Select the correct answer. What is the factored form of 24y5 + 3y?? A. 3y2(2y- 1)(4y2 + 2y + 1) B. 3y2(2y + 1)(4y2 - 2y + 1) C. (2y + 1)2(4y2 - 2y+ 1) D. (2y-1)2(4y2 + 2y + 1)​

Answer:

The instantaneous rate of change as x approaches 3 is 18.

Step-by-step explanation:

From Differential Calculus and Geometry we remember that instantaneous rate of change of the function is represented by a tangent line, whose slope is determined by the first derivative of the curve. Let [tex]f(x) = 3\cdot x^{2}[/tex], the instantaneous rate of change of the function when x approaches 3 is deducted from the definition of derivative:

[tex]f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex] (1)

[tex]f'(x) = \lim_{h\to 0} \frac{3\cdot (x+h)^{2}-3\cdot x^{2}}{h}[/tex]

[tex]f'(x) = \lim_{h\to 0} \frac{3\cdot (x^{2}+2\cdot x\cdot h +h^{2})-3\cdot x^{2}}{h}[/tex]

[tex]f'(x) = \lim_{h\to 0} \frac{3\cdot x^{2}+6\cdot x\cdot h+3\cdot h^{2}-3\cdot x^{2}}{h}[/tex]

[tex]f'(x) = \lim_{h\to 0} \frac{6\cdot x\cdot h +3\cdot h^{2}}{h}[/tex]

[tex]f'(x) = \lim _{h\to 0} (6\cdot x+3\cdot h)[/tex]

[tex]f'(x) = 6\cdot x \cdot \lim_{h\to 0} 1 + 3\cdot \lim_{h\to 0} h[/tex]

[tex]f'(x) = 6\cdot x[/tex] (2)

If we know that [tex]x = 3[/tex], then the instantaneous rate of change as x approaches 3 is:

[tex]f'(3) = 6\cdot (3)[/tex]

[tex]f'(3) = 18[/tex]

The instantaneous rate of change as x approaches 3 is 18.

Answer:

[tex]T_n = 8+ 4n[/tex]

[tex]T_{11} = 52[/tex]

Step-by-step explanation:

Given

[tex]Sequence: 12, 16, 20, 24[/tex]

Solving (a): Write a formula

The above sequence shows an arithmetic progression

Hence:

The formula can be calculated using:

[tex]T_n = a + (n - 1) d[/tex]

In this case:

[tex]a = First\ Term = 12[/tex]

Difference (d) is difference of 2 successive terms

So:

[tex]d = 16 - 12 = 20 - 16 = 24 - 20[/tex]

[tex]d = 4[/tex]

Substitute 4 for d and 12 for a in [tex]T_n = a + (n - 1) d[/tex]

[tex]T_n = 12 + (n - 1) * 4[/tex]

Open Bracket

[tex]T_n = 12 + 4n - 4[/tex]

Collect Like Terms

[tex]T_n = 12 - 4+ 4n[/tex]

[tex]T_n = 8+ 4n[/tex]

Hence, the explicit formula is: [tex]T_n = 8+ 4n[/tex]

Solving (b): 11th term

This implies that n = 11

Substitute 11 for n in: [tex]T_n = 8+ 4n[/tex]

[tex]T_{11} = 8+ 4 * 11[/tex]

[tex]T_{11} = 8+ 44[/tex]

[tex]T_{11} = 52[/tex]

Answer:

A) The explicit formula for the sequence is [tex]f(n) = 12+4\cdot n[/tex], [tex]n \in \mathbb{N}_{O}[/tex].

B) The 11th term of the sequence is 62.

Step-by-step explanation:

A) Let [tex]f(0) = 12[/tex], we notice that sequence observes an arithmetic progression, in which there is a difference of 4 between two consecutive elements. The formula for arithmetic progression is:

[tex]f(n) = f(0) +r\cdot n[/tex] (1)

Where:

[tex]f(0)[/tex] - First value of the sequence, dimensionless.

