37. Multiple Choice

Which conditional and its converse are both true?
A If x= 1, then 2x 2.
B If x= 3, then x² = 6.
DIf x² = 4, then x = 2.

C If x = 2, then x² = 4.

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.

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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Answer:3 5/7

Step-by-step explanation:

Answer:   A ----------------3 5/7

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?

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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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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Answer:

number 2. A
number 3. C

number 4. B

Step-by-step explanation:

if the answer's are correct then comment or like

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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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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Answer:

anaaaa

Step-by-step explanation:

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:

128°

Step-by-step explanation:

The three INTERIOR angles of the triangle are 90  38 and 52°  ( they sum to 180 °)    

   52 °  and 'x'  form a straight line = 180 °    so x = 128°

Answer:

128

Step-by-step explanation:

Add the two farthest angles, 90 and 38, so that's 128

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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 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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Answer:

-1/4 ,-(-1/-4) and 1/-4 are the answers please

The data is qualitative one.

Qualitative Data:

Qualitative data consists of Labels, Attributes, Descriptions

This type of data is observed not measured

Examples: Colors, categories, appearances, dogs, etc.

Basically it considers the qualities of the data.

Quantitative Data:

Quantitative data Consists of numbers or counts in the data.

This type is mainly focused on the measurement. Which means it only consider the quantities.

Examples: Length, height, area, speeds, dollar amounts, ages, etc.

Given,

The colors of automobiles on a used car lot.

Here we need to determine the given data is qualitative or quantitative.

Based on the definition of the qualitative or quantitative,

We conclude that the given data is qualitative.

Because it describe the quality of the car.

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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:

0.4761

Step-by-step explanation:

It is in the 10ths place making it bigger than 0.04761 and 0.04671

Then in the hundreths place for 0.4761  7 is bigger than the 6 in in the hundreths place of 0.4671, so the answer is

0.4761

[tex] \frac{f(x)}{g(x)} = \frac{x + 5}{ \sqrt{3x + 1} } [/tex]

[tex]x ∈ \: \: ] \frac{ - 1}{3} ,∞[[/tex]

[tex]f(x) - g(x) = x + 5 - \sqrt{3x + 1} [/tex]

[tex]x ∈ \: \: [ \frac{ - 1}{3} ,∞[[/tex]

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.

when multiplicity is removed, you get 2^(2n+1)/2 members, which is 2^(2n).

Take the power set. It has 2^(2n+1) members.

Replace any member which has n+1 or more elements with its complements.

Now the power set has members, which have n or fewer elements, and each such member appears twice.

Therefore, when multiplicity is removed, you get 2^(2n+1)/2 members, which is 2^(2n).

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The sum of the first twenty terms of the given AP is 1380.

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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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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:-4

Step-by-step explanation:

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:

160

Step-by-step explanation:

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

20 * 8 = 160

Check:

160 + 20 = 180

Considering the definition of an equation and the way to solve it, the number of points Carlos scored in the last game is 19.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:

Being:

and knowing that in the last game, Fabio had 7 points less than 2 times as many points as Carlos, the equation to determine the number of points Carlos scored in the last game is:

2C - 7= F

Fabio scored 31 points in the game. So you get:

2C - 7= 31

Solving:

2C= 31 + 7

2C= 38

C= 38 ÷ 2

C=19

Finally, the number of points Carlos scored in the last game is 19.

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