What is the sum of the rational expressions below? 3x/x+9 + x/x-4

first, lets solve by factoring:

Let's solve your equation step-by-step.

2x2+14x−4=−x2+3x

Step 1: Subtract -x^2+3x from both sides.

2x2+14x−4−(−x2+3x)=−x2+3x−(−x2+3x)

3x2+11x−4=0

Step 2: Factor left side of equation.

(3x−1)(x+4)=0

Step 3: Set factors equal to 0.

3x−1=0 or x+4=0

x=

1

3

or x=−4

we can also solve using the quadratic formula:

2x2+14x−4=−x2+3x

Step 1: Subtract -x^2+3x from both sides.

2x2+14x−4−(−x2+3x)=−x2+3x−(−x2+3x)

3x2+11x−4=0

Step 2: Use quadratic formula with a=3, b=11, c=-4.

x=

−b±√b2−4ac

2a

x=

−(11)±√(11)2−4(3)(−4)

2(3)

x=

−11±√169

6

x=

1

3

or x=−4

lastly, we can complete the square.

2x2+14x−4=−x2+3x

Step 1: Add x^2 to both sides.

2x2+14x−4+x2=−x2+3x+x2

3x2+14x−4=3x

Step 2: Subtract 3x from both sides.

3x2+14x−4−3x=3x−3x

3x2+11x−4=0

Step 3: Add 4 to both sides.

3x2+11x−4+4=0+4

3x2+11x=4

Step 4: Since the coefficient of 3x^2 is 3, divide both sides by 3.

3x2+11x

3

=

4

3

x2+

11

3

x=

4

3

Step 5: The coefficient of 11/3x is 11/3. Let b=11/3.

Then we need to add (b/2)^2=121/36 to both sides to complete the square.

Add 121/36 to both sides.

x2+

11

3

x+

121

36

=

4

3

+

121

36

x2+

11

3

x+

121

36

=

169

36

Step 6: Factor left side.

(x+

11

6

)2=

169

36

Step 7: Take square root.

x+

11

6

=±√

169

36

Step 8: Add (-11)/6 to both sides.

x+

11

6

+

−11

6

=

−11

6

±√

169

36

x=

−11

6

±√

169

36

x=

1

3

or x=−4

Answer:

x=

1

3

or x=−4

Final answer:

The equation [tex]2x^2 + 14x - 4 = -x^2 + 3x[/tex] is a quadratic equation, which can be solved by standard methods such as factoring, completing the square, or applying the quadratic formula and then validated by substituting the solutions back into the original equation.

Explanation:

To solve the quadratic equation, [tex]2x^2 + 14x - 4 = -x^2 + 3x[/tex], first combine like terms by getting all terms on one side of the equation, resulting in [tex]3x^2 + 11x - 4[/tex] = 0. This is a standardized quadratic equation [tex]ax^2[/tex] + bx + c = 0. To find the solutions for this equation, you can either factorize it, complete the square or use the quadratic formula, (-b ± √([tex]b^2[/tex] - 4ac)) / (2a). After finding the roots (values for x), verify them by plugging them back into the original equation to ensure they satisfy it.

Answer:

[tex]-\frac{1}{3}[/tex]

Step-by-step explanation:

To find the slope of a line using two points, employ the use of the slope formula.

[tex]\frac{y_{2}-y_{1}}{x_{2}- x_{1}}[/tex]

Your y1 term is -2, your y2 term is -3.

Your x1 term is -3, your x2 term is 0.

[tex]\frac{-3-(-2)}{0-(-3)} \\\\\\\frac{-3+2}{0+3} \\\\\frac{-1}{3} \\[/tex]

The algebraic expression 3y+1 has a term with a coefficient of 3.

A coefficient is a constant value accompanying a variable that is multiplied by it. For example, 2 is the coefficient of x in 2x.

We can evaluate the given options.

In Option A, we have 3y+1. Here the expression has a term with a coefficient of 3.

In Option B, we have -2y + 5+ 3. Here the expression does not have a term with a coefficient of 3.

In Option C, we have 5y-7. Here the expression does not have a term with a coefficient of 3.

In Option D, we have 3(y-6). Here the expression does not have a term with a coefficient of 3.

Therefore, we have found that the algebraic expression 3y+1 has a term with a coefficient of 3.

Learn more about coefficients here: https://brainly.com/question/3189867

#SPJ2

Answer:

Option C and D are correct options

Step-by-step explanation:

The correct options are C and D.

We know that i = √-1

i² = -1

i³ = -i

and i^4 = 1

Lets solve the options one by one:

i^6 =1

Break the power:

i² *i ² * i² = (-1)(-1)(-1)

= -1

Therefore A is wrong

B) i^18 = 1

Lets break the power:

i²* i² *i² *i²*i²*i²*i²*i²*i²

put the value of i^2

= (-1) (-1) (-1) (-1) (-1) (-1) (-1) (-1)(-1)

= -1

Therefore option B is incorrect.

C) i^7 = -i

= i² * i² *i² *i

=(-1) (-1) (-1) * √-1

= - √-1

We know that √-1 = i

So,

- √-1 = -i

Therefore option C is correct.

D) i^16 = 1

= i² * i² * i² * i² * i² * i² *i² *i²

= (-1) (-1) (-1) (-1) (-1) (-1) (-1) (-1)

= 1

Therefore option D is correct.

Thus option C and D are correct option....

Answer: Option C and Option D

Step-by-step explanation:

Remember that by definition we have to:

[tex]i=\sqrt{-1}[/tex] and [tex]i^2=-1[/tex]

So for the option A we have to:

[tex]i^6=(\sqrt{-1})^2*(\sqrt{-1})^4\\\\i^6=-1*(-1)^2\\\\i^6=-1[/tex]

Option A is false

So for the  option B we have to:

[tex]i^{18}=(i^6)^3[/tex]

We know that [tex]i^6=-1[/tex]

So

[tex]i^{18}=(-1)^3[/tex]

[tex]i^{18}=-1[/tex]

Option B is false

So for the option C we have to:

[tex]i^7=(i)^6*i^1[/tex]

[tex]i^7=-i[/tex]

Option C is true

Finally for the option D we have to:

[tex]i^{16}=(i^4)^4[/tex]

[tex]i^{16}=((-1)^2)^4[/tex]

[tex]i^{16}=(1)^4[/tex]

[tex]i^{16}=1[/tex]

Option D is true

volume of a cylinder = pi×r^2×h

Answer:

I can increase r and decrease h, or I can decrease r and increase h.

Step-by-step explanation:

answer given in edmentum

Answer:

Step-by-step explanation:

<, > - dotted line

≤, ≥ - solid line

x ≤ a or x < a - the region below the horizontal line x = a

x ≥ a or x > a - the region above the horizontal line x = a

y ≤ a or y < a - the region on the left side of the vertical line y = a

y ≥ a or y > a - the region to the right of the vertical line y = a

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

We have dotted line (<, >).

The vertical line (y).

The region on the left side of the vertical dotted line y = -3

Answer:

This relation is a function.

Step-by-step explanation:

A function is a process or a relation that associates each element x of a set X, to a single element y of another set Y.

We have

{(-3, -6), (-1, -6), (5, -6), (8, -6)}

x = -3 → y = -6

x = -1 → y = -6

x = 5 → y = -6

x = 8 → y = -6

YES. This relation is a function.

/each x has one value of y/

Answer: Yes, it is a function

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

We are to find the value of the following:

[tex] log _ 3 5 \times log _ { 2 5 } 9 [/tex]

[tex] \log _ { 3 } 5 \times \log _ { 2 5 } 9 =\dfrac{1}{\log_{5}3}\times\log_{25}9=\dfrac{1}{\log_{5}3}\times\log_{5^2}9=\dfrac{1}{\log_{5}3}\times\dfrac{1}{2}\log_{5}9[/tex]

[tex] \dfrac { 1 } { \log _ { 5 } 3 } \times \dfrac { 1 } { 2 } \log_ { 5 } 9 = \dfrac{1}{\log_{5}3}\cdot\dfrac{1}{2}\log_{5}3^2=\dfrac{1}{\log_{5}3}\cdot\dfrac{2}{2}\log_{5}3=\dfrac{1}{\log_{5}3}\cdot\log_{5}3=\dfrac{\log_{5}3}{\log_{5}3}=[/tex] 1

Answer:

The value is: 1

Step-by-step explanation:

Use the Change of base formula. This is:

[tex]log_a(x)=\frac{log_b(x)}{log_b(a)}[/tex]

Using base 10:

[tex]log_3(5)*log_{25}(9)=\frac{log(5)}{log(3)}*\frac{log(9)}{log(25)}[/tex]

We know that:

[tex]9=3^2\\25=5^2[/tex]

And according to the logarithms properties:

[tex]log(x)^n=nlog(x)[/tex]

Then, we can simplify the expression:

[tex]=\frac{log(5)}{log(3)}*\frac{log(3)^2}{log(5)^2}=\frac{log(5)}{log(3)}*\frac{2log(3)}{2log(5)}=\frac{log(5)}{log(3)}*\frac{log(3)}{log(5)}=\frac{log(5)*log(3)}{log(3)*log(5)}=1[/tex]

Answer:

cos theta = -4/5.

sec theta = -5/4.

tan theta = 3/4.

cot theta = 4/3.

Step-by-step explanation:

sin^2 theta + cos^2 theta = 1

(-3/5)^2 + cos^2 theta = 1

cos^2 theta = 1 - 9/25

cos^2 theta = 16/25

cos theta = -4/5 (negative because  it is in Quadrant 3).

sec theta = 1 / cos theta = -5/4.

tan theta = sin theta / cos theta = -3/5 / - 4/5

= -3/5 * -5/4

=  3/4.

cot theta  =  1 / tan theta = 4/3.

The other trigonometric functions can be found using the Pythagorean Identity and the definitions of the trigonometric functions. The values are cos theta = -4/5, tan theta = 3/4, csc theta = -5/3, sec theta = -5/4, and cot theta = 4/3.

The given values are sin theta = -3/5 and cos theta = -5/3, which are located in quadrant 3. In this quadrant, sine and cosine are both negative. To find the values of the other trigonometric functions, we will use the Pythagorean Identity and the definitions of the trigonometric functions.

We can find cosine through the Pythagorean Identity, sin² theta + cos² theta = 1. Solving for cos theta, we get cos theta = sqrt(1 - sin² theta) = sqrt(1 - (-3/5)²) = -4/5. Note the negative sign since we are in quadrant 3.

Next, we can find tan theta = sin theta/cos theta = (-3/5) / (-4/5) = 3/4.

For the reciprocal functions, we have csc theta = 1/sin theta = -5/3, sec theta = 1/cos theta = -5/4, and cot theta = 1/tan theta = 4/3.

https://brainly.com/question/31540769

#SPJ2

$0.30 (farmer's market) < $0.35 (grocery store), the farmer's market offers blueberries at a lower price per ounce.

To compare the cost of blueberries from a grocery store and a farmer's market below:-

Cost of blueberries at the grocery store:

Cost of blueberries at the farmer's market:

Thus,

Answer:

Continuous because there are no breaks.

The graph is included as an attachment.

Step-by-step explanation:

Alright we want to graph:

y=x-4 for x<2

y=-2x+2 for x=2 or x>2

So let's graph the first piece y=x-4 for x<2.

I'm going to plug in 2 for x:   y=2-4=-2.   So this one line is going to contain an open circle at (2,-2). I say open circle because we did not have that we could actually include x=2 here because it says for x less than 2.

Now we are going to enter in one more number less than 2....your choice.

Let's go with x=0. When you plug in 0 for x into y=x-4 you get y=0-4=-4. So our line is going to include (0,-4).