[tex]r[/tex] - Arithmetic increase rate, dimensionless.

[tex]n[/tex] - Term of the value in the sequence, dimensionless.

If we know that [tex]f(0) = 12[/tex] and [tex]r = 4[/tex], then the explicit formula for the sequence is:

[tex]f(n) = 12+4\cdot n[/tex], [tex]n \in \mathbb{N}_{O}[/tex]

B) If we know that [tex]f(n) = 12+4\cdot n[/tex] and [tex]n = 10[/tex], the 11th term of the sequence is:

[tex]f(10) = 12+4\cdot (10)[/tex]

[tex]f(10) = 62[/tex]

The 11th term of the sequence is 62.

Answer:

See steps below

Step-by-step explanation:

WS ⊥ MH , HS = SM ......... Given

<HSW = <MSW = 90  .....  From WS ⊥ MH

Triangle HWS = Triangle WMS .... SAS  theorem

<M = <H  .... based on triangle congruency, and angle opposed to equal side WS

Answer:

280

Step-by-step explanation:

Month 1: 100 + 30 = 150

Month 2: +30

Month 3: +30

Month 4: +30

Month 5: +30

Month 6: +30

Total: 280

Hope this helps!

Answer:

$280

Step-by-step explanation:

For this problem, we simply need to take the initial cost of membership and add that to the reoccurring cost from a time period, in this case, 6 months.  So let's make an equation to represent this.

The initial cost is $100

The per month cost is $30

Total cost after 6 months = Inital cost + Per Month Cost * 6 months

Total cost = $100 + $30 * 6

Total cost = $100 + $180

Total cost = $280

Thus, a member will spend $280 after 6 months on the membership.

Cheers.

Answer:

 [tex]y= -\frac{1}{3}x -6[/tex]

Step-by-step explanation:

Using the slope formula, you can form this equation! The slope of any equation would replace the m, and the y intercept would replace b!

I added in the slope formula at the bottom, just in case, so you'll see what I mean!

I hope this helps, and I explained enough! Have a great day c:

Answer:

5

Step-by-step explanation:

Answer:

Less Than :)

Step-by-step explanation:

Answer:

a: -6

Step-by-step explanation:

[tex]\sqrt{5(-6)+6} =\sqrt{-24} = -6\\[/tex]

This equation is not correct, therefore A is not a root and is extraneous

Answer:

so what is the question?

Answer:

y = 4/5x

Step-by-step explanation:

Her ya go!

Answer:

4350

Step-by-step explanation:

Linda's net and first term of the expression is correct and the surface area of the attic is 4425 square feet.

The area of a three dimensional object on it's outer surface is called the surface area of the object.

Given the attic of Linda's home.

Attic is in the shape of triangular prism.

The net that Linda drawn is correct since she expresses all the measurements right in the net.

So, the net Linda drew is correct.

We can find the surface area from the net of the prism.

Net of the prism consists of 2 identical triangles, 2 identical rectangles and a rectangle.

Area of triangle is  [tex]\frac{1}{2}[/tex] × base × height and that of rectangle = length × width

Area of 2 triangles = 2 × [tex]\frac{1}{2}[/tex] × 25 × 15 = 25 × 15

Area of rectangles = (45 × 40) + (45 × 25) + (45 × 25)

                               = 45(40 + 25 + 25)

Total surface area = 45(40 + 25 + 25) + (25 × 15)

The first term of Linda's expression, 45(40 + 25 + 25) is correct.

The second term of Linda's expression, ([tex]\frac{1}{2}[/tex] × 25 × 15) is not correct.

Surface area of the attic = 45(40 + 25 + 25) + (25 × 15)

                                        = 4425 square feet

Hence the surface area of the attic is 4425 square feet.

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The complete question is given below.

Answer:

A) None of the above

Step-by-step explanation

it's distributive property

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

A right turn represents a clockwise rotation of the direction vector by 90°. It is equivalent to multiplying the complex number representation by -i.

