Point Q is the image of point P under a dilation with center O and scale factor 4. If PQ = 18, then what is OP?

Answer:

x=7

Step-by-step explanation:

Answer:   {(x + 2), (x - 1), (x - 3)}

Step-by-step explanation:

Presented symbolically, we have:

x^3 - 2x^2 - 5x + 6

Synthetic division is very useful for determining roots of polynomials.  Once we have roots, we can easily write the corresponding factors.  

Write out possible factors of 6:  {±1, ±2, ±3, ±6}

Let's determine whether or not -2 is a root.  Set up synthetic division as follows:

-2   /   1   -2   -5   6

              -2     8   -6

     -----------------------

        1     -4      3    0

since the remainder is zero, we know for sure that -2 is a root and (x + 2) is a factor of the given polynomial.  The coefficients of the product of the remaining two factors are {1, -4, 3}.  This trinomial factors easily into {(x -1), (x - 3)}.

Thus, the three factors of the given polynomial are {(x + 2), (x - 1), (x - 3)}

Amount of interest on loan at Rimrock Bank, using ordinary interest at a rate of 15%, is $48,750 and at rate of 14.5%, is $47,125. In Southside National Bank , interest at a rate of 15%, is $49,500.

To compete with Rimrock Bank's offer, Southside National Bank would need to quote a rate of 14.38% using exact interest.                                    (a) To calculate the amount of interest on the loan at Rimrock Bank, we use the formula I = PRT, where I is the interest, P is the principal amount, R is the interest rate, and T is the time in years. Plugging in the values, we have I = $1,300,000 * 0.15 * (90/365) = $48,750.

(b) The amount of interest on the loan at Southside National Bank using exact interest is calculated the same way as in part (a), resulting in I = $1,300,000 * 0.15 * (90/360) = $49,500.                                                        (c) Similarly, using the same formula, we find the interest on the loan at Rimrock Bank with a rate of 14.5% to be I = $1,300,000 * 0.145 * (90/365) = $47,125.

(d) To determine the rate at which Southside National Bank should quote to compete with Rimrock Bank's last offer, we subtract the given interest difference of $1,125 from the interest calculated in part (b). Solving for R, we have $48,750 - $1,125 = $1,300,000 * R * (90/360). Solving this equation results in R ≈ 0.1438, which is 14.38% rounded to the nearest hundredth of a percent.

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The equation of the path of the parabola is y = a(x - 13)² + 27

Given data ,

To represent the path of Al's toss, we can assume that the path is a parabolic trajectory.

The equation of a parabola in vertex form is given by:

y = a(x - h)² + k

where (h, k) represents the vertex of the parabola

Now , the balloon was released from the 10-yard line and landed at the 16-yard line, we can determine the x-values for the vertex of the parabola.

The x-coordinate of the vertex is the average of the two x-values (10 and 16) where the balloon was released and landed:

h = (10 + 16) / 2 = 13

Since the height of the balloon reached 27 yards, we have the vertex point (13, 27)

Now, let's substitute the vertex coordinates (h, k) into the general equation:

y = a(x - 13)² + k

Substituting the vertex coordinates (13, 27)

y = a(x - 13)² + 27

To determine the value of 'a', we need another point on the parabolic path. Let's assume that the highest point reached by the balloon is the vertex (13, 27).

This means that the highest point (13, 27) lies on the parabola

Substituting the vertex coordinates (13, 27) into the equation

27 = a(13 - 13)² + 27

27 = a(0) + 27

27 = 27

Hence , the equation representing the path of Al's toss is y = a(x - 13)² + 27, where 'a' can be any real number

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Answer:

V + F - 2 = E

Step-by-step explanation:

V - E + F = 2 --- add E to both sides

V + F = 2 + E --- subtract 2 from both sides

V + F - 2 = E

Hope this helps! :)

Step-by-step explanation:

Maximum area enclosed will be a square enclosure

  since the river is one side , the other three sides of the square will be

       1440 / 3 = 480 ft long

Square with sides 480 ft

area =480 x 480 = 230 400 ft^2

Answer:

1 2/6

Step-by-step explanation:

3 1/2 - 2 and 6 inches

change 6 to 1/6

3 1/2 = 3/6

2 1/6 = 1/6

-

_____

1 2/6

Answer:

y = -2/3(x) - 8

Step-by-step explanation:

y = mx + b

y = -2/3(x) + b

given: (-3, -6) x=-3 y=-6

-6 = -2/3(-3) + b

-6 = 2 + b

b= -8

so..

y = -2/3(x) - 8

The main difference between an area variance and a use variance is that area variance allows for an exception to zoning regulations related to the physical characteristics of a property, while use variance allows for an exception to regulations related to the intended use of a property.

An area variance is typically granted when a property owner is unable to comply with zoning regulations related to setbacks, building height, lot coverage, or other physical characteristics of a property.

In contrast, a use variance allows a property owner to use their property for a purpose that is not permitted under the current zoning regulations. This may include using a residential property for commercial purposes or using a commercial property for residential purposes.

Use variances are generally more difficult to obtain than area variances, as they require a showing of a unique hardship or practical difficulty that cannot be addressed through other means.

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Answer:

799800000 larger

Step-by-step explanation:

So . . Subtract

800000000 - 200000 = 799800000

Answer: 799800000

Step-by-step explanation: For 8 x 10^8, do 10 x 10 x 10  10 x 10 x 10  10 x 10 to get 100,000,000 and x 8 is 800,000,000

For 2 x 10^5  do 10^5 ( 10 x 10 x 10 x 10 x 10) which is 100,000 and then x 2 is 200,000

Then subtract.

800,000,000 - 200,000 is 799800000

Answer:

C. 84%

Step-by-step explanation:

If the mean male height is 70.8 inches (5 feet 10.8 inches)

and 6 feet falls within one deviation of the mean.

Through a normal distribution curve about 85 percent of men would be able to fit through the door

The other closest answer would be 65%, but this is incorrect as it only accounts for the men who fall under 1 standard deviation away from the mean, while all the men who are on the short outlier side would still be able to fit through the door.

Answer:

His third law states that for every action (force) in nature there is an equal and opposite reaction

Step-by-step explanation:

for example, if you push a brick wall using 30 newton to the right, the wall will push back at you with 30 newtons to the left

Answer:

y = - 9x + 14

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 )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 4, 50 ) and (x₂, y₂ ) = (5, - 31 )

m = \(\frac{-31-50}{5-(-4)}\) = \(\frac{-81}{5+4}\) = \(\frac{-81}{9}\) = - 9 , then

y = - 9x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (5, - 31 )

- 31 = - 9(5) + c = - 45 + c ( add 45 to both sides )

14 = c

y = - 9x + 14 ← equation of line

Answer:

$1673.25

Step-by-step explanation:

si year 1 = $1500 * 0.0385 =57.75       si yr 3 =57.75*3 = $173.25    return total = 1500+ 173.25 = $1673.25

Answer:

9

Step-by-step explanation:

1/9(9^2)

1/9(81)

9

Step-by-step explanation:

the correct answer is 1/7

The equation of the given line is y = -3x + 5 and the coordinate point (70, -205) is on the line.

The equation of a straight  line in slope-intercept form is expressed as:

y = mx + b

where:

m is the slope

b is the y-intercept

Using the coordinate points (0, 5) and (1, 2), the slope of the line is calculated as:

m = 2-5/1-0

m = -3/1

m = -3

Since the line cuts the y-axis at b = 5, hence the y intercept is 5. The required equation of  the line is y = -3x + 5

Check if (70, -205) is on the line

If  x= 70, calculate the value of "y"

y = -3(70) + 5

y = -210 + 5

y = - 205

Since the corresponding y-value is -205, hence the coordinate point (70, -205) is on the line.

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The range of the average width of the index finger which is between 1.6 centimeters and 2 centimeters gives;

1. The symbols to use for the inequality are ≤ and ≥

2. The average width expressed as an inequality is; 1.6 ≤ w ≤ 2

3. The inequality for the average width in inches is 0.624 ≤ w ≤ 0.78

1. With regards to working with number ranges or intervals, the term inclusive means that the endpoints of the (closed) interval are included in the range.

The inequality symbol to be used in an inclusive interval are ≤ and ≥ (the symbols < and > are used for an exclusive measurements)

2. The minimum width = 1.6 centimeters

Maximum width = 2 centimeters

The average width in centimeters, w, written as an inequality is therefore;

3. The given conversion factor is 1 cm. = 0.39 inches.

Therefore;

1.6 cm = 1.6 × 0.39 in. = 0.624 in.

2 cm = 2 × 0.39 in. = 0.78 in.

The inequality for the average width in inches is therefore;

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Answer:

C

Step-by-step explanation:

Because 3 * 3/6 or 3* 1/2 equals 1.5 or 1 and 1/2 and that is what is shown on the graph!

Hope this Helps!

Answer:

\(x=67.38^\circ\)

Step-by-step explanation:

Use trigonometry

Recall that cos(x)=adjacent side/hypotenuse

You can remember this with SohCahToa

Also remember that if cos(x)=y then \(cos^{-1}(y)=x\)

In this case, we know the adjacent side and hypotonous

Adjacent side=5000

Hypotenuse=13000

Therefore

\(Cos(x)=\frac{5000}{13000}=\frac{5}{13}\)

Now to solve for x, take the inverse cosine

\(cos^{-1}(\frac{5}{13})=x=67.38^\circ\)

Answer:

x=67.38

Step-by-step explanation:

I took the quiz and got it correct!

Answer:

with what do you need help with your life

Step-by-step explanation:

Maka should plan to spend $13.10 + $7.10 = $20.20.

Based on the given menu, the price of a combo meal is the same as purchasing each item separately.

Maka wants 2 burritos and 1 enchilada, so let's calculate the cost.

From combo meal 1, the price of one burrito is $6.55.
From combo meal 2, the price of one enchilada is $7.10.

Since Maka wants 2 burritos, she will spend $6.55 x 2 = $13.10 on burritos.
She also wants 1 enchilada, so she will spend $7.10 on the enchilada.

Adding the two amounts together, Maka should plan to spend $13.10 + $7.10 = $20.20.

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Answer:

11

Step-by-step explanation:

\(101011_{2 = } 43_{10} \\ 1101_{2} = 13_{10} \\ \frac{43}{13} =3.3076923076923 \\ 3.3076923076923_{10} = 11_{2}\)

Answer:

You would need to sell each cupcake for at least 2.80$

Step-by-step explanation:

If you sell each cupcake at 2.80$ you will make 134.4$

Answer: C

Step-by-step explanation: To find the volume of a cylinder with a height of 10 cm and a radius of 3 cm, you can use the formula V = r^2*h, where r represents the radius and h represents the height of the cylinder. Plugging in the values for r and h gives:

V = 3^2 * 10 = 9 * 10 = 90

So the volume of the cylinder is 90 cm^3.

Therefore, the correct answer is (C) 282.6cm³.

Answer: Both A, and C

Step-by-step explanation:

The answer to the first system of equations (2x+2y=16) would be

x=3 and y=5 ( 3x-y=4 )

Which means we have to find out which of the other equations has an x value of 3, and a y value of 5.

If A is 2x+2y=16, then x=3 and y=5

           6x-2y=8

If B is x+y=16, then x=5 and y=11

         3x-y=4

If C is 2x+2y=16, then x=3 and y=5

           6x-2y=8

If D is 6x+6y=48 , then x=-2 and y=10

            6x+2y=8

Both A and C are equal to the first system of equations, which means they are both correct answers.

Answer:

Step-by-step explanation:

You'll need to find a way to share the graph or graphs associated with this problem.

The period is 4.  The relationship between period and b (the coefficient of the independent variable of the cosine function) is (period) =(2π.b).  Given that the period here is 4,

       2π                          2π

4 = ---------, and so b = ------- = π/2.

                                       4

So now our y  = a*cos (bx + c) becomes

                    π

y = 10*cos (------x + 0 + 10

                     2

The horizontal center line of this cosine curve is y = 10.  The maximum value of the curve is 20, which is 10 + 10, and the minimum value is 0, which is 10 - 10.

The function that describes the given situation is \(\rm y = 10\;cos\left(\dfrac{\pi}{2}x\right) + 10\) and this can be determined by using the properties of the trigonometric function.

Given :

The following steps can be used in order to determine the function could be the function described:

Step 1 - According to the given data, the cosine function has a period of 4.

Step 2 - Now, the independent variable of the cosine function is given by:

\(\rm 4b = 2\pi\)

\(\rm b =\dfrac{\pi}{2}\)

Step 3 - The maximum value of the cosine function is 1 and the minimum value of the cosine function is -1.

Step 4 - From the above steps, the function that described the given situation is given by:

\(\rm y = 10\;cos\left(\dfrac{\pi}{2}x\right) + 10\)

Therefore, the correct option is C).

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Answer:

It will be the answer , i think

Step-by-step explanation:

Let me know if it was wrong or you wanted further explanation .