evaluate the expression when b=5

Step-by-step explanation:

Let [tex]P_1(-1, -8)\:\text{and}\:P_2(-4, -9)[/tex]

The slope of the line through these two points is

[tex]m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{(-9 + 8)}{(-4 + 1)} = \dfrac{1}{3}[/tex]

So the slope-intercept form of the line passing through the two points is

[tex]y = mx + b = \frac{1}{3}x + b[/tex]

To find b, we use either point into our equation. Let's use (-1, -8):

[tex]-8 = \frac{1}{3}(-1) + b \Rightarrow b = -\dfrac{23}{3}[/tex]

Therefore, the slope-intercept form of the equation for the line is

[tex]y = \dfrac{1}{3}x - \dfrac{23}{3}[/tex]

The standard form of the equation can be written as

[tex]x + 3y + 23 = 0[/tex]

Answer:

Step-by-step explanation:

(4c1×6c4)+(4c2×6c3)+(4c3×6c2)+(4c4×6c1)

(4×15) +(6×20) +(4×15) +(1×6)

60+120+60+6

246 ways

[tex] \large \mathfrak{Solution : }[/tex]

Answer:

initial population : 89

after 9 years : 676

Step-by-step explanation:

no need for panic. this is just plain calculator mechanics. yes, we need to do some more complicated typing and use e, but it is still only typing.

the initial population is P(0). or t = 0.

simply when there were 0 years since the fish were added.

that is simple.

we get (as -0.42×0 = 0)

800 / (1 + 8e⁰) = 800 / (1+8×1) = 800 / 9 ≈ 89

now, after 9 years we have to calculate P(9). or t=9.

let's pre-calculate : -0.42×9 = -3.78

e to the power of -3.78 = 0.022822691...

8 times this is 0.182581531...

and plus 1 is 1.182581531...

800 / 1.182581531... = 676.486127 ≈ 676

Answer:

[tex]\displaystyle \lim_{x\rightarrow 0^{+}} \frac{x\ln x}{\tan x}=-\infty\implies \text{B. Nonexistent (best answer)}[/tex]

Step-by-step explanation:

Recall L'Hopital's rule:

[tex]\displaystyle \lim_{x\rightarrow c}\frac{f(x)}{g(x)}=\lim_{x\rightarrow c}\frac{f'(x)}{g'(x)}[/tex]

First derivative of [tex]x\ln x[/tex]:

Recall the product rule:

[tex](f\cdot g)'=f'\cdot g+g'\cdot f[/tex]

[tex]\displaystyle \frac{d}{dx} (x\ln x)=\frac{d}{dx}(x)\cdot \ln (x)+\frac{d}{dx}(\ln x)\cdot x[/tex]

Note that:

[tex]\displaystyle \frac{d}{dx}(x)=1,\\\frac{d}{dx}(\ln (x))=\frac{1}{x}[/tex]

Simplifying, we get:

[tex]\displaystyle \frac{d}{dx} (x\ln x)=1\cdot \ln x+\frac{1}{x}\cdot x,\\\frac{d}{dx}(x\ln x)=\ln x+1[/tex]

First derivative of [tex]\tan x[/tex]:

[tex]\displaystyle \frac{d}{dx}(\tan x)=\sec^2 x[/tex]

Therefore, we have:

[tex]\displaystyle \lim_{x\rightarrow 0^{+}}\frac{x\ln x}{\tan x}=\lim_{x\rightarrow 0^{+}}\frac{\ln x+1}{\sec^2{x}}[/tex]

By definition, [tex]\cos x=\frac{1}{\sec x}[/tex]. Therefore,

[tex]\displaystyle \lim_{x\rightarrow 0^{+}}\frac{x\ln x}{\tan x}=\lim_{x\rightarrow 0^{+}}\frac{\ln x+1}{\sec^2{x}}=\lim_{x\rightarrow 0^{+}}\cos^2x(\ln x+1)[/tex]

Note:

[tex]\displaystyle \lim_{x\rightarrow 0^{+}}\cos^2x=1,\\\lim_{x\rightarrow 0^{+}}\ln x+1=-\infty[/tex]

Substitute:

[tex]\displaystyle \lim_{x \rightarrow0^{+}} \cos^2x(\ln x+1)=1\cdot (-\infty)=-\infty[/tex]

Therefore, we have:

[tex]\displaystyle \lim _{x\rightarrow 0^{+}}\frac{x\ln x}{\tan x}=-\infty \text{}[/tex], which best corresponds with [tex]\boxed{\text{B. Nonexistent}}[/tex]

*Commentary:

Technically speaking, a limit exists only if it is equal to a real number. By proper definition, infinity is not a number. With that being said, you will see limits expressed as infinity or negative infinity.

Here's what I will say about this specific problem.

The problem is stipulating that we approach [tex]x[/tex] from the right side. Because of this condition, it may be unorthodox to say this limit doesn't exist. However, if the problem just asked for [tex]\displaystyle \lim_{x\rightarrow 0}\frac{x\ln x}{\tan x}[/tex], it is common and preferred to say this limit does not exist, since [tex]\displaystyle \lim_{x\rightarrow 0^{-}}\frac{x\ln x}{\tan x}\neq \displaystyle \lim_{x\rightarrow 0^{+}}\frac{x\ln x}{\tan x}[/tex].

For example, [tex]\displaystyle \lim_{x\rightarrow 0}\frac{1}{x}=\text{DNE}[/tex], because [tex]\displaystyle \lim_{x\rightarrow 0}\frac{1}{x}[/tex] diverges. In other words, [tex]\displaystyle \lim_{x\rightarrow 0^{-}}\frac{1}{x}=-\infty \neq \displaystyle \lim_{x\rightarrow 0^{+}}\frac{1}{x}=\infty[/tex].

But again, the problem is asking for the limit as [tex]x[/tex] approaches from the right, in which case [tex]\displaystyle \lim _{x\rightarrow 0^{+}}\frac{x\ln x}{\tan x}=-\infty }[/tex]. It's really a pedagogical choice whether to say a limit equal to infinity or negative infinity exists or not since infinity implies there is no limit, so saying the limit of something is infinity becomes an oxymoron. In this case, the person who wrote the answer choices chose to express a limit of infinity as nonexistent, but it is worth mentioning that someone else solving this problem might express [tex]-\infty[/tex] as the answer, and they would be just as, if not more, correct.

Without resorting to L'Hopital's rule, recall that

[tex]\displaystyle \lim_{x\to0}\frac{\sin(ax)}{ax} = 1[/tex]

for a ≠ 0. Then

[tex]\displaystyle \lim_{x\to0^+} \frac{x \ln(x)}{\tan(x)} = \lim_{x\to0^+}\frac x{\sin(x)} \times \lim_{x\to0^+}\cos(x) \times \lim_{x\to0^+}\ln(x)[/tex]

The first two limits exist and are equal to 1, but the last limit is -∞.

9a^2 - 9

Uejdjeujdksjdndkdkdk

Answer:

x=-5,6

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

HAVE A GREAT DAY

Answer:

20.

Step-by-step explanation:

when you add how far Kyle's already traveled you get sixty, the rest of the lecture explains the rest, leaving you with 20 seconds. Lol.

Answer:

100,000 x $15 = 1.5 million US$

Answer

4

Step by step explanation

2/3=x/10-x

cross multiply

2(10-x)=3x

20-2x=3x

20=3x+2x

20=5x

x=4

Answer:

1/2 x > 20

Step-by-step explanation:

Let x be the unknown number

1/2 x > 20

Answer:

z = 40 + 26.00x + 15.00y

Coefficients: 26.00, 15.00

Constant: 40

Variables: z, x, y

Step-by-step explanation:

Let x be the number of canoe rentals and y be the number of bicycle rentals.

(The family can hold only one annual pass, so we don't need a variable for that. Rather, we'll use a "constant." But the number of bicycle/canoe rentals can change!)

