. Suppose that the following represents the graph of the function f(x).
N
a. (5 points) Determine the x intercepts and give a number line for the function
f(x). Are there any horizontal or vertical asymptotes?
b. (5 points) Give a number line for f'(x) and classify any local maxima or minima.
c. (5 points) Give a number line for f"(x) and list any points of inflection.

Answer:

\(\frac{1}{32} yards^{3}\)

Step-by-step explanation:

\(V=w*h*l\)

↓

\(V= \frac{1}{4} *\frac{1}{4} *\frac{1}{2}\)

=

\(\frac{1}{32} yards^{3}\\\)

Hope this helps!

Answer:

i. 33.51 cm³

ii. 14.14 cm³

iii. 231.61 g

Step-by-step explanation:

(i) the total volume of the paper weight,

Since the paper weight is in the form of a cone, its volume is the volume of a cone V = πD²h/12 where D = diameter of cone = 4 cm and h = height of cone = 8 cm

So, V = πD²h/12

V = π(4 cm)² × 8 cm/12

V = 16π cm² × 8 cm/12

V = 128π cm³/12

V = 402.124 cm³/12

V = 33.51 cm³

(ii) the volume of the wooden portion,

The volume of the wooden portion, V' = πr'²h'/3 where r' = radius of wooden portion and h' = height of wooden portion

From similar triangles in the figure, we have

height of wooden portion, h'/radius of wooden portion, r' = height of paper weight, h/radius of paper weight, r

h'/r' = h/r where r = D/2 where D =diameter of paper weight = 4 cm. So, r = 4 cm/2 = 2 cm

and h' = height of paper weight - height of lead portion = 8 cm - 2 cm = 6 cm

So,

r' = rh'/h = 2 cm × 6 cm/8 cm = 12 cm²/8 cm = 1.5 cm

So, V' = πr'²h'/3

V' = π(1.5 cm)² × 6 cm/3

V' = π2.25 cm² × 2 cm

V' = 4.5π cm³

V' = 14.14 cm³

(iii) the total mass of the paper weight.

The total mass of paper weight, m = mass of wooden portion + mass of lead portion = ρ'V' + ρ"V" where ρ' = density of wood = 0.9 g/cm³, V' = volume of wooden portion = , ρ" = density of lead = 11.3 g/cm³ and V" = volume of lead portion = V - V' = 33.51 cm³ - 14.14 cm³ = 19.37 cm³

So, m = 0.9 g/cm³ × 14.14 cm³ + 11.3 g/cm³ × 19.37 cm³

m = 12.726 g + 218.881 g

m = 231.607

m ≅ 231.61 g

Answer:

1

Step-by-step explanation:

6 or less is half the numbers on the cube.

6/6 simplifies to 1

The true statement is that proves the congruence of both triangles is:

∠ABC ≅ ∠DCB;

alternate interior angles of parallel lines are congruent.

Here, we have

to prove that angles are congruent

From the complete question, we have the following highlights

Angles B and C are alternate interior angles

The triangles are bounded by parallel lines

The above highlights mean that:

Angles ABC and DCB are congruent, by the theorem of alternate interior angles of parallel lines

Hence, the true statement is (c)

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complete question:

Isabelle proves that the triangles are congruent by using the parallel lines to determine a second set of angles are congruent. What statement and reason could she have used? ∠ABC ≅ ∠BAC; corresponding angles of parallel lines are congruent. ∠CAB ≅ ∠DCB; alternate interior angles of parallel lines are congruent ∠ABC ≅ ∠DCB; alternate interior angles of parallel lines are congruent ∠ACD ≅ ∠ABD; corresponding angles of parallel lines are congruent.

The statement about the unit prices which is true is Kitty Kibbles has a lower unit price of $1.30/pound.

The correct answer choice is option D.

Cost of 16-pound bag of Kitty Kibbles = $20.80

Unit price of kitty kibbles = Price / number of pounds

= $20.80 / 16

= $1.30 per pound.

Cost of 8-pound bag of Feline flavor = $11.20

Unit price of feline flavor = Price / number of pounds

= $11.20 / 8

= $1.40 per pound

Ultimately, the unit price of kitty kibbles and feline flavor is $1.30 and $1.40 respectively.

Complete question:

A 16-pound bag of Kitty Kibbles is $20.80. An 8-pound bag of Feline Flavor is $11.20. Which statement about the unit prices is true?

A. Feline Flavor has a lower unit price of $1.40/pound.

B. Feline Flavor has a lower unit price of $1.30/pound.

C. Kitty Kibbles has a lower unit price of $1.40/pound.

D. Kitty Kibbles has a lower unit price of $1.30/pound.

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Answer:

Step-by-step explanation:

step 1

100%/the total number = percent for one probability

100/5 = 20%

2 and 4 is even.

total even number * percent for one probability = total percent for even number

20% * 2 = 40%

therefore total even number is 40%

The probability is:

Step-by-step explanation:

Remember the formula for probability:

\(\boxed{\!\!\boxed{\bold{Probability=\frac{Favourable~outcome}{total~outcomes}\quad}}\!\!}\)

In this case, the favourable outcome (an even number) is 2, because there are only 2 even numbers in the set.

As for the total outcomes, there are 5 of them, because we have 5 numbers total.

So the probability of choosing an even number is 2/5.

Answer:

It may

Step-by-step explanation:

Vertically shift the graph of f(x) up 7 units.

By:-"||Ziddiboy||"

Answer:g

Step-by-step explanation:

The perimeter and area of the given composite shape are respectively;  10a² + 10b and 37a²b

The perimeter of the composite figure here will simply be the sum of the entire boundary lengths and as such we have;'

Perimeter = 2(a² + 3a² + a²) + 2(4b) + b + b

= 10a² + 8b + 2b

= 10a² + 10b

The area of a rectangle is;

Area = Length * width.

Thus;

Area of composite shape = Overall area of rectangle - Area of cut out rectangle

Area = (10a² * 4b) - (3a² * b)

Area = 40a²b - 3a²b

Area = 37a²b

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Answer:

1/x^9

Step-by-step explanation:

I don't actually understand this question, but if you are asking (x^(-9)), then its the answer above

Answer:

4

Step-by-step explanation:

The greatest common factor (GCF)

The greatest common factor of 16 and 100 is 4, and it represents the largest number that can evenly divide both 16 and 100.

Here,

To find the greatest common factor (GCF) of two numbers, we need to identify the largest number that can evenly divide both numbers.

Here's the step-by-step process to find the GCF of 16 and 100:

Step 1: List the factors of each number.

The factors of 16 are 1, 2, 4, 8, and 16.

The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.

Prime factorization of 16:

16 = 2 * 2 * 2 * 2

Prime factorization of 100:

100 = 2 * 2 * 5 * 5

Step 2: Identify the common factors.

The common factors of 16 and 100 are 1, 2, 4.

Step 3: Find the greatest common factor.

Among the common factors, the greatest common factor (GCF) is the largest one, which is 4.

So, the GCF of 16 and 100 is 4.

In conclusion, the greatest common factor of 16 and 100 is 4, and it represents the largest number that can evenly divide both 16 and 100.

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Answer:

Step-by-step explanation:

15

Answer:

tan(θ)= dn/de

θ=arctan(dn/de)

Step-by-step explanation:

The behavior of the function is given as follows:

A function from a set X to a set Y allocates precisely one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.

End behavior of a function f defines the behavior of the function's graph at the "ends" of the x-axis. Said differently, the end behavior of a function explains the graph's trend when we look at the right end of the x-axis (as x approaches +∞) and the left end of the x-axis (as x approaches -∞).

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The curve of the function for the segments AB, BC, CD, and DE is decreasing, constantly increasing, and decreasing respectively.

Given that,
A graph has been shown the behavior of the graph is to be discussed.

When a function is graphed, the function must show something likewise increasing, decreasing, and contant relationship.