A left turn represents a counterclockwise rotation of the direction vector by 90°. It is equivalent to multiplying the complex number representation by i.

The attached table shows the desired values and expressions.

Step-by-step explanation:

[tex]\boxed{\begin{array}{c|c|c} \underline{Intial -d} & \underline {Left-turn} & \underline{Right-turn} \\ -1 & -i & i \\ 1 & i & -i \\ i & -1 & 1\\ -i & 1 & -1 \\ d & di & -di \end{array}}[/tex]

Answer:

x=5

Both are vertical lines and parallel to each other.

Answer:

Step-by-step explanation:

6x+9=63

6x=63-9

6x=54

x=54/6

x=9

I encourage you to figure out the justification yourself.

Answer:

S(-2, -3)

Step-by-step explanation:

Find the diagram attached below,=. Frim the diagram, the coordinate of R and T are (-5, 3) and (-1, -5) respectively. If the ratio of RS to ST is 3:1, the coordinate of S can be gotten using the midpoint segment formula as shown;

S(X, Y) = {(ax1+bx2/a+b), (ay1+by1/a+b)} where;

x1 = -5, y1 = 3, x2 = -1, y2 = -5, a = 3 and b =1

Substitute the values into the formula;

X = ax2+bx1/a+b

X = 3(-1)+1(-5)/3+1

X = -3-5/4

X = -8/4

X = -2

Similarly;

Y = ay2+by1/a+b

Y = 3(-5)+1(3)/3+1

Y = -15+3/4

Y = -12/4

Y = -3

Hence the coordinate of the point (X, Y) is (-2, -3)

Answer:

a. 50 - 4h < 32

Step-by-step explanation:

The question is "When will the temperature be below 32F?" so it can't be less than or equal to (≤), it has to be less than (<).

If the temperature is decreasing every hour you have to decrease 4 for each hour.

hope that helps!

Answer:

The anti-derivative of f(x) will be:

[tex]\int \:10x^4+12.5dx=2x^5+12.5x+C[/tex]

Step-by-step explanation:

Given the function

[tex]\:f\left(x\right)=10x^4\:+\:12.5[/tex]

Taking the anti-derivative of f(x)

[tex]\int \left(10x^4\:+\:12.5\right)\:dx\:[/tex]

[tex]\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx[/tex]

[tex]\int \left(10x^4\:+\:12.5\right)\:dx\:=\int \:10x^4dx+\int \:12.5dx[/tex]

Solving

[tex]\int 10x^4dx[/tex]

[tex]\mathrm{Take\:the\:constant\:out}:\quad \int a\cdot f\left(x\right)dx=a\cdot \int f\left(x\right)dx[/tex]

[tex]=10\cdot \int \:x^4dx[/tex]

[tex]\mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1[/tex]

[tex]=2x^5[/tex]

similarly,

[tex]\int 12.5dx[/tex]

[tex]\mathrm{Integral\:of\:a\:constant}:\quad \int adx=ax[/tex]

[tex]=12.5x[/tex]

so substituting these values

[tex]\int \left(10x^4\:+\:12.5\right)\:dx\:=\int \:10x^4dx+\int \:12.5dx[/tex]

                                [tex]=2x^5+12.5x[/tex]

                               [tex]=2x^5+12.5x+C[/tex]   ∵ Add constant to the solution

Therefore, the anti-derivative of f(x) will be:

[tex]\int \:10x^4+12.5dx=2x^5+12.5x+C[/tex]

Answer:

Is this in a different language?

Step-by-step explanation:ok:)

Answer: Add 11 to the other side of the equation, giving you 81. Then, since x is square you are going to need to square root both sides ([tex]\sqrt{x}[/tex] this symbol). When you do that, you should get what x is! Let me know if you still need help!

Answer:

68≥25+3x

x≥15

Step-by-step explanation:

the overall goal is to have $68, so the goal needs to be less then or equal to the weekly $25 plus each additional subscription at $3 (x represents the needed amount of subscriptions he sells) the inequality would look something like 68≥25+3x because he wants the money this week.

to solve the inequality you would subtract the 25 from the 68, leaving you with 43≥3x as the new inequality, now you need to divide both sides by 3. Which comes out to 14.33333..... since we cant sell a fraction of a subscription you must round up giving you the new inequality of x≥15

this means that in order for Andre to get the cleats this week, he must sell at least 15 subscriptions

hope this helped

a.)   25x + 3y ≥ 68

b.) x = 1, y = 43

c.) As x increases, y decreases

A linear inequality is a mathematical relation which gives the range of values a variable or a function can take.

Given,

Wage per week= $25

Subscription earning = $3

Let x and y be the number of weeks and number of subscriptions.

Therefore, 25x + 3y ≥ 68

Hence, 25x + 3y ≥ 68 is the required inequality.

Let x = 1

Therefore  minimum value of y = 43.

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Answer:

The data is not appropriately normal.

Step-by-step explanation:

In inferential statistics, a normal distribution is said to be symmetric and should be single-peaked when working with a random selection of a large sample.

The high number of the sample is 100 which is further from other samples, the central limit theorem explains that the sample size of independent mean must be large enough to mimic the population for the sample to be normal or nearly normal. So, the sample is not appropriately normal and should be larger in size.

Answer:

The values of a and b are:

Step-by-step explanation:

Given the exponential model

[tex]y=a\cdot \:b^x[/tex]

Given the points

(0, 2) and (3, 128)

We know that the y-intercept of [tex]y=a\cdot \:b^x[/tex] is (0, a).

so

a = 2

putting x = 3, y = 128 and a = 2

[tex]y=a\cdot \:b^x[/tex]

[tex]128=2\cdot \:b^3[/tex]

Switching sides

[tex]2b^3=128[/tex]

[tex]\frac{2b^3}{2}=\frac{128}{2}[/tex]

[tex]b^3=64[/tex]

Taking the real value such as:

[tex]\mathrm{For\:}x^3=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt[3]{f\left(a\right)}[/tex]

so

[tex]b=\sqrt[3]{64}[/tex]

[tex]b=\sqrt[3]{4^3}[/tex]

[tex]b=4[/tex]

Therefore,

Answer:

he will fill 6 pitchers

Step-by-step explanation:

4.8÷0.8=6

Answer:

Two complex (imaginary) solutions.

Step-by-step explanation:

To determine the number/type of solutions for a quadratic, we can evaluate its discriminant.

The discriminant formula for a quadratic in standard form is:

[tex]\Delta=b^2-4ac[/tex]

We have:

[tex]3x^2+7x+5[/tex]

Hence, a=3; b=7; and c=5.

Substitute the values into our formula and evaluate. Therefore:

[tex]\Delta=(7)^2-4(3)(5) \\ =49-60\\=-11[/tex]

Hence, the result is a negative value.

If:

Since our discriminant is negative, this means that for our equation, there exists two complex (imaginary) solutions.

Answer:

Getting my point back lol

Step-by-step explanation:

Answer:

x = 16

m<Y = 34°

Step-by-step explanation:

∆XYZ is an isosceles ∆. An isosceles ∆ has two equal sides, as well as the bases of the isosceles triangle are congruent. In this case, therefore:

<X = <Z

(6x - 23)° = (4x + 9)

Solve for x

6x - 23 = 4x + 9

Collect like terms

6x - 4x = 23 + 9

2x = 32

Divide both sides by 2

x = 16

m<Y = 180° - (m<X + m<Z) (sum of ∆)

m<Y = 180 - ((6x - 23) + (4x + 9))

Plug in the value of x

m<Y = 180 - ((6(16) - 23) + (4(16) + 9))

m<Y = 180 - (73 + 73)

m<Y = 34°

Answer:

$14.4

Step-by-step explanation:

I don't quite understand this question, but this is what I think