**WITH STEPS ASAP
1. If you know that limx→−1 f(x)=−3 and limx→0 g(x)=3, then evaluate the following limit:
limx→0 f(x−1)g(x)=
2. If you know that limx→4 f(x)=3 and limx→0 g(x)=−5, then evaluate the following limit:
limx→0 f(x+4)+g(x)=

Answer:

B

Step-by-step explanation:

Answer B is the result of simplifying

The range of the situation is 30 to 55.

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used when you do not know the exact number in a calculation.

Given:

A vinyl decal shop charges a set-up fee of $25.00

$5.00 for each decal printed.

as, f(x)=5x+25 represents the total cost of the set-up fee

we have 6 cheerleaders

put x= 1

5x+25 = 5+25 = 30

and x=6

5x+25= 5*6+25= 30+25= 55

Hence, the range is 30 to 55.

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The polynomial function will be y = (x⁴-14x³+70x²-144x+104)

2 and 5+i are the roots of the given polynomial and the multiplicity of 2 and 5+i are 2 and 1 respectively.

Thus, the general form of the polynomial will be given as:

y = (x-2)² (x-(5+i)) (x-(5-i))                                  [as (5-i) is conjugate of (5+i)]

y = (x²+4-4x) (x-5-i) (x-5+i)

y = (x²-4x+4) (x²-5x+xi-5x+25-5i-xi+5i-i²)

y = (x²-4x+4) (x²-10x+25+1)                                            [as i²= -1]

y = (x²-4x+4) (x²-10x+26)  

y = (x⁴-10x³+26x²-4x³+40x²-104x+4x²-40x+104)

y = (x⁴-14x³+70x²-144x+104)

Thus, the polynomial is y = (x⁴-14x³+70x²-144x+104)

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The circumference of a circle with radius, r = 9.5m is 19π

What is circumference of circle?

The perimeter of a circle or ellipse is its circumference. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter.

What does a circle's circumference mean?

The complete length of a circle's arc is known as its circumference. The circumference of the circle is another name for it. The radius of the circle is the distance measured from any point on the circle to its center.

Given,

radius of the circle = 9.5m

The formula to calculate the circumference is -

C = 2πr

where r = radius of the circle

⇒ 2 × π × 9.5

⇒ 19π

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The given bounded region is the set

[tex]R = \left\{(x,y) ~:~ 0 \le x \le 1 \text{ and } x^4 \le y \le x^{1/4} \right\}[/tex]

assuming the curves are [tex]y=x^4[/tex] and [tex]x=y^4\implies y=x^{1/4}[/tex] (since [tex]x>0[/tex] in the first quadrant).

The coordinates of the centroid are [tex](\bar x, \bar y)[/tex] where [tex]\bar x[/tex] and [tex]\bar y[/tex] are the average values of [tex]x[/tex] and [tex]y[/tex], respectively, over the region [tex]R[/tex]. These are given by the ratios

[tex]\bar x = \dfrac{\displaystyle \iint_R x \, dA}{\displaystyle \iint_R dA} \text{ and } \bar y = \dfrac{\displaystyle \iint_R y\,dA}{\displaystyle \iint_R dA}[/tex]

Compute the area of [tex]R[/tex].

[tex]\displaystyle \iint_R dA = \int_0^1 \int_{x^4}^{x^{1/4}} dy \, dx \\\\ ~~~~~~~~ = \int_0^1 \left(x^{1/4} - x^4\right) \, dx \\\\ ~~~~~~~~ = \frac45 - \frac15 = \frac35[/tex]

Integrate [tex]x[/tex] and [tex]y[/tex] over [tex]R[/tex].

[tex]\displaystyle \iint_R x \, dA = \int_0^1 \int_{x^4}^{x^{1/4}} x \, dy \, dx \\\\ ~~~~~~~~ = \int_0^1 x \left(x^{1/4} - x^4\right) \, dx \\\\ ~~~~~~~~ = \int_0^1 \left(x^{5/4} - x^5\right) \, dx \\\\ ~~~~~~~~ = \frac49 - \frac16 = \frac5{18}[/tex]

[tex]\displaystyle \iint_R y \, dA = \int_0^1 \int_{x^4}^{x^{1/4}} y \, dy \, dx \\\\ ~~~~~~~~ = \frac12 \int_0^1 \left((x^{1/4})^2 - (x^4)^2\right) \, dx \\\\ ~~~~~~~~ = \frac12 \int_0^1 \left(x^{1/2} - x^8\right) \, dx \\\\ ~~~~~~~~ = \frac12 \left(\frac23 - \frac19\right) = \frac5{18}[/tex]

Then the centroid's coordinates are

[tex]\bar x = \dfrac{\frac5{18}}{\frac35} = \boxed{\frac{25}{54}} \approx 0.463[/tex]

[tex]\bar y = \dfrac{\frac5{18}}{\frac35} = \boxed{\frac{25}{54}}[/tex]

There are 7 rabbits sold for $7 and 13 rabbits sold for $11.

Substitution method:

In the substitution method, we must substitute the value of one given variable in terms of the other given variable and find the solution.

Given,

A pet shop sold 20 rabbits for $192.