Let z be how much the family spends in a year.

The family spends $26 for each canoe rental, so

26.00x for x canoe rentals

Similarly, 15.00y for y canoe rentals

So z = 40 + 26.00x + 15.00y

The coefficients are the 26.00 and the 15.00. Coefficients are the numbers attached to the variables.

The constant is 40. A constant is a number by itself.

The variables are z, x, and y. Variables are our unknowns.

Answer:

is this u want?

Step-by-step explanation:

if no so sorry..

Answer:

4.5m

Step-by-step explanation:

The formula for triangle is

1/2 x base x height = area

1/2 x 3 x h = 6.75m

h = 6.75 ÷3÷1/2

h = 4.5m

Graphs can be created by inputting data in MS Excel and choosing a chart type that represents the type of data to display

Please find attached the required graph of the function of the Incidence of mumps (cases per 100,000 people)

The known data for the incidence of mumps is presented in the following table;

[tex]\begin{array}{|c|cc|}Year&&Incidence \ of \ Mumps \ per \ 100,000 \ People\\1984&&1\\1985&&1\\1987&&5.5\\1988&&2\\1989&&2.5\\1999&&0.1\\2004&&0.1\end{array}[/tex]

The data from the above table can be entered in MS Excel and a graph can be plotted as follows;

Please find attached the required graph created with MS Excel

Learn more about plotting graphs here:

https://brainly.com/question/20623868

Answer:

maybe but (-4,2) only because the -4 is in the x place (x,y)

Step-by-step explanation:

Ordered pair usually refers to a set of two numbers used to locate a point in a coordinate plane. When an ordered pair refers to the location of a point in the coordinate plane, they are called the coordinates of the point.

Answer:

90

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

10 x 9 = 90 which is what the question asked but. re worded

Answer:

[tex] \frac{3}{50} [/tex]

Step-by-step explanation:

[tex] \frac{1}{5} \times \frac{3}{10} [/tex]

➡️ [tex] \frac{1 \times 3}{5 \times 10} [/tex]

➡️ [tex] = \frac{3}{50} [/tex] ✅

Answer:

tea

Step-by-step explanation:

just cuz lol

Answer:

Gin

Step-by-step explanation:

Answer:

p = k(d)/u^2

Step-by-step explanation:

BRAINLIEST, PLEASE!

Answer:

[tex] \sqrt{5} \times \sqrt{10} \\ = \sqrt{5} \times \sqrt{2 \times 5} \\ = \sqrt{5} \times \sqrt{2} \times \sqrt{5} \\ = 5 \sqrt{2} \\ thank \: you[/tex]

Answer:

x = 3^2

Step-by-step explanation:

2x^2 = 18

x^2 = 18 / 2

x^2 = 9

x = √9

= 3

Answer:

C

Step-by-step explanation:

The volume of a box (rectangular prism) is given by:

[tex]\displaystyle V = \ell wh[/tex]

We are given that the desired volume is 540 cubic inches. The width is three inches longer than the length and the height is four inches longer than the length. Substitute:

[tex]\displaystyle (540) = \ell(\ell + 3)(\ell + 4)[/tex]

Solve for the length. Expand:

[tex]\displaystyle \begin{aligned} 540 &= \ell (\ell^2 + 7\ell +12) \\ 540&= \ell ^3 + 7\ell^2 +12\ell \\ \ell^3 + 7\ell ^2 +12\ell -540 &= 0\end{aligned}[/tex]

We cannot solve by grouping, so we can consider using the Rational Root Theorem. Our possible roots are:

±1, ±2, ±3, ±4, ±5, ±6, ±9, ±10, ±12, ±15, ±18, ±20, ±27, ±30, ±36, ±45, ±54, ±60, ±90, ±108, ±135, ±180, ±270, and/or ±540.

(If you are allowed a graphing calculator, this is not necessary.)

