which equation(s) have x=2 as the solution. ​

Answer:

[tex]\large\boxed{_4P_3>_4C_3}[/tex]

Step-by-step explanation:

[tex]\left\begin{array}{ccc}_nP_r=\dfrac{n!}{(n-r)!}\\\\_nC_r=\dfrac{n!}{r!(n-r)!}\end{array}\right\}\Rightarrow\dfrac{n!}{(n-r)!}>\dfrac{n^!}{r!(n-r)!}\Rightarrow_nP_r>_nC_r\\\\\text{because}\\-\text{the nominators are the same}\\-\text{the denominator}\ (n-r)!\ \text{is graeter than the denominator}\ r!(n-r)![/tex]

[tex]\text{Let's check our example:}\\\\n!=1\cdot2\cdot3\cdot4\cdot...\cdot n\\\\_4P_3=\dfrac{4!}{(4-3)!}=\dfrac{1\cdot2\cdot3\cdot4}{1!}=\dfrac{24}{1}=24\\\\_4C_3=\dfrac{4!}{3!(4-3)!}=\dfrac{1\cdot2\cdot3\cdot4}{1\cdot2\cdot3\cdot1!}=\dfrac{24}{6}=4\\\\24>4\Rightarrow_4P_3>_4C_3[/tex]

[tex]nPr = \dfrac{n!}{(n-r)!} \\ \\ nCr = \dfrac{n!}{r!(n-r)!}\\ \\ \Rightarrow nPr > nCr\\ \\ \Rightarrow \boxed{4P3 > 4C3}[/tex]

Replace t with 2.3 and solve:

8(2.3)^2 +4(2.3) + 125

Simplify:

8(5.29) + 9.2 + 125

42.32 + 9.2 + 125

51.52 + 125

176.52 meters

Answer:

176.52m

Step-by-step explanation:

Given is the height of a ball as

[tex]h(t) = 8t^2+ 4t +125[/tex]

where t is time, in seconds, after the ball was thrown and h(t) is the corresponding height, in meters

When t=2.3, substitute this for t

h(2.3) = [tex]8(2.3)^2 +4(2.3)+ 125 \\=176.52m[/tex]

Answer:

Step-by-step explanation:

Well, there is no given equation, but I can tell you that perpendicular lines have OPPOSITE MULTIPLICATIVE INVERSE [RECIPROCAL] rate of changes [slopes].

Ex: 2 --> -½; -2 --> ½

Answer:

Step-by-step explanation:

Well, there is no given equation, but I can tell you that perpendicular lines have OPPOSITE MULTIPLICATIVE INVERSE [RECIPROCAL] rate of changes [slopes].

Ex: 2 --> -½; -2 --> ½

[tex]4x^2+28x + 48=\\4(x^2+7x+12)=\\4(x^2+3x+4x+12)=\\4(x(x+3)+4(x+3))=\\4(x+3)(x+4)[/tex]

Answer:

A

Step-by-step explanation:

Given

4x² + 28x + 48 ← factor out 4 from each term

= 4(x² + 7x + 12)

To factor the quadratic

Consider the factors of the constant term (+ 12) which sum to give the coefficient of the x- term

The factors are + 4 and + 3, since

4 × 3 = 12 and 4 + 3 = 7, thus

x² + 7x + 12 = (x + 3)(x + 4) and

4x² + 28x + 48 = 4(x + 3)(x + 4) → A

Answer:

[tex]x_1=-2.9\\x_2=0.2[/tex]

Step-by-step explanation:

The first step is to move the [tex]5x[/tex] to the left side of the equation and then add the like terms:

[tex]4x^2+16x-2=5x\\\\4x^2+16x-2-5x=0\\\\4x^2+11x-2=0[/tex]

Now we can apply the Quadratic formula. This is:

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

In this case we can identify that:

[tex]a=4\\b=11\\c=-2[/tex]

Finally, we must substitute these values into the Quadratic formula. Then we get:

[tex]x=\frac{-11\±\sqrt{(11)^2-4(4)(-2)}}{2(4)}[/tex]

[tex]x_1=-2.9\\x_2=0.2[/tex]

Answer:

1 & 4

Step-by-step explanation:

Answer:

Answer 1 & 4 IS CORRECT

Step-by-step explanation:

1.  The composite figure consists of two rectangular pyramids.

4. The total volume is 45 units3.

Answer:

50

Step-by-step explanation:

You can use that sum of the opposite interior angles is equal to that exterior one.

So (30)+(4x+2)=8+6x

Combine like terms on left

32+4x=8+6x

Subtract 4x on both sides

32=8+2x

Subtract 8 on both sides

24=2x

So x=12

To find Q replace x in 4x+2 with 12 giving you 4(12)+2=48+2=50

just to add to the great reply above

Check the picture below.

Q = 4(12) + 2 = 50.

Answer:

The Greast Common Factor of 18 and 72 is 18

Step-by-step explanation:

Factors of 18: 1, 2, 3, 6, 9, 18

Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Answer:

GCF of 18 and 72 is 18

Step-by-step explanation:

To find the GCF of two or more numbers

we need two steps

Step 1: List the prime factors of each number.

Step 2: Multiply those factors all numbers have in common. If there are no common prime factors, the GCF is 1.

To find the GCF of 18 and 72

18 = 2 * 3* 3

72 = 2 * 2 * 2 * 3 * 3

Common prime factors 2, 3, 3

Therefore GCF = 2* 3 * 3 = 18

Answer:

{(-3, 1), (1, 4), (-2, 1), (0, 3)}

Step-by-step explanation:

If a set of ordered pairs represents a function, then there must not be any first coordinate that repeats itself more than once in any of the ordered pairs.

In other words, no x-coordinate should correspond to more than one y-coordinate.

From the given options, the only set of ordered pairs that satisfies the conditions of a function is;

{(-3, 1), (1, 4), (-2, 1), (0, 3)}

The correct answer is the last option.

Answer:

36

Step-by-step explanation:

You take 1/2 the linear term's coefficient and square it.

The linear term is the term that contains just an x and a number -- in this case 12x

Take 1/2 12 = 6

and square it

6^2 = 36

So when you've done that you should get

x^2 + 12x + 36 = 11 + 36

x^2 + 12x + 36 = 47

For this case we have to:

Initial weight = [tex]123 \frac {1} {4} = \frac {4 * 123 + 1} {4} = \frac {493} {4} = 123.25 \ pounds[/tex]

Final weight =[tex]120 \frac {1} {2} = \frac {2 * 120 + 1} {2} = \frac {241} {2} = 120.5 \ pounds[/tex]

We subtract to know how many pounds he lost:

[tex]123.25-120.5 = 2.75[/tex]

So, Kerry lost 2.75 pounds.

ANswer:

Kerry lost [tex]2 \frac {3} {4}[/tex] pounds.

Answer:[tex]2.75\ pounds[/tex] or [tex]2\frac{3}{4}\ pounds[/tex]

Step-by-step explanation:

You can convert the mixed numbers to decimal numbers. Divide the numerator by the denominator of the fraction and add it to the whole number part:

[tex]123\ \frac{1}{4}\ pounds=(123+0.25)\ pounds=123.25\ pounds[/tex]

[tex]120\ \frac{1}{2}\ pounds=(120+0.5)\ pounds=120.5\ pounds[/tex]

To calculate how many pounds Kerry lost, you need to subtract his weigth of a month ago and his actual weigth.

Therefore, you get that he lost:

[tex]pounds\ lost=123.25\ pounds-120.5\ pounds[/tex]

[tex]pounds\ lost=2.75\ pounds[/tex] or [tex]2\frac{3}{4}\ pounds[/tex]

Answer: B. 2764 + x ≥ 5000

Step-by-step explanation: edge

Answer:

Yes.

Step-by-step explanation:

The longest diagonal in the box is the line between one of the top corners to the opposite bottom corner.

Calculate the length of the longest diagonal in the box:

The diagonal of the base =  √(6^2 + 8^2)

= √100 = 10 inches.

The longest diagonal = √( 24^2 + 10^2)

= √676

=  26 inches

=  26 * 2.54

=  66.04 cms.

Therefore the cylinder (length 63.5 cms) rod can fit in the box.

Answer:

[tex]\large\boxed{x>-7\to\{x\ |\ x>-7\}}[/tex]

Step-by-step explanation:

[tex]4x-12<16+8x\qquad\text{add 12 to both sides}\\\\4x-12+12<16+12+8x\\\\4x<28+8x\qquad\text{subtract 8x from both sides}\\\\4x-8x<28+8x-8x\\\\-4x<28\qquad\text{change the signs}\\\\4x>-28\qquad\text{divide both sides by 4}\\\\\dfrac{4x}{4}>-\dfrac{28}{4}\\\\x>-7[/tex]

Your question asks to find the sales price of the boots.

In order to solve your question, we're going to need to find the sales price of the boots.

Lets gather some important information from the question.

Important information:

Original price is $120

40% off

With the information above, we can find the sales price.

Since we know that the original price of the boots is $120, and the boots are 40% off, we're going to need to find how much of 120 is 40% and then subtract it to get our sales price.

[tex]120*.40=48\\\\120-48=72[/tex]

Once you're done solving, you should get 72.

This means that the sales price of the boots is $72.

$72 should be your FINAL answer.

Answer: $72

Step-by-step explanation:

10% of $120 = $12 so

40% is $48, subtracted from $120 = $72

Answer:A

Step-by-step explanation:

Think about it as a process of elimination.

It can't be "B' for the simple fact that "increased by'' is a term that is often used for addition problems.

It can't be "C" because, as previously stated, sum is a term that is used in addition problems.

It can't be "D" because this is a unit that you are using.

A. "c cubed" matches the expression c^3, which means raising c to the power of 3, not the other options.

The correct phrase that matches the expression c^3 is "A.) c cubed."

In mathematics, when you see an exponent of 3 (as in c^3), it indicates that you should multiply the base, c, by itself three times. This is commonly referred to as "c cubed." It signifies that you should raise c to the power of 3, meaning c * c * c. The other options are not accurate representations of c^3:

B.) "c increased by 3" does not involve exponentiation; it implies adding 3 to c.

C.) "the sum of 3 and c" is simply c + 3 and does not involve cubing.

D.) "3 cubed" represents 3^3, which equals 27, and is different from c^3.

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Answer:

Step-by-step explanation:

Error is the difference from the nominal value, hence the nominal value is what is subtracted from x. We want the magnitude of that difference, | x-11.93 |, to be less than the maximum error value, 0.02, so the inequality is ...

  |x -11.93| ≤ 0.02

__

We can solve this by "unfolding" it, then adding 11.93:

  -0.02 ≤ x -11.93 ≤ 0.02

  11.91 ≤ x ≤ 11.95

Answer:

The maximum height  is 191.063 ft

Step-by-step explanation:

We can easily solve this question by plotting the graph of the equation below

h(t)=-16t^2+Vt+h

Where

h = initial height = 2ft

V = initial speed = 110 ft/s

t = time in seconds

Please, see attached image below

The maximum height corresponds to

191.063 ft

The maximum height the ball will attain is 115.02 feet.

The maximum height can be found by identifying the vertex of the quadratic equation representing the projectile's height.

Given the equation h(t) = -16t^2 + Vt + h, where V is the initial speed of the ball and h is the initial height, we substitute the given values V = 110 and h = 2 into the equation.

The equation becomes h(t) = -16t^2 + 110t + 2.

To find the maximum height, we need to find the vertex of this quadratic equation. The x-coordinate of the vertex can be found using the formula x = -b/2a, where a = -16 and b = 110. Plugging in these values, we have x = -110 / (2*(-16)) = 110/32 = 3.4375.

Now we can substitute this x-value back into the equation to find the y-coordinate of the vertex. h(3.4375) = -16(3.4375)^2 + 110(3.4375) + 2 = 115.02 feet.

Therefore, the ball will attain a maximum height of 115.02 feet.

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Answer: stocks

^^^^^^^^^^^^^^^^

Answer:

The best answer would be D

Step-by-step explanation:

This would be best because if you sketch about an object or thing you are making it can help you better picture what you are making or someone else therefore the answer is D

Answer:

Yes, it's the same number.

Answer: Of course, it's just that mathematician geniuses added a point and two zeros after it.

Answer:

# m∠A = 65.3°

# m∠A = 25.8°

# m∠A = 22.7°

Step-by-step explanation:

* Lets revise the trigonometry function to solve the problem

- In any right angle triangle:

# The side opposite to the right angle is called the hypotenuse

# The other two sides are called the legs of the right angle

* If the name of the triangle is ABC, where B is the right angle

∴ The hypotenuse is AC

∴ AB and BC are the legs of the right angle

- ∠A and ∠C are two acute angles

- For angle A

# sin(A) = opposite/hypotenuse

∵ The opposite to ∠A is BC

∵ The hypotenuse is AC

∴ sin(A) = BC/AC

# cos(A) = adjacent/hypotenuse

∵ The adjacent to ∠A is AB

∵ The hypotenuse is AC

∴ cos(A) = AB/AC  

# tan(A) = opposite/adjacent

∵ The opposite to ∠A is BC

∵ The adjacent to ∠A is AB

∴ tan(A) = BC/AB

* Lets solve the problems

# In Δ ABC

∵ m∠B = 90°

∵ AB = 2.3 ⇒ adjacent to angle A

∵ BC = 5 ⇒ apposite to angle A

- To find m∠A use the tangent function because we have opposite

  and adjacent sides

∴ tan A = BC/AB

∴ tan A = 5/2.3 ⇒ use tan^-1 to find m∠A

∴ m∠A = [tex]tan^{-1}\frac{5}{2.3}=65.29756[/tex]

* m∠A = 65.3°

# In Δ ABD

∵ m∠B = 90°

∵ AB = 5.4 ⇒ adjacent to angle A

∵ DA = 6 ⇒ the hypotenuse

- To find m∠A use the cosine function because we have adjacent

  and hypotenuse sides

∴ cos A = AB/DA

∴ cos A = 5.4/6 ⇒ use cos^-1 to find m∠A

∴ m∠A = [tex]cos^{-1}\frac{5.4}{6}=25.84193[/tex]

* m∠A = 25.8°

# In Δ ABE

∵ m∠B = 90°

∵ EB = 2.4 ⇒ opposite to angle A

∵ EA = 6.8 ⇒ the hypotenuse

- To find m∠A use the sine function because we have opposite

  and hypotenuse sides

∴ sin A = EB/EA

∴ sin A = 2.4/6.8 ⇒ use sin^-1 to find m∠A

∴ m∠A = [tex]sin^{-1}\frac{2.4}{6.8}=22.6673[/tex]

* m∠A = 22.7°

Answer:

b and f

c and e

Step-by-step explanation:

Basically, this question is testing your knowledge on supplementary angles (angles that add up to 180) and corresponding angles (angles that are across from each other that have the same value).

Using the information the diagram has given you, you just need to plug in the correct values for each angle. Once you've completed that, you just match them up. If two of the top right corners are 90.5, then they match! I made a little diagram, though it might be a little confusing :/// I hope I helped a little :)

Answer:

yes, no, no

Step-by-step explanation:

For odd functions : −f(x) = f(−x) for all x

For even functions :f(x) = f(−x) for all x

1) -f(x)= -2x^3 -2x

f(-x) = -2x^3-2x

yes

2 ) f(-x) = 5x^3 -4 ≠ f(x)

no

3  )  f(-x) = -4x -4   ≠ f(x)

no

1) [tex]f(-x) = -2x^3-2x[/tex]

The function [tex]f(x)=2x^3 + 2x[/tex] is odd function.

2 ) [tex]f(-x) = 5x^3 -4[/tex] ≠ f(x)

The function [tex]f(x) = -5x^3 - 4[/tex] is not even function.

3 ) f(-x) = -4x - 4 ≠ f(x)

The function f(x) = 4x - 4 is not an even even function.

If we obtain an expression that exists equivalent to f(x), we have an even function; if we obtain an expression that stands equivalent to -f(x), we contain an odd function; and if neither occurs, it is neither!

For odd functions :

−f(x) = f(−x) for all x

For even functions :

f(x) = f(−x) for all x

1) [tex]f(-x) = -2x^3-2x[/tex]

Therefore, the function [tex]f(x)=2x^3 + 2x[/tex] is odd function.

2 ) [tex]f(-x) = 5x^3 -4[/tex] ≠ f(x)

Therefore, the function [tex]f(x) = -5x^3 - 4[/tex] is not even function.

3 ) f(-x) = -4x - 4 ≠ f(x)

Therefore, the function f(x) = 4x - 4 is not an even even function.

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Answer:

Option B.  [tex]y-45=5(x-9)[/tex]

Step-by-step explanation:

Let

x -----> the number of hours

y ----> the number of goods

we know that

The equation of a line in point slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=5\ \frac{goods}{h}[/tex] ----> the rate is the same that the slope of the linear equation

[tex]point\ (9,45)[/tex] --->(At hour 9, the company had produced 45 goods)

substitute

[tex]y-45=5(x-9)[/tex]

Answer:

587.18 in^2

Step-by-step explanation:

Given:

Diameter = d = 11 inches

Slant height = l =28.5 inches

Radius will be half of diameter

r = d/2 = 11/2 = 5.5 in

We know that the formula for surface area of cone is:

[tex]SA = \pi rl+\pi r^2\\Putting\ the\ values\\SA = (3.14*5.5*28.5)+(3.14 * 5.5 * 5.5 )\\= 492.195+94.985\\=587.18\ in^2[/tex]

Hence, second option is correct ..

Answer: second option.

Step-by-step explanation:

We know that we can calculate the surface area of a cone with this formula:

[tex]SA=\pi rl + \pi r^2[/tex]

Where "r" is the radius and "l" is the slant heigth.

We know that the radius is half the diameter, then the radius of this cone is:

[tex]r=\frac{11in}{2}\\\\r=5.5in[/tex]

Since we know tha radius and the slant height, we can substitute values into the formula, using 3.14 for π.

Therefore, we get:

 [tex]SA=(3.14)(5.5in)(28.5in) + (3.14)(5.5in)^2=587.18in^2[/tex]  

The equation of a function whose parent function, f(x) = x + 5, is shifted 3 units to the right will be; g(x) = x + 2

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that, the parent function f(x) = x + 5 is shifted 3 units to the right

If the function of x is translated horizontally to the right by h units, then the new function will be g(x) = f(x - h)

If the function of x is translated horizontally to the left by h units, then the new function will be g(x) = f(x + h)

Thus, f(x) = x + 5 is shifted 3 units to the right:

The new function is

g(x) = f(x - h)

Here h = 3

f(x) = x + 5

The x in f(x) will change to (x - 3)

= (x - 3) + 5

The new function g(x) = x + 2

Hence, Option D is correct

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Final answer:

The correct equation after shifting the parent function f(x) = x + 5 three units to the right is g(x) = x + 2.

Explanation:

The equation of a function that is shifted 3 units to the right from its parent function, f(x) = x + 5, will incorporate that horizontal shift by subtracting 3 from the variable x before applying the rest of the function. Therefore, the new function, g(x), will have the form g(x) = (x - 3) + 5 which simplifies to g(x) = x + 2. This accounts for the fact that the input to the function is effectively 3 units greater for the same output as the original function.

Answer:

Look to the bold answer down

Step-by-step explanation:

* Lets explain how to restrict the domain of the quadratic function

- The quadratic function is two-to-one function

- The inverse of it is one-to-two which is not a function

- So we can not find the inverse of the quadratic function until restrict its

 domain

- We restrict the domain at the x-coordinate of the vertex of the function

∵ f(x) = (x - h)² + k is the standard form of the quadratic function, where

  (h , k) are the coordinates of its vertex

- To restrict the domain we put x > h for the right part of the parabola

  or x < h for the left part of the parabola

* Lets solve the problem

∵ f(x) = (x - 2)²

∵ f(x) = (x - h)² + k is the standard form of the quadratic function

∴ h = 2 and k = 0

∴ The vertex of the parabola is (2 , 0)

- We will restrict the domain at x = 2

∴ The domain of the function f(x) to have inverse is x > 2 or x < 2

* The restriction domain is x > 2 or x < 2

- To find the inverse of the function switch x and y and solve for the

  new y

∵ f(x) = (x - 2)²

∵ f(x) = y

∴ y = (x - 2)²

- Switch x and y

∴ x = (y - 2)²

- take square root for both sides

∴ ± √x = y - 2

- Add 2 for both sides

∴ ± √x + 2 = y

∴ [tex]f^{-1}=\sqrt{x}+2=====OR=====f^{-1}=-\sqrt{x}+2[/tex]

* For the domain x > 2 of f(x) the inverse is [tex]f^{-1}(x) = \sqrt{x}+2[/tex]

 For the domain x < 2 of f(x) the inverse is [tex]f^{-1}(x)=-\sqrt{x}+2[/tex]