So we are going to graph the points (0,-4) and (2,-2) again where (2,-2) is an open circle.  Connect these points. You may extend your line left because we have x<2, but do not extend it right of x=2.

Let's look at the other piece now: y=-2x+2 for x=2 or x>2.

I'm going to plug in 2 for x:  y=-2(2)+2=-4+2=-2 so we are going to include the point (2,-2) on our line.  This was actually a point we used from above that we didn't want to include.  We do now want to include because of the x=2 in our inequality so the dot can now be filled in. We need one more point to graph this line.  Let's plug in a number greater than 2 since our inequality say x=2 or x>2.  You choose.  How about x=3?

y=-2(3)+2=-6+2=-3.   So we are going to include the point (3,-3). So starting at (2,-2) and going right to connect it to (3,-3), you could extend passed the (3,-3) to the right.

I will show you my graph.

There are no breaks in the "curve", so it is continuous for all real numbers.

Answer:

x=-2

Step-by-step explanation:

-9x+1=-x+17

Add 9x on both sides:

     1=8x+17

Subtract 17 on both sides:

   -16=8x

Divide both sides by 8:

     -2=x

Check x=-2!

-9x+1=-x+17     with x=-2

-9(-2)+1=-(-2)+17

18+1=2+17

19=19

19=19 is a true equation so x=-2 is correct.

Answer: b

Step-by-step explanation:

Answer:

HL

SAS

SSS

Step-by-step explanation:

Since these are right triangles, and you have the two hypotenuses are congruent to each other and two legs that are also congruent to each other, then HL can be applied.

For HA to work we must have been given something else about one of those angle (besides the 90 degree one).

Since you have two corresponding sides that are congruent, then the 90 degree angles in both are congruent, and then the sides right after that 90 degree angle are also congruent to each other, so SAS can be applied.

We can't use AAS.  We only know something about one angle per each triangle due to the markers.

LA? Needed another angle besides the 90 degree one.

All three corresponding sides are congruent. The markers tell us this. So we can apply SSS.

Answer:

HL

SAS

SSS

Step-by-step explanation:

Answer:

The answer to this question is True

Answer: true

Step-by-step explanation:

Answer:

6.68%

Step-by-step explanation:

First find the z-score:

z = (x − μ) / σ

z = (13.30 − 13.00) / 0.2

z = 1.50

Look the value up in a z-score table, or use a calculator.

P(z>1.50) = 1 − 0.9332

P(z>1.50) = 0.0668

6.68% of players on the team run the 100 meter dash in 13.30 seconds or faster.

Answer:

1. the value of x can equal 25

the shortest length can equal 7

the longest length can equal 30

2. 2x+2.1=7.5

Step-by-step explanation:

Given:

1.

A scalene triangle with sides y, 4y and x

and perimeter,p= 60cm

As per perimeter formula:

p= sum of all sides

Putting values we get

60=x+4y+y

60=x+5y

so correct options are

the value of x can equal 25

the shortest length can equal 7

the longest length can equal 30

2. An isosceles triangle with sides y=2.1, x and x

and perimeter,p = 7.5

As per perimeter formula:

p= sum of all sides

Putting values we get

7.5=2.1 + x +x

7.1=2.1+2x !

Answer:

1)

[tex] \frac{26 + 16 + 11 + 13 + 24}{5} = \frac{90}{5} = 18[/tex]

2)

[tex] \frac{51 + 20 + 32 + 18 + 45 + 8}{6} = \frac{174}{6} = 29[/tex]

3)

[tex] \frac{17 + 39 + 15 + 42 + 37 + 61 + 19 + 40}{8} = \frac{270}{8} = 33.75[/tex]

4)

[tex] \frac{62 + 21 + 18}{3} = \frac{101}{3} = 33.67[/tex]

5)

[tex] \frac{9.2+8.6+9.4+9.2}{4} = \frac{36.4}{4} = 9.1[/tex]

Answer:

∛x²-8 = 2

-2∛x² = 2

∛x² = 2+2

x² = 4³

x = √64

x = 8

Answer:

