Write a linear equation that is parallel to the line 3x−2y=14 and passes through the point (−6,−11) in slope-intercept form.

y=1/4x-2 is a perpendicular line and y=-4x+3 is a parallel line.

The equation y= -2 -4x in the form of slope intercept form y=mx+b is y=-4x-2.

Where m represents the slope and y intercept is -2.

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line.

The negative reciprocal of -4 is 1/4.

Therefore, the slope of the perpendicular line is 1/4.

The perpendicular line is y=1/4x-2.

We know that the parallel lines have same slope.

y=-4x+3

Hence, y=1/4x-2 is a perpendicular line and y=-4x+3 is a parallel line.

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Answer:

In one in. there is 10 mm

Answer:

The answer is 10 mm

Step-by-step explanation:

it takes 10 mm to make 1 cm

-TheUnknownScientist 72

Answer:

7:9

Step-by-step explanation:

Just divide 35 and 45 by 5.

Answer:

The constant of proportionality(Unit rate) is 0.23

Step-by-step explanation:

Given equation is:

\(P = 0.23n\)

Here

P is the price and n is the number of apples

The price is usually directly proportional to quantity so the relationship can be written as:

P ∝ n

Removing the proportionality symbol, we get

P = kn

Comparing the given equation with this equation we get

k = 0.23

Hence,

The constant of proportionality(Unit rate) is 0.23

Answer:

1) 30 pounds is the weight of the bag all together

2) science book is the heaviest book

Step-by-step explanation:

bag=4 pounds

library book=2 pounds

maths book=2×4=8 pounds

science book=8×2=16 pounds

4+2+8+16=30 pounds all together

heaviest book= science book (16 pounds)

I have 42 dimes in my piggy bank according to the given condition of 66 coins and amount $10.20 and used the system of equation as well as substitution method.

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system. A group of two or more equations that share the same variables is known as a system of equations. A set of values for a variable that simultaneously satisfy each equation is the solution to a system of equations.

Finding the value of any variable from one equation in terms of another variable is the first step in the substitution method. For instance, if there are two equations, x+y=7 and x-y=8, we can deduce that x=7-y from the first equation. Applying the substitution method begins with this.

Here,

x+y=66    ......(1)

1 dime values 10 cents.

1 quarter values 25 cents.

10x+25y=1020       ........(2)

x=66-y

10(66-y)+25y=1020

660-10y+25y=1020

15y=360

y=360/15

y=24

x=66-24

x=42

I used the system of equations and the substitution method to determine that I have 42 dime coins in my piggy bank in accordance with the requirement of 66 coins totaling $10.20.

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Step-by-step explanation:

check the image for detailed solution

well, let's say the regular price is "x", which oddly enough is the 100%, and we know the store is doing a 25% sale, that means the new prices are 100% - 25% = 75%, 75% of the regular price, so when buying item for "$x", the sale price will just be

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{75\% of x}}{\left( \cfrac{75}{100} \right)x}\implies \text{\LARGE 0.75}\cdot x\)

The program is an illustration of loops and conditional statements and the part of the complete program is

n = int(input())

for i in range(1,n+1):

  if not(i%3 == 0 or i%5==0):

The program written in Python where comments are used to explain each line is as follows:

#This gets input for n

n = int(input())

#This iterates through n

for i in range(1,n+1):

  #If the current number is not a multiple of 3 and 5

  if not(i%3 == 0 or i%5==0):

      #This prints the number

      print(i,end="")

  else:

      #This prints "Fizz", if the current number is a multiple of 3

      if i%3 == 0:

          print("Fizz",end="")

      #This prints "Buzz", if the current number is a multiple of 5

      if i%5==0:

          print("Buzz",end="")

  #This prints a new line

  print()

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Do you have a picture of your problem?

Answer: 26129.6

Step-by-step explanation:

6721 x 381 = 2560701

14 + 84 = 98

2560701  / 98 = 26129.6

Given

Write the next three terms of the arithmetic sequence. -13, -8, -3, 2, _, _, _

Procedure

-13+5=-8

-8+5=-3

-3+5=2

2+5=7

7+5=12

12+5=17

The sequence is -13, -8, -3, 2, 7, 12, 17

Answer:

\((x - 6)^2 + (y - 2)^2 = 4\)

Step-by-step explanation:

Required

The equation of the circle

The equation of a circle is:

\((x - h)^2 + (y - k)^2 = r^2\)

Where:

\(Center = (h,k)\)

\(radius \to r\)

From the graph, we have

\((h,k) = (6,2)\)

\(r = 2\)

So:

\((x - h)^2 + (y - k)^2 = r^2\) becomes

\((x - 6)^2 + (y - 2)^2 = 2^2\)

\((x - 6)^2 + (y - 2)^2 = 4\)

Answer:

Step-by-step explanation:

Range: what the numbers range from the smallest to largest.   Subtract the largest number and smallest.

Range =  9 - 1

Range = 8

Median:  Middle number.  If you listed numbers in order from smallest to largest, it is the middle number

Median = 5

Answer:

2 2/5

Step-by-step explanation:

Follow these steps to get a mixed number:

Divide 12 by 5. The quotient is 2 and the remainder is 2. The divisor remains 5. 12/5 in mixed fraction is 2 2/5

Hence, 12/5 can be written as a mixed number 2 2/5.

a) The polar coordinates of point A are (√(18), π/4).

b) The curve is a circle centered at the origin with radius 6.

c) The directed distance is the value of r, which is 6 √(3).

To find the polar coordinates of point A on the curve, we need to convert the point from Cartesian to polar coordinates. The conversion formula is:

r = √(x² + y²)

θ = arctan(y/x)

Using the values of point A, we have:

r = √((-3)² + (-3)²) = √(18)

θ = arctan((-3)/(-3)) = arctan(1) = π/4

To find the polar form of the equation x² + y² + 6y = 0, we need to convert it from Cartesian to polar coordinates. The conversion formulae are:

x = r cos(θ)

y = r sin(θ)

Using these formulae, we can rewrite the equation as:

r² cos²(θ) + r² sin²(θ) + 6r sin(θ) = 0

Simplifying this equation, we get:

r = -6 sin(θ) / (1 - cos²(θ))

To find the directed distance when θ equals 4 π over 3, we need to substitute this value of θ into the polar equation we found in Part B. Doing so, we get:

r = -6 sin(4 π/3) / (1 - cos²(4 π/3))

r = -6(-√(3)/2) / (1 - (-1/2)²)

r = 6 √(3)

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Answer:

5 thirds

Step-by-step explanation:

Make 1 2/3 into a improper fraction. Now you have 5/3. 5/3-(1/3*5)=0

Therefore, 5x1/3=5/3=1 2/3

Answer:

This guy is wrong. 1 2/3 is equal to 5/3. But that is not the answer(like that dummy above said)

The Question is asking "How many 1/3's are in 1 2/3" (5/3)

The answer is 5, not 5/3's.

Answer:

20%, 30%

Step-by-step explanation:

A diamond ring that normally sells for $1275 is now being sold at $1020

The percent mark down of the diamond ring can be calculated as follows

= 1275-1020

= 255

= 255/1275 ×100

= 0.2 ×100

= 20%

A ruby ring that sells for $290 is now being sold at $203

= 290-203

= 87

= 87/290 ×100

= 0.3×100

= 30%

Hence the percent mark down for the diamond ring and ruby ring is 20% and 30% respectively

Answer:

If cosine theta < 0 and cotangent theta > 0, then the terminal point determined by theta is in: quadrant 3.

Step-by-step explanation:

hope this helps you :) my answer is the Step-by-step explanation: and the answer :)

Considering the signals of the sine and the cosine of the trigonometric function, it is found that it's quadrant is given by:

B. Quadrant 3

In this problem, we have that the cosine is negative, and the cotangent is positive. Cotangent is cosine divided by sine, hence if it is positive, both cosine and sine have the same signal, since cos < 0, sine is negative, they are in third quadrant and option B is correct.

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Answer:

Step-by-step explanation:

d = 13.416408

For:

(X1, Y1) = (-4, -5)

(X2, Y2) = (8, 1)

Answer:

L = 9.49 units

Step-by-step explanation:

From the 1st point to the 2nd, x changes by 12; from the 1st to the 2nd, y changes (increases) by 6.  These results (12 and 6) represent the leg length of a right triangle whose diagonal length we wish to calculate using the Pythagorean Theorem:

12^2 = 144 and 6^2 = 36.

Combining these results in the length of the diagonal:

L = √(144 + 36) = √180 = 13.42 units using the Pythagorean Theorem

Rounding off, we get L = 9.49 units

Answer:

\(\textsf{B)} \quad f(x) = 5 \sin (16x) + 7}\)

Step-by-step explanation:

The sine function is periodic, meaning it repeats forever.

\(\boxed{f(x) = A \sin (B(x + C)) + D}\)

where:

Given values:

Calculate the value of B:

\(\dfrac{2\pi}{B}=\dfrac{\pi}{8}\implies 16\pi=B\pi\implies B=16\)

Substitute the values of A, B C and D into the standard formula:

\(f(x) = 5 \sin (16(x + 0)) + 7\)

\(f(x) = 5 \sin (16x) + 7\)

Therefore, the sine function with an amplitude of 5, a period of π/8, and a midline at y = 7 is:

\(\Large\boxed{\boxed{f(x) = 5 \sin (16x) + 7}}\)

Answer:

B. Positive linear

Step-by-step explanation:

First, this graph is a linear graph because a linear graph is a straight line. The graph in the diagram is also a straight line, so it is linear.
Also, notice how as x increases, y increases. This means that the graph is positive

Answer:

69.12 in.2

Step-by-step Explanation:

1/3 of 14.4 is the same as dividing 14.4 by 3

14.4÷3=4.8

To find the area, multiply the two.

So, 14.4×4.8=69.12

Answer:

There were 120 employees prior to the layoffs.

Step-by-step explanation:

x is original amount of employees

0.7x=84

divide by 0.7 both sides

x=120 employees

downsize 30% is 36, 120-36=84

Answer:

1000

Step-by-step explanation:

\(\\ \ast\sf\longmapsto -12.405\)

\(\\ \ast\sf\longmapsto -\dfrac{12405}{1000}\)

\(\\ \ast\sf\longmapsto -\dfrac{2481}{200}\)

Now

\(\\ \ast\sf\longmapsto -12\dfrac{81}{200}\)