Testing values, we see that:

[tex]\displaystyle (6)^3 +7(6)^2 + 12(6) -540 \stackrel{\checkmark}{=} 0[/tex]

Hence, one factor is (x - 6).

By synthetic division (shown below), we can see that:

[tex]\displaystyle \ell^3 + 7\ell^2 +12\ell -540 =(\ell -6)(\ell ^2 + 13\ell +90)[/tex]

The second factor has no real solutions. Hence, our only solution is that l = 6.

In conclusion, our answer is C.

Answer:

6 inches

Step-by-step explanation:

I just took the test

Answer:

7.5 -ln(0.25)

Step-by-step explanation:

We can first graph this function. Looking at the graph, we can separate this into two ranges -- from x=0.25 to x=1 and from x=1 to x=4.

From x=0.25 to x=1, we want to find the area above y=1/x and below y=4. To do this, we can take the integral of y=4 from x=0.25 to x=1 to encompass the whole area under y=4 from that range. Then, we subtract the area under y=1/x as we don't need that (we only want what's above it). Therefore, we have

[tex]\int\limits^{1}_{0.25}{4} \, dx - \int\limits^{1}_{0.25} {1/x} \, dx \\= 4(1) - 4 (0.25) - (ln(1) - ln(0.25))\\= 4 - 1 - ln(1) + ln(0.25)\\= 3 - ln(1) + ln(0.25)[/tex]

Next, we know that ln(x/y) = ln(x) - ln(y), so ln(0.25) - ln(1) = ln(0.25/1) = ln(0.25), so we have

3 - ln(0.25)

For x=1 to x=4, we want to find the area above y=x and below y=4. We can apply a similar strategy, subtracting the area below y=x from the area below y=4 to get

[tex]\int\limits^{4}_{1}{4} \, dx - \int\limits^{4}_{1} {x} \, dx \\ \\= 4(4) - 4(1) - (4^{2} /2 - 1^2/2)\\= 16 - 4 - 8 + 0.5\\= 4.5[/tex]

Add these two areas up to get

3-ln(0.25) + 4.5 = 7.5 -ln(0.25)

Answer: 7 bags.

Step-by-step explanation:

Since the baker needs 56 apples, he needs to buy enough apples to fulfill his recipe. Since each bag contains 8 apples, he must divide 56/8, in this case yielding 7.

Answer:

7 bags

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

HAVE A GREAT DAY

Hence commission will be 7%

[tex]\\ \rm\longmapsto 23458\times \dfrac{7}{100}[/tex]

[tex]\\ \rm\longmapsto \dfrac{164206}{100}[/tex]

[tex]\\ \rm\longmapsto 1642.06[/tex]

Vito Avido's commission on $23,458 in sales is $1466.06.

Here, we have to calculate Vito Avido's commission on $23,458 in sales, we'll break down the sales amount into different ranges and apply the respective commission rates for each range.

For the first $5,000 of sales: 5% commission

Commission = 5% of $5,000 = 0.05 * $5,000 = $250

For the next $15,000 of sales: 6.5% commission

Commission = 6.5% of $15,000 = 0.065 * $15,000 = $975

For the remaining amount over $20,000: 7% commission

Sales above $20,000 = $23,458 - $20,000 = $3,458

Commission = 7% of $3,458 = 0.07 * $3,458 = $241.06

Now, add up the commissions from each range:

Total Commission = $250 + $975 + $241.06 = $1466.06

Vito Avido's commission on $23,458 in sales is $1466.06.

To learn more on percentage click:

brainly.com/question/13450942

#SPJ3

Answer:

4 2/4 2/3 3/4 5/8

Step-by-step explanation:

Answer:

[tex]3x - \frac{29}{5} = - 4 \\ 3x = - 4 + \frac{29}{5} \\ 3x = \frac{ - 20 + 29}{5} \\ \\ 3x = \frac{9}{5} \\ x = \frac{9}{5} \div 3 \\ x = \frac{9}{5} \times \frac{1}{3} \\ x = \frac{3}{5} [/tex]

I hope I helped you^_^