Using both the distributive property and combining like terms, simplify the following expressions. Match each expression with its simplified version.
3(x+2)+4 x-3
-2(4 x+3)-4
8-(4 x+3)Be careful...order matters!
2(-5 x+3)+15 x
-4 x+5 5 x+6 7 x+3 -8 x-10

According to the given algebraic expression the missing value is [tex]$18 x^8 y^3+48 x^2 y^5= 6x^2y^3 \left(3 x^6+8 y^2\right)$$[/tex].

An equation that includes constants, variables, and a few algebraic procedures is said to be algebraic. A good example of an algebraic equation is 3x2 2xy + d. So, three different sorts of fundamental building blocks make up an algebraic expression: Correlation (i.e. integers) (i.e. numbers)

The subsequent five categories provide further categorization of various algebraic expression forms. These include the monomial, polynomial, binomial, trinomial, and multinomial.

[tex]$6.3 x^2x^6 y^3+8.6 x^2 y^3y^2[/tex]

[tex]$18 x^8 y^3+48 x^2 y^5= 6x^2y^3 \left(3 x^6+8 y^2\right)$$[/tex]

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The complete question is-

[tex]\\$factor the algebraic expression.\\$$18 x^8 y^3+48 x^2 y^5=x-y-\left(3 x^6+8 y^2\right)\\\\$Enter the missing values below\\\\$18 x^8 y^3+48 x^2 y^5=\square x\square y\square (3 x^6+8 y^2)$$[/tex]

The Local maxima and minima will be at X = 0 , 4 , -5 and point of inflation will be at [tex]\frac{(-1 + \sqrt{61})}{3},[/tex] [tex]\frac{(-1 - \sqrt{61})}{3}[/tex].

The curve of a function has peaks and troughs called maxima and minima. A function may have any number of peaks and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph. Maxima will be the curve's highest point within the specified range, while minima will be its lowest.

Extrema is the result of maxima and minima combined. The graph in the graphic below shows several peaks and falls. We obtain the function's maximum and lowest values at x = a and 0 respectively, and at x = b and c respectively. The valleys are the minima and all the peaks are the maximum.

The peaks and minima of the function that appear in a certain interval are known as local maxima and minima. The value of a function at a place in a certain interval for which the values of the function near that point are always smaller than the value of the function at that point would be considered a local maximum. Local minima, on the other hand, would be the value of the function at a location where the values of the function nearby are higher than the value of the function at that location.

When the concavity of a function's graph (or picture) changes, a point of inflection is identified. We need to determine where the second derivative of the function switches from negative to positive, or vice versa, in order to determine this in algebra. So, we calculate the provided function's second derivative.

The fuction is :

[tex]3x^{4} + 4x^{3} -120x^{2} + 120[/tex]

So for local Maxima and minima first derivatives should be zero

Therefore,

[tex]\frac{d}{dx}\\[/tex] ([tex]3x^{4} + 4x^{3} -120x^{2} + 120[/tex] ) = 0

⇒ [tex]12x^{3} + 12x^{2} - 240x = 0[/tex]

⇒ [tex]x^{3} + x^{2} - 20x = 0[/tex]

⇒[tex]x(x^{2} + x - 20) = 0 \\[/tex]

⇒x(x-4)(x+5) = 0

For x = 0, 4 , -5 there is a local maxima or minima.

Now for Point of Inflation second derivative is zero

Therefore,

[tex]\frac{d^{2} }{dx^{2} }[/tex] ( [tex]3x^{4} + 4x^{3} -120x^{2} + 120[/tex]) = 0

⇒  [tex]\frac{d}{dx}[/tex][tex]12x^{3} + 12x^{2} - 240x = 0[/tex]

⇒ [tex]36x^{2} + 24x - 240 = 0[/tex]

⇒[tex]3x^{2} + 2x - 20 = 0[/tex]

⇒ x = [tex]\frac{(-1 + \sqrt{61})}{3},[/tex] [tex]\frac{(-1 - \sqrt{61})}{3}[/tex]

So the point of inflations are [tex]\frac{(-1 + \sqrt{61})}{3},[/tex] [tex]\frac{(-1 - \sqrt{61})}{3}[/tex].

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Answer:

A and B

Step-by-step explanation:

actually the 180° rotation does the same as the reflection over the x-axis and then the reflection over the y-axis.

There is no solution to the given system of equations which is the correct answer would be an option (A).

The system of equations is given in the question as:

y = -3x+2 and 6x+2y = 10

These are two equations in the form y = mx + b, where m is the slope and b is the y-intercept.

The first equation, y = -3x + 2, has a slope of -3 and a y-intercept of 2.

The second equation, 6x + 2y = 10, can be rewritten in slope-intercept form as y = -3x + 5. This has a slope of -3 and a y-intercept of 5.

Since both equations have the same slope, they are parallel to each other. This means that they will never intersect, and there is no solution to this system of equations.

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The question seems to be incomplete the correct question would be:

Which statement is true about this system of equations?

y = -3x+2 and 6x+2y = 10

A. there is no solution

B. there is one solution

C. there is many infinite solutions

Option c is most likely to get unbiased results.

The best option for collecting unbiased data in this case would be option c: asking customers who visit retailers within a 15 mile radius of the company headquarters. This method would involve sampling a diverse group of customers who are not affiliated with the company in any way, and therefore are likely to provide more objective feedback about the new brand of soup.

Option a, asking distributors who supply the products to local retailers about the popularity of different soup brands, could be biased because the distributors may have their own interests in promoting certain brands over others.

Option b, asking the employees in the company which soup is the best, could also be biased because the employees may have a vested interest in the success of the company and its products, and therefore may not provide completely objective feedback.

Option d, asking customers who visit the grocery store nearest to the manager's house which soup they like the best, could also be biased because it may not be representative of the overall customer base for the soup. It is important to sample a diverse group of customers in order to get a more accurate sense of how the new brand of soup is being received.

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Answer: sqrt(89)

Step-by-step explanation:

let  x1=4 & y1=2

    and   x2=9 &y2=10

d= sqrt (x2-x1)^2+(y2-y1)^2

   =sqrt (9-4)^2+(10-2)^2

   =sqrt (5)^2+(8)^2

  =sqrt (25+64)

  =sqrt(89)

Answer: 6,250

Step-by-step explanation: As the equation states there are 25 boxes with 250 packs of ketchup take the 25 boxes and multiply the 250 packets

250x25=6,250

Answer:

Step-by-step explanation:

To find f(4), you can substitute 4 for x in the equation f(x) = 3x + 4. This gives you:

f(4) = 3(4) + 4

= 12 + 4

= 16

Therefore, f(4) = 16.

Refer to the photo taken. Would appreciate a rate :)

As no. of crews and time are inversely proportional 10 workers will finish the job in 10 hours.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, A crew of six workers completes a job in 15 hours.

We know more crew will finish the job in less no. of hours so they are inversely proportional.

So, C = k/t.

6 = k/15.

k = 90.

Now, C = 10 hence,

10 = 90/t.

t = 90/10.

t = 10 hours.

So, They can finish in 10 hours.

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The details about the highlighted graph of the periodic cosine function are presented as follows;

The feature of the graph that corresponds with the highlighted segment is the period of the graph

The meaning of the period which is 10 seconds is that the time it takes to complete one cycle is 10 seconds. The correct option is option C

C; The mill completes a single cycle in 10 seconds

A periodic function is one which the function's value repeats itself at regular intervals.

The meaning of the highlighted segment is that the period is 10 seconds, therefore, the time it takes the mill to complete a single cycle is 10 seconds

The trigonometric graph is a graph of a periodic function such that the parts of the graph are described as follows;

Period

From the period indicated on the graph, the time axis value within the interval of one period, highlights the time it takes for the periodic function to complete a cycle.

The time interval of one period of the attached graph created with MS Excel is between 10 and 20 seconds, indicating that the time it takes to complete a period of the function is 10 seconds.

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Answer:

1st & 4th answers are correct.

Step-by-step explanation:

-6 ( 2x + 5 )

Solve the brackets.

- 12x - 30

We can also write the answer like this.

Take -2 out of the brackets.

- 12x - 30 → -2 ( 6x + 15 )

Therefore, 1st & 4th answers are correct.

Answer:

$28.89

Step-by-step explanation:

he subscription is on sale for 25% off, so the cost is $36 - (25% * $36) = $36 - $9 = $27.

Then, a 7% tax is added at checkout, so the total cost is $27 + (7% * $27) = $27 + $1.89 = $28.89.

Therefore, the total cost is $28.89.

Answer:

Step-by-step explanation:

36 will be 27 and  7% of 27 should be added 1,89 so 28,89

a) The y-intercept is 7500 ft. It is related to skydiver’s position relative to the ground as the sum of both distance must be equal to 7500 ft.

b) The slope of the line is -2500 ft/min and it denotes that the skydiver is descending.

c) The x-intercept is; 3 seconds

d) An equation for the line is; y = -2500x + 7500

a) In a distance time graph, the y-intercept is the point at which the time (t) is equal to zero.

We are told that  at time t = 0, the altitude is 7500 ft. Thus;

y-intercept = 7500. It is related to skydiver’s position relative to the ground as the sum of both distance must be equal to 7500.

b) Slope;

m = -7500/3

m = -2500.

Thus, as slope is in negative, it means that the skydiver is descending

c) x-intercept is the point at which y = 0 and as such as seen in the graph online;

x-intercept = 3 seconds

d) Equation in slope-intercept form is given by the general form;

y = mx + c

where;

m is slope

c is y-intercept

Thus, in this question, we have;

y = -2500x + 7500

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Answer:143

Step-by-step explanation: When subtracting a negative number from a negative number(a minus sign followed by a negative turns the two signs into a positive sign) you are then adding a positive

The result of the hypothesis test is that we cannot say if the mean is lower than 56.

Hypothesis are ,

H0 : ц = ц 1

H1 : ц ≠ ц 1

It is to be tested whether the mean daily high temperature for October in a large Midwestern city is actually lower than

56 F or not.

Then the test statistic is equal to minus 2.64610 degrees of tritomas degree of to equal to 1 equal to 29 point,

The appropriate conditions to be sufficed before performing the one-sample z-test are:

(i) The measurement of the sample drawn for the observation must be extensive. The desired threshold is 30.

(ii) Each observation should have an equal opportunity of getting selected in the sample.

(iii) The data need to be normal.

On performing the analysis we conclude that  it can not be said with 99 % confidence that the true mean temp is less than 56 F.

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For sketching the graph we need to know the coordinate of the vector which are r(1) = ⟨−1, 2⟩, r′(1) = ⟨1, 2⟩

Given:-

x = t − 2,

y = t² + 1 ⇒ t = x + 2

⇒ y = (x + 2)2 + 1

⇒ y = x² + 4x + 5

For find r′(t) we have to ,

r′(t) = ⟨1, 2t⟩

To sketch the position vector r(t) and the tangent vector r′(t) for t = 1.

r(1) = ⟨−1, 2⟩, r′(1) = ⟨1, 2⟩

See the above figure. The red vector is r(1) and the blue one is r′(1)

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Rounding to seven decimal places, the probability that one individual would be selected by all witnesses is 0.0000128.

Six different witnesses chose the same individual from a lineup in a homicide case. There were 5 guys in the lineup. The likelihood that each of the six witnesses would choose the same person if the identifications were done based just on guesswork.

P = 1 ÷ 5 is the likelihood that a witness will choose a certain individual at random.

The likelihood that all seven witnesses would select the same subject is P = [tex](\frac{1}{5})^{7}[/tex]= 0.0000128.

Simply put, the probability is the likelihood that something will occur. We can discuss the probabilities of different outcomes to determine how likely they are if we are unclear about how an event will turn out.

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Answer:

f(x) = 5/2x

Step-by-step explanation:

The parent function for the given equation is f(x) = 1/2x. When this function is vertically stretched by a factor of 5, the resulting function will be f(x) = 5/2x. This means that for any value of x, the output of the transformed function will be 5 times greater than the output of the parent function.

For example, if x = 2, then f(x) = 1/2 * 2 = 1 for the parent function, and f(x) = 5/2 * 2 = 5 for the transformed function. Similarly, if x = 3, then f(x) = 1/2 * 3 = 1.5 for the parent function, and f(x) = 5/2 * 3 = 7.5 for the transformed function.

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The value of y from the equation y = 150x when x = 2(1/4) is 337.5.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 - 9 is an equation.

We have,

y varies directly with x.

y ∝ x

y = kx

Now,

y = 75 when x = 1/2

75 = k(1/2)

k = 75 x 2

k = 150

Now,

y = kx

y = 150x

When x = 2(1/4) = 9/4

y = 150 x 9/4

y = 337.5

Thus,

The value of y is 337.5.

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Answer:

86.3

Step-by-step explanation:

86.345

step 1

identify their place values

8 — Tens

6 — Units

.3 — tenth( 1 decimal place)

.34 — Hundredth (2 decimal place)

.345 — Thousandth ( 3 decimal place)

to one decimal place is

= 86.3

remember 4 is a round down number so .345 can't actually affect the 3

i hope this answered helped.

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The median, lower quartile, maximum upper and minimum quartile are

Median = 46.5,Minimum = 32, Maximum = 62, Lower quartile = 38, Upper quartile = 59

The given data for the computations are

32  34  37  39  41  45  48  53  58  60  61  62

We should know that the median is the middle value when the values are arranged in ascending or descending order of magnitude. There are 12 sets of numbers, the median is the mean of the two middle numbers

(45+48)/2=93/2 = 46.5

From the set of numbers, the maximum is the largest number while the minimum is the smallest number.  These numbers are 62 and 32 respectively

The lower and upper quartiles,  when the set of data is divided into 4 parts, The first part is the lower quartile, the middle is the median and the third is the upper quartile

32  34  37 |  39  41  45 | 48  53  58 | 60  61  62

The lower quartile is given thus

37 + 39 = 76

76 ÷ 2 = 38

The upper quartile is given thus

58 + 60 = 118

118 ÷ 2 = 59

In conclusion, the Median = 46.5, Minimum = 32, Maximum = 62, Lower quartile = 38, Upper quartile = 59

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Complete question:

what is the median,lower quartile,maximum,upper quartile,and the minimum of 34, 37, 39, 32, 48, 45, 53, 62, 58, 61, 60, 41

The statistical measures for the data points are

Generally, Statistical measures are techniques or formulas used to describe and summarize data in a meaningful way. They provide a way to quantitatively summarize and interpret data and can help to identify patterns, trends, and relationships in the data. Some common statistical measures include:

Mean: This is the average of a set of numbers, calculated by adding all the numbers together and dividing by the total number of items.

Mean=(34+37+39+32+48+45+53+62+58+61+60+41)/12

Mean= 47.5

Median: This is the middle value in a set of numbers when the numbers are arranged in order from least to greatest.

Median= (45+ 48)/2

Median=46.5

Mode: This is the most frequently occurring value in a set of numbers.

There are no numbers that occurred more than once, so no mode

Range: This is the difference between the highest and lowest values in a set of numbers.

Range 62-32

Range =30

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Answer: ok

Step-by-step explanation:

Answer:

96

Step-by-step explanation:

product = multiplication

multiply 12*8

The area of each section is 3/4 square feet. To solve the give question use division operation.

What is mixed fraction?

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder.

Given that the area of the garden is [tex]5\frac{1}{4}[/tex] square feet.

Now convert the mixed fraction with improper fraction:

[tex]5\frac{1}{4}[/tex] = [(5×4) + 1]/4

[tex]5\frac{1}{4}[/tex] = 21/4

We have to divide the area 7 equal area.

Thus divide 21/4 by 7.

21/4 ÷ 7

To convert the division sign into multiplication sign, take the reciprocal of 7:

21/4 × 1/7

= (21 × 1)/(4 × 7)

Divide the denominator and numerator by 7:

= 3/4

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We are given that [tex]\overline\lambda[/tex] is in the point spectrum and we are to prove that the conjugate is the union of the point and residual spectra of the adjoint.

If [tex]\overline\lambda[/tex] ∈ σp(T∗), then T∗v = [tex]\overline\lambda[/tex]v for some v ∈ D(T∗).

Hence, for all u ∈ D(T) we have -

⟨Tu,v⟩ = ⟨u,T∗v⟩ = ⟨u,[tex]\overline\lambda[/tex]⟩ = λ⟨u,v⟩,

⟨(T−λ)u,v⟩ = 0, for all u ∈ D(T)

If λ ∈ σp(T∗), then T∗v = [tex]\overline\lambda[/tex]v for some v∈D(T∗).

Hence, for all u∈D(T), we have ⟨Tu,v⟩=⟨u,T∗v⟩=⟨u,[tex]\overline\lambda[/tex]v⟩=λ⟨u,v⟩,

and therefore,

⟨(T−λ)u,v⟩=0, for all u∈D(T)

i.e. the range of T−λ is not dense and we will have λ ∈ σr(T) ∪ σp(T).

Hence, proved.

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Answer: The degree of a polynomial is the highest exponent of the variable in the polynomial. The leading coefficient of a polynomial is the coefficient of the term with the highest degree.

In the expression "n + 8", the highest degree of the variable is 1 and the coefficient of the term with the highest degree is 1. Therefore, the degree of the polynomial is 1 and the leading coefficient is 1.

So, the degree of the polynomial is 1 and the leading coefficient is 1.

Note: If the expression had included terms with higher degrees of the variable, such as "n^2 + 3n + 8", the degree of the polynomial would have been 2 and the leading coefficient would have been 1.

Answer:

X=54

Step-by-step explanation:

equate both the equations since angles of opposite sides are equal

2x+2=3x-52

3x-2x= 52+2

x=54

answer:

x=54

Step-by-step explanation:

2x+2=3x-52

move the 2x to 3x because x can't be negative

and add 52 to 2 so x=54

Answer:

(x+5)^2 - 13

Step-by-step explanation:

If you work out the target expression, you get:

(x+a)^2-b = (x+a)(x+a)-b = x^2 + 2ax + a^2 - b

so 2ax must be 10x, hence a = 5

also a^2 - b must be 12, and with a being 5, this means b = 25-12 = 13

Answer:

[tex](x+5)^2 - 13[/tex]

Step-by-step explanation:

In order to convert the given quadratic [tex]x^2 + 10x + 12[/tex] into the form [tex](x+a)^2 - b[/tex], you need to put the given quadratic into vertex form.

⭐What is vertex form?

⭐How do you rewrite a quadratic in vertex form?

I will demonstrate how to "partially complete the square" with the given quadratic.

Given: [tex]x^2 + 10x + 12 = 0[/tex]

Subtract the constant from the LHS and RHS.

[tex]x^2 + 10x = -12[/tex]

Divide the coefficient of the middle term by 2, square that result, and add it to the LHS and RHS.

[tex](\frac{10}{2})^2\\(5)^2\\= 25[/tex]

[tex]x^2 + 10x + 25 = -12 + 25[/tex]

[tex]x^2 + 10x + 25 = 13[/tex]

Write the LHS into the polynomial identity: [tex](a+b)^2[/tex] by factorising

[tex]x^2 + 5x + 5x + 25 = 13[/tex]

[tex]x(x + 5) + 5(x + 5) = 13[/tex]

[tex](x+5)(x+5) = 13[/tex]

[tex](x+5)^2 = 13[/tex]

Subtract 13 from the LHS and RHS.

[tex](x+5)^2 - 13[/tex]

That's it!

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