please hurry, 100 points

Answer:

fg(x) = 3x² + 1

Step-by-step explanation:

f(g(x))

f(3x² - 1)

(3x² - 1) + 2

The system has an infinite number of solutions, but the only solution is (a, b) = (0, 0).

The given system of equations can be solved using the substitution method. We can begin by solving the first equation,[tex]a^2 + b^2[/tex], for either a or b. Let's solve for a:

[tex]a^2 + b^2 = 0[/tex]

[tex]a^2 + b^2 = 0[/tex]

[tex]a^2 = -b^2[/tex]

[tex]a = \pm\sqrt(-b^2)[/tex]

We can substitute this expression for a into the second equation, [tex]3a^2 - 2ab - b^2 = 0[/tex], and simplify:

[tex]3(\pm\sqrt(-b^2))^2 - 2(\pm\sqrt(-b^2))b - b^2 = 0[/tex]

[tex]3b^2 - 2b^2 - b^2 = 0[/tex]

0 = 0

Since 0 = 0, this means that the system of equations has an infinite number of solutions. In other words, any values of a and b that satisfy the equation [tex]a^2 + b^2 = 0[/tex] will also satisfy the equation [tex]3a^2 - 2ab - b^2 = 0[/tex]

However, the equation [tex]a^2 + b^2 = 0[/tex] only has a single solution, which is a = b = 0. Therefore, the solution to the system of equations is (a, b) = (0, 0).

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The Sanjay method used  to calculate the median is an incorrect formula. The correct value of the median is 7.5 kilometers.

Given:

the distances traveled by the Sanjay on his recent walks - 5, 6, 6, 7, 8, 8, 9, 9

The Median which is calculated by Sanjay = 7 kilometers

We need to find the mistake that Sanjay made in calculating the median

Solution:

We have the following data

5, 6, 6, 7, 8, 8, 9, 9

There are an even number of values, the median is determined by determining the average of the n/2th term and {(n/2) + 1}th term, where:

n = total number of values

= n/2

= 8/2

= 4

= (n/2) + 1

= (8/2) + 1

= 5

The 4th value in the given data = 7

The 5thvalue in the given data = 8

The median is the average of 7 and 8 = (7 + 8)/2 = 7.5

Therefore, the median will be the 7.5

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A point that best represent the location for them to put the science project is: A. (6.5, 6).

In order to determine the midpoint of a line segment with two (2) end points, we would add each point together and then divide by two (2):

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

By substituting the given end points into the formula for the midpoint of a line segment, we have the following;

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Midpoint = [(5 + 8)/2, (8 + 4)/2]

Midpoint = [(13)/2, 12/2]

Midpoint = (6.5, 6).

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Answer:

Step-by-step explanation:

You want the formula that describes the decay of an insect population from 10000 by 9% per year, and the years it takes for the population to decline by half.

An exponential function will have the form ...

  f(t) = (initial value) · (growth factor)^t

where ...

  growth factor = 1 + growth rate

Here, the growth rate is -9% per year, so the growth factor is ...

  1 -9% = 1 -0.09 = 0.91

The population is then ...

  f(t) = 10000·0.91^t . . . . . formula for number of insects

We can solve for t when f(t) = 5000 (half the original population):

  5000 = 10000·0.91^t

  1/2 = 0.91^t . . . . . . . . . . . divide by 10,000

  ln(1/2) = t·ln(0.91) . . . . . take logarithms

  t = ln(0.5)/ln(0.91) ≈ 7.3496 ≈ 7.3 . . . . years

It would take about 7.3 years for the population to reduce to less than half its present size.

__

Additional comment

We have rounded the time period to the nearest tenth, 7.3 years. At the end of that period, the population is modeled to be about 5023, not quite "less than half." To get below half the original population would take almost 7.35 years.

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Answer:

x=20

Step-by-step explanation:

On line n, the two unknown angles are supplementary, so we need their sum to be 180° and we can find x that way:

(6x-4)°+(3x+4)°=180°

6x+3x-4+4=180

9x=180

x=20

Answer:

300 per year??

Step-by-step explanation:

I'm not sure what you're trying to find...I'm guessing it's how many people it grew by per year

3000-1500 is 1500

1500/5 is 300

hope this helped

Answer:

Step-by-step explanation:

The area of the figure will be 17 square centimeters.

The area of a two-dimensional figure is the area that its perimeter encloses. The quantity of unit squares that occupy a closed figure's surface is its region.

The area of the figure is the summation of the area of the two rectangles. Then the area of the figure is calculated as,

A = 3 x 5 + 1 x 2

A = 15 + 2

A = 17 square cm

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The volume of the figures are;

4.  27. 18 in³

5. 3. 024 m³

6.  23 6/18 yd³

The formula for calculating the volume of a triangular prism is expressed with the equation;

V = Bl

Given that the parameters are;

4.  We have that;

Base area = 1/2 × 2.6 × 4.1

Multiply the values

Base area = 5. 33in²

Then,

Volume = 5.33 × 5.1

Volume = 27. 18 in³

5. Base area = 1/2 × 2. 4 × 1.4

Multiply the values

Base area = 1. 68 m²

Volume = 1.8 ×1.68

Multiply the values

Volume= 3. 024 m³

6. Base area = 1/2 × 10/3 × 14/3

Multiply the values

Base area = 7 14/18yd²

Volume = 140/18 × 3

Multiply the values

Volume = 23 6/18 yd³

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Answer:

10

Step-by-step explanation:

2 / 10 = 0.2

2 divided by ten is two-tenths.

Answer: 2 divided by 10 is 0.2

The length of the AB in the curved road path comes out to be 98.2 feet

Given:

Radius = 88 feet

DE = 15 feet

CD is the radius of the circle

CD = CE + DE

88 = CE + 15

CE = 73 feet

Since the CD is the perpendicular bisector the AE and BE are equal in length

In triangle CBE,

It is right-angled at E,

By Pythagoras' theorem:

hyp² = height² + base²

88² = 73² + BE²

7744 = 5329 + BE²

BE² = 2415

BE = 49.1 feet

AB = BE + AE

AB = BE + BE

AB = 2BE

AB = 2 * 49.1

= 98.2 feet

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The complete question is:

The curved road at the right is part of circle C which has a radius of 88 feet. What is AB as shown in the figure? Round to the tenth

Answer: (5x+6)(x+4)

Step-by-step explanation:

5x^2 + 26x + 24

5x^2 + 20x + 6x + 24

(5x^2 + 20x) + (6x + 24)

5x(x + 4) + 6(x + 4)

5x(x + 4) + 6(x + 4)

(5x + 6)(x + 4)

Answer:

64 - (6 x 8)

Step-by-step explanation:

"The product of 6 and 8" means 6 and 8 multiplied together, therefore this part can be expressed as 6x8. "Subtracted from 64" means that the product of 6x8 is being taken away from 64, therefore it is 64-(6x8).

The greatest common divisor of 120, 70, and 30 using prime factorization is 10.

To find the greatest common divisor (GCD) of 120, 70, and 30 using prime factorization  we need to first express each number as a product of its prime factors.

Prime factorization of 120

2³ × 3 × 5

Prime factorization of 70

= 2 × 5 × 7

Prime factorization of 30

= 2 × 3 × 5

common prime factors among the three numbers

common prime factors

= 2 × 5

= 10

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Steve is correct. Steve can find the difference in temperature between 7 AM and 12 PM on Wednesday by adding the distances from 0.

By using a number line, Steve can find the difference in temperature between 7 AM and 12 PM on Wednesday by adding the distances from 0. One temperature is negative and the other is positive, but by adding their distances, he can find the difference. Kelly's method of subtracting -5.1 from the temperature at 12 PM on Wednesday is not necessarily incorrect, but it does not give the exact difference in temperature between the two times. Therefore, using Steve's method, the change in temperature would be the sum of the distance from 0 to the temperature at 7 AM (which is 2.5) and the distance from 0 to the temperature at 12 PM (which is also 2.5), resulting in a difference of 5 degrees.

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The profit percentage is 20% when car cost 450000 and sold for 540000.

The formula i.e., Profit = Selling Price - Cost Price can be used to determine the profit when the price at which something is sold and the cost price of a product are known. The formula for calculating profit percentage is then applied, which is profit % = (profit/cost price) x 100 (A profit algorithm is used to determine how much profit was generated from the sale of a specific product.)

Cost Price= 4500000

Selling price= 540000

Profit = Selling price - cost price

Profit= 540000-450000

Profit = 90000

Profit as a percentage of cost price= [tex]\frac{90000}{45000}*100= 20%[/tex]

Therefore, the profit as a percentage of cost price is 20%.

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1. The location of point A  and B in complex (a + bi) form is 4 + 3i, B is -6 + 4i.

2. The modulus of point A is 5.

3. The length of AB is 10.

4. B in polar form is 2√13 × (cos(146°) + i sin(146°))

5. The product of two complex numbers in rectangular form is  -36 - 2i

6. z1/z2 in polar form is z1/z2 = 4 cis (7π/6 - π/4)

1. The location of each point A and B are as follows  Arrow A is at (4, 3) and arrow B (-6, 4). therefore the location in complex (a + bi) form is 4 + 3i, B is -6 + 4i.

2. The modulus of a complex number (a + bi) is represented as √(a² + b²) ⇒ √(4² + 3²) = √(16 + 9) = √25 = 5.

3. We can calculate the length of vector AB with √(x₂-x₁)² + (y₂-y₁)²)

AB = √((-6 - 4)² + (4 - 3)²)

AB = √((-10)² + 1)

AB = √(100 + 1)

AB = √101 ⇒ 10

4. The modulus of B, r = √((-6)² + 4²) = √(36 + 16) = √52 = 2√13

θ = 180° - arctan(|4/-6|) = 180° - arctan(2/3)

θ = 180° - 33.69° = 146.31°

5. The product of the complex number can be see as follows

(4 + 3i) × (-6 + 4i) = (4×-6 - 34) + (4×4 + 3×-6)i

= (-24 - 12) + (16 - 18)i

= -36 - 2i.

6. (7π/6 - π/4) = (14π/12 - 3π/12) = 11π/12.

11π/12 × (180/π) = 165°.

In Polar form z1/z2 = 4 cis (7π/6 - π/4)

= 4 cis 165°.

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Answer:

Step-by-step explanation:

[tex]\frac{925!}{(925-3)!}= 923*924*925=788,888,100[/tex]

To determine the number of ways the first, second, and third prizes can be awarded in a contest with 925 contestants, we can use the concept of permutations.

For the first prize, there are 925 contestants eligible to win. After the first prize is awarded, there are 924 remaining contestants for the second prize. Finally, for the third prize, there are 923 remaining contestants.

The number of ways to award the prizes can be calculated as the product of the number of choices for each prize:

Number of ways = 925 * 924 * 923

Calculating this expression, we find:

Number of ways = 779,449,100

Therefore, there are 779,449,100 ways to award the first, second, and third prizes in the contest with 925 contestants.

That's quadratic.

y=x^2

It's a very simple version of y=ax^2+bx+c. Just in this case, a = 1, b = 0 and c = 0.

The solution of the exponential equation [tex]5^{({\frac{-x}{16})}}= 5[/tex] in terms of logarithms, or correct to four decimal places, is x ≈ -4.4431.

An exponential function is a mathematical function in the form of [tex]f(x) = a^x[/tex], where "a" is a constant and "x" is a variable. The value of the function at a particular value of "x" is found by raising "a" to the power of "x". Exponential functions are characterized by their rapid growth or decay.

We can solve for x by taking the logarithm of both sides with base 5:

[tex]5^{(\frac{-x}{16})} = 5[/tex]

[tex]log_5(5^{(\frac{-x}{16}))} = log_5(5)[/tex]

(-x/16)log₅(5) = 1

-x/16 = 1/log₅(5)

x = -16/log₅(5)

Using a calculator, we get:

x ≈ -4.4431

Therefore, the solution of the exponential equation [tex]5^{({\frac{-x}{16})}}= 5[/tex]  in terms of logarithms, or correct to four decimal places, is x ≈ -4.4431.

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The volume of the largest piece is given as follows:

V = 10603 cm³.

The volume of a cone of radius r and height h is given by the equation presented as follows:

V = πr²h/3.

The dimensions for the largest piece in this problem are given as follows:

Hence the volume of the largest piece is given as follows:

V = π x 15² x 45/3

V = 10603 cm³.

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Step-by-step explanation:

First, let's find the square root of 30.6:

√30.6 ≈ 5.53 (rounded to two decimal places)

Now, let's multiply the square root by 2:

5.53 × 2 = 11.06

The marginal cost (MC) function tells us the additional cost of producing one more unit of the Senior Executive model.

To find the average cost, we need to know the fixed costs, which are not given in the problem. Therefore, we cannot calculate the average cost.

To find the marginal cost, we need to take the derivative of the total cost function with respect to x:

MC(x) = dC(x) / dx

MC(x) = [tex]0.3x^2[/tex] - 16x + 500

Interpreting the results, the marginal cost (MC) function tells us the additional cost of producing one more unit of the Senior Executive model. It is an increasing function, which means that the cost of producing an additional unit increases as the production level increases. When MC is greater than the price of the product, it is not profitable to produce additional units, and the optimal production level is reached when MC equals the price.

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Question

Custom Office makes a line of executive desks. It is estimated that the total cost for making x units of their Senior Executive model is represented by the following function:

C(x) = 0.1x^3 - 8x^2 + 500x + 4000

where C(x) is measured in dollars/year.

The value of sin Ф is 72/97.

We have,

Since cos Ф = -65/97 and Ф terminates in quadrant III, we know that cos Ф is negative (since cosine is negative in quadrants II and III).

We can use the Pythagorean identity to find sin Ф:

sin² Ф + cos² Ф = 1

Substituting cos Ф = -65/97, we get:

sin² Ф + (-65/97)² = 1

Simplifying, we get:

sin² Ф = 1 - (-65/97)²

Taking the square root of both sides (since sin Ф is positive in quadrant III), we get:

sin Ф = √(1 - (-65/97)²)

sin Ф = √(1 - 4225/9409)

sin Ф = √(5184/9409)

sin Ф = 72/97

Therefore,

The value of sin Ф is 72/97.

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Answer: 48 cm square

Step-by-step explanation:

We can first divide this shape into two rectangles, cutting it off at the 6cm line. The rectangle below has an area of 20cm square, noted by the 10 cm base and 2 cm base thickness. For the other rectangle, we can see that the height is 9cm, but since we already have done the bottom rectangle, we can subtract 2cm away from the 9cm ad get 7 cm. So the height for the top rectangle is 7cm. Then doing the same thing for the width with 10cm and 6cm gives us 4 cm. This then gives us a total of 28cm for the top and 20cm for the bottom. This combines to get us 48 cm. THE FIGURE IS NOT TO SCALE.

The solution is: I. ∠1 and ∠2 are same-side interior angles and,

III. m∠1 + m∠2 = 90, are the two statements about angles on a transversal crossing parallel lines contradict each other.

Here, we have,

given that,

We have to find which two statements about angles on a transversal crossing parallel lines contradict each other.

we know that,

If a transversal intersects or crosses parallel lines, adjacent angles are supplementary.

Corresponding angles are those that are in the same relative position, between the crossing line and the parallel lines.

now, we have,

I. ∠1 and ∠2 are same-side interior angles it can be possible.

Same side interior angles are two angles that are on the same side of the transversal and on the interior of (between) the two lines.

Same Side Interior Angles Theorem: If two parallel lines are cut by a transversal, then the same side interior angles are supplementary. If , then m ∠ 1 + m ∠ 2 = 180 ∘ .

so, if number-l is true, so, we get,

II. m∠1 = m∠2 may be true,

III. m∠1 + m∠2 = 90, never can be true.

so, we get,

if, l. holds then lll. contradicts that.

Hence, The solution is: I. ∠1 and ∠2 are same-side interior angles and,

III. m∠1 + m∠2 = 90, are the two statements about angles on a transversal crossing parallel lines contradict each other.

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Answer: yes 2,0193-029712123,

Step-by-step explanation: