The population of Brownsville, Texas increased by 41 thousand
people from 1990 to 2000. In 2000, the population of Brownsville
was 140 thousand people. Write an equation to find the population
of Brownsville in 1990. Then use mental math to solve the equation.

The graph of the rational function is shown below

From the question, we are to graph the given rational function

To determine the graph that corresponds to the given rational function,

First, we will graph the given rational function.

The given rational function is

x²+3x-1/x+1

The graph of the rational function is shown below

Now, we will compare each of the rational graphs in the provided options with the attached graph

The graph that corresponds to the given rational graph in the attachment below is the graph that represents the given rational function.

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The graph of the circle equation is graph (d)

The equation is given as:

x^2 + y^2 - 4x + 9y -7 = 0

Rewrite as:

x^2 - 4x + y^2 + 9y = 7

Express (x^2 - 4x) and (y^2 + 9y) as perfect squares.

So, we have:

(x - 2)^2 + (y + 3)^2 = 7 + 4 +  20.25

Evaluate the sum

(x - 2)^2 + (y + 3)^2 = 31.25

A circle equation is represented as:

(x - h)^2 + (y - k)^2 = r^2

Where

Center = (h, k)

Radius = r

So, we have:

(h, k) = (2, -3)

r^2 = 31.25

r = 5.5

The circle that has a center of (2, -3) and a radius of 5.5 is graph d

Hence, the graph of the circle equation is graph (d)

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The probability that each guest of each type m+n will receive a roll is 79.

Given that the breakfast should have consisted of three types of rolls, one each of the nut, cheese and fruit rolls, and the cook should have wrapped each of the nine rolls.

The denominator of m/n equals the total number of possible role configurations assigned to the three people. It [tex]${9 \choose 3}{6 \choose3}$[/tex] is the same as the number of ways to choose three roles out of 9 to give to the first person [tex]${9 \choose 3}$[/tex], and three rolls of 6 [tex]${6 \choose3}$[/tex]. After that, the remaining three roles have no more configurations.

The numerator is the number of ways to assign a roll of each type to each of the three people, which can be done by defining the three types of roles such as flavored x, flavored y and flavored z.

xxx, yyy, zzz

So we have to choose one x, one y and one z to give to the first person. There are 3x, 3y and 3z to choose from, resulting in 3³ combinations. Multiply that by the combinations of xs, ys and zs for the second person, which is clearly 2³ since there are two of each letter left. simplify to our fraction m / n, which is 9/70. If you add them together, you get 9 + 70 = 79.

Thus, the probability that each guest has obtained a roll of each type is m / n, where m and n are relatively prime, so m + n is 79.

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Answer:

1/4

Step-by-step explanation:

I think that you forgot the addition or the subtraction sign between -4x  and 5.  I will assume that it was an addition sign

3(-4x+5) = 12  Multiply everything in the parentheses by 3

-12x + 15 = 12  Subtract 15 from both sides

-12x = -3  Divide both sides by -12

x = -3/-12 = 3/12 =1/4

Answer:

3rd option

Step-by-step explanation:

y is negative below the x- axis , that is for values of x in the interval

x > - 6 and x < 6

During the month of May, there were 130 births, of which the newborn death rate is 38.4615.

According to the question,

There were 130 births, of which 127 were full-term births and three were premature births. There were five newborn deaths.

In order to find the newborn death rate we have the formula:

=  [tex]\frac{number of death under 28 days of age }{Total live births in the same year}[/tex]  × 1000

= [tex]\frac{5}{130}[/tex] × 1000

=[tex]\frac{5000}{130}[/tex]

=38.4615

Hence, the new born death rate is 38.4615.

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By taking the quotient between the total number of hours and the number of shifts each shift is 1.5 hours long.

We know that Paolo worked (2 + 3/4) hours this week, and that is equivalent to (1 + 5/6) shifts.

To find the number of hours that each shift takes, we need to take the quotient between the total number of hours and the number of shifts:

[tex]\frac{(2 + 3/4)h}{1 + 5/6} = 1.5 h[/tex]

This means that each shift is 1.5 hours long.

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Answer:

Option D is correct

Step-by-step explanation:

there were no corn muffins sold.

Answer:

No corn muffins were sold at the bake sale :)

Step-by-step explanation:

Lets go thru each answer choice to see why it is incorrect/correct :)

A.

A is incorrect because more cookies were sold than muffins! that is why A is incorrect :)

B.

This calls for adding! lets do that now :)

Chocolate chip: 5

Oatmeal: 1

Peanut: 3

6 + 1 + 3 = 10

10 < 11

10 is not greater than 11 so B is incorrect!! :)

C.

We need to add again so lets do that now!

Corn: 0

Muffin: 2

2 + 0 = 2

2 < 3

2 is less than 3 so C is incorrect!! :)

D.

It is true that 0 corn muffins were sold at the bake sale so D is our answer!! :D

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

[tex]\frac{1}{5}[/tex]

Step-by-step explanation:

Prime numbers between 20 - 29 = 23 and 29.

There are 2 prime numbers out of these 10.

Therefore,

P(choose prime number) = [tex]\frac{2}{10} \\=\frac{1}{5}[/tex]

We have proven that ∠BEC ≅ ∠BCE by using the alternate interior angles theorem

From the question, we are to write a proof to prove that ∠BEC ≅ ∠BCE

From the given information, we have that

BC || EF

Note that line DE is a transversal

Thus, by the alternate interior angles theorem, we have that

∠BCE ≅ ∠FEC

Also, we were given that line EC bisects ∠BEF

That is,

Line EC divides ∠BEF into two equal angles.

Therefore,

∠BEC ≅ ∠FEC

By the substitution property of equality, we get

∠BEC ≅ ∠BCE

Hence, we have proven that ∠BEC ≅ ∠BCE by using the alternate interior angles theorem

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Answer:

  a) payment: $1677.99

  b) total repaid: $604,076.40

  c) saved: $168,231.60

Step-by-step explanation:

The amortization formula can be used to find the monthly payment on the loan. The total repaid will be the sum of payments made. The amount saved will be the difference between the total repaid amounts for the different loans.

The payment A on a loan of principal P at annual rate r for t years is given by ...

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

The loan of interest is for $425,000 × (1 -30%) = $297,500. Then the payments on a 30 year loan are ...

  A = $297,500(0.0544/12)/(1 -(1 +0.0544/12)^-360) ≈ $1677.99

For a 15-year loan, the payments are ...

  A = $297,500(0.0544/12)/(1 -(1 +0.0544/12)^-180) ≈ $2421.36

The above calculation shows the monthly payment is $1677.99.

The total repaid is the sum of 360 monthly payments:

  360×$1677.99 = $604,076.40

The total repaid is the sum of 180 monthly payments:

  180×$2421.36 = $435,844.80

and the savings is ...

  $604,076.40 -435,844.80 = $168,231.60

__

Additional comment

We are asked to round to the nearest cent. The payment amounts here are accurately calculated to that precision. The total repaid on an actual loan will be slightly different, because the final payment will be slightly different.

The 30-year mortgage will have a slightly lower final payment because the monthly amount is rounded up. The 15-year mortgage will have a slightly higher final payment because the monthly amount is rounded down.

Overall, this means the totals of payments shown here, and their difference, vary slightly from the reality of loans of this kind. (They're probably not accurate to the nearest cent.)

Even using the "exact" payment value may not give the actual loan values. This is because the actual amortization schedule is rounded to the nearest cent each month. The cumulative effect of this rounding seems to be calculable only by figuring the 360 (or 180) actual monthly balance amounts.

We have calculated the answers in the manner we suppose is expected. Producing an actual amortization spreadsheet is a bit more work.

The charges of entrance fee for a bus containing 30 people is $98

let

Charges For 2 people = mx + y

14 = 2x + y

Charges For 4 people = mx + y

20 = 4x + y

14 = 2x + y

20 = 4x + y

20 - 14 = 4x - 2x

6 = 2x

x = 6/2

x = 3

Substitute x = 3 into

14 = 2x + y

14 = 2(3) + y

14 = 6 + y

14 - 6 = y

8 = y

Charges For 8 people = mx + y

= 8(3) + 8

= 24 + 8

= $32

Therefore,

Charges For 30 people = mx + y

= 30(3) + y

= 90 + 8

= $98

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Answer:

x = -7 and x = 4.

Step-by-step explanation:

f(x) = x^2 + 3x - 28

= (x + 7)(x - 4).

The reciprocal of f(x) can be written as

1 / (x + 7)(x - 4).

When the denominator is zero we have vertical asymptotes

so they are x = -7 and x = 4.

The volume will be one-eighth times the volume.

The scale factor k is given as

k = 1/2

Let the initial volume be v

When each side is multiplied by the scale factor, we have the new volume to be

V = k^3 * v

Substitute 1/2 for k in the above equation

V = (1/2)^3 *v

Evaluate the exponent

V = 1/8 *v

This gives

V = 1/8v

Hence, the volume will be one-eighth times the volume.

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Answer:

The correct answer choice is D

The ratio of major to minor arc = 2 : 1

What is a Circle?

A circle is the locus of a point such that its distance from a fixed point (center) is always constant.

Calculation

The length of an arc (L) with center angle θ is given by:

                                          L = (θ/360) * 2πr

where r is the radius.

Putting the values in the above formula.

For the major arc:

L = (240/360) * 2πr

For the major arc:

l = ((360-240)/360) * 2πr

l = (120/360) * 2πr

The ratio of major to minor arc = [(240/360) * 2πr] / [(120/360) *2πr] = 2 : 1

The ratio of major to minor arc = 2 : 1.

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Answer:c

Step-by-step explanation:

Now you can equate it with second one to get x

Answer:

Substitute y = 3x + 2 into x² - 3x + 2y = -4

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}x^2-3x+2y=-4\\y=3x+2\end{cases}[/tex]

Since y is already isolated in the second equation, the best first step would be to substitute the second equation into the first equation, then solve for x.

Substitute equation 2 into equation 1:

[tex]\implies x^2-3x+2(3x+2)=-4[/tex]

Expand the brackets and simplify so that the equation equals zero:

[tex]\implies x^2-3x+6x+4=-4[/tex]

[tex]\implies x^2+3x+4+4=0[/tex]

[tex]\implies x^2+3x+8=0[/tex]

Now use the Quadratic Formula to solve for x.

Quadratic Formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Define the variables:

[tex]\implies a=1, \quad b=3, \quad c=8[/tex]

Substitute the values into the formula and solve for x:

[tex]\implies x=\dfrac{-3 \pm \sqrt{3^2-4(1)(8)}}{2(1)}[/tex]

[tex]\implies x=\dfrac{-3 \pm \sqrt{-23}}{2}[/tex]

[tex]\implies x=\dfrac{-3 \pm \sqrt{-1 \cdot 23}}{2}[/tex]

[tex]\implies x=\dfrac{-3 \pm \sqrt{-1}\sqrt{23}}{2}[/tex]

Remember that [tex]i^2=-1[/tex]

[tex]\implies x=\dfrac{-3 \pm i\sqrt{23}}{2}[/tex]

Therefore, the solutions to the system of equations are:

[tex]x=\dfrac{-3 + i\sqrt{23}}{2}, \quad \dfrac{-3 - i\sqrt{23}}{2}[/tex]

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The slope of the line is - 3 / 2 .

The slope of a line is the change in y coordinate with respect to the change in x coordinate.

Therefore, using (0, 6)(4, 0)

Hence,

m = slope = y₂ - y₁ / x₂ - x₁

slope = 0 - 6 / 4 - 0

slope = -6 / 4

slope = - 3 / 2

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The domain of the function is [1,  ∞) and the range is [0,  ∞)

The equation of the function is given as:

g(x) = 3√x - 1

The domain is the possible values of x.

Set the radicand to greater than or equal to 0

x - 1 >= 0

Add 1 to both sides

x >= 1

This can be rewritten as:

[1,  ∞)

Breakdown

g(x) = 3√x - 1

x - 1 >= 0

x >= 1

[1,  ∞)

The range is the possible values of y.

Set the radicand to 0

g(x) = 3 * 0

Evaluate the product

g(x) = 0

This can be rewritten as:

[0,  ∞)

Breakdown

g(x) = 3√x - 1

g(x) = 3 * 0

g(x) = 0

[0,  ∞)

Hence, the domain of the function is [1,  ∞) and the range is [0,  ∞)

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Answer:

Correct answer is D: [1, ∞) and R: (-∞, 0]

Step-by-step explanation:

Insert the given function on desmos to observe the following explanation.

The domain (x values) begin at 1, and go on to positive infinity (the squared bracket indicates a stop/start at that certain point). The range goes into negative infinity (y values) and begins at the y value of 0, so it does not go above that point on the y axis (hence the squared bracket).

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathbf{1 \dfrac{1}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}[/tex]

[tex]\huge\textbf{Solve:}[/tex]

[tex]\mathbf{1 \dfrac{1}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}[/tex]

[tex]\mathbf{\rightarrow \dfrac{1\times5+1}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}[/tex]

[tex]\mathbf{\rightarrow \dfrac{5 + 1}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}[/tex]

[tex]\mathbf{\rightarrow \dfrac{6}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathbf{\rightarrow \dfrac{2}{5}x = \dfrac{9}{10}}[/tex]

[tex]\huge\textbf{Multiply \boxed{\bf \dfrac{5}{2}} to both sides:}[/tex]

[tex]\mathbf{\rightarrow \dfrac{5}{2}\times \dfrac{2}{5}x = \dfrac{5}{2}\times \dfrac{9}{10}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathbf{\rightarrow x = \dfrac{5}{2}\times \dfrac{9}{10}}[/tex]

[tex]\mathbf{\rightarrow x = \dfrac{5\times9}{2\times10}}[/tex]

[tex]\mathbf{\rightarrow x = \dfrac{45}{20}}[/tex]

[tex]\mathbf{\rightarrow x = \dfrac{45\div5}{20\div5}}[/tex]

[tex]\mathbf{\rightarrow x = \dfrac{9}{4}}[/tex]

[tex]\mathbf{x \approx 2 \dfrac{1}{4}}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x = }\frak{2 \dfrac{1}{4}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Question :

Solution :

>> (5 × 1 + 1 / 5) × (x / 3) = 9 / 10

>> (5 + 1 / 5) × (x / 3) = 9 / 10

>> (6 / 5) × (x / 3) = 9 / 10

>> 6 × x / 5 × 3 = 9 / 10

>> 6x / 15 = 9 / 10

>> 2x / 5 = 9 / 10

>> 2x × 10 = 5 × 9

>> 20x = 45

>> x = 45 / 20

>> x = 9 / 4

Therefore,

Answer:

the answer you can find onlinde \\\\

Step-by-step explanation:

The values which would help complete the table according to the complete part of the task content are as evaluated.

First, the total number of average players can be evaluated by summing up the total number of players vertically as follows;

180 + average + 80 = 600

The number of average players is therefore; 600-180-80 = 340 average players.

Also, the number of female expert players can be evaluated vertically as;

50 + 50 + female expert = 150

Female expert = 150-50-50 = 50 female experts.

The number of male novice players can be evaluated horizontally as;

Male novice + 50 = 180

Male novice = 180 - 50 = 130.

The number of average male players is therefore easily evaluated vertically as;

130 + male average + 30 = 600

male average = 600-130-30 = 440.

Remarks: The table which is required to be completed is that which is in the attached image.

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Answer:

130, 290, 340, 50

Step-by-step explanation:

just do the math, I got it right on edmentum.

The additional set of values which could be included in the table is; (10,2).

As evident in the task content, it follows that for a 15 unit increase in x, depth, there is a 3 unit increase in y, pressure.

On this note, it follows that with each 5 unit increase in x corresponds to 1 unit increase in y.

And ultimately, at x = 10, y = 2 × 1 = 2.

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Answer: (2, 18)

Step-by-step explanation:

When x=2, [tex]f(2)=2(3)^{2}=18[/tex].

So, it should pass through (2, 18).

Used formula

Answer:

6x+5

Step-by-step explanation:

the derivative of a sum is equal to the sum of derivatives:

(3x^2 + 5x + 2)' = (3x^2)' + (5x)' + (2)' = 6x + 5

Q.E.D.

Answer:

[tex]y \geq - 6[/tex]

Step-by-step explanation:

the range is all the y values shown in the graph, so as you can see, the y values are all those greater than or equal to -6

A type of sampling in which individuals to be interviewed are selected based on their proportion or quota in the general population being polled is known as public opinion.

What is sampling type of public opinion ?

A survey that measures the entire target population is called a census. A sample refers to a group or section of a population from which information is to be obtained. Survey samples can be broadly divided into two types: probability samples and super samples.

The collective opinion of large segment of the population on an issue, candidate or public policy on which the public may be much divided and lake a consensus.

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