Find the domain and range of the function below

Answer: I believe the answer is 8 although I might be wrong. The reason why is because both of the numbers have 8 when you break down their multiples and its the greatest value.

Step-by-step explanation:

16: 1,16 2,(8) 4,4

24: 1,24 2,12 3,(8) 4,6

Multiply the numerator together and the denominators together.

1 x 5 / 6 . 7 = 5/42

42 is not a multiple of 5 so the answer is already in the lowest term.

The answer is 5/42

Answer:

x ≥5  or  5 ≤x

Step-by-step explanation:

2x ≤ 5x - 15

Subtract 5x from each side

2x-5x ≤ -15

-3x ≤-15

Divide each side by -3, remembering to flip the inequality

-3x/-3 ≥ -15/-3

x ≥5

Check x=10

2*10 ≤5*10 -15

20 ≤50 -15

20 ≤35

True

Answer:

360 more pencils.

45x18=810 large pencils

25x18=450 small pencils

810-450+360

Step-by-step explanation:

       </3 PureBeauty

Answer:

360

Step-by-step explanation:

So we do 45*18 for the large boxes which is 810 and 25*18 for the small boxes which is 450 so now we subtract 450 from 810 which is 360!

Answer:

probably 4 times since it is not 100% accurate I guess

The angle made by an arc at the centre of the circle is double the angle made by the same arc at any point on the circle. The measure of the angle θ will be 45°.

According to the arc and subtended angle theorem, The angle made by an arc at the centre of the circle is double the angle made by the same arc at any point on the circle.

The angle made by an arc at the centre of the circle is double the angle made by the same arc at any point on the circle. Therefore, the measure of the angle θ will be half the measure of the ∠P.

As it can be observed the measure of the angle ∠P is 90°, therefore, the measure of the angle θ can be written as,

∠P = 2 × ∠θ

90° = 2 × ∠θ

∠θ = 45°

Hence, the measure of the angle θ will be 45°.

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Step-by-step explanation:

Per year it goes up by $180

What about in 5years?

180×5=900

1400+900=2300

=$2300

Answer:

$2,120

Step-by-step explanation:

180 times 4 = 720

1,400 + 720 = 2,120

Year 1: $1,400 a month

Year 2: $1, 580 a month

Year 3: $1,760 a month

Year 4: $1,940 a month

Year 5: $2,120 a month

Answer:

A.

Step-by-step explanation:

55x is the number of hours

then the initial 150 needs to equal less that $450

Answer:

it is 13x=2

Step-by-step explanation:

i ran the math through my multipurpose calculator

Answer:

32.60

Step-by-step explanation:

cause u multiple y by 5 just trust me

These sketches represent the invariant curves for each transformation, indicating the paths that the points on the complex plane take when transformed by the given functions.

To evaluate \((sqrt3 - i)^{10}\), we can use De Moivre's theorem, which states that for any complex number z = r(cosθ + isinθ) raised to the power of n, the result is:

\(z^n = r^n\) (cos(nθ) + isin(nθ)).

In this case, z = √3 - i, so we have:

z = √3(cos(θ) + isin(θ)),

where θ is the argument of z.

To find θ, we can use the arctan function:

θ = arctan(-1/√3) = -π/6.

Substituting the values into De Moivre's theorem:

(√3 -\(i)^{10}\) = (√3\()^{10}\) (cos(-10π/6) + isin(-10π/6))

             = 3^5 (cos(-5π/3) + isin(-5π/3))

             = 243 (-1/2 - i√3/2)

             = -121.5 - 210.315i.

Therefore, (√3 - i)^10 is approximately -121.5 - 210.315i.

Now, let's sketch a few invariant curves for the given transformations:

a. f(z) = 2z:

To sketch the invariant curves for f(z) = 2z, we can consider points on the complex plane and multiply them by 2.

If we take a point z = x + yi, where x and y are real numbers, the transformed point f(z) = 2z becomes:

f(z) = 2(x + yi) = 2x + 2yi.

So, the transformed point has its real and imaginary parts scaled by a factor of 2.

b. g(z) = \(e^{(i\pi /4)}\) * z:

To sketch the invariant curves for g(z) = \(e^{(i\pi /4)}\) * z, we can consider points on the complex plane and multiply them by \(e^{(i\pi /4)}.\)

If we take a point z = x + yi, where x and y are real numbers, the transformed point g(z) = \(e^{(i\pi /4)}\) * z becomes:

g(z) = \(e^{(i\pi /4)}\) * (x + yi) = \(e^{(i\pi /4)}\)x +\(e^{(i\pi /4)}\)yi.

So, the transformed point has its real part scaled by e^(iπ/4) and its imaginary part scaled by e^(iπ/4).

c. h(z) = \(2e^{(i\pi /4)}\)) * z:

To sketch the invariant curves for h(z) = 2\(e^{(i\pi /4}\)) * z, we can consider points on the complex plane and multiply them by 2\(e^{(i\pi /4)}\).

If we take a point z = x + yi, where x and y are real numbers, the transformed point h(z) = 2\(e^{(i\pi /4) }\)* z becomes:

h(z) = 2\(e^{(i\pi /4)}\)) * (x + yi) = 2e^(iπ/4)x + 2\(e^{(i\pi /4)}\)yi.

So, the transformed point has its real and imaginary parts scaled by a factor of 2\(e^{(i\pi /4)}\)).

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Answer:

We have:

If:

Cos(θ) + Sin(θ) = √2*cos(θ)

We want to prove that:

Cos(θ) - Sin(θ) = √2*Sin(θ)

Well, let's start with the first relation:

Cos(θ) + Sin(θ) = √2*cos(θ)

Now we can subtract 2*Sin(θ) and we will get:

Cos(θ) + Sin(θ) - 2*Sin(θ) = √2*cos(θ) - 2*sin(θ)

Cos(θ) - Sin(θ) = √2*cos(θ) - 2*sin(θ)

Now, we also can rewrite the first equation as:

Cos(θ) + Sin(θ) = √2*cos(θ)

Cos(θ) - √2*cos(θ) = -  Sin(θ)

Cos(θ)*( 1 - √2) = -Sin(θ)

Cos(θ) = -Sin(θ)/( 1 - √2) = Sin(θ)/(- 1 + √2)

We can replace this in the right side of theequation:

Cos(θ) - Sin(θ) = √2*cos(θ) - 2*sin(θ)

Cos(θ) - Sin(θ) = √2* Sin(θ)/(- 1 + √2) - 2*sin(θ)

Cos(θ) - Sin(θ) = (√2/(- 1 + √2) - 2)*Sin(θ)

Now we have this:

√2/(- 1 + √2)) - 2 = a

if we multiply all by (-1  + √2) we get:

√2 - 2*(-1  + √2) = a*(-1  + √2)

√2  + 2 - 2*√2 =  a*(-1  + √2)

2 - √2 = a*(-1  + √2)

√2*(√2 - 1) = a*(-1  + √2)

√2*(√2 - 1)/(-1  + √2) = a

√2 = a

Then:

√2/(- 1 + √2)) - 2 = √2

If we replace this in the equation:

Cos(θ) - Sin(θ) = (√2/(- 1 + √2) - 2)*Sin(θ)

We get:

Cos(θ) - Sin(θ) = √2*Sin(θ)

Which is the thing we wanted to get.

Please find attached herewith the solution of your question.

If you have any query, feel free to ask.

Answer:

Option 2

Step-by-step explanation:

For two angles to be adjacent they need to have a common side/ray and a common vertex!

Hope this helps!!!

Answer:

Step-by-step explanation:

In geometry, two angles are adjacent if they have a common side and a common vertex. In other words, adjacent angles are directly next to each other and do not overlap.

->No, the two indicated angles do not share common vertex

The area of each triangle should be rounded to the nearest hundredth.

The area of a triangle can be calculated using the formula A = (1/2)bh, where A represents the area, b represents the length of the base, and h represents the height of the triangle. To find the area, we need to know the values of the base and height.

For example, let's consider a triangle with a base of 5 units and a height of 8 units. Using the formula A = (1/2)bh, we can substitute the given values to calculate the area:

A = (1/2) * 5 * 8

A = (1/2) * 40

A = 20

Therefore, the area of the triangle is 20 square units.

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Step-by-step explanation:

b.

\(( \sqrt{x + 2} ) { }^{2} =( 5) { }^{2} \\ \\x + 2 = 25 \\ x = 25 - 2 \\ x = 23 \)

Step-by-step explanation:

\( {9}^{ \frac{ - 1}{2} } \\ {3}^{2 \times - \frac{1}{2} } \\ {3}^{ - 1} \\ \frac{1}{3} \)

Now for another

\( {27}^{ \frac{ - 2}{3} } \\ {3}^{3 \times \frac{ - 2}{3} } \\ {3}^{ - 2} \\ \frac{1}{9} \)

Hope it will help :)❤

The frequency of the dominant allele in the population is 0.6.

Let's begin with the fundamental Hardy-Weinberg equations.

p + q = 1 and p² + 2pq + q² = 1

whereby "q" is the recessive allele and "p" is the dominant allele.

Recessed traits are present in 16% of people, or 0.16 percent. This indicates the percentage of the population that possesses the recessive trait,

q², is 0.16.

It is possible to calculate q using the value for q². What comes next is that q = 0.4.

This information allows for the calculation of "p".

1 − q = p , which results in "p" being 0.6.

This 0.6 is the frequency at which the dominant allele is prevalent in the population.

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The complete question is:

In a population that is in Hardy-Weinberg equilibrium, 16% of the individuals show the recessive trait. What is the frequency of the dominant allele in the population?

Answer:

32%

Step-by-step explanation:

50-34=16

16/50=0.32

0.32 x 100= 32

Answer:

X = 6y-2 is the easier substitution for another equation because all you have to do is just plug in the equation into the value of x.

The house's value Increase in dollars by $37,760.

The current value of the house is $509, 760.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

A house on the market was valued at $472,000.

After several years, the value increased by 8%.

Then, the value of house increased

= 472000 x 8/100

= $37,760

So, the current value of house

= 472000 + 37760

= $509, 760

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Answer:

L^2 = area of square = As

As = 14 L H / 2      where L H /2 = area of triangle

L^2 = 14 L H / 2

H = L / 7    or L = 7 H

Let the length of one side of square = 7 in

As = 7^2 = 49 in^2        area of square

H = 7     height of one side of triangle (other side = 1)

Area of triangle = 7 * 1 / 2 = 7/2 in^2

14 * At = 49

Area of square 7 * 7 = 49 in^2      Seems to checkout

Answer:

what are you ment to do...............

The answer is approximately 68% of the scores in a normally distributed set of data will fall within one standard deviation (-1 to +1) of the mean, according to the empirical rule.

According to the empirical rule, approximately 68% of the scores in a normally distributed set of data will fall within one standard deviation (i.e., within -1 to +1 standard deviation) of the mean. This is also known as the 68-95-99.7 rule or the three-sigma rule, which states that:

Approximately 68% of the data falls within one standard deviation of the mean. Approximately 95% of the data falls within two standard deviations of the mean. Approximately 99.7% of the data falls within three standard deviations of the mean.

Therefore, the answer to the question is 68%.

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Answer:

Milan puts 1/4 of her lawn-mowing money in savings and uses 1/2 of the remaining money to pay back her sister. If she has $15 left

Step-by-step explanation:

The formula for the volume of a cone is:

V = (1/3)πr²h

where r is the radius of the base, h is the height of the cone, and π is pi.

In this case, the slant height is given as 17 cm, which we can use with the radius to find the height of the cone using the Pythagorean theorem:

h² = s² - r²

h² = 17² - 8²

h² = 225

h = 15

Now that we have the height, we can plug in the values for r and h into the formula for the volume:

V = (1/3)π(8²)(15)

V = (1/3)π(64)(15)

V = (1/3)(960π)

V = 320π

Therefore, the volume of the cone is 320π cubic cm. Answer: 320π.

a. The price of the consol is approximately $133.33.

b. The new price of the consol would be $100. The price of the consol falls by 24.99% and the interest rate rises by 1%.

c. Your holding period return is approximately -49.99%.

a. The price of the consol can be calculated using the formula for the present value of a perpetuity:

Price = Annual Payment / Interest Rate

In this case, the annual payment is $4 and the interest rate is 3%. Substituting these values into the formula:

Price = $4 / 0.03 ≈ $133.33

Therefore, the price of the consol is approximately $133.33.

b. To calculate the new price of the consol if the interest rate rises to 4%, we use the same formula:

New Price = Annual Payment / New Interest Rate

Substituting the values, we get:

New Price = $4 / 0.04 = $100

The percentage change in the price of the consol can be calculated using the formula:

Percentage Change = (New Price - Old Price) / Old Price * 100

Substituting the values, we have:

Percentage Change in Price = ($100 - $133.33) / $133.33 * 100 ≈ -24.99%

The percentage change in the interest rate is simply the difference between the old and new interest rates:

Percentage Change in Interest Rate = (4% - 3%) = 1%

Comparing the two percentages, we can see that the price of the consol falls by approximately 24.99%, while the interest rate rises by 1%.

c. The holding period return can be calculated using the formula:

Holding Period Return = (Ending Value - Initial Value) / Initial Value * 100

The initial value is the purchase price of the consol, which is $133.33, and the ending value is the price of the consol after one year with an interest rate of 6%. Using the formula for the present value of a perpetuity, we can calculate the ending value:

Ending Value = Annual Payment / Interest Rate = $4 / 0.06 = $66.67

Substituting the values into the holding period return formula:

Holding Period Return = ($66.67 - $133.33) / $133.33 * 100 ≈ -49.99%

Therefore, the holding period return is approximately -49.99%.

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Answer:

3,240 sq m

Step-by-step explanation:

12*15*18=3,240

The given parabolic equation is y = 4x - x² and the point is (1, 3). We are to determine the slope of the tangent line at (1, 3) and then obtain an equation of the tangent line.  we must first calculate the derivative of the given equation.

We can do this by using the power rule of differentiation. The derivative of x² is 2x. So the derivative of y = 4x - x² is dy/dx = 4 - 2x.Since we want to find the slope of the tangent line at (1, 3), we need to substitute x = 1 into the equation we just obtained. dy/dx = 4 - 2x = 4 - 2(1) = 2. Therefore, the slope of the tangent line at (1, 3) is 2.We can now write the equation of the tangent line. We know the slope of the tangent line, m = 2, and we know the point (1, 3).

We can use the point-slope form of the equation of a line to obtain the equation of the tangent line. The point-slope form of the equation of a line is given as: y - y₁ = m(x - x₁)where m is the slope, (x₁, y₁) is a point on the line.Substituting in the values we have, we get:y - 3 = 2(x - 1)We can expand this equation to obtain the slope-intercept form of the equation of the tangent line:y = 2x + 1Therefore, the equation of the tangent line to the parabola y = 4x - x² at the point (1, 3) is y = 2x + 1.

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Answer:

482

Step-by-step explanation:

Answer:

68.21 and 39.79

Step-by-step explanation:

When it says that they are going to "share" it means that the number  (108) is going to be divided amongst the two of them. So you are going to do an addition problem which is 12+7=19. So you are going to do 12/19*108=68.21.  Then to find the second number it's 7/19*108=39.79.