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Answer:  (x - 5)(6x + 11)

Step-by-step explanation:

Let's factorie the given expression using middle term splitting method.

Thus, we have ;

=> 6x² - 19x - 55

=> 6x² - 30x + 11x - 55

=> 6x(x - 5) + 11(x - 5)

=> (x - 5)(6x + 11)

Hence,

The equivalent expression of 6x² - 19x - 55 is :

(x - 5)(6x + 11).

Answer:

16/3

Step-by-step explanation:

A fundamental feature of matter known as mass quantifies has magnitude but no clear direction because it is a scalar quantity. Mass is typically expressed in quantities such as kilograms (kg), grams (g), or pounds (lb). It is an inherent quality of an object and is unaffected by where it is or what is around it.

We must divide the mass of the salt by the entire mass of the combination, multiply by 100, and then calculate the percentage of salt (by mass) in the mixture.

The mass of salt and the mass of water together make up the mixture's total mass:

Total mass equals the sum of the salt and water masses, or 1.21 lb plus 4.18 lb, or 5.39 lb.

We can now determine the salt content as follows:

The formula for percentage of salt is (salt mass/total mass) x 100, or (1.21 lb/5.39) x 100, or 22.46%.

Consequently, the amount of salt (by mass) in the combination is roughly 22.46 percent.

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Answer:

2

Step-by-step explanation:

Answer:

A Trapezium..................

Answer:

60 I believe

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want two methods of choosing points on the line with slope 1/2 through A(-1, 2).

Writing the equation in standard form, we can find the x- and y-intercepts. To get there, we can start from point-slope form:

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y -2 = 1/2(x -(-1)) . . . . . using given slope and point

  2y -4 = x +1 . . . . . . . . . . multiply by 2

  x -2y =  -5 . . . . . . . . . . . . add -1 -2y

Setting x=0 tells us the y-intercept is ...

  0 -2y = -5

  y = -5/-2 = 5/2

So, the y-intercept is (0, 5/2).

Setting y=0 tells us the x-intercept is ...

  x -2(0) = -5

  x = -5

So, the x-intercept is (-5, 0).

It will be convenient to choose an arbitrary y-value to find another point on the line. We can pick y = 6, for example, Then the corresponding x-value is ...

  x -2y = -5

  x = -5 +2y = -5 +2(6) = 7

Another point on the line is (7, 6).

__

Additional comment

If we were to choose an arbitrary value for x, we would want it to be odd, so the corresponding y-value would be an integer. We chose to pick an arbitrary value of y so we didn't have to worry about how to make the x-value an integer.

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Answer:

graph D

Step-by-step explanation:

if x = 0

y = 2 |-1| - 3

y = 2 (1) - 3

y = 2 - 3

y = -1

A (0, -1)

if x = 1

y = 2 |1-1|  - 3

y = 2 (0) - 3

y = -3

B (1,-3)

The quotient is \(\rm x^2+x+1\).

Given

Use synthetic division to solve (x4 – 1) ÷ (x – 1).

Synthetic division can be defined as a simplified way of dividing a polynomial with another polynomial equation of degree 1.

Therefore,

The quotient is;

\(\rm =\dfrac{x^3-1}{x-1}\\\\=\dfrac{x^3+x^2+x-x^2-x-1}{x-1}\\\\ \rm\rm =\dfrac{x(x^2+x+1)-1(x^2+x+1)}{x-1}\\\\= \dfrac{(x-1)(x^2+x+1)}{x-1}\\\\= x^2+x+1\)

Hence, the quotient is \(\rm x^2+x+1\).

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Answer: C

Step-by-step explanation:

Answer:

\(9x = 3x - 36 \\ 6x = - 36 \\ x = - 6\)

hopefully this will u...^⁠_⁠^

The average speed of Renee over the last 2 hours of her trip is 9 miles/hour.

Let the average speed of Renee in 2 hours in between 6th and 8th hour be x miles / hours.

So the distance covered by Renee in 6 hours is = 6x

So the distance covered by Renee in 8 hours is = 8x

So the distance covered by Renee in this 2 hours in between 6th and 8th hours is = 8x - 6x

So according to the information the distance covered by Renee in this same 2 hours = 74 - 56 = 18 miles.

The equation best situated to the situation is,

8x - 6x = 18

2x = 18

x = 18/2

x = 9

Hence the average speed of Renee over the last 2 hours of her trip is 9 miles/hour.

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Answer: SSS (Side- Side- Side) Congruence Postulate

Step-by-step explanation:

Answer:

25/32 inches

Step-by-step explanation:

Alright so, the perimeter of the square is 3 1/8 inches. And we also know all the sides of a square are equal.

The equation for solving perimeter is 2x+2y=perimeter. (Whereas x and y are the length and widths). But since a square has all of its sides equal, we could simply multiply all sides by 4:

4x=3 1/8

x=25/32

Hope this helps :)

Answer: it is {101, 110, 119, 128, 137, 146}

Step-by-step explanation:

a) The expected number of people to die before their 71st birthday is given as follows: 128.

b) The probability that a 67 year old woman will live to her 68th birthday is given as follows: 0.8876 = 88.76%.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

0.025679 of the 70 year old men die, hence the expected number out of 5000 is given as follows:

0.025679 x 5000 = 128.

The probability for item b is given as follows:

0.016798/0.018925 = 0.8876 = 88.76%.

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Therefore, by the Intermediate Value Theorem, the equation x³ + eˣ - 2 = 0 has at least one solution on the interval [0, 1].

To show that the equation x³ + eˣ - 2 = 0 has at least one solution, we can use the Intermediate Value Theorem.

The Intermediate Value Theorem states that if a continuous function f(x) changes sign on an interval [a, b], then there exists at least one solution to the equation f(x) = 0 on that interval.

In this case, let's consider the interval [0, 1]. We need to show that the function f(x) = x³ + eˣ - 2 changes sign on this interval.

First, let's evaluate f(0):
f(0) = (0)³ + e(0) - 2 = 1 - 2 = -1

Next, let's evaluate f(1):
f(1) = (1)³ + e(1) - 2 = 1 + e - 2

Since e is a positive constant, f(1) will be positive.

Since f(0) is negative and f(1) is positive, we can conclude that the function f(x) = x³ + eˣ - 2 changes sign on the interval [0, 1].

Therefore, by the Intermediate Value Theorem, the equation x³ + eˣ - 2 = 0 has at least one solution on the interval [0, 1].

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The chi-square value to test the hypothesis of random mating is 0.

To determine the chi-square value for testing the hypothesis of random mating in this population, we need to compare the observed frequencies of the blood types (M, MN, N) with the expected frequencies under the assumption of random mating.

First, we calculate the expected frequencies. Assuming random mating, the expected frequency for each blood type can be calculated by multiplying the total population size by the expected proportions for each blood type. The expected proportions can be obtained by dividing the total count for each blood type by the sum of all counts.

Total count: 550 + 725 + 225 = 1500

Expected proportions:

M: 550 / 1500 = 0.3667

MN: 725 / 1500 = 0.4833

N: 225 / 1500 = 0.1500

Expected frequencies:

M: 0.3667 * 1500 = 550

MN: 0.4833 * 1500 = 725

N: 0.1500 * 1500 = 225

Now we can calculate the chi-square value using the formula:

chi-square = Σ((observed frequency - expected frequency)^2 / expected frequency)

Calculating for each blood type:

For M: ((550 - 550)^2 / 550) = 0

For MN: ((725 - 725)^2 / 725) = 0

For N: ((225 - 225)^2 / 225) = 0

Summing the individual chi-square values: 0 + 0 + 0 = 0

The chi-square value is 0 (to the nearest hundredth) when testing the hypothesis of random mating in this population.

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Answer:

hi, have a great day

Step-by-step explanation:

Correct option is

B

f(x)=x

2

+6

f(g(x))=h=4x

2

+4x+7=(2x+1)

2

+6=(g(x))

2

+6

⇒f(x)=x

2

+6

The value of x in terms of b is   x = -3/b

The value of x when b is 3 is    x = -1

===========================================

Work Shown:

Let's isolate x

-2(bx - 5) = 16

bx - 5 = 16/(-2) ... dividing both sides by -2

bx - 5 = -8

bx = -8+5 ... adding 5 to both sides

bx = -3

x = -3/b ... dividing both sides by b

That wraps up the first part.

-----------

To answer the second part, we plug in b = 3 to get

x = -3/b

x = -3/3

x = -1

The percentage by which population is growing each year is 2%

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

The formula for the population of the town as a function of time t is:

g(t) = 15,000(1.02)ⁿ

To find the percent growth rate, we need to determine the percent change in population from one year to the next. Let's consider the population at two different times, n and n+1 (i.e., one year later).

The population at time n is:

g(t) = 15,000(1.02)ⁿ

The population at time n+1 is:

g(t+1) = 15,000(1.02)ⁿ⁺¹

To find the percent change in population from t to t+1, we can divide g(t+1) by g(t) and express the result as a percentage:

(g(t+1)/g(t) - 1) x 100%

= ((15,000(1.02)⁽ⁿ⁺¹⁾)/(15,000(1.02)ⁿ) - 1) x 100%

= (1.02⁽ⁿ⁺¹⁾ - 1.02ⁿ) x 100%

= 1.02ⁿ x (1.02 - 1) x 100%

= 2%

Therefore, the population grows by 2% each year, which corresponds to option (D).

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Answer:

Step-by-step explanation:

Answer: 4:3

Step-by-step explanation:

The side length of the triangle is 48/3 = 16.

The side length of the square is 48/4 = 12.

So, the ratio is 16:12 = 4:3.

Answer:

Story Pole

Step-by-step explanation:

Source : Trust me bro

The degrees of freedom for a chi-square goodness-of-fit test are calculated as the number of categories minus 1.

Suppose we wish to determine if an ordinary-looking six-sided die is fair, or balanced, meaning that each face has a probability of 1/6

of arrival on top when the die is tossed. We could toss the die dozens, maybe hundreds, of times and compare the actual number of times each face arrival on top to the scheduled number, which would be 1/6

of the total number of tosses. We would not expect each number to be exactly 1/6 of the total, but it should be close.

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Answer:

What's you question?

Step-by-step explanation:

the only student that is correct is Stepheh. "The vertex is at (–4, –1)."

Here we have the quadratic equation:

f(x) = (x + 3)*(x + 5)

The first claim is: "The y-intercept is at (15, 0)."

This is clearly false, as the y-intercept is at x = 0, and in that point we have x = 15.

The second claim is:

"The x-intercepts are at (–3, 0) and (5, 0)"

This is false, in the factored equation we can see that the x-intercepts are x =-3 and x = -5.

Third claim:

"The vertex is at (-4, -1)"

The middle value between the zeros is:

(-3 + (-5))/2 = -4

Evaluating the function in x = -4 we get the y-value of the vertex:

f(-4) = (-4 + 3)*(-4 + 5) = -1*1 = -1

So the vertex is at (-4, -1), this claim is true.

The fourth claim is:

"The midpoint between the x-intercepts is at (4, 0)."

Which is false, we already saw that the midpoint between the x-intercepts is at x = -4

Then the only student that is correct is Stepheh. "The vertex is at (–4, –1)."

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Answer:

They are 12, 13, 14 and 15.

Step-by-step explanation:

If the least integer is x, then:

x + x + 1 + x + 2 + x + 3 = 54

4x + 6 = 54

4x = 48

x = 12.

Answer:

you would need to cross multiply 37/45 = x/100

Step-by-step explanation:

The first part represents the 37 dollars out of the original 45 and the second part represents x= the unknown percent out of 100 percent.

Answer:

1/8 and 2/1 or 1:8 and 2:1

Step-by-step explanation: