Which is a rational function??

Answer:

1. Option A

2. Option B

3. Option D

4. Option C

Step-by-step explanation:

The given vertices of triangle ABC are A(-3, 6), B(2,1), C(9, 5).

We have to fine the distance AB, BC and AC.

To calculate the distance between two vertices we will use the formula

[tex]d=\sqrt{(x-x')^{2}+(y-y')^{2}}[/tex]

For the length of side AB

AB=[tex]\sqrt{(2+3)^{2}+(1-6)^{2}}=\sqrt{5^{2}+5^{2}}=\sqrt{50}[/tex]

Option A. is the correct option

For the length of side BC

[tex]BC=\sqrt{(9-2)^{2}+(5-1)^{2}}=\sqrt{7^{2}+4^{2}}=\sqrt{65}[/tex]

Option B is the answer.

For the length of side AC

[tex]AC=\sqrt{(9+3)^{2}+(5-6)^{2}}=\sqrt{12^{2}+(-1)^{2}}=\sqrt{145}[/tex]

Option D is the answer.

For ∠ABC we will use the formula [tex]tan\theta =\frac{m_{1}-m_{2}}{1+m_{1}m_{2}}[/tex]

Since angle ABC is formed by two sides AB and BC

So we will find the slopes of these two lines and find the angle

Now slope of AB, [tex]m_{1}=\frac{y-y'}{x-x'}=\frac{1-6}{2+3}=\frac{-5}{5}=-1[/tex]

Slope of BC, [tex]m_{2}=\frac{5-1}{9-2}=\frac{4}{7}[/tex]

[tex]tan\theta =\frac{m_{1}-m_{2}}{1+m_{1}m_{2}}[/tex]

[tex]tan\theta =\frac{(-1)-(\frac{4}{7})}{1+(-1)(\frac{4}{7})}=\frac{\frac{-11}{7}}{1-\frac{4}{7}}=\frac{\frac{-11}{7}}{\frac{3}{7}}=\frac{-11}{7}\times \frac{7}{3}=-\frac{11}{3}=-3.67[/tex]

[tex]\theta =tan^{-1}(-3.67)=74.75[/tex]

Since angle between them [tex]tan\theta[/tex] is negative that means angle theta will be obtuse angle.

So the angle between AB and BC = (180 - 74.75) = 105.26°

Therefore Option C. 105.26° is the answer.

Answer:

- 213

Step-by-step explanation:

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a + (n - 1)d

where a is the first term and d the common difference

d = 27 - 32 = - 5 and a = 32, hence

[tex]a_{50}[/tex] = 32 + (49 × - 5) = 32 - 245 = - 213

The 50th term of the arithmetic sequence is -213.and this can be determined by using the [tex]\rm T^{th}[/tex] term of the arithmetic sequence formula.

Given :

Arithmetic sequence  ---  32,27,22,17,12

The difference of the arithmetic operation is given by the formula:

[tex]a_2-a_1 = 27 - 32 = - 5[/tex]

The [tex]\rm T^{th}[/tex] term of the arithmetic sequence is given by the formula:

[tex]\rm T_n = a + (n-1)d[/tex]

where a is the first term, n is the total number of terms, d is the difference, and [tex]\rm T^{th}[/tex] is the term of the arithmetic sequence.

[tex]\rm T_{50} = 32 - (50-1)5[/tex]

[tex]\rm T_{50} = 32 - (49)\times 5[/tex]

[tex]\rm T_{50} = -213[/tex]

The 50th term of the arithmetic sequence is -213.

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Answer:

- 4 > n and Notion form : [ -4 , -∞).

Step-by-step explanation:

Given : (n-7)>2n-3.

To find : Solve the inequality.

Solution : We have given

(n - 7) > 2 n - 3.

On adding both sides by 3

n - 7+ 3 > 2n .

n - 4 > 2n .

On subtracting b both sides by n

-4 > 2n -n.

- 4 > n.

So, we can say value of n is less  than - 4 like -5,-6, -7 ........-∞

Notion form : [ -4 , -∞).

Therefore, - 4 > n and Notion form : [ -4 , -∞).

n  = {n | n ∈ R,  n < -4}

The given inequality is:

n  -  7   >  2n  -  3

Collect like terms

n  -  2n  >   -3  +  7

-n    >   4

Multiply both sides by -1 and change the sign to <

-1(-n)  <  -1(4)

n    <   -4

In set notation:

n  = {n | n ∈ R,  n < -4}

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Answer:

907,450

Step-by-step explanation:

This is a problem of exponential decay. The population is decreasing at 0.1% per year.

