what is the domain of f

the solutions are (x = 2) and (y = 4).

To find the values of x and y in the given equations, let's solve them step by step:

1. (3^{2x-y} = 1)

For any nonzero number raised to the power of 0, the result is always 1. Therefore, we can rewrite the equation as:

[2x - y = 0]

Now, we have one equation in terms of (x) and (y).

2.[tex]\( \frac{16^x}{4} = 8^{3x-y} \)[/tex]

We'll simplify the left side first:

[tex]\[ \frac{16^x}{4} = \frac{(4^2)^x}{4} = \frac{4^{2x}}{4} = 4^{2x-1} \][/tex]

Now, the equation becomes:

[4^{2x-1} = 8^{3x-y}]

We know that (8 = 2^3), so we can rewrite the right side of the equation in terms of 2:

[4^{2x-1} = (2^3)^{3x-y} = 2^{9x-3y}]

Now, we have:

[4^{2x-1} = 2^{9x-3y}]

Since (4 = 2^2), we can rewrite the left side as:

[ (2^2)^{2x-1} = 2^{4x-2} ]

So, the equation becomes:

[2^{4x-2} = 2^{9x-3y}]

Since the bases are the same, the exponents must be equal:

[4x - 2 = 9x - 3y]

Now, we have two equations:

[2x - y = 0]

[4x - 2 = 9x - 3y]

From the first equation, we can solve for (y):

[y = 2x]

Substituting (y = 2x) into the second equation:

[4x - 2 = 9x - 3(2x)]

[4x - 2 = 9x - 6x]

[4x - 2 = 3x]

[x = 2]

Now, substituting (x = 2) into the first equation to find (y):

[2(2) - y = 0]

[4 - y = 0]

[y = 4]

So, the solutions are (x = 2) and (y = 4).

Answer:

An exponent value in a would make the system inconsistent because it will either gain or lose height over time.

Any real number without an exponent value will make the system consitent.

Any infintite/repeating number will make the system both consistent and inconsistent. it is consisent because it will stay at a constant rate but also inconsistent because it is repeating and will never end.

Answer:

When a = 3 and b ≠ 5, the system will be inconsistent because the lines will be parallel. When a = 3 and b = 5, the system will be consistent and dependent because they represent the same line.

Answer:

you cant do that but the answer would be 0

Step-by-step explanation:

because if you eat something it would be gone in our tummy

Answer:

Equation:

[tex]15=\dfrac{1}{2}x+8[/tex]

Student ticket price = $14

Step-by-step explanation:

An adult ticket = $15

Let a student ticket = $x

An adult ticket is half the price of a student ticket plus $8, then an adult ticket

[tex]=\$\left(\dfrac{1}{2}x+8\right)[/tex]

Equate the prices for the adult ticket:

[tex]15=\dfrac{1}{2}x+8[/tex]

Subtract 8 from both sides:

[tex]15-8=\dfrac{1}{2}x+8-8\\ \\7=\dfrac{1}{2}x[/tex]

Multiply this equation by 2:

[tex]7\cdot 2=x\\ \\x=\$14[/tex]

Answer:

(1/2)x + 8 = 15

Step-by-step explanation:

Answer:

There are four sisters and three brothers in the family.

Step-by-step explanation:

Each brother has only half as many brothers as sisters.

1 boy = 4 sisters and 3 brothers

1 girl = 3 sisters and four brothers

Be sure to count the sisters and brothers in total and in terms of their own number of siblings.

Answer:

12,6

Step-by-step explanation:

The explicit rule for the arithmetic sequence on which the series is based is an = 12 + (n - 1)  * 6

Series are sum of sequences. The nth term of an arithmetic series is expressed as:

an = a + (n - 1)d

where

a is the first term = 12

n is the number of terms

d is the common difference = 18 - 12 = 24 - 18 = 6

Substitute

an = 12 + (n - 1)  * 6

Hence the explicit rule for the arithmetic sequence on which the series is based is an = 12 + (n - 1)  * 6

Learn more on explicit rule here: https://brainly.com/question/2059043

Answer:

Step-by-step explanation:

The first one I would factor the difference of cubes on top and then cancel a common factor this would end up giving you sin^2(A/2)+sin(A/2)cos(A/2)+cos^2(A/2)

(the 1st+3rd term here actually equals 1)

now you have

1+sin(A/2)cos(A/2)

1+1/2*2sin(A/2)cos(A/2)    (this step was just to help show how I'm going to use the next identity)

1+1/2sin(A)                    (double angle identity for sine)

hint for the next one: I would multiply top and bottom by bottom's conjugate first

Answer:

B) 3

Step-by-step explanation:

The parts on the right side are to figure out which one to use so since g(3) then you plug in 3 to the equations on the right to see which one is true. The one that it matches into then plug in 3 for x in the equation directly to the left of it:

3 ≥ 3 so 6 - (3) = 3

Answer:

The degree of the polynomial is 2

Step-by-step explanation:

The absolute degree is obtained with the sum of the exponents of all the variables of each term. The terms are the elements of the polynomial with numbers and letters separated by addition or subtraction.

Answer:

(p-6)(3c + 4)

Step-by-step explanation:

Note that (p-6) is a factor of both terms.  Factoring out (p-6), we get:

(p-6)(3c + 4).

Answer:

All real numbers

Step-by-step explanation:

f(x) is a polynomial and is well defined for all real values of x

Domain is x ∈ R

The domain of the function[tex]$$f(x)=x^{2}+3 x+5$$[/tex] is (D). All real numbers

It is provided that,

[tex]$$f(x)=x^{2}+3 x+5$$[/tex]

This exists as the equation of a vertical parabola opens upward.

The vertex exists at a minimum

utilizing a graphing tool

The vertex is the point (-1.5,2.75)

The range is the interval -------> [2.75.∞)

[tex]y \geq 2.75[/tex] ------->All real numbers greater than or equal to 2.75

The domain is the interval -------> (-∞,∞) -----> All real numbers

Hence, The domain of the function[tex]$$f(x)=x^{2}+3 x+5$$[/tex] is (D). All real numbers.

To learn more about the Domain of  function refer to:

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Answer:

see explanation

Step-by-step explanation:

To find the y- intercept let x = 0

f(0) = 0² - 8(0) - 10 = 0 - 0 - 10 = - 10

The y- intercept is (0, - 10)

To find the x- intercepts let f(x) = 0, that is

2x² - 8x - 10 = 0 ( divide through by 2 )

x² - 4x - 5 = 0

Consider the factors of the constant term (- 5) which sum to give the coefficient of the x- term (- 4)

The factors are - 5 and + 1, since

- 5 × 1 = - 5 and - 5 + 1 = - 4, hence

(x - 5)(x + 1) = 0

Equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

x + 1 = 0 ⇒ x = - 1

The x- intercepts are (- 1, 0) and (5, 0)

Final answer

The y-intercept of the function f(x) = 2x²8x-10 is at (0, -10), and the x-intercepts are (-1,0) and (5,0).

To determine the y-intercept and the other x-intercept of the quadratic function f(x) = 2x²-8x-10, we can use the standard forms and properties of quadratic equations.

The y-intercept occurs when x=0. Substituting x with 0 in the function, we get f(0) = 2(0)²- 8(0) - 10 = -10. Thus, the y-intercept is at (0, -10).

To find the other x-intercept given one of them as (-1,0), we can factor the quadratic equation, or use the quadratic formula. Factoring gives us:

(2x + 2)(x - 5) = 0

2x + 2 = 0 would give us an x-intercept at x = -1, which we already have. x - 5 = 0 gives us the other x-intercept at x = 5. So, the other x-intercept is at (5,0).

Answer:

D

Step-by-step explanation:

By definition:

rational number = fraction or decimals that are non-whole numbers

negative = well..... negative numbers have a minus (-) in front of them.

Looking at the options, only D has a fraction that has a (-).

Answer:

see explanation

Step-by-step explanation:

Since the sequence is geometric then the common ratio (r) is

r = [tex]\frac{18}{24}[/tex] = [tex]\frac{3}{4}[/tex] = 0.75

To find the next term in the sequence, multiply the previous term by r

The next 3 terms are

18 × 0.75 = 13.5

13.5 × 0.75 = 10.125

10.125 × 0.75 = 7.59375

The n th term equation of a geometric sequence is

[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]

where a is the first term, that is a = 24, hence

[tex]a_{n}[/tex] = 24[tex](0.75)^{n-1}[/tex]

Answer:

x= -10

Step-by-step explanation:

(3)8+ [tex]\frac{\sqrt{2x+29} }{3}[/tex]= 9(3) (multiply both sides by 3)

24+ [tex]\sqrt{2x+29}[/tex]= 27  (move the 24 to the right)

[tex]\sqrt{2x+29}[/tex]=27-24 (subtract)

([tex]\sqrt{2x+29}[/tex])²= 3²  (square both sides)

2x+29=9 (move the 29 to the other side)

2x=9-29 (subtract)

2x= -20 (divide both sides by 2)

x= -10

hope this helps and good luck! :)

Step-by-step explanation:

[tex]x {}^{2} = 7x + 4[/tex]

It can also be written as:-

[tex]x {}^{2} - 7x - 4 = 0[/tex]

Now, here a=1, b= -7 and c = -4

Now by quadratic formula,

[tex]d = b {}^{2} - 4ac[/tex]

Calculate d which is

[tex] \sqrt{65} [/tex]

Now, the roots will be:-

[tex]x = ( - b + \sqrt{d} ) \div 2a[/tex]

and hence it will become:-

[tex]x = (7 + \sqrt{65} ) \div 2[/tex]

and

[tex] x = (7 - \sqrt{65} ) \div 2[/tex]

Answer: third option.