C. x = –4 or x = 4

Step-by-step explanation:

B. s = 7 (for the second one)

Answer:

m∠5+m∠6=180°

m∠2+m∠3=m∠6

m∠2+m∠3+m∠5=180°

Step-by-step explanation:

Verify each option

case A) we have

m∠5+m∠3=m∠4 ----> equation A

we know that

m∠3+m∠4=180° -----> by supplementary angles

m∠4=180°-m∠3 ----> equation B

substitute equation B in equation A

m∠5+m∠3=180°-m∠3

m∠5+m∠3+m∠3=180°

This equation is true when m∠2=m∠3

therefore

Is not always true

case B) we have

m∠3+m∠4+m∠5=180° ----> equation A

we know that

m∠3+m∠4=180° -----> by supplementary angles

m∠4=180°-m∠3 ----> equation B

substitute equation B in equation A

m∠3+(180°-m∠3)+m∠5=180°

m∠5=0°

This option is not true

case C) we have

m∠5+m∠6=180°

we know that

m∠5 and +m∠6 are supplementary angles

so

Their sum is always 180 degrees

therefore

This option is always true

case D) we have

m∠2+m∠3=m∠6 -----> equation A

we know that

m∠5+m∠6=180° ----> by supplementary angles

m∠6=180°-m∠5 ----> equation B

substitute equation B in equation A

m∠2+m∠3=180°-m∠5

m∠2+m∠3+m∠5=180°

Remember that the sum of the interior angles of a triangle must be equal 180 degrees

therefore

This option is always true

case E) we have

m∠2+m∠3+m∠5=180°

Remember that the sum of the interior angles of a triangle must be equal 180 degrees

therefore

This option is always true

Answer:

CDE

Step-by-step explanation:

Answer:

                 -8

If cot Ф = ------

                  3

Step-by-step explanation:

Justine, when you're given answer choices, please share them.  Thank you.

                 -3

If tan Ф = ------

                  8

then:

                 -8

If cot Ф = ------

                  3

Answer:

"number line with open circles on negative 9 and 5, shading going in the opposite directions."

Step-by-step explanation:

Your inequality doesn't include an equal sign so there will be no closed holes. It will only be open holes.

|u|>14 means that the number u has to be greater than 14 or less than -14.  These numbers I describe just now all have a distance greater than 14 from 0.

So |u|>14 implies u>14 or u<-14.

But we are solving |2x+4|>14 so this implies we have 2x+4>14 or 2x+4<-14.

2x+4>14

Subtract 4 on both sides:

2x    >10

Divide both sides by 2:

x      >5

2x+4<-14

Subtract 4 on both sides:

2x    <-18

Divide both sides by 2:

x      <-9

So our solution is x>5 or x<-9.

