jose bought "n" packs of pencils. Each pack has 12 pencils. Write an equation to represent the total number of pencils "p" that josé bought.

Answer:

f (4) = 8

Step-by-step explanation:

f (x) =2

2 x 4 = 8

The angles represented by (2x - 60) and (60 - 2x) cannot be supplementary because their sum add up to zero instead of 180°.

Answer:

The answer is below

Step-by-step explanation:

The endpoints of AB are A(2, 3) and B(8, 1). The perpendicular bisector of AB is CD, and point C lies on AB. The length of CD is (root of 10) units.

The coordinates of point C are (-6, 2) (5, 2) (6, -2) (10, 4) . The slope of is -3 -1/3 1/3 3 . The possible coordinates of point D are (4, 5) (5, 5) (6, 5) (8, 3) and (2, 1) (4, -1) (5, -1) (6, -1) .

Solution:

Since CD is the perpendicular bisector of AC, hence line CD is perpendicular to AB and divides line AB into two equal parts.

Point C(x, y) is the midpoint of AB.

hence:

x = (2 + 8) / 2 = 5

y = (3 + 1)/2 = 2

The coordinates of point C = (5, 2)

The slope of line AB is:

slope of AB = (1 - 3) / (8 - 2) = -1/3

Since CD is perpendicular to AB, hence the product of the slope of AB and the slope of CD is -1

slope of AB * slope of CD = -1

slope of CD * -1/3 = -1

slope of CD = 3

Line CD has slope of 3 and pass through C(5, 2). The equation of line CD is:

y - 2 = 3(x - 5)

y = 3x - 13

The possible coordinates of point D are (6, 5) and (4, -1), because this point lie on line CD.

Answer:

The rate (or speed) of the wind is 40 meters per minute.

Step-by-step explanation:

Let's define:

S = speed (or rate) of the duck alone

S' = speed (or rate) of the wind.

When the duck travels with the wind, its speed is:

(S + S')

While when the duck travels against the wind, its speed is:

(S - S')

Also, remember the relation:

Distance = Speed*Time

ok, we know that the duck can travel a distance of 2400 m in 10 minutes with the wind, then:

2400m = (S + S')*10 min

And against the wind, it can travel 2/3 of that distance, then we can write:

(2/3)*2400m = (S - S')*10 min

Then we have a system of 2 equations:

2400m = (S + S')*10 min

(2/3)*2400m = (S - S')*10 min

We want to find the speed of the wind, then we want to find the value of S'.

To solve this, we first need to isolate S in one of the equations.

Let's isolate S in the first one:

2400m = (S + S')*10 min

2400m/10min = (S + S')

240 m/min = S + S'

240 m/min - S' = S

Now we can replace this in the other equation:

(2/3)*2400m = (S - S')*10 min

(2/3)*2400m = ( 240 m/min - S' - S')*10 min

Now let's solve this for S'

(2/3)*2400m/10min = 240 m/min - 2*S'

(2/3)*240 m/min = 240 m/min - 2*S'

2*S' = 240 m/min - (2/3)*240 m/min

2*S' = (1/3)*240 m/min

2*S' = 80 m/min

S' = (80 m/min)/2

S' = 40 m/min

The rate (or speed) of the wind is 40 meters per minute.

Answer:

x = - 52

Step-by-step explanation:

Given

[tex]\frac{1}{3}[/tex] x - [tex]\frac{2}{3}[/tex] = - 18 ( multiply through by 3 to clear the fractions )

x - 2 = - 54 ( add 2 to both sides )

x = - 52

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {b. \:-52}}}}}}[/tex]

[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}[/tex]

[tex] \frac{1}{3} x - \frac{2}{3} = - 18\\[/tex]

➺[tex] \: \frac{1}{3} x = - 18 + \frac{2}{3}\\ [/tex]

➺[tex] \: \frac{1}{3} x = \frac{ - 18 \times 3}{1 \times 3} + \frac{2}{ 3} \\[/tex]

➺[tex] \: \frac{1}{3} x = \frac{ - 54 + 2}{3}\\ [/tex]

➺[tex] \: \frac{1}{3} x = \frac{ - 52}{3} \\[/tex]

➺[tex] \: x = \frac{ - 52 \times 3}{3}\\ [/tex]

➺[tex] \: x = - 52\\[/tex]

[tex]\sf\pink{Therefore, \:the \:value \:of\: x\:is \:-52.}[/tex]

[tex]\sf \bf {\boxed {\mathbb {TO\:VERIFY:}}}[/tex]

[tex] \frac{1}{3} \times ( - 52) - \frac{2}{3} = - 18\\[/tex]

➼[tex] \: \frac{ - 52}{3} - \frac{2}{3} = - 18\\[/tex]

➼[tex] \: \frac{ - 52 - 2}{3} = - 18\\[/tex]

➼[tex] \: \frac{ - 54}{3} = - 18\\[/tex]

➼[tex] \: - 18 = - 18\\[/tex]

➼ L. H. S. = R. H. S.

Hence verified.

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

Answer:

y >= x/2 - 1

Step-by-step explanation:

the slope (rise/run) is 1/2 and the y-intercept is -1 so in point-slope form

y = x/2 - 1 but everything above the line (unshaded part) is valid so y is equal to or greater than.

Answer:

isosceles triangle

Step-by-step explanation:

Answer:

A, B, and, D

Step-by-step explanation:

I'm not 100% sure but i'm pretty sure these are it.

Hope thus helps!

Answer:

[tex]x = \frac{7}{2}[/tex]

Step-by-step explanation:

[tex]6^{x-1} = 36 \sqrt6\\\\6^{x-1} = 6^2 \times 6^{\frac{1}{2}}\\\\6^{x-1} = 6^{2 + \frac{1}{2} }[/tex]                        [tex][ \ a^x \times a^ y = a^{x+ y} \ ][/tex]

[tex]x - 1 = 2 + \frac{1}{2}[/tex]                          [tex][ \ b^x = b^y => x = y \ ][/tex]

[tex]x = 2 + \frac{1}{2} + 1\\\\x = 3 + \frac{1}{2} \\\\x = \frac{6+ 1}{2} \\\\x = \frac{7}{2}[/tex]

Answer:

x = 3.5

Step-by-step explanation

Using the rules of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex] and [tex]\sqrt{a}[/tex] = [tex]a^{\frac{1}{2} }[/tex]

Then

36[tex]\sqrt{6}[/tex] = 6² × [tex]6^{\frac{1}{2} }[/tex] = [tex]6^{(2+0.5)}[/tex] = [tex]6^{2.5}[/tex]

Thus

[tex]6^{x-1}[/tex] = [tex]6^{2.5}[/tex]

Since the bases on both sides are equal, both 6, equate the exponents

x - 1 = 2.5 ( add 1 to both sides )

x = 3.5

Answer:

option C

Step-by-step explanation:

Hey there!

Before we get to know an Integer and Rational Number, we have to know the Real Number system first.

1. What is Real Number System?

But do you know that the Real Number system can be broken into two categorizes? And what are them?

Real Numbers can be broken into these main two categorizes which are:

These numbers can also be broken into other categorizes as well! Crazy, ain't it? Well that's how maths work!

Anyways, we will skip Irrational Number since it is off-topic and not related to your question. We will talk about Rational Number instead.

2. What is Rational Number?

Now we know the meaning of Rational Number. But like I said, the Rational Number can be broken into other categorizes which are:

And Integers can also be broken into:

3. Conclusion and Answer

Hope this helps, and let me know if you have any doubts regarding Real Number system.

Answer:

57

Step-by-step explanation:

5|x^³-2|+7

let x=-2

5|(-2)^3-2|+7

work inside the absolute value first

5|-8-2|+7

5|-10|+7

Take the absolute value, which make it positive

5 *10+7

multiply

50+7

=57

nakita ko lng po yan but hope that helpsツ

Answer:

Correct Answer: A.

Step-by-step explanation:

A) The height of the water increases 2 inches per minute.

Step-by-step explanation:

Slope is the rate of change of height

m = (16 - 12)/(4 - 2) = 4/2 = 2

2 inch per min

Positive slope implies increase

Answer:

1/4

Step-by-step explanation:

because there 25% change

Answer:

for the blue its 1/4 or 2/8 and not likely.

For the yellow one it is 7/8 and likely.

Answer:

There is no answer

Step-by-step explanation:

because 3√5=6,7082039232 > 6

So 6-3√5 < 0

But √x always >0

So there is no answer

the answer is on the picture

Answer:

if you add 14 to 1750 you will get 1764 which equals 42²

Step-by-step explanation:

Answer:

40.2

Step-by-step explanation:

To better analyze this problem, we can first draw a picture. Looking at the one attached, we can see that the stake is represented by the point in the bottom right of the screen, and the kite is 45 meters away from it, representing the 45. Then, the height is 38, and this is directly above the 45 meters away from the stake.

This forms a right triangle, and we can use sohcahtoa to help use. As we don't have the hypotenuse, we can use tan. Tan(θ) = opposite/adjacent, or 38/45. Thus, arctan(38/45) = θ, and plugging that into a calculator, we get 40.2 as our answer

The answer to your question is 137

Given:

The two functions are:

[tex]f(x)=2x^2+1[/tex]

[tex]g(x)=3x-6[/tex]

To find:

The correct statement about the function [tex]f+g[/tex].

Solution:

We have,

[tex]f(x)=2x^2+1[/tex]

[tex]g(x)=3x-6[/tex]

Adding both functions, we get

[tex]f+g=f(x)+g(x)[/tex]

[tex]f+g=2x^2+1+3x-6[/tex]

[tex]f+g=2x^2+3x-5[/tex]

It is a quadratic function. So, option A is incorrect and option B is correct.

The domain of [tex]f+g[/tex] is all real numbers because it is defined for all real values of x. So, option C is incorrect.

The range of [tex]f+g[/tex] cannot be the all real numbers because it has a minimum value of y as the leading coefficient is positive. So, option D is incorrect.

Therefore, the correct option is B.

Answer:

7x

or 7*x

Step-by-step explanation:

Answer: F. is a linear relation.

Step-by-step explanation:

Answer:

G

Step-by-step explanation:

Equation of the eventual line:

(y-4)/(5-4) = x

y-4 = x

y = x + 4

this equation can’t be used to determine the last three values. In fact, for examples:

7 = 2 + 4

7 = 6 (false)

So the relation is non linear

Answer:

π × d

Step-by-step explanation:

The relationship between the diameter and circumference is that the circumference is equal to π multiplied by the diameter. This means that our answer is π × d, or the third option

Step-by-step explanation:

profit = sold price - bought price

= 140,000 - 60,000 k

= 80,000 k

% profit = (80,000/60,000)×100

= 133.33 %

Answer:

-1

Step-by-step explanation:

anything to the power of zero is always going to be 1 or -1

Answer:

What is 5/8 x 128? Answer: This is the same as working out 5/8 of 128. Do this by dividing by the bottom numbers, and multiplying by the top number. So 128 divided by 8 is 16, 16 times 5 is 80.