Write the equation 9y = 12x + 0.2 in standard form. Identify A, B, and C.
Question 19 options:

45x – 60y = 1 where A = 45, B = –60, and C = –1

45x – 1y = 1 where A = 45, B = –60, and C = 1

60x + 45y = –1 where A = 60, B = 45, and C = 1

60x – 45y = –1 where A = 60, B = –45, and C = –1

a regular polygon has all equal angles, interior and exterior, as well as all equal sides.

Check the picture below.

the one on the left is a regular octagon, as well as a convex one.

the one on the right is also an octagon, but is concave, the  issue is that, though all sides remain equal, the angles do not, and so is not a regular octagon.

Answer:

A. y=1-2x

Step-by-step explanation:

if to substitute the values of 'x'=1; 2; 3; 4 into the equations, only the 'A' is correct.

Answer:

A. y=1-2x

Step-by-step explanation:

if to substitute the values of 'x'=1; 2; 3; 4 into the equations, only the 'A' is correct.

Step-by-step explanation:

ANSWER

(-2,-1)

(3,14)

EXPLANATION

The given system is

[tex]y = {x}^{2} + 2x - 1[/tex]

[tex] y - 3x = 5[/tex]

or

[tex]y = 3x + 5[/tex]

Equate both of them:

[tex]{x}^{2} + 2x - 1 = 3x + 5[/tex]

This implies that,

[tex]{x}^{2} - x - 6 = 0[/tex]

[tex](x - 3)(x + 2) = 0[/tex]

x=-2 or x=3

When x=-2, y=y=3(-2)+5=-1

(-2,-1) is a solution.

When x=3 , y=3(3)+5=14

(3,14) is also a solution.

Answer:

Problem 12 is 112° and problem 13 is 68°

Step-by-step explanation:

Angles EPF and DPG are vertical angles; therefore, they are congruent.  That means, algebraically, that

4x + 48 = 7x

Solving for x:

48 = 3x  and  x = 16

Now that we know the value of x we can sub it back into the expression for the angle:

4(16) + 48 = 112.

For problem 13, angles DPE and EPF are supplementary, so that means that they add up to equal 180 degrees.  Therefore, 180 - 112 = 68 degrees.

Part A is incorrect because for negative numbers, the greater the magnitude the smaller the number. -2 is smaller than -1, for example, and -20 is smaller than -15.

An elevation of -15ft means 15 ft below sea level, an elevation of -20ft means 20 ft below sea level, and an elevation of (+) 7ft means 7 ft above sea level.

If John started the trail at sea level (0ft elevation), then the greatest change in elevation would be between that and the second rest stop. Take the absolute value of all the numbers and see which one is the largest.

-5°C < 4°C

An object that is cooler, or colder, than a second object means that the first object has a lower, or lesser, temperature than the second object. So, we write the inequality that states that -5°C is less than 4°C.

Answer:

The answer for this question would be 4°C > −5°C

Answer:

3.8 meters

Step-by-step explanation:

In order to find the circumference for a circle, we use the formula π(radius)²

The circumference give is 45.84 and the π given is 3.14

All we have to do is to just substitute them.

45.84 = 3.14(radius)²

45.84 / 3.14 = radius²

14.6 = radius²

radius = √14.6

radius = 3.82 ≅ 3.8

Answer:

approx. 7.3 m

Step-by-step explanation:

The formula for the circumference of a circle is  s = r·Ф, where r is the radius and Ф is the central angle in radians.

Here C = 45.84 m = 2π·r.  Solving for the radius, r, we get:

       45.84 m

r = --------------- = 7.299 m, or approx. 7.3 m.

          2(3.14)

Answer:

11 inches by 11 inches

Step-by-step explanation:

The dimensions of the original photo were 11 inches by 11 inches.

We are informed that the area of the reduced photo is 64 square inches and that In the equation (x – 3)^2 = 64, x represents the side measure of the original photo.

In order to solve for x, we shall first take square roots on both sides of the equation;

The square root of (x – 3)^2 is simply (x - 3).

The square root of 64 is ±8 but we ignore -8 since the dimensions of any figure must be positive.

Therefore, we have the following equation;

x - 3 = 8

x = 8 + 3

x = 11

Answer:

Option 1: 11 inches by 11 inches

Step-by-step explanation:

What are the choices

Answer: 8 I think!

Hope it helps

Answer:

b. (w -4)(w +1)

Step-by-step explanation:

The problem statement asks for an expression for the rug area "based on the width of the room." Looking at the answer choices, we see that the variable "w" is used to represent the width of the room.

The dimensions of the room are its width (w) and its length, which is 5 more than its width (w+5).

The dimensions of the rug are 4 ft smaller in each direction (2 ft on each side), so the width of the rug is w-4, and the length of the rug is w+5-4 = w+1.

The area of the rug is the product of its width and length, so is ...

(w-4)(w+1) . . . . . matches selection B

Answer: $47,880

Step-by-step explanation:

APEX

Answer:

Leif makes $47880 in interest.

Step-by-step explanation:

Given: Interest rate (r) = 26,100%

r = [tex]\frac{26600}{100} = 266[/tex]

Principle (p) = $180

time (t) = 1

Now we have to find the simple interest. The simple interest formula is  I=prt

Plugging in the given values, we get

I = 180×266×1

I = $47880

So Leif makes $47880 in interest.

Since [tex]X\sim\mathrm{Geom}(p)[/tex], [tex]X[/tex] has PMF

[tex]P(X=x)=\begin{cases}(1-p)^{x-1}p&\text{for }x\in\{1,2,3,\ldots\}\\0&\text{otherwise}\end{cases}[/tex]

By definition of conditional probability,

[tex]P(X=n+k\mid X>n)=\dfrac{P(X=n+k\text{ and }X>n)}{P(X>n)}[/tex]

[tex]X[/tex] has CDF

[tex]P(X\le x)=\begin{cases}0&\text{for }x<1\\1-(1-p)^x&\text{for }x\ge1\end{cases}[/tex]

which is useful for immediately computing the probability in the denominator:

[tex]P(X>n)=1-P(X\le n)=(1-p)^n[/tex]

Meanwhile, if [tex]X=n+k[/tex] and [tex]k\ge1[/tex], then it's always true that [tex]X>n[/tex], so

[tex]P(X=n+k\text{ and }X>n)=P(X=n+k)=(1-p)^{n+k-1}p[/tex]

Then

[tex]P(X=n+k\mid X>n)=\dfrac{(1-p)^{n+k-1}p}{(1-p)^n}=(1-p)^{k-1}p[/tex]

which is exactly [tex]P(X=k)[/tex] according to the PMF.

The memoryless property states that given there are no successes in the first n trials, the probability that the first success comes at trial n + k is the same as the probability that a freshly started sequence of trials yields the first success at trial k.

To show that if X ∼ Geom(p) then P(X = n + k|X > n) = P(X = k), for every n, k ≥ 1, we use the memoryless property of the geometric distribution. The memoryless property states that given that there are no successes in the first n trials, the probability that the first success comes at trial n + k is the same as the probability that a freshly started sequence of trials yields the first success at trial k. So, we have P(X = n + k|X > n) = P(X = k).

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Answer:

[tex]f^{-1}(x)=\frac{1}{2}ln(x)+2[/tex]

Step-by-step explanation:

Start by changing the f(x) into a y.  Then switch the x and the y.  Then solve for the new y.  Like this:

[tex]y=e^{2x-4}[/tex] becomes

[tex]x=e^{2y-4}[/tex]

To solve for the new y, we need to get it out of its current exponential position which requires us to take the natural log of both sides.  Since a natural log has a base of e, natural logs and e's "undo" each other, just like taking the square root of a squared number.  

[tex]ln(x)=ln(e)^{2y-4}[/tex]

When the ln and the e cancel out we are left with

ln(x) = 2y - 4.  Add 4 to both sides to get

ln(x) + 4 = 2y.  Divide both sides by 2 to get

[tex]\frac{1}{2}ln(x) + 4 = y[/tex].

Since that is the inverse of y, we can change the y into inverse function notation:

[tex]f^{-1}(x)=\frac{1}{2}ln(x)+4[/tex]

Final answer:

To find the inverse function of f(x) = e²ˣ - 4, you switch x and y, solve for the new y, and arrive at the inverse function f^-1(x) = (1/2) * ln(x + 4).

Explanation:

To find the inverse function of f(x) = e²ˣ - 4, we first need to switch the roles of x and f(x), and then solve for the new x. Here are the steps:

So, the inverse function of f(x) = e²ˣ - 4 is f-1(x) = (1/2) * ln(x + 4).

Answer:

-8a(a+3b)

Step-by-step explanation:

(2a+6b)(6b−2a)−(2a+6b)^2

(2a+6b) {(6b−2a)−(2a+6b)(2a+6b)}

2(a+3b) (6b-2a-2a-6b)

2(a+3b) (-4a)

-2(a+3b) x 4a

-2 x 4a (a+3b)

-8a(a+3b)

The  simplified expression is -8a² - 24ab.

Given expression: (2a + 6b)(6b - 2a) - (2a + 6b)^2

First, let's expand the squared term (2a + 6b)^2:

(2a + 6b)(6b - 2a) - (2a + 6b)(2a + 6b)

Now, we have a common factor of (2a + 6b) in both terms, so let's factor it out:

(2a + 6b)[(6b - 2a) - (2a + 6b)]

Now, simplify the expression inside the brackets:

(2a + 6b)[6b - 2a - 2a - 6b]

Combining like terms within the brackets:

(2a + 6b)[-4a]

Now, multiply the remaining terms:

-4a(2a + 6b)

-8a² - 24ab

Therefore, the simplified expression is -8a² - 24ab.

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Answer:

  $0.20

Step-by-step explanation:

Cost per customer is cost divided by the number of customers:

  cost/customer = $97,500/(0.65·750000) = $0.20

The cost per customer is 20¢.

Answer:

  {-12, -11}

Step-by-step explanation:

Let x represent the smaller of the two integers. The problem statement tells us ...

  x +1 = (1/3)x -7

  (2/3)x = -8 . . . . . . subtract 1/3x +1

  x = -12 . . . . . . . . . multiply by 3/2

The integers are -12 and -11.

Final answer:

To find two consecutive integers where the greater is 7 less than one-third the smaller, we defined the smaller integer as x and set up an equation: x + 1 = (x/3) - 7. Solving through algebraic operations, we found the integers to be -12 and -11.

Explanation:

To solve for two consecutive integers where the greater is 7 less than one-third the smaller integer, let us denote the smaller integer as x and the greater as x + 1. According to the problem, the greater integer (x + 1) is 7 less than one-third the smaller integer (x/3). Thus, we can set up the equation:

x + 1 = (x/3) - 7

To solve for x, we perform the following steps:

Multiply all terms by 3 to eliminate the fraction: 3(x + 1) = x - 21.

Distribute the 3: 3x + 3 = x - 21.

Combine like terms: 2x = -24.

Divide both sides by 2: x = -12.

Now that we have found the smaller integer to be -12, the greater integer is just one more, so it is -11.

Therefore, the two consecutive integers are -12 and -11.

The car, which depreciates at an annual rate of 1.4%, will be worth approximately £2590.34 in 5 years.

This is a problem related to depreciation, which is a concept in finance and economics. In this case, the car depreciates at a rate of 1.4% per year. This means that each year, the value of the car decreases by 1.4% of its value at the start of that year. This is an example of exponential decay.

To calculate the car's value after 5 years, we raise the depreciation rate (99.6%, or 0.996 in decimal form because the value decreases) to the power of 5, and then multiply it by the initial price of the car, £2700.

That is, Car Value = £2700 * (0.996)^5 = £2590.34

So, the car will be worth approximately £2590.34 in 5 years to the nearest penny.

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Answer:

[tex]\boxed{3x - y = 5}}[/tex]

Step-by-step explanation:

The coordinates of the two points are (4, 7) and (3, 4).

(a) Calculate the slope of the line

[tex]\begin{array}{rcl}m & = & \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\&= & \dfrac{7 - 4}{4 - 3}\\\\& = & \dfrac{3}{1}\\\\ & = &3\\\end{array}[/tex]

(b) Calculate the y-intercept

[tex]\begin{array}{rcl}y & = & mx + b\\7 & = & 3 \times 4 + b\\7 & = & 12 + b\\b & = & -5\\\end{array}[/tex]

(c) Write the equation for the line

y = 3x - 5

This is the point-slope form of the equation.

(d) Convert to standard form

[tex]\begin{array}{rcl}y & = & 3x - 5\\-3x + y & = & -5\\3x - y & = & -5\\\end{array}\\\text{The standard form of the equation is }\boxed{\mathbf{3x- y = -5}}[/tex]

The equation of the line in the form of Ax + By = C is 3x - y = 7.

Given that,

The equation of the line in the form Ax +By = C,

Which passes through the points (4, 3) and (3,4).

We have to determine,

The equation of the line.

According to the question,

The equation of the line in the form Ax +By = C,

The co-ordinate passes through the points (4, 3) and (3,4).

To determine the equation of the line following all the steps given below.

                   [tex]m = \dfrac{y_2-y_1}{x_2-x_2}\\\\m = \dfrac{4-7}{3-4}\\\\m = \dfrac{-3}{-1}\\\\m = 3[/tex]

                The slope of the line is 3.

                    [tex]y = mx + c\\\\7= 3 \times 4 + c\\\\7 = 12+ c\\\\c = 7-12\\\\c = -5[/tex]

                    The y-intercept of the line is -7.

                     [tex]y = mx + c \\\\y = 3x-7[/tex]

                    [tex]y = 3x - 7\\\\3x -y = 7[/tex]

Hence, The equation of the line in the form of Ax + By = C is 3x - y = 7.

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Step-by-step explanation:

A sequence is an ordered list of numbers.

lim n → ∞ an = 8 means that as n approaches infinity (becomes large), an approaches 8.

lim n → ∞ an = ∞ means that as n approaches infinity (becomes large), an approaches infinity (becomes large).

A sequence is an ordered list of numbers, and when lim n → ∞ an = 8, it means the sequence's terms approach 8 as n becomes large. Saying lim n → ∞ an = ∞ indicates that the sequence's terms grow without bound as n increases.

Answering your questions on sequences and limits:

(a) What is a sequence?

A sequence is an ordered list of numbers. Unlike a set where the order of elements does not matter, in a sequence, every number has a distinct place. For instance, the sequence of natural numbers is an ordered list starting from 1 and proceeding indefinitely in the order 1, 2, 3, 4, ... etc.

(b) What does it mean to say that lim n → ∞ an = 8?

This statement means that the terms an approach 8 as n becomes large. In other words, as you progress further along in the sequence, the values of the terms get closer and closer to 8, virtually reaching 8 as the sequence goes towards infinity. This is a fundamental concept in understanding sequences' behavior at their extremities.

(c) What does it mean to say that lim n → ∞ an = ∞?

This implies that the terms an become large as n becomes large. As the n value increases, the sequence's terms grow unlimitedly, indicating the sequence's divergence rather than converging to a definite number.

Answer:

yes, x > 4

Step-by-step explanation:

Add 7 to your inequality to get ...

3x > 12

Then divide by 3, and you have ...

x > 4

_____

We're not understanding the meaning of your " = 4" in the problem statement. It appears to have no place, either in the problem or in the solution.

Answer:

[tex]5x-40y=4[/tex]

Step-by-step explanation:

we know that

The standard form of a line is in the form Ax + By = C where A is a positive integer, and B, and C are integers

In this problem we have

[tex]8y=x-0.8[/tex]

Multiply by 5 both sides

[tex]40y=5x-4[/tex]

Adds both sides 4

[tex]40y+4=5x[/tex]

Subtract 40y both sides    

[tex]4=5x-40y[/tex]

Rewrite

[tex]5x-40y=4[/tex] ----> equation of the line into standard form

A=5

B=-40

C=4

Answer:

The total is 8.

And the total of not green is 6

so the probability is 6/8 or you can write as

3/4

Answer:

[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

[tex]\bf 2m^2+3=m\implies 2m^2-m+3=0 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{2}m^2\stackrel{\stackrel{b}{\downarrow }}{-1}m\stackrel{\stackrel{c}{\downarrow }}{+3} ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution}\qquad \checkmark\\ &\textit{two \underline{non-real roots}} \end{cases} \\\\\\ (-1)^2-4(2)(3)\implies 1-24\implies -23[/tex]

Answer:

c. 3 + 2 cosθ

Step-by-step explanation:

a = 3, b = 2

Since a > b, 1 < [tex]\frac{3}{2}[/tex] <2

we get a dimpled limacon.

Answer:

Correct option is C ) [tex]r=3+2\,cos\theta[/tex]

Step-by-step explanation:

Limacons are polar functions of the type:

[tex]r=a\pm\,b\,cos\theta[/tex]

[tex]r=a\pm\,b\,sin\theta[/tex]

Where [tex]|\frac{a}{b}|<1\,or\,1<|\frac{a}{b}|<2\,or\,|\frac{a}{b}|$\geq$2[/tex]

In provided options part (a) and (d) constants 'a' and 'b' does not satisfied the condition,

in part (b) and (c) both satisfies the condition but in part (b) we get loop  inside the sketch.

so,  [tex]r=3+2\,cos\theta[/tex] satisfies the condition of graph.

hence correct option is c )  [tex]r=3+2\,cos\theta[/tex] .

Answer:

  about 14° south of east

Step-by-step explanation:

The river speed is about ...

  (2.35 m/s)×(1 mi/(1609.344 m))×(3600 s)/(1 h) ≈ 5.2568 mi/h

The angle of interest is such that its sine is the ratio of river speed to boat speed:

  sin(α) = (5.2568 mi/h)/(21.8 mi/h) = 0.241138

  α = arcsin(0.241138) = 13.9537°

Since the river is flowing north, the boat should be directed south of its intended course by this angle.

The boat should be directed 14° south of east.

To counteract the effect of the river current, the boat should be directed slightly upstream. The specific direction can be calculated using trigonometric relationships between the boat's velocity and the river's velocity.

In order to answer this question, one must understand the basic concepts of vectors and relative velocity in physics. These concepts are essential in determining the correct direction for the ferry captain to steer the boat.

To make the journey directly across the river, the captain needs to counteract the effect of the south-to-north current. This essentially means that the boat should be directed slightly upstream. Applying basic physics concepts, the velocity of the boat relative to the ground (or the river bank) is the sum of the boat's velocity relative to the river (21.8 mph toward the east) and the river's velocity (2.35 m/s to the north).

The direction to aim can be obtained by using trigonometric relationships. The direction is tan^-1((2.35 m/s)/(21.8 mph in m/s)) to the north of east. Note that you need to convert 21.8 mph to m/s before solving.

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Answer:

27 ft

Step-by-step explanation:

I hope I helped

Answer:

C

Step-by-step explanation:

We need to write this in an algebraic form.

Therefore, the equation we would have is: [tex]x+3x+5x+2=47\\9x+2=47\\9x=45\\x=45/9\\x=5[/tex]

Thus, the longest piece is 27 feet long.

Answer:

  1.92, 3.84, 4.8, 5.76

Step-by-step explanation:

In the given set, the sum of the last two numbers is 5+6 = 11; the sum of the first two numbers is 2+4 = 6. The difference between these sums is 11-6 = 5.

You want to scale all the numbers by a factor of 4.8/5 = 0.96 so that the difference computed the same way is 4.8 instead of 5.

Then the numbers are ...

  0.96{2, 4, 5, 6} = {1.92, 3.84, 4.8, 5.76}

Answer:

[tex]\boxed{\text{1.92, 3.84, 4.80, and 5.76}}[/tex]

Step-by-step explanation:

The numbers  must be in the ratio 2:4:5:6.

Let's call them 2x, 4x, 5x, and 6x. Then

5x + 6x =  11x = sum of last two numbers

2x + 4x =    6x = sum of first two numbers

According to the condition,

11x – 6x = 4.8

        5x = 4.8

          x = 0.96

2x = 1.92; 4x = 3.84; 5x = 4.80; 6x = 5.76

The numbers are [tex]\boxed{\textbf{1.92, 3.84, 4.80, and 5.76}}[/tex]

Check:

(4.80 + 5.76) – (1.92 + 3.84) = 4.8

     10.56       –       5.76       = 4.8

                              4.8         = 4.8

OK.

Answer:

r > 17

Step-by-step explanation:

r -7> 10

Add 7 to each side

r-7+7 > 10+7

r > 17

What's the question?

Answer:

80%

Step-by-step explanation:

"He will start with the Brachiosaurus which has an estimated height of 15 meters and make the model 3 meters on height. by what percent will Ruben decrease the size of the Brachiosaurus in order to fit it into the display"

The percent decrease is the difference in heights divided by the original height.

(15 - 3) / 15

12/15

0.8

So Ruben will decrease the size by 80%.

Answer:

pizza: $4, coke: $3, chips: $2

Step-by-step explanation:

Lets make the price of a pizza=p a coke= k and a bag of chips=c

then we have the following equations

p+k+c=9

p+2k=10

2p+2c=12

Because p is common in all the equations we shall make it the subject of each equation.

p=9-(k+c)...........i

p=10-2k..............ii

p=6-c...................iii

We then equate i and iii

9-(k+c)=6-c

9-k-c=6-c

putting like terms together we get:

9-6=-c+c+k

1 coke, k=$3

replacing this value in equation ii

we get  p=10-2(3)

p=10-6= 4

1 pizza, p=$4

replacing this value in equation iii

4=6-c

c=6-4

=2

a bag of chips, c=$2

Thus, a pizza, a coke and a bag of chips= pizza: $4, coke: $3, chips: $2