Evaluate when a= 4 and b = 50.
b-6a​

Answer:

x^3+4x^2−23x+6

Step by Step:

(x−3)(x2+7x−2)

=(x+−3)(x2+7x+−2)

=(x)(x2)+(x)(7x)+(x)(−2)+(−3)(x2)+(−3)(7x)+(−3)(−2)

=x3+7x2−2x−3x2−21x+6

=x3+4x2−23x+6

The best description of the transformation for the image being projected on the retina is A. A dilation with a scale factor between 0 and - 1 and center at the nodal point.

An mage is inverted and reversed as it passes through the lens of the eye, and is then projected upside down and reversed onto the retina. The process of transforming the image is called "rectification."

In mathematical terms, a dilation would have taken place because the object was shrunken by the eyes at the nodal point. When an object shrinks , then the scale factor is between 0 and 1 but because this image is inverted, the scale factor is between 0 and - 1.

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An integral for the volume of the solid obtained by rotating the region in the first quadrant bounded by the curves y = tan² x, y = 3, and x = 0 about the line y = 3 is V = ∫[0, arctan(√3)] 2πx(3 - tan²(x)) dx.

The method of cylindrical shells can be used to set up the integral for the solid's volume after rotating the first quarter region defined by the curves y = tan² x, y = 3, and x = 0 about the line y = 3.

We must take into account an infinitesimally thin strip of width dx at a distance x from the y-axis in order to set up the integral.

This cylindrical shell's volume can be estimated by multiplying its height, radius, and thickness (dx) together. Consequently, each shell's volume is as follows:

dV = 2πx(3 - tan²(x)) dx

Setting 3 = tan²(x), we have:

tan²(x) = 3

tan(x) = √3

x = arctan(√3)

Thus, the integral for the volume of the solid is: V = ∫[0, arctan(√3)] 2πx(3 - tan²(x)) dx

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The standard deviation of the monthly amount charged is 346.41

Step 1: Identify the values of a and b, where [a , b] is the interval over which the continuous uniform distribution is defined.

Since it takes between 300 and 1500 minutes to be seated at the restaurant, we have:

a = 300

b = 1500

Step 2: Calculate the variance using the formula Var(x) = \(\frac{(b-a)^{2} }{12}\)

Using the formula for the variance and the values identified in step 1

(a = 300 , b = 1500), we have:

Var(x) = \(\frac{(b-a)^{2} }{12}\)

         = \(\frac{(1500 - 300)^{2} }{12}\)

         = 1440000/12

         = 120,000

the variance is 120,000

Step 3: Calculate the standard deviation by taking the square root of the variance. σ = \(\sqrt{Var(x)}\)

The standard deviation is the square root of the result from step 2 (variance = 120,000)

σ = \(\sqrt{Var(x)}\)

σ = \(\sqrt{120000}\)

   = 346.41

The standard deviation of the monthly amount charged is 346.41

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Answer:

4x + 11 is the answer when you combine like terms

The shortest distance between the first and third base is 127.28 feet.

The shortest distance can be determined using Pythagoras theorem.

The Pythagoras theorem: \(\sf a^2 + b^2 = c^2\)

where:

a = length

b = base

c = hypotenuse

\(\sf 90^2+ 90^2\)

\(\sf 8100 + 8100\)

\(\sf = \sqrt{16200} = 127.28 \ foot\)

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Answer:

3/4 cups

Step-by-step explanation:

1/8 for 1/3 refipe

1/8 * 3 = 3/8

3/8 for 1 whole recipe

3/8 * 2 = 6/8 = 3/4

3/4 for 2 whole recipes

Answer:

27x^6 y^9

z^9

Step-by-step explanation:

That should be the answer,if not...sorry!:)

Answer:

Step-by-step explanation: y= x -2 i hope this helps

Answer: Neither

Step-by-step explanation:

We would solve this as angle, side, side. Unfortunately, there are no bad words in math. For your specific case it would be Neither, but it really would be HL (Hypotenuse leg)

Answer:

235

Step-by-step explanation:

to get 235 first you get your #'s  

# 1= 90

#2= 90

#3= 55

Add!

90

90

55

_____

235

A) The annual growth rate between 1993 and 2004, is approximately 5.68%.  B) Converting the growth rate from part A to percentage form, is approximately 5.68%.  C) Assuming the house value continues to grow at the same annual growth rate, the estimated value in the year 2009 would be approximately $215,000

A) The annual growth rate between 1993 and 2004, assuming exponential growth, can be calculated using the formula: growth rate = (final value / initial value) ^ (1 / number of years) - 1. In this case, the initial value is $95,000, and the final value is $165,000. The number of years is 2004 - 1993 = 11. Plugging these values into the formula, we get: growth rate = (165,000 / 95,000) ^ (1 / 11) - 1 ≈ 0.0568.

B) Converting the growth rate from part A to percentage form, we multiply it by 100. Therefore, the correct answer in percentage form is approximately 5.68%.

Now let's move on to part C. Assuming the house value continues to grow at the same percentage, we can calculate the value in the year 2009. We know that the value in 2004 was $165,000. To find the value in 2009, we need to calculate the growth over a period of 5 years. Using the growth rate of 5.68% (or 0.0568 as a decimal), we can calculate the value in 2009 as follows: value in 2009 = value in 2004 (1 + growth rate) ^ number of years = 165,000 (1 + 0.0568) ^ 5 ≈ $215,291.

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Answer:

The ratios 2.56/32 and 0.48/6 are equivalent; y = 0.08x.

Step-by-step explanation:

$2.56 for 32 oz is a unit price of $2.56/(32 oz) = $0.08/oz

$0.48 for 6 oz is a unit price of $0.48/(6 oz) = $0.08/oz

The unit prices are equal, so the cost of both sizes are proportional.

If x is the weight in oz, multiply the weight by 0.08 to get the cost, y, in dollars.

y = 0.08x

The ratios 2.56/32 and 0.48/6 are equivalent; y = 0.08x.

Answer:

Distance of boy from tree (base) = 6.3 m (Approx.)

Step-by-step explanation:

Given:

Height of tree (perpendicular) = 9 m

Given angle = 55°

Find:

Distance of boy from tree (base)

Computation:

Using trigonometry function

tanθ = Perpendicular / Base

tan 55 = 9 / Base

1.4281 = 9 / Base

Base = 6.3

Distance of boy from tree (base) = 6.3 m (Approx.)

Greetings from Brasil...

Here we have supplementary angles, that is, the sum of both results in 180. Therefore,

A + B = 180 ⇔ ∠1 + ∠2 = 180

∠1 + ∠2 = 180     by defining supplementary angles

143 + ∠2 = 180

∠2 = 180 - 143

The probability that the dart lands inside the triangle is \(\frac{1}{4}\).

we know that

Probability = \(\frac{Favourable outcomes}{total outcomes}\)

Probability = \(\frac{162}{648} = \frac{1}{4}\)

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Answer:

25%.

Step-by-step explanation:

The equation of a line is given by the equation;

From the given graph, the intercept on y-axis is 7.

To find the slope, we would make use of the slope formula given as:

From the graph, we have:

Hence, the equation of the line is:

We can estimate with standard deviation of 8 that the true population mean length of adult corn snakes is between 53.88 and 62.12 inches.

What is standard deviation?

Standard Deviation is a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean. it's a well-liked live of variability as a result of it returns to the first units of live of the info set.

Main body:

x = ​ 58

σ = ​ 8

n = ​ 25

z α/2​​ = ​ 2.576

(53.88, 62.12)

the given values σ=8, n=25, and z α/2=2.576 for a confidence level of 99%, we have

margin of error=(2.576)(8/√25)

≈ (2.576)(1.6)

≈4.12

With x¯=58 and a margin of error of 4.12, the confidence interval is

(58−4.12,58+4.12)

= (53.88 , 62.12).

therefore we can estimate with 99% confidence that the true population mean length of adult corn snakes is between 53.88 and 62.12 inches.

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To create a sinusoidal function with an amplitude of 4, minimum at 2, and horizontal phase shift of 45 degrees, use the following formula:\(f(x)=a\sin(bx-c)+d\)

Where a is the amplitude, b is the horizontal stretch or shrink, c is the horizontal phase shift, and d is the vertical shift.

Using the values provided in the question, we get: Amplitude, a = 4(minimum), d = 2, Horizontal phase shift, c = 45 degrees.

The value of b can be found using the formula,\(b = 360/period\). Since we are not given a period, we can assume it to be 360 degrees, which makes b = 1.

Substituting the values into the formula,\(f(x)=4\sin(x-\frac{45}{1})+2\Rightarrow f(x)=4\sin(x-45)+2\).

Therefore, the required sinusoidal function is \(f(x)=4\sin(x-45)+2\).

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0.625

Explanation:
We know that 0.125 is equal to 1/8, so you can then multiply 0.125 by 5.

Dividing 5/8, It's Equal To 0.625

Step-by-step explanation:

5/8 = O.625

Given:

The vertices of parallelogram PQRS are P(-5,5) Q(2,5) , R(4,-3) and S(-3,-3).

To find:

The intersection of the diagonals of parallelogram PQRS.

Solution:

We know that the diagonals of a parallelogram bisect each other.

In parallelogram PQRS, PR and QS are the diagonals of the parallelogram.

It means the intersection of PR and QS is the midpoint of PR and QS.

Midpoint formula:

\(Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)\)

Midpoint of diagonal PR is:

\(Midpoint=\left(\dfrac{(-5)+4}{2},\dfrac{5+(-3)}{2}\right)\)

\(Midpoint=\left(\dfrac{-1}{2},\dfrac{2}{2}\right)\)

\(Midpoint=\left(-0.5,1\right)\)

Therefore, the coordinates of the intersection of the diagonals of parallelogram PQRS are (-0.5,1).

If 624 minutes are used, the total cost will be dollars is $2,493.92.

Part A :

With the information given in the problem, we know that (i) "if a customer uses 150 minutes, the monthly cost will be $83" and (ii) "if the customer uses 980 minutes, the monthly cost will be $332."

From the information given in (i), we can set up the equation where y = total monthly payment = 83, x = minutes = 150, and where b = monthly fee which is an unknown value.

This gives the equation : y = mx+b --> 83 = 150m + b

*Note: m = the slope = rate, which can be defined as the $/min.

From the information given in (ii), we can set up the equation where y = total monthly payment = 332, x = minutes = 980, and where b = monthly fee which is an unknown value.

This gives the equation: y = mx + b --> 332 = 980m + b

At this point, we have two equations with two unknown values, m and b which are constant in both equations. The values that were given are the (x,y) values. To find the unknown m and b values, we can first use an equation to isolate one of the variables.

Solving for m:

From the first equation, b = 83 - 150m.

We can substitute this value of b into the second equation: 332 = 980m + (83 - 150m)

Solve for m:

332 - 83 = 980m - 150m

249 = 830m

m = 3.33

Solving for b:

From the first equation, since solving for m, we know that 83 = 150(3.33) + b

Now, we know that b = 83 - (150)3.33 = 416.50

Answer for Part A: y = 3.33 x + 416

Part B:

Using the equation y = 3.33 x + 416, we can substitute 624 minutes for x.

y = 3.33 (624) + 416

y = 2493.92

Answer for Part B: If 624 minutes are used, the total cost will be $2,493.92.

Hence the answer is If 624 minutes are used, the total cost will be dollars is $2,493.92.

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Answer:

52

Step-by-step explanation:

A=2(wl+hl+hw)=2·(2·3+4·3+4·2)=52

Answer:

A=bxh

=3x4

=12

(12 x a total of 2 same sides =24)

A=bxh

= 3x2

=6

(6x2=12)

A= bxh

= 2x4

= 8

(8x2=16)

24 + 12 +16 =52

Total surface area is 52

Hope this helps!

Answer:

The equation has only one solution, x = -9

Step-by-step explanation:

We want to find how many solutions the equation:

8x = -9 + 7x

has.

To find it, let's simplify the equation.

First, let's move all the terms with x to the left side, and the terms without x to the right side:

8x - 7x = -9

(8 - 7)*x = -9

1*x = -9

x = -9

So we can see that we have only one solution, x = -9

Answer:

y = 3x - 8

Step-by-step explanation:

Slope = m = 3 ; (2 , -2)

Equation : y = mx + b

Plug in x = 2 and y = -2 in the above equation

-2 = 3*2 + b

-2 = 6 + b

-2 -6 = b

b = -8

Equation:  y = 3x - 8

Answer: m=6

Step-by-step explanation:

\(9+12m=6+15\left(m-1\right)\)

\(6+15\left(m-1\right)=15m-9\)

\(9+12m=15m-9\)

subtract 9 on both sides

\(9+12m-9=15m-9-9\)

\(12m=15m-18\)

subtract 15m on both sides

\(12m-15m=15m-18-15m\)

\(-3m=-18\)

divide by -3 on both sides

\(\frac{-3m}{-3}=\frac{-18}{-3}\)

since \(\frac{-a}{-b}=\frac{a}{b}\)

\(\frac{-18}{-3}=6\)

\(m=6\)