At what value of x does the graph of the following function F(x) have a vertical asymptote

Step-by-step explanation:

Equation: y= [tex]-x^2+3x+9[/tex]

To create a parabola:

Does your parabola open up or down: If up, a>0 if down, a<0

This one opens down.

Is there a vertical strech or vertical compression:

No

What is the y-intercept: (0,9)

What strategy: Quadratic formula

Why?: You can fully factor the equation. You just get

-([tex](x^2-3x-9)[/tex]  which isn't factorable.

Use the quadratic formula, where a= -1, b= 3, and c=9 to show your work.

Quadratic formula: [tex]\frac{-b+\sqrt{b^2-4ac} }{2a} \frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]

[tex]\frac{-(3)+\sqrt{(3)^2-4(-1)(9)} }{2(-1)}[/tex] and [tex]\frac{-(3)-\sqrt{(3)^2-4(-1)(9)} }{2(-1)}[/tex]

[tex]\frac{-3+\sqrt{9-4(-9)} }{-2}[/tex] and[tex]\frac{-3-\sqrt{9-4(-9)} }{-2}[/tex]

[tex]\frac{-3+\sqrt{9+36} }{-2}[/tex] and [tex]\frac{-3-\sqrt{9+36} }{-2}[/tex]

[tex]\frac{-3+\sqrt{45} }{-2}[/tex] and[tex]\frac{-3-\sqrt{45} }{-2}[/tex]

[tex]\sqrt{45}[/tex] = [tex]\sqrt{9 (5)} = 3\sqrt{5}[/tex]

[tex]\frac{-3+3\sqrt{5} }{-2}[/tex] and [tex]\frac{-3-3\sqrt{5} }{-2}[/tex]

Cancel the negatives (-3) and (-2)

[tex]\frac{3 +3\sqrt{5} }{2} or\frac{3 -3\sqrt{5} }{2}[/tex] = end result

Good luck!

Answer:

x=3.5

Step-by-step explanation:

Perimeter: 8.5+8.5+2x=24

Simplifying we get: 17+2x=24

Subtracting 17 we get: 2x=7

Dividing by 2 we get: x=3.5

Answer:

The answer would be f(a)=-1

-AC I hope this helps<3

Answer:

Step-by-step explanation:

Given figure : Trapezium

Upper base of trapezium ( b1 ) = 7

Lower base ( b2 ) = 3

Height ( h ) = 3

Now, finding the area of trapezium:

[tex] \frac{1}{2} (b1 + b2)h[/tex]

Plugging the values

[tex] \frac{1}{2} \times (7 + 3) \times 3[/tex]

Calculate the sum

[tex] \frac{1}{2} \times 10 \times 3[/tex]

Reduce the numbers with G.C.F 2

[tex]5 \times 3[/tex]

Calculate the product

[tex] = 15 \: {units}^{2} [/tex]

Hope this helps..

Best regards!

Answer:

6 km

Step-by-step explanation:

40 min = 40/60 h = 4/6 h = 2/3 h

1 h ................. 9 km

2/3 h ..............x km

x = 2/3×9km = 18/3 km = 6 km

Answer:

[tex]\boxed{\sf \ \ \ x^3-2x^2-19x+20 \ \ \ }[/tex]

Step-by-step explanation:

hello,

by definition we can write

[tex](x-5)(x+4)(x-1)[/tex]

as 5,-4,1 are the zeroes

now we have to write it in the standard form, let's do it

[tex](x-5)(x+4)(x-1)=(x^2+4x-5x-20)(x-1)\\=(x^2-x-20)(x-1)=x^3-x^2-20x-x^2+x+20\\=x^3-2x^2-19x+20[/tex]

hope this helps

Answer:

Step-by-step explanation:

quotient of a number and -5 is written as

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

Equate it to 2

We have

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

Cross multiply

That's

x = 2 × - 5

x = - 10

Hope this helps you

Answer: -10

Step-by-step explanation:

So to set up the equation, it will be x/-5 = 2.

Then, you multiply (because it is the inverse of dividing) 2 by -5, and you get -10.

Answer:

B) 40 ft

Step-by-step explanation:

Use the picture for a reference.

1. We can see the diagonal forms a triangle. Since the angles of a rectangle are right, we can use the Pythagorean Theorem to solve for x.

2. The Pythagorean Theorem

a^2 (a squared) + b^2 (b squared) = c^2 (c squared)

a = 30 ft (width)

b = x ft (unknown length)

c = 50 ft (diagonal)

3. Substitute in the values:

    30^2 + x^2 = 50^2

    900 + x^2 = 2500

    x^2 = 1600

    x = 40

The length of the field is 40 ft.

Answer:

[tex]\boxed{\sf \ \ \ x=-9 \ \ or \ \ x=2 \ \ \ }[/tex]

Step-by-step explanation:

hello,

[tex]2x^2+7x-14=x^2+4\\<=> 2x^2+7x-14-x^2-4=0\\<=> x^2+7x-18=0\\<=>x^2-2x+9x-18=0\\<=> x(x-2)+9(x-2)=0\\<=> (x+9)(x-2)=0\\<=> x+9 = 0 \ \text{or} \ x-2=0\\<=> x = -9 \ \text{or} \ x=2[/tex]

hope this helps

Answer:

30 cm²

Step-by-step explanation:

Step 1: Find the value of xy using the formula for area of triangle with 2 sides and an angle between

Area = ½*x*y*sinB

Area of ∆ABC = 30 cm²

sin B = sin 70 = 0.9397

Thus,

30 = ½*x*y*0.9397

30 = (x*y*0.9397)/2

Multiply both sides by 2

60 = xy*0.9397

Divide both sides by 0.9397

60/0.9397 = xy

xy = 63.85

Step 2: calculate the area of ∆PQR with the same formula used in step 1, and also, using the value of the product of x and y gotten in step 1

Area of ∆PQR = ½*x*y*sinQ

x*y = xy = 63.85

sin Q = sin 110 = 0.9397

Area = ½*63.85*0.9397

Area of ∆PQR ≈ 30 cm²

Answer: 315.3 min^-1

Step-by-step explanation:

Given the following :

Speed = 45miles per hour

Diameter of wheels = 48inches

Number of complete revolutions the wheel makes in one minute =?

Since wheel diameter is in inches, we convert speed (miles/hour) to inch per minute

1 mile = 63360 ; 60minutes = 1 hour

45 miles / hour = (45 × 63360) / 60

= 2851200 inch/60 min

= 47520inch/min

Distance covered per revolution:

Circumference of a circle (C) = 2πr

Where r = radius ; r = diameter / 2

r = 48/2 = 24 inches

C = 2 * 3.14 * 24 = 150.72inches

Number of revolutions per minute:

Speed per minute / distance covered per revolution

(47520inch/min)/ (150.72 inch)

= 315.286 min^-1

Answer:

200 = 100*2, so √200 = √100 * √2. √100 = 10, so I can replace it with 10 to get 10 * √2 as my final answer for the square root of 200.

Step-by-step explanation:

read it

In the given problem the expression equivalent to square Root 200 is, 10√2

In mathematics, square roots is a concept in which, if we multiply square roots of any number by itself then it will give us an original number.

if 'a' is square root of 'b' then it will represent as, a = √b

Given number,

√200

we can write it in factor of 200,

⇒ √(2×100)

⇒ √2×√100

⇒  10√2

Hence, The expression is   10√2

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Answer:

Perimeter of rectangle 1=4x+4

Perimeter of rectangle 2=4x+4

Step-by-step explanation:

Two squares with the same dimension

Square 1: let length=x

Square 2: let length=x

Since they have same dimensions

He added two inches to the length of square 1 to make it a rectangle

Rectangle 1: width=x, length=x+2

Perimeter=2(l+w)

=2{(x+2)+x}

=2(x+2+x)

=2(2x+2)

=4x+4

He added two inches to the width of square 2 to make it a rectangle

Rectangle 2: length=x, width=x+2

Perimeter=2(l+w)

=2{(x+(x+2)}

=2(x+x+2)

=2(2x+2)

=4x+4

The two rectangles have equal perimeter

Answer:

(A)Cost of Rental A, C= 15x

Cost of Rental B, C=5x+50

Cost of Rental C, C=9x+20

(B)

i. Rental C   ii. Rental A     iii. Rental B

Step-by-step explanation:

Part 1

Let x be the number of hours of the barbeque use by the club.

Rental A: $15/h

Cost of Rental A, C= 15hx

Rental B: $5/h + 50

Cost of Rental B, C=5x+50

Rental C: $9/h + 20

Cost of Rental C, C=9x+20

Part 2

The graph of the three models is attached below

Part 3(11.05-4.30)

If the barbecue's usage hour is from 11.05 to 4.30 when the football match ends.

Number of Hours between 11.05am and 4.30pm=4 hours 25 Minutes = 4.42 Hours

Cost of Rental A, C= 15x=15(4.42)=$66.30

Cost of Rental B, C=5x+50 =5(4.42)+50=$72.10

Cost of Rental C, C=9x+20=9(4.42)+20=$59.78

Rental C should be chosen as it offers the lowest cost.

Part 4 (11.05-12.30)

Number of Hours = 12.30 -11.05 =1 hour 25 Minutes = 1.42 Hours

Rental A should be chosen since it offers the lowest cost.

Part 5

If the barbecue is returned the next day, say after 24 hours

Rental B should be chosen as it offers the lowest cost.

Answer:

[tex]\left[\begin{array}{ccc}-5\\-5\\\end{array}\right][/tex]

Step-by-step explanation:

Consider any one of the vertices of A

To translate to the corresponding vertex in B , the requirement is

shift 5 to the left, that is negative 5

shift 5 units down that is negative 5

The single translation is [tex]\left[\begin{array}{ccc}-5\\-5\\\end{array}\right][/tex]

Answer:

k-4.7

Step-by-step explanation:

It is k minus 4.7 because when it says less than it means the number that is stated before the phrase is being subtracted :)

Answer:

k-4.7

Step-by-step explanation:

For writing algebraic expressions, we have translate the words to math.

4.7 less than a number k, means subtraction (notice the word- less)

Thus, we have k-4.7

Hope this helps :)

Answer:

Oregon:

Median: 467.5

Mean: 451.33

Standard Deviation: 113.6

Washington:

median: 380

Mean: 396.6

Standard deviation: 56.3

Step-by-step explanation:

To calculate the median, we need to organize the price and select the value that is in the middle position.

To calculate the mean, we need to sum all the values and divide them by the number of values

To calculate the standard deviation, we need to square the distances between every price and the mean, sum it all and divide them by the number of values less 1 and finally calculate the square root.

So, for Oregon, the organized values are:

$295, $345, $460, $475, $538, $595

The median is a value between $460 and $475. it is calculated as:

[tex]\frac{460+475}{2}=467.5[/tex]

The mean is:

[tex]\frac{295+475+345+595+538+460}{6}=451.33[/tex]

The standard deviation is:

[tex]\sqrt{\frac{(295-451.3)^2+(475-451.3)^2+(345-451.3)^2+(595-451.3)^2+(538-451.3)^2+(460-451.3)^2}{6-1}}=113.6[/tex]

At the same way, we can calculate the median, mean, and standard deviation for Washington and get:

median: 380

Mean: 396.6

Standard deviation: 56.3

Answer:

  y = (1/3)x +4

Step-by-step explanation:

The line intercepts the y-axis at y=4. It has a "rise" of 1 unit for each "run" of 3 units, so its slope is rise/run = 1/3.

The slope-intercept form of the equation of a line is ...

  y = mx + b . . . . . where m is the slope and b is the y-intercept.

When we put the proper numbers in the equation, we have ...

  y = (1/3)x + 4

Answer:

reflection and rotation

Step-by-step explanation:

Answer:

0.13591

Step-by-step explanation:

What we do here is find a score of both values;

Mathematically;

z-score = (x - mean)/SD

for 825, we have (825-750)/75 = 1

For 900, we have (900-750)/75 = 150/75 = 2

So the probability we want to find is;

P(1<x<2) = P(x<2) - P(x<1)

We use the standard table for this and we arrive at;

P(1<x<2) = 0.13591

Answer:13.5

Step-by-step explanation:

Step-by-step explanation:

prisms are of varying types from

1. Triangular.

2. Square.

3. Rectangular.

4. Pentagonal.

5. Hexagonal prism

From the give information the prism is a square prism

length in meters= m

width in meters = m

height in meters= m

the volume of a square prism is expressed as

volume= length* width* height

[tex]volume= = m*m*m= m^3[/tex]

I hope this helps you

Answer:  B) sin θ = 5/13    and    D) tan θ = 5/12

Step-by-step explanation:

[tex]\csc\theta=\dfrac{r}{y}=\dfrac{13}{5}[/tex]

Use Pythagorean Theorem: x² + y² = r² to calculate x = 12

[tex]\sin \theta=\dfrac{y}{r}=\dfrac{5}{13}\qquad \qquad \qquad \csc \theta=\dfrac{r}{y}=\dfrac{13}{5}\\\\\\\\\cos \theta=\dfrac{x}{r}=\dfrac{12}{13}\qquad \qquad \qquad \sec \theta=\dfrac{r}{x}=\dfrac{13}{12}\\\\\\\\\tan \theta=\dfrac{y}{x}=\dfrac{5}{12}\qquad \qquad \qquad \cot \theta=\dfrac{x}{y}=\dfrac{12}{5}[/tex]

Answer:

x=42

Step-by-step explanation:

The tens digit of a two-digit number is twice the units digits. put it in an equation:

10(2x)+x = 10x+2x+18

21x=12x+18

21x-12x=18

x=18/9=2

substitute x:

10(2x)+x = 10x+2x+18

10(2*2)+2=10(2)+2(2)+18

42=24+18

Answer:

No

Step-by-step explanation:

For X and Y to be in proportion, The values should both be the same so if x is 10 y is 10 and so on.

Answer: 240 seconds OR 4 minutes

Step-by-step explanation:

Length of the train = 1 km

Length of the tunnel = 1 km

Therefore, length of the train + length of the tunnel = (1 + 1) km = 2 km

= 2000 m

Speed of the train = 30 km/hr = 8.333 metres per second

Therefore, time taken by the train to cross the tunnel = 2000 m/ 8.333 m/sec.

= 240 seconds = 4 minutes

Answer:

They can make 70 king sized bars and 10 regular sized bars.

70*2=140 oz

140+10=150 oz

Answer: Hope this helps <3

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

The slope is the change in the y direction over the change in the x direction

6/12

1/2

Answer:

Step-by-step explanation:

Slope is the ratio of the vertical change with respect to the horizontal change. In other words, you want to find the ratio of the change in y over the change in x. So, start by finding the change in y? What is it? Then find the change in x. What is it? Now, make a ratio of the two quantities. Change in y must be at the numerator, while the change in x must be at the denominator. What did you get? Let me know. ~Lendy

Answer:

√29

Step-by-step explanation:

Use the distance formula √((x2-x1)^2+(y2-y1)^2)

Since the first point is on the origin, (x1, y1) is (0, 0)

The second point is (2, -5)

Plug both points into the distance formula to get √29

The distance from origin to the point P is √29 units

The given parameters are:

Origin = (0,0)

Point P = (2, -5)

The distance between these points is calculated as:

d =  √((x2-x1)^2+(y2-y1)^2)

So, we have:

d = √((2-0)^2+(-5 -0)^2)

Evaluate

d = √29

Hence, the distance from origin to the point P is √29 units

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