F(x)=2/3x-1 show creat points to graph
Label values on thex&y axis

Answer:

The function \(f(x) = \frac{x^{2}-4\cdot x}{x^{2}-16}\) has the following set of solutions:

\(f(4.1) = 0.506173\), \(f(4.05) = 0.503106\), \(f(4.01) = 0.500624\), \(f(4.001) = 0.500062\), \(f(4.0001) = 0.500006\), \(f(4.0001) = 0.500006\)

\(f(3.9) = 0.493671\), \(f(3.95) = 0.496855\), \(f(3.99) = 0.499374\), \(f(3.999) = 0.499937\), \(f(3.9999) = 0.499994\)

Step-by-step explanation:

Let be \(f(x) = \frac{x^{2}-4\cdot x}{x^{2}-16}\), we proceed to simplify the expression by Algebraic means:

1) \(\frac{x^{2}-4\cdot x}{x^{2}-16}\) Given

2) \(\frac{x\cdot (x-4)}{(x-4)\cdot (x+4)}\) Associative, commutative and distributive properties/\(a^{2}-b^{2} = (a+b)\cdot (a - b)\)

3) \(\frac{x}{x + 4}\) Commutative, associative and modulative properties/Existence of multiplicative inverse/Result

Now we evaluate the function for each value:

\(x = 4.1\)

\(f(4.1) = \frac{4.1}{4.1+4}\)

\(f(4.1) = 0.506173\)

\(x = 4.05\)

\(f(4.05) = \frac{4.05}{4.05 + 4}\)

\(f(4.05) = 0.503106\)

\(x = 4.01\)

\(f(4.01) = \frac{4.01}{4.01 + 4}\)

\(f(4.01) = 0.500624\)

\(x = 4.001\)

\(f(4.001) = \frac{4.001}{4.001+4}\)

\(f(4.001) = 0.500062\)

\(x = 4.0001\)

\(f(4.0001) = \frac{4.0001}{4.0001 + 4}\)

\(f(4.0001) = 0.500006\)

\(x = 3.9\)

\(f(3.9) = \frac{3.9}{3.9+4}\)

\(f(3.9) = 0.493671\)

\(x = 3.95\)

\(f(3.95) = \frac{3.95}{3.95+4}\)

\(f(3.95) = 0.496855\)

\(x = 3.99\)

\(f(3.99) = \frac{3.99}{3.99+4}\)

\(f(3.99) = 0.499374\)

\(x = 3.999\)

\(f(3.999) = \frac{3.999}{3.999 + 4}\)

\(f(3.999) = 0.499937\)

\(x = 3.9999\)

\(f(3.9999) = \frac{3.9999}{3.9999 + 4}\)

\(f(3.9999) = 0.499994\)

Answer:

1kg = Rs. 42.50

3.5kg = 3.5*42.50

=Rs. 148.75

I hope you know this answer

Hello!

We have all angles of the triangle:

We will use the law of cosines. This relation is valid for all sides of any t

We have:

angle A = 12°

côté a = 10

angle B = 150°

This is therefore the first case of application of the sine law.

So:

\(\sf \dfrac{b}{sin~B} = \dfrac{a}{sin~A}\)

\(\sf b =\dfrac{sin~B~*~a}{sin~A} = \dfrac{sin~150~*~10cm}{sin~12} = \dfrac{arcsin~0.5~*~10cm}{arcsin~0.2079116908} = \dfrac{30~*~10cm}{12} = \dfrac{300cm}{12} = \boxed{\sf25cm}\)

Answer:

i hope this helpes

Step-by-step explanation:

a) A group of 16 pays $40 + ($2 x (16 - 10)) = $40 + $6 = $46.

b) The cost function can be represented as C(x) = 40 + 2(x - 10) for x > 10 and C(x) = 40 for x <= 10, where x is the number of people in the group and C(x) is the cost for the group.

c) The domain of the cost function is all non-negative real numbers less than or equal to 50 (0 <= x <= 50), since the maximum group size is 50. The range of the cost function is all non-negative real numbers greater than or equal to 40 (C(x) >= 40), since the minimum charge for a group is $40.

Answer:

a) $52

b) C(x) = 40 + 2x, if x > 10 and x ≤ 50

C(x) = 40, if x ≤ 10

c) Domain = {x ≥ 1 and x ≤ 50}

Range = { from 40 to 140}

Answer: 15/2

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The false statement considering the dilation is given as follows:

d) A'B' = 68 units.

A dilation is defined as a non-rigid transformation that multiplies the distances between every point in a polygon or even a function graph, called the center of dilation, by a constant factor called the scale factor.

The scale factor for the dilation in this problem is given as follows:

k = 2.

The length of AB is given as follows:

AB = 34.

Hence the length of A'B' is given as follows:

A'B' = 2 x 34 = 68 units.

The triangle and the options are given by the image presented at the end of the answer.

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Answer:

15 ways

Step-by-step explanation:

girl 1 and boy 1

girl 2 and boy 1

girl 3 and boy1

girl 1 and boy 2

girl2 and boy 2

girl 3 and boy 2

girl 1 and boy 3

girl 2 and boy 3

girl 3 and boy 3

girl 1 and boy 4

girl 2 and boy 4

girl 3 and boy 4

girl 1 and boy 5

girl 2 and boy 5

girl 3 and boy 5

Answer:

???

Step-by-step explanation:

Answer:

3c + 10

Step-by-step explanation:

1c = c

2c + 4 + c + 6

(combine like terms)

3c + 10

Answer:

Dominic is right

Step-by-step explanation:

equation:

2c + 4 + c + 6

combine like terms:

2c + c = 3c

4 + 6 = 10

new equation:

3c + 10

Answer:

Amadi: 20 years old

Chima : 4 years old

Answer:

Area of annulus is 40.85cm² to 2d.p

Step-by-step explanation:

Area of shaded part=Area of bigger circle -Area of smaler circle

Area of annulus= πR²- πr²= π(R²-r²)

A=3.142(7²-6²)

A=3.142(49-36)

A=3.142×13

A=40.846cm²

A=40.85cm² to 2d.p

Noting that the tip is one among the total sum charged on the bill is the best strategy for computing the required 20% tip using fractions.

aggregate attempting to determine the whole amount, time, or quantity. The amount at issue or under investigation is very active. the overall outcome, significance, or import. a third accounting, the principal, and the interest. There are word forms for quantities, amounting, and amounted. adaptable noun A thing's quantity is how much of it there is, that however much someone have, the amount you require or how much you can get. He needs that much money to make ends meet.

given

You can use a fraction to express the percentage 20%.

This is inferred from the fact that the sign for percentage,% means to divide by 100.

Therefore, it is important to understand that 20% equals 20/100, or 1/5.

As a result, the 20% tip represents one-fifth of the total.

Noting that the tip is one among the total sum charged on the bill is the best strategy for computing the required 20% tip using fractions.

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Complete Question:

Johnny printed two maps of a walking trail near his home. The length of the walking trail on the first map is 8 cm.

(a) Choose a length between 5 cm and 15 cm for the walking trail on the second map: ________cm.  

(b) Determine the scale factor from the first map to the second map.

(c)  A landmark on the first map is a triangle with side lengths of 3 cm, 4 cm, and 5 cm. What are the side lengths of the triangle landmark on the second map?  

(d) Draw one of the triangles from part C. Label the side lengths and vertices accordingly. You may use this drawing tool or draw your triangle on paper:

Answer:

(a) Length = 4cm

(b) Scale factor = 0.5

(c) 3cm, 4cm and 5cm are represented by 1.5cm, 2cm and 2.5cm respectively, on the second scale

(d) See attachment for triangle

Step-by-step explanation:

(a) Choose a length between 5 cm and 15 cm

\(Length =4cm\) --- This is solely up to you (you can make use of any length between 5 cm and 15 cm)

(b) The scale factor

The scale factor (k) is calculated as:

\(k = \frac{New\ Length}{Old\ Length}\)

\(k = \frac{4cm}{8cm}\\\)

\(k = 0.5\)

(c) What are side lengths of 3 cm, 4 cm, and 5 cm on the second landmark

Using:

\(k = \frac{New\ Length}{Old\ Length}\)

The old lengths, in this case are: 3cm, 4cm and 5cm

Make New length the subject

\(New\ Length = k * Old\ Length\)

When \(Length = 3cm\)

\(New\ Length = 0.5 * 3cm = 1.5cm\)

When \(Length = 4cm\)

\(New\ Length = 0.5 * 4cm = 2cm\)

When \(Length = 5cm\)

\(New\ Length = 0.5 * 5cm = 2.5cm\)

So: 3cm, 4cm and 5cm are represented by 1.5cm, 2cm and 2.5cm respectively, on the second scale

(d) See attachment for triangle

Answer:

y = -34x - 270

Step-by-step explanation:

m = -34, y = 2, x = -8

y = mx + b

2 = -34(-8) + b

b = 2 - 272

b = -270

y = -34x - 270

Answer: The measure of angle A is 31 degrees and be will be 31

Answer: Shade 6 pieces

Step-by-step explanation:

Because 2/5 of 15 is 6

Answer:

15) 2.08m

Step-by-step explanation:

We kow tanA= p/b

Here, A=33°

b=3.2m

Then,

tan33°=p/3.2

0.65=p/3.2

p=0.65*3.2

p=2.08

So, The height of tree is 2.08m

14) 59.58ft

tan50°=p/b

1.19=p/50

p=59.58ft

So, The height of signpost is 59.58ft

In both of these problems, we will be using trigonometry! Remember, SOH-CAH-TOA.

14. x = 13.5950 ft

Visualization of the problem is attached below.

We want to find out the opposite side to the angle, and we know the adjacent side. Therefore, we should use the tangent function.

tan(50) = x / 50

x = tan(50) * 50

x = 13.5950 ft (round off wherever you need)

15. x = 241.0016 m

The visualization of the problem is already given. We know the same information as we need in the previous problems, an angle and an adjacent side, and we want to find the opposite side. Therefore, we should use the tangent function.

tan(33) = x / 3.2

x = tan(33) * 3.2

x = 241.0016 (round off wherever you need)

Hope this helps!! :)

Check the picture below.

\(\sin( \theta )=\cfrac{\stackrel{opposite}{0.5}}{\underset{hypotenuse}{0.64}} \implies \sin^{-1}(~~\sin( \theta )~~) =\sin^{-1}\left( \cfrac{0.5}{0.64} \right) \\\\\\ \theta =\sin^{-1}\left( \cfrac{0.5}{0.64} \right)\implies \theta \approx 51.4^o\)

Make sure your calculator is in Degree mode.

Answer:

$1200

Step-by-step explanation:

Answer:

B.18. 44 miles

Step-by-step explanation:

We are given that

Distance between A and B=8 miles

Angle B=Angle BCQ=40 degree (Alternate interior angles)

Angle ACB=180-Angle ACP-Angle BCQ

Angle ACB=180-40-40=100 degree

In triangle ABC

Angle A+ Angle B +Angle C=180 degree using sum of angles of triangle property

Substitute the values

\(\angle A+40+100=180\)

\(\angle A+140=180\)

\(\angle A=180-140\)

\(\angle A=40\) degree

Angle A=Angle B

When two angles are equal of a triangle then the triangle is isosceles triangle.

Therefore, triangle ABC is an isosceles triangle.

\(\implies BC=AC \)

Now, Sine law

\(\frac{a}{sin A}=\frac{b}{sin B}=\frac{c}{sin C}\)

Using the sine law

\(\frac{BC}{sin 40}=\frac{AB}{sin 100}\)

\(\frac{BC}{sin 40}=\frac{8}{sin 100}\)

\(BC=\frac{8\times sin40}{sin 100}\)

BC=5.22

AC=BC=5.22 miles

Now, total distance covered by the boat=AB+BC+AC

Total distance covered by the boat=8+5.22+5.22=18.44 miles

Hence, option B is correct.

Answer:

There will be lots

Step-by-step explanation:

It is actually infinite.

The number of square inches of cardboard that are needed to make one

the container is 18.

We have,

The volume of the triangular prism.

= Area of the triangle x height

Now,

Height = 6 in

And,

To find the area of a triangle, we can use Heron's formula.

A = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case, the side lengths of the triangle are 3.2 in, 3.2 in, and 2 in.

Let's calculate the area using Heron's formula:

s = (3.2 + 3.2 + 2) / 2 = 4.2

A = √(4.2(4.2 - 3.2)(4.2 - 3.2)(4.2 - 2))

A = √(4.2 x 1 x 1 x 2.2)

A = √(9.24)

A ≈ 3.04 square inches

Now,

The volume of the triangular prism.

= Area of the triangle x height

= 3.04 x 6

= 18.24 in²

Now,

Area of one cardboard.

= 1² in²

= 1 in²

Now,

The number of square inches of cardboard that are needed to make one

container.

= The volume of the triangular prism / Area of one cardboard

= 18.24 in² / 1 in²

= 18.24

= 18

Therefore,

The number of square inches of cardboard that are needed to make one

the container is 18.

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The symbolic quantified statement is given as:

For all real integers x and y, if x³ = y³, then x = y.

Using quantifiers, this can be written as:

∀x,y∈ℝ, (x³ = y³) → (x = y)

The symbolic quantified statement represents the original sentence using logical symbols and quantifiers.

The universal quantifier (∀) is used to denote "for all," while the implication arrow (→) represents "if... then." The statement asserts that if the cubes of any two real integers x and y are equal, then x and y are equal as well.

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The binomial expansion is solved and the error in Dakota's statement is the incorrect substitution of 36g^2h^2 for the correct expression

Given data ,

Dakota made a mistake because the third term of the expansion of (2g + 3h) should have been 36g2h2. The binomial theorem asserts that the expansion of (2g + 3h) is as follows:

( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ

Here, x = 2g and y = 3h. Since term numbers begin at 0, since we are seeking for the third term, r = 2.

So , on simplifying the equation , we get

= nC2 * (2g)⁽ⁿ⁻²⁾ * (3h)²

= (n! / (2! * (n - 2)!)) * (2g)⁽ⁿ⁻²⁾ * (3h)²

= ((n * (n - 1)) / 2) * (2g)⁽ⁿ⁻²⁾ * (3h)²

Hence , the correct expression for the third term of the expansion of (2g + 3h) is ((n * (n - 1)) / 2) * (2g)^(n - 2) * (3h)², where n is the exponent in the binomial expansion.

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One angle measure provided (27 degrees), to determine the lengths of the sides or the measures of the other Angles.

The triangle, we need more information about the triangle, such as the lengths of the sides or the measures of other angles. The given information, "27 degrees," only specifies one angle of the triangle, but it is not sufficient to solve the triangle completely.

To solve a triangle, we typically need at least three pieces of information, which can include side lengths, angle measures, or a combination of both. With only one angle measure provided (27 degrees), we are unable to determine the lengths of the sides or the measures of the other angles.

To fully solve the triangle, we would need additional information such as the lengths of the sides or measures of at least two more angles. Without this additional information, it is not possible to provide a complete solution or determine the lengths of the sides or the measures of the other angles in the triangle.

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The distribution used to obtain the critical value in this situation is the Student's t-distribution.

Critical value is a statistical value used to determine whether a hypothesis test result is statistically significant or not. It is the value that is compared to the test statistic to determine whether the null hypothesis should be rejected or not. The critical value is determined by the level of significance chosen for the study, the sampling distribution of the test statistic, and the degrees of freedom.

The Student's t-distribution is a symmetric probability distribution that is used when the population standard deviation is unknown. It is used in situations where there is a small sample size (less than 30) and the sample is drawn from a normally distributed population. In this case, the owner is interested in developing a 90% confidence interval estimate, so the critical value will be obtained from the Student's t-distribution.

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The students corresponding to those 200 numbers would beasked to participate in the survey.

What is corresponding ?

Having or participating in the same relationship (such as kind, degree, position, correspondence, or function) especially with regard to the same or like wholes (such as geometric figures or sets) corresponding parts of similar triangles. : related, accompanying.

Have given,

a) The administrators could number an alphabetical list of students from 1 to 2,500.Then use a random number generator from a calculator or computer to generate 200 unique random numbers from 1 to2,500.(if you don’t say “unique”, then say “ignoring repeats”)The students corresponding to those 200 numbers would beasked to participate in the survey.

b) One advantage is that stratified random sampling guarantees that each of the school-level strata will have some representation, because it is possible that a simple random sample would miss one or more of the strata completely.(NOTE: It is NOT sufficient to say that a stratified sample “makes it MORELIKELY that all school-levels are represented in the sample”… the student must state that stratifying by school level GUARANTEES or ENSURES that all school levels are represented in the sample.)

The students corresponding to those 200 numbers would beasked to participate in the survey.

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