Determine the missing information in the paragraph proof.


Given: Line PQ is rotated 90° counterclockwise to form line P’Q’. The lines are perpendicular. Line PQ contains the points (a, b) and (c, d). Line P’Q’ contains the points (–b, a) and (–d, c).


Prove: The slopes of perpendicular lines are negative reciprocals.



The slopes of lines PQ and P’Q’ can be determined using the formula m = StartFraction v 2 minus v 1 Over x 2 minus x 1 EndFraction


The product of these slopes is ________. This product shows that the slopes are negative reciprocals. It is given that the lines are perpendicular and we have shown that the slopes of the lines are negative reciprocals.

Answer:

B. 62°

Step-by-step explanation:

According to the Supplementary Angles Theorem, in this case, ∠s and 152° form a straight angle, so you use the Supplementary Angles Theorem:

-152° + 180 = 28°; 28° = m∠s

Then, use the Triangular Interior Angles Theorem to find the m∠t:

28° + 90° = 118°

↑

∠s

-118° + 180° = 62°; 62° = m∠t

I am joyous to assist you anytime.

Answer:  Option 'b' is correct.

Step-by-step explanation:

Since we have given that

Measure of exterior angle = 152°

and measure of one opposite interior angle = 90°

Measure of another opposite interior angle be 't'.

As we know that

Sum of interior angle is equal to exterior angle.

[tex]90^\circ+t=152^\circ\\\\t=152^\circ-90^\circ\\\\t=62^\circ[/tex]

Hence, the measure of t is 62°.

Therefore, Option 'b' is correct.

Answer: -0.85

Step-by-step explanation: a = score-mean/ standard deviation

Mean (add them all up and divide by amount) = 18.8745

Standard deviation =

σ2 = Σ(xi - μ)2/N

= 5.333458985499

SCORE = 14.23

= -0.85

Answer:

all work is pictured/shown

Answer:

3 with a remaider of 2

Step-by-step explanation:

10+8=18 5/18=3 with a remainder of 2

5x/8+10=2

-10 each side of the equation

5x/8=-8

multiply each side by 8

5x=-64

divide each side by 5

And then you have your answer x=12 4/5

1 cm is approximately 0.394 inches which is the fraction of an inch for 1 cm. This can be discovered by inverting the known relation (1 in = 2.54 cm) or by using dimensional analysis method.

The subject of your question concerns the conversion between the units of length, centimeters and inches. In measurement, it is known that 1 inch is equal to 2.54 centimeters. However, you asked what fraction of an inch is 1 centimeter. To find this, we need to invert the relation we know. Thus, 1 cm = 1/2.54 inches.

For a clearer understanding, 2.54 cm is exactly 1 inch (by definition). To find the fractional value of 1 cm in inches, we simply take the reciprocal (invert) of 2.54, because we are essentially asking the question, 'How many cm are there in 1 inch?'. This yields about 0.394, and thus 1 cm = 0.394 inch approximately.

Another method to understand this conversion is dimensional analysis. It tells us that we're able to convert one unit to another as long as the units are in the same dimension (in this case, length). So based on the relation 1 inch = 2.54 cm, we establish the conversion factor of 1/2.54 = 0.394 inch/cm. So 1 cm * 0.394 inch/cm gives us 0.394 inch.

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Answer: 3/4 (8x + 16) simplified expression is 6x + 12

                2x - 5x + 5 - 4 simplified expression is -3x + 1

                 x + x + x +3 + 5 - 2 simplified expression is 3x + 6

               6x - 7 + 3x + 5 simplified expression is 9x  - 2

                3 + 2(2x + 5) simplified expression is 4x + 13

Step-by-step explanation:

3/4 (8x + 16) in the example the 3 is multiplying and the 4 is dividing,

so you can start with multiplication, multiply the 3 for each value into the parenthesis after that you can place 4 as the divisor of this equation

(3 * 8x + 3 * 16) / 4

after we perform this equation the product is the following

(24x + 48) / 4

after this step you can divide the each value into the parenthesis between 4, this process give us separate equations.

(24x/ 4) + (48/4)

if you proceed with the division of each value we will find the last equation.

(24x/ 4) = 6x

(48/4) = 12

then the simplified expression is 6x + 12.

2x - 5x + 5 - 4, with this case you can resolve the equation with the similar values, for example, you can start with the values that has the x, and after that proceed with the simple values.

2x - 5x = -3x

5 - 4 = 1

after we resolve this, you only need placed the values with its sign in one equation then the simplified expression is  -3x + 1.

x + x + x +3 + 5 - 2, in this example you can start with the sum of x, and after that proceed with sum of the simple values.

x + x + x = 3x

3 + 5 - 2 = 6

after that we place the values in one expression , then the simplified expression is 3x + 6.

6x - 7 + 3x + 5, in this equation we can star with the similar values, the values with x and after that the simple values

6x + 3x = 9x

-7 + 5 = -2 ( as the 7 is bigger than 5 the result get value of the biggest number.

after you only need to place the values in one equation, then the simplified expression is 9x - 2.

3 + 2(2x + 5), with this example you can start with the product of 2 with the values into the parenthesis.

2 * (2x + 5) the 2 is passing to multiply each value into the parenthesis.

2 * 2x + 2 * 5

4x + 10

after that we can place the result of this product in the first equation

3 + 4x + 10

after that you only need to sum the similar values and we get that the simplified expression is 13 + 4x

Final answer:

Explanation of matching simplified expressions to problems in a math question that is option D is correct

Explanation:

Match the simplified expression with the correct problem:

3/4(8x + 16) matches with 6x - 7 + 3x + 5

2x - 5x + 5 - 4 matches with x + x + x + 3 + 5 - 2

x + x + x + 3 + 5 - 2 matches with 3 + 2(2x + 5)

Answer:

A=0

Step-by-step explanation:

i think this is right if not im so sorry

Answer:

[tex]\large\boxed{x=-2-\sqrt2\ or\ x=-2+\sqrt2}[/tex]

Step-by-step explanation:

[tex]3x^2+12x+6=0\qquad\text{divide both sides by 3}\\\\\dfrac{3x^2}{3}+\dfrac{12x}{3}+\dfrac{6}{3}=\dfrac{0}{3}\\\\x^2+4x+2=0\qquad\text{subtract 2 from both sides}\\\\x^2+4x+2-2=0-2\\\\x^2+4x=-2\\\\x^2+2(x)(2)=-2\qquad\text{add}\ 2^2\ \text{to both sides}\\\\x^2+2(x)(2)+2^2=-2+2^2\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+2)^2=-2+4\\\\(x+2)^2=2\iff x+2=\pm\sqrt2\qquad\text{subtract 2 from both sides}\\\\x=-2\pm\sqrt2[/tex]

Answer:

3 is your answer

Step-by-step explanation:

What you do is PEMDAS

7 + 3 + (-7) You will add 7 and 3 together first.

10 + (-7) You will subtract 10 and -7

3 is your answer.

Answer:

7.

Step-by-step explanation:

y = 2x^2 - x + 4

The derivative y' = 2*2x^(2-1) - 1

= 4x - 1

At x = 2 y' = 4(2) - 1 = 7.

Answer:

7

Step-by-step explanation:

Differentiate using the power rule

[tex]\frac{d}{dx}[/tex](a[tex]x^{n}[/tex]) = na[tex]x^{n-1}[/tex]

Given

y = 2x² - x + 4, then

[tex]\frac{dy}{dx}[/tex] = (2 × 2)x - 1 = 4x - 1

At x = 2 ⇒ [tex]\frac{dy}{dx}[/tex] = (4 × 2) - 1 = 8 - 1 = 7

Answer:

1188 divided by 12 is 99

Answer:

this is a hard one

Step-by-step explanation:

Hey there you answer is -26°F  Because, if you subtract -45 from -71 you would get -26 because it is still in the negative's place. Hope this helped! Your fellow Brainly user, GalaxyGamingKitty.

Answer:

Step-by-step explanation:

There are many ways to solve this:

- factorising

- formula

- perfect squaring

FACTORISING:

The first step would be to multiple the coefficient of x^2 and 6.

Then find which of the factors of 6 sum up to 5. (In this case it is 2 and 3.)

So you would rewrite the equation like this:

x2 -3x -2x + 6 = 0

Then factorise

x(x-3) - 2(x-3) = 0

Then factorise again

(x-2)(x-3) = 0

So if we were to divide each side by (x-2)

(x-3) =0

so x = 3

OR

if we were to divide each side by (x-3)

(x-2) = 0

x = 2

FORMULA:

The formula is

-b±[tex]{\sqrt{b^2 -4ac}[/tex] / 2a

where

ax^2 + bx + c = 0

The first step would be to substitute.

PERFECT SQUARING:

The first step would be to half the second term.

[tex](x - \frac{5}{2})^{2} - \frac{25}{4} - 6 = 0[/tex]

Then solve for x.

Answer:D

Step-by-step explanation:1 divied by 16 =16

4 divied by 64 = 16

Answer:

If i understood correctly n = 4

Step-by-step explanation:

You are looking for the smallest n that gives a result to the square root so you have to try known squares.

Since you have 60+n, you have to start with 64, 81, 100, etc

First try with 64 means n equals 4

Then you go for the next expresion and replace 4:

2(4) + 28 = 36 which is 6*6

So thats your answer

Final answer:

The smallest natural number that could be the square root of (60 + n) and (2n + 28) is 4.

Explanation:

The smallest natural number that could be √(60 + n) and √(2n + 28) is 8. To find this, we need to solve the equations:

√(60 + n) = 8 and √(2n + 28) = 8.

Squaring both sides of each equation, we get:

60 + n = 64 and 2n + 28 = 64.

Solving these equations, we find:

n = 4 and n = 18.

Since we are looking for the smallest natural number, the answer is 4.

Answer:

Step-by-step explanation:

Answer:

yes they're congruent.

The given information does not provide specific triangles or measurements needed to determine congruency, making it impossible to answer the question.

The question asks about determining whether pairs of triangles are congruent and identifying the congruence criteria (SSS, SAS, ASA).

Unfortunately, the provided information does not include any pairs of triangles or any specific measurements needed to determine congruency.

Therefore, it is not possible to answer the question based on the given information.

let's firstly convert the mixed fractions to improper fractions.

[tex]\bf \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}~\hfill \stackrel{mixed}{1\frac{3}{4}}\implies \cfrac{1\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{7}{4}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} \stackrel{size}{actual~miles}&\stackrel{size}{map~inches}\\ \cline{1-2} 210&\frac{7}{2}\\\\ x&\frac{7}{4} \end{array} \implies \cfrac{210}{x}=\cfrac{~~\frac{7}{2}~~}{\frac{7}{4}}[/tex]

[tex]\bf \cfrac{210}{x}=\cfrac{~~\begin{matrix} 7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{\stackrel{2}{~~\begin{matrix} 4\\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{~~\begin{matrix} 7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} \implies \cfrac{210}{x}=2\implies 210=2x\implies \cfrac{210}{2}=x\implies 105=x[/tex]

Answer:

1 1/14

Step-by-step explanation:

To divide by a fraction, multiply by the reciprocal of that fraction

5/7 x 12/8

Reduce the fraction with 4

5/7 x 3/2

Multiply the fractions

To multiply the fractions, multiply the numerators and denominators separately

15/14

Alternative form is

1  1/14

Answer: 15/14 or 1 1/14

Step-by-step explanation:

Answer:

12 cubic units

Step-by-step explanation:

Each square has a length of 1 unit (2units/2 squares = 1unit), therefore since the height of the prism is made up of 3 squares, its length is 3 units.

Using the equation

V = l x w x h

V = 2 x 2 x 3

V = 12 cubic units

$12870 hope this helps bebe :)

Answer:

Area of a square = side times side. Since each side of a square is the same, it can simply be the length of one side squared. If a square has one side of 4 inches, the area would be 4 inches times 4 inches, or 16 square inches.

Step-by-step explanation:

Answer:

9x + 36 = 10

Step-by-step explanation:

Given

[tex]\frac{3}{4}[/tex] x + 3 = [tex]\frac{5}{6}[/tex]

Multiply by the lowest common multiple of 4 and 6, that is 12

12 × [tex]\frac{3}{4}[/tex] x + 12 × 3 = 12 × [tex]\frac{5}{6}[/tex], that is

9x + 36 = 10 ← equation without fractions

Answer:

[tex]a=3,\text{ then } x\in(-\infty,\infty)\\ \\a\in(-\infty,3),\text{ then }x\in \left[\dfrac{-4a-8}{3-a},\infty\right)\\ \\a\in(3,\infty),\text{ then }x\in \left(-\infty, \dfrac{-4a-8}{3-a}\right][/tex]

Step-by-step explanation:

In the inequality

[tex]3x+8+2ax\ge 3ax-4a\ \ \ (1)[/tex]

a is an arbitrary real number.

Separate the terms with x into left side and the terms without x in the right side:

[tex]3x+2ax-3ax\ge -4a-8\\ \\3x-ax\ge -4a-8\\ \\(3-a)x\ge -4a-8\ \ \ (2)[/tex]

First, look at the leading coefficient at x. If this coefficient is equal to 0 (when [tex]a=3[/tex]), then the inequality is

[tex]0\ge -4a-8\\ \\0\ge -12-8\ [\text{Substituted }a=3]\\ \\0\ge -20[/tex]

This is true inequality for all x, so at [tex]a=3,[/tex] the inequality (1) has the solution [tex]x\in (-\infty,\infty)[/tex]

Now, if the leading coefficient

[tex]3-a>0\\ \\a<3,[/tex]

then we can divide the inequality (2) by this positive number [tex]3-a[/tex] and get

[tex]x\ge \dfrac{-4a-8}{3-a}[/tex]

If the leading coefficient

[tex]3-a<0\\ \\a>3,[/tex]

then we can divide the inequality (2) by this negative number [tex]3-a[/tex] and get

[tex]x\le \dfrac{-4a-8}{3-a}[/tex]

So, the answer is

[tex]a=3,\text{ then } x\in(-\infty,\infty)\\ \\a\in(-\infty,3),\text{ then }x\in \left[\dfrac{-4a-8}{3-a},\infty\right)\\ \\a\in(3,\infty),\text{ then }x\in \left(-\infty, \dfrac{-4a-8}{3-a}\right][/tex]

Answer: the false one is the last one (if a number is an integer, then it is irrational)

Step-by-step explanation:

Answer:

D is the correct answer.

2|b| = 2

2b= 2

divide by 2 to get b, by itself

2b/2= 2/2

b=1

2|b| =- 2

2b= -2

2b/2= -2/2

b= -1

Answer:

b= 1, b= -1

Answer: D because the two longer sides are 7 unites longer, meaning you need to add 14 (7x2) to the final product

Answer:

Option D [tex]4x+14[/tex]

Step-by-step explanation:

Given: The longer sides are 7 units longer than the shorter sides. The shorter side is x.

To find: Write an expression below that represents the perimeter.

Solution: It is given that the shorter side is x.

The longer side is 7 units longer than the shorter side. So, the longer side is [tex]x+7[/tex]

We know that the perimeter of the rectangle is [tex]2(\text{length}+\text{breadth})[/tex]

So, the expression for the perimeter

[tex]=2(x+x+7)[/tex]

[tex]=2(2x+7)[/tex]

[tex]=4x+14[/tex]

Hence, the expression for perimeter is [tex]4x+14[/tex].

So, option D is correct.

Answer:

6.3 kilograms

Step-by-step explanation:

Because 1 kilo is 2.2 pounds, divide 13.86 pounds by 2.2 to get 6.3 kilograms

Answer:

There are 6.3 Kilograms

Step-by-step explanation:

1 kilogram = 2.2 pounds

13.86 pounds = ? kilograms

[tex]\frac{13.86}{2.2} = 6.3[/tex]

The natural numbers for which x/8 is a proper fraction and x/4 is an improper fraction are 4, 5, 6, and 7.

Firstly, let's understand what proper and improper fractions are. A proper fraction is a fraction whose numerator is less than the denominator, and an improper fraction is a fraction whose numerator is equal to or greater than the denominator.

Given that x/8 is a proper fraction and x/4 is an improper fraction, we are looking for a number that is less than 8 (for the proper fraction) and equal to or greater than 4 (for the improper fraction). These restrictions on x mean that x must be in the range 4 ≤ x < 8.

When we consider that x should be a natural number, the only numbers that meet this criterion are 4, 5, 6, and 7. Hence, these are the natural values of x for which x/8 is a proper fraction and x/4 is an improper fraction.

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Final answer:

The values of x that meet both conditions are 5, 6, and 7.

Explanation:

In order to find natural values for x where x/8 is a proper fraction and x/4 is an improper fraction, we must first understand what proper and improper fractions are. A proper fraction is one where the numerator is less than the denominator, whereas an improper fraction has a numerator larger than or equal to the denominator. Given that x/8 must be a proper fraction, x must be less than 8. For x/4 to be an improper fraction, x must be greater than or equal to 4. Therefore, to satisfy both conditions simultaneously, x must fall within the range of 5, 6, or 7. This is because these are the only natural numbers less than 8 and greater than 4.

Answer: -79.6°F

Formula

(-62°C × 9/5) + 32 = -79.6°F

Answer:

Step-by-step explanation:

The answer is the -558.9