Consider the quadratic equation below.
4x²5= 3x + 4
Determine the correct set-up for solving the equation using the quadratic formula.
O A.
OB.
O C.
H=
AH=
O D.
H=
H =
-(3) ± √(3)²-4(-4)(1)
2(1)
−(−3) ± √(-3)² − 4(4)(9)
2(4)
-(3)± √(3)¹-4(-4)(-9)
2(-4)
-(-3) ± √(-3)²-4(4)(-9)
2(4)

a) The probability of selecting two even numbered balls before odd numbered balls is 1/6.

b) The probability of not selecting balls in size order is 22/24 or 11/12.


a) There are 4! (24) ways to arrange the four balls. There are 2! ways (2) to arrange the even balls and 2! ways (2) to arrange the odd balls, so there are 2x2=4 favorable ways (2,4,1,3 and 4,2,1,3). The probability is 4/24, which simplifies to 1/6.

b) There are only 2 ways to select balls in size order (1,2,3,4 and 4,3,2,1). Subtracting these from the total arrangements (24-2) results in 22 non-size ordered selections. The probability is 22/24, which simplifies to 11/12.

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Step-by-step explanation:

First no. is 12

Second no. is 8

Third no. of 25

Way 1 of grouping the numbers,

(12×8)×25

We can use associative law of multiplication as follows :

(a×b)×c = a×(b×c)

(12×8)×25 = (96) × 25

= 2400

Way 2,

12×(8×25) = 12 × 200

= 2400

Way 2 is easier to simplify because when we multiply 8 and 25, we get 200. It is very easy to multiply any number with a number that have zeroes. As a result we easily get the answer i.e. 2400.

Answer:

ionk

Step-by-step explanation:

If she continues to increase the length of her runs the same way, it will not be enough to reach the half-marathon distance of 13.1 miles within the remaining time of the training program.

Sariah has just begun training for a half-marathon, which is 13.1 miles. There are 6 weeks of training runs remaining before the race. In her first week of training, Sariah ran 3 miles. She ran 4.5 miles the second week and 6 miles the third week.

To determine if there is enough time left in the training program for her to get up to half-marathon distance, let's analyze the pattern of her weekly increases in distance:

Week 2 - Week 1 = 4.5 miles - 3 miles = 1.5 miles increase
Week 3 - Week 2 = 6 miles - 4.5 miles = 1.5 miles increase

Sariah is consistently increasing her weekly mileage by 1.5 miles. With 3 weeks of training already completed, she has 3 more weeks to go. Let's see if she can reach the half-marathon distance of 13.1 miles:

Week 4: 6 miles + 1.5 miles = 7.5 miles
Week 5: 7.5 miles + 1.5 miles = 9 miles
Week 6: 9 miles + 1.5 miles = 10.5 miles

After 6 weeks of training, Sariah will have increased her longest run to 10.5 miles. Unfortunately, this is not enough to reach the half-marathon distance of 13.1 miles within the remaining time of the training program.

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When the spring is stretched and the distance from point a to point b is 5.3 feet, the value of θ is 53.13  degrees

The distance between point a to point b = 5.3 feet

The length of the top side = 3 feet

Therefore, it will form a right triangle

Here we have to use trigonometric function

Here adjacent side and the hypotenuse of the triangle is given

The trigonometric function that suitable for the given conditions is

cos θ = Adjacent side / Hypotenuse

Substitute the values in the equation

cos θ = 3 / 5

θ = cos^-1(3 / 5)

θ = cos^-1(0.6)

θ = 53.13 degrees

Therefore, the value of θ is 53.13  degrees

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Answer:

See below

Step-by-step explanation:

Factor the numerator and denominator

\(\displaystyle f(x)=\frac{x^2-9}{(x^2-x-6)(x^2+6x+9)}\\\\f(x)=\frac{(x+3)(x-3)}{(x-3)(x+2)(x+3)(x+3)}\\\\f(x)=\frac{x-3}{(x-3)(x+2)(x+3)}\)

Because \(x-3\) exists in both the numerator and denominator, there will be a hole at \(x=3\) because the function is not continuous at that point.

If we check if the function is continuous at \(x=2\), we can see that the denominator will not be 0, thus, the function is continuous at \(x=2\).

Answer:

j = 175

Step-by-step explanation:

Step 1: Write equation

35 = j/5

Step 2: Multiply both sides by 5

35(5) = j/5(5)

175 = j

Step 3: Rewrite

j = 175

Answer:

b=4  c=7

Step-by-step explanation:

I think not positive

Answer:

453+557 = 1010

hence b is 5 and c is 3

Answer:

\(p\left( A|B\right) =0\)

Step-by-step explanation:

Formula:

\(p\left( A|B\right) =\frac{p\left( A\cap B\right) }{p\left( B\right) }\)

The only prime outcome is 3

Then

The set A = {3}

1 and 2 are the divisors of 2

Then

The set B = {1 , 2}

Therefore , p(A∩B) = 0

Also p(B) = 0.4+0.1 = 0.5

\(\Longrightarrow p\left( A|B\right) =\frac{0 }{0.5 }=0\)

The asymptotes for the given function are y = 1 and x = 4 respectively.

An asymptote to any function can be defined as a line that touches the graph of the function as the coordinates of the graph approaches infinity.

\(\lim_{x \to \infty}\)The given function is R(x) = (x² - 25)/(x² - 8x + 16)

Since, the given function is not defined at  x² - 8x + 16 = 0.

The values of x can be found as below,

x² - 8x + 16 = 0

⇒ (x - 4)² = 0

⇒ x = 4

Now, \(\lim_{x \to \ 4}} R(x)\) = \(\lim_{x \to \ 4}\) (x² - 25)/(x² - 8x + 16)

                              = -9/0

                              = -∞

Hence, at x = 4 the function has a y asymptote.

Again, in order to find x asymptotes compute the following limit,

\(\lim_{x \to \infty} R(x)\) = \(\lim_{x \to \infty}\) (x² - 25)/(x² - 8x + 16)

Apply L' Hospital rule to get,

\(\lim_{x \to \infty}\) (x² - 25)/(x² - 8x + 16) =  \(\lim_{x \to \infty}\) 2x/ (2x - 8)

⇒ \(\lim_{x \to \infty}\) 2/2 = 1

Thus, the x asymptote of the function is at y = 1.

Hence, the horizontal and vertical asymptotes of the given function are  y = 1 and x = 4 respectively.

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The solution of the equation 3z minus 2 is equal to 46 is 16.

The given equation '3z minus 2 is equal to 46' can be written as

    3z - 2  =   46

Now solving for z because the value of z will give the required solution of the given equation. So now finding the z from the equation:

   3z = 46  + 2

   3z =  48

   z = 48/3

   z = 16

The value of the z is 16 which represents the solution of the given equation i.e 3z minus 2 is equal to 46.

Therefore it is concluded that the solution of the equation 3z minus 2 is equal to 46 is 16.

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Answer:

(b - 1) (5b - 6)

Step-by-step explanation:

Answer: The answer is C, 1/3 cup.

Based on the graph given, the option that will show the same amplitude as function m is graph D.

The cosine function is seen as:

f(x) = A*cos(kx) + M

And the functions are:

When the function is m(x) = -2*cos(x+π).

The absolute value of the amplitude will be 2*|-2| = 4

Therefore, the option that can have the requirement above is graph D.

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Answer: 3rd brand.

Step-by-step explanation:

1st brand:

6 oz cost $1.25

The amount per ounce will be:

= $1.25/6

= $0.21

2nd brand:

8 oz cost $1.33

The amount per ounce will be:

= $1.33/8

= $0.17

3rd brand:

12 oz cost $1.50

The amount per ounce will be:

= $1.50/12

= $0.125

4th brand:

16 oz cost $2.10

The amount per ounce will be:

= $2.10/16

= $0.13

From the calculation, the 3rd brand of orange juice is the better but as it's cheaper than others.

1. The inequality when the distance between 2 and 5 times a number is no less than 8 is 1. |5x−2|≥8

2. The correct option is A. Trey is not necessarily correct. He will need to ensure that the compass width remains the same for each arc drawn from P and R.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥  <  >   ≤.

The distance between 2 and 5 times a number is no less than 8.

Let the number be x

This will be |5x−2|≥8. The correct option is 1.

For the second question, it should be noted that Trey is not necessarily correct. He will need to ensure that the compass width remains the same for each arc drawn from P and R. The correct option is A.

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Answer:

y = 4x - 12

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer/how I got this answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)

Answer:

x=0

Step-by-step explanation:

because you divide by x^12

x^n=x^0

x=0

The equation of the problem is \(5(n+7)\)

The sentence is asking 5 times the sum of n+7, so you are multiplying (n+7) by 5.

Answer:

-8, 7

Step-by-step explanation:

Set up an equation.

x² + x = 56

Set the equation equal to zero and factor.

x² + x - 56 = 0

(x + 8)(x - 7) = 0

Solve for x.

x + 8 = 0

x = -8

x - 7 = 0

x = 7

The possible x values are -8 and 7.

Answer: 49

Step-by-step explanation:

Answer:

MN = 15.5 units

------------------------------

The triangles are similar since all three angles are equal on both.

We know corresponding sides of similar triangles are proportional.

Set up proportions and find the missing side length:

Step-by-step explanation:

Start at the orgin.

The y intercept in the equation is -1 so I would shift 1 unit down to the orgin at (0,-1)

Then at the point, since the slope is -4. I would go down -4 units then go over 1 unit to the right.. So the next point would be (1,-5) then so on and so on.

You can check if your graph is correct by writing out specific points on the linear equation and making sure there slope is equal to -4.

Answer:

0.986

Step-by-step explanation:

You have to subtract  3.256 -  2.27 and get 0.986. Hope this is right and helps!

The numerator for the given rational expression is 3 + 5k.

In the given rational expression, (3 + 5k) represents the numerator. The numerator is the part of the fraction that is located above the division line or the horizontal bar.

In this case, the expression 3 + 5k is the numerator because it is the sum of 3 and 5k. The term 3 is a constant, and 5k represents the product of 5 and k, which is a variable.

The numerator consists of the terms 3 and 5k, which are combined using addition (+). Therefore, the numerator can be written as 3 + 5k.

To clarify, the numerator is the value that contributes to the overall value of the fraction. In this case, it is the sum of 3 and 5k.

Hence, the correct answer for the numerator of the given rational expression (3 + 5k) / (74/k^2) is 3 + 5k.

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Answer:

13.9188 dollars

Step-by-step explanation:

1.1599 * 12 = 13.9188

Answer:

1 gallon fill = $1.1599

Step-by-step explanation:

we have to fill 12-gallons

Simple-Answer:

12 gallon  = 12 * $1.1599

12 gallon = $13.9188

All of the criteria's are fulfilled the survey is valid.

We have the information from the question:

The proportion of college football players who have had at least one concussion is estimated to be 34% in the united states.

Then, 34% = 0.34

The sample size of the data is = 100

p: the ‘proportion’ of ‘college’

The required conditions for testing the hypothesis of population proportion are,

(i) The population is larger than the sample

(ii) np > 10

=> 100 × 0.34

      =34

(iii) n(1-p) > 10

100 × (1 - 0.34)

=> 100 × 0.66

      =66

iv)The ‘sample’ is drawn randomly from the population.

Since all of the above criteria's are fulfilled the survey is valid.

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Answer:

11.5 foot (rounded to one decimal)

Step-by-step explanation:

x = 20×sin(35)

x ≈ 11.47153.. ≈ 11.5

Answered by GAUTHMATH

The intervals where the function f(x) = 2x^3 - 54x + 7 is increasing are (-∞, -3) and (3, ∞), and the function is decreasing in the interval (-3, 3), the critical points of the given function are x = ±3, and the inflection points are x = 0 and x = 3.

For the function f(x) = 2x^3 - 54x + 7, we need to find the intervals where the function is increasing and decreasing, identify the critical points, and determine the inflection points.

To determine the increasing and decreasing intervals, we start by finding the first derivative of f(x). The derivative f'(x) is given by f'(x) = 6x^2 - 54. Setting f'(x) equal to zero, we have 6x^2 - 54 = 0, which simplifies to x^2 - 9 = 0. Solving for x, we find x = ±3.

Critical points: x = ±3.

Next, we analyze the sign of f'(x) in intervals around the critical points x = ±3. We observe that f'(x) is positive in the interval (-∞, -3) and (3, ∞), and negative in the interval (-3, 3).

Therefore, the function f(x) = 2x^3 - 54x + 7 is increasing in the intervals (-∞, -3) and (3, ∞), and decreasing in the interval (-3, 3).

Inflection points:

To find the inflection points, we need to determine the second derivative of f(x). The second derivative f''(x) is given by f''(x) = 12x(x-3).

For inflection points, we look for values of x where f''(x) changes sign. We find that f''(x) changes sign at x = 0 and x = 3.

Inflection points: x = 0 and x = 3.

In summary, the intervals where the function f(x) = 2x^3 - 54x + 7 is increasing are (-∞, -3) and (3, ∞), and the function is decreasing in the interval (-3, 3). The critical points of the given function are x = ±3, and the inflection points are x = 0 and x = 3.

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Answer: Around 67%

Step-by-step explanation:

92+70+41=203

203/3=67 2/3

Around 67%

Answer:

I think it's a 67.667

Step-by-step explanation:

1.Multiply each grade by the credits or weight attached to it

2. add all of the weighted grades together (or just the grades if there's no weighting)

3. divide the sum by the number of grades you added together