A certain element has a half-life of 69 years. An experiment starts with 1,500 grams of the element. The amount of the element remaining x years after the experiment began can be modeled with the function f(x) = 1,500(2)–x/69. The mathematical domain of the function is all real numbers.

Which statement describes how the reasonable domain compares to the mathematical domain?

1The reasonable domain is restricted to integers.
2The reasonable domain is restricted to positive real numbers.
3The reasonable domain has a minimum value of 1,500.
4The reasonable domain has a maximum value of 1,500.

Answer:

C) The discriminant is 0.

Step-by-step explanation:

Since the graph of the quadratic equation has only one x-intercept, we can conclude that the quadratic has only one real root.

If a quadratic equation has only one real root, then the discriminant is 0

Answer:

Quotient: y^2 -2y +3

Remainder = 0

Step-by-step explanation:

We need to solve he equation:

y^3-4y^2+7y-6 ÷ y -2

It is solved in the figure attached below:

After solving we get

Quotient: y^2 -2y +3

Remainder = 0

Answer:

48 in³

Step-by-step explanation:

The volume (V) of a pyramid is calculated as

V = [tex]\frac{1}{3}[/tex] × area of base × height

here area of base = 24 and height = 6, so

V = [tex]\frac{1}{3}[/tex] × 24 × 6 = 8 × 6 = 48 in³

Answer:

It is answer C

Step-by-step explanation:

Answer:

C.) y = x^2 -5

Step-by-step explanation:

The table pair (x, y) = (0, -5) tells you that the constant will be -5. Only answer choice C has that value for the constant.

___

You can check other (x, y) values in the rule to see that they work.

Answer

B. 4/5

Explanation

Since Clarissa has 20 DVDs, it is safe to assume that the denominator will be 20 since that is the complete total.

She also owns 16 comedy movies which is the numerator.

So far, the fraction we have is 16/20

Now reduce that number into simplest terms

16/4 = 4

20/4 = 5

4/5

Answer:

x = -2

Step-by-step explanation:

In order to find the axis of symmetry, we will have to find the x-value of the vertex.

Vertex = (-b/2a, f(-b/2a))

In x² + 4x + 6,

a = 1 , b = 4 , c = 6

Vertex = (-4/2,f(-4/2))

Vertex = (-2,f(-2))

We have found the x-value of the vertex which is -2.

Hence, line/axis of symmetry is x = -2

The axis of symmetry for f(x) = [tex]x^2 + 4x + 6[/tex]  is -2.

Given that,

Based on the above information, the calculation is as follows:

Here we have to determine the x-value of the vertex.

[tex]Vertex = (-b\div 2a, f(-b\div 2a))[/tex]

Now as per the given equation i.e [tex]x^2 + 4x + 6[/tex]

Here,

a = 1 , b = 4 , c = 6

Now  

[tex]Vertex = (-4\div 2,f(-4\div 2))[/tex]

 = (-2,f(-2))

= -2

Therefore we can conclude that the axis of symmetry for f(x) = [tex]x^2 + 4x + 6[/tex]  is -2.

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Answer:

Step-by-step explanation:

The formula of a Surface Area of a sphere:

[tex]S.A.=4\pi R^2[/tex]

R - radius

We have

[tex]S.A.=1024\pi\ in^2[/tex]

Substitute:

[tex]4\pi R^2=1024\pi[/tex]               divide both sides by π

[tex]4R^2=1024[/tex]             divide both sides by 4

[tex]R^2=256\to R=\sqrt{256}\\\\R=16\ in[/tex]

To find the radius of a sphere when you are given the surface area, you can use the formula for the surface area of a sphere, which is:
\[ \text{Surface area of a sphere} = 4 \pi r^2 \]
where \( r \) is the radius of the sphere. Now, let's solve for \( r \) using the surface area provided:
We are given that the surface area is \( 1024 \pi \) square inches, so we set that equal to the formula for the surface area:
\[ 1024 \pi = 4 \pi r^2 \]
To solve for \( r^2 \), we first divide both sides of the equation by \( 4 \pi \):
\[ \frac{1024 \pi}{4 \pi} = \frac{4 \pi r^2}{4 \pi} \]
On simplifying the left-hand side and cancelling \( 4 \pi \) from the right-hand side, we get:
\[ 256 = r^2 \]
Now, to solve for \( r \), we take the square root of both sides:
\[ r = \sqrt{256} \]
This results in:
\[ r = 16 \]
So, the radius of the sphere is 16 inches.

Answer:

C ≈ 56.55

Step-by-step explanation:

First I translated this into English.

"Find the circumference of a circle whose diameter is 18 cm."

Formula:

C = 2πr

Translated in Spanish:

Primero tienes que dividir la circunferencia por dos. Luego lo enchufas en la fórmula para "R" y resuelves.

English Translation:

First you have to divide the circumference by two. Then you plug it into the formula for "R" and solve.

For this case according to the order PEMDAS we have:

P: Perform the parenthesis calculations

E: Simplify exponential expressions

MD: Multiplications and divisions from left to right

AS: Addition and subtraction from left to right.

We have:

23 + 5 * 10÷2-33 + (11-8) =

23 + 5 * 10÷2-33 + 3 =

23 + 50÷2-33 + 3 =

23 + 25-33 + 3 =

48-33 + 3 =

15 + 3 =

18

Thus, the value of the expression is 18

ANswer:

18

Answer:

1st option because those angles are a linear pair.

Answer:

f(x) = (x + 2)(x - 5)(x - 6)

Step-by-step explanation:

given the zeros of f(x) are x = a, x= b and x = c, then the factors are

(x - a), (x - b) and (x - c)

The function is then the product of the factors

f(x) = (x - a)(x - b)(x - c)

Here zeros are x = - 2, x = 5 and x = 6, thus the factors are

(x + 2), (x - 5) and (x - 6), so

f(x) = (x + 2)(x - 5)(x - 6) ← in factored form

Final answer:

To create a polynomial with zeros at -2, 5, and 6, the factored form is (x + 2)(x - 5)(x - 6).

Explanation:

To write a polynomial function in factored form with zeros at −2, 5, and 6, we start by creating factors based on these zeros. Each zero corresponds to a factor of the polynomial where the variable x is set equal to the zero value. Therefore, the factors would be (x + 2), (x - 5), and (x - 6). We then multiply these factors together to get the polynomial.

The factored form of the polynomial is then (x + 2)(x - 5)(x - 6). If you wanted to write this polynomial in standard form, you would expand the factors to get x³ - 9x² + 4x + 60.

The radius of the circle with a circumference of 12.56 inches is 2 inches, calculated using the formula C = 2πr and rearranging it to find the radius.

The circumference of a circle is given by the formula C = 2πr, where C stands for the circumference and r stands for the radius of the circle. The value of π (pi) is approximately 3.14159. Given the circumference of the circle as 12.56 inches, you can find the radius by rearranging the equation to r = C / (2π).

Now, let's calculate the radius using the given circumference:

r = 12.56 inches / (2 × 3.14159)

r = 12.56 inches / 6.28318

r = 2 inches

Therefore, the measure of the radius of the circle is 2 inches, which corresponds to option A.

To find the measure of the radius of the circle given its circumference, we can use the circumference formula of a circle, which is:
\[ C = 2 \pi r \]
Where \( C \) is the circumference, \( \pi \approx 3.14159 \), and \( r \) is the radius of the circle.
Now, we know the circumference (\( C \)) is 12.56 inches. We can solve for the radius (\( r \)) by rearranging the formula:
\[ r = \frac{C}{2 \pi} \]
Plugging the given circumference into the equation, we get:
\[ r = \frac{12.56}{2 \times \pi} \]
\[ r = \frac{12.56}{2 \times 3.14159} \]
\[ r = \frac{12.56}{6.28318} \]
\[ r = 2 \]
Rounding the result to two decimal places as may be required for some comparisons, we still get \( r = 2.00 \) inches.
Therefore, the measure of the radius of the circle is 2 inches, which corresponds to option A.

Answer:

see explanation

Step-by-step explanation:

Given

[tex]\frac{x}{4}[/tex] > - 16 ( multiply both sides by 4 )

x > - 64

To show the solution on a number line

Place an open circle ( indicating x ≠ - 64 ) at - 64

greater than - 64 is to the right of - 64 , hence the direction of the shaded line points to the right of - 64

Tell me if you have troubles understanding something!

To find the two numbers, we set up a system of equations and solve it to find the values of x and y.

To solve this problem, we can set up a system of equations. Let's represent the two numbers as x and y. Since the sum of the two numbers is 24, we can write the equation:

x + y = 24

Twice the smaller number, which is 2x, is 3 less than the larger number, so we can write the equation:

2x = y - 3

Now we can solve this system of equations using substitution or elimination method. Let's start with substitution method:

Therefore, the two numbers are 7 and 17.

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the two numbers are 7 and 17.

The problem states that the sum of two numbers is 24 and that twice the smaller number is 3 less than the larger number. Let's denote the smaller number as 'x' and the larger number as 'y'. According to the first condition, we have:

x + y = 24 ... (1)

For the second condition, twice the smaller number (2x) is 3 less than the larger number (y), so we have:

2x = y - 3 ... (2)

To find the two numbers, we solve these equations simultaneously. By rearranging equation (2), we get y = 2x + 3. Substituting this into equation (1), we have:

x + (2x + 3) = 24

3x + 3 = 24

3x = 24 - 3

3x = 21

x = 7

Now that we have the smaller number, we substitute x back into equation (1) to find the larger number:

7 + y = 24

y = 24 - 7

y = 17

Thus, the two numbers are 7 and 17.

B is the correct choice

We used the quadratic formula (-b ± √(b² - 4ac) / 2a) to solve the quadratic equation x² - 2x - 7 = 0. We identified a, b, and c from the equation, plugged them into the formula, and solved for x to find the roots of the equation.

The subject of your question involves solving the equation

x2 - 2x - 7 = 0

using the

quadratic formula.

This is a task in Algebra, a branch of Mathematics. The quadratic formula is a tool for solving equations of the form

ax² + bx + c = 0

, also known as quadratic equations. If we apply the quadratic formula, which is -b ± √(b² - 4ac) / 2a, to solve for your equation, we start by identifying a = 1, b = -2, and c = -7 from your equation. Substituting these into the formula gives:

x = [2 ± √((-2)² - 4*1*(-7))] / 2*1

After simplifying the above, we will get the solutions for x which are the roots of the quadratic equation.

We used the quadratic formula to solve the algebraic equation x2 - 2x - 7 = 0.

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Answer:

∛x^4

Step-by-step explanation:

x^(4/3) = ∛x^4

Last option is the answer

Answer:

$5.15

Step-by-step explanation:

A dog collar usually consists of a base(collar), the embellishments and the bag in which it is packed.

As we are given,

Collar Price = c = $3

Embellishment price = e = $2

and

Bag price = b =$0.15

The cost of one collar will be the cost of all these combined.

So,

Cost of collar = c+e+b

=3+2+0.15

=5.15

So the price of one collar is $5.15 ..

Answer:

5.15

Step-by-step explanation:

The inside angle next to the 70 degrees would be 180 - 70 = 110 degrees.

The measure of an outside angle is equal the the sum of the two opposite inside angles.

X is an exterior angle and it's 2 opposite inside angles are 40 and 110.

X = 40 + 110 = 150 degrees.

The answer is E.

How much money you will make is included in a financial plan to protect assets. Hence, option A is correct.

Financial plan is the compressive study and understanding of the financial goals with looking the current situation or current financial condition. Financial plan is the best way to achieve the targeted goal in life, as it give a map and blueprint to the person to go with.

Some of the strategies to make the financial plan -

Thus, option A is correct.

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On what I don’t see anything on here

Answer:

I know that A is correct

B the first part is correct, But the second part isnt.

C I dont know, not a good grapher

D would be correct if there was tax.

Step-by-step explanation:

Answer:A,B,D are correct!

Step-by-step explanation:

Answer:

9/4 (Answer 2)

Step-by-step explanation:

Take half the coefficient of x and square that result:

(1/2)(-3) = -3/2

Squaring this, we get 9/4 (Answer 2)

To create a perfect square trinomial [tex]\frac{9}{4}[/tex] should be placed in the space shown in x^2 - 3x +___

The trinomial equation is of the form
[tex]x^{2}[/tex] - 2ax + [tex]a^{2}[/tex]

given equation is [tex]x^{2}[/tex] - 3x + _

comparing the two equation

2ax = 3x

a = [tex]\frac{3}{2}[/tex]

[tex]a^{2}[/tex] = [tex]\frac{9}{4}[/tex]

[tex]x^{2}[/tex] - 3x +  [tex]\frac{9}{4}[/tex]  =  [tex]( x- \frac{3}{2} )^{2}[/tex]

Therefore, option 2) 9/4 is the correct answer

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Answer:

x = 4 ± [tex]\sqrt{19}[/tex]

Step-by-step explanation:

Given

x² - 8x = 3

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 4)x + 16 = 3 + 16

(x - 4)² = 19 ( take the square root of both sides )

x - 4 = ± [tex]\sqrt{19}[/tex] ( add 4 to both sides )

x = 4 ± [tex]\sqrt{19}[/tex]

Final answer:

To solve the equation x^2 - 8x = 3 by completing the square, we first rearrange the equation, add 16 to both sides to form a perfect square, and then take the square root of both sides resulting in the solution set {4 + √19, 4 - √19}.

Explanation:

Completing the Square Method

To solve the equation x2 − 8x = 3 by completing the square, follow these steps:

The solution set for the equation is {4 + √19, 4 − √19}.

Answer:

[tex]\large\boxed{B.\ \dfrac{7}{8}}[/tex]

Step-by-step explanation:

[tex]\text{Put the values}\ x=\dfrac{15}{8}\ \text{and}\ y=-3\ \text{to the expression}\ \dfrac{3}{8}y^2-\dfrac{4}{3}x:\\\\\dfrac{3}{8}(-3)^2-\dfrac{4}{3\!\!\!\!\diagup_1}}\cdot\dfrac{15\!\!\!\!\!\diagup^5}{8}=\dfrac{(3)(9)}{8}-\dfrac{(4)(5)}{8}=\dfrac{27}{8}-\dfrac{20}{8}=\dfrac{27-20}{8}=\dfrac{7}{8}[/tex]

The first blank is "division" and the second blank is "multiplying"

12 / (3) = 4

5 x 3 = 15

15 + 4 = 19

The student's equation 12 _ (7 - 4) + 5 _ 3 = 19 is solved by inserting addition after 12 and subtraction after 5, resulting in 12 + (7 - 4) + 5 - 3. Following correct order of operations, we get the desired result of 19.

The student has presented a mathematical equation with missing operations that needs to be solved to equal 19. To find the correct operations, we can see that 12 with an addition operation followed by 5 minus 3 gives us 14. Adding this to the original 12 gives us the desired result of 19. Hence, the missing operations are addition after the 12 and subtraction after the 5.

The equation now looks like 12 + (7 - 4) + 5 - 3 = 19. Here, we first perform the operation inside the parentheses, which is 7 - 4 = 3. Then, we substitute this result into the expression and proceed with the operations: 12 + 3 + 5 - 3. Next, we add the numbers together, which gives us 12 + 3 + 5 = 20, and finally deduct 3 to get 20 - 3 = 19.

This kind of problem teaches us the significance of operation placement within equations, as seen in different examples provided. Understanding the properties of arithmetic operations and the correct application of the order of operations (parentheses, exponents, multiplication and division, addition and subtraction) is crucial for solving such mathematical puzzles.

Answer:

Option C.

Step-by-step explanation:

It is given that a box contains red, blue, green, purple, and yellow crayons such that the probability of drawing a purple crayon is 3/7.

We draw two crayons randomly such that both draws are independent.

Let X be a random variable that assigns the number of purple crayons to each outcome.

We need to find the range of X.

If no purple crayon is selected, then X=0

If 1 purple crayon is selected, then X=1

If 2 purple crayons are selected, then X=2

The range of X is {0,1,2}.

Therefore, the correct option is C.

ANSWER

First choice

EXPLANATION

The graph of f(x) and

[tex] {f}^{ - 1} (x)[/tex]

are symmetric about the line y=x.

This means that the graph of

[tex]{f}^{ - 1} (x)[/tex]

is the reflection of f(x) in the line y=x.

This explains why the composition of a function and its inverse yields x, as the result.

The first choice is correct.

[tex]\bf \cfrac{\textit{small prism}}{\textit{large prism}}\qquad \qquad \stackrel{~\hfill \textit{yes 1:4}}{\cfrac{18}{72}\implies \boxed{\cfrac{1}{4}}\qquad \cfrac{4}{16}\implies \boxed{\cfrac{1}{4}}\qquad \cfrac{3}{12}\implies \boxed{\cfrac{1}{4}}}[/tex]

The figures are same and the ratio of the adjacent sides of the small rectangular prism to big is 1:4 option first is correct.

It is defined as the six-faced shape, a type of hexahedron in geometry.

It is a three-dimensional shape.

As we can see in the figure two three-dimensional figures are given.

To know whether the two figures are similar or not we first find the ratio of the adjacent sides.

4/16 = 1/4

3/12 = 1/4

18/72 =1/4

The ratios are equal that's why the two figures are same, and the ratio is: 1:4

Thus, the figures are same and the ratio of the adjacent sides of the small rectangular prism to big is 1:4 option first is correct.

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12,  x 1 = 12

12 x 2 =24  

12 x 3 = 36

12 x 4 =48

12 x 5= 60  

12 x 6 =72  

12 x 7 = 84

12 x 8= 96

12 x 9= 108  

12 x 10 = 120  

12 x 11=132

12x 12= 144

hope this helps

Answer:

D. The last one

Step-by-step explanation:

When you convert measures into m³ the measurement is the SAME but it changed from cm to m. That's it.