Someone pls help I’ve been stuck on this all day and it’s due tomorrow!

The simplified expression of the function [tex]f (x)= \frac{x-4}{x^2+13x+36}[/tex] is

[tex]f (x)= \frac{x-4}{(x+9)(x+4)}[/tex]. f(x) is increasing for all x > –4

A function is defined as a relation between the set of inputs having exactly one output each.

The function expression is given as:

[tex]f (x)= \frac{x-4}{x^2+13x+36}[/tex]

Expand the denominator

[tex]f (x)= \frac{x-4}{x^2+4x+9x+36}[/tex]

Factorize the denominator

[tex]f (x)= \frac{x-4}{x(x+4)+9(x+4)}[/tex]

Factor out x + 9

[tex]f (x)= \frac{x-4}{(x+9)(x+4)}[/tex]

Hence, the simplified expression of the function [tex]f (x)= \frac{x-4}{x^2+13x+36}[/tex] is

[tex]f (x)= \frac{x-4}{(x+9)(x+4)}[/tex].  f(x) is increasing for all x > –4

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Answer: f(x) is increasing for all x > -4

Proof of validity is shown below.

since we have the area of the front side, to get its volume we can simple get the product of the area and the length, let's firstly change the mixed fractions to improper fractions.

[tex]\stackrel{mixed}{23\frac{2}{3}}\implies \cfrac{23\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{71}{3}} ~\hfill \stackrel{mixed}{4\frac{7}{8}}\implies \cfrac{4\cdot 8+7}{8}\implies \stackrel{improper}{\cfrac{39}{8}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{71}{3}\cdot \cfrac{39}{8}\implies \cfrac{71}{8}\cdot \cfrac{39}{3}\implies \cfrac{71}{8}\cdot 13\implies \cfrac{923}{8}\implies 115\frac{3}{8}~in^3[/tex]

Answer:

[tex]\dfrac{dy}{dx}=\cot x+\dfrac{1}{x}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Product\:Rule}\\\\$\dfrac{d}{dx}[f(x)g(x)]=f(x)g'(x)+f'(x)g(x)$\\\\\\\underline{Chain\:Rule}\\\\$\dfrac{dy}{dx}=\dfrac{dy}{du} \times \dfrac{du}{dx}$\\\end{minipage}}[/tex]

[tex]\textsf{Given}:y=\log (x \sin x)[/tex]

[tex]\textsf{Let }u=x \sin x \implies y=\log(u)[/tex]

Using the product rule, differentiate y with respect to [tex]u[/tex]:

[tex]\textsf{If }y=\log(u) \implies \dfrac{dy}{du}=\dfrac{1}{u}\implies \dfrac{dy}{du}=\dfrac{1}{x \sin x}[/tex]

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

Differentiate [tex]u=x \sin x[/tex] with respect to x using the product rule:

[tex]\implies \textsf{Let }f(x)=x \implies f'(x)=1[/tex]

[tex]\implies \textsf{Let }g(x)=\sin x \implies g'(x)=\cos x[/tex]

[tex]\implies \dfrac{du}{dx}=x \cos x + \sin x[/tex]

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

Use the chain rule to differentiate y with respect to x:

[tex]\implies \dfrac{dy}{dx}=\dfrac{dy}{du} \times \dfrac{du}{dx}[/tex]

[tex]\implies \dfrac{dy}{dx}=\dfrac{1}{x \sin x} \times (x \cos x + \sin x)[/tex]

[tex]\implies \dfrac{dy}{dx}=\dfrac{x \cos x + \sin x}{x \sin x}[/tex]

[tex]\implies \dfrac{dy}{dx}=\dfrac{x \cos x}{x \sin x}+\dfrac{\sin x}{x \sin x}[/tex]

[tex]\implies \dfrac{dy}{dx}=\cot x+\dfrac{1}{x}[/tex]

Answer:

[tex]\displaystyle \large{\dfrac{d}{dx}[\log(x\sin x)] = \dfrac{1}{x\ln 10} + \dfrac{\cot x}{\ln 10}}[/tex]

Step-by-step explanation:

Given:

[tex]\displaystyle \large{y=\log (x\sin x)}[/tex]

Recall the (common) logarithmic differentiation & chain rules:

[tex]\displaystyle \large{\dfrac{d}{dx}[\log (u)] = \dfrac{u'}{u\ln 10}}[/tex]

Let [tex]\displaystyle \large{u=x\sin x}[/tex] then:

[tex]\displaystyle \large{\dfrac{d}{dx}[\log(x\sin x)] = \dfrac{(x\sin x)'}{x\sin x \ln 10}}[/tex]

Recall product rules:

[tex]\displaystyle \large{[f(x)g(x)]' = f'(x)g(x)+f(x)g'(x)}[/tex]

Hence:

[tex]\displaystyle \large{\dfrac{d}{dx}[\log(x\sin x)] = \dfrac{(x)'\sin x + x(\sin x)'}{x\sin x \ln 10}}\\\\\displaystyle \large{\dfrac{d}{dx}[\log(x\sin x)] = \dfrac{\sin x + x\cos x}{x\sin x \ln 10}}\\\\\displaystyle \large{\dfrac{d}{dx}[\log(x\sin x)] = \dfrac{\sin x}{x \sin x \ln 10} + \dfrac{x \cos x}{x\sin x \ln 10}}\\\\\displaystyle \large{\dfrac{d}{dx}[\log(x\sin x)] = \dfrac{1}{x\ln 10} + \dfrac{\cot x}{\ln 10}}[/tex]

From above, recall that:

[tex]\displaystyle \large{\dfrac{d}{dx}(\sin x) = \cos x}\\\\\displaystyle \large{\dfrac{A\pm B}{C} = \dfrac{A}{C} \pm \dfrac{B}{C}}\\\\\displaystyle \large{\dfrac{\cos x}{\sin x} =\cot x}[/tex]

Hence, the answer is:

[tex]\displaystyle \large{\dfrac{d}{dx}[\log(x\sin x)] = \dfrac{1}{x\ln 10} + \dfrac{\cot x}{\ln 10}}[/tex]

The second box is less expensive to make since it has a smaller surface area and hence requires less wood to construct the sides.

It is defined as the six-faced shape, a type of hexahedron in geometry.

It is a three-dimensional shape.

Here some data is not given, so we are assuming the volume of the box is 24 cubic feet.

If the volume is 24 cubic feet, the box's three dimensions must multiply to equal 24.

We can make two designs:

2 × 2 × 6 and 2 × 3 × 4.

Now, finding the surface area for each design.

First box

SA = 2wl + 2wh + 2hl

SA = 2×2×2 + 2×2×6 + 2×2×6

SA = 56 square feet

Second box

SA = 2×2×3 + 2×2×4 + 2×3×4

SA = 52 square feet

At $4 per square foot

For 56 ft², the price is $224

For 52 ft², the price is $208

Thus, the second box is less expensive to make since it has a smaller surface area and hence requires less wood to construct the sides.

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Answer:

0.7453

Step-by-step explanation:

[tex]arcsin( \frac{4}{6} ) = 0.7297 \\ cos(0.7297) = 0.7453[/tex]

Answer:

x = 80

Step-by-step explanation:

The diagram shows that arc AB is 80 degrees, and the measure of an arc defined as being equal to the central angle(the minor angle of the arc). Because the arc AB is 80, the central angle x is 80 degrees as well. Although if point O wasn't at the center of the circle, x might not be 80.

Answer:

105cm

Step-by-step explanation:

please click crown below my answer.

Answer:\frac{2p}{7}+\frac{1}{7}

Step-by-step explanation:you have to simplify these two number thats all can give u bro

Find the amount of decay:

1200 - 900 = 300

Divide amount of decay by original amount:

300/1200 = 0.25

The percent of decay is 25 %

The decay factor is 1.00 a 0.25 = 0.75

Answer:

C. Segment AB is congruent to segment A'B'.

Step-by-step explanation:

Since ABC is being dilated by 1.5, it means that A'B'C will be bigger than ABC.

So, since A'B'C will be bigger than ABC, it sides  will also be bigger than the sides in ABC.

And since the sides/segments are bigger than the original, they are not congruent (congruent means equal).

