question below thanks

Answer:

math is a difficult subject

9514 1404 393

Answer:

  5x -3y = -21

Step-by-step explanation:

The parallel line will have the same x- and y-coefficients, but a constant suitable for the given point.

  5x -3y = constant

  5(-6) -3(-3) = constant = -30 +9 = -21

The equation of the line is ...

  5x -3y = -21

Answer:

Length of a side of a square = 2√2 units

Step-by-step explanation:

Let the length of a square is 'x' units.

Therefore, Area of the square A = (Side)²

                                                      = x² square units

And by Pythagoras theorem,

(Diagonal)²= (Side 1)² + (Side 2)²

                 = x² + x²

                 = 2x²

Diagonal 'p' = x√2 units

It is given in the question that area of the square is increasing four times as fast as the diagonals.

[tex]\frac{d(A)}{dt}=4(\frac{dp}{dt} )[/tex] -------(1)

[tex]\frac{d(A)}{dt}=\frac{d(x^2)}{dt}[/tex]

[tex]\frac{d(A)}{dt}=2x\frac{d(x)}{dt}[/tex]

Similarly, [tex]\frac{d(p)}{dt}=\frac{d(x\sqrt{2})}{dt}[/tex]

                      [tex]=\sqrt{2}\frac{dx}{dt}[/tex]

Now by placing the value of [tex]\frac{d(A)}{dt}[/tex] and [tex]\frac{d(p)}{dt}[/tex] in equation (1),

[tex]2x\frac{dx}{dt}=4\sqrt{2}\frac{dx}{dt}[/tex]

[tex](2x - 4\sqrt{2})\frac{dx}{dt}=0[/tex]

Since, [tex]\frac{dx}{dt}\neq 0[/tex]

[tex](2x - 4\sqrt{2})=0[/tex]

x = 2√2

Therefore, length of a side of the square is 2√2.

Answer:

730% 23% and 40%

Step-by-step explanation:

.......

Answer:

Step-by-step explanation:

This is about converting polar coordinate to rectangular

Relationship between coordinates is:

then

We have θ = 5π/6, finding the value of tan:

Substitute tan with its value:

Correct option is D

Answer:

I did option d !!

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

The perimeter is the sum of the sides, so we have

2x+x+15+4x-7=57

= 7x+8

Subtracting 8 from both sides, we get

7x= 49

Dividing 7 from both sides, we get

x=7

Our sides are then 2x=14, x+15=22, and 4x-7=21. 14 is our answer

Answer:

The shortest length of the triangle is: 14

Hence, option B is correct.

Step-by-step explanation:

Given the triangle with the lengths

Given that the perimeter of triangle = P = 57

We know that the perimeter of a triangle is the sum of the lengths of the sides of a triangle.

so

[tex]P = (x+15)+(4x-7)+(2x)[/tex]

substitute P = 57

[tex]57 = (x+15)+(4x-7)+(2x)[/tex]

switch sides

[tex]\left(x+15\right)+\left(4x-7\right)+\left(2x\right)=57[/tex]

[tex]x+15+4x-7+2x=57[/tex]

Group like terms

[tex]x+4x+2x+15-7=57[/tex]

Add similar elements

[tex]7x+15-7=57[/tex]

[tex]7x=49[/tex]

divide both sides by 7

[tex]\frac{7x}{7}=\frac{49}{7}[/tex]

simplify

[tex]x=7[/tex]

Now, measuring the lengths by substituting x = 7

Therefore, the shortest length of the triangle is: 14

Hence, option B is correct.

Answer:

Step-by-step explanation:

The distance required is the length of the tunnel added to the length of the train

Time is:

Answer:

a. The count of rolling an odd number from a sample proportion size of 100 can be approximated with a normal distribution.

Step-by-step explanation:

Whenever we roll a fair dice, the possible outcomes are { 1, 2, 3, 4, 5, 6}. In this three numbers are even numbers, i.e. {2, 4, 6}.

The probability of getting an even number is [tex]$p (\text{even}) =\frac{3}{6} = \frac{1}{2}$[/tex]

Since each of the rolls is independent and each probability of getting even remains the same.

Using the central limit theorem, the sampling distribution of a large sample, usually more than 30 can be approximated by the normal distribution. A single roll of an even or odd number cannot be approximated by a normal  distribution, it follows the Binomial distribution.

If number of rolls are large, then a normal approximation can be used.

Answer:

The count of rolling an odd number from a sample proportion size of 100 can be approximated with a normal distribution.

Step-by-step explanation:

Answer:

1/20

Step-by-step explanation:

Take 1/12 and 2/15 and find a common denomitator of 180 then multiply the tops to get 24/180 for 1/2 and 15/180 for 2/15 and then subtract to get 9/180

Finally simify to get 1/20

Answer:

Step-by-step explanation:

Discount amount:

Sale price:

Answer:

9.60

Step-by-step explanation:

i did the quiz

Answer:

4 14/15 more pounds of roast beef

Step-by-step explanation:

subtract 4 2/3 from 9 3/5

9 3/5 - 4 2/3= 4 14/15

So your answer is 4 14/15

Answer:

[tex]\displaystyle \frac{dh}{dt} = \frac{1}{20 \pi} \ cm/s[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Geometry

Calculus

Derivatives

Derivative Notation

Differentiating with respect to time

Basic Power Rule:

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle \frac{r}{h} = \frac{2}{3} \\\frac{dV}{dt} = 5 \ cm^3/s\\h = 15 \ cm[/tex]

Step 2: Rewrite Cone Volume Formula

Find the volume of the cone with respect to height.

Step 3: Differentiate

Step 4: Find Height Rate

Find dh/dt.

Answer:

NO.

Step-by-step explanation:

An irrational number cannot be written as a fraction.

Answer:

[tex]3x - 15 = 150 \\ 3x = 165 \\ x = 55[/tex]

Answer:

Solution will be 1/15625

Step-by-step explanation:

Substitute the value of first term for ar^(4-1) for the third term with 1/25 on RHS, make r the subject (which is the common ratio)

you'll get r as 1/5

Now for the eighth term, replace the "4" in the formula with "8" and a with "5" and observe the magic.

Answer:

graph attached

Step-by-step explanation:

27x - 15y = 1350

15y = 27x -1350

y = 27/15 x - 1350/15

y = 9/5 x - 90

y = mx + b     y intercept (b) = -90

y=0  x = 90 * 5/9 = 50   x intercept

Step-by-step explanation:

Given function

Easy way to find x- and y-intercepts and graph the line:

x-intercept found when y = 0

y-intercept found when x = 0

So the points are:

Plot these two points on a coordinate plane and connect with a line

Answer:

Dana has 20 French fries.

They can purchase 5 bottles.

Step-by-step explanation:

1.

Let x rep. the amount of French fries Johnathan has.

Let 2x rep. the amount of French fries Abdullah has.

Let 10x rep. the amount of french fries Dana has.

If :

x+2x+10x=26

13x=26

x=2

So Johnny boy has 2 french fries which means Dana has 10 times as much as that.

10(x)=10(2)

10x=20

Therefore Dana has 20 French fries.

2.

Well

5.12+2.77+4=$11.89

11.89/1.99= APPROX. 5.9

Note you can't buy a fraction of a bottle. We gotta round down for this question cause you can't just give less amount of cash to get an extra bottle even if it's very close. Unless your teacher said to round something.

Therefore they can only purchase 5 bottles.

===================================================

Work Shown:

Subtract the values to get 2.1-1.5 = 0.6

Brianna is off by 0.6 liters

Divide that error by the true value 1.5 to get 0.6/1.5 = 0.40

Then move the decimal point 2 spots to the right to arrive at 40%

Therefore, the percent error is 40%

------------------

The formula you can apply is:

[tex]P = \frac{|G-T|}{T}*100\%[/tex]

where

P = percent error

G = guess value (in this case it is 2.1)

T = true value (which is 1.5 in this case)

If we were to apply the formula, then we get:

[tex]P = \frac{|G-T|}{T}*100\%\\\\P = \frac{|2.1-1.5|}{1.5}*100\%\\\\P = \frac{|0.6|}{1.5}*100\%\\\\P = \frac{0.6}{1.5}*100\%\\\\P = 0.40*100\%\\\\P = 40\%\\\\[/tex]

Answer:

30 times three

Step-by-step explanation:

because all the bottom number are multiplying buy three.

Answer:

8.333

Step-by-step explanation:

F(x) α 1/ x

F(x) = k/x

F(x) = 25 ; x = 6

Lets use the information above to obtain the value of k

25 = k/6

k = 25 * 6 = 150

k = 150

Therefore, the value of f(x) when x = 18 will be :

Using the relation :

F(x) = k/x

k = 150, x = 18

F(x) = 150 / 18

F(x) = 8.333

Answer:

72 miles

Step-by-step explanation:

60% times 45 = 27

27 + 45 = 72

Answer is 72 miles

Answer:

Ema's Family would drive 72 miles

Step-by-step explanation:

Hope this helps :)

And I hope this is correct

Step-by-step explanation:

x° + (x - 34)° = 180°. (C-angles)

Thereforr 2x - 34 = 180 and x = 107.

x° = 107°.

(x - 34)° = 73°.

Answer:

1 /100

Step-by-step explanation:

Probability = (number of required outcomes / number of total possible outcomes)

Total possible outcomes = count of all 3 digit numbers ={100, 101,... 999} = 900

Required outcome = count of Three digit numbers with all 3 digits being the same = {111,222,333,444,555,666,777,888,999} = 9

Hence, probability that selected number has all 3 digits being the same :

9 / 900 = 1 /100

Answer:

[tex]\frac{12a^3b^6c^5}{3a^2b^4c^5}=4ab^{2}[/tex]

Step-by-step explanation:

Given

[tex]\frac{12a^3b^6c^5}{3a^2b^4c^5}[/tex]

Required

Simplify

[tex]\frac{12a^3b^6c^5}{3a^2b^4c^5}[/tex]

To solve this, we apply the following law of indices:

[tex]\frac{m^x}{m^y} = m^{x-y}[/tex]

[tex]\frac{12a^3b^6c^5}{3a^2b^4c^5}[/tex] becomes

[tex]\frac{12}{3}a^{3-2}b^{6-4}c^{5-5}[/tex]

[tex]\frac{12}{3}a^{1}b^{2}c^{0}[/tex]

[tex]c^0 = 1[/tex]; So, we have

[tex]\frac{12}{3}a^{1}b^{2}*1[/tex]

Finally,

[tex]4ab^{2}[/tex]

Hence:

[tex]\frac{12a^3b^6c^5}{3a^2b^4c^5}=4ab^{2}[/tex]

Answer:

36.04

The amount of the tip is approximately $

$7.00

O $7.20

0 $7.25

$7.50

Step-by-step explanation:

Answer:

He rode 20 miles in 2 hours

Answer:

[tex]Amount = 8.31[/tex]

Step-by-step explanation:

Given

[tex]Rate = 6 + 0.77t[/tex]

Required

Determine the gallons of oil lost between 1pm to 4pm

[tex]Rate = 6 + 0.77t[/tex]

Where t represents number of hours

First, we need to calculate the duration between 1pm and 4m.

[tex]t = 4pm - 1pm[/tex]

[tex]t = 3\ hours[/tex]

Substitute 3 for t in [tex]Rate = 6 + 0.77t[/tex]

[tex]Amount = 6 + 0.77 * 3[/tex]

[tex]Amount = 6 + 2.31[/tex]

[tex]Amount = 8.31[/tex]

Hence, 8.31 gallons of oil has been lost

Answer:

0.4245

Step-by-step explanation:

The probability that Z lies between -0.558 and 0.558 can be written as;

P(-0.558 < z < 0.558) = P(z < 0.558) - P(z < -0.558)

Using z - distribution table, we have;

P(z < 0.558) = 0.7122

P(z < -0.558) = 0.2877

Thus;

P(z < 0.558) - P(z < -0.558) = 0.7122 - 0.2877 = 0.4245