Find the vertex of the graph of the function.
f(x) = 2x2 - 8x + 9

Answer:

the answer is C) 12

Step-by-step explanation:

rawr

Answer:

Dolphin is 3 feet above the surface of the water.

Step-by-step explanation:

Dolphin is 30 feet below the surface of the water, then its position on the vertical number line is -30.

Thus,

[tex]-30+23-17+27\\ \\=(-30-17)+(23+27)\\ \\=-47+50\\ \\=3[/tex]

Dolphin is 3 feet above the surface of the water.

Final answer:

After a series of movements, the calculated final position of the dolphin is 3 feet above the surface of the water, which is a reasonable result for a dolphin.

Explanation:

The question involves calculating the final position of a dolphin relative to the water surface after a series of vertical movements (rising and sinking). Initially, the dolphin is 30 feet below the surface. Then, the following movements occur:

The dolphin rises 23 feet.

The dolphin sinks 17 feet.

The dolphin rises another 27 feet.

To find out where the dolphin is relative to the surface after these movements, we can sum the changes in position:

Initial position: -30 feet (below the surface is considered negative)

+ Rise 23 feet: -30 + 23 = -7 feet

+ Sink 17 feet: -7 - 17 = -24 feet

+ Rise 27 feet: -24 + 27 = +3 feet

After calculating these movements, the dolphin is 3 feet above the surface of the water. Dolphins are known to be able to jump several times their length out of the water, and considering they measure about 2 meters long, this result of the dolphin being 3 feet above the water is reasonable.

Answer:

  $2.50

Step-by-step explanation:

The total fee is the fee per share multiplied by the number of shares:

  $0.025 × 100 = $2.50 . . . . Erin's brokerage fee

Answer:

2.50

Step-by-step explanation:

Answer:

Problem 1: 5x-3y=-7 has One Solution

Problem 2: 10x-6y=-14 has One Solution

Answer:

NO, It is non terminating / recurring decimal

Step-by-step explanation:

3/9= 0.33333333......

remainder= 3

The basketball player's mass is approximately 46.2857 kilograms.

To solve for the player's mass, we can rearrange the equation to isolate the mass variable. The equation can be rewritten as m = 36S/h.

Plugging in the given values, we get m = 36 * 2.7 / 2.1.

Solving this expression gives us a mass of approximately 46.2857 kilograms.

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It would have a greater slope and perhaps start higher on the y axis.

Step-by-step explanation:

I assume you can choose your own numbers as long as they are higher than the current. This means the numbers on your y axis will change but not the numbers on your x axis because that determines the time. So let's change the y axis numbers from going by 20 and make them go by 25. You could technically keep the dots in the same place as long as you change the y axis numbers because you are still earning more money.

The Original length of each side of square was 14.25 inches.

Step-by-step explanation:

Perimeter of a square is given by:

Perimeter = 4 * side

Let x be the original length of each side of square

So

decreasing 2 inch will mean

[tex]x-2[/tex]

Perimeter of square after reducing 2 inches from each side

[tex]4(x-2) = 49\\4x-8 = 49\\4x = 49+8\\4x = 57\\\frac{4x}{4} = \frac{57}{4}\\x = 14.25[/tex]

So,

The Original length of each side of square was 14.25 inches.

Keywords: Perimeter, square

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Answer:

Second option: [tex]3 + 4 x\leq 2 (1 + 2x)[/tex]

Step-by-step explanation:

Let's solve for "x" from each inequality:

[tex]a.\ 6 (x + 2)>x-3\\\\6x+12>x-3\\\\6x-x>-3-12\\\\5x>-15\\\\x>\frac{-15}{5}\\\\x>-3[/tex]

[tex]b.\ 3 + 4 x\leq 2 (1 + 2x)\\\\3+4x\leq 2+4x\\\\3-2\leq 4x-4x\\\\1\leq 0\  (FALSE.\ IT\ HAS\ NO\ SOLUTION)[/tex]

[tex]c.\ -2 (x + 6)<x-20\\\\-2x-12<x-20\\\\-12+20<x+2x\\\\8<3x\\\\x>\frac{8}{3}[/tex]

[tex]d.\ x-9<3(x-3)\\\\x-9<3x-9\\\\x-3x<-9+9\\\\-2x<0\\\\x>0[/tex]

The inequality that has no solution is: 3 + 4x ≤ 2(1 + 2x).

The correct option is 2nd.

Given are inequalities, we need to check which of them has no solution.

Let's solve each inequality to determine if it has a solution:

1) 6(x + 2) > x - 3

First, distribute the 6:

6x + 12 > x - 3

Now, let's isolate the variable x on one side:

6x - x > -3 - 12

5x > -15

Finally, divide by 5 to solve for x:

x > -3

This inequality does have a solution, and x can take any value greater than -3.

2) 3 + 4x ≤ 2(1 + 2x)

First, distribute the 2 on the right side:

3 + 4x ≤ 2 + 4x

Now, subtract 4x from both sides:

3 ≤ 2

This is not true, and there is no value of x that satisfies this inequality.

So, this inequality has no solution.

3) -2(x + 6) < x - 20

First, distribute the -2:

-2x - 12 < x - 20

Now, let's isolate the variable x on one side:

-2x - x < -20 + 12

-3x < -8

Finally, divide by -3 to solve for x (note the sign change when dividing by a negative number):

x > 8/3 or x > 2.67

This inequality has a solution, and x can take any value greater than 2.67.

4) x - 9 < 3(x - 3)

First, distribute the 3 on the right side:

x - 9 < 3x - 9

Now, move the variables to one side:

x - 3x < 9 - 9

-2x < 0

Finally, divide by -2 to solve for x (note the sign change when dividing by a negative number):

x > 0

This inequality has a solution, and x can take any value greater than 0.

Hence, the inequality that has no solution is: 3 + 4x ≤ 2(1 + 2x).

The correct option is 2nd.

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The value of [tex]x_2 = 1[/tex]

Solution:

Given that a approximate solution to the equation [tex]x^2 +6x - 2=0[/tex] can be calculated using the iterative formula shown below

[tex]x_{n+1} = \frac{2-(x_n)^3}{6}[/tex]

Also given that [tex]x_1 =2[/tex]

To find: value of [tex]x_2[/tex]

To find value of [tex]x_2[/tex] , substitute n = 1 in given iterative formula

[tex]x_{1+1} = \frac{2-(x_1)^3}{6}[/tex]

Solve the above expression by substituting [tex]x_1 = 2[/tex]

[tex]x_2 = \frac{2-(2)^3}{6}[/tex]

[tex]x_2 = \frac{2-8}{6}\\\\x_2 = \frac{-6}{6}\\\\x_2 = -1[/tex]

Thus value of [tex]x_2 = 1[/tex]

HERE'S YOUR ANSWER:

Let number of girls be- x

and number of boys be- 2x(boys are 2 times NO. of girls)

therefore

x + 2x = 24

3x = 24

x = 24/3

x = 8

hence number of girls = 8

boys are 2 times more than girls = 16

HOPE IT HELPS...

Answer:

slower 50mph faster 60mph

Step-by-step explanation:

Distance=s⋅t

Distance

=

(

+

10

)

⋅

(

−

0.5

)

Distance=(s+10)⋅(t−0.5)

Equate the distances:

⋅

=

(

+

10

)

⋅

(

−

0.5

)

s⋅t=(s+10)⋅(t−0.5)

Expand and simplify:

⋅

=

⋅

−

0.5

+

10

−

5

s⋅t=s⋅t−0.5s+10t−5

0

=

−

0.5

+

10

−

5

0=−0.5s+10t−5

Rearrange to find

t:

0.5

=

10

−

5

0.5s=10t−5

10

=

0.5

+

5

10t=0.5s+5

=

0.5

+

5

10

t=

10

0.5s+5

​

Substitute

t back into the distance equation:

⋅

0.5

+

5

10

=

(

+

10

)

⋅

(

0.5

+

5

10

−

0.5

)

s⋅

10

0.5s+5

​

=(s+10)⋅(

10

0.5s+5

​

−0.5)

Simplify and solve for

s:

After solving, you will find that the average speeds are approximately:

Slower car: 50 mph

Faster car: 60 mph

Which polynomial is equal to  (-3x^2 + 2x - 3) subtracted from  (x^3 - x^2 + 3x)?

The polynomial equal to (-3x^2 + 2x - 3) subtracted from  (x^3 - x^2 + 3x) is [tex]x^3 + 2x^2 + x + 3[/tex]

Given that two polynomials are: [tex](-3x^2 + 2x - 3)[/tex] and [tex](x^3 - x^2 + 3x)[/tex]

We have to find the result when [tex](-3x^2 + 2x - 3)[/tex] is subtracted from  [tex](x^3 - x^2 + 3x)[/tex]

In basic arithmetic operations,

when "a" is subtracted from "b" , the result is b - a

Similarly,

When [tex](-3x^2 + 2x - 3)[/tex] is subtracted from  [tex](x^3 - x^2 + 3x)[/tex] , the result is:

[tex]\rightarrow (x^3 - x^2 + 3x) - (-3x^2 + 2x - 3)[/tex]

Let us solve the above expression

There are two simple rules to remember:

So the above expression becomes:

[tex]\rightarrow (x^3 - x^2 + 3x) + 3x^2 -2x + 3[/tex]

Removing the brackets we get,

[tex]\rightarrow x^3 - x^2 + 3x + 3x^2 -2x + 3[/tex]

Combining the like terms,

[tex]\rightarrow x^3 -x^2 + 3x^2 + 3x - 2x + 3[/tex]

[tex]\rightarrow x^3 + 2x^2 + x + 3[/tex]

Thus the resulting polynomial is found

Answer:

The given numbers from smallest to largest is

[tex]0.012, \frac{1}{10}, 32\%, 65\%, \frac{7}{10}, 0.721, 0.721, \frac{652}{900}[/tex]

Step-by-step explanation:

Given numbers are

[tex]\frac{652}{900}, 0.012,\frac{7}{10}, 32\%,\frac{1}{10}, 0.721, 65\%[/tex]

We have to arrange the given numbers from smallest to largest

That is to write in ascending order.

Rewritting the given numbers are

[tex]\frac{652}{900}, 0.012,\frac{7}{10}, \frac{32}{100},\frac{1}{10}, 0.721, \frac{65}{100}[/tex]

[tex]\frac{652}{900}, 0.012,0.7, 0.32, 0.1, 0.721, 0.65[/tex]

[tex]0.724, 0.012, 0.7, 0.32, 0.1, 0.721, 0.65[/tex]

Now arranging the above numbers from smallest to largest

[tex]0.012, 0.1, 0.32, 0.65, 0.7, 0.721, 0.724[/tex]

ie, 0.12, [tex]\frac{1}{10}, 32\%, 65\%, \frac{7}{10}, 0.721, 0.721, \frac{652}{900}[/tex]

The given numbers in ascending order is

[tex]0.012, \frac{1}{10}, 32\%, 65\%, \frac{7}{10}, 0.721, 0.721, \frac{652}{900}[/tex]

Answer:

y=1/3x+2

Step-by-step explanation:

y=3x-6

x=3y-6

3y=x+6

y=1/3x+6/3

y=1/3x+2

Answer:

Option A) x=4,12 is correct.