Some of the rabbits sold for $7 each and the rest for $11 each.

Here we need to find the number of rabbits sold in each case.

Let us consider x be the number of rabbits sold for $7 and y be the number of rabbits sold for $11.

We know that, the total number of rabbits sold = 20.

So, it can be written as,

=> x + y = 20

Here we have to rewritten this equation as,

=> x = 20 - y ----------------------(1)

We know that, total amount for sold rabbits = 192

So, it can be written as,

=> 7x + 11y = 192 -----------------------(2)

Apply the value of x to equation (2),

Then we get,

=> 7(20 - y) + 11y = 192

=> 140 - 7y + 11y = 192

=> 4y + 140 = 192

=> 4y = 192 - 140

=> 4y = 52

=> y = 52/4

=> y = 13.

Apply the value of y on the equation (1),

Then we get,

=> x = 20 - y

=> x = 20 - 13

=> x = 7

Therefore, there are 7 $7 rabbits and 13 $11 rabbits are sold.

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The ratio of circumference/diameter for all circles is π. And the ratio of force/mass for all freely-falling bodies will be g.

Let d be the diameter of the circle. The circumference of the circle will be

C = πd units

The ratio of circumference to diameter for all circles is pie.

C/D = πd / d

C/D = π

Then the ratio of force to mass for all freely-falling bodies will be

The force acting on a free-falling body of mass (m) is mg. Then we have

Force/Mass = mg / m

Force/Mass = g

Where g is the acceleration due to gravity.

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We get the values of m as 1 and n as 0.

We are given a function:

f(x) = m / (x - 1) + n

We are also given that:

f (-2) = 1 and f (4) = 3

We have to find the value of m and n.

f (-2) = m (2 - 1) + n

1 = m + n

n = 1 - m

f (4) = m / (4 - 1) + n

3 = 3 m + n

3 = 3 m + 1 - m

3 = 2 m + 1

2 m = 3 - 1

2 m = 2

m = 2 / 2

m = 1

m + n = 1

1 + n = 1

n = 0.

Therefore, we get the values of m as 1 and n as 0.

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20/100

That is the answer if u want it simplified it is 1/5

Answer:

20/100 simplified is 1/5

Step-by-step explanation:

it is the fraction form

Answer:

LCM = 240

GCF = 8

Step-by-step explanation:

Least common multiple (LCM) is the smallest number that both 40 and 48 go into

Greatest common factor (GCF) is the largest number that can go into 40 and 48.

Answer: 9x^2-9x-10 ==> D

Step-by-step explanation:

(3x+2)(3x-5)=

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

9x^2 - 5(3x) + 6x - 5(2)=

9x^2-15x+6x-10=

9x^2-15x+6x-10= 9x^2-9x-10 ==> D

=================================================

Explanation:

Let's make

y = 3x+2

So we can replace the (3x+2) with y

We go from (3x+2)(3x-5) to y(3x-5)

Distribute that y term through

y(3x-5)

y(3x) + y(-5)

3xy - 5y

Then plug in y = 3x+2 and distribute two more times

3xy - 5y

3x( y ) - 5( y )

3x( 3x+2 ) - 5( 3x+2 )

3x(3x) + 3x(2) - 5(3x) - 5(2)

9x^2 + 6x - 15x - 10

9x^2 - 9x - 10

which seems to point to choice D assuming the -9 in the middle is supposed to be -9x

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

Side note: Alternative methods are the FOIL rule and the box method.

Answer:

64 and 13 I hope this helps

Step-by-step explanation:

The domain q is a set of real numbers as(0, 0.25, 0.50, 0.75, 1.00, 1.25, 1.50).

The range is going to be a set of real numbers from 0 to 6.

The domain of a function is the set of input values that we are allowed to plug into our function. This set is the x-values in a function.

The range of a function is the set of output values that the function assumes.

Now, we are told that there is a set of ordered pairs (q, T), where T is the total value of q quarters in dollars, up to $1.50 in quarters

Now, from conversions, we know that 1 quarters is equal to 0.25 dollar.

Thus, the domain q is a set of real numbers as(0, 0.25, 0.50, 0.75, 1.00, 1.25, 1.50).

The maximum output value will be; 1.5/0.25 = 6

Meanwhile, the range is going to be a set of real numbers from 0 to 6.

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(2x6)^3/2  in it's simplest form is equal to 41.56. See the computation below.

Using BODMAS, we say

(2 x 6) = 12

12^(3/2)

= 41.5692

[tex]$\approx$[/tex] 41.56

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The solution to the expression is x= 18

15 over x=2 equals 3 over 4 can be written as follows

15/x+2 = 3/4

Cross multiply both sides

15×4= 3(x+2)

60= 3x +6

collect the like terms

3x= 60-6

3x= 54

divide both sides by the coefficient of x which is 3

3x/3 = 54/3

x= 18

Hence the value of x in the expression is 18

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The slope of the line shown is 1/5, and being parallel means having the same slope. So it’s either a or b.

Next, you plug in (-2, 2) into y=1/5x+b to find b.

Solving you get: 2=1/5 * -2 +b

2=-2/5+b

B=2 2/5

12/5 = 2 2/5

So the answer is b.

Hope this helps!