Step-by-step explanation:

Move the [tex]7x[/tex] and [tex]4[/tex] to the left side of the equation:

[tex]x^2 = 7x+ 4[/tex]

 [tex]x^2 -7x- 4=0[/tex]

Now you need to apply  the Quadratic formula:

[tex]x=\frac{-b\±\sqrt{b^2-4ac} }{2a}[/tex]

In this case you can identify that:

[tex]a=1\\b=-7\\c=-4[/tex]

Then you can substitute values into the Quadratic formula and get the following solutions:

[tex]x=\frac{-(-7)\±\sqrt{(-7)^2-4(1)(-4)} }{2*1}\\\\x_1=\frac{7-\sqrt{65} }{2}\\\\x_2=\frac{7+\sqrt{65} }{2}[/tex]

Answer:

No

Step-by-step explanation:

To determine if the 3 sides form a right triangle.

Use the converse theorem of Pythagoras.

If the square of the longest side is equal to the sum of the squares of the other two sides then the triangle is right,

longest side = 14 and 14 ² = 196

9² + 12² = 81 + 144 = 225

Since 196 ≠ 225 the triangle is not right

Answer:

Infinitely many solutions

Step-by-step explanation:

There is a solution, but not one, there is an infinite amount of them.

Thats why if you were to graph this it'd just be a line continuously going up

Konichiwa~! My name is Zalgo and I am here to help you out on the marvelous day! The answer to your question is Answer Choice C;Infinitely Many Solutions.

I hope that this helps! :D

"Stay Brainly and stay proud!" - Zalgo

(By the way, do you think you could give me Brainliest? I'd really appreciate it! Have a nice day! :3)

Answer:

4845 ways

Step-by-step explanation:

To solve this problem we use the formula of combinations

[tex]nCr=\frac{n!}{r!(n-r)!}[/tex]

Where n is the total number of students that can be chosen and you choose r from them.

So

[tex]n = 20\\r = 4[/tex]

Note that in this case the order in which the 4 students are chosen does not matter.

Then

[tex]20C4=\frac{20!}{4!(20-4)!}[/tex]

[tex]20C4=\frac{20!}{4!*16!}=4845\ ways[/tex]

Answer:

4845

Step-by-step explanation:

Total number of students : 20

Students to be picked : 4

Does order matter? : No

Use combination formula (see attached)

Answer:

undefined

Step-by-step explanation:

A line with a slope of zero is a horizontal line parallel to the x- axis

Thus, a line perpendicular to it is a vertical line parallel to the y- axis, with an undefined slope.

The new surface area of a square pyramid when its dimensions are multiplied by 1/3 is calculated by squaring the scale factor (1/3) and multiplying it with the original surface area. In this case, the new surface area is 121 in².

When the dimensions of a square pyramid are multiplied by 1/3, each linear dimension of the pyramid becomes one-third of its original size. Since surface area is a two-dimensional measure (length × width), when you scale down each dimension by a factor of 1/3, the new surface area will be the square of that scale factor times the original area. The surface area is proportional to the square of the scaling factor because area is calculated using two dimensions.

The original surface area is 1,089 in². To find the new surface area, we use the scale factor squared: (1/3) ² = 1/9. We then multiply the original surface area by this factor:

New Surface Area = Original Surface Area × (Scale Factor)²
New Surface Area = 1,089 in² × 1/9
New Surface Area = 1,089 in² / 9
New Surface Area = 121 in²

Therefore, the new surface area of the square pyramid when the dimensions are multiplied by 1/3 will be 121 in².

Answer:

y = 5x + 29

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 5x + 2 is in this form with slope m = 5

• Parallel lines have equal slopes, hence

y = 5x + c ← is the partial equation of the parallel line

To find c substitute (- 6, - 1) into the partial equation

- 1 = - 30 + c ⇒ c = - 1 + 30 = 29, thus

y = 5x + 29 ← in slope- intercept form

Answer:8

Step-by-step explanation:

Solving the given equation we get  [tex]\[ -\frac{5}{4} < x < \frac{5}{2} \][/tex]

1. We start by isolating the absolute value expression by adding 7 to both sides of the inequality.

2. Then, we split the inequality into two cases based on the inner expression of the absolute value: when [tex]\( 5 - 8x \)[/tex] is non-negative and when it is negative.

3. Solving each case separately, we find the range of values for [tex]\( x \).[/tex]

4. Finally, we combine the solutions from both cases to get the final solution: [tex]\( -\frac{5}{4} < x < \frac{5}{2} \).[/tex]This means that[tex]\( x \)[/tex]lies between -5/4 and 5/2.

To solve the inequality[tex]\( |5 - 8x| - 7 < 8 \)[/tex], we'll first isolate the absolute value expression and then solve for [tex]\( x \).[/tex]

1. Add 7 to both sides:

[tex]\[ |5 - 8x| < 15 \][/tex]

2. Now, we'll split the inequality into two cases based on the inner expression of the absolute value:

Case 1: [tex]\( 5 - 8x \geq 0 \)[/tex]

[tex]\[ 5 - 8x < 15 \][/tex]

[tex]\[ -8x < 10 \][/tex]

[tex]\[ x > \frac{10}{-8} \][/tex]

[tex]\[ x > -\frac{5}{4} \][/tex]

Case 2:[tex]\( 5 - 8x < 0 \)[/tex]

[tex]\[ -(5 - 8x) < 15 \][/tex]

[tex]\[ -5 + 8x < 15 \][/tex]

[tex]\[ 8x < 20 \][/tex]

[tex]\[ x < \frac{20}{8} \][/tex]

[tex]\[ x < \frac{5}{2} \][/tex]

So, we have two sets of solutions:

Case 1: [tex]\( x > -\frac{5}{4} \)[/tex]

Case 2:[tex]\( x < \frac{5}{2} \)[/tex]

Combining these two cases, we get:

[tex]\[ -\frac{5}{4} < x < \frac{5}{2} \][/tex]

1. We start by isolating the absolute value expression by adding 7 to both sides of the inequality.

2. Then, we split the inequality into two cases based on the inner expression of the absolute value: when \( 5 - 8x \) is non-negative and when it is negative.

3. Solving each case separately, we find the range of values for \( x \).

4. Finally, we combine the solutions from both cases to get the final solution: [tex]\( -\frac{5}{4} < x < \frac{5}{2} \).[/tex] This means that [tex]\( x \)[/tex] lies between -5/4 and 5/2.

Complete question

Solve |5-8x| -7 < 8

Answer:

A rectangle has rotational symmetry of order 2.

Step-by-step explanation:

The rotational symmetry involves rotation.

The rotational symmetry of order is the number of times a shape is mapped onto itself during a 360° rotation.

A rectangle has rotational symmetry of order 2.

When a rectangle is rotated on 180° or 360° it is mapped onto itself.

Answer:

2

180 & 360

Step-by-step explanation:

Answer:

First day: 45x +20y = 875

Second day: 25x + 40y = 775

Adult ticket price: $15

Step-by-step explanation:

See paper attached. (:

The system of equations that model this scenario is:

45x + 20y = $875 equation 1

25x + 40y = $775 equation 2

The price of adults tickets is $15. The price of student's ticket is $10.

In order to determine this value, multiplot equation 1 by 2 and subtract the resulting equation from equation 2.

90x + 40y = 1750 equation 3

975 = 65x

x = 15

Substitute for x in equation 1

45(15) + 20 = 875

675 + 20y = 875

y = (875 - 675) / 20

y = 10

To learn more about simultaneous equations, please check: https://brainly.com/question/25875552

Answer:

[tex]\frac{5}{6}\ of\ the \ test[/tex]

Step-by-step explanation:

we know that

Landon finished 1/2 of the test in 3/5 of an hour

so

by proportion

Find out how much of the test will he have done in one hour

[tex]\frac{(1/2)}{(3/5)}\frac{test}{hours} =\frac{x}{1}\frac{test}{hour}\\ \\x=(1/2)*(5/3)\\ \\x=\frac{5}{6}\ of\ the \ test[/tex]

Answer:

5/6

Step-by-step explanation:

you just do it.

Answer:

x = 7

Step-by-step explanation:

The property of a parallelogram is the opposite sides are congruent, hence

AD = BC ← substitute values

5x + 3 = 38 ( subtract 3 from both sides )

5x = 35 ( divide both sides by 5 )

x = 7

Step-by-step explanation:

The expected value is the sum of each probability times the value.

E = 0.25 (10) + 0.75 (-5)

E = -1.25

The stock is expected to decrease by $1.25.