whats the correct answer?

The solution of the equation 3x² + 17x - 6 = 0 are, x = 1/3 and x = - 6.

An algebraic equation with the second degree of the variable is called an Quadratic equation.

We have to given that;

The quadratic equation is,

⇒ 3x² + 17x - 6 = 0

Now, We can solve the equation as;

⇒ 3x² + 17x - 6 = 0

⇒ 3x² + (18 - 1)x - 6 = 0

⇒ 3x² + 18x - x - 6 = 0

⇒ 3x (x + 6) - 1 (x + 6) = 0

⇒ (3x - 1) (x + 6) = 0

This gives two solutions,

⇒ 3x - 1 = 0

⇒ x = 1/3

And, x + 6 = 0

⇒ x = - 6

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Answer:

The team can assign field positions to 9 of the 19 players in 181,440 different ways.

Step-by-step explanation:

Since the outfielders (left field, center field, right field) can play any outfield position, the infielders (1st base, 2nd base, 3rd base, short stop) can play any infield position, the pitchers can only pitch, and the catchers can only catch, supposing a certain team has 20 players, of whom 3 are catchers, 4 are outfielders, 6 are infielders, and 7 are pitchers, to determine how many ways can the team assign field positions to 9 of the 19 players, putting each of the 9 selected players in a position he can play, and ensuring that all 9 field positions are filled, the following calculation must be performed:

3 x 7 x 6 x 5 x 4 x 3 x 4 x 3 x 2 = X

21 x 30 x 12 x 24 = X

630 x 12 x 24 = X

181,440 = X

Therefore, the team can assign field positions to 9 of the 19 players in 181,440 different ways.

Answer:

40m

Step-by-step explanation:

to find the area of a triangle you must do bh/2

So you do 10 times 8 which is 80.

Then you do 80 divided by 2 which is 40.

I hope this helps!

Answer:

C

Step-by-step explanation:

Hypergeometric distribution

[tex]\frac{{6\choose2}}{{12\choose2}}=\frac{15}{66}= \frac{5}{22}[/tex]

1.621 kN

Step-by-step explanation:

Let the centerline of the canal be the x-axis. Because the forces exerted by the horses are symmetric to the centerline, only the x-components of these forces contribute to the resultant force on the barge, i.e., the y-components cancel out. Each x-component is equal to [tex]F_x = 839\cos 15[/tex] = 810.4 N. Therefore, the resultant force on the barge is twice this:

[tex]F_{net} = 2(839\:\text{N})\cos 15 = 1620.8\:\text{N}[/tex]

[tex]= 1.621\:\text{kN}[/tex]

Step-by-step explanation:

100% = $70.99

there is a discount of 25%.

that means 75% (100 - 25) of the original price remains.

the equation to get any x% amount of a 100% total is simply

x% amount = 100% total amount × x/100

25% = 70.99 × 25/100 = $17.75

Answer:

Following are the solution to the given question:

Step-by-step explanation:

Have a Spanish Jury possibility[tex]= 0.40[/tex]

Jury member No. to be chosen[tex]= n= 12[/tex]

Hispanic Juror Expected [tex]= np = 12\times 0.40 = 4.8[/tex]

The jury group will be constituted by Hispanic Jurors [tex]4.8[/tex]

OR

The binomial distribution defines the behavior of a count variable X, provided:

There are a set number of data points n.

Set [tex]n=12[/tex]

Each perception is independent. This will not affect others if your first juror is selected

One of two results is that each observation ("success" or "failure"). English or not

Each result has the same chance of "success" p. for every [tex]p=0.40[/tex]

Well by the binomial distribution. Mean[tex]=E(x)=np=4.8[/tex]

Answer:

$ 2,600 was invested at 4% and $ 3,600 was invested at 9%.

Step-by-step explanation:

Given that in investing $ 6,200 of a couple's money, a financial planner put some of it into a savings account paying 4% annual simple interest, and the rest was invested in a riskier mini-mall development plan paying 9% annual simple interest, and the combined interest earned for the first year was $ 428, to determine how much money was invested at each rate, the following calculation must be performed:

3000 x 0.04 + 3200 x 0.09 = 408

2500 x 0.04 + 3700 x 0.09 = 433

2600 x 0.04 + 3600 x 0.09 = 428

Therefore, $ 2,600 was invested at 4% and $ 3,600 was invested at 9%.

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

[tex]\large\text{15 - 7x = 14}[/tex]

[tex]\large\text{-7x + 15 = 14}[/tex]

[tex]\underline{\large\text{SUBTRACT 15 to BOTH SIDES}}[/tex]

[tex]\large\text{-7x + 15 - 15 = 14 - 15}[/tex]

[tex]\underline{\underline{\large\text{CANCEL out: 15 - 15 because that gives you 0}}}[/tex]

[tex]\underline{\underline{\large\text{KEEP: 14 - 15 because that helps solve for the x-value}}}[/tex]

[tex]\large\text{14 - 15 = \bf -1}[/tex]

[tex]\underline{\underline{\underline{\large\text{NEW EQUATION: -7x = -1}}}}[/tex]

[tex]\underline{\large\text{DIVIDE -7 to BOTH SIDES}}[/tex]

[tex]\mathsf{\dfrac{-7\mathsf{x}}{-7}=\dfrac{-1}{-7}}[/tex]

[tex]\underline{\underline{\large\text{CANCEL out: } \dfrac{-7}{-7} \large\text{ because that gives you 1}}}[/tex]

[tex]\underline{\underline{\large\text{KEEP: }\dfrac{-1}{-7}\large\text{ because helps you get the x-value}}}[/tex]

[tex]\mathsf{x = \dfrac{-1}{-7}}[/tex]

[tex]\mathsf{x = \dfrac{-1\div-1}{-7\div-1}}[/tex]

[tex]\mathsf{x =\bf \dfrac{1}{7}}[/tex]

[tex]\boxed{\boxed{\large\text{Therefore, your answer is: \bf x = }\bf \dfrac{1}{7}}}\huge\checkmark[/tex]

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

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

Answer:

285

Step-by-step explanation:

First, you would add 752 and 158. The sum is 910. Then, you subtract 625 and get 285.

Answer:

you can make 3 outfits

Step-by-step explanation:

because,if you just have 3 shoes aotomaticly you just wear 3 shirt and 3 pants.

for the socks, one people wear 2 socks so there you have 3 outfits

Answer:

[tex]810[/tex]

Step-by-step explanation:

For each shirt, there are 6 different pairs of pants to pair with it. For each of these pairs of pants, there are 3 different shoes to pair and so on.

Therefore, there are [tex]5\cdot 6\cdot 3\cdot 9=\boxed{810}[/tex] combinations you can make.

Answer:

Here you go

Ans is in pictures.

Answer:

OS = 10

Step-by-step explanation:

We can use a ratio to solve

QP     PR

-----  = ------

QO     OS

14          7

-----   = -------

14+6      OS

14          7

-----   = -------

20        OS

Using cross products

14 * OS = 7*20

14 OS = 140

Divide by 14

OS = 140/14

OS = 10

Part 1: You can simplify [tex]a_n[/tex] to

[tex]\dfrac{3n+1}{3n}-\dfrac{3n}{3n+1} = \dfrac1{3n}+\dfrac1{3n+1}[/tex]

Presumably, the sequence starts at n = 1. It's easy to see that the sequence is strictly decreasing, since larger values of n make either fraction smaller.

(a) So, the sequence is bounded above by its first value,

[tex]|a_n| \le a_1 = \dfrac13+\dfrac14 = \boxed{\dfrac7{12}}[/tex]

(b) And because both fractions in [tex]a_n[/tex] converge to 0, while remaining positive for any natural number n, the sequence is bounded below by 0,

[tex]|a_n| \ge \boxed{0}[/tex]

(c) Finally, [tex]a_n[/tex] is bounded above and below, so it is a bounded sequence.

Part 2: Yes, [tex]a_n[/tex] is monotonic and strictly decreasing.

Part 3:

(a) I assume the choices are between convergent and divergent. Any monotonic and bounded sequence is convergent.

(b) Since [tex]a_n[/tex] is decreasing and bounded below by 0, its limit as n goes to infinity is 0.

Part 4:

(a) We have

[tex]\displaystyle \lim_{n\to\infty} \frac{10n^2+1}{n^2+n} = \lim_{n\to\infty}10+\frac1{n^2}}{1+\frac1n} = 10[/tex]

and the (-1)ⁿ makes this limit alternate between -10 and 10. So the sequence is bounded but clearly not monotonic, and hence divergent.

(b) Taking the limit gives

[tex]\displaystyle\lim_{n\to\infty}\frac{10n^3+1}{n^2+n} = \lim_{n\to\infty}\frac{10+\frac1{n^3}}{\frac1n+\frac1{n^2}} = \infty[/tex]

so the sequence is unbounded and divergent. It should also be easy to see or establish that the sequence is strictly increasing and thus monotonic.

For the next three, I'm guessing the options here are something to the effect of "does", "may", or "does not".

(c) may : the sequence in (a) demonstrates that a bounded sequence need not converge

(d) does not : a monotonic sequence has to be bounded in order to converge, otherwise it grows to ± infinity.

(e) does : this is true and is known as the monotone convergence theorem.

Answer:

7

Step-by-step explanation:

You can convert the fourth square roots to [tex]7^{\frac{1}{4}}} * 7^{\frac{1}{4}}} * 7^{\frac{1}{4}}} * 7^{\frac{1}{4}}}[/tex]. Using the product of powers rule, we can add the four terms' exponents, resulting in [tex]7^1[/tex], which is 7.

9514 1404 393

Answer:

Step-by-step explanation:

The transformation g(x) = f(x -h) +k is a translation of f(x) to the right by h units and up k units.

1. h = -1, so the graph of g(x) is the graph of f(x) shifted left 1 unit. (blue)

__

2. k = -2, so the graph of g(x) is the graph of f(x) shifted down 2 units. (green)

Answer:

4 and -1

Step-by-step explanation:

A quadratic function is given to us and we need to find the x Intercepts of the given function . The function is ,

[tex]\bf \implies g(x) = -2( x -4)(x+1)[/tex]

Step 1 : Equate the function with 0,

[tex]\bf \implies -2( x -4)(x+1) = 0 [/tex]

Step 2: Equating with 0 :-

Now equate each factors seperately with 0 , to get the x Intercepts.

Step 3: Finding the intercepts :-

[tex]\bf \implies x - 4 = 0 \\\\\implies\boxed{\bf\blue{ x = 4 }} [/tex]

Again ,

[tex]\bf \implies x + 1 = 0 \\\\\implies\boxed{ \blue{\bf x = -1}} [/tex]

Hence the x intercepts are 4 and -1 .

Answer:D (4,0) and (-1,0)

Step-by-step explanation:

Answer:

11/2

Step-by-step explanation:

Given 12x+16y=11

Halving both sides gives 6x+8y=11/2.

Answer:

[tex](x + 3)(x - 2)(x - 1)[/tex]

Step-by-step explanation:

[tex] {x}^{3} - 7x + 6[/tex]

Factor using Rational Root Theorem.

This means our possible roots are

positve or negative (1,2,3,6). If we try positve 1, it is indeed a root.

This means that

[tex](x - 1)[/tex]

is a root.

We can divide the top equation by the root (x-1). Our new equation is

[tex]( {x}^{2} + x - 6)[/tex]

Now we can factor this completely

[tex](x + 3)(x - 2)[/tex]

So this equation in factored form is

[tex](x + 3)(x - 2)(x - 1)[/tex]

a perfect square trinomial, (x + y)² = x² + 2xy + y²

so, if we have the x of the bx, what is left is the b

the expression would have to be (x + 7)², since we have the 49 and the x²

so, what's left: x² + 14x + 49,

b = 14

hope it helps :)

Answer:

1 page of a report per hour

Step-by-step explanation:

2/2= 1 page per hour

Lets find unit rate

[tex]\\ \sf\longmapsto \dfrac{2\dfrac{1}{2}}{2}[/tex]

[tex]\\ \sf\longmapsto \dfrac{5}{2}\div 2[/tex]

[tex]\\ \sf\longmapsto \dfrac{5}{4}[/tex]

[tex]\\ \sf\longmapsto 1.2pages/hour[/tex]

9514 1404 393

Answer:

  (c) √49

  (d) 2.544544...(3-digit repeat)

Step-by-step explanation:

Square roots of perfect squares are rational, as are repeating decimals.

Answer: The probability would be zero

Step-by-step explanation:

There are two children and one is a boy, so the probability of both being girls is a zero

Answer:

(a) Hence the maximum error in the calculated area of the disk is 32.67[tex]cm^{2}[/tex].

(b) Hence the relative error is 1.54%.

Step-by-step explanation:

Here the given are,

The Radius of the circle r = 26cm.

The maximum error in measurement dr = 0.2 cm.

Answer:

(a) [tex]A =(4245.28\pm32.66) cm^2[/tex]

(b) [tex]\frac{dA}{A}=\frac{32.66}{4245.28}=0.0077[/tex]

Step-by-step explanation:

radius, r = 26 cm

error = 0.2 cm

(a) The area of the disc is given by

[tex]A = \pi r^2\\\\dA = 2\pi r dr\\\\dA = 2 \times 3.14\times 26\times 0.2= 32.66[/tex]

Now

A = 3.14 x r x r = 3.14 x 26 x 26 = 4245.28 cm^2

So, the area with error is given by

[tex]A =(4245.28\pm32.66) cm^2[/tex]

(b) The relative error is

[tex]\frac{dA}{A}=\frac{32.66}{4245.28}=0.0077[/tex]

9514 1404 393

Answer:

  x = 36

Step-by-step explanation:

The interior angle at E is (180-2x). The interior angle at F is (180-4x). The sum of the interior angles of the triangle is 180, so we have ...

  (180 -2x) +x +(180 -4x) = 180

  180 = 5x . . . . . . add 5x-180 to both sides

  36 = x . . . . . . . divide by 5

__

Additional comment

This value of x makes the exterior angles at E and F be 72° and 144°, respectively. The internal angles at E, F, G are then 108°, 36°, 36°, making the triangle isosceles with EF = EG.

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Answer:

  12°

Step-by-step explanation:

We assume you mean ...

  ∠x = 174°

Angle a is supplementary to angle x, so is ...

  ∠a = 180° -174° = 6°

Angle b is a vertical angle with respect to angle 'a', so is the same measure.

  ∠a +∠b = 6° +6° = 12°

Answer:

110100

Step-by-step explanation:

Answer:

115

Step-by-step explanation:

The opposite angles (115degree angle and angle 4) are equal.

Angle 3=65

Angle 4=115

Angle 5=115

Angle 6=65

Angle 7=65

Angle 8=115

Brainliest please~