Which expressions are equivalent?

The set of equations that corresponds to the specified function are

y = 5 - x and 5 - x = 9x².

What is linear equation in two variables?

If an equation is expressed as ax + by + c=0, where a, b, and c are all real integers and a and b, the coefficients of x and y, respectively, are not equal to zero, then it is said to be a linear equation in two variables.

The given equation is :

\(y=9x^{2}\) equation 1.

\(x+y=5\) equation 2.

From equation 2.

\(x+y=5\\y=5-x\)

substituting into 1 equation.

\(5-x=9x^{2}\)

The system of equations that is equivalent to the provided function is shown by the resulting equation, which is y = 5 - x and \(5-x=9x^{2}\)

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Answer:

4

Step-by-step explanation:

The mode is the number that appears the most!!!!

Now lets solve :)

2, 2, 3, 3, 4, 4, 4, 4,

There are 2 2s.

There are 2 3s.

There are 4 4s.

The mode is 4!!! :)

Have an amazing day!!

Plese rate and mark brainliest!!

The mode of the data set is 4

The mode is the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all. Other popular measures of central tendency include the mean, or the average of a set, and the median, the middle value in a set.

Therefore, the mode of the data set is 4

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The simplified expression for (f ∘ g)(x) is 2 + x (option d).

To find and simplify (f ∘ g)(x), we need to substitute the expression for g(x) into f(x) and simplify.

Given:

f(x) = log₃(9x)

g(x) = \(3^x\)

Substituting g(x) into f(x):

(f ∘ g)(x) = f(g(x)) = log₃\((9 * 3^x)\)

Now, we simplify the expression:

log₃\((9 * 3^x)\) = log₃(9) + log₃\((3^x)\)

Since logₓ(a * b) = logₓ(a) + logₓ(b), we have:

log₃(9) + log₃\((3^x)\) = log₃\((3^2)\) + x

Using the property logₓ\((x^a)\) = a * logₓ(x), we get:

log₃\((3^2)\) + x = 2 * log₃(3) + x

Since logₓ\((x^a)\) = a, where x is the base, we have:

2 * log₃(3) + x = 2 + x

Therefore, (f ∘ g)(x) simplifies to:

(f ∘ g)(x) = 2 + x

So, the correct answer is (d) 2 + x.

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Complete Question:

Given f(x)=log₃(9x) and g(x)=\(3^x\). Find and simplify (f ∘ g)(x)

(a) 2x

(b) x

(c) \(27^x\)

(d) 2+x

(e) None of these.

Answer:

For example, the phrase "3 more than an unknown number" becomes the mathematical expression "x + 3." Because the unknown number has no explicitly stated value, we label it with a variable x. To get a value three more than x, simply add 3 to it.

hope it helps ya mate. ~^~

Answer:

3 + x

Step-by-step explanation:

"More than" means addition. 3 more than x is saying 3 plus x. In an algebraic expression, this would look like:

3 + x

The values of x and y for the diagram are angle measures of triangles 60° and 120° respectively.

For any triangle to be formed, its three interior angles must sum up to 180°. Thus the sum of the interior angles of a triangle is 180°

Considering, the equilateral triangle with one angle x, we can solve for the angle measure x as follows:

x + x + x= 180° {sum of interior angles of a triangle}

3x = 180°

x = 180°/3

x = 60°

For the isosceles triangle with angle y, one of its base angle is calculated as:

90° - x

90° - 60° = 30°

so;

y + 2(30) = 180° {sum of interior angles of a triangle}

y + 60° = 180°

y = 180° - 60°

y = 120°

Therefore, the values of x and y for the diagram are angle measures of triangles 60° and 120° respectively.

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The domain of this relation (-1,5) (-2,1) (3,-1) (3,-4) is  {-2,1,3,4}

What is domain ?

A domain name is a word or phrase that designates a sphere of administrative control, authority, or autonomy on the Internet. Websites, email services, and other online services are frequently identified by their domain names. There were 330.6 million registered domain names as of 2017.

First we learn what is relation

Let A and B are two sets. Then the Cartesian product of A and B is denoted by A × B and defined as

Now a Relation R from A to B is a Subset of A × B

Here the given relation is {(-1,5) (-2,1) (3,-1) (3,-4)}

Let R be the relation

Then R ={(-1,5) (-2,1) (3,-1) (3,-4)}

Now domain of the relation

= { x : (x, y) ∈ R }

= {-2,1,3,4}

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The simplified form of the given expression is 9b

From the question, we are to simplify the given expression

The given expression is 3√b^2

This expression can be properly written as

(3√b)²

To simplify the expression,

First, we will expand the expression by applying one of the rules of exponents

(3√b)²

Applying the rule of exponent

3² × (√b)²

9 × b

= 9b

Hence,

The simplified expression is 9b

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The probability that none of 200 women using the pill will become pregnant is found to be 0.002.

Given: Assume a birth control pill has a 97% success rate in avoiding pregnancies.

Probability that none of 200 women using the pill will become pregnant is given as

= 0.97(200)

=0.0023

=0.002

Therefore, probability that none of 200 women using the pill will become pregnant is found to be 0.002.

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Answer:

4.5

Step-by-step explanation:

Domain means that value of x and range means the value of f(x) so

\(f(x)=2x+1 \\f(1.75)=2(1.75)+1\\f(1.75)=4.5\)

so the range value is 4.5

1. The intersection of the two surfaces is an ellipse centered at the origin, with semi-major axis a = 3/√2 and semi-minor axis b = 3/√10.

2. The triple integral in rectangular coordinates to find the volume enclosed by the region D is:

∫∫∫ 1 dV

The summing of discrete data is indicated by the integration. To determine the functions that will characterise the area, displacement, and volume that result from a combination of small data that cannot be measured separately, integrals are calculated.

To find the intersection of the two surfaces, we can set their equations equal to each other:

2 - 5x² - y² = 4x² + 4y²

Rearranging the equation:

9x² + 5y² = 2

Now, let's solve this equation to find the intersection points:

1) Find the intersection points:

Start by dividing both sides of the equation by 2:

9x²/2 + 5y²/2 = 1

Simplifying further:

(9/2)x² + (5/2)y² = 1

Divide both sides by (9/2):

x² + (5/2)(2/9)y² = 1/((9/2))

Simplifying:

x² + (5/9)y² = 2/9

Now, we have an equation in standard form for an ellipse:

x²/a² + y²/b² = 1

Comparing this equation with our current equation:

a² = 9/2

b² = 9/10

Taking the square root of a² and b²:

a = √(9/2) = 3/√2

b = √(9/10) = 3/√10

Therefore, the intersection of the two surfaces is an ellipse centered at the origin, with semi-major axis a = 3/√2 and semi-minor axis b = 3/√10.

2) To set up the triple integral in rectangular coordinates to find the volume enclosed by the region D, we can integrate over the region D with respect to x, y, and z.

The triple integral is given by:

∫∫∫ f(x, y, z) dV

In this case, since we want to find the volume, f(x, y, z) is equal to 1.

The limits of integration for x and y are determined by the ellipse representing the region D. We can choose appropriate limits based on the symmetry of the ellipse.

For x, the limits will be -a to a, which is -3/√2 to 3/√2.

For y, the limits will be -b to b, which is -3/√10 to 3/√10.

For z, the limits will depend on the specific problem or the given boundaries of the region D.

The triple integral in rectangular coordinates to find the volume enclosed by the region D is:

∫∫∫ 1 dV

Integration limits:

x: -3/√2 to 3/√2

y: -3/√10 to 3/√10

z: dependent on the specific problem or given boundaries of the region D

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In order to simplify and verify trig identities, one needs to use the rules of trigonometry and algebra to manipulate the equation until it is in a simplified form.

The most common trig identities to remember include the Pythagorean identity, reciprocal identities, quotient identities, and sum and difference identities. When simplifying an equation, it is important to remember to include the negative sign when necessary and to factor out any common factors.

After simplifying, it is important to verify the equation. This can be done by plugging in known values for the variables and verifying that the equation is true. By utilizing the rules of trigonometry and algebra, one can simplify and verify trig identities. This process is essential for working with trigonometric functions.

