PLEASE HELP! If a factor of the denominator of a rational function cancels with a factor of the numerator and the inequality is closed, then the zero of the canceled factor should be included in the solution for the inequality.
True or False?

The roots of the quadratic equation 4x² - 2x - 20 = x² + 9x are x = 5 and

x = - 7/6 respectively.

We have the following equation -

4x² - 2x - 20 = x² + 9x

We have to find its roots.

A quadratic equation is an algebraic equation of the second degree in x. In the standard form it can be written as ax² + bx + c = 0. In this - a and b are the coefficients of 'x' and 'x²' respectively and c is a constant term.

According to the equation -

4x² - 2x - 20 = x² + 9x

4x² - x² - 2x - 9x - 20 = 0

3x² - 11x - 20 = 0

Using quadratic formula, the roots of the equation will be -

x = (- b ± [tex]\sqrt{b^{2} - 4ac}[/tex]) / 2a

x = (11 ± 19)/6

x = 30/6   and  x = -7/6

x = 5  and  -7/6

Hence, the roots of the quadratic equation are 5 and -7/6.

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Answer:

.06%

Step-by-step explanation:

multiply the number by 100 to get it as a percentage

Answer:

0.0006 = 0.06%

Hope this helps :)

Hope this helps :)Explanation below.

Step-by-step explanation:

To convert a decimal to a percent, move the decimal 2 times to the right.

0.0006 = 0.06%

↑JJ

Answer:

Step-by-step explanation:

Log 64 base 4

64=[tex]4^{X}[/tex]

[tex]4^{3} =4^{X} \\\\The base cancels out\\3= X[/tex]

  22)

[tex]Log 16 base 4 = x\\\\16=4^{x} \\4^{2} =4^{x} \\[/tex]

The base will cancel out

2=x          

30) Log 1/216 base 6

[tex]\frac{1}{216} = 6^{x} \\\216^{-1} =6^{x} \\6^{(3)(-1)} =6^{x} \\6^{-3} =6^{x}[/tex]

The base will cancel out

x=-3

The equation of the line in slope-intercept form is: y = -3/10x + 13/10.

Given the points, (1,1) and (11,−2). Follow the steps explained below.

Step 1: Find the slope of the line:

Slope (m) = change in y / change in x = (-2 - 1)/(11 - 1)

Slope (m) = -3/10

Step 2: Substitute m = -3/10 and (a, b) = (1, 1) into y = mx + b to find the value of b

1 = -3/10(1) + b

1 = -3/10 + b

1 + 3/10 = b

b = 13/10

Step 3: Substitute m = -3/10 and b = 13/10 into y = mx + b

y = -3/10x + 13/10

Thus, the equation of the line in slope-intercept form is: y = -3/10x + 13/10.

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La altura del cono es de 8 centimetros.

Sabemos que para un cono de radio R, altura H, y generatriz G se cumple la relación:

R^2 + H^2 = G^2

Resolviendo para la altura obtenemos:

H = √(G^2 - R^2)

En este caso sabemos que le diámetro es de 30 cm, entonces el radio será de:

R = 30cm/2 = 15cm

Y la generatriz es de 17cm, entonces G = 17cm

Reemplazando eso en la ecuación para la altura obtendremos:

H = √((17cm)^2 - (15cm)^2) = 8cm

Concluimos que la altura del cono es de 8 centimetros.

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Answer: 834,976

Step-by-step explanation:

The results for the connected graph H, obtained by using graph theory are;

First part;

There are 22 vertices in the spanning tree

Second part;

There are 22 vertices in H

Third part;

D. H has at least 21 edges

The given parameters are;

H = A connected graph

Number of edges in the spanning tree of H = 21

First part

Required:

The number of vertices in the spanning tree of H

Solution;

In graph theory, a spanning tree is one that contains all the vertices of the graph.

The number of edges in a tree that has n vertices is 'n - 1'

Therefore;

Number of edges = n - 1 = 21

n = 21 + 1 = 22

Second part;

From the definition of a spanning tree, the number of vertices in H is equal to the number of vertices in the spanning tree which is 22

Third part;

Let m represent the number of edges in H.

Therefore, the number of edges that should be deleted from H to get the spanning tree is 'm - (n - 1)', which gives;

The number of edges in the given spanning tree is n - 1 = 21

Which gives;

Therefore;

D. H has at least 21 edges

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The value of 8+3e when e=2 will be 14.

It should be noted that the equation or expression is given as:

8 + 3e

Therefore, we will put the value of E as 2 int the equation. This will be:

8 + 3e

= 8 + 3(2)

= 8 + 6

= 14

The value is 14.

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I think what was meant here was -23 + a = -12.

a = 11

To solve for a, let’s subtract -12 from -23:

-23 - (-12) = 11

a = 11

Let's plug 11 in for reassurance:

-23 + 11 = -12

a = 11

Answer:

The domain of this function is (in order of least to greatest) is [-2,-1,0,3.5,4,5.5, and 8]

The range of this function is (in order from greatest to least) is [6,5.5,4,0,-1, and -3.5]

Step-by-step explanation:

To find the domain you need to look at all of you input or x values so the question is asking to name the values of x for your domain. You look at the table to where x is and name the numbers listed in this case it's [-2,-1,0,3.5,4,5.5, and 7]

To find the range you need to look at the listed outputs or y values. You are essentially doing the same steps but instead you looking at y for the listed values. Generally when it comes to domains that have the same range (for example (4,-1) and (5.5,-1)) you would only write it once in the list of ranges so like [6,5.5,4,0,-1, and -3.5]

The equation has infinite solutions.

The value of x that makes the equation true is: 2. After substitution, we would have: 8 = 8

Another value of x that makes the equation true is: 3. After substitution, we would have: 10 = 10

If an equation has infinite solutions, it means that any value of the variable in the equation would make the equation true.

Given the equation, 2(x + 2) = 2x + 4, the value of x that makes the equation true is: 2.

Substitute x = 2 into the equation and simplify it would make both sides equal:

2(2 + 2) = 2(2) + 4

8 = 8

Another value of x that makes the equation true is: 3.

Substitute x = 3 into the equation and simplify it would make both sides equal:

2(3 + 2) = 2(3) + 4

10 = 10

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Answer: x = [tex]\frac{20}{7}[/tex]

(or)

x = 2.86 ( rounded )

Step-by-step explanation:

3.5(x +2) = 17

3.5x + 7 = 17

3.5x = 17 - 7

3.5x = 10

x = 10/3.5

x = [tex]\frac{20}{7}[/tex]

(or)

x = 2.86 ( rounded )

Answer:

  (a)  8

Step-by-step explanation:

You did not provide the example problem shown, so we have to do the division to find the repeated remainder.

The attachment shows the repeated remainder is 8, the result of subtracting 72 from 80.

Answer:

I believe the answer is y=3,−3

Step-by-step explanation:

m<6 = 117° based on the same-side-interior angles theorem

m<7 = 63° based on the corresponding angles theorem

Angles 3 and 6 are same-side interior angles, therefore, based on the same-side-interior angles theorem, their sum equals 180 degrees because they are supplementary to each other.

Thus:

m<3 + m<6 = 180

Substitute

63 + m<6 = 180

m<6 = 180 - 63

m<6 = 117°

m<7 = m<3 [corresponding angles theorem]

m<7 = 63°

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The ratio that is equivalent to Stefanie's rate is 1 : 2

The given parameters are

Distance = 4 miles

Trips = 2

The ratio that is equivalent to Stefanie's rate is represented as

Rate = Trips/Distance

So, we have

Rate = 2 trips /4 miles

Evaluate

Rate = 1/2 trip per mile

Express as raton

Ratio = 1 : 2

Hence, the ratio that is equivalent to Stefanie's rate is 1 : 2

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Based on the fact that the researchers were able to conclude that a range of percentages of the female Osprey hatch-lings in the US succeed in growing up to lay their own eggs, this is Inferential statistics.

In inferential statistics, data is used to be able to reach a conclusion on a phenomenon. This means that data is not just taken and then presented like in the case of descriptive statistics, it is also analyzed and evaluated to reveal patterns.

In this scenario, female Osprey hatch-lings success in growing up and laying their eggs was researched and data was used to make conclusions on the subject so this is inferential statistics.

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Answer: Average velocity = 11.1 m/s

Step-by-step explanation:

Given data,

A baseball is tossed up into the air at an initial velocity = 16 m/s​.

The height of the baseball at time t​ in seconds is given by,

                            h(t) =  16t - 4.9t²  ​​(in meters).

So,  

The average velocity is,            

To calculate the velocity travelled by the ball, differentiate the function.

                           dh/dt = 16 - 2(4.9t)

                           dh/dt = 16 - 9.8t               (eq-1)

Let us assume,    t = [1,1.5]​

Substitute t for 1 in the above Differential function

                            dh/dt = 16 - 9.8 (1)

But ,

                           dh/dt = velocity

So,                     dh/dt = V                        

                          V = 16 - 9.8

                          V =  6.2 m/s

Therefore,

               Average velocity = ( U + V ) / 2

               Average velocity = (16 + 6.2)/2

               Average velocity = 22.2/2

               Average velocity = 11.1 m/s

Hence, Average velocity = 11.1 m/s.

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Answer:

The answer would be $16,660.

Step-by-step explanation:

The car would cost $16,660 after one year.

Answer:

0.250

Step-by-step explanation:

Given from the question, we know that the summation (adding all values together) of all P(x) values is equal to 1.

And, we do know that P(2) = P(4).

This means , we will subtract all the known P(x) values from 1 to get the value of P(2) + P(4).

P(2) + P(4) = 1 - 0.0425 - 0.3750 - 0.0625 - 0.0200 = 0.500

Since P(2) = P(4), we divide 0.500 by 2 to get the value of P(2) and P(4).

P(2) = P(4) = 0.500 ÷ 2 = 0.250

In this case we know that the parabola does not cross the x-axis, thus, the quadratic equation has no solutions.

For a quadratic function (also called a parabola)

y = a*x^2 + b*x + c

the solutions of the quadratic equation are the values of x such that:

a*x^2 + b*x + c = 0

Now, remember that the values with y = 0 are called the x-intercepts, then the solutions of the above equation are x-intercepts.

And here we know that the parabola does not cross the x-axis, thus, the quadratic equation has no solutions.

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Answer:

Step-by-step explanation:

Answer:

so you're answer is 30 inches in total because if you add up all the inches and the hours that's tire answer glad if i could help.

The number between 10 and 100 which has 5 base ten blocks and one of the digits is 4 will be 41.

Let the two digits be x and y

There are 5 base ten blocks therefore the sum of the numbers will be 5

i.e. x + y = 5                                                                                             ..eq-1

One of the digit is 4

So, let the value of x = 4

Putting the value of x in eq-1

4 + y = 5

y = 5 - 4

y = 1

Since tens placed number block is a greater than the ones block,

y > x

4 > 1

therefore 4 will be at tens place and 1 will be kept at ones place and number so formed will be 41.

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Answer: 74.539

Step-by-step explanation:

The correct statement regarding the end behavior of the functions is given by:

As x→∞, f (x)→∞ and g(x)→0.

It is given by the limits of f(x) as x goes to infinity.

In this problem, the function f(x), the limits are given as follows:

For function g(x), the limit is given as follows, as it is not defined for negative values:

[tex]\lim_{x \rightarrow \infty} f(x) = 0[/tex].

Hence the correct statement is:

As x→∞, f (x)→∞ and g(x)→0.

As it considers both positive infinity and negative infinity just as infinity.

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Answer:

-4×(2×1)=8x-2-4

solve in ( )

-4×3=8x-2-4

multiply -4 to 3

-12=8x-2-4

add 2 and 4 to both sides

-6=8x

divide -6 to 8 and you will get the answer

x=-0.75

Answer:

x = -0.25 (or) -1/4

Step-by-step explanation:

Let's solve the problem,

→ -4 × (2 × 1) = 8x - 2 - 4

→ -4 × 2 = 8x - 6

→ -8 = 8x - 6

→ 8x = -8 + 6

→ x = -2/8

→ [ x = -0.25 ]

Thus, solution is -0.25.

Answer:

7

Step-by-step explanation:

[tex]f^{-1}(-33)=k \implies f(k)=-33 \\ \\ 9-6k=-33 \\ \\ -6k=-42 \\ \\ k=7[/tex]

Answer:

f^-1(33) = 7

Step-by-step explanation:

As the question is asking for the inverse function we do the following steps:

Change f(x) into y :

y = 9 -6x

Swap x and y :

x = 9-6y

Solve for y :

Subtract 9 from both sides :

x-9 = -6y

Divide both sides by -6 :

(x-9)÷ -6 = y

Change y back into f(x) :

f(x)  = (x-9)÷ -6

Now substitute -33 into x :

((-33)-9) ÷ - 6 =

-42 ÷ -6 =

+7

Hope this helped and have a good day