Here
As per the observation, the graph starts from A and seems to be decreasing up to B and further it is Constant up to C and then increases up to D, afterward it is decreasing up to E.

Thus, the curve of function for the segments AB, BC, CD, and DE is decreasing, constantly increasing, and decreasing respectively.

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Answer:

(4 x 1) + (9/10) + (0/100) + (2/1000)

Step-by-step explanation:

\(\bold{\huge{\underline{ Solution \:1}}}\)

Here, We have given

Let assume the given triangle as ΔABC and ΔXYZ

According to the similarity theorem

Therefore, By using above theorem :-

\(\sf{\dfrac{ A}{X}}{\sf{=}}{\sf{\dfrac{ B}{Y}}}{\sf{=}}{\sf{\dfrac{ C}{Z}}}\)

Subsitute the required values

\(\sf{\dfrac{ 8}{10}}{\sf{=}}{\sf{\dfrac{ 15 }{Y}}}{\sf{=}}{\sf{\dfrac{18}{Z}}}\)

For other two sides of another similar triangle

\(\sf{\dfrac{ 8 }{10}}{\sf{=}}{\sf{\dfrac{ 15}{Y}}}\)

\(\sf{Y =15}{\sf{\times{\dfrac{ 10}{8}}}}\)

\(\sf{Y =15}{\sf{\times{\dfrac{ 5}{4}}}}\)

\(\sf{Y = }{\sf{\dfrac{ 75}{4}}}\)

\(\bold{Y = 18.75 }\)

And,

\(\sf{\dfrac{ 8 }{10}}{\sf{=}}{\sf{\dfrac{ 18}{Z}}}\)

\(\sf{Z =18 }{\sf{\times{\dfrac{ 10}{8}}}}\)

\(\sf{Z =18}{\sf{\times{\dfrac{ 5}{4}}}}\)

\(\sf{Z = }{\sf{\dfrac{ 90}{4}}}\)

\(\bold{Z = 22.5 }\)

Hence, The two sides of the another similar triangle is 18.75 and 22.5

\(\bold{\huge{\underline{ Solution \:2}}}\)

Here, We have

Let assume the two triangle be ΔABC and ΔPQR

According to the similarity theorem :-

That is,

\(\sf{\dfrac{ A}{P}}{\sf{=}}{\sf{\dfrac{ B}{Q}}}{\sf{=}}{\sf{\dfrac{ C}{R}}}\)

Subsitute the required values,

\(\sf{\dfrac{4 }{5}}{\sf{=}}{\sf{\dfrac{ 12}{15}}}{\sf{=}}{\sf{\dfrac{ 20 }{25}}}\)

\(\sf{\dfrac{4 }{5}}{\sf{=}}{\sf{\cancel{\dfrac{ 12}{15}}}}{\sf{=}}{\sf{\cancel{\dfrac{ 20 }{25}}}}\)

\(\bold{\dfrac{4 }{5}}{\sf{=}}{\bold{\dfrac{ 4}{5}}}{\sf{=}}{\bold{\dfrac{ 4 }{5}}}\)

Hence, The scale factor of the given similar triangles is 4/5

\(\bold{\huge{\underline{ Solution \: 3}}}\)

Here, we have given that

But,

Therefore,

According to the scale factor

The actual distance will be

\(\sf{=}{\sf{\dfrac{ 12 }{0.5}}}\)

\(\bold{ = 24 \: km }\)

Hence, The map distance corresponds to actual distance of 12 km is 24 km.

#3 Answer:

The other sides are 18.75 and 22.5

#3 Step-by-step explanation:

Because of the similar triangle

So, \(\frac{8}{10}=\frac{15}{x}=\frac{18}{y}\)               \(\left\{The\ corresponding\ sides\ are\ proportional\right\}\)

\(x=18.75,\ y=22.5\)

#4 Answer:

4:5

#4 Step-by-step explanation:

\(\frac{4}{5}=\frac{12}{15}=\frac{20}{25}=\frac{6}{5}\)

\(So\ the\ scale\ factor\ is\ 4:5\)

#5 Answer:

24 cm

#5 Step-by-step explanation:

\(12\div0.5\)

Calculate

\(\frac{12}{0.5}\)

Multiply both the numerator and denominator with the same integer

\(\frac{120}{5}\)

Cross out the common factor

24

I hope this helps you

:)

Answer: We want to find the value of (a+b)² given that a² + b² = 39 and ab = 4.

One way to approach this problem is to use the identity:

(a+b)² = a² + 2ab + b²

We can substitute the values we have into this identity:

(a+b)² = a² + 2ab + b²

= (a² + b²) + 2ab

= 39 + 2(4)

= 47

Therefore, (a+b)² = 47.

Step-by-step explanation:

Answer:

3z(5z-3)

Step-by-step explanation:

first you choose the common items which in this case was 3z the you divide 15 by 3 and 9 by 3

Applying the sine rule the value of side w is calculated to be 6.2

The size of w is calculated using the sine rule which states that the ratio of a side and the opposite angles are equal

the formula is

Sin A / a = Sin B / b = Sin C / c

applying the formula for the problem

Sine W / w = Sine X / x

plugging in the values

Sine 38 / w = Sine 84 / 10

cross multiplying

w = 10 x Sin 38 / Sine 84

x = 6.185

x =  6.2 to the nearest tenth

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then solve for y

answer

x = 2

y = 7

Answer:

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

Answer:

A.  80.6

B.  83

Step-by-step explanation:

Average Test Score (Language Arts class) function:

\(f(x)=0.3x+80\)

To determine the test average after completing test 2, substitute x = 2 into the given function:

\(\begin{aligned} \implies f(2)&=0.3(2)+80\\&=0.6+80\\&=80.6\end{aligned}\)

Average Test Score (Social Studies class) table:

\(\begin{array}{|c|c|}\cline{1-2} x&g(x)\\\cline{1-2} 1&85\\\cline{1-2} 2&83\\\cline{1-2} 3&81\\\cline{1-2} \end{array}\)

To determine the test average after completing test 2, find the value of the function from the table when x = 2:

\(\implies g(2)=83\)

Answer:

0.3

Step-by-step explanation:

Answer:

0.3

Step-by-step explanation:

I hope this is what you where asking for?

Answer: 519 120

Step-by-step explanation:

84*84=7056

7056/7=1008

1008*515=519 120

Step-by-step explanation:

s1 = 5

s2 = s1 × -2 = 5×-2 = -10

s3 = s2 × -2 = -10 × -2 = 20

...

now, we could do all that manually.

but there is also a formula for geometric sequence.

in fact, there are 2 - one for finite and one for infinite sequences.

and I was not completely honest, each of these 2 had some sub-forms depending on the size of the multiplier or ratio.

since we need the sum of the first 5 terms, which of the 2 do you think we need ?

of course, finite, because 5 is a normal number we can "touch". it is not infinity.

so, the formulas for finite sums of geometric sequences are :

if |r| < 1, Sn = a(1 - r^n)/(1 - r)

if |r| > 1, Sn = a(r^n - 1)/(r - 1)

if r = 1, Sn = na

if r = -1, then Sn = a or 0 depending on if n is odd or even.

the sequence is in general

s1 = a

sn = sn-1 × r

in our case a = 5, r = -2.

so, what form of the formula do we need ?

|-2| = 2, and 2 > 1, so ...

S5 = 5(-2^5 ‐ 1)/(-2 - 1) = 5(-32 - 1)/-3 = 5×-33/-3 =

= 5 × 11 = 55

quick check, as the 5 terms are

5

-10

20

-40

80

and their sum is : 55

correct !

Answer:

Quadrilateral: 20.5 units

Triangle: 8.6 units

Step-by-step explanation:

Quadrilateral:
We can use the following formula to find the perimeter of a quadrilateral.

Perimeter = AB + BC + CD + DA

where AB, BC, CD, and DA are the lengths of the four sides of the quadrilateral.

In your case, the coordinates of the vertices of the quadrilateral are A(-3,-1), B(-3,3), C(2,3), and D(4,-1).

Using the distance formula, we can find the lengths of the four sides of the quadrilateral as follows:

\(AB = \sqrt{(-3 - (-3))^2 + ((-1) - 3)^2} = \sqrt{16} = 4\)

\(BC = \sqrt{(-3 - 2)^2 + ((3) - 3)^2} = \sqrt{25}= 5\)

\(CD = \sqrt{(2 - 4)^2 + ((3) - (-1))^2} = \sqrt{4+16} = 2\sqrt{5}\)

\(DA = \sqrt{(4 - (-3))^2 + ((-1) - 1)^2} = \sqrt{49} =7\)

Therefore, the perimeter of the quadrilateral is:

Perimeter = AB + BC + CD + DA

= \(4+5+2\sqrt5+7=20.5\) units

Triangle

The perimeter of a triangle is the total length of all three sides of the triangle. To find the perimeter of a triangle, we can use the following formula:

Perimeter = AB + BC + CA

where AB, BC, and CA are the lengths of the three sides of the triangle.

In your case, the coordinates of the vertices of the triangle are

E(-4,1), F(-2,3), and G(-2,4). Using the distance formula, we can find the lengths of the three sides of the triangle as follows:

\(EF = \sqrt{(-4 - (-2))^2 + ((1) - (3))^2} = 2\sqrt{2}\)

\(FG = \sqrt{(-2 - (-2))^2 + ((3) - (4))^2} = 1\)

\(EG = \sqrt{(-4 - (-2))^2 + ((1) - (4))^2} = \sqrt{4 + 9} = \sqrt{13}\)

Therefore, the perimeter of the triangle is:

Perimeter = EF + FG + EG

= 4 + 1 + \(\sqrt{13}\)

=8.6 units

Therefore, the perimeter of the quadrilateral is 20.5 units and the perimeter of the triangle is 8.6 units

The rate of pounds per square inch is 1.5 pound.

According to the question, the given data is as written below:

The quantity of rice carried by Penny is: 36 pounds

The given area between strap and shoulder: 24 square inches

As per the question, weight is equally distributed, therefore the expression can be written as:

Required expression: 36/12 = 24/12 = 3/2 = 1.5

Therefore, the rate of pounds per square inch is 1.5 pound.

What is pound?

The term pound is used for the measurement of the mass. Basically, it is the unit of mass or weight. And one pound is equal to the 454 grams.

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Answer:

\(x-3\)

Step-by-step explanation:

The area of the flagpole base is \(x^2-6x+9\ \text{yd}\)

where the factor of the equation is the length of the base.

In order to find the length we need to factorize the equation

\(x^2-6x+9\)

\(=x^2-3x-3x+9\)

\(=x(x-3)-3(x-3)\)

\(=(x-3)(x-3)\)

The length of the base of the flagpole is \((x-3)\ \text{yd}\).

The area of a square base is the product of the side lengths.

The length of the base is x - 3

The area is given as:

\(\mathbf{Area =x^2 - 6x + 9}\)

Expand

\(\mathbf{Area =x^2 - 3x - 3x + 9}\)

Factorize

\(\mathbf{Area =x( x- 3) - 3(x - 3)}\)

Factor out x - 3

\(\mathbf{Area =( x- 3) (x - 3)}\)

Express as squares

\(\mathbf{Area =( x- 3)^2}\)

Rewrite the area as:

\(\mathbf{Length^2 =( x- 3)^2}\)

Take square roots of both sides

\(\mathbf{Length =x- 3}\)

Hence, the length of the base is x - 3

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Answer:

14/37

Step-by-step explanation:

14/37 is already in the simplest form. It can be written as 0.378378 in decimal form (rounded to 6 decimal places).

Steps to simplifying fractions

Find the GCD (or HCF) of numerator and denominator

GCD of 14 and 37 is 1

Divide both the numerator and denominator by the GCD

14 ÷ 1

37 ÷ 1

Reduced fraction:

14/37

Therefore, 14/37 simplified to lowest terms is 14/37.