which operation results in a trinomial. (4x5-8x) (3x2-8x+9)

The value of distance AB is 187.5 units

Law of sines defines the ratio of sides of a triangle and their respective sine angles are equivalent to each other.

sine rule can be expressed as;

a/sinA = b/sinB = c/sinC

The opposite side to angle A is BC

the opposite side to angle C is AB

therefore;

A = 180-( 117 +24)

A = 180- 141

A = 39°

290/sin 39 = x/ sin24

xsin39 = 290 × sin24

0.629x = 117.95

x = 117.95/0.629

x = 187.5

therefore the distance AB is 187.5

learn more about sine rule from

https://brainly.com/question/20839703

#SPJ1

Answer:

  (a)  twenty-eight ninths, square root of nineteen, cube root of eighty-eight

Step-by-step explanation:

When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.

The attachment shows the ordering, least to greatest, to be ...

  \(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)

__

Additional comment

We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.

One way to do the comparison is to convert these to values that need to have the same root:

  √19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)

  ∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)

The roots will have the same ordering as 19³ and 88².

Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...

  19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859

  88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744

Then the ordering is ...

  28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Answer:

the ordering is

28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Step-by-step explanation:

We are given:

Probability of passing = p

Probability of Failing = 6p²

__________________________________________________________

Finding the value of 'p':

We know that the sum of the probabilities of an event occurring and not occurring is 1

So, Probability of passing + Probability of Failing = 1

p + 6p² = 1

6p² + p - 1 = 0

We can see that we now have a quadratic equation

Splitting the middle term:

6p² + 3p - 2p - 1 = 0

3p(2p + 1) - (2p + 1) = 0

(3p - 1)(2p + 1) = 0                      [factoring out 2p + 1]

Now, we can either divide both sides by (3p-1) or by (2p + 1) and both the cases will give us different answers.

Dividing both sides by (3p - 1):

2p + 1 = 0/(3p-1)

2p + 1 = 0

p = -1/2

Dividing both sides by (2p+1):

(3p - 1) = 0 / (2p + 1)

3p - 1 = 0

p = 1/3

Now, we have 2 values of p: -1/2 and 1/3

Using the value: -1/2 will mean that the probabilities are negative

but we know that probabilities cannot be negative.

So, -1/2 is not a valid value for p

Therefore, the value of p is 1/3

Answer:24ft

Step-by-step explanation:

Professor Holmes is making this effort to ensure the (C) reliability of the TAs' grades.

Certain mistakes might never be corrected. It is also possible to later reverse an edit that fixed a mistake.

Wikipedia shouldn't be used as the sole source of information, for this reason.

The Signpost, non-article pages, articles, and non-English Wikipedias are all included in this.

In contrast to reference books, many items in the online encyclopedia are well-researched, reviewed for quality, and frequently kept up to date.

Nonetheless, even 20 years after its inception, the content of the encyclopedia can still be changed, sometimes almost imperceptibly.

Therefore, professor Holmes is making this effort to ensure the (C) reliability of the TAs' grades.

Know more about reliability here:

https://brainly.com/question/1265793

#SPJ1

Perimeter of the parallelogram = 210 in.

Area of parallelogram = 2,484 in.²

Perimeter of parallelogram = 2(a + b), where a and b are its sides.

Area of parallelogram = (b)(h), where h is its height and b is the length of one of its bases.

Given:

a = 51 in.

b = 54 in.

h = 46 in.

Perimeter of the parallelogram = 2(54 + 51) = 210 in.

Area of parallelogram = (b)(h) = (54)(46) = 2,484 in.²

Learn more about parallelogram on:

https://brainly.com/question/3050890

#SPJ1

Answer:

y = -2x - 10

Step-by-step explanation:

1. rearrange to find the gradient.

the gradient of the original equation is 1/2 hence why a line PERPENDICULAR to that equation would have a gradient of -2.

2. substitute into y - y1 = m (x - x1)

y - (-2) = -2 (x - (-4))

y = -2x - 10

The factorized form of \(x^3 - (y - z)^3\ is \ (x - y + z)(x^2 - xy + 2xz + yz - 2z^2).\)

The Factorization is derived from the application of a mathematical identity. As an AI language model, the information provided is generated based on existing knowledge and formulas.

The given expression is \(x^3 - (y - z)^3.\)To factorize it,  the difference of cubes, which states that a^3 - b^3 can be factorized as\((a - b)(a^2 + ab + b^2).\)

Applying this identity to our expression, we have:

\(x^3 - (y - z)^3 = (x - (y - z))((x - (y - z))^2 + (x - (y - z))(y - z) + (y - z)^2)\)

Simplifying further, we get:

\(= (x - y + z)(x^2 - 2xy + 2xz - y^2 + 2yz - z^2 + xy - y^2 + yz - z^2 + y^2 - 2yz + z^2)\\= (x - y + z)(x^2 - 2xy + xy + 2xz + yz - 2yz - y^2 + y^2 - y^2 + 2yz - 2z^2 + y^2 - z^2 + z^2)\\= (x - y + z)(x^2 - xy + 2xz + yz - 2z^2)\)

So, the factorized form of \(x^3 - (y - z)^3 \ is\ (x - y + z)(x^2 - xy + 2xz + yz - 2z^2).\)

the above factorization is derived from the application of a mathematical identity.

To know more about factorized .

https://brainly.com/question/14268870

#SPJ11

Answer:C.4,384

Step-by-step explanation:

1,096 × 4 = 4,384

This is why the answer is C.4,384.

Answer:

0.2061 = 20.61% probability, given a class size of 30 students, the average time to complete the test is less than 48.5 minutes

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 50 minutes and a standard deviation of 10 minutes.

This means that \(\mu = 50, \sigma = 10\)

Class size of 30 students

This means that \(n = 30, s = \frac{10}{\sqrt{30}}\)

What is the probability, given a class size of 30 students, the average time to complete the test is less than 48.5 minutes.

This is the p-value of Z when X = 48.5. So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{48.5 - 50}{\frac{10}{\sqrt{30}}}\)

\(Z = -0.82\)

\(Z = -0.82\) has a p-value of 0.2061

0.2061 = 20.61% probability, given a class size of 30 students, the average time to complete the test is less than 48.5 minutes

Answer:

  v = 13

Step-by-step explanation:

The diagonals of a parallelogram bisect each other, so AB ≅ AD. This relation gives rise to an equation we can solve for v.

  2v -3 = 6v -55

  52 = 4v . . . . . . . . . add 55-2v to both sides

  13 = v . . . . . . . divide by 4

The value of v is 13 in this parallelogram.

Answer:

60³

Step-by-step explanation:

Hi again.

This time we are working with a triangular prism which is a bit trickier than a rectangular prism but it is still pretty easy once you know the formula.

The formula for a triangular prism is :

V = 1/2 x b x h x l

Or in full terms :

Volume = 1/2 x Base x Height x Length

So basically we are going to plug in the base , height, and width like we did before but this time at the end we are going to divide it in half.

So like last time, lets look at what we are given :

Base = 5

Height = 3

Length = 8

And now we put these numbers into the formula :

Volume = 1/2 x Base x Height x Length

Volume = 1/2 x 5 x 3 x 8

Lets save the 1/2 for last and do the others first.

So we can do 5 x 3 and get 15.

Then 15 x 8 and we get 120.

Now the equation is literally :

Volume = 1/2 x 120

(This is the same as 120 / 2 just in multiplication terms)

So lets do this :

120 / 2

=

60

So now we have your answer :

Volume = 60³

(Don't forget the little 3)

Again, I hope this helps!

Any questions or concerns please comment or message me ofc :)

The quantity of ribbon that Ali started with was 16/21 feet, based on the mathematical operation of addition.

The basic mathematical operations include addition, subtraction, division, and multiplication.

In the addition operation, two or more addends are added to obtain a result called the sum or total using the equation symbol (=) and the addition operand (+).

The quantity of ribbon attached to the rearview mirror = 2/7

The remaining quantity of ribbon after the attachment = 10/21

The quantity of ribbon Ali started with = 16/21 (2/7 + 10/21)

Thus, using the addition operation, we can conclude that Ali started with 16/21 feet of ribbon.

Learn more about mathematical operations at https://brainly.com/question/4721701

#SPJ1

Answer:

reflect it about the x axis and  stretch it  by 2 in the y direction

Step-by-step explanation:

f(x) = |x|  to f (x)=-2|x|

y = −f(x)  Reflects it about x-axis

y = Cf(x)  C > 1 stretches it in the y-direction

so we reflect it about the x axis and  stretch it  by 2 in the y direction

Answer: reflect it about the x axis and stretch it by 2 in the y direction

Step-by-step explanation:

The additional acres that the parks occupy will be 33.75 acres.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this case, the additional acres that the parks occupy will be:

= (12.5 × 3) - 3.75

= 33.75 acres.

Note that the information is incomplete and the complete information is given below.

Learn more about word problem on:

brainly.com/question/21405634

#SPJ1

A city is building 3 parks in a new subdivision. Each park will be 1.25 acres. How many total acres will the 3 parks be? 3.75 acres

The city acquired more land next to the subdivision. If it decides to make each park 12.5 acres, how many additional acres would the parks occupy?

Answer:

10, 14

Step-by-step explanation:

A + B = 24, so A = 24 - B

5.8A + 7.4B = 161.6

Substitute the first equation into the second

5.8(24 - B) + 7.4B = 161.6

139.2 - 5.8B + 7.4B = 161.6

139.2 + 1.6B = 161.6

1.6B = 22.4

B = 14, So he works 14 hours at job B.

Together they make 24, so he works 10 hours at job A.

The linear equation that describes this situation is:

y = 2500 + 300*x

A general linear equation is written as:

y = ax + b

where a is the slope and b is the initial value.

Here we know that she starts with 2,500 points in the game, and then she wins 300 points for every minute.

Then the initial value is 2,500, and the slope is 300, then we can write the linear equation:

y = 2500 + 300*x

That is the correct option.

Learn more about linear equations at:

https://brainly.com/question/1884491

#SPJ1

The value of the expression f(a) is f(a) = a^2 + 7a, based on the given function f(x) = x^2 + 7x and the value x = a

The given parameters in the question are:

f(x) = x^2 + 7x and

x = a as in f(a)

This means that the equation of the function f(x) is given as:

f(x) = x^2 + 7x

To calculate the value of the function f(a), we simply substitute a for x in the equation of the function f(x) = x^2 + 7x.

This means that we set x to a in the equation of the function f(x) = x^2 + 7x.

So, we have;

f(a) = a^2 + 7a

The above equation cannot be further simplified or expanded

So, we conclude that

Based on the given function f(x) = x^2 + 7x and the value x = a, the value of the expression f(a) is f(a) = a^2 + 7a

Read more about functions at:

https://brainly.com/question/15602982

#SPJ1

Answer: They'll have the same amount of money in 9 months. They'll have $190

Step-by-step explanation:

Make a chart showing each month, with how much they have. Every time you add a month, subtract 45 to Sonya's amount of add 15 to Cameron's amount. Eventually, you'll get that they will both have $190 in 9 months. Hope this helped!

By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

For more such questions on graph

https://brainly.com/question/19040584

#SPJ8

Answer:$1.5

$30*5/100=15/10=3/2=$1.5

Step-by-step explanation:

Answer:It's called the "y intercept" and it's the y value of the point where the line intersects the y- axis. For this line, the y-intercept is "negative 1." You can find the y-intercept by looking at the graph and seeing which point crosses the y axis. This point will always have an x coordinate of zero.

Step-by-step explanation:

The Y intercept of a straight line is simply where the line crosses the Y axis.

Example

Y intercept

In the above diagram the line crosses the Y axis at 1.

The Y intercept is equal to 1 and the point is written as (0,1). Notice that for the y-intercept the x-coordinate of the point is always zero..

The arrangements of the digits is an illustration of factorials

The digits of 7,444,000 can be arranged in 140 ways

The number is given as: 7,444,000

From the given number, we have the following parameters:

Total (n) = 7

n(4) = 3

n(0) = 3

So, the number (N) of arrangement is:

\(N = \frac{n!}{n(4)! * n(0)!}\)

Substitute known values

\(N = \frac{7!}{3! * 3!}\)

Evaluate the factorials

\(N = \frac{5040}{6 * 6}\)

Evaluate the quotient

\(N = 140\)

Hence, the digits of 7,444,000 can be arranged in 140 ways

Read more about arrangements at:

https://brainly.com/question/4658834

Answer:

D or the fourth option

Step-by-step explanation:

because you just multiply the numbers in the bracket by 4. so it will be 8, -16, 20, -4.

I hope this helped. :)

The amount that would be in the account when Alana is 21  is $2890

We have to know the formula for simple interest.

This is expressed as;

S.I = PRT/100

Given that the parameters of the formula are enumerated as;

From the information given, substitute the values, we have;

SI = 1000 × 9 × 21/100

Multiply the values,

Then, divide by the denominator, we have;

SI = $1890

Learn more about simple interest at: https://brainly.com/question/20690803

#SPJ1

Answer:

yes

Step-by-step explanation:

because we are simply "adding" 2 negative numbers.

-8n + -7 = -7 + -8n

as long as we flip the terms around with their signs, the commutative principle of addition applies.

what we CANNOT do is e.g.

8n - 7 = 7 - 8n

THERE would be a problem.

but again, by also keeping the signs with the terms, it is all OK.

so, yes, we could also do

8n - 7 = -7 + 8n

that is true again.

Answer:

Yes

Step-by-step explanation:

They give the same value

Example:       -3-2 and -2-3 give the same value.

The linear function that represent this problem is 7y = 22x + 127, and the temperature at 11:15am is 53.19 degrees

a.

We can take two points from this to find the slope and y - intercept to determine the linear function.

A(6, 59)

B(13, 81)

The slope of a linear equation has a formula of ;

m = y₂ - y₁ / x₂ - x₁

m = 81 - 59 / 13 - 6

m = 22/7

Using the slope to find the y - intercept, we need just one point;

y = mx + c

59 = 22/7(13) + c

59 = 286/7 + c

c = 59 - 286/7

c = 127/7

The equation can be written as;

y = 22/7x + 127/7

rewriting this;

7y = 22x + 127

b. The temperature at 11.15am

Substituting this into the equation;

7y = 22(11.15) + 127

7y = 372.3

y = 53.19 degrees Fahrenheit

Learn more on linear function here;

https://brainly.com/question/15602982

#SPJ1

Translation:

The room temperature at 6 am was 59 degrees Fahrenheit. It was increasing linearly until 1 pm when the thermometer marked 81 degrees. a) Write a linear equation that shows the temperature as a function of time in that interval. b) Calculate with this equation the temperature at 11:15 am. Round to the nearest tenth of a degree Fahrenheit if necessary.

The quantity of candy that Eric ate would be = 14/15

The quantity of Candy Kim had = 2⅓ pounds.

The quantity of Kims candy that Eric ate = 2/5

That is 2/5 of 2⅓.

The actual quantity of candy that Eric ate = 2/5× 7/3 = 14/15

Learn more about fraction here:

https://brainly.com/question/28699958

#SPJ1

Answer:

8 83/104.

Step-by-step explanation:

4 9/13 * 1 7/8

= 61/13 * 15/8

= 915/104

= 8 83/104.