Which function, g or h, is the inverse function for function f?

The independent Variable in the situation presented in the table is the temperature (T), which is measured in degrees Celsius (°C), and the dependent variable is the volume (V), which is measured in milliliters (mL).

The table above illustrates the relationship between the temperature of a substance and its volume. The independent variable is the temperature of the substance and the dependent variable is the volume of the substance.

The symbol or name used to represent the independent variable is "T" for temperature and its units are given as degrees Celsius or °C.The symbol or name used to represent the dependent variable is "V" for volume, and its units are given as milliliters or mL.

The temperature is the independent variable as it is being manipulated in the experiment while the volume is dependent on the temperature as it is changing based on the temperature.

An independent variable is a variable in an experiment that is being manipulated by the experimenter, while the dependent variable is the variable that is being measured in response to changes in the independent variable.

In summary, the independent variable in the situation presented in the table is the temperature (T), which is measured in degrees Celsius (°C), and the dependent variable is the volume (V), which is measured in milliliters (mL).

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\(\textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh ~~ \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ h=14\\ A=161 \end{cases}\implies 161=\cfrac{1}{2}b(14) \\\\\\ 161=7b\implies \cfrac{161}{7}=b\implies 23=b\)

Answer:

\( \frac{1}{x {}^{2} y {}^{4} }\)

Step-by-step explanation:

\( \frac{x {}^{ - 2} }{y {}^{4} } = x {}^{ - 2} \times \frac{1}{y {}^{4} } \)

\(x {}^{ - 2} = \frac{1}{x {}^{2} } \)

\(therefore \: \frac{x {}^{ - 2} }{y {}^{4} } = \frac{1}{x {}^{2} } \times \frac{1}{y {}^{4} } \\ = \frac{1}{x {}^{2}y {}^{4} }\)

Answer:

10 ft

Step-by-step explanation:

perpendicular (p)= 6 ft

base(b) =8 ft

hypotenuse (h) = ?

we know by using Pythagoras theorem

h = \(\sqrt{p^{2}+b^{2} }\)

= \(\sqrt{6^{2}+8^{2} }\)

= 10 ft

hope it helps :)

The value of x is equal to: A. 7.2 units.

In Mathematics, the basic proportionality theorem states that when any of the two (2) sides of a triangle is intersected by a straight line which is parallel to the third (3rd) side of the triangle, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.

By applying the basic proportionality theorem to the given triangle, we have the following:

LM/MO = LN/NO

18/x = 10/4

By cross-multiplying, we have the following:

10x = 72

x = 72/10

x = 7.2 units.

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Complete Question:

LO bisects ∠NLM, LM=18, NO=4, and LN=10

What is the value of x?

A. 7.2

B. 45

C. 5.43

D. 2.22

Answer: BC = 24

Step-by-step explanation:

Given:

AB = x+33

AC = 3x - 15

BC = x

<B = <C

Solution:

Because <B = <C, you can say the corresponding sides AB and AC are equal as well

AB = AC

x + 33 = 3x -15  

48 = 2x

x = 24

Since x = BC

BC = x

BC = 24

Answer:

The coefficient of \(x^{4}\)\(y^{3}\) is -280

Step-by-step explanation:

Solving the Binomial expansion using the Pascal's triangle, it would be observed that an expansion to the power of 7 can be solved using;

1  7  21  35  35  21  7  1

Thus;

\((x - 2y)^{7}\) = 1. \(x^{7}\) + 7.\(x^{6}\)(-2y) + 21.\(x^{5}\)\((-2y)^{2}\) + 35.\(x^{4}\)\((-2y)^{3}\) + 35.\(x^{3}\)\((-2y)^{4}\) + 21.\(x^{2}\)\((-2y)^{5}\) + 7.x\((-2y)^{6}\) + \((-2y)^{7}\)

        = \(x^{7}\) -14\(x^{6}\)y +84\(x^{5}\)\(y^{2}\) -280\(x^{4}\)\(y^{3}\) + 560\(x^{3}\)\(y^{4}\) - 672\(x^{2}\)\(y^{5}\) + + 448x\(y^{6}\) - 128\(y^{7}\)

Therefore, the coefficient of \(x^{4}\)\(y^{3}\) is -280

Let c be the event that the outcome on the die is 3 or larger so:

A is the outcome is an even number

A →{2, 4, 6}

B is outcome is 4 or smaller

B→{1, 2, 3, 4}

C is outcome is 3 or larger

C→{3, 4, 5, 6}

A∩B = {2, 4}

P(A∩B) = 2/6

⇒P(A∩B) = 1/3

B∩C = {3, 4}

P(B∩C) = 2/6

⇒P(B∩C) = 1/3

P(A) = 1/2 ,   P(B) = 2/3,   P(C) = 2/3

⇒P(A∩B) = 1/3 = P(A) P(B)

Therefore, A and B are independent

P(B∩C) = 1/3 ≠ P(B) P(C)

Therefore, B and C are not independent .