Graphing!

~~~~~~~O                                         O~~~~~~~~

-----------(-9)---------------------------------(5)---------------

So we shaded to the right of 5 because our inequality says x is bigger than 5.

We shaded to the left of -9 because our inequality says x is less than -9.

Answer:

Step-by-step explanation:

Josh has to drive at least 6 hours.                 d≥ 6 Answer 2

Amelia walking 35 min or less                       b ≤ 35 Answer 3

Nancy < 35 hours = part time                         y < 35 Answer 1

Sarah at least 6 hours math                           f > 6 Answer 4

Answer:

Step-by-step explanation:

The point-slope of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the poinys (-1, -10) and (5, 2). Substitute:

[tex]m=\dfrac{2-(-10)}{5-(-1)}=\dfrac{12}{6}=2[/tex]

Put the value of the slope and the coordinateso f the point (5, 2), to the equation of a line:

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

In the question we have y - 6 = ...

Therefore

[tex]y-2=2(x-5)[/tex]    subtract 4 from both sides

[tex]y-6=2(x-5)-4[/tex]          use the distributive property

[tex]y-6=2x-10-4[/tex]

[tex]y-6=2x-14[/tex]      distributive

[tex]y-6=2(x-7)[/tex]

Answer:

36

Step-by-step explanation:

I think it may be 36. I did 6×6, but I'm not fully positive

There are 720 different arrangements in which the 6 friends can sit in the 6 seats of the rollercoaster.

To calculate the number of different arrangements in which the 6 friends can sit in the 6 seats of the rollercoaster, we can use the concept of permutations.

Since each friend occupies one seat and no two friends can occupy the same seat, we have 6 choices for the first seat, 5 choices for the second seat, 4 choices for the third seat, and so on until 1 choice for the last seat.

So, the total number of arrangements is the product of these choices:

[tex]\[ 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \][/tex]

Answer:

[tex]\frac{1}{x^2y^6}[/tex]

Step-by-step explanation:

We are given [tex](xy^3)^2 \cdot (xy^3)^{-4}[/tex]

First rule I'm going to use is [tex](m^rn^p)^s=m^{r \cdot s}n^{p \cdot s}[/tex].

This gives us:

[tex](xy^3)^2 \cdot (xy^3)^{-4}[/tex] is

[tex](x^2y^6) \cdot (x^{-4}y^{-12})[/tex].

Now pair up the bases that are the same:

[tex](x^2x^{-4}) \cdot (y^6y^{-12})[/tex].

Add the exponents when multiplying if the bases are the same:

[tex]x^{-2} \cdot y^{-6}[/tex]

Now usually teachers don't like negative exponents.

To get rid of the negative exponents just take the reciprocal:

[tex]\frac{1}{x^2} \cdot \frac{1}{y^6}[/tex]

[tex]\frac{1}{x^2y^6}[/tex]

To find the number of miles Lissette biked, the provided information leads to an algebraic equation where Lissette's distance is represented as 'x' and Shane's as '3x + 1', combining to equal 7 miles.

The subject of this question is mathematics, specifically algebra, where you need to write an equation based on a word problem.

The problem states that Shane biked 1 mile more than three times the number of miles Lissette biked, and their combined total is 7 miles. If we let x represent the number of miles Lissette biked, then Shane biked 3x + 1 miles. The equation to determine the number of miles Lissette biked is:

x + (3x + 1) = 7

Answer:

The answer is 6.

Step-by-step explanation:

A fifth of 10, or 10 divided by 5, is 2. Two is a third of 6. Therefore, the answer must be 6.

The number whose one - third is equal to one - fifth of 10 is 6.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is a number such that one - third of it is equal to a one - fifth of 10.

Assume that the number is [x].

Then, one - third of the number = 1/3 of x = x/3

Now, one - third of the number = one - fifth of 10, so we can write -

x/3 = 1/5 of 10

x/3 = 1/5 x 10

x/3 = 10/5

x = 10/5 x 3

x = 6

The number is 6.

Therefore, the number whose one - third is equal to one - fifth of 10 is 6

To solve more questions on Equation modelling, visit the link below-

https://brainly.com/question/28698426

#SPJ2

Out of those 80 counters, 20 counters may have a white dab on them.

Total number of counters in the bag = 200

counters that have a white dab = 50

counters that are now taken out of the bag = 80

Let's first take the ratio of counters that have a white dab to the total number of counters in the bag.

[tex]\rm{=\dfrac{counters\ that\ have\ a\ white\ dab}{Total\ number\ of\ counters\ in\ the\ bag}[/tex]

[tex]=\dfrac{50}{200} = \dfrac{1}{4} = 0.25[/tex]

Therefore, the ratio of counters that have a white dab to the total number of counters in the bag is 0.25.

As the bag is given  a good shake to ensure even distribution of the marked counters.

Those 80 counters will follow the same ratio of the bag, so, the number of tokens with white dab will be,

Number of tokens taken out x ratio of the bag

= 80 x 0.25

= 20

Hence, out of those 80 counters, 20 counters may have a white dab on them.

Learn more about ratio:

https://brainly.com/question/1504221

You need a picture deficiencies did that for 20 characters

Answer:

1,440

Step-by-step explanation:

1.5 percent of 96k