Can anyone explain this?

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: A quarter turn

Step-by-step explanation:

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:x=1.

Step-by-step explanation:

3x-x+2=4

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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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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Answer:

J and I

Step-by-step explanation:

If possible use a graphing calculator this is from Desmos

If you are not allowed to then use the rise over run rule or Rise/run

if the constants or numbers Infront of x match then the lines are parallel for these kinds of lines. The black line was added to show that it is parallel with the same constant

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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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:

False. If a factor of the denominator of a rational function cancels with a factor of the numerator, the zero of the canceled factor should not be included in the solution for the inequality.

Step-by-step explanation:

Give me Brainliest if that helped! :)

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:

-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:

its the first one

146 r 6

hope this helped! :)

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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Use the definition of absolute value to rewrite each equation or inequality.

[tex]|x| = \begin{cases} x & \text{if } x\ge0 \\ -x & \text{if }x < 0 \end{cases}[/tex]

1. (E) From the definition it follows that

[tex]x-4 \ge 0 \implies |x-4| = x-4 = 8 \implies x = 12[/tex]

[tex]x-4 < 0 \implies |x-4| = -(x-4) = 4-x = 8 \implies x = -4[/tex]

Then the solution set contains exactly 2 elements, and we write it as shown in choice (E), [tex]x\in\{-4,12\}[/tex].

2. (D) We solve the inequality in essentially the same way as in (1), we just need to keep track of the direction of the inequality.

[tex]x-4\ge0 \implies|x-4|=x-4\ge8 \implies x\ge12[/tex]

[tex]x-4<0 \implies|x-4|=4-x\ge8 \implies x\le-4[/tex]

Note the inclusion of [tex]x=12[/tex] and [tex]x=-4[/tex]. We write this as a union of two half-closed intervals, [tex]x\in(-\infty,-4]\cup[12,\infty)[/tex].

3. (C) This follows from the same steps as in (2). This time the inequality is strict, so we exclude the endpoints and with open intervals write [tex]x\in(-\infty,4)\cup(12,\infty)[/tex].

4. (A) Since [tex]|x|[/tex] always returns a non-negative number, any real number [tex]x[/tex] satisfies the inequalty [tex]|x-4|<\infty[/tex]. We write the solution set as the entire real line, [tex]x\in(-\infty,\infty)[/tex].

5. This leaves us with (B) for the last solution set. This inequality is complementary to the one in (3), which means the solution set to [tex]|x-4|\le8[/tex] is the complement of the set we found in (3). That interval removes everything between and including -4 and 12 from the real line. So the solution in this case is what we omit from the solution to (3), and we write [tex]x\in[-4,12][/tex].

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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From pie chart, responses of community for each category is

a. One fourth of community chosen by cat category.

b. Approximately 30% of community chosen cat or other.

c. If 6% chosen None then dog was chosen by approximately 18%.

As given,

From pie chart ,responses of community for each category is

Bird>cat>dog>fish>none>other

Fish+ none +other +cat=Approximately 50%

a. Cat chosen by approximately 25%.

b. Cat or Other= Approximately 30%

c. If 6% chosen None then dog

    Approximately three times of none=6×3

                                                               = 18%.

Therefore, from pie chart

a. One fourth of community chosen by cat category.

b. Approximately 30% of community chosen cat or other.

c. If 6% chosen None then dog was chosen by approximately 18%.

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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]

Answer:

What are the options I can choose from?

Step-by-step explanation:

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 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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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:

Step-by-step explanation:

The domain of the function is [-3,5]

The range of the function is [-16,infinity)

X=3 is a zero of the function

X = -3 is a zero of the function  

The probability that a club member owns neither a house nor a car is 0.08 or 8%.

As per the survey of a club's members-

percentage of members who own a home 40% = 0.4

percentage of members who own a car → 90% = 0.9

Further, 95% of the homeowners also own a car

⇒ percentage of members who own a car as well as a home = 95% of 40%

= 95/100 x 40/100

= 3800/10000

= 0.38

Let P(A) be the probability that a member owns a home and P(B) be the probability that a member owns a car

we have,

P(A) = 0.4

P(B) = 0.9

also P(A∩B) = 0.38

we need to find the probability that a club member owns neither a house nor a car, that is, P(A'∩B')

According to the rules of probability-

P(AUB) = P(A) + P(B) - P(ANB)

⇒ P(AUB) = 0.4 +0.9 -0.38

P(AUB) = 0.92

Thus, P(A'U B') = 1 - 0.92

= 0.08

Thus, the probability that a club member owns neither a house nor a car is 0.08 or 8%.

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Answer: 80 degrees ==> 3rd option

Step-by-step explanation:

m<5=m<2   ==> angles 5 and 2 are opposite interior angles, so they're congruent.

m<2=38 degrees

m<2+m<6+m<3=180 degrees

38+62+m<3=180

100+m<3=180

m<3=80 degrees ==> 3rd option

[tex]\begin{array}{ccll} US\$&CA\$\\ \cline{1-2} 0.77 & 1\\ 200& c \end{array} \implies \cfrac{0.77}{200}~~=~~\cfrac{1}{c} \\\\\\ 0.77c=200\implies c=\cfrac{200}{0.77}\implies c\approx 259.74[/tex]