13. Prove 6n + 3 is equivalent to 3n + 2 + 3n + 1 by substituting n = 5 into both
expressions.

Answer:

The height of the cliff CD is approximately 539.76 m

Step-by-step explanation:

The given parameters are;

The first angle of elevation with which the captain sees the person on the cliff = 61°

The second angle of elevation with which the captain sees the person on the cliff after moving 92 m closer to the cliff = 69°

The angle made by the adjacent supplementary angle to the second angle of elevation = 180° - 69° = 111°

∴ Whereby, the rays from the first and second angle of elevation and the distance the ship moves closer to the cliff forms an imaginary triangle, we have;

The angle in the imaginary triangle subtended by the distance the ship moves closer to the cliff = 180° - 111° - 61° = 8°

By sine rule, we have;

AB/(sin(a)) = BC/(sin(c))

Which gives;

92/(sin(8°)) = BC/(sin(61°))

BC = (sin(61°)) × 92/(sin(8°)) ≈ 578.165 m

BC ≈ 578.165 m

The height CD = BC × sin(69°)

∴  The height of the cliff CD = 578.165 m × sin(69°) ≈ 539.76 m.

The height of the cliff CD ≈ 539.76 m.

Answer:

18 gallons from container [tex]a[/tex] and 22 gallons from the container [tex]b[/tex] to be mixed to get the required mixture.

Step-by-step explanation:

Given that the container [tex]a[/tex] has 20% concentrated cleaner

and container [tex]b[/tex] has pure water which has 0% cleaner.

Let x gallons from container a and y gallons from the container b are mixed to get a 9% concentrated solution.

So,

[tex]9\%\; \text{of}\; (x+y) = (20\% \; \text{of}\; x )+(0\% \; \text{of}\; y)\cdots(i)[/tex]

As the total amount of the final solution= 40 gallons

So, [tex]x+y=40\cdots(ii)[/tex]

Using the value of equation (ii) in equation (i), we have

9% of 40 = 20% of x

[tex]\Rightarrow 0.09\times 40=0.2 \times x[/tex]

[tex]\Rightarrow x=\frac{0.09\times 40}{0.2}[/tex]

[tex]\Rightarrow x=18[/tex] gallons.

From equation (ii),

18+y=40

[tex]\Rightarrow y=40-18=22[/tex] gallons.

Hence, 18 gallons from container [tex]a[/tex] and 22 gallons from the container [tex]b[/tex] to be mixed to get the required mixture.

Answer: 984.8

Step-by-step explanation:

Answer: right angles x equals 7 and both m1 and 1 arre 5

Step-by-step explanation:

Answer: CA

Step-by-step explanation:

corresponding angles

90=5x

x=18

m1=90

m2=90

Answer:

-11x+8y

Step-by-step explanation:

Answer:

y=7(x-5)+3

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Answer:

8 apples

Step-by-step explanation:

By saying gets rid of, it means subtraction

So, the equation would be

10-2

=8

Hope that clarified your answer!

Answer:

Step-by-step explanation:

11-2.5= 8.5

8.5-2.5=6

your answer is 2.5

Answer:

(c) A convenience sample error was made in this design. This type of sampling is only representative of one neighborhood and not the entire city population.

Answer:

-9x+16

Step-by-step explanation:

-3x+7+-6x+9=-9x+16

-3-6= (tecnectly adding but put negative sign with ur answer!)

7+9=16

Put together and Done!

Hope helps :D

Answer: 1: Given

2: Distribution

3: Subtraction

4: subtraction

5:division

Step-by-step explanation:

Answer: 9 goes into 63 7 times, but 9 does not go into

72 9 times, so the answer is no.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

I Can't explain it,I'm sorry

Answer:

25%

Step-by-step explanation:

Given parameters:

Amount earned per month = 800

Her savings goal = 2400

Unknown:

Percentage of monthly income that must go into savings = ?

Solution:

In a year, Jessica will earn:

          12(800) = 9600

Now;

      To earn 2400;

 Let y be the percentage of her earning that goes into saving per year;

         2400 = [tex]\frac{y}{100}[/tex] x 9600

         2400 = 96y

               y = 25%

Answer:

Option 4

Step-by-step explanation:

Answer:

To find the x-intercept, substitute in  

0

for  

y

and solve for  

x

. To find the y-intercept, substitute in  

0

for  

x

and solve for  

y

.

x-intercept(s):  

(

3

,

0

)

y-intercept(s):  

(

0

,

2

)

Step-by-step explanation:

Answer:

I can barley see it but i think i know what to do.

Step-by-step explanation:

First i have to write down on a piece of paper:D

Answer:

I believe it is 1.) SAS (angle side angle) 2.) SSA (side side angle), but can not be proven as a postulate, so not enough information, 3.) SAS (side angle side) 4.) SSS (side side side)

Step-by-step explanation:

Answer:

1) ASA (angle side angle postulate)

2) not enough information

3)SAS (side angle side)

4) SSS (side side side)

Answer:

-0.81818181818

Step-by-step explanation:

Answer:

-9/11

Step-by-step explanation:

Answer:

B- 20 yards

Step-by-step explanation:

First you have to find the hypotenuse by finding the square root of 28 squares plus 45 squared which equals 53 yards. Next you have to add the two legs of the right triangle so we can subtract the shortcut length from that. So you have to do 28 plus 45 which equals 73 yards. 73 minus 53 is 20. So the answer is 20 yards.

Answer:

20

you have to find the hypotenuse by finding the square root of 28 squares plus 45 squared which equals 53 yards.  you have to add the two legs of the right triangle so we can subtract the shortcut length from that. So you have to do 28 plus 45 which equals 73 yards. 73 minus 53 is 20. So the answer is 20 yards.

The other person provided a great answer but i do it a little different....                            

                                        [tex]\left[\begin{array}{ccc}A^2=C^2-B^2\\A^2=10^2-6^2\\A^2=100-36\\A^2=64\\\sqrt{64}=8 \end{array}\right][/tex]

All i did was use the formula A^2=C^2-B^2. I Plugged in the numbers to the formula and got A^2=10^2-6^2. Next, I found what 10^2 equals by doing 10*10 which equals 100. Then, i found out what 6^2 equals by doing 6*6 which equals 36. Next, what i did was subtracted 100 from 36 and got 64. Finally i found the square root of the number 64 which equal 8 since 8x8=64.  

The measure of the unknown variable {x] is 8 inches.

The Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. Mathematically, it can be written as -

(hypotenuse)² = (base)² + (perpendicular)²

Given is a right angle triangle.

Using the Pythagoras theorem, we can write -

(hypotenuse)² = (base)² + (perpendicular)²

(10)² = (base)² + (6)²

(base)² = (10)² - (6)²

(base)² = (10 - 6)(10 + 6)

(base)² = 4 x 16

(base)² = 64 inches

(base) = 8 inches

x = 8 inches

Therefore, the measure of the unknown variable {x] is 8 inches.

To solve more questions on Pythagoras theorem, visit the link below -

https://brainly.com/question/343682

#SPJ2

Answer:

-12

Step-by-step explanation:

Answer:

-12

Step-by-step explanation:

Plug in x.

2(2)-3(2)+(-10)

Simplify.

4-6-10=-12

Hope this helps...have a great day c:

Answer:

how are you

Step-by-step explanation:

Answer:

The y intercept would be (0, 1/3)

The number at the end is always the y value. In a y intercept x is always 0.