Use the Law of Syllogism to draw a conclusion from the given information.
Given: If two lines are perpendicular, then they form right angles. If two lines meet at a 90 angle, then they are perpendicular. Two lines meet at a 90 angle.
a.Conclusion: The lines are parallel.
b.Conclusion: The lines are perpendicular and meet at a 90 angle.
c.Conclusion: The lines meet at a 90 angle.
d.Conclusion: The lines form a right angle.

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 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

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:

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

The student's clues form the equation 3x + 4 = 22. When solved, this equation reveals that the original number x is 6.

The student is creating an algebraic equation to find an unknown number. Starting with the clues given:

Now, we can solve this equation to find x:

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Answer:

75

Step-by-step explanation:

97^2 = 65^2 +x^2

9409 = 4225 +x^2

9409 -4225 = 5184

Sqrt(5184) = 72

length of missing side = 72 inches

1 yard = 3 feet

1 foot = 12 inches

 so 36 inches = 1 yard

765 / 36 = 21.25 yards

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.

For the first question; we have a problem dealing with translations. Our goal is to translate the word problem into an algebraic one. So our numbers are 60, 2, and 5. Our variable, or the letter holding the unknown number's place value,  is N. 

The problem states that 60 is MORE THAN the PRODUCT of 5 and N. Focus on the words I bolded and capitalized. These are your key words that tells you what operations you need to use. Note that 'product' signals the operation of multiplication (Since the answer you get from multiplying numbers is called the 'product'.) and 'more than' signals the operation of addition (Because you are left off with more than you originally had before adding). 

Now that we know that our algebraic expression contains multiplication, addition, letter N and the numbers 2 and 5; we can start plugging the numbers in.

60 = 2 (more than) + (product of) 5N. The answer for the first attachment is B. 

_____________________________________________________________

All we need to do for the AB problem (Question 25 on your material) is solve AB.

Note 1: When a problem has no operation separating two letters or numbers, this means multiplication.

Note 2: A and B are variables. Variables are letters that stand for and hold the place of our unknown quantities. However, the values are not unknown anymore given the fact that the question tells us that A= 42 and B = 2. Thus we substitute A with 42 and B with 2, then work from there. 42 * 2 =84. Answer = A.

____________________________________________________________________

And finally, for question 26, we use PEMDAS. P = parenthesis (), E = exponent x^2, M/D = x or /, A/S means + or subtraction.

According to PEMDAS, we first solve what's parenthesis, which is 77 – 32. Using mental math, 77 – 32 = 45. ( 7 – 3 = 4 and 7 – 2 = 5.). 5/9 * 45 is what we have left. 5 divided by 9 =0.5555555555555556. 0.5555555555555556 * 45 = 25. Answer is D. 

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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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

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

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

Step-by-step explanation:

Final answer:

The volume of a sphere increases by 72.8%, which after calculations, results in a 20% increase in the radius of the sphere.

Explanation:

The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere. An increase in volume by 72.8% implies that the new volume V' is equal to 1.728 times the original volume V. To find the percentage increase in the radius, we use the relationship between volume and radius:

V' = (4/3)πr'^3, where r' is the new radius after increase. Since V' = 1.728V, we have:

After taking the cube root of both sides, we obtain:

Thus, the new radius is approximately 120% of the original radius, which means there is a 20% increase in the radius.

Final answer:

To calculate the percentage increase in the radius of the sphere when the volume is increased by 72.8%, we can use the formula for volume and solve for the new radius in terms of the original radius. The percentage increase in radius is then calculated by comparing the new and original radius.

Explanation:

The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere. If the volume of the sphere is increased by 72.8%, we can calculate the new volume by multiplying the original volume by 1 + 0.728. Let's denote the original radius as r1 and the new radius as r2.

The formula for volume can be written as V = (4/3)πr³. Substituting r1 and r2 into the formula, we get:

Since the two volumes are related by the percentage increase (1 + 0.728), we can write the equation:

(1 + 0.728)V1 = V2

Now, let's solve for r2 in terms of r1:

(1 + 0.728)V1 = (4/3)πr2³

r2 = ([(1 + 0.728)V1] * (3/4π))^(1/3)

Finally, we can calculate the percentage increase in the radius by comparing r2 to r1:

Percentage increase in radius = (r2 - r1) / r1 × 100%

Final answer:

A linear equation perpendicular to y=5 is a vertical line, expressed as x=c, where c is any real number. For instance, x=2 is perpendicular to y=5.

Explanation:

A linear equation perpendicular to y=5 would need to have an undefined slope, meaning it's a vertical line. Since y=5 is a horizontal line, a perpendicular line will have no slope value that we can put in terms of y=mx+b, where m represents the slope and b represents the y-intercept. Thus, the equation will be of the form x=c, where c is any real number. This represents a vertical line that crosses the x-axis at the point (c,0).

For example, the linear equation x=2 is perpendicular to y=5 and crosses the x-axis at the point (2,0).

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