Function limits: Solve the activities in each image (full development)

Answer with the method that is possible to solve adequately (approximation, factorization, rationalization or evaluation)

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

7 a)

Step 1 :

Make the denominators the same

           [tex]-\frac{1}{7} \ and \ \frac{2}{9}[/tex]

[tex]-\frac{1}{7} \times \frac{9}{9} = -\frac{9}{63}\\\\\frac{2}{9} \times \frac{7}{7} = \frac{14}{63}\\[/tex]

Step 2 :

Now find rational between (-9/63) and (14/63).

Just change the number in the numerator. Write any numbers between -9 and 14 in the numerator.

                            [tex]\frac{ -8}{63}, \ \frac{-7}{63},\ \frac{3}{63},\ \frac{6}{63},\ \frac{8}{63}[/tex]

7 b )

       [tex]x = 3 + 2\sqrt2\\\\x + \frac{1}{x} = (3 + 2\sqrt2) + \frac{1}{3+2\sqrt2}[/tex]

[tex][ Rationalize \ the \ denominator : \frac{1}{3 + \sqrt2} \times \frac{3 - 2\sqrt2}{3-2\sqrt 2} = \frac{3 - 2 \sqrt2}{3^2 - (2 \sqrt2)^2 } = \frac{3 - 2\sqrt2}{9 - 8} = 3 - 2\sqrt 2 \ ][/tex]

       [tex]therefore , x + \frac{1}{x} = 3 + 2\sqrt 2 + 3 - 2 \sqrt 2 = 6 + 0 = 6[/tex]

...........................................................................................................................................................................................................................................................................................................................................................................

[tex]-6h^{2}+5h+2=0\\h^{2} -\frac{5}{6} h-\frac{1}{3} =0\\h^{2} -\frac{5}{6} h+(\frac{5}{12} )^{2} -(\frac{5}{12} )^{2}-\frac{1}{3} =0\\(h-\frac{5}{12} )^{2} =\frac{1}{3} +(\frac{5}{12} )^{2}\\(h-\frac{5}{12} )^{2} =\frac{73}{144} \\[/tex]

[tex]h-\frac{5}{12} = \sqrt{\frac{73}{144}} \\h=\sqrt{\frac{73}{144}} +\frac{5}{12}[/tex]

or

[tex]h-\frac{5}{12} = -\sqrt{\frac{73}{144}} \\h=-\sqrt{\frac{73}{144}} +\frac{5}{12}[/tex]

Answer:

[tex]sin \theta = \frac{3}{5}[/tex]

Step-by-step explanation:

[tex]cos \theta = \frac{12}{15}\\\\cos^2 \theta = 1 - sin^2 \theta\\\\sin^2\theta = 1 - cos^2 \theta\\\\[/tex]

       [tex]= 1 - (\frac{12}{15})^2\\\\= 1 - \frac{144}{225}\\\\= \frac{225 - 144}{225}\\\\=\frac{81}{225}[/tex]

[tex]sin \theta = \sqrt{\frac{81}{225}} = \frac{9}{15} = \frac{3}{5}[/tex]

Answer:9/15

Step-by-step explanation:

Answer:

The correct answer is -

1. B. stratified sampling

2. C. Systematic Sampling

3. A. Cluster Sampling

4. E. Simple Random Sampling

5. D. Convenience Sampling

Explanation:

Stratified sampling is a method in which samples have collected from a population that can be partitioned into subpopulations, categories or strata.

Systematic sampling is the method in which samples are at low risk of manipulation due to the getting samples ordered sampling range or frame.

Cluster sampling is the sampling that has random clusters of samples and data collected from selected clusters.

In a simple random sampling method, there are equal chances to get selected from a population in the sampling method.

Convenience Sampling is the sampling there is a selection of the data as these samples are convenient to collected and selected.

Answer:

135 cm

Step-by-step explanation:

Let Jose's height = x

The mean of their heights = 150

Given the Heights:

150cm, 170cm, 140cm, 155cm

The mean is the sum if the heights divided by the number of people

Here :

(150 + 170 + 140 + 155 + x) / 5 = 150

(615 + x) / 5 = 150

615 + x = 750

x = 750 - 615

x = 135 cm

Answer:

Step-by-step explanation:

V = L * W * H

L = 4

W = 3

H = 2

V = 4 * 3 * 2

V = 24

Density = mass / Volume

density = 11.34

volume = 24

mass = ?

11.34 = mass / 24                   Multiply both sides by 24

11.34 * 24 = 24 * mass /24

mass = 272.16 grams

Answer:

Step-by-step explanation:

Bấm máy tính hệ phương trình là ra

Answer:

[tex]3\sqrt{5}i[/tex]

Step-by-step explanation:

[tex]\sqrt{-45}[/tex]

[tex]\sqrt{-9*5}[/tex]

[tex]\sqrt{-9}\sqrt{5}[/tex]

[tex]3i\sqrt{5}[/tex]

[tex]3\sqrt{5}i[/tex]

9514 1404 393

Answer:

  {-12, -8, 0, 8}

Step-by-step explanation:

The range is the set of y-values that correspond to the given set of x-values. I like to figure them "all at once", since the math is repetitive.

  f(x) = -2x +6

  f({-1, 3, 7, 9}) = -2{-1, 3, 7, 9} +6 = {2, -6, -14, -18} +6

  f({-1, 3, 7, 9}) = {8, 0, -8, -12}

The range for the given domain is {-12, -8, 0, 8}.

Answer:

The height of the antenna is 7.0 m

Step-by-step explanation:

Let the height of the antenna be represented by x, and the distance from Avani's eyes to the top of the building A by y. And let z = x + y, so that:

Tan 42 = [tex]\frac{y}{21}[/tex]

y = Tan 42 x 21

  = 0.9004 x 21

  = 18.9084

y = 18.91 m

Also,

Tan 51 = [tex]\frac{z}{21}[/tex]

z = Tan 51 x 21

  = 1.2349 x 21

  = 25.9329

z = 25.93 m

Therefore,

x = z - y

  = 25.93 - 18.91

  = 7.02

x = 7.02 m

The height of the antenna is 7.0 m

Answer:

0

Step-by-step explanation:

f(x)=2•3x

f(x)=6x+0

Answer:

-37.8

Step-by-step explanation:

Answer:-37.8

Step-by-step explanation:

Answer:

$0.37 and $0.31

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

here

https://decabonner.weebly.com/uploads/1/6/4/8/1648294/day_1_-_practice_wksht_-_basic_probability_key.pdf

Answer:

x= 3

Step-by-step explanation

Answer:

the answer is x = 3, but i gave you the explanation to figure it out on your own.

Step-by-step explanation:

x = 3

27 + 5/8 = 32

Answer:

The answer is 4.

Step-by-step explanation:

Edge 2021

Answer:

4

Step-by-step explanation:

EDGE2021

Answer:

340

Step-by-step explanation:

To find the cost of 4 liters of juices, take the cost of 1 liter and multiply by 4

4 *85 = 340

Answer: It's $340

Step-by-step explanation:

4 liters of juice - 3 liters = 1 liter

Multiply 1 liter by 4 = 340 (4 x 85)

Answer: $340

9514 1404 393

Answer:

Step-by-step explanation:

The applicable relation in each case is ...

  s = rθ

where s is arc length, r is radius, and θ is rotation angle in radians. Of course the relation between degrees and radians is that π radians = 180°.

__

1. s = (1.5 m)(302.2/180π) ≈ 7.91 m

About 7.91 meters of wire will be wound on the drum.

__

2. The area of a sector is found by a formula that is similar to that for the area of a triangle. For a triangle, the area is A=1/2bh, where b is the base length and h is the height of the triangle. For a sector, the area is A=1/2sr, where s is the arc length and r is the radius. Usually, this is put in the form ...

  A = 1/2sr = 1/2(rθ)r

  A = 1/2r²θ

The angle through which the pendulum sweeps is ...

  (9°/s)(4 s) = 36° = (36°/180°)π radians = π/5 radians

Then the swept area is ...

  A = 1/2(14 cm)²(π/5) = 19.6π cm² ≈ 61.58 cm²

Each complete right to left swing sweeps an area of about 61.58 cm².

__

3. Each rotation is 2π radians of angle, so the angular speed is ...

  angle/time = (2π radians/revolution)(17 revolutions)/(32 s) = 17/16π radians/s

  ≈ 3.34 radians/s

The distance covered per unit time is found using the arc length formula above.

 (arc length)/time = (rθ)/time = (25 cm)(17/16π rad/s)

 = (426/16)π cm/s ≈ 83.45 cm/s . . . . . pulley rim speed

Answer:

128

Step-by-step explanation:

The two angles form a straight line so they add to 180

2m+62  + 3m +143 = 180

Combine like terms

5m+205=180

Subtract 205 from each side

5m+205-205=180-205

5m = -25

Divide by 5

5m/5 = -25/5

m = -5

We want to find the angle so we substitute the value of m into the the formula for the angle.

< RBM =3m +143 = 3(-5) +143 = -15+143 =128

Answer:

[tex]y=4x-16[/tex]

Step-by-step explanation:

Hi there!

What we need to know:

1) Determine the slope (m)

[tex]y=4x-6[/tex]

4 is in the place of m, making it the slope. Because parallel lines have the same slope, the slope of the line is therefore 4. Plug this into [tex]y=mx+b[/tex]:

[tex]y=4x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=4x+b[/tex]

Plug in the given point (6,8) and solve for b

[tex]8=4(6)+b\\8=24+b[/tex]

Subtract 24 from both sides to isolate b

[tex]8-24=24+b-24\\-16=b[/tex]

Therefore, the y-intercept of the line is -16. Plug this back into [tex]y=4x+b[/tex]:

[tex]y=4x-16[/tex]

I hope this helps!

Answer:

y=4x−16

Step-by-step explanation:

Because we want a parallel line to the given one, we know it needs to have the same slope. Therefore, the new line must be y=4x+b for some b. Knowing that the line goes through the point (6,8), we can plug this in and solve for b:

y=4x+b

8=4(6)=b

b=-16

So the equation of the line is y=4x−16.

Answer:

3n-18

Step-by-step explanation:

let n be the number

n

3 times a number

3n

decreased by is subtraction

3n-18

Answer:

see below

Step-by-step explanation:   6  13  8  09

area = π r²    is the equation to calculate the area of the pool   r = radius

I don't no if the 1.11 ft is the diameter of the radius, so I will use the 1.11 ft as the diameter

diameter = 2×radius

diameter / 2 = radius

area = π (d/2)²   = T (d/2)²              d = diameter      π  = T      

        = 3.14(1.11 / 2)²              

        = 3.14 × (0.555)²

        = 0.9677 ft²    which seems like a small pool!

Answer:

220 yards in one minute

Step-by-step explanation:

15 miles in 120 minutes equals 26,400 (15 · 1760) yards in 120 minutes

26,400 yards in 120 minutes equals 220 yards in 1 minute (after dividing both 26400 and 120 by 120)

Answer:

220

Step-by-step explanation:

The first guy explained it, look above. I was about to say something similair

Answer:

$5850 is the answer

Step-by-step explanation:

P = $3000

R = 9.5%

T = 10 year

A = ?

So,

I = PTR/100

=(3000×9.5×10)/100

=285000/100

= $2850

So,

I = A-P

I+P = A

$2850 + $3000 = A

so, A = $5850

Answer:

its x^4

Step-by-step explanation:

its x^4