ft[/tex]

[tex]h=7\ ft[/tex]

substitute

[tex]A=\frac{1}{2}(7+12)7=66.5\ ft^{2}[/tex]

Answer:

Step-by-step explanation:

Remember that in a isosceles trapezoid, its angles on the base are always congruent.

Also, we know by definition that the sum of interior angles of a trapezoid is equal to 360°, so

[tex]2(2x)+2(10x+24)=360\\4x+20x+48=360\\24x=360-48\\x=\frac{312}{24}\\ x=13[/tex]

Therefore, the right answer is D.

Answer: 13

a p e x confirmed

Answer: Every 60th caller would win both.

Step-by-step explanation:

Since we have given that

every 12th caller receives a free concert ticket.

And

every 15th caller receives a limo ride.

We need to find the first caller who would win.

So, for this we would find L.C.M. of 12 and 15.

And we know the least common multiple of 12 and 15 is 60.

Hence , every 60 th caller would win both.

Answer:

Hope it helps

Step-by-step explanation:

Solution: As given, Volume of a rectangular prism is given by the formula V = l w h, where l is the length of the prism, w is the width, and h is the height.

also , h=2x+9

l= x+2

w= 3 x

So, volume of prism= (2 x+9)(x+2)(3 x)= (3 x)(2 x+9)(x+2)→Using associative property

       =3 x[2 x(x+2)+9(x+2)]→Using (x+a)(x+b)= x(x+a)+a(x+b)=x²+(a+b)x+ab

      = 3 x [ 2 x²+ 4 x+ 9 x+18]

      = 3 x[ 2 x² +13 x+18]

 = (3 x)(2 x²) + (3 x)×(13 x) + (3 x)×(18)→ Using distributive property

= 6 x³+ 39 x² + 54 x → [ use [tex]x^{m} \times x^{n}= x^{m+n}[/tex]

Option (C) is correct.

The expression which represents the volume of the rectangular prism is; Choice C: 6x³+39x²+54x

The volume of the rectangular prism as given is;

where, h=2x+9, l= x+2, and w= 3x

Therefore, Volume;

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Realized income refers to the amount of income you expect to have, not yet received, including anticipated earnings and future investments.

Realized income represents the income an individual or entity expects to receive but has not yet received. It encompasses anticipated earnings, future investments, and any other income sources that have not yet materialized.

This includes income from salaries, investments, rental properties, or any other sources.

Unlike earned income, which refers to income already received, realized income is a forward-looking concept, reflecting the anticipated financial gains.

It plays a crucial role in financial planning and budgeting, guiding individuals and organizations in making decisions about expenditures, savings, and investment strategies based on expected future income streams.

We are given the two constraints:

x ≥ 5 and y ≥ 10

Now the other constraint must of course be based on the sum of the two. It was given that the budget is $5000 so the sum must be greater than that, that is:

500 x + 150 y ≤ 5000

divide total km by time

6561 / 9 = 729 km per hour

Answer-

[tex]\boxed{\boxed{(x+2)^4=x^4+8x^3+24x^2+32x+16}}[/tex]

Solution-

Given expression is [tex](x+2)^4[/tex]

Applying Binomial Theorem

[tex]\left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i[/tex]

Here,

a = x, b = 2 and n = 4

So,

[tex]\left(x+2\right)^4=\sum _{i=0}^4\binom{4}{i}x^{\left(4-i\right)}\cdot \:2^i[/tex]

Expanding the summation

[tex]=\dfrac{4!}{0!\left(4-0\right)!}x^4\cdot \:2^0+\dfrac{4!}{1!\left(4-1\right)!}x^3\cdot \:2^1+\dfrac{4!}{2!\left(4-2\right)!}x^2\cdot \:2^2+\dfrac{4!}{3!\left(4-3\right)!}x^1\cdot \:2^3+\dfrac{4!}{4!\left(4-4\right)!}x^0\cdot \:2^4[/tex]

[tex]=\dfrac{4!}{0!\left(4\right)!}x^4\cdot \:2^0+\dfrac{4!}{1!\left(3\right)!}x^3\cdot \:2^1+\dfrac{4!}{2!\left(2\right)!}x^2\cdot \:2^2+\dfrac{4!}{3!\left(1\right)!}x^1\cdot \:2^3+\dfrac{4!}{4!\left(0\right)!}x^0\cdot \:2^4[/tex]

[tex]=1\cdot x^4\cdot \:1+4\cdot x^3\cdot \:2+6x^2\cdot \:4+4\cdot x\cdot \:8+1\cdot 1\cdot \:16[/tex]

[tex]=x^4+8x^3+24x^2+32x+16[/tex]

Answer:

The answer to this question can be viewed in the images attached.

Hope it helps. Thanks

Answer:

gh

Step-by-step explanation:

Final answer:

The function f(x) =[tex]x^4 + 4x^2[/tex]  is factored using the difference of squares method to achieve its linear factorization. The final factorization over complex numbers is f(x) = x * x * (x + 2i) * (x - 2i).

Explanation:

To write a linear factorization of the function f(x) = [tex]x^4 + 4x^2[/tex]  to find the factors of the polynomial that are linear, meaning each factor will be of the form (x - c) where c is a constant.

First, notice that the given polynomial is a quadratic in form, where [tex]x^2[/tex] is our variable. This gives us [tex]f(x) = (x^2)2 + 4(x^2)[/tex]which resembles the sum of squares [tex]a^2 + 2ab + b2 = (a + b)^2.[/tex] However, we only have [tex]a^2 + 2ab[/tex], with b being 2, and a being  [tex]x^2[/tex].

To create a perfect square, we can write it as a difference of squares by adding and subtracting 4: [tex]f(x) = (x^2 + 2)^2 - (2)^2[/tex]. This can be factored further using the difference of squares formula, giving us[tex]f(x) = (x^2 + 2 + 2)(x^2 + 2 - 2)[/tex] which simplifies to [tex]f(x) = (x^2 + 4)(x^2).[/tex]

The linear factorization can be found by recognizing that x2 is already a product of linear factors x * x. Since  [tex]x^2[/tex] + 4 cannot be factored over the real numbers, we need to use complex numbers to factor it further.

Using the sum of squares, we get  [tex]x^2[/tex] + 4 = (x + 2i)(x - 2i), resulting in the final linear factorization over the complex numbers: f(x) = x * x * (x + 2i) * (x - 2i).

Answer:

its 12.94%

Step-by-step explanation