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Answer:

\(x=89\)

Step-by-step explanation:

We can plug into the formula for the mean to get \((87+73+84+82+x)/5=83\).

We can combine like terms on the left side to get \((326+x)/5=83\).

We can multiply by \(5\) on both sides to get \(326+x=415\).

We can finally subtract \(326\) from both sides to get \(x=89\).

So, the answer is \(\boxed{x=89}\) and we're done!

Step-by-step explanation:

2X - 20 =86 ( Alternate angles are equal)

2X = 86 - 20

2X = 66

X = 33

The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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1) The area of a circle circumscribed about a square is 307.7 cm².

2.a.) The angle ACB is 39 degrees.°.

2b.) The value of x is 5.42.

We shall find the radius to determine the area of a circle.

First,  find the side length of the square:

Since the perimeter of the square = 56 cm, then, each side of the square is 56 cm / 4 = 14 cm.

Next, find the diagonal of the square, using the Pythagorean theorem:

Diagonal = the diameter of the circumscribed circle.

Diagonal² = side length² + side length²

= 14 cm² + 14 cm²

= 196 cm² + 196 cm²

= 392 cm²

Take the square root of both sides:

Diagonal = √392 cm ≈ 19.80 cm (rounded to two decimal places)

Then, the radius of the circle which is half the diagonal:

Radius = Diagonal / 2 ≈ 19.80 cm / 2 ≈ 9.90 cm (rounded to two decimal places)

Finally, compute the area of the circle using the formula:

Area = π * Radius²

Area = 3.14 * (9.90 cm)²

Area ≈ 307.7 cm² (rounded to two decimal places)

Therefore, the area of the circle that is circumscribed about a square with a perimeter of 56 cm is 307.7 cm².

2. a) We use the property of angles in a circle to solve for angle ACB: an angle inscribed in a circle is half the measure of its intercepted arc.

Given that arc AB has a measure of 78°, we can find angle ACB as follows:

Angle ACB = 1/2 * arc AB

= 1/2 * 78°

= 39°

Therefore, the angle ACB is 39 degrees.

2b.) To solve for the value of x, we use the information that the angle ADB =  (3x - 12)⁴.

Given that angle ADB is (3x - 12)⁴, we can equate it to the measure of the intercepted arc AB, which is 78°:

(3x - 12)⁴ = 78

Solve the equation for x, by taking the fourth root of both sides:

∛∛((3x - 12)⁴) = ∛∛78

Simplify,

3x - 12 = ∛(78)

Isolate x by adding 12 to both sides:

3x - 12 + 12 = ∛(78) + 12

3x = ∛(78) + 12

Finally, divide both sides by 3:

x = (∛(78) + 12) / 3

x = (4.27 +12) / 3

x = 5.42

So, x is 5.42

Therefore,

1) The area of the circle is 154 cm².

2a.) Angle ACB is equal to 102°.

2b.) The value of x is 5.42

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Answer:

-39 cm²/h

Step-by-step explanation:

The area of the rectangle is A = hw where h = height and w = width.

So the rate of change of area with respect to time is

dA/dt = d(hw)/dt

dA/dt = hdw/dt + wdh/dt

Given that at an instant h = 3cm, w = 8 cm and dh/dt = + 11 cm/h and dw/dt = -9 cm/h(negative since it is decreasing)

So, dA/dt = hdw/dt + wdh/dt

dA/dt = 3 cm × (+11 cm/h) + 8 cm × (-9 cm/h)

dA/dt = 33 cm²/h - 72 cm²/h

dA/dt = -39 cm²/h

Answer:

1)5:9 ,5 of 9 5/9 2) 36x5 3) 95x5

Since the variable type of writing utensil assumes labels and not numbers, it is classified as qualitative.

In this problem, the type of writing utensil has 4 labels: regular pencil, mechanical pencil, pen, whatever.

Hence, since the variable assumes labels and not numbers, it is classified as qualitative.

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As x tends to negative one from the left, the value of f(x) tends to positive infinity. As x → -1⁻, f(x) → ∞.

In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).

By critically observing the graph of this rational function f(x) shown below, we can logically deduce that its vertical asymptote is at x = -1 and x = 2, and its horizontal asymptote is at y = 3.

In this context, we can logically deduce that the value of f(x) tends towards positive infinity, as x tends to negative one from the left;

As x → -1⁻, f(x) → ∞.

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Answer:

m - 7 = 39

The answer is 46

Step-by-step explanation:

Add 7 to 39 to get the answer

The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.

Let's assume the width of the rectangle is "b" cm.

According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.

The formula for the perimeter of a rectangle is given by:

Perimeter = 2 * (length + width)

Substituting the given perimeter value, we have:

7 1/3 cm = 2 * (2b + b)

To simplify the calculation, let's convert 7 1/3 to an improper fraction:

7 1/3 = (3*7 + 1)/3 = 22/3

Rewriting the equation:

22/3 = 2 * (3b)

Simplifying further:

22/3 = 6b

To solve for "b," we can divide both sides by 6:

b = (22/3) / 6 = 22/18 = 11/9 cm

Therefore, the width of the rectangle is 11/9 cm.

To find the length, we can substitute the width back into the equation:

Length = 2b = 2 * (11/9) = 22/9 cm

So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.

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Answer:

To prove triangles are similar, you need to prove two pairs of corresponding angles are congruent

Step-by-step explanation:

SSS similarity postulate

The SSS similarity postulate says that if the lengths of the corresponding sides of two triangles are proportional then the triangles must be similar.

In the given figure , we have two triangles ΔABC and ΔXYZ such that the corresponding sides of both the triangles are proportional.

i.e.

Then by SSS-similarity criteria , we have

ΔABC ≈ ΔXYZ

BRAINLIEST PLEASE????

Step-by-step explanation:

sqrt(3)/2 = cos(pi/6)

therefore,

2x = pi/6

x = pi/12

that means in the interval of [0, 2pi) there is a second solution : pi/12 below 2pi

x = 2pi - p/12 = 23pi/12

so, the solutions are

x = pi/12

or

x = 23pi/12

in other words x = 15° or 345°.

Answer:

The slope is 1.

Answer:

Genotype: 100% rr
phenotype: 100% white

Step-by-step explanation:

since there are no dominant genes the cross will definitely be a rr genotype

Answers:

5)

a.Highest- 96

Lowest-52

b.74

c. 70-80

d. 13

e. 7

6)

a. 89%

b. 51%

c. In the morning(89%)

Answer:

The answer correct (D).

The x-intercepts for the parabola defined by the equation y= x²-9x+ 18 are (3, 0) and (6.0)

A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .

We have to find the  x-intercepts for the parabola y= x²-9x+ 18

We have to make y as zero to find the x intercepts

x²-9x+ 18 = 0

This equation is in the form of quadratic equation

x² -6x-3x+18=0

x(x-6)-3(x-6)=0

(x-3)(x-6)=0

x=3 or x=6

Hence, the x-intercepts for the parabola defined by the equation y= x²-9x+ 18 are (3, 0) and (6.0)

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Answer:

C. \( f(-1) = 0 \)

Step-by-step explanation:

The value of \( f(-1) \), is the value of \( f(x) \) when x = -1.

What we are being asked to find what value of \( f(x) \) corresponds with x = -1. Or what output would an input of value of -1 give us.

From the table given, when x = -1, \( f(x) = 0 \).

Therefore, the value of \( f(-1) = 0 \).

Expected value = $0.17

Explanation:

we find the probability of each numbers

Total numbers = 6

probability of 1 = 1/6

probability of 2 = 1/6

probability of 3 = 1/6

probability of 4 = 1/6

probability of 5 = 1/6

probability of 6 = 1/6

Expected value = sum of (the probabilty of each number × the amount for rolling each)

A win = positive while a loss is negative

no win or loss = 0

rolls a 1, wins $3; if she rolls a 2, she wins $1. If she rolls a 3,4, or5, she loses $1 and if a 6 is rolled, she doesn't win or lose

Expected value = (1/6 × 3) + (1/6 × 1) - (1/6 × 1) - (1/6 × 1) - (1/6 × 1) + (1/6 × 0)

= 3/6 + 1/6 - 1/6 - 1/6 -1/6 + 0 = 1/2 -2/6 = 1/2 - 1/3

Expected value = 0.5 - 0.33

Expected value = 0.17 (nearest cent)

Hence, it means Janet gained money.

Answer:

12.9x-9

Step-by-step explanation:

5.3x-9+7.6x

5.3x+7.6x = 12.9x

=12.9x-9

there are a total number of 78,364,164,096 different ways of arranging the letter and digits on the license plate.

In case there are 26 letters and 10 digits permitted in each of 7 places (and no spaces permitted), at that point there are total

36^7= 78,364,164,096 number of plates conceivable, but no question the issuing organization will forbid a subjective subset of these on tasteful grounds, for foulness, or for political incorrectness. If spaces are permitted, the number of plates is 37^7 or 94,931,877,133.In the case, as it were one space or marker is permitted (Ontario, Canada presently employments ‘ABCD*123’, for case), the number is 78,364,164,096 * 6 or 470,184,984,576, since there are 6 spots between 7 characters.

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Answer:

(x+1) (x-2)

Step-by-step explanation: