Evaluate 4+2(x+6)^2 for x=-3

x=±a

1. take the square root of both sides

Answer:

113.04

Step-by-step explanation:

A box with a square base and a top is to be constructed from 10 square meters of material. 40 square meters will maximize the volume that the box can hold.

LSD use among secondary school understudies is a specific concern. More Volume is a proportion of consumed three-layered space. It is frequently evaluated mathematically utilizing SI inferred units or by different supreme units. Volume is characterized as the space involved inside the limits of an article in three-layered space. It is otherwise called the limit of article. Volume is a proportion of consumed three-layered space. It is frequently measured mathematically utilizing the SI determined unit, the cubic meter. The volume of a compartment is by and large comprehended to be the limit of the compartment, how much liquid (gas or fluid) that the holder could hold, instead of how much space the actual holder dislodges. Three layered numerical shapes are additionally relegated volumes.

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Answer: 4r-8+4y

Step-by-step explanation: Distribution is when you multiply every term inside the parantheses by the outside term. So 4(r-2+y)=4(r)+4(-2)+4(y). This is the same as 4r-8+4y. Since none of these are like terms we have the fewest symbols possible.

The remainder when polynomial function is divide by linear function is 773.

Given that the polynomial functon f(x)=3x⁴+5 and the linear function is x+4.

As it is given that we have to find the remainder the polynomial

f(x)=3x⁴+5 is divided by the linear expression g(x)=x+4.

f(x)=3x⁴+5    .......(1)

g(x)=x+4       .......(2)

We know the remainder theorem that when a polynomial f(x) is divided by a linear expression (x−a), the remainder will be f(a).

From equation (2), we have a linear expression.

Now, on simplifying equation (2) to obtain the zero of g(x), we get

g(x)=x+4=0

x+4=0

Now, on comparing (x+4) and (x−a), we get

a=-4      ......(3)

Here, we have to get the value of f(a).

Now, using the remainder theorem, we can say that to get the remainder when the polynomial f(x)=3x⁴+5 is divided by g(x)=x+4, we have to replace x by -4 in the polynomial f(x)=3x⁴+5, we get

f(-4)=3(-4)⁴+5

f(-4)=3(256)+5

f(-4)=768+5

f(-4)=773

Therefore, the remainder when the polynomial f(x)=3x⁴+5 is divided by the linear expression g(x)=x+4 is 773.

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Answer:

108525975,11111111111111111111111

Answer: 108525975.111

Step-by-step explanation:

The populations of both towns would be​ equal in nine months.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let's assume that both town's populations will be equal in x months.

After x months, the population of the first town is given by

200x - 75x + 57,900  

The population of the second town after x months is  given by

60,600 - 175x

In order for the population of both towns to be equal, we have

200x - 75x + 57,900 = 60,600 - 175x

This is the required equation that represents the given situation.

200x - 75x + 57,900 = 60,600 - 175x

Rearrange the likewise terms and apply arithmetic operation

200x - 75x + 175x = 60,600 - 57,900

300x = 2700

x = 2700/300

x = 9

Therefore, the populations of both towns would be​ equal in nine months.

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The two equations to set up to solve the equation are 3x - 2 = 19 and 3x - 2 = -19

The equation is given as

|3x - 2| = 19

The above equation is an absolute value equation.

When it is split, the constant would be represented as positive and negative

So, the equivalent equations are

3x - 2 = 19 and 3x - 2 = -19

Hence, the two equations to set up to solve the equation are 3x - 2 = 19 and 3x - 2 = -19

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If two markers are selected at random, one after another, without replacement, the probability that both will be blue = 0.0316

For given question,

there are 20 colored markers in a package – 8 black, 4 blue, 4 red, 4 green.

if two markers are selected at random, one after another, without replacement, we need to find the probability that both will be blue.

The probability that the selecting one blue marker is:

4/20

After selecting one blue marker, there are 19 markers in a package -  8 black, 3 blue, 4 red, 4 green.

The probability of selecting second blue marker would be,

3/19

So, the probability that both will be blue:

4/20 × 3/19

= 0.2 × 0.16

= 0.0316

Therefore, if two markers are selected at random, one after another, without replacement, the probability that both will be blue = 0.0316

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The equation which can be used to determine the number of pounds of peaches and crumbles that Stephen could have purchased is 1.8x+2.5y=19.4 and if Stephen purchased 8 pounds of peaches then he also purchased 2 pounds of crumbles.

Given that the cost of peaches is $1.80 per pound and cost of crumbles is $2.50 per pound and the total expenditure done by Stephen is $19.40.

We are required to find the equation that can be used to determine the number of pounds of peaches and crumbles that Stephen could have purchased and find the number of crumbles that Stephen purchased if he had 8 pounds of peaches.

Suppose the number of pounds of peaches be x and the number of crumbles be y.

The equation will be as under:

x*1.80+y*2.50=19.40

1.80x+2.50y=19.40---------1

Put the value of x=8 to find the number of crumbles.

1.8 *8+2.50y=19.40

14.4+2.50y=19.40

2.50y=19.4-14.4

2.50y=5

y=5/2.5

y=50/25

y=2

Hence the equation which can be used to determine the number of pounds of peaches and crumbles that Stephen could have purchased is 1.8x+2.5y=19.4 and if Stephen purchased 8 pounds of peaches then he also purchased 2 pounds of crumbles.

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Answer:

Step-by-step explanation:

(-3, 2)

Horizontal is y = 2

Vertical is x = -3

In the same way (1, 4) is

y = 4

x = 1.

Average of 5 courses is 72

• In simple words, average is the number which is the representative of the list of the numbers.

• Average of numbers is calculated by the sum of the numbers divided by total numbers.

We are given that

Number of courses took by Adrianna = 4

Average of her course grade = 90

Number of course took by Roberto = 5

We also know that , Both students have the same sum of course grades

Let the average of Roberto be x

Average = Sum / Total Subjects

Sum = Average * Total Subjects

So,

90 * 4 = x * 5

x = 360/5

x = 72

Therefore, average of Roberto is 72

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There are 1176 is the minimum whole number of tiles Tomás needs to completely cover the rectangular floor.

Rectangle:

Rectangle means a four sided-polygon, having all the internal angles equal to 90 degrees. The two sides at each corner or vertex, meet at right angles.

Given,

Tomás wants to tile a rectangular floor with square tiles that measure 12 inches on a side. The floor measures 10 feet 6 inches long by 8 feet 6 inches wide.

Here we need to find if he is able to cut the tiles without waste, what is the minimum whole number of tiles Tomás needs to completely cover the floor.

Here we have to convert the feet into inches for easy calculation,

1 feet = 12 inches

So, the length is ,

l = 120 + 6 = 126 inches

w = 96 + 6 = 112 inches

So, the area of the floor is,

=> l x w

=> 126 x 112

=> 14,112

Here we need to use 12inches square tile,

So,

=> 14112 / 12

=> 1176.

Therefore, there are 1176 tiles are need to cover the floor.

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Darren's monthly payment on car loan is $210.83

Given,

Cost of the car Darren purchased = $11000

The simple interest for the car loan = 3%

Time period of loan = 5 years

We have to find the monthly payment amount:

Simple interest = PRT / 100

Where,

P = Principal amount = $11000

R = Rate of interest = 3%

T = Time period = 5 years

Now,

SI = PRT / 100

SI = (11000 × 3 × 5) / 100

SI = 110 × 3 × 5

SI = 1650

Here, the simple interest for 5 years is $1650

Now,

Total amount to be paid after 5 years = Principal amount + Simple interest

A = P + SI

A = 11000 + 1650

A = 12650

The amount to be paid after 5 years is $12650

Next,

The monthly payment amount:

Number of months in 5 years = 12 × 5 = 60 months

So,

Monthly payment amount = Total amount after 5 years / Total months in 5 years

Monthly payment amount = 12650 / 60 = 210.83

That is, the monthly payment amount on car loan is $210.83

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The linear equation for the remaining Federal Helium Reserves, r(t) = 20 -1.9t

There is 20 billion cubic feet of Helium in 2010. Helium is depleted by about 1.9 billion cubic feet each year.

Let 'r' denotes the remaining Federal Helium Reserves in billions of cubic feet.

Let 't' denotes the number of years since 2010.

We have to find a linear equation to represent the depletion of Helium through years since 2010. A linear equation will have two variables, one dependent and one independent variable. Here, let 'r' be the dependent variable and 't' be the independent variable.

Then the amount of Helium depleted in 't' years = 1.9t

So, the remaining Helium in the Federal Helium Reserve since 2010 = 20 - 1.9t.

Thus, r(t) = 20 - 1.9t

This is a linear equation because it depends on only one variable, 't'.

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The probability that i will end up with one card from each suit is 3/32.

Probability:

Probability refer the possibility of the event.

The formula for the probability of the event is,

Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes

Given,

If i choose four cards from a standard 52-card deck, with replacement,

Then we need to find the  probability that i will end up with one card from each suit.

In the first draw, we can take one card, if it is a spade one,

Then for the second draw we have 39 options

For the third draw we have 26 options

For the fourth draw we have 13 options,

So, the probability that i will end up with one card from each suit is

=> 1 x 39/52 x 26/52 x 13/52

=> 1 x 3/4 x 1/2 x 1/4

=> 3/32

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If the equation of the circle is [tex]x^{2} +y^{2}-8x+6=0[/tex] then the center and radius of the circle is (4,0) and [tex]\sqrt{10}[/tex] respectively

Given,

The equation,

[tex]x^{2} +y^{2}-8x+6=0[/tex]

Rearrange the equation

[tex]x^{2} -8x+6+y^{2} =0[/tex]

Add 10 on both sides

[tex]x^{2} -8x+16+y^{2} =10[/tex]

Change to standard form

[tex](x-4)^{2}+(y-0)^{2}=(\sqrt{10})^{2}[/tex]

Standard form of the equation of a circle is

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

Here the r is the radius of the circle and (h,k) is the center

So,

Center = (4,0)

Radius = [tex]\sqrt{10}[/tex]

Hence, if the equation of the circle is [tex]x^{2} +y^{2}-8x+6=0[/tex] then the center and radius of the circle is (4,0) and [tex]\sqrt{10}[/tex] respectively.

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Given the midpoint, the value of PT will be 10 2/7.

Q is the midpoint of PT,

so PQ = QT.

R is the midpoint of QT,

so QR=RT.

S is the midpoint off RT,

so RS=ST.

Let us say RS = ST = x .

Then, RT= RS + ST= x + x = 2x ,

so RT = QR = 2x

Then, QT = QR+RT = 2x+2x = 4x ,

and PQ = QT = 4x .

Then, PS= PQ+QR+RS=4x+2x+x=7x ,

and PT=PQ+QT=4x+4x=8x

The problem says that PS = 9

Therefore, 7x = 9 and x = 9/

PT = 8x = 8 × 9/7 = 10 2/7.

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P, Q, R, S, and T are on line k such that Q is the midpoint of segment PT, R is the midpoint of segment QT, and S is the midpoint of segment RT. If segment PS = 9, then what is PT?

Answer:

number 2. A
number 3. C

number 4. B

Step-by-step explanation:

if the answer's are correct then comment or like

Answer:

160

Step-by-step explanation:

180 (a straight angle's degrees) /9 = 20

20 * 8 = 160

Check:

160 + 20 = 180

Answer:

Answer is option A.

X cannot be equal to -4

The solution of the of the expression is as follows:

Three less than the quotient of a number and two has a result of thirteen.

Therefore,

let

the number = x

The quotient of the number and two  = x / 2

Therefore,

x  / 2 - 3 = 13

add 3 to both sides

x  / 2 - 3 = 13

x  / 2 - 3 + 3 = 13 + 3

x / 2 = 16

cross multiply

x = 2 × 16

x = 32

Therefore, the solution of the of the expression is as follows:

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The height of the building is 1122.528 feet.

Angle of elevation:

Angle of elevation means an angle between the horizontal plane and oblique line from the observer's eye to some object above his eye.

Given,

The angle of elevation to the top of a building in New York is 12° from the ground and 1 mile from the base of the building.

Here we need to find the height of the building.

We know that,

The expression for the height of the building is,

h = tanΘ × x

Where the value of

tan Θ = 12°

x = 1 mile

So, When we apply the value on the formula,

The we get,

h = tan 12° x 1

So, apply the value of tan 12 degree,

h = 0.2126 x 1

h = 0.2126 mile

Simplify the above equation using the information

1 mile = 5280 ft.

That is equal to

h = 1122.528 feet.

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Answer:

k = 2.25 or  9/4

Step-by-step explanation:

2x^2 - 6x + k = 0

2(x^2 - 3x + 2.25) = 0

x                 -1.5

x                 -1.5

-------------------------------------

(x - 1.5) (x - 1.5) = 0

x = 1.5 or 15/10 = 3/2

one solution

Answer:

Let's call the number of Twix bars "x".

Since there are three times as many Twix bars as Milky Ways, the number of Milky Ways is x / 3.

And, since there are 5 fewer Snickers bars than there are Twix bars, the number of Snickers bars is x - 5.

So, the total number of candy bars can be found by adding the number of each type of candy bar:

x + x / 3 + x - 5 = total number of candy bars

Combining like terms, we get:

5x / 3 - 5 = total number of candy bars

To find the value of x, we can solve this equation for x.

5x / 3 = total number of candy bars + 5

5x / 3 = total number of candy bars + 5

5x = 3(total number of candy bars + 5)

5x = 3(total number of candy bars) + 15

5x = 3(total number of candy bars) + 15

5x - 15 = 3(total number of candy bars)

5x - 15 = 3(total number of candy bars)

(5x - 15) / 3 = total number of candy bars

So, the total number of candy bars can be found by dividing (5x - 15) by 3. The value of x represents the number of Twix bars, and the rest of the candy bars can be found using the relationships described in the problem.

Answer:

anaaaa

Step-by-step explanation:

The meaning of the function notation is the inital amount of money (in dollars) it costs you to be a member at the YMCA

The function is given as

m(x) represents the amount of money (in dollars) it costs you to be a member at the YMCA after x months

The function notation is given as

m(0)

The function notation m(0) implies that

We determine the value of m(x) when x = 0

This represents the x-intercept of the function

The x-intercept of the function is the initial value of the function

Hence, the meaning of the function notation is the inital amount of money (in dollars) it costs you to be a member at the YMCA

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The set of ordered pairs that represents a function is: {(0, 2), (1, 4), (2, 6), (3, 6)}

We know that a function defines a relation between input and output values.

In function for each input there is exactly one output.

We need to find the set of ordered pairs that represents a function.

We need to find the set of ordered pairs such that for each x value (x coordinate) there is unique y value (y coordinate).

1) {(0, 1), (1, 3), (1, 5), (2, 8)}

This set of ordered pairs cannot be a function.

As for x = 1, there are two output values 3 and 5.

2) {(0, 0), (1, 2), (2, 6), (2, 8)}

This set of ordered pairs cannot be a function.

As for x = 2, there are two output values 6 and 8.

3) {(0, 0), (0, 2), (2, 0), (2, 4)}

This set of ordered pairs cannot be a function.

As for x = 0, there are two output values 0 and 2.

and for x = 2, the output values are 0 and 4.

4) {(0, 2), (1, 4), (2, 6), (3, 6)}

This set of ordered pairs represents a function.

Here, for each input value there is unique output value.

Therefore, the set of ordered pairs that represents a function is: {(0, 2), (1, 4), (2, 6), (3, 6)}

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