When the graph of a quadratic function crosses the x-axis twice, the x-coordinate of the vertex lies ______ the two x-intercepts.

Answer:

Step-by-step explanation:

The first question is asking you how many visitors there were, using the function model provided, when x = 0.  Filling that in gives you:

[tex]y=18,582(.90)^0[/tex]

Anything to the 0 power = 1, so

y = 18,582(1) and

y = 18,582

The second question is asking you how many visitors there were on the 9th weekend, when x = 9:

[tex]y=18,582(.90)^9[/tex] and

[tex]y=18,582(.387420489)[/tex] so

y = 7199

The last question is asking on what weekend (unknown x) are there

y = 15.051 visitors.  That requires using a log to solve for x.  Set it up first:

[tex]15,051=18,582(.90)^x[/tex]

Start by dividing both sides by 18,582 to get:

[tex].8099773975=(.90)^x[/tex]

Now we need to take the log of both sides to get that x out from its exponential position.  By taking the log of the right side, we are given the ability to bring the x down in front:

log(.8099773975) = x log(.90)

Now divide both sides by log(.90) to get

x = 2.000

That means that on the second weekend, there were approximately 15,051 visitors.

Answer:

1. august price = c + 0.25c

2. august price = 1.25c

Step-by-step explanation:

The problem statement tells us that the price of gas in August is 25% more than in July. Thus, 25% of the July price (0.25c) is added to the July price (c) to get the August price.

  c + 0.25c

The sum in the first part can be simplified by combining the coefficients of c.

  1.25c

Answer:

The interest is: $1575

The total is: $8575

Step-by-step explanation:

7000*5*0.045 gets you the interest

Then you add the original amount, 7000, to the total

1575+7000=$8575

By using the Simple Interest formula (Principal * Rate * Time), we find that Jill will earn $1575 in interest over 5 years. Therefore, she will have $8575 in her account after 5 years.

To calculate how much Jill will have in her account after 5 years, we can use the simple interest formula, which is Principal * Rate * Time.

In Jill's case, the principal is the amount she initially deposited which is $7000. The rate is the simple interest rate offered by the bank annually, expressed as a decimal, so 4.5% becomes 0.045. The time is the number of years that the money remains in the account, which is 5 years.

By substituting these values into the formula, we have: $7000 * 0.045 * 5 = $1575.

This means the total interest Jill would earn over 5 years is $1575. The total amount in the account after 5 years would be the initial amount plus the interest, so $7000 + $1575 = $8575.

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Answer:

19

Step-by-step explanation:

Here we have to find out number of people attended the party. we are given with the number of the handshakes in the party .

We are going to use the following formula to determine the number of guests

Nos. of handshakes

[tex]H=\frac{1}{2}(n^2-n)[/tex]

Here we have H = 171

Hence our equation becomes

[tex]171=\frac{1}{2}(n^2-n)[/tex]

now we solve it by splitting the middle term method

[tex]171=\frac{1}{2}(n^2-n)\\2*171 =n^2-n\\n^2-n=342\\n^2-n-342=0\\[/tex]

Now we have to find the factors of 342 whose difference to 1. The factors are 19 and 18 in this case. hence we slit our middle term like this

[tex]n^2-n-342=0\\n^2-19n+18n-342=0\\n(n-19)+18(n-19)=0\\(n-19)(n+18)=0\\[/tex]

Hence

either

(x+18)=0 or (x-19) =0 Thus

x=-18 which is not possible as no of people can not be less than 0

x=19 which will our answer

Answer:

The equation is P(L or S) = 0.3 + 0.2 - 0.15

Step-by-step explanation:

* Lets study the meaning of "or" , "and" on probability

- The use of the word "or" means that you are calculating the

  probability  that either event A or event B happened

- Both events do not have to happen

- The use the word "and" means that both event A and B have

  to happen

* The addition rules are:

# P(A or B) = P(A) + P(B) ⇒ mutually exclusive (events cannot happen

  at the same time)

# P(A or B) = P(A) + P(B) - P(A and B) ⇒ non-mutually exclusive (if they  

  have at least one outcome in common)

- The union is written as "A∪B" or "A or B"  

- The Both is written as "A∩B" or "A and B"

* Lets solve the question

- The probability P(L) of a visitor riding its largest roller coaster is 30%

∵ P(L) = 30% = 30/100 = 0.3

- The probability P(S) of a visitor riding its smallest roller coaster is 20%

∵ P(S) = 20% = 20/100 = 0.2

- The probability of a visitor riding both roller coasters is 15%

∵ P(L and S) = 15% = 15/100 = 0.15

- To find P(L or S) lets use the rule of non-mutually exclusive

∵ P(A or B) = P(A) + P(B) - P(A and B)

∴ P(L or S) = P(L) + P(S) - P(L and S)

- Substitute the values above to find the probability of a visitor riding

  the largest or the smallest roller coaster

∴ P(L or S) = 0.3 + 0.2 - 0.15 = 0.35

∴ The probability of a visitor riding the largest or the smallest roller

   coaster is 0.35

* The equation is P(L or S) = 0.3 + 0.2 - 0.15

Answer: P(largest or smallest) = 0.30 + 0.20 - 0.15

Step-by-step explanation:

Answer:

  D. similar; proportional; congruent

Step-by-step explanation:

Any pair of figures is similar if their corresponding sides are proportional and their corresponding angles are congruent. That is the meaning of similarity.

Answer:

D. similar; proportional; congruent

Step-by-step explanation:

Answer:

x = 4 or x = 1

Step-by-step explanation:

Solving absolute value equations can be a bit tricky.  Absolute values are actually distance measurements.  A very simple example is I x - 3 I = 2 says that "x is 2 units away from 3 on a number line".  2 units from 3 going to the right is 5, 2 units from 3 going to the left is 1.  So in other words, absolute value equations will have 2 answers, in this case 2 units to the right (+2) and 2 units to the left (-2).  That means that x - 3 = 2 OR x - 3 = -2.  Let's start to solve this one:

5I 2x - 5 I - 3 = 12

Start by adding 3 to both sides:

5I2x-5I = 15

Now divide both sides by 5:

I2x-5I = 3

We will set the left side equal to both +3 and -3 to get our 2 solutions:

2x - 5 = 3  and  2x - 5 = -3

Solving the first one for x:

2x = 8 and x = 4

Solving the second one:

2x = 2 and x = 1.

Fit these into the original absoute value statement and see if they are both true:

5I2(4)-5I-3=12 --> 5I3I - 3 = 12 and 15 - 3 = 12

5I2(1)-5I-3 = 12 --> 5I-3I - 3 = 12.  The absolute value of -3 is 3, so 15 - 3 = 12.  They both check out@

Answer:

  $16,000

Step-by-step explanation:

Revenue is the product of price and the number sold. Using the given relation for number sold, the revenue as a function of price is ...

  R(p) = p(-40p +1600) = -40p(p -40)

This is the equation of a quadratic that opens downward and has zeros at p=0 and p=40. The vertex is halfway between those zeros, at p=20. The revenue at this price is ...

  R(20) = -40·20(20 -40) = 16,000 . . . . dollars

Answer:

80%

Step-by-step explanation:

We are given the results of survey of one thousand families to determine the distribution of families by their size.

We are to find the probability (to the near percent) that a given family has more than 6 people.

Frequency of people with less than 5 people = 350 + 200 + 245 = 795

Total frequency = 1000

P (families with fewer than 5 people) = (795 / 1000) × 100 = 79.5% ≈ 80%

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]f(x)=2(3)^{x}[/tex]

This is a exponential function of the form

[tex]y=a(b)^{x}[/tex]

where

a is the initial value (a=2)

b is the base (b=3)

r is the rate of change

b=1+r

1+r=3

r=3-1=2

r=200%

using a graphing tool

The graph in the attached figure

Answer:

A

Step-by-step explanation:

She can type 3.75 words per second.

There are 60 seconds in a minute

Therefore she can type 3.75 * 60 = 225 words per minute.

If 1 page contains 675 words, it will take 675 // 225 words /min = 3 minutes

Therefore 25 pages will take 75 minutes (3 * 25 = 75)

75 minutes = 1 hour with 15 minutes left over.

Final answer:

The court reporter, typing at a minimum rate of 3.75 words per second, would have spent 1 hour and 15 minutes actively typing a 25-page trial transcript with an average of 675 words per page.

Explanation:

The question asks us to calculate the time a court reporter would have spent actively typing a transcript. To find this duration, we first determine the total number of words the trial transcript contains by multiplying the number of pages by the average number of words per page. Then, we divide the total number of words by the court reporter's typing speed in words per second to find the total time in seconds. Finally, we convert the total time from seconds into minutes and hours to get the answer in a more understandable format.

First, calculate the total number of words:

25 pages × 675 words per page = 16,875 words

Next, convert the court reporter's minimum typing speed into words per second:

3.75 words per second

Now, calculate the time spent typing:

Total time (in seconds) = Total number of words ÷ Words per second

Total time (in seconds) = 16,875 words ÷ 3.75 words/second = 4,500 seconds

Convert seconds to minutes: 4,500 seconds ÷ 60 = 75 minutes

Convert minutes to hours: 75 minutes ÷ 60 = 1.25 hours

Therefore, the court reporter was actively typing for 1 hour, 15 minutes, which corresponds to option A.

Answer:

Option B.

Step-by-step explanation:

Cecelia studied for the SAT for 20 minutes every day in the first week, 30 minutes in the 2nd week, 40 minutes in 3rd week and 50 minutes in 5th week.

So the sequence formed is 20, 30, 40, 50

This sequence has a common difference of [tex]T_{2}-T_{1}=30-20=10[/tex]

[tex]T_{3}-T_{2}=40-30=10[/tex]

Therefore, this sequence is an arithmetic sequence or linear sequence.

Christopher studied for the SAT for 5 minutes every day in the first week, 10 minutes in 2nd week, 20 minutes in 3rd, 40 minutes in 4th week.

Sequence formed is 5, 10, 20, 40.

It's an exponential or geometric sequence which has a common ratio

r = [tex]\frac{T_{2} }{T_{1}}=\frac{T_{3} }{T_{2}}[/tex]

 = [tex]\frac{20}{10}=2[/tex]

Therefore, Option B will be the answer.

Answer:

The answer is B

Answer:

  -3, 1, 4 are the x-intercepts

Step-by-step explanation:

The remainder theorem tells you that dividing a polynomial f(x) by (x-a) will result in a remainder that is the value of f(a). That remainder will be zero when (x-a) is a factor of f(x).

In terms of finding x-intercepts, this means we can reduce the degree of the polynomial by factoring out the factor (x-a) we found when we find a value of "a" that makes f(a) = 0.

__

For the given polynomial, we notice that the sum of the coefficients is zero:

  1 -2 -11 +12 = 0

This means that x=1 is a zero of the polynomial, and we have found the first x-intercept point we can plot on the given number line.

Using synthetic division to find the quotient (and remainder) from division by (x-1), we see that ...

  f(x) = (x -1)(x² -x -12)

We know a couple of factors of 12 that differ by 1 are 3 and 4, so we suspect the quadratic factor above can be factored to give ...

  f(x) = (x -1)(x -4)(x +3)

Synthetic division confirms that the remainder from division by (x -4) is zero, so x=4 is another x-intercept. The result of the synthetic division confirms that x=-3 is the remaining x-intercept.

The x-intercepts of f(x) are -3, 1, 4. These are the points you want to plot on your number line.

Remember that the slope intercept formula is:

y = mx + b

m is the slope

b is the y-intercept

so...

y = -3x + 5

If lines are parallel then they have the same slope (m)

This means that the slope of the line will be -3

y = -3x + b

Now we must find b

To do that you must plug in the point the line goes through in the x and y of the equation.

(0, 2)

2 = -3(0) + b

2 = 0 + b

2 = b

y = -3x + 2

Hope this helped!

~Just a girl in love with Shawn Mendes

In the equation y = mx + b, where m represents the slope and b represents the y-intercept, we can determine the slope of the line to be -3. When two lines are parallel, they have the same slope (m).

To find the value of b, we need to substitute the coordinates of a point the line passes through into the equation. In this case, the point is (0, 2).

By plugging in the values, we get:

2 = -3(0) + b

2 = 0 + b

2 = b

Answer:

a = -4

b = 3

c = 6

Step-by-step explanation:

x^2 + 8x = 38

We take the coefficient of the x term

Divide by 2 and then square it

8/2 =4

4^2 = 16

Add 16 to both sides

x^2 +8x + 16 = 38 + 16

x^2 +8x +16 = 54

Take b/2 and use it in the the (x+b/2)^2

(x+4)^2 = 54

Take the square root of each side

sqrt((x+4)^2) = ± sqrt(54)

x+4 =  ± sqrt(54)

Subtract 4 from each side

x+4-4 = -4  ± sqrt(54)

x = -4  ± sqrt(54)

Simplify the square root

x = -4  ± sqrt(9*6)

x = -4 ± sqrt(9) sqrt(6)

x = -4 ± 3 sqrt(6)

Answer:

  A.  215x + 780 = 2500

Step-by-step explanation:

Multiply both sides of the equation by 100 to eliminate the decimal fractions.

  (2.15×100)x + 7.8×100 = 25×100

  215x + 780 = 2500

Answer:

  about 2.9° north of east

Step-by-step explanation:

If we orient the directions so north is in the +y direction and east is in the +x direction, the car is traveling 13 km at an angle of -45°, then 16 km at an angle of +40°. We can add these vectors by adding their components in the x- and y-directions.

  13(cos(-45°), sin(-45°)) ≈ (9.19239, -9.19239)

  16(cos(40°), sin(40°)) ≈ (12.25671, 10.28460)

The sum of these vectors is then ...

  = (21.44910, 1.09221)

and the resultant angle is ...

  arctan(1.09221/21.44910) ≈ 2.915° . . . . measured north of east

The resultant direction is about 2.9° north of east.

Answer:

Magnitude of resultant direction = 3.253 Km

Direction of resultant motion = 19.62° North of East

Step-by-step explanation:

Here we have

13 km in SE direction and

16 km 40 ° North of East

Therefore

13 cos 45, 13 sin 45 = (9.192, 9.9192)

16 cos 40, 16 sin 40 = (12.2567, 10.245)

x₂ - x₁ = 3.064

y₂ - y₁ = 1.092

The Magnitude = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 -y_1)^2}[/tex] = 3.253

The direction = Arctan (y₂ - y₁)/(x₂ - x₁) =  Arctan 1.092/3.064 = 19.62° North of East

The parenthesis denote multiplication. Also, a negative times a positive will always be a negative and visa-versa.

-28(16) = -448

Answer: A. -448

Answer:

  A.  2x² +12x

Step-by-step explanation:

If the mobile is balanced, the weights at each level are the same. Each of those in the lowest tier will be equivalent to 3x, for a total of ...

  4×3x = 12x

Each of those in the top tier shown will be equivalent to x², for a total of ...

  2×x² = 2x²

Then the sum of all parts will be ...

  top tier + bottom tier = 2x² +12x

Answer:

tbh bro i need help to

Step-by-step explanation:

Answer:

A( 3, 2)

B( 1, 2)

y=kx+b

3k+b=2

k+b=2

3k-k+b-b=0

2k=0

k=0

b=2

The equation is y=2

Answer: B is correct, y=2

Step-by-step explanation:

The formula for a line is y=mx+b, m is slope, and b is the y-intercept.

The line AB is completely flat, which means the slope is 0, so it won't show up in the equation. So right now we know the equation will be y=b. Now, we mist find b, the y-intercept. The line AB is crossing the y-axis at 2, meaning that's your y-intercept/b! The equation is y=2

Answer:

D. [tex]\left[\begin{array}{ccc}-12&-4\\9&3\end{array}\right][/tex]

Step-by-step explanation:

In order for a matrix to be singular, the determinant has to be zero.

The determinant has to be zero for singular. The singular matrix from the given options is D. [tex]\left[\begin{array}{ccc}-12&-4\\9&3\end{array}\right] \\[/tex]

In order for a matrix to be singular, the determinant has to be zero.

we need to find the singular matrix from the given options.

Let the matrix

[tex]\left[\begin{array}{ccc}-12&-4\\9&3\end{array}\right] \\[/tex]

So, it determinant will be

-12 x 3 - (-4) x 9

= -36 + 36

= 0

Hence, the determinant of the matrix is zero.

Therefore, the matrix is a singular matrix .

Learn more about matrix here;

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Answer:

Step-by-step explanation:

[tex]6b<36\ or\ 2b+12>6\\\\6b<36\qquad\text{divide both sides by 6}\\b<6\\\\2b+12>6\qquad\text{subtract 12 from both sides}\\2b>-6\qquad\text{divide both sides by 2}\\b>-3\\\\b<6\ or\ b>-3[/tex]

The correct option is "b > 6 or b < -3" because it represents the solutions to the compound inequality 6b < 36 or 2b + 12 > 6. The correct option is C).

Here's the explanation:

We have two inequalities to solve: 6b < 36 and 2b + 12 > 6.

For the first inequality, 6b < 36, we can divide both sides by 6: b < 6.

For the second inequality, 2b + 12 > 6, we can subtract 12 from both sides: 2b > -6. Then, dividing both sides by 2: b > -3.

Now, we need to combine the results from both inequalities. The compound inequality should include values that satisfy either of the individual inequalities.

Combining "b < 6" from the first inequality and "b > -3" from the second inequality, we get the compound inequality: b < 6 or b > -3.

So, the correct option is "b > 6 or b < -3," which represents the solutions to the compound inequality 6b < 36 or 2b + 12 > 6.

The correct option is: C: b > 6 or b < -3

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[tex]\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\pi \theta r^2 }{360}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} r=6\\ \theta =55 \end{cases}\implies A=\cfrac{\pi (55)(6)^2}{360}\implies A=\cfrac{11\pi }{2} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill A\approx 17.28~\hfill[/tex]

Answer:

B. Clara incorrectly combined the r coefficients. The correctly simplified expression is 6b-3r

Step-by-step explanation:

Simplifying the expression by opening the brackets we get:

8b - 4r-2b+r

A negative coefficient multiplied by a negative coefficient results to a positive coefficient.

Combining like terms together:

8b-2b-4r+r

=6b-3r

The correct answer is A. She incorrectly combined the b coefficients. The only symbols that have an effect on a number is the symbol BEFORE the number. Thus, in 2b-r, they would separate into 2b and -r.

Using this knowledge, combine like terms the right way.

8b+2b=10b

-4r-r=-5r

The correct equation is 10b-5r

Hope this helps!

The angle that subtends a chord is half the measure of the arc, so we have an arc QS of 2(84)=168 degrees.

Answer: 168 degrees

Answer:

Step-by-step explanation:

  = x²(-3 +5) +y²(2 -3) +5xy -2y

  = 2x² -y² +5xy -2y

a) there are 4 terms in the simplified expression

b) 2 terms have negative coefficients (-y² and -2y)

Answer:

  (6, -2)

Step-by-step explanation:

To get to x=1 from x=-2, you must add 3 to the x-coordinate. Only one answer choice has an x-coordinate that is 3 more than that of the given point:

  3 + 3 = 6

The image point is (6, -2).

_____

Check

To get from a y-coordinate of 5 to an image point y-coordinate of 1, you must subtract 4. If you subtract 4 from the y-coordinate of (3, 2), you get 2-4 = -2, the y-coordinate in the chosen answer above.