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3 years ago

Solve the following inequality for n. Write your answer in simplest form. 1+4(-6n-4)<10n+4-n

Mathematics

1 answer:

liberstina [14]3 years ago

8 0

Answer

n>- 19/33

1 Simplify 10n+4-n10n+4−n to 9n+49n+4.

1+4(-6n-4)<9n+41+4(−6n−4)<9n+4

2 Expand.

1-24n-16<9n+41−24n−16<9n+4

3 Simplify 1-24n-161−24n−16 to -24n-15−24n−15.

-24n-15<9n+4−24n−15<9n+4

4 Add 24n24n to both sides.

-15<9n+4+24n−15<9n+4+24n

5 Simplify 9n+4+24n9n+4+24n to 33n+433n+4.

-15<33n+4−15<33n+4

6 Subtract 44 from both sides.

-15-4<33n−15−4<33n

7 Simplify -15-4−15−4 to -19−19.

-19<33n−19<33n

8 Divide both sides by 3333.

-\frac{19}{33}<n−

33

19

 <n

9 Switch sides.

n>-\frac{19}{33}n>−

33

19

Done

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Pls solve part b) iii thanks

Viktor [21]

The bearing of the tree from Q is 296.565°

<h3>How to determine the height of the tree?</h3>

The figure that illustrates the bearing and the distance is added as an attachment

The given parameters are:

Base of the tree, b = 50 meters

Angle (x) = 32 degrees

Calculate the height (h) of the tree using:

tan(x) = height/base

So, we have:

tan(32°) = h/50

Make h the subject

h= 50 × tan(32°)

Evaluate

h = 31.24

Hence, the height of the tree is 31.24 meters

<h3>How to determine the distance between Q and the base of the tree?</h3>

The distance (d) between Q and the base of the tree

This is calculated using the following Pythagoras theorem

d = √(100² + 50²)

Evaluate

d = 111.80

Hence, the distance between Q and the base of the tree is 111.80 meters

<h3>How to determine the angle of elevation?</h3>

The angle of elevation (x) using the following tangent trigonometric ratio

tan(x) = h/d

This gives

tan(x) = 31.24/111.80

Evaluate the quotient

tan(x) = 0.2794

Take the arc tan of both sides

x = 15.61

<h3>The bearing of the tree from Q </h3>

This is calculated using:

Angle of bearing = 270 + arctan(50/100)

Evaluate the arc tan

Angle of bearing = 270 + 26.565

Evaluate the sum

Angle of bearing = 296.565

Hence, the bearing of the tree from Q is 296.565 degrees

Read more about bearings at:

brainly.com/question/24142612

#SPJ1

4 0

2 years ago

Line joins ordered pairs negative 4, 3, 2, negative 3. Second joins negative 4, negative 3, 2, 3. A shaded above first second li

xxMikexx [17]

Answer

That should be it!

Step-by-step explanation:

Question 1 (Multiple Choice Worth 1 points) (04.03) The expression below shows the population of foxes in a forest after 12x years: f(x) = 50(1.05)12x Which of the following is an equivalent function? f(x) = 50(1.7959)x f(x) = 50(12.6000)x f(x) = 600(1.05)x f(x) = 4.2(1.05)x Question 2 (Multiple Choice Worth 1 points) (04.01) Which of the following best defines 3 to the power of 2 over 3? Square root of 9 Cube root of 9 Cube root of 3 Square root of 3 Question 3 (Multiple Choice Worth 1 points) (04.06) A sequence has its first term equal to 4, and each term of the sequence is obtained by adding 2 to the previous term. If f(n) represents the nth term of the sequence, which of the following recursive functions best defines this sequence? f(1) = 2 and f(n) = f(n − 1) + 4; n > 1 f(1) = 4 and f(n) = f(n − 1) + 2n; n > 1 f(1) = 2 and f(n) = f(n − 1) + 4n; n > 1 f(1) = 4 and f(n) = f(n − 1) + 2; n > 1 Question 4 (Multiple Choice Worth 1 points) (05.05) Look at the graph below: First line joins ordered pairs negative 4, 3 and 2, negative 3. Second line joins negative 4, negative 3 and 2, 3. Part A shaded above first and second line. Part B shaded below first line and above second line. Part C shaded below first and second lines. Part D shaded above first line and below second line. Which part of the graph best represents the solution set to the system of inequalities y ≤ x + 1 and y + x ≤ −1? Part A Part B Part C Part D Question 5 (Multiple Choice Worth 1 points) (04.03) The number of bacteria in a sample increased by a factor of 2 every minute from 9:05 AM to 9:55 a.m.. The function below shows the number of bacteria in the sample f(x) after x minutes from 9:05 a.m.: f(x) = 10(2)x Which of the following is a reasonable domain for the function? 0 ≤ x ≤ 10 5 ≤ x ≤ 55 0 ≤ x ≤ 50 All positive integers Question 6 (Multiple Choice Worth 1 points) (03.05) The graph below shows the velocity f(t) of a runner during a certain time interval: graph of line going through ordered pairs 0, 2 and 6, 8. Graph of another line through ordered pairs 6, 8 and 8, 0. Label on the x axis is time in second and label on the y axis is velocity in meters per second Which of the following describes the intercepts on the graph? The initial velocity of the runner was 8 m/s, and the runner stopped after 2 seconds. The initial velocity of the runner was 2 m/s, and the runner stopped after 8 seconds. The initial acceleration of the runner was 8 m/s2, and the runner stopped after 2 seconds. The initial acceleration of the runner was 2 m/s2, and the runner stopped after 8 seconds. Question 7 (Multiple Choice Worth 1 points) (03.03) Choose the equation that represents the graph below: Graph of a line passing through points negative 3 comma 0 and 0 comma 3 y = x − 3 y = −x + 3 y = −x − 3 y = x + 3 Question 8 (Multiple Choice Worth 1 points) (04.03) Jake forgot to replace the cap on a bottle of cologne. The cologne began to evaporate at the rate of 18% per day. If the original amount of cologne in the bottle was 50 grams, which of the following graphs best represents the amount of cologne f(x) remaining in the bottle after x days? graph of function f of x equals 30 multiplied by 0.88 to the power of x graph of exponential function going down from left to right in quadrant 1 through the point 0, 40 and approaching the x axis graph of function f of x equals 50 multiplied by 0.82 to the power of x graph of exponential function going down from left to right in quadrant 1 through the point 0, 4 and approaching the x axis

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3 years ago

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Chan hee bought 3.4 pounds that cost 6.95 per pound how much did he spend on coffee? sl

Aleks [24]

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8 0

3 years ago

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marin [14]

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