The formula to figure this out is  [tex]A=P(1+r)^t[/tex]

Where

A will be the future population (after 50 years)

P is the initial population (which is 954,000)

r is the rate of decrease (which is -0.1% or -0.001)

t is the time in years (which is 50)

Plugging these information into the formula and figuring out A will give us the answer. Shown below:

[tex]A=P(1+r)^t\\A=954,000(1-0.001)^{50}\\A=954,000(0.999)^{50}\\A=907,450.17[/tex]

Since fractional/decimal population is not feasible, we round it off.

The population in 50 years would be around 907,450

the value of x = the answer is D 11/2

Answer:

T T → T

Step-by-step explanation:

The following table represents the truth table.

(p)  (q)  (p->q)

T     T       T

T     F       F

F     T       F

F     F       F

Now we have the hypothesis that 5 = 3 + 2.

5 = 3 + 2 is True

Then we have the conclusion that 3 + 2 = 5.

3 + 2 = 5 is True

Therefore, we can conclude that (p->q) is True

This can also be represented as:

T T → T

Answer:

C

Step-by-step explanation:

Simply plug in x for all the questions to see if the x is the solution

A.) 3(20-14) = 44

3(16)=48

so A is incorrect

B.) 3(12-14) = 6

3(-2) = -6

so B is incorrect

C.) 2(14-3) =22

2(11) =22

C is correct

D.) 2(14)-3=22

28-3 = 25

so D is incorrect

Answer:

the answer would be 2(x - 3) = 22  (C)

Step-by-step explanation:

step 1:

2(x - 3) = 22

step 2: divide both sides by the equation 2

x - 3 = 11

step 3: move constant (3) to the right and change its sign

x = 11 + 3

step 4: add the numbers (11 and 3)

x = 14

Answer:

The least balance is your own because -50$ is the farthest from 0 on the number line

Step-by-step explanation:

Answer:

Step-by-step explanation:

Look at the picture.

The edge of the cube is equal to the diagonal of the sphere.

Therefore, the length of the cube's edge is 3 inches.

The formula of a surface area of a cube:

[tex]S.A.=6a^2[/tex]

Substitute a = 3 in:

[tex]S.A.=6(3^2)=6(9)=54\ in^2[/tex]

Answer:

TRUE, because you are adding a unit more to a, then by logic laws, the quantity grow.

Best regards

Answer:

b > a - True

Step-by-step explanation:

We are given the following expression and we are to determine whether [tex] b > a [/tex] is true or not:

[tex] a + 1 = b [/tex]

Considering the given equation, if we take both the variables on one side so we will get:

[tex] 1 = b - a [/tex]

Sign of the variable [tex]a[/tex] will change to negative while [tex]b[/tex] remains positive.

It means that [tex][/tex] is greater than [tex]a[/tex] (b > a) so it is true.

Answer:

120,000

Step-by-step explanation:

Rolando would get back 120,000. Because the insurance limit is 250k, Rolando only put in 120k, so he should get everything back.

Answer: 1625

Step-by-step explanation: If Adrian has 5 times as many times is a keyword to know its multiplication. 325x5=1625

Derrick has 65 stickers.

To find out how many stickers Derrick has, we need to divide the number of stickers Adrian has by 5. Since Adrian has 325 stickers, we divide 325 by 5.

325 ÷ 5 = 65.

Therefore, Derrick has 65 stickers.

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Answer:

Step-by-step explanation:

D) 221

Answer:

g≥34

Step-by-step explanation:

To solve the inequality g-17≥17, add 17 to both sides to get g≥34, and graphically represent it with a closed circle at 34 and shade the area to the right.

To solve the inequality g−17≥17, add 17 to both sides of the inequality. This yields g ≥ 34. The graph of this solution will include a number line with a closed circle at 34 and a shaded area to the right of 34, indicating all the values of g that are greater than or equal to 34. When graphically representing inequalities, it is important to use a closed circle to indicate that the number is included in the solution.

Answer:

Step-by-step explanation:

[tex]3m\leq36\qquad\text{divide both sides by 3}\\\\\dfrac{3m}{3}\leq\dfrac{36}{3}\\\\m\leq12\\\\a.\ m=4\leq12\to\boxed{SOLUTION}\\\\b.\ m=9\leq12\to\boxed{SOLUTION}\\\\c.\ m=12\leq12\to\boxed{SOLUTION}\\\\d.\ m=15>12\to\boxed{NOT\ A\ SOLUTION}[/tex]

Answer:x=10

Step-by-step explanation:

5/2 × 2/5 = 4/1 × 5/2

Multiply and simplify and x=10

The solution to the equation 2/5x = 4 is x = 10. You can find the solution by multiplying both sides of the equation by 5/2, which cancelled out the 2/5 on the left side, and then performing the operation on the right side.

