Select which form to use when you know the slope of the line and one of the points on the line. a. horizontal line c. slope-intercept form b. vertical line d. point-slope form Please select the best answer from the choices provided

The true statement about the graph of [tex]f(x) = \frac{x^2 + 2x + 1}{2x^2 - 10x+12}[/tex]  is (c) its vertical asymptote are x = 3 and x = 2

The function is given as:

[tex]f(x) = \frac{x^2 + 2x + 1}{2x^2 - 10x+12}[/tex]

Set the denominator to 0

2x^2 - 10x + 12 = 0

Divide through by 2

x^2 - 5x + 6 = 0

Expand

x^2 - 2x - 3x + 6 = 0

Factorize

(x - 2)(x - 3) = 0

Solve for x

x = 2 or x = 3

The above represents the vertical asymptote of the graph

Hence, the vertical asymptote are x = 3 and x = 2

Read more about vertical asymptote at:

https://brainly.com/question/4084552

#SPJ1

The x-intercept of p(x) is x = 2, the x-intercept of g(x) is x = 0, then the correct option is B.

For a function f(x), the x-intercept is the value of x such that:

f(x) = 0.

Here we have:

p(x) = log₂(x - 1)

Remember that:

logₙ(1)  = 0

For any base n, then the x-intercept of p(x) is x = 2, because:

p(2) = log₂(2 - 1) = log₂(1) = 0.

The other function is:

g(x) = 2ˣ - 1

Remember that any number to the power of zero is equal to 1, then:

g(0) = 2⁰ - 1 = 1 - 1 = 0

The x-intercept of p(x) is x = 2, the x-intercept of g(x) is x = 0, then the correct option is B.

If you want to learn more about x-intercepts:

https://brainly.com/question/3951754

#SPJ1

Answer:

The x-intercept of function p is greater than the x-intercept of function q.

Step-by-step explanation:

Plato/Edmentum

Answer:

the answer is 8.ITS 88888888888888888888

Using a system of equations, it is found that the lengths of the sides of the triangle are given as follows:

5.29 feet, 2.43 feet, 5.79 feet.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are the lengths, that are x, y and z.

The length of one side of a triangle is 2 feet less than three times the length of its second side, hence:

x = 3y - 2.

The length of the third side is 3/4 of the sun of the lengths of the first two sides, hence:

z = 0.75(x + y).

Find the lengths of all three sides if the perimeter of the triangle is 17.5 feet, hence:

x + y + z = 17.5.

3y + 2 + y + 0.75(3y - 2 + y) = 17.5

4y + 0.75(4y - 2) = 15.5.

7y = 17

y = 2.43 feet.

Hence:

More can be learned about a system of equations at https://brainly.com/question/24342899

#SPJ1

Using compound interest, it is found that she will earn $23 in interest during the 18-month period.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

The parameters in this problem are given as follows:

[tex]P = 1200, r = 0.0125, n = 12, t = 1.5[/tex].

The amount of money at the end of the 18 months will be of:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]A(t) = 1200\left(1 + \frac{0.0125}{12}\right)^{12(1.5)}[/tex]

A(t) = $1,223.

The amount of interest earned is:

I = $1,223 - $1,200 = $23.

More can be learned about compound interest at https://brainly.com/question/25781328

#SPJ1

Step-by-step explanation:

1 week is 3 rats

( w × 3 ) + 4

hope this helps

Answer:

P(w) = 3w+4

Step-by-step explanation:

For a Linear Equation , it takes the Form y = mx + c

where c is the Constant which is y-value at x=0

and the m is the Slope which is the change in y-value for a 1-unit change in x-value

So for our Question

y-value is represented by P(w) , Number of Rats

x-value is represented by w , Number of Weeks

So the Constant (c) is the P(w) at w=0 which is 4

and the Slope is the Change in P(w) value as w changes by 1 unit , which from week 0 to week 1 , P(w) changed from 4 to 7 , so the Change =7-4=3

Then the Slope m = 3

So the Linear Equation will be P = mw+c

Then P(w) = 3w+4

probability//

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

1/6(216/1)

Answer: Choice A) It has a range of 17

Reason:

The smallest value is 8 and the largest is 14. The range is the distance between these min and max

range = max - min = 14 - 8 = 6

So the range is 6 instead of 17.

The range of a data set is the difference between maximum and minimum thus the range of the given data set 8, 10, 10, 12, 12, 12, 12, 14, 14,16 is 8 so option (A) does not describe the data set.

Mode is the highest frequency number while the median is the middle value of a data set after writing in either an increasing or decreasing manner.

For example;

Set { 1,2,2,3,4,5,6} here mode is 2 and median is 3.

As per the given data set.

8, 10, 10, 12, 12, 12, 12, 14, 14,16

The range = maximum - minimum

Range = 16 - 8 = 8

The median of the data set is 12.

The mode is the highest frequency thus 12 is the mode of the data set.

Hence "The range of a data set is the difference between maximum and minimum thus the range of the given data set 8, 10, 10, 12, 12, 12, 12, 14, 14,16 is 8".

To learn more about mode and median,

brainly.com/question/300591

#SPJ2

Answer:

Step-by-step explanation:

As the length AB increases, the measure of C increases

As the length AB increases, the measure of C increases.

An angle is formed when two lines or rays meet at a single point. The common point is referred to as the vertex. The length of the angle formed when two rays or arms intersect at a common vertex is known as an angle measure in geometry.

Angles and sides in relation to one another:

The biggest side and angle of any triangle are in opposition to one another.

The smallest side and angle in every triangle are on opposing sides.

The middle side and middle angle are always in opposition to one another in triangles.

When we extend vertex A further to the left of vertex B,

we increase the side length of AB.

As the length AB increases, the measure of opposite angle increases.

Let C be the angle opposite to AB.

Therefore, as the length AB increases, the measure of C increases.

To learn more about the angle measure;

brainly.com/question/14684647

#SPJ2

Answer:

A

Step-by-step explanation:

Complex roots of quadratic functions occur when the discriminant is negative.

Discriminant

[tex]b^2-4ac\quad\textsf{when}\:\:ax^2+bx+c=0[/tex]

Evaluate the discriminant of each of the given equations.

[tex]\textsf{A.} \quad 3x^2+2=0[/tex]

[tex]\implies a=3, \quad b=0, \quad c=2[/tex]

[tex]\implies b^2-4ac=0^2-4(3)(2)=-24[/tex]

As -24 < 0 the equation will have complex roots.

[tex]\textsf{B.} \quad 2x^2+1=7x[/tex]

[tex]\implies 2x^2-7x+1=0[/tex]

[tex]\implies a=2, \quad b=-7, \quad c=1[/tex]

[tex]\implies b^2-4ac= (-7)^2-4(2)(1)=41[/tex]

As 41 > 0 the equation does not have complex roots.

[tex]\textsf{C.} \quad 3x^2-1=6x[/tex]

[tex]\implies 3x^2-6x-1=0[/tex]

[tex]\implies a=3, \quad b=-6, \quad c=-1[/tex]

[tex]\implies b^2-4ac=(-6)^2-4(3)(-1)=48[/tex]

As 48 > 0 the equation does not have complex roots.

[tex]\textsf{D.} \quad 2x^2-1=5x[/tex]

[tex]\implies 2x^2-5x-1=0[/tex]

[tex]\implies a=2, \quad b=-5, \quad c=-1[/tex]

[tex]\implies b^2-4ac=(-5)^2-4(2)(-1)=33[/tex]

As 33 > 0 the equation does not have complex roots.

Learn more about discriminants here:

https://brainly.com/question/27444516

https://brainly.com/question/27869538

Learn more about complex roots here:

https://brainly.com/question/26344541

Answer:

3800grams

Step-by-step explanation:

multiply by 1000

Answer:

divide 792 by 2

792÷2=304

then add 92 to the cost 304

304+92=396

The radius of the base of the vase in cm is 8.26 cm

P = F / A

700 = 15 / A

Cross multiply

700 × A = 15

Divide both sides by 700

A = 15 / 700

Multiply by 10000 to express in cm²

A = (15 / 700) × 10000

A = 214.29 cm²

A = πr²

Divide both side by π

r² = A / π

Take the square root of both sides

r = √(A / π)

r = √(214.29 / 3.14)

r = 8.26 cm

Learn more about pressure:

https://brainly.com/question/1393320

#SPJ1

Answer:

The amount of gross profit earned by Abbey Co. on the above transactions is $7,554.00

Step-by-step explanation:

What is the gross profit of Abbey Co?

Note that after sales of goods of $29,300 whose cost is $20,510 to Gomez Co, Gomez returned goods whose selling price is $2,500 and cost originally $1,800 to Abbey Co.

The implication of such goods returned is that $2,500 would be deducted from selling price and $1,800 would be deducted from cost of goods sold.

selling price=$29,300-$2,500

selling price=$26,800.00

cost of goods sold=$20,510-$1,800

cost of goods sold=$18,710.00

Note again that Gomez paid the invoice within the discount period, which means that net sales is the selling price of $26,800.00  minus 2% discount(2/15 means a discount of 2% is available if credit sales is settled in cash within the first 15 days of making sales0

net sales=$26,800.00*(1-2%)

net sales=$26,264.00

The gross profit is net sales minus the cost of goods sold

gross profit= $26,264.00-$18,710.00

gross profit=$7,554.00

Below is the link to a similar question which gives further guidance

https://brainly.com/question/14680275

#SPJ1

Answer:

  35

Step-by-step explanation:

The equations will be "consistent" when they describe lines that are not parallel.

The slope of a line whose equation is written in this form is the opposite of the ratio of the y-coefficient to the x-coefficient:

  line 1 slope = -8/20 = -2/5

  line 2 slope = -14/35 = -2/5

These lines have the same slope, so will be parallel unless they have the same y-intercept.

The y-intercept of each line is the ratio of the constant to the y-coefficient:

  line 1 y-intercept = 20/20 = 1

  line 2 y-intercept = k/35

We want these lines to have the same y-intercept so that they are not inconsistent. This requires ...

  k/35 = 1

  k = 35

For the equations to be consistent, we must have k = 35.

__

Additional comment

Linear equations are generally categorized as "consistent" or "inconsistent," and "dependent" or "independent."

Equations are "inconsistent" if there are no values of the variables that satisfy all of the equations. They are "dependent" if they describe exactly the same relation between the variables. "Consistent" equations may be "dependent" (describing the same line, as here), or "independent" (describing lines with different slopes.)

Answer:

Step-by-step explanation:

Loss is 20% of the C.P.

        =

[tex]=\frac{20}{100}*100\\ =3040\\[/tex]

Selling price= Cost Price-Loss

[tex]=15200-3040\\=12160[/tex]

Answer:

20 / the losssssssssssss

Answer:

62 cm^2

Step-by-step explanation:

Surface area of a rectangular prism is the area of each of the 6 faces added up. And area is length x width. There are three unique sets of sides, since each has another identical area opposite from it.

2(5 x 2) + 2(2 x 3) + 2(5 x 3)

2(10) + 2(6) + 2(15)

20 + 12 + 30

62 cm^2

Answer:

Step-by-step explanation:

SA=2lw+2lh+2hw

2 * 2 * 3 + 2 * 2 * 5 + 2 * 3 * 5 =

62 cm²

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathbf{8-|2(-3.5)-5|}[/tex]

[tex]\huge\textbf{Solving:}[/tex]

[tex]\mathbf{8-|2(-3.5)-5|}[/tex]

[tex]\mathbf{= 8 - |-7 - 5|}[/tex]

[tex]\mathbf{= -8 - |-12|}[/tex]

[tex]\mathbf{= 8 - 12}[/tex]

[tex]\mathbf{= -4}[/tex]

[tex]\huge\textbf{Answer:}[/tex]

[tex]\huge\boxed{\mathsf{-4}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

-4

Step-by-step explanation:

resolve the absolute value

I 2(-3.5) -5 I = I -7 -5 I = I -12 I = 12 The absolute value of any number is always positive

Then:

8 - 12 = -4

Hope this helps

Answer: 16 hours

Step-by-step explanation: If 180 miles was completed in 3 hours, it means 60 miles was completed in 1 hour (180 ÷ 3 = 60.) Now we just do 960 ÷ 60 and we get 16 hours of time at a constant speed, assuming no further alterations were made to accelerations.

If my problem was helpful, please mark it as Brainliest. It helps me earn reputation and ranks!

Arianna can travel 960 mi in 16 hours.

Speed is defined as the rate of change of position of an object in any direction.

Given that, Arianna drove 180 miles in 3 hours.

As we know, Speed is the ratio of distance to the time in which the distance was covered.

Speed = distance/time

Ariana's speed = 180/3 = 60 mi/hr

Therefore, time taken by her to travel 960 mi = 960/60 = 16 hr.

Hence, Arianna can travel 960 mi in 16 hours.

For more references on speed, click;

https://brainly.com/question/28224010

#SPJ1

The values that show a linear relationship is "Day" on the x-axis and "number of seeds" on the y-axis.

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

The standard form of a linear equation is given by:

y = mx + b

Where m is the slope of the line and b is the y intercept.

The values that show a linear relationship is "Day" on the x-axis and "number of seeds" on the y-axis.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer: Day on the x-axis and "log(seeds)" on the y-axis

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

22.5÷2.5=9 this is how you solve it

Option A. The answer to the question is Marcelina spends the intended amount of money and buys the intended amount of corn.

We can see a point that takes us to the amount that the corn was bought and the quantity that was obtained.

This shows that she is in range of what she was asked to buy. E shows us the amount that was spent as 12 dollars and the quantity of 50kg.

Read more on graphs here:

https://brainly.com/question/19040584

#SPJ1

Answer:

D (2, 1)

Step-by-step explanation:

Fir an in-detailed representation, image below

Learn more about Circles here: https://brainly.com/question/10368742

Answer:

14-2a

Step-by-step explanation:

Since 15 and 21 are not included: we will have

=15-2a-1

=14-2a

Side a, angle B and angle C of triangle ABC are 26.6 units, 61.9 degrees and 8.1 degrees respectively.

Given that;

First we determine the length of side a

[tex]a = \sqrt{b^2-c^2-2bc*cos(A)}[/tex]

We substitute our values into the above equation[tex]a = \sqrt{25^2-4^2-(2*25*4*cos(110)}\\\\a = 26.6[/tex]

Side a has a length of 26.6 units.

[tex]B = cos^{-1}(\frac{a^2+c^2-b^2}{2ac}) \\\\B = cos^{-1}(\frac{26.63464^2+4^2-25^2}{2*26.63464*4}) \\\\B = 61.9[/tex]

Angle B is 61.9 degrees.

[tex]C = cos^{-1}(\frac{a^2+b^2-c^2}{2ab} )\\\\C = cos^{-1}(\frac{26.63464^2+25^2-4^2}{2*26.63464*25} )\\\\C =8.1[/tex]

Angle C is 8.1 degrees.

Therefore, side a, angle b and angle c of the triangle ABC are 26.6 units, 61.9 degrees and 8.1 degrees respectively.

Learn more about triangles here: https://brainly.com/question/14882091

#SPJ1

Step-by-step explanation:

a).

n! is

[tex]n(n - 1)(n - 2)(n - 3)(n - 4).........(1)[/tex]

(n-3)! is

[tex](n - 3)(n - 4)(n - 5)..........(1)[/tex]

If we divide the two, everything behind (n-3) will just cancel out so we would be left with only

[tex](n)(n - 1)(n - 2)[/tex]

So the answer to a is

[tex]n(n - 1)(n - 2)[/tex]

b

Permutations formula of P(6,4) is

6!/(6-4)!, or 6!/2!.

[tex] \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 1} = 360[/tex]

Then we divide by 4!

[tex] \frac{360}{4 \times 3 \times 2 \times 1} = 15[/tex]

The answer to b is 15