Question 67
Use substitution to solve the system of equations.
y=x+8
2x-3y=5
O (19,27)
O (-21, -29)
O (-29, -21)
O (-5,3)

The complete factorization of 3x⁵- 75x³ is:- 3x³(x + 5)(x - 5)

How to solve factor?

To factor completely the expression 3x⁵ - 75x³, we can first factor out the greatest common factor (GCF) of the two terms, which is 3x³:

3x³(x² - 25)

Next, we can factor the expression inside the parentheses using the difference of squares formula:

3x³(x + 5)(x - 5)

Therefore, the complete factorization of 3x⁵ - 75x³ is:

3x³(x + 5)(x - 5)

We can check that this is the correct factorization by using the distributive property of multiplication and verifying that the product of the factors is equal to the original expression:

3x³(x + 5)(x - 5) = 3x³(x² - 25)

= 3x³x² - 3x³(25)

= 3x⁵ - 75x³

So the factorization is correct.

In summary, to factor completely an expression like 3x⁵ - 75x³, we should first factor out the GCF and then look for further factorization opportunities using various factorization techniques such as the difference of squares formula, the sum or difference of cubes formula, or the quadratic formula. It's important to remember to check our work by multiplying the factors back together to ensure that we get the original expression.

To know more about factors visit:-

https://brainly.com/question/25829061

#SPJ1

Step-by-step explanation:

To convert degrees into radians you would multiply the degrees number by pi/180

So

555/1 times pi/180

Which would equal

555

pi/180

And you would then simplify by dividing each side with 15 then equaling

37pi/12 radians

And to turn radians into degrees you would multiply by 180/pi

12m² is the area of the table top in rectangle .

What is a rectangle, exactly?

The parallel sides of a rectangle are equal to one another, and each of its four vertices is 90 degrees, making it a form of quadrilateral. As a result, it is sometimes referred to as an equiangular quadrilateral.

                               The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.

area = length x width

We know that the width is 2 meters, and since the length is three times the width, the length would be 6 meters.

Therefore, the area of the table = 2 x 6 = 12 m2.

Learn more about rectangle

brainly.com/question/29123947

#SPJ4

Given the expression:

Answer:

x^2-6x, 4x^2-1x,10x^2+8x,15x^2-3xy

Just use the distributive property like you have before and you will get these answers, Hope this helped!

Answer:

a.\( {x}^{2} - 6x\)

b. \(4 {x}^{2} - x\)

c. \(10 {x}^{2} + 8x\)

D. \(15 {x}^{2} - 3xy\)

Step-by-step explanation:

a.

\( x(x - 6)\)

Multiply each term in the parentheses by X

\(x \times x - x \times 6\)

Calculate

\( {x}^{2} - 6x\)

b.

\(x(4x - 1)\)

Multiply each term in the parentheses by X

\(x \times 4 - x \times 1\)

Calculate

\(4 {x}^{2} - x\)

c.

\(2x(5x + 4)\)

Multiply each term in the parentheses by 2x

\(2x \times 5x + 2x \times 4\)

Calculate

\(10 {x}^{2} + 8x\)

d.

\(3x(5x - y)\)

Multiply each term in the parentheses by 3x

\(3x \times 5x - 3x \times y\)

Calculate

\(15 {x}^{2} - 3xy\)

Hope this helps..

Good luck on your assignment

Answer:

Step-by-step explanation:

Help Plz

If the slice of pizza below has an area of 18.86 cm?, what is the measure of the central angle to the nearest

degree?

8 cm

The probability of an adult getting a NEG result and truly having tuberculosis is 0.01725, which is closest to option (A) 0.0373.

Let's use the following notation:

P(TB) represents the probability that an adult has tuberculosis, which is given as 0.05.

P(POS|TB) represents the probability that the test is positive given that an adult has tuberculosis, which is given as 0.746.

P(NEG|TB) represents the probability that the test is negative given that an adult has tuberculosis, which is 1 - P(POS|TB) = 0.254.

We are asked to find the probability of an adult getting a NEG result and truly having tuberculosis, which can be calculated using Bayes' theorem as follows:

P(TB|NEG) = P(NEG|TB) * P(TB) / P(NEG)

We can calculate P(NEG) using the law of total probability, which considers the two possible cases for an adult: having tuberculosis (TB) or not having tuberculosis (TB').

P(NEG) = P(NEG|TB) * P(TB) + P(NEG|TB') * P(TB')

= 0.254 * 0.05 + 0.7653 * 0.95

= 0.7352

Now we can substitute the values into Bayes' theorem:

P(TB|NEG) = 0.254 * 0.05 / 0.7352

= 0.01725

Therefore, the probability of an adult getting a NEG result and truly having tuberculosis is 0.01725, which is closest to option (A) 0.0373.

Learn more about Bayes' theorem here: brainly.com/question/29598596

#SPJ4

Ok, so

Here we have the expression:

We want to solve this expression for x.

The first thing we're going to do is to distribute the letter outside the bracket in the terms inside of it.

This is:

Now, we could substract "cb" to both sides of the equation:

And then, divide by c:

And the solution for x will be:

x = (y-cb)/c

Answer:

x = (y-cb)/c

Step-by-step explanation:

First expand the right side :

y = cx + cb

Subtract cb from both sides :

y - cb = cx

Divide both sides by c :

(y-cb)/c = x

x = (y-cb)/c

Hope this helped and have a good day

To show that every member of the family of functions \(y = \frac{\ln x}{cx}\) is a solution of the differential equation \(x^2y' - xy = \frac{1}{x^2}\), we need to substitute \(y\) and \(y'\) into the differential equation and verify that it satisfies the equation.

Let's start by finding the derivative of \(y\) with respect to \(x\):

\[y' = \frac{d}{dx}\left(\frac{\ln x}{cx}\right)\]

Using the quotient rule, we have:

\[y' = \frac{\frac{1}{x}\cdot cx - \ln x \cdot 1}{(cx)^2} = \frac{1 - \ln x}{x(cx)^2}\]

Now, substituting \(y\) and \(y'\) into the differential equation:

\[x^2y' - xy = x^2\left(\frac{1 - \ln x}{x(cx)^2}\right) - x\left(\frac{\ln x}{cx}\right)\]

Simplifying this expression:

\[= \frac{x(1 - \ln x) - x(\ln x)}{(cx)^2}\]

\[= \frac{x - x\ln x - x\ln x}{(cx)^2}\]

\[= \frac{-x\ln x}{(cx)^2}\]

\[= \frac{-\ln x}{cx^2}\]

We can see that the expression obtained is equal to \(\frac{1}{x^2}\), which is the right-hand side of the differential equation. Therefore, every member of the family of functions \(y = \frac{\ln x}{cx}\) is indeed a solution of the differential equation \(x^2y' - xy = \frac{1}{x^2}\).

In summary, by substituting the function \(y = \frac{\ln x}{cx}\) and its derivative \(y' = \frac{1 - \ln x}{x(cx)^2}\) into the differential equation \(x^2y' - xy = \frac{1}{x^2}\), we have shown that it satisfies the equation, confirming that every member of the family of functions \(y = \frac{\ln x}{cx}\) is a solution of the given differential equation.

Learn more about differential equation here:

brainly.com/question/32645495

#SPJ11

Answer:

  2. 26.2 m

  3. 117.2 cm

Step-by-step explanation:

You want the perimeters of two figures involving that are a composite of parts of circles and parts of rectangles.

The circumference of a circle is given by ...

  C = πd . . . . . where d is the diameter

The length of the semicircle of diameter 12.6 m will be ...

  1/2C = 1/2(π)(12.6 m) = 6.3π m ≈ 19.8 m

The two lighted sides of the rectangle have a total length of ...

  3.2 m + 3.2 m = 6.4 m

The length of the light string is the sum of these values:

  19.8 m + 6.4 m = 26.2 m

The length of the string of lights is about 26.2 meters.

The perimeter of the figure is the sum of four quarter-circles of radius 11.4 cm, and 4 straight edges of length 11.4 cm.

Four quarter-circles total one full circle in length, so we can use the formula for the circumference of a circle:

  C = 2πr

  C = 2π·(11.4 cm) = 22.8π cm ≈ 71.6 cm

The four straight sides total ...

  4 × 11.4 cm = 45.6 cm

The perimeter of the figure is the sum of the lengths of the curved sides and the straight sides:

  71.6 cm + 45.6 cm = 117.2 cm

The design has a perimeter of about 117.2 cm.

__

Additional comment

The bottom 12.6 m edge in the figure of problem 2 is part of the perimeter of the shape, but is not included in the length of the light string.

<95141404393>

The amount of the down payment and the fixed rate mortgage are; $ 28,000 and $630.

According to the statement

We have given that Thomas is looking to buy a house for 140,000 with a 20% down payment.

since down payment is the percentage of the down payment is 20%

So,

Amount = 20/100*140,000

Amount = 28,000$

And the percentage of the fixed rate mortgage with 4.5%

So,

Amount = 4.5/100*140,000

Amount = $630.

This is the amount of the down payment with the given percentage and with the fixed rate mortgage.

Learn more about the percentage here

brainly.com/question/11360390

#SPJ1

The required linear equation that depicts the given situation is W = 8.34A +21

A large water container weighs 21 pounds. If 8.34 pounds are contained in a gallon of water,

Total weight = W

Amount of water = A gallons

Weight of container = 21 pounds

Gallon of water = 8.34 pounds

we need to find an equation that relates the weight of the water and the container, W, in pounds and the amount of water, A, in gallons,

So, the required equation will be W = 8.34A + 21

To read more about linear equations, visit https://brainly.com/question/11897796

#SPJ9

Answer:

n = s/18 + 20

Step-by-step explanation:

A polynomial function of degree n has at most n real zeros and at most n - 1 turning points.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Linear function is a function whose graph is a straight line

We are given that;

A polynomial function

Now,

Because of the Fundamental Theorem of Algebra states that a polynomial function of degree n has exactly n complex roots (or zeros), some of which may be repeated or non-real. The number of real roots is equal to or less than the number of complex roots.

A turning point is a point where the graph of the polynomial function changes direction from increasing to decreasing or vice versa. The number of turning points is equal to or less than one less than the degree of the polynomial function. This is because each turning point corresponds to a change in the sign of the first derivative of the function, and the first derivative is a polynomial function of degree n - 1.

Therefore, by the function the answer will be n - 1.

Learn more about function here:

https://brainly.com/question/2253924

#SPJ1

Answer:

40

Step-by-step explanation:

since they are Similar

m∠E = m∠A =40°

There are 3003 ways to distribute the songs amongst the couples, as long as the couple having a fight only receives one song.

There are a total of 16 songs that can be played in one hour. If we subtract one song for the couple having a fight, then there are 15 songs that can be distributed amongst the remaining 6 couples.

To distribute the songs, we can use the stars and bars method. We have 6 couples, which means we need 5 bars to divide the songs amongst them. For example, if we have 4 songs for couple 1, 3 songs for couple 2, 2 songs for couple 3, 1 song for couple 4, 3 songs for couple 5, and 2 songs for couple 6, we can represent this distribution as follows:

****|***|**|*|***|**

The stars represent the songs, and the bars represent the division between couples. The first couple gets 4 songs, the second couple gets 3 songs, and so on.

Using this method, we can count the number of ways to distribute the songs. We need to choose 5 positions out of the 15 remaining songs to place the bars, so the number of ways is:

${15\choose 5} = 3003$

Therefore, there are 3003 ways to distribute the songs amongst the couples, as long as the couple having a fight only receives one song.

Learn more about distribute here:

brainly.com/question/15917929

#SPJ11

A circle has a center, radius, diameter and points in a plane. Depending on the context, the definition of a circle must contain at least one of the following terms:

Based on James' definition of a circle, he needed to specify that the points are in a plane (option c).

As presented in his definition "the set of all the points" can be interpreted in several ways. Some of which are:

Of this numerous possible interpretation, James should have specified that the set of points is in a plane

Learn more about circles at:

https://brainly.com/question/12930236

The statement holds true for the base case and it holds true for any k=n assuming it holds true for k=n, we can conclude that the statement holds true for all positive integer values of k. Hence, if we remove the root of a \($\mathrm{k}^{\text {th }}$\) order binomial tree, it results in k binomial trees of the smaller orders.

The statement to be proven is: "If we remove the root of a \($\mathrm{k}^{\text {th }}$\) order binomial tree, it results in \($\mathrm{k}$\) binomial trees of the smaller orders."

We will prove this statement by mathematical induction.

Base case k=1 :

Inductive step:

Suppose the statement holds true for some \($\mathbf{k}=\mathbf{n}$\), i.e., if we remove the root of an \($\mathbf{n}^{\text {th }}$\) order binomial tree, it results in \($\mathrm{n}$\) binomial trees of the smaller orders. We need to show that it also holds true for \($\mathbf{k}=\mathbf{n}+1$\)

using definition of mathematical induction.

Consider a \($(\mathrm{n}+1)^{\text {th }}$\) order binomial tree, which can be formed by joining two \($\mathrm{n}^{\text {th }}$\) order binomial trees. If we remove the root of this \($(\mathrm{n}+1)^{\text {th }}$\) order binomial tree, we are left with two nth order binomial trees. By the induction hypothesis, each of these \($\mathbf{n}^{\text {th }}$\) order binomial trees will result in n binomial trees of the smaller orders. Hence, the result of removing the root of the \($(n+1)^{\text {th }}$\) order binomial tree will be n + n = 2n binomial trees of the smaller orders, which implies that the statement holds true for \($\mathrm{k}=\mathrm{n}+1$\) as well.

For more such questions on  binomial tree

https://brainly.com/question/29612326

#SPJ4

Answer:

by helping some one fast

Answer:

Its 5

Step-by-step explanation:

25 divided by 5 is 5

The probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours is approximately 0.9564, or 95.64%.

To find the probability that the average number of hours of overtime worked by a random sample of 140 employees exceeds 20 hours, we can use the Central Limit Theorem (CLT). The CLT states that for a large enough sample size, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.

Given that the population mean is 18.9 hours and the population standard deviation is 7.8 hours, we can calculate the standard error of the mean using the formula: standard error = population standard deviation / sqrt(sample size).

For this problem, the sample size is 140, so the standard error is 7.8 / sqrt(140) ≈ 0.659.

To calculate the probability, we need to standardize the sample mean using the z-score formula: z = (sample mean - population mean) / standard error.

In this case, the sample mean is 20 hours, the population mean is 18.9 hours, and the standard error is 0.659. Plugging these values into the formula, we get z = (20 - 18.9) / 0.659 ≈ 1.71.

Now, we can use a standard normal distribution table or calculator to find the probability associated with a z-score of 1.71. Looking up this value in the table, we find that the probability is approximately 0.9564.

Therefore, the probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours is approximately 0.9564, or 95.64%.

Here's a sketch to visualize the calculation:

                  |

                  |

                  |

                  |       **

                  |      *  *

                  |     *    *

                  |    *      *

                  |   *        *

                  |  *          *

                  | *            *

-------------------|--------------------------

      18.9        |       20

The area under the curve to the right of 20 represents the probability we're interested in, which is approximately 0.9564 or 95.64%.

for more such questions on probability visit:

https://brainly.com/question/251701

#SPJ8

The approximation of f(2.003, 1.04) using the tangent plane method is approximately 13.0121.

The tangent plane approximation is a method used to approximate the value of a multivariable function at a given point based on the values of the function and its partial derivatives at that point.

To apply the tangent plane approximation to find f(2.003, 1.04) for the function f(x, y) = 3x^2 + y^2, we first need to find the partial derivatives of f with respect to x and y.

fₓ(x, y) = 6x

f₀(x, y) = 2y

Next, we evaluate these partial derivatives at the given point (2.003, 1.04):

fₓ(2.003, 1.04) = 6(2.003) ≈ 12.018

f₀(2.003, 1.04) = 2(1.04) ≈ 2.08

Now, we can use the equation for the tangent plane approximation:

f(x, y) ≈ f(a, b) + fₓ(a, b)(x - a) + f₀(a, b)(y - b)

where (a, b) is the point of approximation.

Substituting the given values, we get:

f(2.003, 1.04) ≈ f(2, 1) + 12.018(x - 2) + 2.08(y - 1)

Evaluating this equation at (2.003, 1.04), we get:

f(2.003, 1.04) ≈ f(2, 1) + 12.018(0.003) + 2.08(0.04)

f(2.003, 1.04) ≈ 13.0121

To learn more about tangent plane click on,

https://brainly.com/question/13144934

#SPJ4

Answer:

#1 - y (0, 5) x (1, 8)

#2 - y (0, -2) x (1, 1)

(things in brackets are coordinates for the line)

Step-by-step explanation:

hope that helps :)

Answer:

2.5x+50

Step-by-step explanation:

Tavius would earn his best value if he invests in a  three-year certificate of deposit with a nominal interest rate of 4 percent.

Tavius would invest in the option that yields the highest interest. This is the best value. In order to determine which option is the best, the interest rate of each option has to be determined.

Interest rate of the first option

Interest earned = amount invested x time x interest rate

$2500 x 0.03 x 2 = $150

Interest rate of the second option

Interest earned = amount invested x time x interest rate

$2500 x 0.03 x 1 = $75

Interest rate of the third option

Interest earned = amount invested x time x interest rate

$2500 x 0.04 x 3 = $300

Interest rate of the fourth option

FV = P x (1 + r) n

$2500 x (1.03) = $75

A similar question was answered here: https://brainly.com/question/24748787?referrer=searchResults

Answer:

D

Step-by-step explanation:

a savings account with 3 interest compound annually

The inequality that describes and suitable for this situation is 9.99+1.29n≤50 under the condition that Lin got a $50 gift card to an online music store. She uses the gift card to buy an album for $9.99. Then the correct option is Option C.

Given,
Lin has a $50 gift card and she spends $9.99 on an album. The amount of money left on the gift card is $50 - $9.99
= $40.01.

In the event that Lin buys n songs at $1.29 each, the total cost of the songs will be evaluated as  $1.29n.

The total amount spent on the album and songs cannot reach the level to exceed the amount left on the gift card, which is determined as $40.01.

So we can write the inequality equation
9.99 + 1.29n ≤ 50

To learn more about inequality
https://brainly.com/question/30238989
#SPJ4

The complete question is
Lin got a $50 gift card to an online music store. She uses the gift card to buy an album for $9.99. She also wants to use the gift card to buy some songs. Each song costs $1.29. Which of these inequalities describes this situation, where n is the number of songs Lin wants to buy?9.99+1.29n≥50

a) 9.99+1.29n≤50

b) 9.99−1.29n≥50

c) 9.99−1.29n≤50

Answer:

m<3 = 87

m<4 = 93

Step-by-step explanation:

The sum of the measures of supplementary angles is 180 deg.

m<3 + m<4 = 180

5x + 22 + 7x + 2 = 180

12x + 24 = 180

12x = 156

x = 13

m<3 = 5x + 22 = 5(13) + 22 = 65 + 22 = 87

m<4 = 7x + 2 = 7(13) = 91 + 2 = 93

Answer:

3/5 c

Step-by-step explanation:

_________________