The solution of the given quadratic equation is x=4,12

Step-by-step explanation:

Given equation is in quadratic form

Given quadratic equation is

[tex]0=4x^2-64x+192[/tex]

Rewriting the above equation

[tex]4x^2-64x+192=0[/tex]

Now dividing the equation by 4 we get

[tex]\frac{1}{4}(4x^2-64x+192)=\frac{0}{4}[/tex]

[tex]x^2-16x+48=0[/tex]

For quadratic equation [tex]ax^2+bx+c=0[/tex]

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

where a and b are coefficients of [tex]x^2[/tex] and x respectively, c is a constant

Here a=1, b=-16, c=48

[tex]x=-\frac{(-16)\pm\sqrt{(-16)^2-4(1)(48)}}{2(1)}[/tex]

[tex]=\frac{16\pm\sqrt{16^2-192}}{2}[/tex]

[tex]=\frac{16\pm\sqrt{256-192}}{2}[/tex]

[tex]=\frac{16\pm\sqrt{64}}{2}[/tex]

[tex]x=\frac{16\pm 8}{2}[/tex]

Therefore

[tex]x=\frac{16+8}{2}[/tex] and [tex]x=\frac{16-8}{2}[/tex]

[tex]x=\frac{24}{2}[/tex] and [tex]x=\frac{8}{2}[/tex]

[tex]x=12[/tex] and [tex]x=4[/tex]

Therefore the solution of the given quadratic equation is x=4,12

Option A) x=4,12 is correct.

Answer:

$200,000

Step-by-step explanation:

Base Salary = 40,000

Total Salary = 70,000

So, the rest, Allison earns from commissions. How much??

70,000 - 40,000 = 30,000

So, 15% of total sales is equal to 30,000

Let total sales be "t", so we can write an equation as:

15% * t = 30,000

15% in decimal is:

15/100 = 0.15

So, equation to solve is:

0.15t = 30,000

Finding t:

t = 30,000/0.15 = 200,000

Allison's total sales were $200,000

Skippy should invest $ 7500 in account offering 4 % interest and $ 2500 in account offering 8 % simple interest

Solution:

Given that Skippy has a total of $10,000 to split between two investments

One account offers 4% simple interest, and the other account offers 8% simple interest

Total interest earned = 500

Number of years = 1

Let the principal with rate of interest 4 % is x

So the principal for rate of interest 8 % is 10000 - x

Total interest earned = simple interest for 4 % interest + simple interest for 8 % interest

Simple interest is given as:

[tex]S.I = \frac{pnr}{100}[/tex]

Where "p" is the principal and "r" is the rate of interest and "n" is the number of years

Therefore,

[tex]\text{ Total interest earned } = \frac{x \times 1 \times 4}{100} + \frac{10000-x \times 1 \times 8}{100}[/tex]

[tex]500 = 0.04x + (10000 - x)0.08\\\\500 = 0.04x + 800 - 0.08x\\\\-300 = -0.04x\\\\x = 7500[/tex]

Therefore skippy should invest $ 7500 in account offering 4 % interest

And skippy should invest (10000 - x) = (10000 - 7500) = $ 2500 in account offering 8 % interest

Step 3 of the argument could be that the translation preserves the size of circle A.

Step 3 of the argument could be: 3. The translation preserves the size of circle A.

Explanation: In step 2, it is stated that there exists a translation that can be performed on circle A so that it will have the same center as circle B.

In order for this translation to be possible, the size of circle A must be preserved. This means that the radius of this circle A remains the same even after the translation is applied.

Therefore, step 3 could be that the translation preserves the size of the given circle A.

Answer:

The time after which only 40 mg of medicine left inside body is 9.8 hours

Step-by-step explanation:

Given as :

The initial quantity of medicine ingest in body = i=200 mg

The final quantity of medicine in body = f= 40 mg

The rate at which body remove medicine = r = 15%

Let The time taken to remove = t hours

According to question

The final quantity of medicine in body after t hours = The initial quantity of medicine ingest in body × [tex](1-\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

I.e f = i × [tex](1-\dfrac{\textrm r}{100})^{\textrm t}[/tex]

Or, 40 mg = 200 mg × [tex](1-\dfrac{\textrm 15}{100})^{\textrm t}[/tex]

Or, [tex]\dfrac{40}{200}[/tex] = [tex](1-\dfrac{\textrm 15}{100})^{\textrm t}[/tex]

Or , 0.2 = [tex](\frac{100 - 15}{100})^{t}[/tex]

Or,  [tex](\frac{85}{100})^{t}[/tex] = 0.2

Taking Log both side

So, [tex]Log_{10}[/tex] [tex](\frac{85}{100})^{t}[/tex] = [tex]Log_{10}[/tex]0.2

Or, t ×  [tex]Log_{10}[/tex]0.85 =  [tex]Log_{10}[/tex]0.2

Or, t (-0.07) = - 0.69

∴  t = [tex]\dfrac{.69}{.07}[/tex]

I.e t = 9.8 hours

So, The time after which only 40 mg left inside body = t = 9.8 hours

Hence,The time after which only 40 mg of medicine left inside body is 9.8 hours .Answer

Answer:

B. Investors will have to pay tax on the interest income received from the bonds.

Step-by-step explanation:

Investors will have to pay tax on the interest income received from the bonds because it is a taxable income.

The interest earned from a corporate bond is subject to taxation by both the federal and state governments.

Again, the maturity of the bond is determined at the time they are issued. Creditworthiness will only affect the bond price but not its maturity period.

The equation D is the equation that best fits the data.

Why?

We can find the best option by substituting the easiest values into the given options.

Let's substitute f(0), f(1) and f(4) for each equation:

A.

[tex]f(0)=3.02(3.67)^{0}=3.02[/tex]

[tex]f(1)=3.02(3.67)^{1}=11.08[/tex]

[tex]f(4)=3.02(3.67)^{4}=547.86[/tex]

We can see that the values are too far from the given values, so the equation A is discarded.

B.

[tex]f(0)=2.27(2.09)^{0}=2.27[/tex]

[tex]f(1)=2.27(2.09)^{1}=4.74[/tex]

[tex]f(4)=2.27(2.09)^{1}=43.31[/tex]

We can see that the values are too far from the given values, so the equation B is discarded.

C.

[tex]f(0)=8.04(0.98)^{0}=8.04[/tex]

[tex]f(1)=8.04(0.98)^{1}=7.87[/tex]

[tex]f(4)=8.04(0.98)^{4}=7.41[/tex]

We can see that the values are too far from the given values, so the equation B is discarded.

D.

[tex]f(0)=6.61(1.55)^{0}=6.61[/tex]

[tex]f(1)=6.61(1.55)^{0}=10.26[/tex]

[tex]f(4)=6.61(1.55)^{0}=38.15[/tex]

We can see that the values are the closest values from the given values, so the equation D is the equation that best fits the data.

Have a nice day!

Answer:

Option C -> None of the above.

Step-by-step explanation:

Given-

2 r + ( t + r )

⇒ 2 r + t + r

⇒ 2 r + r + t

⇒ 3 r + t

∵ 2 r + ( t + r ) = 3 r + t.

∴ The given expression is equivalent to Option C : None of the above.

Answer:

C. None of the above

Step-by-step explanation:

Answer: -7/-3.

Step-by-step explanation: In this problem we're asked to find the slope of the line that passes through the points (4,3) and (1,-4).

Using our slope formula, we take the second y minus the first y which in this case is -4 - 3 over our second x minus our first x which in this case is 1 - 4.

-4 - 3 is -7 and 1 - 4 is -3.

So the slope of this line is -7/-3.

Answer:

-7/-3

Step-by-step explanation:

Slope is represented as m

m = Rise/Run =( Y2 - Y1) / (X2 - X1)

m =  (-4  -3) / (1 - 4)

m = -7 / -3

The negative sign (minus) will cancel out

Therefore,

m = 7 / 3

m = 2 whole number, 1/3

Answer:

192

Step-by-step explanation:

Your sequence of numbers is

131 517 … 123

Space them as a two-digit sequence

13 15 17 19 21 23

Now, regroup then as a three-digit sequence

131 517 192 123

The missing number is 192.

The volume of the solid generated by rotating triangle ABC around AB is 24π cubic units.

To find the volume of the solid generated by rotating triangle ABC around side AB, you can use the method of cylindrical shells. The volume of the solid generated by rotating a region bounded by a curve around an axis is given by the formula:

[tex]\[ V = \int_{a}^{b} 2\pi x \cdot h(x) \, dx \][/tex]

Where:

[tex]\( a \) and \( b \) are the limits of integration along the x-axis (in this case, from 0 to the length of side AB),[/tex]

[tex]\( h(x) \) is the height of the curve at the position x, and[/tex]

[tex]\( 2\pi x \) represents the circumference of the cylindrical shell with radius x and height \( h(x) \).[/tex]

In this case, triangle ABC is a right triangle, so rotating it around AB will generate a cone with height AB and base radius AC.

Given that AB = 2 and AC = 6, the radius of the base of the cone formed by rotating the triangle will be [tex]\( r = AC = 6 \)[/tex]. The height of the cone will be the same as the length of side AB, so [tex]\( h = AB = 2 \).[/tex]

Now, we can calculate the volume:

[tex]\[ V = \int_{0}^{2} 2\pi x \cdot 6 \, dx \][/tex]

[tex]\[ = 12\pi \int_{0}^{2} x \, dx \][/tex]

[tex]\[ = 12\pi \left[\frac{x^2}{2}\right]_{0}^{2} \][/tex]

[tex]\[ = 12\pi \left(\frac{2^2}{2} - \frac{0^2}{2}\right) \][/tex]

[tex]\[ = 12\pi \left(\frac{4}{2}\right) \][/tex]

[tex]\[ = 12\pi \cdot 2 \][/tex]

[tex]\[ = 24\pi \][/tex]

So, the volume of the solid generated by rotating triangle ABC around side AB is [tex]\( 24\pi \)[/tex] cubic units.

The solid formed by rotating triangle ABC around side AB is a cone. The volume of this cone is calculated using the formula V = (1/3)πr^2h where r is the radius of the base and h is the height, resulting in approximately 57.91 cubic units.

The question asks for the volume of the solid generated by rotating a triangle around one of its sides. In this case, rotating triangle ABC with AB = 2, BC = 5, and AC = 6 around side AB will generate a conical surface. Since side AB will be the axis of rotation, the other two sides will act as generating lines of the cone, where side AC becomes the slant height (l) and side BC becomes the base's radius (r).

To calculate the volume of the cone, we use the formula V = (1/3)\u03c0r^2h, where r is the radius of the base, and h is the height of the cone. Here the height (h) of the cone is not directly provided, but with the Pythagorean theorem, we can find it since we know the slant height and radius: h = \\/(l^2 - r^2) = \\/(6^2 - 5^2) = \\/(36 - 25) = \\/11. Finally, the volume can be calculated: V = (1/3)\\(3.1415)\(5)^2\\/11\approx 57.91 cubic units.

The theorem of Pappus is a useful approach to solving this problem, but it requires knowing the centroid's distance from the axis of rotation, which is not provided, so we are not using that method here.

Answer: 138

Step-by-step explanation:

Let the first number be x , the second number be x + 2 and the third number be x + 4 since they are consecutive even numbers.

Their sum implies:

x + x + 2 + x + 4 = 408

3x + 6 = 408

subtract 6 from both sides

3x + 6 - 6 = 408 - 6

3x = 402

divide through by 3

3x/3 = 402/3

Therefore x = 134.

The numbers are :

134 , 136 and 138 , this means that the largest number is 138

answer: 828$

Step-by-step explanation:

step 1

Find out the total cost of the land

Multiply the total area in acres by $1,863 per acre

step 2

we know that

To determine the selling price of each lot to reach break even, divide the total cost by the number of lots.

Answer:

5/2

Step-by-step explanation:

Answer:

m∠1 = 30°

m∠2 = 60°

Step-by-step explanation:

There are two 30-60-90 triangles. For each, the angles have to add up to 180°

Answer:

m∠1 = 30°

m∠2 = 60°

Step-by-step explanation: