Cooking and shopping Forty-five percent of Americans like to cook and 59% of Americans like to shop, while 23% enjoy both activities. What is the probability that a randomly selected American either enjoys cooking or shopping or both

Answer:

4

Step-by-step explanation:

{ }

{Apple}

{Banana}

{Apple, Banana}

Answer:

u => 4,028

Step-by-step explanation:

To find the answer, we have the following formula:

u => m - t (alpha, n-1) * [sd / (n) ^ (1/2)]

where m is the mean.

where sd is the standard deviation.

where n is the sample size.

t is a parameter that depends on the confidence interval and the sample size.

alpha = 1 - ci

ci = 90% = 0.9

Therefore, alpha = 1 - 0.9 = 0.1.

n - 1 = 25 - 1 = 24

So it would come being t (0.1, 24), if we look in the table, which I will attach the value of t is equal to 1.318.

We know the rest of the values, m = 4.05; sd = 0.08; n = 25

u => 4.05 - 1,318 * [0.08 / (25) ^ (1/2)]

u => 4.028

Which means that the interval with a 90% confidence of the wall thickness measurement is:

u => 4.028

Answer:

C option is correct 5/8.

Step-by-step explanation:

Ela ate chocolate on Tuesday = 1/8

Remaining chocolate = 1 - 1/8

                                    = 7/8

Ela ate chocolate on Wednesday = 7/8

Chocolate left = 7/8 - 2/8

                        = 5/8

Answer:

The answer to your question is Positive

Step-by-step explanation:

Function

                  g(x) = x⁴ - 8x³ + x² + 42x

To know if the function is positive or negative in the interval (0, 3), look for two numbers between this interval and evaluate the function.

The numbers I chose were 1 and 2

-  g(1) = (1)⁴ - 8(1)³ + (1)² + 42(1)

         = 1 - 8 - 1 + 42

        = + 36    positive

-  g(2) = (2)⁴ - 8(2)³ + (2)² + 42(2)

          = 16 - 64 + 4 + 84

          = + 40

Conclusion

The function is positive in the interval (0, 3)  

Answer:

9 boxes of chopsticks.

Step-by-step explanation:

The first thing is to calculate the number of chopsticks spent in a day, the problem tells us that they are 15 ^ 2 = 15 * 15 = 225 chopsticks daily.

To calculate the number of chopsticks in 30 days, it is to calculate the previous amount by 30:

225 * 30 = 6750 chopsticks spent in one month.

To know how many boxes you should order is to divide the total number of chopsticks in a month and the number of chopsticks that a box brings that are 750:

6750/750 = 9 boxes of chopsticks.

Therefore you should order exactly 9 boxes of chopsticks for the restaurant's need.

Answer:

P [  1689  ≤   X  ≤  2267 ]  = 54,88 %

Step-by-step explanation:

Normal Distribution

Mean        μ₀  =  1730

Standard Deviation      σ  = 257

We need to calculate  z scores for the values   1689     and      2267

We apply formula for z scores

z =  ( X -  μ₀ ) /σ

X = 1689     then

z = (1689 - 1730)/ 257      ⇒ z = - 41 / 257

z  = -  0.1595

And from z table we get  for  z =  - 0,1595

We have to interpolate

        - 0,15          0,4364

        - 0,16          0,4325

Δ  =   0.01           0.0039

0,1595  -  0,15  =  0.0095

By rule of three

0,01                  0,0039

0,0095                 x ??      x  =  0.0037

And    0,4364  -  0.0037  = 0,4327

Then    P [ X ≤ 1689 ]  =  0.4327     or    P [ X ≤ 1689 ]  = 43,27 %

And for the upper limit  2267  z  score will be

z  =  ( X - 1730 ) / 257       ⇒  z =  537 / 257

z  =  2.0894

Now from z table   we find  for score   2.0894

We interpolate and assume  0.9815

P [ X ≤ 2267 ]  =  0,9815

Ths vale already contains th value of   P [ X ≤ 1689 ]  =  0.4327

Then we subtract  to get    0,9815  -  0,4327   = 0,5488

Finally

P [ 1689  ≤   X  ≤  2267 ]  =  0,5488  or  P [  1689  ≤   X  ≤  2267 ]  = 54,88 %

The equivalent equation is [tex](x+5)(x+12)=0[/tex]

The solution are [tex]x=-5, x=-12[/tex]

Explanation:

Given that the equation is [tex]-7 x-60=x^2+10 x[/tex]

Simplifying the equation, we get,

[tex]0=x^2+10 x+7x+60[/tex]

Switch sides, we have,

[tex]x^2+17 x+60=0[/tex]

Equivalent equation:

Let us factor the quadratic equation.

Thus, we have,

[tex]x^{2} +5x+12x+60=0[/tex]

Grouping the terms, we get,

[tex]x(x+5)+12(x+5)=0[/tex]

Factoring out (x+5), we get,

[tex](x+5)(x+12)=0[/tex]

Thus, the equivalent equation is [tex](x+5)(x+12)=0[/tex]

Solution:

Solving the equation [tex](x+5)(x+12)=0[/tex], we get,

[tex]x+5=0[/tex]  and   [tex]x+12=0[/tex]

  [tex]x=-5[/tex]   and       [tex]x=-12[/tex]

Thus, the solutions are  [tex]x=-5[/tex] and [tex]x=-12[/tex]

Answer:

A. 5

B. 12

C. -12 or -5

Step-by-step explanation:

(x + 5)(x + 12) = 0

What are the solutions of –7x – 60 = x2 + 10x?

x = -12 or -5

Answer:

View Image

Step-by-step explanation:

To identify if it's a polynomial, look at the x and its exponent.

x CANNOT be:

1. In the denominator: [tex]\frac{1}{x}[/tex] NOT polynomial

2. In the exponent: [tex]2^x[/tex]  NOT polynomial

3. In a root: [tex]\sqrt{x}[/tex] NOT polynomial

The exponent on the x must be a positive integer, therefore,

exponent:

1.) Cannot be a fraction:  [tex]x^{1/2}[/tex] NOT polynomial

2.) Cannot be negative: [tex]x^{-2}[/tex]  NOT polynomial

Answer:

the answer is a

Step-by-step explanation:

Answer:

x = 13

Step-by-step explanation:

One of the THEOREM for triangles states that, A LINE DRAWN PARALLEL TO ONE SIDE OF THE TRIANGLE DIVIDES THE OTHER TWO SIDES IN THESAME RATIO.

From the figure above:

VW is parallel to SU.

VW divides ST and TU in thesame ration.

Hence:

TV / SV = TW / UW

14 / 6 = 21 / (x - 4)

Cross Multiplying gives:

14( x - 4) = 6 * 21

14x - 56 = 126

14x = 126 + 56

14x = 182

Divide through by 14.

x = 182/14

x = 13

Answer:

The tank would hold 40 gallons of water when full.

Step-by-step explanation:

The tank is already 3/4 full of water

If Henry added 5 gallons, it will be 7/8 full.

Therefore the fraction added by Henry =7/8-3/4=1/8

It means that 1/8 of the total=5 gallons of water

Let the total capacity of the tank=x

[tex]\frac{1}{8}Xx=5 gallons\\ x=8X5=40 gallons[/tex]

The tank would hold 40 gallons of water when full.

Answer:

system of equations i think

Step-by-step explanation:

A group of equations that have a common intersection point is called: system of equations.

A system of equations can be defined as an algebraic equation of the first order with two (2) variables and each of its term having an exponent of one (1).

Generally, a system of equations in two (2) variables must have at least two (2) solution.

This ultimately implies that, a system of equations must have a common intersection point.

In Mathematics, an example of a system of equations include the following:

Additionally, the above system of equations can easily be solved by using an elimination method.

In conclusion, a solution of the group of equations is an ordered pair that satisfies all the equations in a system of equations.

Read more: https://brainly.com/question/24085666

Answer:

85%

Step-by-step explanation:

The probability of finding our satisfactory service in the three visits in a row would be the multiplication of the probability of each event.

The event is always the same. 95% of the service will be satisfactory. That is a probability of 95/100

Then the final probability would be:

(95/100) * (95/100) * (95/100) = 0.85

In other words, the probability that a customer who visits three times will find our service satisfactory is 85%

Answer: There are 45 miles that she have to travel to get to the next down.

Step-by-step explanation:

Since we have given that

1 inch = 15 miles

If there are given 3 inches.

We need to find the number of miles she have to travel to get to travel to get to the next town.

So, it becomes,

[tex]\dfrac{1}{15}=\dfrac{3}{x}\\\\x=15\times 3\\\\x=45\ miles[/tex]

Hence, there are 45 miles that she have to travel to get to the next down.

Answer:

The correct option is

d) Five-sixths = StartFraction 5 times 3 over 6 times 3 EndFraction = Fifteen-eighteenths = 15/18 ÷ 1 = 15/18 ÷ 3/3 = 5/6

Step-by-step explanation:

Which method can be used to find a fraction equivalent to Five-sixths?

a) Five-sixths = StartFraction 5 times 2 over 6 times 3 EndFraction = Ten-eighteenths

Here 10/16 = 5/8 ≠ 5/6

b) Five-sixths = StartFraction 5 times 3 over 6 times 4 EndFraction = StartFraction 15 over 24 EndFraction

15/24 = 5/8 ≠ 5/6

c) Five-sixths = StartFraction 5 times 5 over 6 times 6 EndFraction = StartFraction 25 over 36 EndFraction

25/36 ≠ 5/6

d) Five-sixths = StartFraction 5 times 3 over 6 times 3 EndFraction = Fifteen-eighteenths

15/18 ⇒ 15/18÷3/3 = 5/6

note that 3/3 = 1

Answer:

Its D buddy!

Step-by-step explanation:

Cuz 3 People said it was D.

The simplified expressions for the area and perimeter of the rectangle are 16x and 4x, respectively.

To simplify the expressions for the area and perimeter of the rectangle, we can extract common factors:

Area: [tex]\(8(x + x) = 8 \times 2x = 16x\)[/tex]

Perimeter: [tex]\(2(x + x) = 2 \times 2x = 4x\)[/tex]

Therefore, the simplified expressions are:

Area: 16x

Perimeter: 4x

Answer:

The answer to your question is   Momentum  = [tex]\frac{(x + 2)^{2}}{x - 3}[/tex]

Step-by-step explanation:

Data

mass = [tex]\frac{x^{2}+ 4x + 4 }{x^{2}- 9}[/tex]

velocity = [tex]\frac{x^{2}+ 5x + 6}{x + 2}[/tex]

Formula

Momentum = mass x velocity

Substitution

    Momentum = [tex]\frac{x^{2}+ 4x + 4}{x^{2}- 9} \frac{x^{2} + 5x + 6}{x + 2}[/tex]

Factor    The first numerator is a perfect square trinomial and the second one is a trinomial of the form x² + bx + c.

    Momentum = [tex]\frac{(x + 2)^{2}}{(x - 3)(x + 3)} \frac{(x + 2)(x + 3)}{x + 2}[/tex]

Simplify and result

   Momentum  = [tex]\frac{(x + 2)^{2}}{x - 3}[/tex] or [tex]\frac{x^{2} + 4x + 4}{x - 3}[/tex]

Answer:

  $1550.69

Step-by-step explanation:

Deposits get added and withdrawals and bill payments get subtracted from the balance. The new balance is ...

  $1349.85 -80 +699.65 -215.70 -53 -49.76 -100.35 = $1550.69

Answer:

[tex]\left(3+x\right)^4:\quad x^4+12x^3+54x^2+108x+81[/tex]

Step-by-step explanation:

Considering the expression

[tex]\left(3+x\right)^4[/tex]

Lets determine the expansion of the expression

[tex]\left(3+x\right)^4[/tex]

[tex]\mathrm{Apply\:binomial\:theorem}:\quad \left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i[/tex]

[tex]a=3,\:\:b=x[/tex]

[tex]=\sum _{i=0}^4\binom{4}{i}\cdot \:3^{\left(4-i\right)}x^i[/tex]

Expanding summation

[tex]\binom{n}{i}=\frac{n!}{i!\left(n-i\right)!}[/tex]

[tex]i=0\quad :\quad \frac{4!}{0!\left(4-0\right)!}3^4x^0[/tex]

[tex]i=1\quad :\quad \frac{4!}{1!\left(4-1\right)!}3^3x^1[/tex]

[tex]i=2\quad :\quad \frac{4!}{2!\left(4-2\right)!}3^2x^2[/tex]

[tex]i=3\quad :\quad \frac{4!}{3!\left(4-3\right)!}3^1x^3[/tex]

[tex]i=4\quad :\quad \frac{4!}{4!\left(4-4\right)!}3^0x^4[/tex]

[tex]=\frac{4!}{0!\left(4-0\right)!}\cdot \:3^4x^0+\frac{4!}{1!\left(4-1\right)!}\cdot \:3^3x^1+\frac{4!}{2!\left(4-2\right)!}\cdot \:3^2x^2+\frac{4!}{3!\left(4-3\right)!}\cdot \:3^1x^3+\frac{4!}{4!\left(4-4\right)!}\cdot \:3^0x^4[/tex]

[tex]=\frac{4!}{0!\left(4-0\right)!}\cdot \:3^4x^0+\frac{4!}{1!\left(4-1\right)!}\cdot \:3^3x^1+\frac{4!}{2!\left(4-2\right)!}\cdot \:3^2x^2+\frac{4!}{3!\left(4-3\right)!}\cdot \:3^1x^3+\frac{4!}{4!\left(4-4\right)!}\cdot \:3^0x^4[/tex]

as

[tex]\frac{4!}{0!\left(4-0\right)!}\cdot \:\:3^4x^0:\:\:\:\:\:\:81[/tex]

[tex]\frac{4!}{1!\left(4-1\right)!}\cdot \:3^3x^1:\quad 108x[/tex]

[tex]\frac{4!}{2!\left(4-2\right)!}\cdot \:3^2x^2:\quad 54x^2[/tex]

[tex]\frac{4!}{3!\left(4-3\right)!}\cdot \:3^1x^3:\quad 12x^3[/tex]

[tex]\frac{4!}{4!\left(4-4\right)!}\cdot \:3^0x^4:\quad x^4[/tex]

so equation becomes

[tex]=81+108x+54x^2+12x^3+x^4[/tex]

[tex]=x^4+12x^3+54x^2+108x+81[/tex]

Therefore,

[tex]\frac{1}{3}[/tex]Answer:

2/9

Step-by-step explanation:

given that Tyler selects one card from the three(4,5, and a King), and rolls a number cube.

We find that A the event of selecting one card and B getting a number on rolling a number cube are independent events.

No of cards = 3

Prob of selecting 5 from 3 cards = [tex]P(1,2,3, or 4) = \frac{2}{3}[/tex]

When rolling a number cube (assuming fair) there is equally likely for all numbers to appear from 1 to 6

Prob of getting 5 =[tex]\frac{1}{6}[/tex]

Prob of getting less than 5 =

Since these two events are independent,

the probability that she selects the 5, and rolls a number less than 5

= Product of probabilities

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

=[tex]\frac{2}{9}[/tex]

Answer:

  y = -9

Step-by-step explanation:

Standard form of the equation of a line is ...

  ax + by = c

When that line is a horizontal line, this can be reduced to ...

  y = c

The value of c must be the same as the y-coordinate of the point you want this line to go through.

  y = -9 . . . . . . horizontal line through (3, -9)

Answer:

Step-by-step explanation:

it has no solution (8,2)

just took the test

This calculation shows that Mary Ward's lease term is 36 months.

The question is asking us to find out for how many months Mary Ward's car lease lasts. To do so, we need to calculate the total monthly payments and then subtract the initial $1600 fee to find the total cost of the monthly payments alone. Then, we divide this amount by the monthly lease payment to determine the total number of months for the lease duration.

First, we deduct the initial fee from the total lease cost:

Total lease cost - Initial fee = Total of monthly payments

$26,800 - $1,600 = $25,200

Next, we divide this result by the monthly lease payment to find out the number of months:

$25,200 / $700 = 36 months

Therefore, the lease agreement lasts for 36 months, which is typically the term for most vehicle leases.

Answer:

x - ( 16 , 0 ) , ( -16 , 0 )

y - ( 0 ,  4√7 ) , ( 0 , -4√7)

Step-by-step explanation:

Solution:

- The sum of the distances from a point on the ellipse to its foci is constant. You have both foci and a point, so you can find the sum of the distances.

-Then you can find the vertices since they are points on the ellipse on the x-axis whose sum of distances to the foci are that value.

- The 7 in y coordinate of (12,7) is the length of semi-latus rectum. Also c is 12:

                                     c^2 = a^2 + b^2

Where, a: x-intercept

            b: y-intercept

- The length of semi-latus rectum is given by:

                                     b^2 = 7*a

- Substitute latus rectum expression in the first one we get:

                                    c^2 = a^2 + 7a

                                    a^2 + 7a - 144 = 0

                                    ( a - 16 ) * ( a - 9 ) = 0

                                    a = +/- ( 16 )

- The y-intercept we will use latus rectum expression again:

                                    b = +/- √(7*16)

                                    b = +/- 4√7

- The intercepts are:

                                    x - ( 16 , 0 ) , ( -16 , 0 )

                                    y - ( 0 ,  4√7 ) , ( 0 , -4√7)  

Final answer:

An ellipse is a closed curve where the sum of the distances from any point on the curve to the two foci is constant. To find where this particular ellipse intersects the coordinate axes, we can set y = 0 to find the points of intersection with the x-axis and set x = 0 to find the points of intersection with the y-axis.

Explanation:

An ellipse is a closed curve where the sum of the distances from any point on the curve to the two foci is constant. The focal points of this ellipse are (12, 0) and (-12, 0). We know that the point (12, 7) lies on the ellipse. To find where this curve intersects the coordinate axes, we need to find the points where the ellipse intersects the x-axis and y-axis.

Intersecting the x-axis:

To find the points where the ellipse intersects the x-axis, we set y = 0 and solve for x. In this case, the coordinates of the intersection points will be (x, 0).

Plugging in y = 0 into the equation of the ellipse:

(x - 12)^2 / a^2 + (0 - 0)^2 / b^2 = 1

Simplifying this equation:

(x - 12)^2 / a^2 = 1

Since the ellipse is symmetric about the y-axis, the x-coordinates of the intersection points will have the same absolute value but opposite signs. So, we can solve for a single value of x and then take its negative to find the other intersection point.

(x - 12)^2 / a^2 = 1

x - 12 = a

x = a + 12

The coordinates of the intersection points on the x-axis are (a + 12, 0) and (-a - 12, 0).

Intersecting the y-axis:

To find the points where the ellipse intersects the y-axis, we set x = 0 and solve for y. In this case, the coordinates of the intersection points will be (0, y).

Plugging in x = 0 into the equation of the ellipse:

(0 - 12)^2 / a^2 + (y - 0)^2 / b^2 = 1

Simplifying this equation:

144 / a^2 + y^2 / b^2 = 1

Solving for y:

y^2 / b^2 = 1 - 144 / a^2

y^2 / b^2 = (a^2 - 144) / a^2

y^2 = b^2 * (a^2 - 144) / a^2

y = ± sqrt(b^2 * (a^2 - 144) / a^2)

The coordinates of the intersection points on the y-axis are (0, ± sqrt(b^2 * (a^2 - 144) / a^2)).

Answer: the solutions of the equation are

x = - 1

x = 8

x = 9

Step-by-step explanation:

The given cubic equation is expressed as

x³ - 16x² + 55x + 72 = 0

The first step is to test for any value of x that satisfies the equation when

x³ - 16x² + 55x + 72 = 0

Assuming x = - 1, then

- 1³ - 16(-1)³ + 55(-1) + 72 = 0

- 1 - 16 - 55 + 72 = 0

0 = 0

It means that x + 1 is a factor.

To determine the other factors, we would apply the long division method. The steps are shown in the attached photo. Looking at the photo, we would factorize the quadratic equation which is expressed as

x² - 17x + 72 = 0

x² - 9x - 8x + 72 = 0

x(x - 9) - 8(x - 9) = 0

(x - 9)(x - 8) = 0

Answer:

Step-by-step explanation:

According to the flaring, the triangle expressed in the figure is formed.

Now we have a vector A and vector B, whose components are Ax, Ay and Bx and By respectively.

To calculate these components you must use the following formulas:

Ax = A * cos [angle a] = 32 * cos 37 ° = 25.6

Ay = A * sin [angle a] = 32 * sin 37 ° = 19.3

Bx = B * cos [angle a] = 21 * cos 23 ° = 19.3

By = B * sin [angle b] = 21 * sin 23 ° = - 8.2

In the figure it can be seen that vector B is the result of vector A and vector C

Thus:

B = A + C

reorganizing is:

C = B - A

Now to calculate Cx and Cy, we will do it with the previously calculated components:

Cx = Bx - Ax = 19.3 - 25.6 = -6.3

Cy = By - Ay = -8.2 - 19.3 = -27.5

Now to calculate the value of vector C, we apply the following formula:

C ^ 2 = Cx ^ 2 + Cy ^ 2

Rearranging:

C = (Cx ^ 2 + Cy ^ 2) ^ (1/2)

C = [(-6.3 ^ 2) + (27.5 ^ 2)] ^ (1/2) = 28.2

Then the distance would be 28.2 meters.

Answer:

[tex]x<120[/tex]

Step-by-step explanation:

We have been given an inequality [tex]-30<\frac{x}{-4}[/tex]. We are asked to solve the given inequality.

To solve for x, we will multiply both sides of inequality by negative 4. When we multiply or divide both sides of an inequality, the inequality sign reverses.

[tex]-30\cdot (-4)>\frac{x}{-4}\cdot (-4)[/tex]

[tex]120>x[/tex]

This means that 120 is greater than x or x is less than 120.

[tex]x<120[/tex]

Therefore, our required inequality would be [tex]x<120[/tex].

Final answer:

The solution to the inequality -30 < x / -4 is found by multiplying both sides by -4, which reverses the inequality sign, resulting in the solution x < 120. This demonstrates the manipulation of inequalities, particularly when involving negative multipliers.

Explanation:

The correct interpretation of this question is solving the inequality -30 < x / -4. To solve this inequality, we firstly multiply both sides by -4, remembering that multiplying or dividing by a negative number reverses the inequality sign. Thus, the inequality becomes 120 > x, which means x must be less than 120 for the inequality to hold true.

Therefore, the solution to the given inequality is x < 120. This highlights the importance of carefully handling inequalities, especially when multiplying or dividing by negative numbers, as it requires reversing the inequality sign to maintain the accurate relationship between both sides.

Answer:

[tex]8181.23 \ cm^3[/tex]

Step-by-step explanation:

-A standard basketball has a spherical shape.

-Given the ball has a diameter of 25cm.

-The space available for air is equivalent to the ball's volume and is calculated as:

[tex]V=\frac{4}{3}\pi r^3, D=25\\\\=\frac{4}{3}\pi (D/2)^3\\\\\frac{4}{3}\pi (25/2)^3\\\\=8181.23\ cm^3[/tex]

Hence, the space available for air is [tex]8181.23 \ cm^3[/tex]

Answer:

$ 1.05

Step-by-step explanation:

To solve the problem it is necessary to pose some equations, which are the following:

Debt DVD = New Balance - Old Balance

With this we will calculate the net value that only has to do with the debt of the DVD:

Debt DVD: 7.75 - 2.50 = 5.25

Now, the other equation is the value per day that generates a delay.

Debt DVD / # days

Replacing

5.25 / 5 = 1.05

Then the daily fine for a overdueDVD is $ 1.05

Question 1) Function defining the table:

From the table the x-intercepts are -2 and 1. This means the factors are:

(x+2) and (x-1)

Let

[tex]h(x) = a(x + 2)(x - 1)[/tex]

The point (-1,-1) satisfy this function since it is from the same table.

[tex] - 1 = a( - 1 + 2)( - 1 - 1) \\ - 1 = - 2a \\ a = \frac{1}{2} [/tex]

Therefore the function is

[tex]h(x) = \frac{1}{2} (x + 2)(x - 1)[/tex]

We expand to get:

[tex]h(x) = \frac{1}{2} ( {x}^{2} + x - 2)[/tex]

The standard form is:

[tex]h(x) = \frac{ {x}^{2} }{2} + \frac{x}{2} - 1[/tex]

Question 3) Parabola opening up

The x-intercepts are x=3 and x=7

The factors are (x-3), (x-7)

The factored from is

[tex]y = a(x - 3)(x - 7)[/tex]

The curve passes through (5,-4)

[tex] - 4= a( 5- 3)( 5 - 7) \\ - 4= - 4a \\ a = 1[/tex]

The equation is:

[tex]y = (x - 3)(x + 7)[/tex]

Expand:

[tex]y = {x}^{2} + 7x - 3x - 21[/tex]

[tex]y = {x}^{2} + 4x - 21[/tex]

This is the standard form:

Question 3) Parabola opening down:

The x-intercepts are x=-5 and x=1

The factors are (x+5), (x-1)

The factored form is

[tex]y = - (x + 5)(x - 1)[/tex]

We expand to get:

[tex]y = - ( {x}^{2} - x + 5x - 5)[/tex]

[tex]y = - {x}^{2} - 4x + 5[/tex]

This is the standard form.

Answer:

One

Step-by-step explanation:

9/sin(34) = 6/sinC

sinC = 0.372795269

C = 21.9, 158.1

Since 158.1 + 34 = 192.1 > 180

Only one triangle can be formed with angle 21.9° at C

Sin(146° + ∠B) cannot exceed 1, there is no solution for b that satisfies the triangle inequality. Therefore, no distinct triangle can be drawn with the given measurements.

To determine the number of distinct triangles that can be drawn with the given measurements using the Law of Sines, we need to consider the Ambiguous Case (also known as the SSA case or the "side-side-angle" case).

The Law of Sines states:

sin(A) / a = sin(B) / b = sin(C) / c

Given:

m∠A = 34°

a = 9

c = 6

We want to find ∠B and side b.

First, find ∠B using the Law of Sines:

sin(B) / b = sin(A) / a

sin(B) / b = sin(34°) / 9

Now, find sin(34°):

sin(34°) ≈ 0.5592

Now, solve for sin(B) by multiplying both sides by b:

sin(B) = (0.5592 * b)

Next, find ∠C:

Since the sum of angles in a triangle is 180°:

∠C = 180° - ∠A - ∠B

∠C = 180° - 34° - ∠B

Determine the value of side b:

Using the Law of Sines again, we have:

sin(C) / b = sin(A) / a

sin(C) / b = sin(34°) / 9

Find sin(C):

sin(C) = sin(180° - 34° - ∠B)

We can now use the fact that sin(C) = sin(180° - angle) to find sin(C):

sin(C) = sin(180° - 34° - ∠B) = sin(146° + ∠B)

Now, solve for b by multiplying both sides by b:

sin(146° + ∠B) = (sin(34°) / 9) * b

Since sin(146° + ∠B) cannot be greater than 1 (the maximum value for sine), the number of distinct triangles will depend on the possible values of b.

In this case, we have sin(146° + ∠B) = (sin(34°) / 9) * b, and since sin(34°) ≈ 0.5592, the maximum value for (sin(34°) / 9) * b is approximately 0.5592 * 6 ≈ 3.3552.

Since sin(146° + ∠B) cannot exceed 1, there is no solution for b that satisfies the triangle inequality. Therefore, no distinct triangle can be drawn with the given measurements.

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