What is the value of (3 - ) x 52 + expressed in simplest form?
A. 3
31
1
6
B.
B. 51
C. 121
1
D. 38
3

Answer:

The northern lighthouse is approximately [tex]24.4\; \rm mi[/tex] closer to the boat than the southern lighthouse.

Step-by-step explanation:

Refer to the diagram attached. Denote the northern lighthouse as [tex]\rm N[/tex], the southern lighthouse as [tex]\rm S[/tex], and the boat as [tex]\rm B[/tex]. These three points would form a triangle.

It is given that two of the angles of this triangle measure [tex]40^{\circ}[/tex] (northern lighthouse, [tex]\angle {\rm N}[/tex]) and [tex]21^{\circ}[/tex] (southern lighthouse [tex]\angle {\rm S}[/tex]), respectively. The three angles of any triangle add up to [tex]180^{\circ}[/tex]. Therefore, the third angle of this triangle would measure [tex]180^{\circ} - (40^{\circ} + 21^{\circ}) = 119^{\circ}[/tex] (boat [tex]\angle {\rm B}[/tex].)

It is also given that the length between the two lighthouses (length of [tex]\rm NS[/tex]) is [tex]75\; \rm mi[/tex].

By the law of sine, the length of a side in a given triangle would be proportional to the angle opposite to that side. For example, in the triangle in this question, [tex]\angle {\rm B}[/tex] is opposite to side [tex]\rm NS[/tex], whereas [tex]\angle {\rm S}[/tex] is opposite to side [tex]{\rm NB}[/tex]. Therefore:

[tex]\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of NB}}{\sin(\angle {\rm S})} \end{aligned}[/tex].

Substitute in the known measurements:

[tex]\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of NB}}{\sin(21^{\circ})} \end{aligned}[/tex].

Rearrange and solve for the length of [tex]\rm NB[/tex]:

[tex]\begin{aligned} & \text{length of NB} \\ =\; & (75\; \rm mi) \times \frac{\sin(21^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 30.73\; \rm mi\end{aligned}[/tex].

(Round to at least one more decimal places than the values in the choices.)

Likewise, with [tex]\angle {\rm N}[/tex] is opposite to side [tex]{\rm SB}[/tex], the following would also hold:

[tex]\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of SB}}{\sin(\angle {\rm N})} \end{aligned}[/tex].

[tex]\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of SB}}{\sin(40^{\circ})} \end{aligned}[/tex].

[tex]\begin{aligned} & \text{length of SB} \\ =\; & (75\; \rm mi) \times \frac{\sin(40^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 55.12\; \rm mi\end{aligned}[/tex].

In other words, the distance between the northern lighthouse and the boat is approximately [tex]30.73\; \rm mi[/tex], whereas the distance between the southern lighthouse and the boat is approximately [tex]55.12\; \rm mi[/tex]. Hence the conclusion.

The last option; intersecting, but not perpendicular

Answer:

$6.00 for a pair of gloves and $8.00 for a hat

(d) 2 and 3 because they each have three terms.

Answer:

27/2 km/hr

Step-by-step explanation:

Answer:

x < -4

Step-by-step explanation:

x + 10 < 6

    -10 < -10

      x < -4

Answer:

y-intercept: -23

y = 6x - 23

Step-by-step explanation:

Slope: 6

Point (3, -5)

y-intercept: -5 - (6)(3) = - 5 - 18 = - 23

Answer:

110

Step-by-step explanation:

Substitute x = 4 and y = 7

20 + 2 (3y - 4x)

= 20 + 2 [(3 x 7) - (4 x 4)]

= 20 + 2 (21 - 16)

= 20 + 2 (5)

= 22 (5)

= 110

Answer:

30 (always use .P.E.M.D.A.S.)

Step-by-step explanation:

20+2(3y-4x)

20+2(21-16)

20+2(5)

20+10

30

Answer:

A. 1, 2, 3, 4

Step-by-step explanation:

I. When sample space means all possible case could happend.

In this case we have 4 equal sections numbered 1 to 4.

So from 1st section to 4th sections could happend fairly.

That makes 1, 2, 3, 4 is the right answer.

Hope that help :)

Answer:51273.816238

Step-by-step explanation:

Answer:

they have 490 to buy bean bags

If there is no discount, the amount they can buy is 490/40=12,25>10, so they will get a discount

call the bean bag is X we have: X*40*(100%-10%) ≤ 490

⇒X≤13,6

they can buy at most 13 bag and they will have left 490-40*13*90%=22

Step-by-step explanation:

Answer:  9

Step-by-step explanation:

12m + 80 = 188

        -80    - 80

12m = 108

12m = 108

12         12

m = 9

Answer:

6 p.m.

Step-by-step explanation:

Answer:

The answer is 6, I used  PEMDAS do parenthesis first, exponents if there's any, them multiplication, division, addition, lastly subtraction. When using PEMDAS not all the problems you'll have to solve have subtraction addition multiplication, etc. But follow the order they are put in and skip the ones that aren't there.

Answer:

180 degrees

Step-by-step explanation:

Answer:

your answer is as follows

Step-by-step explanation:

5x+20=3x+60

2x=40

x=20

(equating the slopes)

Answer:

................hfgmehshshdhdjwieir

Answer in fraction form = 83/5

Answer in decimal form = 16.6

==================================================

Explanation:

All eight angles shown are 90 degrees since lines a and c are perpendicular to each other. Perpendicular lines form right angles.

Set 5x+7 equal to 90 and solve for x

5x+7 = 90

5x = 90-7

5x = 83

x = 83/5 is the fraction form of the answer

x = 16.6 is the decimal form of the answer

Answer:

83/5 = 16.6

Step-by-step explanation:

5x+7 = 90

5x = 90-7     subtract 7 from both sides.

5x = 83

x = 83/5   = 16.6    

Answer:

36,864

Step-by-step explantion:

Answer:

upp7fpfpzfpufpufpufpufpu

Step-by-step explanation:

uxcicicovovovovovvNC coordinatorby McKnight

Answer:

I think the answer is C

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

122%=122% 49/29=169% 26/15=173%, 1.98=198%

Step-by-step explanation:

1) 3x - 4 = 86 + 24

→ 3x - 4 = 110

→ 3x = 110 + 4 = 114

→ x = 114/3 = 38

therefore, value of x is 38.

2) -10x = 30 + 90

→ -10x = 120

→ x = 120/10 = 12

→ x = 12

therefore, value of x is 12.

3) -8x + 23 + 51 = 130

→ -8x + 74 = 130

→ -8x = 130 - 74

→ -8x = 56

→ x = 56/8

→ x = 7

therefore, value of x is 7.

4) -9 + 2x = 59 + 90

→ -9 + 2x = 149

→ 2x = 149 + 9

→ 2x = 158

→ x = 158/2 = 79

→ x = 79

therefore, value of x is 79.

hope this answer helps you dear...take care !

Answer: There are two solutions how to get the answer the factor solution and the factor by groupings solution.

Step-by-step explanation:

THE FACTOR SOLUTION

factor x out of 5x^3-3x^2 3x

X(5x^2 - 3x +3)

FACTOR BY GROUPINGS

Group of factors out the greatest common factor (GCF) then combined

X(5x^2 - 3x + 3)

I HOPE IT HELP YOU :)

Answer:

800 miles

Step-by-step explanation:

You would make the equation .15x+ $200 and put that equal to 340 to get the equation:

.15x+$200=340

      -$200        (subtract the like term first)

.15x=120

.15x over 120

Your answer comes out to be x=800.

Hello friend,

The answer to your question is attached in the image uploaded by me. Please refer them.

✍️ By Benjemin ☺️