Answer:

14 pieces

Step-by-step explanation:

Simplify 13 1/8 into fraction with denominator 16

Number of pieces

Answer: choice B

Step-by-step explanation:

Answer:

None of the answer choices.

Step-by-step explanation:

The pattern to this problem is multiply by 4, and subtract 3. However when doing 17 * 4, you get 68. Look how both of the answer chouces start with 68, and we haven't even subtracted 3 yet. This shows that the answer choices are wrong.

Correct Answer: 65, 257

The answer: ———————> 68, 257

Answer:

95 oz

Step-by-step explanation:

37 oz / 30 c   * 77 c = ~ 95 oz    (see how the 'c' cancels and you are left with 'oz' ? )

Answer:

Tank Volume/1 cubic centimeter.

Step-by-step explanation:

We dont know how big the tank is.

Answer: 4/52 = 1/13

Step-by-step explanation: We know that a full deck of cards is 52 and there are 4 suits in a deck. Which means that there are 4 queens in each deck. Now, we can add that up together which gives us 4/52, and can be simplified down to 1/13 because 4/52 isn't the smallest we can get our fraction.

Hope this helps :)

Answer:

0.077

Step-by-step explanation:

1/13 in decimal form is 0.07692307692 which rounds up to 0.077 which will be your answer.

Problem 9

The instructions aren't stated anywhere, but I'm assuming your teacher wants you to find the equation of each parabola.

The vertex here is (h,k) = (-6,-4) which you have correctly determined.

This means

[tex]y = a(x-h)^2 + k\\\\y = a(x-(-6))^2 +(-4)\\\\y = a(x+6)^2 - 4\\\\[/tex]

Next we plug in one of the other points on the parabola. We cannot pick the vertex again. Let's pick the point (-4,0) which is one of the x intercepts. We'll do this to solve for 'a'

[tex]y = a(x+6)^2 - 4\\\\0 = a(-4+6)^2 - 4\\\\0 = a(2)^2 - 4\\\\0 = a(4) - 4\\\\0 = 4a-4\\\\4a-4 = 0\\\\4a = 4\\\\a = 4/4\\\\a = 1\\\\[/tex]

This means

[tex]y = a(x+6)^2 - 4\\\\y = 1(x+6)^2 - 4\\\\y = (x+6)^2 - 4\\\\[/tex]

represents the equation of the parabola in vertex form.

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

Problem 10

The vertex is (h,k) = (-2,-6)

So,

[tex]y = a(x-h)^2 + k\\\\y = a(x-(-2))^2 + (-6)\\\\y = a(x+2)^2 - 6\\\\[/tex]

Now plug in another point on the parabola like (-1,-8) and solve for 'a'

[tex]y = a(x+2)^2 - 6\\\\-8 = a(-1+2)^2 - 6\\\\-8 = a(1)^2 - 6\\\\-8 = a(1) - 6\\\\a-6 = -8\\\\a = -8+6\\\\a = -2\\\\[/tex]

For each equation, you could optionally expand things out to get it into y = ax^2+bx+c form, but I think it's fine to leave it as vertex form.

Answer:

[tex]\textsf{9)} \quad y=(x+6)^2-4[/tex]

[tex]\textsf{10)} \quad y=-2(x+2)^2-6[/tex]

Step-by-step explanation:

Vertex form of a parabola:  

[tex]y=a(x-h)^2+k[/tex]  where (h, k) is the vertex

From inspection of the graph, the vertex is (-6, -4)

[tex]\implies y=a(x+6)^2-4[/tex]

To find [tex]a[/tex], substitute the coordinates of a point on the curve into the equation.

Using point (-4, 0):

[tex]\implies a(-4+6)^2-4=0[/tex]

[tex]\implies a(2)^2-4=0[/tex]

[tex]\implies 4a=4[/tex]

[tex]\implies a=1[/tex]

Therefore, the equation of the parabola in vertex form is:

[tex]y=(x+6)^2-4[/tex]

From inspection of the graph, the vertex is (-2, -6)

[tex]\implies y=a(x+2)^2-6[/tex]

To find [tex]a[/tex], substitute the coordinates of a point on the curve into the equation.

Using point (-1, -8):

[tex]\implies a(-1+2)^2-6=-8[/tex]

[tex]\implies a(1)^2-6=-8[/tex]

[tex]\implies a-6=-8[/tex]

[tex]\implies a=-2[/tex]

Therefore, the equation of the parabola in vertex form is:

[tex]\implies y=-2(x+2)^2-6[/tex]

A number increased by nine (n + 9) is the same as nine increased by a number (9 + n), the correct option is C.

A mathematical phrase is a set of words or a combination of words and numbers that can be written as a mathematical expression.

Given

Jillian was asked to translate the expression 9 + n into words.

She wrote "a number increased by nine.

The expresion can be written into the two formate which is;

(n+9) and (9+n)

Hence, a number increased by nine (n + 9) is the same as nine increased by a number (9 + n), the correct option is C.

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Answer:

Step-by-step explanation:

It is correct. I don't know that getting rid of the  other choices is helpful. The vocabulary (increases) in common usage means "add." I think I would accept it as it is and give her full credit. You can overthink an answer.

Answer:

Step-by-step explanation:

0.1 * 45

= 4.5 miles

Answer:

about 3 cents

Step-by-step explanation:

1.28 divided by 48 = 0.02667

whihc orunds to 0.03

Answer:

Ted is wrong

The triangle is a right triangle because of the right 90° angle formed at the bottom.

Answer:

  (a)  3 ft, 4 ft, 5 ft

Step-by-step explanation:

The triangle inequality requires the sum of the two short sides exceed the long side.

__

a) 3 ft + 4 ft = 7 ft > 5 ft . . . . . triangle is possible

b) 4 yd + 1 2/3 yd = 5 2/3 yd < 10 yd . . . . not a possible triangle

c) 3 ft + 3 ft = 6 ft < 7 ft . . . . not a possible triangle

d) 4 in + 4 in = 8 in . . . . not a possible triangle (not greater than 8 in)

__

The first set of side lengths can form a triangle: 3 ft, 4 ft, 5 ft.

The total ounces she needs to make her recipes is 22 ounces

From the question, we are to determine how many total ounces Marni needs to make her recipe

From the given information,

Marni has 24 ounces of walnuts

Also,

She needs 14 ounces for one recipe

and

1/2 pounds for another

First, we will convert 1/2 pounds to ounces

NOTE: 1 pound = 16 ounces

∴ 1/2 pound = 8 ounces

Then, we can rewrite that

She needs 14 ounces for one recipe

and

8 ounces for another

The total ounces she needs to make her recipes = 14 ounces + 8 ounces

The total ounces she needs to make her recipes = 22 ounces

Hence, the total ounces she needs to make her recipes is 22 ounces

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Answer:

The formula for exponential growth is: Total = Starting value(1 + rate)^time

2018 to 2025 is 7 years:

Step-by-step explanation:

Total = 50,000(1+0.037)^7

Total = 50,000(1.037)^7

Total = 64,479 -(Answer)

Answer:

C

Step-by-step explanation:

the root can be a minnimum of 0 otherwise the function would be imaginary,  sqrt(x-1)+2 has a minimum of 2. This means that g(x), or y is greater than or equal to two.

Answer:

37

Step-by-step explanation:

90 - 53 = 37

Answer:

x = 37°

Step-by-step explanation:

Given angle AOB = 53°, angle AOC = 90°

To find x°

From above figure, angle AOC = angle AOB + angle BOC

Now angle AOB = 53°, angle AOC = 90°

90° = 53° + angle BOC

=> angle BOC = x° = 90 - 53

=> x° = 37°

HOPE THIS HELPS AND HAVE A NICE DAY <3

Answer:

B: π/6

Step-by-step explanation:

A: 0

B: π / 6

C: π / 4

D: π / 3

E: π / 2

F: π

G: 3π / 2

Here is a complete unit circle...

If the radius of the circle is 6 feet. Then the area of the circle will be 113.097 square feet.

It is the centre of an equidistant point drawn from the centre. The radius of a circle is the distance between the centre and the circumference.

The radius of the circle is 6 feet.

Then the area of the circle will be

Area = πr²

where r is the radius of the circle. Then we have

Area = π × 6²

Area = 36π

Area = 113.097 square feet

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