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Answer:0.2 gallons and 1.6 pints

Step-by-step explanation:

1 gallon = 8 pint

1 gallon / 5=0.2 gallon

8 pint / 5=1.6 pint

The simplified fraction expression results into \(\frac{1}{9}\).

What is fraction?

A number that is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

A number that represents a rational number is called a common fraction. The three main sorts of fractions are as follows. Proper fractions, incorrect fractions, and mixed fractions are these three types.

Given,

Expression = \(\frac{3^{-6}}{3^{-4}}\)

                   = \(3^{-6-(-4)}\)

                   = \(3^{-6+4}\)

                   = \(3^{-2}\)

                   = \(\frac{1}{3^2}\)

                   = \(\frac{1}{9}\)

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Answer:

B and D

I hope it helps.

Answer: -7c^2d^2

C^2d^2

Step-by-step explanation:

Answer: B and C

Step-by-step explanation:

the triangle inequality theorem states that any 2 sides of a triangle must be greater than the measure of the third side. now with this rule, let's apply it to all options!

option a:

7 + 5 > 6 .. yes!

6+ 7 > 5 .. yes!

5 + 6 > 7 .. yes!

option b:

9 + 12 > 19 .. yes!

12 + 19 > 9 .. no!

19 + 9 > 12 .. no!

option c:

7 + 11 > 18 .. no!

11 + 18 > 7 .. no!

18 + 7 > 11 .. yes!

option d:

6 + 8 > 11 .. yes!

8 + 11 > 6 .. yes!

11 + 6 > 8 .. yes!

i did this topic years ago so please let me know if there are any mistakes! hope this helped, and good luck! ◝(ᵔᵕᵔ)◜

Answer:

-25x + 50y = 19

Step-by-step explanation: So sorry if I'm wrong

Answer:

x=3

y=2

Step-by-step explanation:

you can either use substitution or elimination method

I find substitution method better

substitute x with 3 and in this method u use one of the equation

10(2)-20y=-10

20-20y=-10=2

y=2

now use y=2 with the same equation

10x-40=-10=30

10x=30

x=3

therefore

x=3

y=2

(1) The significant figure will be 710.

Hence the correct option is (b).

(2) (a) The modulus of A and B are,

| A | = √62

| B | = √30

(b) The value of A + B = 7 i - 2 j + 9 k

(c) The value of A - B = -3 i - 4 j + 5 k

(3) (a) a ⋅ (b × c) is meaningful and result is a scalar.

(b) a × (b ⋅ c) is not meaningful.

(c) a × (b × c) is meaningful and result is a vector.

(d) (a ⋅ b) × c is not meaningful.

(e) (a ⋅ b) × (c ⋅ d) is not meaningful.

(f) (a × b) ⋅ (c × d) is meaningful and result is a scalar.

The not meaningful is because to conduct cross product we need two vectors.

(4) Given lines are parallel because the cross product of the vectors along that lines is zero vector.

(1) Given the multiplication is,

20.6 × 5.5 × 6.27

That gives the result,

20.6 × 5.5 × 6.27 = 710.391

Here significant figure will be 710.

So the correct option is (b).

(2) Given the vectors are,

A = 2 i - 3 j + 7 k

B = 5 i + j + 2 k

(a) The modulus of A and B are,

| A | = √[2² + (-3)² + 7²] = √62

| B | = √[5² + 1² + 2²] = √30

(b) The value of A + B vector is,

A + B = [2 i - 3 j + 7 k] + [5 i + j + 2 k] = 7 i - 2 j + 9 k

(c) The value of A - B vector is,

A - B = [2 i - 3 j + 7 k] - [5 i + j + 2 k] = -3 i - 4 j + 5 k

(3) We know that the cross product gives vector result and dot product gives scalar result.

The statements are,

(a) a ⋅ (b × c) is meaningful and result is a scalar.

(b) a × (b ⋅ c) is not meaningful.

(c) a × (b × c) is meaningful and result is a vector.

(d) (a ⋅ b) × c is not meaningful.

(e) (a ⋅ b) × (c ⋅ d) is not meaningful.

(f) (a × b) ⋅ (c × d) is meaningful and result is a scalar.

The not meaningful is because to conduct cross product we need two vectors.

