As Mercury revolves around the sun, it travels at a rate of approximately 30 miles per second. Convert this rate to miles per minute. At this rate, how many miles will Mercury travel in 4 minutes?

Answer:

Number 4 plot incorrectly represent on dot plot.

C is correct

Step-by-step explanation:

The following data show the number of questions different students of a class could answer in a quiz competition:

2, 4, 2, 5, 1, 4, 5, 7, 3, 5, 6, 2, 2, 5, 5, 5, 4, 6

We are given the dot plot of the data set.

 Data            :    1     2     3    4     5     6     7    

Frequency   :    1     4     1     3     6     2     1

We need to choose which data number plot incorrectly.

For 2: Number of dot should be 4, In graph also 4, 4=4 (True)

For 3: Number of dot should be 1, In graph also 1, 1=1 (True)

For 4: Number of dot should be 3, In graph also 2, 3≠2  (False)

For 5: Number of dot should be 6, In graph also 6, 6=6  (True)

Hence, number 4 plot incorrectly

Answer:  The correct option is (C) 35 sq. meters.

Step-by-step explanation:  We are given to find the area of the kitchen floor in the floor plan shown in the figure.

From the figure, we see that

the kitchen is in the form of a rectangle with length 7 meters and breadth 5 meters.

We know that

the area of a rectangle with length l units and breadth b units is given by

[tex]A=l\times b.[/tex]

For the rectangular kitchen, we have

length, l = 7 meters

and

breadth, b = 5 meters.

Therefore, the area of the kitchen floor in the floor plan is given by

[tex]A=l\times b=7\times 5=35~\textup{sq. meters}.[/tex]

Thus, option (C) is CORRECT.

Answer:

Given equations have no solution

Step-by-step explanation:

Given -

Three set of equations -

[tex]-3x-4y-3z=-7\\2x-6y+2z=3\\5x-2y+5z=9[/tex]

We will now equate "x" in the first equation in terms of "y" and "Z" and put it in second equation -

[tex]-3x-4y-3z=-7\\x = \frac{1}{3} (-4y -3z+7)\\\frac{2}{3}(-4y -3z+7) -6y+2z=3\\-8.667 y = -1.667\\y = 0.192\\[/tex]

We will substitute the value of y in the under given equation-

[tex]x = \frac{1}{3} (-4y -3z+7)\\x = \frac{1}{3} (-4*0.192 -3z+7)\\x= 2.077-z[/tex]

substituting the derived values in last equation, we get -

[tex]5x-2y+5z=9\\5(2.077-z)-2(0.192)+5z=9\\10.385-5z-0.384+5z=9\\0=-1[/tex]

Hence, the  given equations have no solution

The expression [tex]10x^5/2x^2[/tex] simplifies to [tex]5x^3[/tex] by dividing the coefficients (10/2) to get 5 and subtracting the exponents (5 - 2) in [tex]x^5[/tex] and[tex]x^2[/tex]to get 3.

To solve the given expression, [tex]10x^5/2x^2[/tex], you would first divide the coefficients and then deal with the bases (x) separately.

The coefficients (numbers without variables), 10 and 2, divide to give you: 10/2 = 5.

For the part that includes x, [tex]x^5/x^2[/tex], you subtract the lower exponent from the higher exponent because when you divide powers with the same base you subtract the exponents. So 5 - 2 = 3.

Thus, the final answer is: [tex]5x^3[/tex].

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Answer:  The correct option is (A) < .

Step-by-step explanation:  We are given to select the correct mathematical symbol that would best fill in the blank to compare the following two real numbers :

[tex]\sqrt7~~~?~~~\dfrac{14}{5}.[/tex]

First , we need to find the values of both the real numbers in decimal form.

We have

[tex]\sqrt7=2.64575...,\\\\\dfrac{14}{5}=2.8.[/tex]

Since, [tex]2.64575<2.8,[/tex] so we get

[tex]\sqrt7<\dfrac{14}{5}.[/tex]

Thus, the correct mathematical symbol is <.

Option (A) is CORRECT.

81/3 is 27

-29/2 is -14.5

The equation of the line parallel to [tex]\(5x + 2y = 12\)[/tex] and passing through the point (-2, 4) is given as [tex]\(y = -\frac{5}{2}x - 1\).[/tex]

To find the equation of a line parallel to [tex]\(5x + 2y = 12\)[/tex] and passing through the point (-2, 4), we need to follow these steps:

1. Convert the given equation[tex]\(5x + 2y = 12\)[/tex] into slope-intercept form [tex]\(y = mx + b\).[/tex]

2. Determine the slope of the given line.

3. Use the slope and the given point to find the equation of the parallel line using the point-slope form.

4. Convert the equation into slope-intercept form if needed.

Let's start with step 1:

1. Convert [tex]\(5x + 2y = 12\)[/tex] into slope-intercept form [tex]\(y = mx + b\):[/tex]

  Subtract [tex]\(5x\)[/tex] from both sides:

[tex]\[2y = -5x + 12\][/tex]

  Divide both sides by 2:

[tex]\[y = -\frac{5}{2}x + 6\][/tex]

Now, we know that the slope of the given line is [tex]\(-\frac{5}{2}\)[/tex] . Since the line we're looking for is parallel to this line, it will have the same slope.

2. The slope [tex](\(m\))[/tex] of the parallel line is [tex]\(-\frac{5}{2}\).[/tex]

Next, we use the point-slope form[tex]\(y - y_1 = m(x - x_1)\),[/tex]where [tex]\((x_1, y_1)\)[/tex] is the given point (-2, 4) and [tex]\(m\)[/tex] is the slope.

3. Substitute the values into the point-slope form:

 [tex]\[y - 4 = -\frac{5}{2}(x - (-2))\][/tex]

 [tex]\[y - 4 = -\frac{5}{2}(x + 2)\][/tex]

Now, distribute[tex]\(-\frac{5}{2}\):[/tex]

[tex]\[y - 4 = -\frac{5}{2}x - 5\][/tex]

4. Convert to slope-intercept form:

  Add 4 to both sides:

 [tex]\[y = -\frac{5}{2}x - 5 + 4\][/tex]

[tex]\[y = -\frac{5}{2}x - 1\][/tex]

So, the equation of the line parallel to [tex]\(5x + 2y = 12\)[/tex] and passing through the point (-2, 4) is [tex]\(y = -\frac{5}{2}x - 1\).[/tex]

Complete question:

What is the equation of the line that is parallel to the line 5x+2y=12 and passes through the point (-2, 4)?

the answer would be A because 3 rooms would equal 150 and that would only take 6 hours to complete.

An equation is formed of two equal expressions. The number of CDs owned by Carlin is 102.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given the following points:

Let the variables represent the following numbers as shown,

The number of CDs owned by Chad.

M = 2N ______(1)

The number of CDs owned by Carlin.

= N  ________(2)

The number of CDs owned by Bryce.

O = (6+2N) / 7

And O = 30

30 = (6 + 2N) / 7 ________(3)

From (3), the value of N can be written as,

30 = (6 + 2N) / 7

Multiply both sides by 7

30 x 7 = 6 + 2N

210 = 6 + 2N

Subtract 6 on both sides.

210 - 6 = 6 + 2N - 6

204 = 2N

Divide both sides by 2.

102 = N

N = 102

Thus, the number of CDs owned by Carlin is 102.

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Answer: here are the correct answers for the k12 test. Have a great day!!!

Step-by-step explanation:

1 yard = 3 feet

1 foot = 12 inches

 so 36 inches = 1 yard

765 / 36 = 21.25 yards

No, (2,5) is not a solution of y = 3x-10

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, an equation y = 3x-10, we need to check whether (2,5) is solution of the give equation or not,

For that put x = 2 in 3x-10 and check whether it equals to 5 or not, if not then (2,5) is not a solution of the equation,

= 3×2-10

= 6-10

= -4

∵ -4 ≠ 5

Hence, No, (2,5) is not a solution of y = 3x-10

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The amount of discount is $1.095 and the discounted sales price is $9.855.

We need to calculate the amount of discount and then subtract it from the original sales price to find the discounted sales price.

First, we calculate the amount of discount. A 10% discount on an item selling for $10.95 means we need to find 10% of $10.95. To find 10% of a number, we can multiply the number by 0.10 (which is the decimal equivalent of 10%).

Amount of discount = 10% of $10.95

= 0.10 [tex]\times[/tex] $10.95

= $1.095

Now that we have the amount of discount, we can calculate the discounted sales price by subtracting the discount from the original sales price.

Discounted sales price = Original sales price - Amount of discount

= $10.95 - $1.095

= $9.855

The missing parts of the question is required.

The blanks are

2 Definition of bisector

3 Definition of perpendicular

4 [tex]\angle AXP=\angle AXQ[/tex]

6 SAS congruence postulate

7 Corresponding parts of congruent triangles

In the given figure.

Line AX is a perpendicular bisector of PQ.

This means [tex]PX\cong QX[/tex]

[tex]\angle AXP=\angle AXQ=90^{\circ}[/tex]

[tex]AX\cong AX[/tex] because it is the same side.

[tex]\triangle AXP\cong \triangle AXQ[/tex] because of the above three points SAS congruence.

[tex]AP\cong AQ[/tex] because they are corresponding parts of congruent triangles

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x is 14.

Do the problem backwards.

19 - 8 + 3 = x

11 + 4 = x

14 = x

The solutions of the quadratic equation x² = -5x - 3 are [tex]\( x = \frac{-5 - \sqrt{13}}{2} \)[/tex] and [tex]\( x = \frac{-5 + \sqrt{13}}{2} \)[/tex].

To find the solutions of the quadratic equation x² = -5x - 3, first we rearrange it to the standard form:

x² + 5x + 3 = 0

We solve this using the quadratic formula, which is given by:

x = [tex]\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

For our equation, a = 1, b = 5, and c = 3. Substituting these values in, we get:

x = [tex]\frac{-5 \pm \sqrt{5^2 - 4*1*3}}{2*1}[/tex]

x =[tex]\frac{-5 \pm \sqrt{25 - 12}}{2}\\[/tex]

x =[tex]\frac{-5 \pm \sqrt{13}}{2}[/tex]

Hence, the solutions are:

x = [tex]\frac{-5 - \sqrt{13}}{2}[/tex] and x = [tex]\frac{-5 + \sqrt{13}}{2}[/tex]

Complete question: Which are the solutions of the quadratic equation? x² = -5x - 3

The total dollar value of the trees to the homeowner and the community will be $11,000.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

Suppose you planted 3 trees around the north and west sides of one of the houses worth $100,000 on the map. You have increased the property value of the house by $10,000. In addition, the owner will save an average of$50 per year in heating costs.

Assuming that the homeowner lives in the house for another 20 years.

Then the total dollar value of the trees to the homeowner and the community will be

⇒ 10,000 + 50 x 20

⇒ 10,000 + 1,000

⇒ $11,000

The total dollar value of the trees to the homeowner and the community will be $11,000.

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97^2 = 65^2 +x^2

9409 = 4225 +x^2

9409 -4225 = 5184

Sqrt(5184) = 72

length of missing side = 72 inches