To solve the equation 2/5x = 4, you'll first want to isolate the variable 'x' on one side of the equation. You can do this by dividing both sides of the equation by the coefficient of 'x', which is 2/5. However, instead of dividing by a fraction, it's easier to multiply by the reciprocal of the fraction.

So, we multiply both sides of the equation by 5/2. The 5/2 multiplied by 2/5 on the left side of the equation equals 1, leaving us with just 'x' on the left side of the equation.

So, you would have x = 4 * 5/2.

Now, we just perform the operation on the right side to find the value of 'x', and we get x = 20/2 = 10.

So, the solution to the equation 2/5x = 4 is x = 10.

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Answer:

7.5 ft²/student

Step-by-step explanation:

This is a "unit rate" problem.

30 ft²

------------------ = 7.5 ft²/student

 4 students

Each student will  paint 7.5 ft² of the wall.

Answer:

16

2

Step-by-step explanation:

Given in the question an equation

[tex]\frac{x^2 - 10x + 14}{ x-8}[/tex]

The constant term that the numerator must have = 16

To get this number add 2 in the numerator

after which the equation will become

[tex]\frac{x^2 - 10x + 14+2}{ x-8}[/tex]

[tex]\frac{x^2 - 10x + 16}{ x-8}\\[/tex]

Now by using factorisation of quadratic equation we have

[tex]\frac{(x-8)(x-2)}{x-8}[/tex]

(x-2)

but if we add and subtract 2 in the numerator then

[tex]\frac{x^2 - 10x + 16 -2}{ x-8}[/tex]

[tex]\frac{(x-8)(x-2)-2}{x-8}[/tex]

[tex](x-2)-\frac{2}{x-8}[/tex]

Answer:

Help with this please

Step-by-step explanation:

i have the attachment down there

Answer:

The area of the rectangle is [tex](5/18)\ in^{2}[/tex]

Step-by-step explanation:

we know that

The area of rectangle is equal to

[tex]A=LW[/tex]

where

L is the length of rectangle

W is the width of rectangle

substitute the values

[tex]A=(5/6)(1/3)=(5/18)\ in^{2}[/tex]

Answer:

2/3 is the correct answer so C. Hope this helps you. :)

Step-by-step explanation:

In this experiment, the ratio of heads to tails comes out to be 2/1.

Probability is a way to gauge how likely something is to happen. Even while no event can be foreseen with absolute certainty, probability can be used to convey how likely it is that it will happen.

Probability is the ratio of the number of favourable outcomes to the total number of outcomes of an event.

The number of favourable outcomes for an experiment with 'x' and the total outcomes is represented by the symbol 's'. The following formula can be used to determine how likely an event is to occur.

Probability = Favourable Outcomes/Total Outcomes = x/s

The total number of the outcomes are 36.

The total outcome for head is 24 times.

So, the total outcome for tail will be 36 - 24 = 12

The ratio of head to tail is = favourable outcome for heads/ favourable outcomes for tails.

Thus,

heads/ tails = 24/12

heads/tails = 2/1

Therefore, the ratio of heads to tails in the experiment is 2/1.

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room=400

Ppl=25p

Total cost=775

775=25p+400 ⟨—— equation

775-400=25p

375/25=p

15=p

15 people attended his party

The median is 52 you can put this in a stat line in a graphing calculatior

Given the even number of data set, the median which is the average of the middle two numbers in the arranged data set is 52.

Median is simply the middle value in a set of variables arranged in a descending or ascending order.

Given the data set; 40 49 62 56 68 39 50 61 54 44.
First, we arrange is ascending order.

39 40 44 49 50 54 56 61 62 68

Since it is an even number set ( 10 )

We find the average of the middle two numbers

Median = ( 50 + 54 ) / 2

Median = 104 / 2

Median = 52

Therefore, the given the even number of data set, the median which is the average of the middle two numbers is 52.

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Answer:

D.  [tex]f^{-1}(x)=\frac{x-5}{2}[/tex]

Step-by-step explanation:

The given function is

[tex]f(x)=2x+5[/tex]

Let [tex]y=2x+5[/tex]

Interchange  x and y.

[tex]x=2y+5[/tex]

Solve for y.

[tex]x-5=2y[/tex]

Divide both sides by 2

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

Hence [tex]f^{-1}(x)=\frac{x-5}{2}[/tex]

Answer: OPTION D

Step-by-step explanation:

To find the inverse of the function given in the problem, you must apply the proccedure shown below:

1- Rewrite the function:

[tex]y=2x+5[/tex]

2- You must solve for x from the functionn, as following:

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

[tex]f^{-1}(x)=\frac{x-5}{2}[/tex]

Answer:

It isnt possible

Step-by-step explanation:

-5 and -6 cause when you multiply them both u get positive 30 and when you add them you get negative 11

Answer:

Step-by-step explanation:

Triangles

Area of a triangle = 1/2 b * slanted height

b = 6 m

h = 9 m

Area of 1 triangle = 1/2 * 6 * 9

Area of 1 triangle = 27

Area of all 4 triangles = 4*27 = 108 m^2

==================

Base area

The base is a square. All 4 sides are equal.

The formula for a square is s^2

Area = (6 m)^2

Area = 36 m^2

Total area

Total Area = 108 m^2 + 36 m ^2

Total Area = 144 m^2

your answer is 144m2

hope this helps;)

mark brainly

C= 2(3.14)r or 3.14D

so, if the diameter (d) is given just multiply it by 3.14. If the radius (r) is given multiply it by 2 then multiply that answer by 3.14 (or just multiply the radius by 6.28)

Pay attention to the units, then find the answer at the bottom.

Answer:

[tex]x=\frac{2}{5}[/tex] or [tex]x=1[/tex]

Step-by-step explanation:

The given quadratic equation is

[tex]5x^2-7x+2=0[/tex]

Group the constant terms on the right hand side.

[tex]5x^2-7x=0-2[/tex]

[tex]5x^2-7x=-2[/tex]

Divide through by 5.

[tex]x^2-\frac{7}{5}x=-\frac{2}{5}[/tex]

Add the square of half the coefficient of x., which is [tex](\frac{1}{2}\times- \frac{7}{5})^2=\frac{49}{100}[/tex] to both sides of the equation.

[tex]x^2-\frac{7}{5}x+\frac{49}{100}=-\frac{2}{5}+\frac{49}{100}[/tex]

The left hand side is now a perfect square.

[tex](x-\frac{7}{10})^2=\frac{9}{100}[/tex]

Take the square root of both sides;

[tex](x-\frac{7}{10})=\pm \sqrt{\frac{9}{100}}[/tex]

[tex]x-\frac{7}{10}=\pm \frac{3}{10}[/tex]

[tex]x=\frac{7}{10}\pm \frac{3}{10}[/tex]

[tex]x=\frac{7-3}{10}[/tex] or [tex]x=\frac{7+3}{10}[/tex]

[tex]x=\frac{4}{10}[/tex] or [tex]x=\frac{10}{10}[/tex]

[tex]x=1[/tex] or [tex]x=\frac{2}{5}[/tex]

Answer:

[tex]x_1=1\\\\x_2=\frac{2}{5}[/tex]

Step-by-step explanation:

- You must divide the equation by 5:

[tex]x^{2}-\frac{7}{5}x+\frac{2}{5}=0[/tex]

- Add and subtract [tex](\frac{\frac{7}{5}}{2})^2[/tex]:

 [tex]x^{2}-\frac{7}{5}x+(\frac{7}{10})^2+\frac{2}{5}-(\frac{7}{10})^2=0[/tex]

Therefore, you obtain:

[tex](x-\frac{7}{10})^2-0.09=0[/tex]

-add 0.09} to both sides:

[tex](x-\frac{7}{10})^2=0.09[/tex]

- Apply square root to both sides and solve for x:

[tex]\sqrt{(x-\frac{7}{10})^2}=\sqrt{\0.09}\\x-\frac{7}{10}=\sqrt{0.09}\\\\x_1=\frac{7}{10}+\sqrt{0.09}=1\\\\x_2=-\frac{7}{10}-\sqrt{0.09}=\frac{2}{5}[/tex]

Answer: the answer will be 3

Step-by-step explanation:

The scale factor is 3 because the point (0, 2) becomes (0, 6) option third is correct.

The ratio among comparable dimensions of an object and a model with that object is known as an exponent in algebra. The replica will be larger if the scale factor is a whole number. The duplicate will be lowered if the step size is a fraction.

We have:

D O,K = (0, 2) → (0, 6)

The point (0, 2) becomes (0, 6)

The scale factor = 6/2 = 3

Thus, the scale factor is 3 because the point (0, 2) becomes (0, 6) option third is correct.

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Answer:

c

Step-by-step explanation:

thats the answer