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Answer:

1) f(-6) = 8

2) f(3) = -2

3) f(x) = -5 when x = 4

Answer:

the answer is B.(3,6)

because y>2

so,the answer is 3&6.

The required recursive function will  be expressed as an = 3000 + 500n

Given the following parameters

First year salary = $30,000

If it increases by $500 each year, let the number of years be "n", then the increment after "n" years is 500n

The required recursive function will  be expressed as an = 3000 + 500n

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Answer:

  A.  student A is correct; student B was confused by the division

  B.  3: cos²(θ)/(sin(θ)csc(θ)); 4: cos²(θ)

Step-by-step explanation:

Each student correctly made use of the trig identities ...

  csc(θ) = 1/sin(θ)

  1 -sin²(θ) = cos²(θ)

__

Student A's work is correct.

Student B apparently got confused by the two denominators in Step 2, and incorrectly replaced them with their quotient instead of their product.

__

The transition from Step 2 can look like ...

  [tex]\textsf{Step 3: }\ \dfrac{\left(\dfrac{1-\sin^2\theta}{\sin\theta}\right)}{\csc\theta}=\dfrac{1-\sin^2\theta}{\sin\theta}\cdot\dfrac{1}{\csc\theta}=\dfrac{\cos^2\theta}{(\sin\theta)(\csc\theta)}\\\\\textsf{Step 4: }\ \cos^2\theta[/tex]

Answer:

y = 3/2x - 9

Step-by-step explanation:

Finding equation of line m

Equation of line n

Answer:

[tex]\textsf{Equation of line n}:\quad y=\dfrac32x-9[/tex]

Step-by-step explanation:

Equation of line m

If two lines are perpendicular to each other, the product of their slopes will be -1.

The slope of the line [tex]y=-\dfrac23x+6[/tex] is [tex]-\dfrac23[/tex]

Therefore, the slope of the line m is:

[tex]\implies m \times -\dfrac23=-1[/tex]

[tex]\implies m=\dfrac32[/tex]

If line m passes through point (-2, -1), then the equation of line m is:

[tex]\implies y-(-1)=\dfrac32(x-(-2))[/tex]

[tex]\implies y+1=\dfrac32(x+2)[/tex]

[tex]\implies y=\dfrac32x+2[/tex]

Equation of line n

If line n is parallel to line m, then they will have the same slope.

Therefore, slope of line n is [tex]\frac32[/tex]

If line n passes through point (4, -3), then the equation of line n is:

[tex]\implies y-(-3)=\dfrac32(x-4)[/tex]

[tex]\implies y+3=\dfrac32x-6[/tex]

[tex]\implies y=\dfrac32x-9[/tex]

The domain of the function is [-2, 2) while the range is [4, 2) (along the y -axis).

The domain of a function is the input value for which the function exists while the range is the output value for which the function exists.

For the graph, the domain lie across the x-axis. The domain of the function is [-2, 2) while the range is [4, 2) (along the y -axis).

Note that point where the circles are shaded shows a closed interval

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Answer: 1/4

Step-by-step explanation: each person had half of the half of bag.

Answer:

The domain is all real numbers greater than or equal to 4, and the range is all real numbers

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

y = -x - 4

Step-by-step explanation:

m = (-5-0)/(1+4) = -5/5 = -1

b = (0, -4)

y = mx + b

y = -x - 4

Answer:

y = -x - 4

Step-by-step explanation:

Slope-intercept form is:

y = mx + b

The b is the y-intercept. That is where the line crosses the y-axis. This line crosses the y-axis at -4.

You could calculate the slope, but with a graph, you can SEE the slope without doing any calculation. Find a point on the line, any point. To get to the next point, you go DOWN1 and OVER1, (down1, over1, down1, over1)

This is -1/1. The slope is -1. Fill that in for m.

Leave the x and y as-is in

y = mx + b

fill in -1 for m and -4 for b.

y = -x - 4

If your teacher/prof is expecting to see a calc for slope. Find two points on the line. Subtract y-y and put that on top. Subtract x-x and put that on the bottom. Simplify.

Given points:

(1,-5) and (-4,0)

-5 - 0 is -5, put on top.

1 - -4 is 5, put underneath. You get -5/5, which is -1. Slope is -1.

Answer:

The first one should belong in the 54x+18 due to multiplication

The second answer choice has distributive property which has to belong in the 54x+18 category

The third answer choice fits into the 6 times 9x + 6 times one category due to multiplication like the first answer choice.

The last one should be in the 54x+18 category because of the distributive property

Step-by-step explanation:

The Objectives: 54x+18 and (6(9x) + 6

The first one should belong in the 54x+18 due to multiplication

The second answer choice has distributive property which has to belong in the 54x+18 category

The third answer choice fits into the 6 times 9x + 6 times one category due to multiplication like the first answer choice.

The last one should be in the 54x+18 category because of the distributive property

Step-by-step explanation:

[tex] \frac{1}{3x} + \frac{7}{ {x}^{2} } + \frac{x + 2}{x} [/tex]

[tex] \frac{x}{ {3x}^{2} } + \frac{21}{3 {x}^{2} } + \frac{3 {x}^{2} + 6x}{3 {x}^{2} } [/tex]

[tex] \frac{ {3x}^{2} + 7x + 21 }{ {3x}^{2} } [/tex]

Choice D

Similar triangles are those triangles whose corresponding sides are in the same ratio. The measure of m is 6√4.

Similar triangles are those triangles whose corresponding sides are in the same ratio. And the corresponding angles measure the same.

In the given triangles ΔABC and ΔBCD,

∠ACB = ∠DCB {Common Angles}

∠BDC = ∠ABC =90°

Therefore, the two triangles are so, for triangles.

(6+24)/BC = m/n = BC/24

BC² = 30×24

BC = √720

Now, using the Pythagorean theorem,

AC² = AB² + BC²

30² = m² + (√720)²

900 = m² + 720

180 = m²

m = 6√4

Hence, the measure of m is 6√4.

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Answer:

see explanation

Step-by-step explanation:

(a)

5% of N 80000

= [tex]\frac{5}{100}[/tex] × 80000

= 0.05 × 80000

= N4000 ← VAT

(b)

total cost = 80000 + 4000 = N84000

Answer:

26

Step-by-step explanation:

simply count the number of times the team scored more than 50 points by looking at the graph.

the team scored 51-60 points 11 times, 61-70 points 12 times and 71-80 points 3 times.

so the team scored more than 5 points a total of 11 + 12 + 3 = 26 times

Answer:

26

Step-by-step explanation:

Game scores above 50 points can be represented by the last three boxes to the left. To find the total number of times this happened, add up the values measured by the y-axis:

51-60 = 11 games

61-70 = 12 games

71-80 = 3 games

11 + 12 + 3 = 26

I hope this helps!

Answer:

2

Step-by-step explanation:

Answer:

In y = 2x the value of y is twice the value of x, and in y = x + 2 the value of y is two more than the value of x.

Same for the y=4x and y=x+4, just plug the numbers into the sentence.

Step-by-step explanation:

blue stars. let’s talk a bit about temperature. The color of a star is a function of its temperature. If a star looks red, that means its surface temperature is approximately 2,500 Kelvin. Just for comparison, our Sun, which actually looks white from space, measures about 6,000 Kelvin. The hotter the star, the further up the spectrum you go. The hottest stars are the blue stars. A star appears blue once its surface temperature gets above 10,000 Kelvin, or so, a star will appear blue to our eyes.

Answer:

x=5.09 seconds (times at max)

Step-by-step explanation:

Answer:

3x-10=65

Step-by-step explanation:

So, since he used the coupon, you can do 65+10=75.

The cost before the coupon is 75.

The cost of each shirt is 75/3, but that doesn't solve the question.

You can do (assume each shirt's cost is x)

3x-10=65

I could give more in depth but I can't see the options, sorry!

Answer:

(65+10) / 3= x

x would equal what each shirt costs

Step-by-step explanation:

The area of the square pyramid building is the amount of space on it

The maximum base length of the building is 67.42 cm

The given parameters are:

Base = b

Slant height (l) = 5b

The lateral surface area is calculated using:

L = 2bl

So, we have:

L = 2 * b * 5b

Evaluate the product

L = 10b^2

The total surface area is calculated using:

T = L + b^2

So, we have:

T = 10b^2 + b^2

Evaluate the sum

T = 11b^2

The maximum surface area is 50,000 square feet

So, we have:

11b^2 = 50000

Divide both sides by 11

b^2 = 50000/11

Take the square root of both sides

b = 67.42

Hence, the maximum base length of the building is 67.42 cm

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Answer: 71 feet

Step-by-step explanation:

Let's assume that the side length of the base of the square pyramid is x. Then, the slant height of the pyramid would be 5x, as given in the problem.

The lateral surface area of a square pyramid can be calculated using the formula:

Lateral surface area = (perimeter of base) × (slant height) / 2

The perimeter of the square base is 4x. So, the lateral surface area of the square pyramid can be written as:

Lateral surface area = 4x × (5x) / 2 = 10x^2

We are told that the construction material used for the outside of the building is between 20,000 square feet and 50,000 square feet. So, we can set up the following inequality:

20,000 ≤ 10x^2 ≤ 50,000

Dividing both sides by 10, we get:

2000 ≤ x^2 ≤ 5000

Taking the square root of both sides, we get:

44.7 ≤ x ≤ 70.7

Since we are looking for the maximum possible value of x, we can round 70.7 up to the nearest foot, which is 71 feet.

Therefore, the maximum possible side length of the base of the building is 71 feet.

Answer:

above 84°/. of the vehicles have a gas mileage greater then 24 mpg

Answer:

10, 41, 42

Step-by-step explanation:

(n)+(4n+1)+(5n-8)=93 because triangle perimeter

10n-7=93

10n=100

n=10

Answer: 10 cm, 41 cm, and 42 cm

Step-by-step explanation:

       We can set up an equation knowing the perimeter to solve for the lengths of each side. Then, we will plug the value of n into the different expressions that represent each side.

   Perimeter of a triangle:

P = side a + side b + side c

   Plug in our known values:

93 cm = (n) + (4n + 1) + (5n - 8)

   Simplify and combine like terms:

93 cm = n + 4n + 1 + 5n - 8

93 cm = n + 4n + 5n + 1 - 8

93 cm = 10n -7

   Add 7 to both sides of the equation:

100 cm = 10n

   Divide both sides of the equation by 10:

10 cm = n

n = 10 cm

        -

   Solve for the lengths of each side:

n = 10 cm

4n + 1 = 4(10) + 1 = 40 + 1 = 41 cm

5n - 8 = 5(10) - 8 = 50 - 8 = 42 cm

Answer: 421

Step-by-step explanation:

Subtract 3,000 by 1,737 and the product of that divided by 3 which will give you 421

So, here we need to differentiate tan³[tex](\theta)[/tex], wr.t.[tex]\theta[/tex], but let's recall some identities which will be very useful in this question :

Coming back on the question, consider :

[tex]{:\implies \quad \sf \dfrac{d}{d\theta}\{\tan^{3}(\theta)\}}[/tex]

[tex]{:\implies \quad \sf 3\tan^{3-1}(\theta)\dfrac{d}{d\theta}\{\tan (\theta)\}}[/tex]

[tex]{:\implies \quad \sf 3\tan^{2}(\theta)\sec^{2}(\theta)}[/tex]

Using the identity ;

[tex]{:\implies \quad \sf 3\tan^{2}(\theta)\{1+\tan^{2}(\theta)\}}[/tex]

[tex]{:\implies \quad \sf 3\tan^{2}(\theta)+3tan^{4}(\theta)}[/tex]

[tex]{:\implies \quad \sf 3\tan^{4}(\theta)+3\{\sec^{2}(\theta)-1\}}[/tex]

[tex]{:\implies \quad \boxed{\bf 3\tan^{4}(\theta)+3\sec^{2}(\theta)-3}}[/tex]

Hence, Proved

Answer:

56

Step-by-step explanation:

1) Add together all numbers. 30+45+50+75+80 = 280.

2) Divide result by amount of numbers. 280/5 = 56

3) You are welcome. :)

On an average, you sold 56 unit per, day.

A number that is calculated by adding quantities together and then dividing the total by the number of quantities.

Given that, Last week you sold 30, 45, 50, 75, and 80 units each day of the week.

To find the average, we will, first add together all numbers and then divide the result by the sum of numbers.

Therefore,

Adding together all numbers = 30+45+50+75+80 = 280.

Divide result by amount of numbers =  280/5 = 56

Hence, On an average, you sold 56 unit per, day.

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Answer:

Step-by-step explanation:

1/3 + 1/3= 2/3

5/10-2/10=3/10

4/5-2/5=2/5

11+1=12

Answer:

11

Step-by-step explanation:

h - f = 7 - (-4) = 7 + 4 = 11

Answer:

<1 = 88° , <2 = 129°, <3 = 82°, <4 = 147°, <5 = 94°, <6 = 86°

Step-by-step explanation:

<1 + 92° = 180°

<1 = 88°

<2 + 51° = 180°

<2 = 129°

<3 + 98° = 180°

<3 = 82°

<4 + 33° = 180°

<4 = 147°

<1 + <2 + <3 + <4 + <5 = 540°

88° + 129° + 82° + 147 + <5 = 540°

<5 = 94°

<5 + <6 = 180°

94° + <6 =180°

<6 = 86°

Answer: x = -2

Step-by-step explanation:

Given:

Perimeter = 50 cm

=> 2 (2x+15)+ 2(3x+20) =50

=> 4x+30+6x+40=50

=> 10x= -20

=> x= -20/10

=> x = -2