12. Find one solution for each equation. Assume all angles are acute angles
a. cos(0 + 4°) = sin(30 +2°)

Answer:

x= 21/4

Step-by-step explanation:

1- Convert the expressions

5 ( x - 3 3/4 ) = 7 1/2

2- Remove the parentheses

5 ( x - 15/4 ) = 15/2

3- Move the constant to the right

5x - 75/4 = 15/2

4- Calculate the sum

5x = 15/2 + 75/4

5- Divide both sides

5x = 15/2 + 75/4

Answer:

-7

Step-by-step explanation:

Seems like the pattern is adding and then subtracting the next square number up:

7 + 4 = 11

11 - 9 = 2

2 + 16 = 18

so 18 - 25 = -7 is the next number

Answer:

32 quarts

Step-by-step explanation:

1 gallon = 4 quarts

⇒ 8 gallons = 8 x 4 = 32 quarts

Answer:

32 quarts

Step-by-step explanation:

Khan

Answer:

Step-by-step explanation:

I'm going to guess that the question is "How do you represent the distance between the left and right sides?"

The red dots are closed which means that the end points are included.

5 ≤  x  ≤  8

The length is 8 - 5 = 3

[tex] {y}^{2} = 49[/tex]

Move the square to the right-hand side and convert it to underoot

[tex]y = \sqrt{49} [/tex]

Calculate the root of 49

[tex]y = 7 \:or -7[/tex]

Answer:

y = +7 or -7

Step-by-step explanation:

y^2 = 49

square rooting both sides

y = √49

y = +7 or -7

Answer:

so therefore the final answer will be 16

let's firstly convert the mixed fractions to improper fractions and then divide them.

[tex]\stackrel{mixed}{4\frac{2}{3}}\implies \cfrac{4\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{14}{3}} ~\hfill \stackrel{mixed}{1\frac{5}{9}}\implies \cfrac{1\cdot 9+5}{9}\implies \stackrel{improper}{\cfrac{14}{9}} \\\\[-0.35em] ~\dotfill\\\\ -\cfrac{14}{3}\div\cfrac{14}{9}\implies -\cfrac{~~\begin{matrix} 14 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{3}\cdot \cfrac{9}{~~\begin{matrix} 14 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies -\cfrac{9}{3}\implies -3[/tex]

Answer:

-3

Step-by-step explanation:

Lets convert 4 2/3 to an improper fraction

-(4 * 3/3 + 2/3)/1 5/9

Combine 4 and 3/3

-(4 * 3/3 + 2/3)/1 5/9

Combine numerator over denom

-4 * 3 + 2/3/1 5/9

Simplify numerator

-12 + 2/3/1 5/9

Add 12 and 2

-14/3/1 5/9

Now we convert 1 5/9 to an improper.

-14/3/(9/9) + (5/9)

Combine

-14/3/(9 + 5)/9

Add 9 and 5

-14/3/(14/9)

Multiply yhe numerator by the reciprocal of the denom

-14/3 * 9/14

14(-1)/3 * 9/14

-1/3 * 9

Cancel the common factor of 3

-1/3 * (3(3))

-1 * 3 = -3

Answer:

Step-by-step explanation:

I am married. I can tell you, I'd never give any answer but yes, no matter how I felt about her at the time.

Answer:

R330

Step-by-step explanation:

2 + 3 = 5

5x = 825

2x = 825 x 2/5

825 x 2 = 1650

1650/5 = 330

Mandy makes R330.

Mandy's share from the profit is R495

Data;

This is the portion shared between two or more entities in a definite proportion.

To find Mandy's share, let's add 2 and 3 and then take the fraction of 3/5 and multiply it by the profit made.

[tex]2 + 3 = 5\\\frac{3}{5} * 825 = 495[/tex]

Mandy's share from the profit is R495

Learn more on ratio here;

https://brainly.com/question/2914376

Answer:

c = ?

j = 13 bottles

c × j = $9.23

c = $9.23 ÷ j

= $9.23 ÷ 13

= $0.71 / 71 cents

Answer:

$0.71

Step-by-step explanation:

If c x j = $9.23 and j is 13, then c is  $9.23/13

$9.23/13 = $0.71

=$0.71

Answer:(a) getting the equation:

We'll assume that the altitude is represented by the x-axis and that the boiling point is represented by the y-axis.

Therefore, we have two given points:

(8400 , 200.4) and (4200 , 206.7)

Since the relation is linear, therefore, the graph forms of straight line with the general equation:

y = mx + c where m is the slope and c is the y-intercept.

First, we will calculate the slope:

m = (y2-y1) / (x2-x1) = (206.7 - 200.4) / (4200 - 8400) = -0.0015

Therefore, the equation of the line now is:

y = -0.0015x + c

Then, we will need to calculate the y-intercept. In order to do so, we will use any give point and substitute in the previously obtained equation as follows:

y = -0.0015x + c

206.7 = -0.0015(4200) + c

c = 213

Based on the above calculations, the equation of the line is:

y = -0.0015x + 213

(b) getting the boiling point at altitude = 2100 ft:

Now, in order to calculate the boiling point at altitude 2100, we will substitute in the equation of the line as follows:

y = -0.0015(2100) + 213 = 209.85 degrees Fahrenheit

Step-by-step explanation:

Answer:

C or 260.48

Step-by-step explanation:

Find area of both triangles:

20*16/2/2*2=160

Find area of circle;

pi*r*r/2= area of circle

d/2=r

16/2=8

pi*8*8/2 is about 100.53

160+100.53=260.53

Answer:
5y + 2

Step-by-step explanation:

5 - 2y + 7y - 2 - 1

5 - 2 - 1 - 2y + 7y

2 + 5y

Hope it helps ⚜

The length of the ramp is  96.5

Given the following parameters from the question

The vertical rise of the ramp = 8 inches

The angle of elevation =  4.76°.

Required

length of the ramp

Using the SOH CAH TOA identity;

tan theta = opp/hyp

sin4.76 = 8/H
H = 8/sin4.76

H = 8/0.0829

H = 96.5

Hence the length of the ramp is  96.5

Learn more on SOH CAH TOA here; https://brainly.com/question/20734777

Answer:

The exponent is different from each other. One exponent is 3/4 and the other is 2/4. These make the value different.

Step-by-step explanation:

Answer:

a) n = 4 , t = ?

[tex]t = 5 {n}^{2} + 15 \\ \\ t = 5 {(4)}^{2} + 15 \\ \\ t = 5(16) + 15 \\ \\ t = 80 + 15 \\ \\ t = 95 \: min[/tex]

__o__o__

b) n = ? ,

t = 2hours 20mins ––> t = (2× 60) mins + 20 mins

t = 120 + 20 = 140 mins

so; time in the mins = 140 mins

[tex]t = 5 {n}^{2} + 15 \\ \\ 140 = 5 {n}^{2} + 15 \\ \\ 5 {n}^{2} = 140 - 15 \\ \\ 5 {n}^{2} = 125 \\ \\ {n}^{2} = \frac{125}{5} \\ \\ {n}^{2} = 25 \\ \\ n = 5[/tex]

so ; five people in 2hours 20mins

Answer:

Reflection across y

Step-by-step explanation:

Y is the line up and down. Each shape is a reflection of each other across this line.

Answer:

Step-by-step explanation:

Let x represent the width of the garden. Then its length is 3x-1 and its area is ...

  A = LW . . . . . . . . . . . . area of a rectangle is length times width

  A = (3x -1)(x) = 150

  3x^2 -x = 150

  x^2 -1/3x +1/36 = 50 +1/36 . . . . divide by 3 and complete the square

  x -1/6 = √(50+1/36) . . . . . . . . . take the square root

  x = (1 +√1801)/6 ≈ 7.2397 . . . width of Chanda's garden

The length will be ...

  3x -1 = 3(1 +√1801)/6 -1 = (1 +√1801)/2 -1 = (-1 +√1801)/2 ≈ 20.7191

To the nearest tenth meter, the garden is 20.7 m long and 7.2 m wide.

Answer: 17

Step-by-step explanation:

B/c corresponding parts of congruent figures are congruent,

4s = 68

s = 17

Answer:

17

Step-by-step explanation:

C = R

4s = 68

[tex]s = \frac{68}{4} [/tex]

s = 17

Answer:

the diameter is 14cm

Step-by-step explanation:

to get the circumference of a circle you would need to times the diameter (d) by pi or in this case n which is 3.1

this result is 43.4cm

now to figure out the diameter we would have to reverse this so the equation would be

d=43.4/n

which is the same as d= 43.4/3.1

the result of this is d= 14

so the diameter is 14cm.

deserving of brainliest?

Answer:

SOLUTION,

HERE,

Area of whole fig= l×b

=5×15

=75 sq.in

Area of unshaaded part=l×b

=3×8

=24 sq.in

Area of shaded part=(Area of whole fig)-(Area of unshaded part)

=75-24

=51 sq.in

hope it helps u :)

Answer:

choice a

Step-by-step explanation:

angle 45 means, its a isosceles triangle.

so y = √3

x^2 = 3+3= 6

x = √6

Answer:

(4x + 3)(4x - 3)

Step-by-step explanation:

I am going to assume by 16x2 -9 you mean 16x² - 9

     The factorization means the factors are "broken" up. If you multiply them together, we will reach 16x² - 9 again.

     First, we can look at factors of 9. This gives us 1, 3, and 9. We will use 3. Since the nine is negative, one will be + 3 and one will be - 3 since a negative times a positive is a negative.

(   + 3)(   - 3)

     Last we can factor the 16x² portion. I know that 4 times 4 is 16, and 4x times 4x is 16x².

(4x + 3)(4x - 3)

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.

- Heather

[tex]36-b ^ { 2 } -c ^ { 2 } +2bc\\= 36-\left(b^{2}+c^{2}-2bc\right) \\= 6^{2}-\left(b-c\right)^{2} \\=\boxed{ \left(6-b+c\right)\left(6+b-c\right) }[/tex]

Hope it helps ⚜

Answer:

[tex]2x + 2y = 14 \: .....(1) \\ \\ 5x - 2y = 14 \: .....(2) [/tex]

From equation (1) ;

[tex]2x + 2y = 14 \\ \\ 2y = 14 - 2x \\ \\ y = \frac{14 - 2x}{2} \\ \\ y = 7 - x[/tex]

Substitute in equation (2)

[tex]5x - 2y = 14 \\ \\ 5x - 2(7 - x) = 14 \\ \\ 5x - 14 + 2x = 14 \\ \\ 7x = 14 + 14 \\ 7x = 28 \\ \\ x = \frac{28}{7} \\ \\ x = 4[/tex]

[tex]y = 7 - x \\ y = 7 - 4 \\ \\ y = 3[/tex]

Given :

To Find :

Solution :

Let us suppose ,

→ CP = Rs x

Therefore the profit will be ,

→ Profit = SP - CP

→ Profit = 208 - x

Now we know that ,

→ Profit% = profit/CP * 100

Substituting the respective values ,

→ 4 = (208-x)/x * 100

→ 4 * x = (208- x)*100

→ 4x = 20800 - 100x

→ 100x + 4x = 20800

→ 104x = 20800

→ x = 20800/104

→ x = 200

Hence the cost price is Rs 200.

I hope this helps.

Refer to the attachment!

Answer:

Multiplying the lines and the cost.

Step-by-step explanation:

35$ times 6 is 210. 25$ times 6 is 150. This is the cost of both companies.