The Law of Sines: Mastery Test ? In triangle ABC, how long is side a if A = 24°, C = 55°, and c = 3? O 1.49 O 1.31 O 6.04 O 0.1 ​

Answer:

-27k^4 +12k^3+16k^2+56k

---------------------

(9k-4)(2k+7)      

Step-by-step explanation:

8k                  3k^3

---------   -  -----------

9k-4             2k+7

Get a common denominator

8k *(2k+7)          3k^3 *(9k-4)

---------      -           -----------

(9k-4)(2k+7)        (9k-4)(2k+7)

Combine

8k *(2k+7) -3k^3 *(9k-4)

---------------------

(9k-4)(2k+7)        

Distribute

16k^2+56k -27k^4 +12k^3

---------------------

(9k-4)(2k+7)      

-27k^4 +12k^3+16k^2+56k

---------------------

(9k-4)(2k+7)        

Answer:

50.8°

Step-by-step explanation:

In ∆ IJK :-

Answer:

The probability that they each will catch 3 fish is 0.000063956

Step-by-step explanation:

The hyper geometric distribution is used to solve this as it has a population, a sample , number of successes  for both the population and sample.

Here

Population size= N =200

Sample size= n =9= (3*3)

Number of successes in population = k = 3 hours

Number of successes in sample = x= 3

Applying the hyper geometric distribution

P (x=3) = kCx *(N-k) C (n-x)/ N Cn

   = 3 C 3 * 197 C 6/ 200 C 9

    =0.000063956

The probability that they each will catch 3 fish is 0.000063956

Answer:   [tex]\huge\boxed{x=log_2\frac{12\sqrt{2}+4}{17}}[/tex]

Step-by-step explanation:                                                                       [tex]\displaystyle\ \bigg{2^x-3(2^{x+\frac{1}{2} }})+2^2=0 \qquad ; \ \ \boxed{t=2^x} \\\\t-3t\sqrt{2} +4=0 \\\\ t(1-3\sqrt{2} )=-4 \\\\ t=\frac{4}{3\sqrt{2} -1} \cdot \frac{3\sqrt{2}+1 }{3\sqrt{2}+1 } =\frac{12\sqrt{2}+4}{17} \\\\\\2^x=\frac{12\sqrt{2}+4}{17} \\\\x=log_2 \ \ \frac{12\sqrt{2}+4}{17}[/tex]

Answer:

10/3

Step-by-step explanation:

31/8= 3.8

10/3= 3.3

Given:

The gradient of the line passing through A(2,3), B(k,7) is [tex]\dfrac{2}{3}[/tex].

To find:

The value of k.

Solution:

The gradient or slope of a line is:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The gradient of the line passing through A(2,3), B(k,7) is [tex]\dfrac{2}{3}[/tex]. So,

[tex]\dfrac{2}{3}=\dfrac{7-3}{k-2}[/tex]

[tex]\dfrac{2}{3}=\dfrac{4}{k-2}[/tex]

On cross multiplication, we get

[tex]2(k-2)=4(3)[/tex]

[tex]2k-4=12[/tex]

[tex]2k=12+4[/tex]

[tex]2k=16[/tex]

Divide both sides by 2.

[tex]k=\dfrac{16}{2}[/tex]

[tex]k=8[/tex]

Therefore, the value of k is 8.

Answer:

D

Step-by-step explanation:

all the options seems similar..but i can find the D more suitable

Answer:

4x-2

Step-by-step explanation:

X=muffins

Answer:

The perimeter of QRS is 137.5

Step-by-step explanation:

From the given interval angles, we can see that the two triangles are congruent

so it is expected that the ratios of their corresponding sides are equal

this is because; 83 + 53 + 44 = 180

Now, let us work with the side facing the angle marked 53 in both triangles

For the smaller, we have the measure as 16

for the bigger, we have the measure as 44

So the scale factor here is 44/16 = 11/4 = 2.75

We have to multiply the measure of the sides of the smaller triangle by 2.75 to get that of the bigger triangle

in similar vein, we have to multiply the perimeter we have in the smaller triangle by 2.75 to get that of the bigger triangle

The perimeter of the smaller would be the sum of the side lengths

we have this as;

14 + 20 + 16 = 50

So the perimeter of the bigger triangle would be;

2.75 * 50 = 137.5

Answer:

52 in^2

Hope this helps!

Answer:

The first answer

Step-by-step explanation:

Domain refers to the set of x values and range refers to the set of y values. Since x goes from 0 to 3, and does not exclude any values within those numbers, the first answer applies to that set.

Answer:

option 1

that is

{t| 0 <= t <= 3}

Step-by-step explanation:

as the graph plots height ove time

time will be the domain, taken on the x axis, with values ranging from 0 to 3.

so the domain is

{t| 0 <= t <= 3}

Answer:

[tex]{ \bf{total \: ratio = 4 + 3 = 7}} \\ { \tt{let \: population \: be \: p}} \\ \frac{4}{7} \times p = 24 \\ 4p = 168 \\ p = 42 \\ { \bf{there \: are \: 42 \: people}}[/tex]

Boys to girls- 4:3

Boys and girls- 24 and x (let the girls be x)

4/3=24/x

=4x= 72

= x= 72/4

= x= 18 girls

Ans: There are 42 children (24+18)

Answer:

[tex]{ \tt{length = \sqrt{ {( - 2 - 5)}^{2} + {(3 - 7)}^{2} } }} \\ = \sqrt{65} \\ = 8.06 \: units[/tex]

Answer:

(f + g)(x) = 3^x + 12x -4

Step-by-step explanation:

Here, we want to get the value of (f + g)(x)

Mathematically, we have this as;

(f + g)(x) = f(x) + g(x)

= 3^x + 10x + 2x-4

= 3^x + 12x -4

Answer:

103 is my answer.

Step-by-step explanation:

hope it helps

Answer:

70%

Step-by-step explanation:

Finding each side :-

Finding area of unshaded region :-

Overall area :-

Finding percentage :-

Answer:70%

Step-by-step explanation:

Answer:

-50

Step-by-step explanation:

Answer:

I am in 5 classso i did not known answer

Answer: (a) P = 6W + 2

(b) L = 2W + 1

(c) Width = 13cm

Length = 27cm

Step-by-step explanation:

The formula for perimeter of a rectangle is 2(length + width). Since the length is 1 cm more than twice its width, then the length will be:

L = (2 × W) + 1

(b) L = 2W + 1

Therefore, P = 2(L + W)

P = 2( 2W + 1) + 2W

P = 4W + 2 + 2W

(a) P = 6W + 2

Since perimeter is given as 80cm. Therefore,

P = 6W + 2

6W + 2 = 80

6W = 80 - 2

6W = 78

W = 78/6

W = 13

Width is 13cm

Length = 2W + 1

Length = 2(13) + 1

Length = 27cm

The width of the rectangle is 13cm and the length is 27cm.

A rectangle is a quadrilateral. Opposite sides are equal. The four angles in a rectangle is equal to 90 degrees.

The formula for determining the perimeter of a rectangle = 2x (length + width)

P = 2(L + W)

80 = 2(1 + 2w + w)

80 = 2(1 + 3w)

40 = 1 + 3w

40 - 1 = 3w

39 = 3w

w = 13cm

Length = 1 + 2(13) = 27cm

To learn more about rectangles, please check: https://brainly.com/question/16595449

Answer:

[tex]i^{2} (2i^{2} -5)[/tex]

[tex]2i^{2} \times i^{2} -5i^{2}[/tex]

[tex]2(-1)(-1)-5(-1)[/tex]

[tex]2+5[/tex]

[tex]=7[/tex]  [tex]i^{2}(2i-5)[/tex]

------------------

[tex]i^{2} (3+i^{2} )[/tex]

[tex]i^{2} \times 3+i^{2} \times i^{2}[/tex]

[tex](-1)3+(-1)(-1)[/tex]

[tex]-3+1[/tex]

[tex]-2[/tex]  [tex]=i^{2} (3+i^{2} )[/tex]

---------------------

[tex]2i(2i-i^{3} )[/tex]

[tex]2i\times 2i-i^{3} \times2i[/tex]

[tex]4i^{2} -2i^{4}[/tex]

[tex]4(-1)-2(1)[/tex]

[tex]-4-2=[/tex]

[tex]-6=2i(2i-i^{3} )[/tex]

-------------------

[tex]i(4i^{3} -i)[/tex]

[tex]4i^{3} \times i-i\times i[/tex]

[tex]4i^{4} -i^{2}[/tex]

[tex]4(1)-(1)[/tex]

[tex]4+1=5[/tex]

--------------------

ANSWER:

[tex]-6\Longrightarrow 2i(2i-i^{3} )[/tex]

[tex]5\Longrightarrow i(4i^{3} -i)[/tex]

[tex]7\Longrightarrow i^{2} (2i-5)[/tex]

[tex]-2\Longrightarrow i^{2} (3+i^{2} )[/tex]

----------------------------

Hope it helps...

Have a great day!!

Step-by-step explanation:

C = 6 n + 4,500

the set up cost is represented by the initial value of the function, which is $4,500.

the ongoing cost of materials and labor is represented by the rate of change of the function, which is $6 per bottle.

Answer:

The correct answers are:

The variable p is the independent variable.

The number of hours spent reading causes a change in the number of pages read.

The variable p is the dependent variable.

Step-by-step explanation: Hope this helps :)))

These two statements are correct and applicable

(1) The number of hours spent reading causes a change in the number of pages read.

(2) The variable p is the dependent variable.

"A Variable is a quantity that may change within the context of a mathematical problem or experiment. Typically, we use a single letter to represent a variable. The letters x, y, and z are common generic symbols used for variables."

"A dependent variable is the variable that changes as a result of the independent variable manipulation."

"A Line graph is a graphical display of information that changes continuously over time. A line graph may also be referred to as a line chart. Within a line graph, there are points connecting the data to show a continuous change. A Line graph has two axes(X- axis and Y-axis)"

We have,

Kelvin read 35 pages per hour

According to the question,

Number of hours increasing, number of pages also increasing

∵ The table data shows linear graph

We can clearly say that from a line graph definition,

These two are correct and applicable to Kelvin's situation

(1) The number of hours spent reading causes a change in the number of pages read.

(2) The variable p is the dependent variable.

Learn more about Line graph and variable here

https://brainly.com/question/20106471

https://brainly.com/question/20291071

#SPJ2

Answer:

Brianna left home and drove 3 miles in 6 minutes. She then stopped for 4 minutes to pick up coffee. Finally, she traveled the last 4 miles in 6 minutes to arrive at her babysitting job.

Step-by-step explanation:

This answer is from Plato.

Answer:

R= -50t^2 + 300t

-50tt(t-6)

-50(t-12)

so lets say that they sold 10 dollar tickets

-5000(4)

so they would lose -20000 dollars

-50(-2)

and the play would cost 100 dollars

Hope This Helps!!!

Answer:

1 describe the inequality graph

Answer:

x = number of bicycles = 35

y = number of cars = 55

Step-by-step explanation:

Let

x = number of bicycles

y = number of cars

x + y = 80 (1)

2x + 4y = 270 (2)

From (1)

x = 80 - y

Substitute x = 80 - y into (2)

2x + 4y = 270 (2)

2(80 - y) + 4y = 270

160 - 2y + 4y = 270

- 2y + 4y = 270 - 160

2y = 110

y = 110/2

y = 55

Substitute y = 55 into (1)

x + y = 80 (1)

x + 55 = 80

x = 80 - 55

x = 35

x = number of bicycles = 35

y = number of cars = 55

Answer:

a) 6

b) 12:35 ( not so sure about this one)

Step-by-step explanation:

a)

distance = speed * time

ruths distance = 4* 1.5 (because it takes her 1h 30 mins)

distance = 6miles    

b)  1/4 here is quarter so, 15mins

10:30 and then add 50 mins to that.

     she leaves at 11:20 and takes 1h and 15 mins ( 75mins) to walk home

     so 11:20 + 1h 15min

     = 12:35

hope this helps :)

Answer:

a) 6 miles

b) 12:35 pm

Step-by-step explanation:

a) 9 am to 10:30 am = 1 hour and 30 mins = 1.5 hours

4mph x 1.5 = 6miles

b) 10:30 am + 50 mins = 11:20 am

1 hour = 60 mins

60/4 = 15 mins

1 1/4 = 1 hour 15 mins

11:20 am + 1 hour 15 mins = 12:35 pm

Answer:

1

Step-by-step explanation:

x-y+xy=1-1+1*1=0+1=1

Answer:

1

Step-by-step explanation:

X=1

Y=1

here,

x-y+xy=1-1+1×1

or,x-y+xy=0+1=1

Staysafe❤

Answer:

(12/39) * (12/39) or 16/169

Step-by-step explanation: