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1. The slopes of perpendicular lines are  a negative reciprocal

2. Parallel lines have the same slope.

3. The shortest distance from any point to a line is a straight line

The slope of two perpendicular lines is such that the slope of one line is equal to the reciprocal of the negative slope of the other.

if two lines of slope m and m' are perpendicular their slopes is written as

m = -1/m'

Parallel lines grow vertically and flow horizontally at the same rate. they have the same slope, they never cross.

if two lines of slope m and m' are perpendicular their slopes is written as

m = m'

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Answer:

2(4t - 1)

Step-by-step explanation:

8t - 2

The common multiple is 2 because 2 will go into both 8 and 2. Move the multiple of 2 outside, and add ():

2(4t - 1)

The inequalities for x are

x> 0.5 and x> 1.5

Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

1. From the diagram we can see that;

3x + 2 > x + 3 (according to the length)

Solve the resulting inequality

3x - x > 3 - 2

2x > 1

x > 1/2

x> 0.5

2. Again From the figure

4x- 3 > 2x

4x -2x > 3

2x > 3

x>3/2

x> 1.5

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a.) The value of pulses exported by US in billion would be=30 billion.

b.) The ratio of wheat export of UK to maize export of IND would be= 6:5

For question a.)

To calculate the pulses, the following steps should be taken as follows:

From the bar chart, the value of pulses in billions = 30 billions.

For question b.)

The ratio of wheat export at UK and maize export at IND would be calculated as follows:

The quantity of wheat export at UK = 24

The quantity of maize export at IND = 20

Therefore, the ratio of wheat to maize = 24:20= 6:5

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Answer:

Step-by-step explanation:

There is none of these numbers are divisible by 9 and the required number is 474 divisible by 3 which the correct answer would be an option (D)

What is the divisibility rule?

The divisibility rule states that " Divisible By, implies that when two numbers are divided, the result would be a whole number.

The sum of the digits should be divisible by 9

⇒ 474 : (4+7+4=15, and again, 1+5=6)

This number is not divisible by 9

⇒ 127  : (1+2+7=10, and again, 1+0=1)

This number is also not divisible by 9

⇒ 907  : (9+0+7=16, and again, 1+6=7)

This number is also not divisible by 9

The sum of the digits should be divisible by 3

⇒ 474 : (4+7+4=15, and 15÷3 = 5)

This number is divisible by 3

⇒ 127  : (1+2+7=10, and 10÷3 = 3.333)

This number is not divisible by 3

⇒ 907  : (9+0+7=16, and  16÷3 = 5.333)

This number is not divisible by 3

There is none of these numbers are divisible by 9 and the required number is 474 divisible by 3 which the correct answer would be an option (D)

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The question seems to be incomplete the correct question would be

(a) Which numbers are divisible by 9?

(A). 474

(B). 127

(C). 907

(D). None of these

(b) Which numbers are divisible by 3?

(A). 474

(B). 127

(C). 907

(D). None of these

Answer:

Yes, they are equal because of distributive property

Step-by-step explanation:

6(1 + m) = 6 + 6m

Without explicitly solving for x, we can conclude that the solution to the equation 2^x - 2 = 8^4 is x = 12.

To solve the equation 2^x - 2 = 8^4 without explicitly solving for x, we can simplify the equation using exponent rules and observe the relationship between the numbers.

First, let's simplify the equation:

2^x - 2 = 8^4

We know that 8 can be expressed as 2^3, so we can rewrite the equation as:

2^x - 2 = (2^3)^4

Applying the exponent rule (a^m)^n = a^(mn), we can simplify further:

2^x - 2 = 2^(34)

Simplifying the right side of the equation:

2^x - 2 = 2^12

Now, we can observe that both sides of the equation have the same base, which is 2. In order for the equation to hold true, the exponents must be equal:

x = 12

Therefore, we may deduce that the answer to the equation 2x - 2 = 84 is x = 12 without having to explicitly solve for x.

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\(2(n + 5) = - 2\)

Divide sides by 2

\( \frac{2(n + 5)}{2} = - \frac{2}{2} \\ \)

\(n + 5 = - 1\)

Subtract sides 5

\(n + 5 - 5 = - 1 - 5\)

\(n = - 6\)

Done...

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Answer:

The ratio of ozone used to the total amount of water treated per day can be calculated as follows:

Ozone used = 25,000 mg

Amount of water treated = 16,000,000 liters = 16,000,000 x 1000 ml = 16,000,000 x 1000 x 1000 mg = 16,000,000,000,000 mg

Ratio of ozone used to water treated = 25,000 / 16,000,000,000,000 = 1.5625 x 10^-11

So, the ratio of ozone used to the total amount of water treated per day is approximately 1.5625 x 10^-11.

\(15.625*10^{-4}\) miligrams of ozone / liter of water.

16,000,000 liters of water

25,000 milligrams of ozone

A ratio is basically telling how much of one thing corresponds to a unit of another thing. Hence, let's express this as a division in the following fashion:

\(\frac{25,000}{16,000,000} =\\ \\\frac{0.0015625}{1} =\\ \\\frac{15.625*10^{-4} }{1}\)

\(15.625*10^{-4}\) miligrams of ozone / liter of water.

Answer:

a)

X      P[X]

0       5/14

1        15/28

2       3/28

b)

The expected value is 0.75

Step-by-step explanation:

Ok, we know that out of 8 cameras, 3 are defective.

So first let's find the probability for a camera randomly selected to be defective.

This is just the quotient between the number of defective cameras and the total number of cameras.

p = 3/8

then the probability that a camera is not defective is:

q = 5/8.

Ok, now we draw 2 cameras at random from the box.

We can define X as the number of defective cameras in these two drawn, we can have 3 possible values of X.

X = 0  (neither of the cameras is defective)

X = 1 (one of the cameras is defective)

X = 2 (both of the cameras is defective).

Let's find the probabilities for each case.

X = 0.

In this case, we first draw a non-defective camera, with a probability of:

P = 5/8.

The second camera drawn must be also non-defective, but now there are 4 non-defective cameras in the box and a total of 7 cameras (because one was already drawn).

Then the probability now is:

Q = 4/7

The joint probability is the product of the two individual probabilities:

P[0] = P*Q = (5/8)*(4/7) = (5/14)

X = 1

Here we have two cases:

the first is defective and the second is non-defective

the first is non-defective and the second is defective

So we just have a factor of 2, to consider both cases

Assuming the first case

Probability of drawing first a defective camera is equal to the quotient between the number of defective cameras  and the total number of cameras:

P = 3/8

For the second draw we want to get a non-defective camera, here the probability is equal to the number of non-defective cameras remaining (5) and the total number of cameras (7, because we drawn one)

Q = 5/7

The joint probability, taking in account the permutation, is

P[1] = 2*P*Q = 2*(3/8)*(5/7) = (15/28)

finally, for X = 2

This is the case where we draw two defective cameras, we can use a similar approach as the one used in the first case:

For the first camera:

P = 3/8

For the second camera:

Q = 2/7

Joint probability:

P[2] = (3/8)*(2/7) = 3/28

then we have the table:

X      P[X]

0       5/14

1        15/28

2       3/28

b)

The expected value for an event that has the outcomes:

{x₁, x₂, ..., xₙ}

Each one with the correspondent probability

{p₁, p₂, ..., pₙ}

is defined as:

EV = x₁*p₁ + x₂*p₂ + ... + xₙ*pₙ

Then in our case, the expected value is just:

EV = 0*P[0] + 1*P[1] + 2*P[2]

EV = 0  + 15/28  + 2*3/28

EV = (15 + 6)/28 = 21/28 = 0.75

Answer:

14

Step-by-step explanation:

(11/3)/(1/4)=14 2/3 which means you can make 14 complete bows

Answer:

There are infinitely many solutions

Step-by-step explanation:

Whatever number you plug in you'll get the same answer on both sides

Answer:

i think its infinitely many solutions

explanation; b + 14 = X and X can be anything, therefore theres many solutions

Answer: sarah made $425 and frannie made $320

Step-by-step explanation: 5 times 35 is 175 plus 250 is 425. 8 times 40 is 320.

Answer:

f(22) = 1.12

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

f(x) = 3sinx°

f(22) is x = 22

Step 2: Evaluate

Answer: 139.27

Step-by-step explanation:

So let find the area of the black swuare the length is 10 and the widith is 10, using bxh the area is 100. Now let find the aea of the semi-circle. The area of a fill circle is pi radius squared so a semi circle area will be 1/2( pi radius squared). The radius is 5 so we can calculate 1/2 of 25 pi equal = 39.27. Now let add the areas: 100+39.27=139.27.

Answer:

Slope=-1

Step-by-step explanation:

Slope=y1-y2/x1-x2

Where (X1,y1)(0,8) and (X2,y2) (4,4)

Slope=8-4/0-4

=4/-4

=-1

So slope is -1

Answer:

$1.20 less

Step-by-step explanation:

x is the unknown in the equation, the # of miles. so Matthew charges $1.30 per mile and Jayden charges $2.50. $2.50-$1.30 = $1.20.

Let be "x" the greatest distance (in miles) you can drive each day while staying withing your budget.

You know that your daily budget is $76.

Then, using the information given in the exercise, you can set up the following inequality:

As you can notice, the sum of $30 per day and $0.23 per mile must be less than or equal to $76.

Solve for "x":

- Subtract 30 from both sides of the inequality:

- Divide both sides of the inequality by 0.23:

In order to find two other two-step inequalities with the same solution, you can multiply or divide the both sides of the original inequality by the same number. Then:

Inequality 1

Inequality 2

Answers

- You can drive at most 200 miles per day.

- Inequality 1:

- Inequality 2:

Answer:

Step-by-step explanation:

10/2= 5 & 12/3= 4, so no. They are not equivalent.

Answer:

a.9π

b.v=54πcm^3

c.54(π)=169.56

Step-by-step explanation:

a. area of circle = πr^2

3^2π

9π

b. V=πr^2h

v=π(9)(6)

v=54πcm^3

c. 54(π)=169.56

Hey there!

“0.4 as a fraction”

= 0.4 * 10/10

= 0.4/1 * 10/10

= 4 ÷ 2 / 10 ÷ 2

= 2/5

0.4 = 2/5

Therefore, your answer is: 2/5

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

by congrency rule asa

Step-by-step explanation:

i hope it's helpful for you

If n is devisible by 3 then n^2 is devisible by 3 it easy.

n=3k so n^2=9k so 9 is devisible by 3.

In the other way, if n^2 is devisible by 3we have n^2=3k wher k is integer number which has to be devisible by 3. If k is not devisible by 3, then n=/sqrt3*r , r^2=k. So n is not integer, contradiction.

This proof show us that iff doesnt work.

If n is devisile by 4 then n^2 is also devisible by 4. But if we have that n^2 is devisibke by 4 then n hasn’t be devisible by 4. Example: n^2=36 is dev by 4 but n=6 is not dev by4.

Its allow because /sqrt 4 is 2.

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Answer:

C

Step-by-step explanation:

For these types of problems, its important that we focus on the base as well as the lengths of the base and any other given lengths.

Here, the net has a base that forms a square with side lengths of 8mm.

So automatically, we can eliminate choices a and d as both have a base that is a triangle rather than a square.

We've also noticed that the base has a length of 8mm

If we look at B and C closely, we can tell that B has base lengths of 10mm while C has base lengths of 8mm.

So C is the correct answer choice.

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Answer: The third arc should be drawn centered at point F.

Step-by-step explanation:

Answer:

She will sell the shoes for 90 dollars

Step-by-step explanation:

First find the markup

50 * 80%

50 *.8

40

Add this to the original price

50+40 = 90

She will sell the shoes for 90 dollars

Answer: 0.655

Step-by-step explanation:

Let X be a random variable that represents percent of fat calories that a person in America consumes each day.

As per given , X is normally distributed with a mean \(\mu=36\) and a standard deviation \(\sigma=10\).

Sample size : n= 16

The probability that the average percent of fat calories consumed is more than 35:

\(P(\overline{X}>35)=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{35-36}{\dfrac{10}{\sqrt{16}}})\\\\=P(Z>\dfrac{-1}{\dfrac{10}{4}})\ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=P(Z>\dfrac{-4}{10})\\\\=P(Z>-0.4)\\\\=P(Z<0.4)\ \ \ [P(Z>-z)=P(Z<z)]\\\\=0.655\ \ \ [\text{By p-value table}]\)

Hence, Required probability =0.655

Answer:

The correct answer is :

1. Line PQ (One line PQ).

Step-by-step explanation:

The first step to solve this question is to draw the plane A with the points P and Q lying on it.

We know that given two different points there is only one line that contains this two different points.

Let's analyze each option.

''2. Lines PQ and QP''

This option is wrong because there aren't two different lines. In fact it is only one line that can be named line PQ or line QP.

''3. The 2 lines PQ and QP plus another line that does not lie in plane A.''

This option is assuming that exist three lines that contain P and Q. This option is also wrong.

''1. Line PQ''

This option is correct. It will be clarify with the drawing I will attach.

''We can't name them all!''

This option is assuming that exist infinite lines that contain P and Q. This option is wrong.

In the drawing I call the line that contains P and Q as line L.

Given that P and Q lie in plane A necessarily the line L must lie on the plane A.

Only one line contains points P and Q

The given parameters are:

There are at least two points in a line

This means that, a line can contain points P and Q, and any other points

Hence, only one line contains points P and Q

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Step-by-step explanation:

8 cm² is the correct answer for that question

Given:

Board Length = 3/4

6 equal pieces = 3/4 ÷6

= 3/4 × 1/6

= 1/4 × 1/2

= 1/8

Therefore each equal piece will be 1/8 feet long

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