(4) Here for first line vector is,

A = [(-2) - (-4)] i + [0 - (-6)] j + [(-3) - 1] k = 2 i + 6 j - 4 k

for second line vector is,

B = [5 - 10] i + [3 - 18] j + [14 - 4] k = -5 i - 15 j + 10 k

So now the cross product is,

A × B = \(\left[\begin{array}{ccc}i&j&k\\2&6&-4\\-5&-15&10\end{array}\right]\) = 0 i + 0 j + 0 k

So the cross vector is a zero vector so the initial vectors are parallel to each other.

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Answer:

A.

Mean-103.0625

Median- 8, 9

Mode- 8, 1

B.

They should use the shoe size 6, because it has the most women waering it.

Your Welcome!

Step-by-step explanation:

Mean:-

Median:-

Total terms 8

Median =n/2th term +(n/2+1)th term

Mode:-

No modes

The no. of ways could those question be ordered is  1307674368000 ways A combination is what?

When selecting components from a collection using the combination method, the sequence of selection is unimportant, in contrast to permutations. In simpler scenarios, the number of combinations can be counted.

The act of combining n objects into k groups, one at a time, without repetition Repetition-allowed combinations are usually referred to as k-selection or k-combinations with repetition.

Given

that, Total no of question in quiz is 15 The no. of ways could those question be ordered is 15! ways =  1307674368000 ways The number of possible ways for those questions is 1307674368000.

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Answer:

8.6

Step-by-step explanation:

To find the distance between two points we use the formula posted below

All we need to do is figure out what the points are on the graph and plug them into the formula... we end up with

the square root of (5-(-2)^2+(2-(-3)^2 and get the answer of 8.602325267

then we round to the nearest tenth and get 8.6

Answer:

The area is 45 inches

Step-by-step explanation:

L×W=A

Answer:

60 x 120

Step-by-step explanation:

2x(x) = 7200

2\(x^{2}\) = 7200  divide both sides by 2

\(x^{2}\) = 3600

\(\sqrt{x^{2} }\) = \(\sqrt{3600}\)

x = 60

This is one of the dimensions.  The other dimension is twice 60 or 120.

a = lw

a = (60)(12)

a = 7200

Helping in the name of Jesus.

Answer:

same time , 12 minutes

Step-by-step explanation:

'A' can eat 1÷6 pizza in 2 minutes

Therefore, 'A' can eat full pizza in 6×2 minutes=12 minutes

'B' can eat 1÷4 pizza in 3 minutes

therefore, 'B' can eat full pizza in 3×4 minutes=12 minutes

So, Both 'A' and 'B' will finish at same time.

Answer:

1. If x is under a square root then x cannot equal a negative number. If x is in the denominator of a fraction then x cannot equal zero.

2. ax2 + bx + c

Step-by-step explanation: Hope this helps :)

Answer:

j

Step-by-step explanation:

From the given triangle, the statement that julie says "sinA/cosA = tan A and sinB/cosB = tan B" is true.

To prove whether Julie's statement is true or false, we need to use the triangle and the definitions of the trigonometric ratios.

In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. And, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.

Using the definitions of sine and cosine, we can write:

sin A = b/c

cos A = a/c

sin B = a/c

cos B = b/c

Dividing sin A by cos A, we get:

sin A / cos A = (b/c) / (a/c) = b/a

Similarly, dividing sin B by cos B, we get:

sin B / cos B = (a/c) / (b/c) = a/b

We can see that sin A/cos A and sin B/cos B equals to tan A or tan B respectively. Therefore, Julie's statement is true.

In conclusion, we can prove whether a trigonometric statement is true or false by using the definitions of the ratios and the triangle. In this case, Julie's statement was proved to be true.

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Answer:

102

Step-by-step explanation:

Answer:

Amir 20 Rita 45

Step-by-step explanation:

20/4=5

5*9=45

so this satisfices the ration 4:9

Answer:

Amir : 20 sweets and Rita : 45 sweets

Step-by-step explanation:

Rita has 25 more in all answers. to get the answer, this is to see which one : 4:9 ; 20:45.

we multiply 4 and 45 and 9 and 20. if we multiply them, both answers are 180. this means it is equal and that is the answer.