What is the domain of the rational function, f of x equals quantity x minus 5 over quantity 2 times x minus 3

Answer: Yes

Step-by-step explanation: 144 is a perfect square. In other words, it's possible to find a whole number that can be multiplied by itself that gives us 144.

In this case, we multiply 12 by 12 or 12² to get 144 which means 144 is a perfect square. Also, it's on our perfect square list which I will attach below.

13.23  miles

Step-by-step explanation:

The vector creates an inverted right-angled triangle. The westbound car will have covered 20 miles while the southbound car will ahve covered 15 miles in 30 mins;

40 miles /hr * ½ hr = 20 miles

30 miles/ hr * ½ hr = 15 miles

To find the hypotenuse (distance between the two cars), we shall use the formulae;

a² + b² = c²

20² + 15² = c²

c² = 20² – 15²

c² =  175

c = 13.23

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Answer:

C

Step-by-step explanation:

They're solid lines and overlap at that point

Answer:

Step-by-step explanation:

39 cars every 3 hrs.......that means (39/3) = 13 cars every hr

and if its 13 cars every hr....in 7 hrs, there will be (7 * 13) = 91 cars <==

you can either do it that way....the unit rate way...OR

you can set it up as a proportion...

39 cars to 3 hrs = x cars to 7 hrs...

39 / 3 = x / 7....cross multiply

(3)(x)= (39)(7)

3x = 273

x = 273/3

x = 91 <====

either way, u get the correct answer

Answer:

40 min

Step-by-step explanation:

1 x 48 + .20 .48

(1.20) (48)=  40 min

Final answer:

To find the total distance driven to and from work over 3 days, multiply the daily round-trip distance of 4310 miles by 3, resulting in 12,930 miles.

Explanation:

The question asks how many miles you would drive to and from work in 3 days if your round-trip to work is 4310 miles. To calculate this, you just need to multiply the daily round-trip distance by the number of days you travel. In this case, you travel to and from work for 3 days.

Determine the daily round-trip distance. (Already provided as 4310 miles)

Multiply the daily round-trip distance by the number of days traveled: 4310 miles × 3 days.

The calculation would be 4310 miles × 3 which equals 12,930 miles. This is the total distance driven to and from work over the 3 day period.

Answer:

there are 8 pigs because each pig has 4 legs. meanwhile, ducks technically by definition, only have 2 legs,wings do not count as legs.

Step-by-step explanation:

so 1 pig=4 legs.

8 pigs =32 legs

so 32+2x=36

To solve the problem, set up a system of equations using the number of pigs and ducks. Solve the system of equations to find the values of 'p' and 'd'. There are 8 pigs and 2 ducks in the farmhouse.

Let's assume the number of pigs is 'p' and the number of ducks is 'd'. Since each pig has 4 legs and each duck has 2 legs, we can set up the equation: 4p + 2d = 36 (since there are 36 legs in total). We also know that there are 10 animals in total, so we can set up another equation: p + d = 10. Now we have a system of equations which we can solve to find the values of 'p' and 'd'.

Multiplying the second equation by 2, we get 2p + 2d = 20. Subtracting this equation from the first equation, we get 4p + 2d - (2p + 2d) = 36 - 20, which simplifies to 2p = 16. Dividing both sides of the equation by 2, we find that p = 8. Substituting this value back into the second equation, we get 8 + d = 10, which means d = 2.

Therefore, there are 8 pigs and 2 ducks in the farmhouse.

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Answer:

82q

Step-by-step explanation:

-2(-5)q+(-72)(-q)

10q+72q

82q

Hey there! :)

-2(-5)q + (-72)(-q)

Simplify!

10q + (72q)

Since both terms contain "q," we know that we can add them together.

Simply look at it this way: 10+72 , then add the q at the end of your answer.

10 + 72 = 82 --> add the q! Therefore, your final answer is 82q.

~Hope I helped! :)

Answer: 21

Step-by-step explanation:

9  + 10 = 21

The expression simplifies to 81 over 16 by applying the exponent rules, particularly recognizing that any number to the power of 0 is 1 and when raising a power to a power, we multiply the exponents.

The student's question is asking to simplify the expression 3 to the power of 2 multiplied by 5 to the power of 0 whole over 4, the whole squared. To simplify this expression, we should apply the exponent rules.

Let's simplify step-by-step:

First, recognize that any number raised to the power of 0 is 1.

The expression now  simplifies to square of three, since anything multiplied by 1 remains unchanged.

Now, take the entire expression over 4 and square it as indicated.

Thus, the correct answer is 3 to the power of 4 multiplied by 1 squared over 4 squared equals 81 over 16.

Answer:

∠A= 112.5°, ∠B=67.5°, ∠C is 67.5° and ∠D 112.5°.

Step-by-step explanation:

Consider the provided information.

The sum of all interior angle of a polygon is: [tex](n-2)180[/tex]

Substitute n = 8.

[tex](8-2)180=1080[/tex]

Thus, the measure of each angle is: [tex]\frac{1080}{8}=135[/tex]

∠B and ∠C are congruent and their sum is 135°

∠B+∠C=135°

∠B=67.5°

Hence, the m angle B and m angle C is 67.5°.

The sum of all angles of a quadrilateral is 360°.

∠A+∠D+∠B+∠C=360°

∠A+∠D=360°-135°

∠A+∠D=225°

∠A and ∠D are congruent and their sum is 225°

∠A+∠D=225°

∠A=∠D=112.5°

Hence, the m angle A and m angle D is 112.5°.

Answer:

Step-by-step explanation:

A = L * W

A = 99

L = 2w + 7

now we sub

99 = (2w + 7)(w)

99 = 2w^2 + 7w

2w^2 + 7w - 99 = 0

(2w - 11)(w + 9) = 0

2w - 11 = 0

2w = 11

w = 11/2

w = 5 1/2 ft (or 5.5 ft) <==== width is 5 1/2 ft)

L = 2w + 7

L = 2(5.5) + 7

L = 11 + 7

L = 18 ft <====== length is 18 ft

Answer:

B) y=1/2x-3/2

Step-by-step explanation:

y=2x+3

x=2y+3

2y=x-3

y=1/2x-3/2

Answer:

B

Step-by-step explanation:

EDGE 2020

Answer:

The value of [tex]a_{4}=15[/tex]

Step-by-step explanation:

Given that [tex]a_{1}=6[/tex] and [tex]a_{n}=a_{n-1}+3[/tex]

Given sequence is of the form arithmetic sequence

For arithmetic sequence the sequence is [tex]a_{1},a_{2},a_{3},...[/tex]

The nth term is of the form  [tex]a_{n}=a_{n-1}+d[/tex]

Here  [tex]a_{1}=6[/tex] and [tex]a_{n}=a_{n-1}+3[/tex]

from this the common differnce is 3.

Therefore d=3

To find  [tex]a_{2}[/tex], [tex]a_{3}[/tex] , [tex]a_{4}[/tex]

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

put n=2 and d=3 we get

[tex]a_{2}=a_{2-1}+3[/tex]

[tex]a_{2}=a_{1}+3[/tex]

[tex]a_{2}=6+3[/tex]   (here  [tex]a_{1}=6[/tex] )

Therefore [tex]a_{2}=9[/tex]

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

put n=3 and d=3 we get

[tex]a_{3}=a_{3-1}+3[/tex]

[tex]a_{3}=a_{2}+3[/tex]

[tex]a_{3}=9+3[/tex]   (here  [tex]a_{2}=9[/tex] )

Therefore [tex]a_{3}=12[/tex]

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

put n=4 and d=3 we get

[tex]a_{4}=a_{4-1}+3[/tex]

[tex]a_{4}=a_{3}+3[/tex]

[tex]a_{4}=12+3[/tex]   (here  [tex]a_{3}=12[/tex] )

Therefore [tex]a_{4}=15[/tex]

Therefore the sequence is 6,9,12,15,...

Therefore the value of [tex]a_{4}=15[/tex]

Options A, B, and D each have exactly one solution. Option C has no solution because it simplifies to a contradiction.

To determine which of the given equations have exactly one solution, we will analyze each equation to see if it can be simplified or rearranged to form an identity (true for all values of [tex]\( x \))[/tex] or a contradiction (false for all values of [tex]\( x \))[/tex], or if it remains a valid equation with a unique solution for [tex]\( x \).[/tex]

An equation has exactly one solution if it can be simplified to the form [tex]\( ax = b \)[/tex] where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are constants, and [tex]\( a \)[/tex] is not zero.

Let's analyze each option step by step:

Option A: [tex]\( -5x + 12 = -12x - 12 \)[/tex]

1. Add [tex]\( 12x \)[/tex] to both sides: [tex]\( -5x + 12x + 12 = -12 + 12x \).[/tex]

2. This simplifies to [tex]\( 7x + 12 = -12 \).[/tex]

3. Subtract [tex]\( 12 \)[/tex] from both sides: [tex]\( 7x = -24 \).[/tex]

4. Divide by

  This equation has exactly one solution, [tex]\( x = -\frac{24}{7} \).[/tex]

Option B: [tex]\( -5x + 12 = 5x + 12 \)[/tex]

1. Add [tex]\( 5x \)[/tex] to both sides: [tex]\( -5x + 5x + 12 = 5x + 5x + 12 \).[/tex]

2. This simplifies to [tex]\( 12 = 10x + 12 \).[/tex]

3. Subtract \( 12 \) from both sides: [tex]\( 0 = 10x \).[/tex]

4. Divide by [tex]\( 10 \)[/tex]: [tex]\( x = 0 \).[/tex]

  This equation has exactly one solution, [tex]\( x = 0 \).[/tex]

Option C: [tex]\( -5x + 12 = -5x - 12 \)[/tex]

1. Subtract \( -5x \) from both sides: [tex]\( 12 = -12 \).[/tex]

  This simplifies to a contradiction since [tex]\( 12 \)[/tex] does not equal [tex]\( -12 \).[/tex]

  Therefore, this equation has no solution.

Option D: [tex]\( -5x + 12 = 5x - 5 \)[/tex]

1. Add \( 5x \) to both sides: [tex]\( -5x + 5x + 12 = 5x + 5x - 5 \)[/tex].

2. This simplifies to [tex]\( 12 = 10x - 5 \)[/tex].

3. Add [tex]\( 5 \)[/tex] to both sides: [tex]\( 17 = 10x \).[/tex]

4. Divide by [tex]\( 10 \)[/tex]: [tex]\( x = \frac{17}{10} \)[/tex].

  This equation has exactly one solution, [tex]\( x = \frac{17}{10} \)[/tex].

Based on this analysis, Options A, B, and D each have exactly one solution. Option C has no solution because it simplifies to a contradiction.

Answer:

Measure of Angle 5 = 150 degree.

Step-by-step explanation:

Given line g and h are parallel lines.

Let angle measuring [tex]30\ degree[/tex] be a.

From figure we can see that [tex]\angle a\ and\ \angle 3[/tex] both are Linear Pair Postulate,

i.e. [tex]\angle\ a+\angle 3 =180\ degree[/tex]

So,

[tex]30\ degree +\angle 3 =180\ degree[/tex]

[tex]\angle 3 = 180-30[/tex]

[tex]\Therefore \angle 3=150\ degree[/tex]   ------------(equation 1)

Now, [tex]\angle\ a\ and\ \angle\ 4[/tex] are alternate interior angles, and alternate interior angles are equal.

i.e. [tex]\angle\ a = \angle 4[/tex]

Therefore  [tex]\angle\ 4 =30\ degree[/tex]  ------------(equation 2)

Now, [tex]\angle 4\ and\ \angle 7[/tex] both are Linear Pair Postulate,

i.e. [tex]\angle\ 4 +\angle\ 7 = 180\ degree[/tex]

[tex]30+\angle\ 7=180[/tex]    ------------------(from equation 2)

[tex]\angle\ 7 =180-30[/tex]

[tex]\therefore\ \angle\ 7 = 150\ degree[/tex] ---------(equation 3)

Now,  [tex]\angle\ 7\ and \angle\ 5[/tex] are vertically opposite angles, and vertically opposite angles are equal.

So,

[tex]\angle 7=\angle 5[/tex]

[tex]\therefore\ \angle 5=150\ \ degree[/tex] -----------------(from equation 3)

To find kilometers per hour, we need to multiply 2 1/6 by 3, because it took Linley 1/3 hour to ride that far.

2 1/6 * 3 = 6 1/2

So, her average speed in kilometers per hour is 6 1/2 kph

Answer:

-5a - 4 is the expression equivalent

Following are the calculation to the given expression:

Given:

[tex]\bold{7a-8-12a+4}[/tex]

To find:

solve the expression=?

Solution:

[tex]\to \bold{7a-8-12a+4}\\\\\to \bold{-5a-4}\\\\[/tex]

Therefore, the final answer is "[tex]\bold{-5a-4}[/tex]".

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Answer:

The graph of y + 1 = −3/5 (x − 4) would be a straight line. The graph figure is attached below.

Step-by-step explanation:

As the linear equation y + 1 = −3/5 (x − 4) is given.

Since y-y₁ = m (x - x₁) is the Point-slope form is the general form y-y₁=m(x-x₁) for linear equations.

Hence, from the linear equation we can determine the slop which is m = -3/5

Also, when we put x = 0 in the linear equation, we determine the y-intercept as follows:

                            y + 1 = −3/5 (x − 4)

                            y + 1 = -3/5(-4)      ∵x = 0

                            y = 12/5 - 1

                            y = 7/5

y-intercept: 7/5

Hence,

Table for some points can be made for x and values as:

0           7/5

1            4/5

The graph of y + 1 = −3/5 (x − 4) would be a straight line. The graph figure is attached below.

Keywords: graph, straight line

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1. Let x represent the missing angle.

The sum of angles in a triangle is 180°

65° + 57° +x =180

122° +x=180°

x=180-122

x=68°

2. Let y represent the missing angle.

Then

y+90°+40°=180°

y+130°=180°

y=180°-130°

y=50°

3. Let the missing angle be t, then

t+20°+130°=180°

t+150° =180°

t=180°-150°

t=30°

4. Let the missing angle be m, then

m+85°+50°=180°

m=180°-50°-85°

m=180-135°

m=45°

5. Let the missing angle be e, then by the exterior remote angle theorem:

137°=102° +e

137-102=e

e=35°

6. Let the unknown angle p, be the missing angle.

Then by vertical angle property and exterior angle property:

p=35° +100°

p=135°

7. Let g be the missing angle, then

g+20°+30°=180°

g+50°=180°

g=180°-50°

g=130°

8)

Let v be the missing angle:

By angle on straight line, and exterior angle theorem property,

g=(180-155)+60°

g=25°+60°

g=85°

Answer:

y = -2x + 3

Step-by-step explanation:

4x + 2y - 6 = 0

2y - 6 = -4x

2y = -4x + 6

y = -2x + 3

Answer:

The slope-intercept form is,

y = -2x + 3

Step-by-step explanation:

The given equation of the line is,

4x + 2y  - 6 = 0

Subtracting "(4x- 6)" from both sides of the above equation, we get

   4x + 2y - 6 - (4x - 6) = 0 - (4x - 6)

⇒ 4x + 2y - 6 - 4x + 6 = 0 - 4x + 6

⇒ 2y = -4x + 6

Now, dividing both sides by '2' of the above equation, we get

 2y ÷ 2 = (-4x + 6) ÷ 2

⇒y = -2x + 3

This is the required slope-intercept form of the given line.

Answer:

3/5 0r 0.6

Step-by-step explanation:

A mod B = R

3/5 mod 6, because 3/5 < 6

so (3/5) / 6 = 0 ... R 3/5

Answer

Step-by-step explanation:

From the attached diagram below,

< ADC + <D = 180° (sum of linear angle) ------------(1)

<B + <C + <D = 180° (sum of interior angle in a triangle)---------(2)

Since the two equations are equal to 180°, We equate the two equation

i.e

(1) = (2)

< ADC + <D = <B + <C + <D

<D from the left hand side will cancel <D on the right hand side

We are now left with

<ADC = <B + <C

The Exterior Angle Theorem is proven by using the Triangle Sum Theorem, the Linear Pair Postulate, and the Subtraction Property of Equality to show that the sum of the interior opposite angles of a triangle equals the exterior angle.

To complete the proof of the Exterior Angle Theorem using the fact that angle ACD is an exterior angle of triangle BCD and prove that angle B + angle C = angle ACD, follow the steps below:

Answer:

(0,3) (3,0)

Step-by-step explanation:

if your asking for y=-x+3

or y=x+3 is (0,3) (0,-3

Answer:

$20,001

Step-by-step explanation:

Let $x be the amount of dollars Lincoln needs to make in sales to earn more than $1500.

His boss pays him $500 for the week, plus a 5% commission on each vehicle he sells.

5% of $x is $0.05x, the Lincoln earns

[tex]\$(500+0.05x)[/tex] in total.

Hence,

[tex]500+0.05x>1,500[/tex]

Solve this inequality:

[tex]0.05x>1,500-500\\ \\0.05x>1,000\\ \\5x>100,000\\ \\x>20,000[/tex]

Lincoln needs to make in sales more than $20,000, so the minimum amount of dollars Lincoln needs to make in sales is $20,001

Answer:

Step-by-step explanation:its not a improper fraction

Answer:

1 and 2/9

Step-by-step explanation:

7 goes into 9 1 time and there are 2 left over so that 2 would be 2/9 so it's 1 whole and 2/9

Answer:

x + 2 = 0 and y - 3 = 0

Step-by-step explanation:

We have to find the solution of the system of equations  

6x + 2y = - 6 ........... (1)

⇒ 12x + 4y = - 12 .......... (2) and  

3x - 4y = - 18 ........... (3)

Now, solving equations (2) and (3) we get,

15x = - 30

⇒ x = - 2

Hence, from equation (1) we get, 2y = - 6 - 6x = - 6 - 6(- 2) = 6

⇒ y = 3

Therefore, the solution of the given system of equations is (-2,3).

Now, x + 2 = 0 and y - 3 = 0 are another system of equations that have the same solutions. (Answer)

Answer:

Step-by-step explanation:

The domain on all x-squared parabolas is all real numbers.  

The range of an x-squared parabola is always found at the y coordinate of its vertex, and then is determined by whether it opens upwards or downwards. Our vertex has a y coordinate of -1 and opens downwards, so the range is all real numbers less than or equal to -1.

There are no x-intercepts (aka places on the graph that go through the x-axis), but the y-intercept is also the vertex, which is (0, -1).

Because this is an upside down parabola, it has a max point, again at the vertex.  It has no min point.

It increases from negative infinity to its max point and is notated as follows: (-∞, 0]

and decreases from its max point to negative infinity: [0, -∞)

Answer:

I could do 1 and 3

1) 2x-3y=-2 ....1

-

2x+y=14......2

=-4y=-16

y=4

Substitute (y=4) into equation 1

2x-3 (4)=-2

2x-12=-2

2x=-2+12

2x=10

×=5

3) 5x+5y=20....1

-

-3x+5y=4......2

=8x=16

x=2

Substitute (x=2) into equation 1

5 (2)+5y=20

10+5y=20

5y=20-10

5y=10

y=2

Answer: (1) x = 5 , y = 4

(2) x = -3 and y = 0

(3) x = 2 and y = 2

Step-by-step explanation:

(1) 2x - 3y = -2  ................... equation 1

   2x + y = 14 ................ equation 2

solving the system of linear equation by elimination method. We need to decide the variable to eliminate first , in this case , since the coefficient of x are the same  and they have the same signs (+), we can eliminate the variable x first by subtracting equation 1 from equation 2, so we have

2x - 2x + y - (-3y ) = 14 - ( - 2)

4y = 16

divide through by 4

y = 4

substitute y = 4 into equation 1 , we have

2x - 3 (4) = -2

2x - 12 = -2

2x = -2 + 12

2x = 10

x = 5

Therefore :

x = 5 and y = 4

(2) x = -6y - 3 ....................... equation 1

    8x + 8y = -24 ....................... equation 2

Solving the system of linear equation by substitution method , substitute x = -6y - 3 into equation 2 , equation 2 becomes

8(-6y - 3 ) + 8y = -24

expanding , we have

-48y - 24 + 8y = -24

-40y - 24 = -24

Add 24 to both sides , we have

- 40y = -24 + 24

-40y = 0

divide through by -40

y = 0/-40

y = 0

substitute y = 0 into equation 1 , equation 1 then becomes

x = -6(0) - 3

x = -3

Therefore : x = -3 and y = 0

(3)  5x + 5y = 20 ........................ equation 1

    -3x + 5y = 4  ............................ equation 2

solving the system of linear equation by elimination method , we have to decide the variable to eliminate first , since the coefficient of y are the same and are both positive, we will eliminate y by subtracting equation 2 from equation 1 , we have

5x - (-3x) + 5y - 5y = 20 - 4

5x + 3x + 0 = 16

8x = 16

x = 2

substitute x = 2 into equation 1 , equation becomes

5(2) + 5y = 20

10 + 5y = 20

5y = 20 - 10

5y = 10

y = 2

Therefore : x = 2 and y = 2

Answer:

2 units

Question:

Calculate the distance between (3 + i) and (3 − i).

Step-by-step explanation:

This problem is equivalent to the problem:

"Calculate the distance between the points (3,1) and (3,-1)."

Since the [tex]x[/tex]-coordinates are the same, this is a vertical distance.

A vertical distance be be found by computing the positive difference of the [tex]y[/tex]-coordinates. In other words, we need only the find the distance between the numbers [tex]y=1[/tex] and [tex]y=-1[/tex] on a number line.

This distance is 1-(-1)=1+1=2 units.