Simplify the expression by combining like terms 18z +9z

Answer:  The width of the playing field = 45 ft

length of playing fiels =  86ft

Step-by-step explanation:

Step 1

Perimeter of rectangular field is given as 2 ( L+ b)

Let the width be represented as  x

such that the length = 41 ft longer than the width be  x+ 41

To find the length and breadth

Step 2

Perimeter = 2( L+ b)= 2l + 2b

Perimeter =  2 (x+41 ) + 2 x = 262

2x + 82 + 2x= 262

4x+ 82= 262

4x= 262 - 82

4x= 180

x= 180/4

x= 45

width= 45 ft

length = x+ 41= 45+ 41= 86ft

Answer and Step-by-step explanation:

This problem involves the use of trigonometric functions.

First, we will use the tangent trig function, and then the sine trig function.

[tex]tan(32) = \frac{x}{15}[/tex]

We solve for x by multiplying both sides by 15.

15(tan(32)) = x

Put this into a calculator and solve.

x = 9.373

Now, we solve for y.

[tex]sin(32) = \frac{9.373}{y}[/tex]

We multiply by y on both sides first.

y(sin(32)) = 9.373

Now, we divide each side by sin(32).

[tex]y = \frac{9.373}{sin(32)}[/tex]

Put this into a calculator and solve.

y = 17.6877

x = 9.373

y = 17.6877

These are your answers.

#teamtrees #WAP (Water And Plant)

Answer:

$1.50 is 105 Naira

Step-by-step explanation:

If the exchange rate is 1:70, that means that in order to get the amount of Naira equal to some amount of US dollars, you would multiply the number of US dollars by 70. And so we get...

1.5 x 70 = 105 (Naira)

Answer:

105 Naira

Step-by-step explanation:

Please see the attached image.

I hope this helps!

Answer:

The answer would be 0.05

Step-by-step explanation:

This is because it is PER Cent so 5% is 0.05 of 1

Answer:

1/20 and 0.05

Step-by-step explanation:

Answer: just turn them into decimals and use a calculator then turn them back into fractions in simplified form

Step-by-step explanation:

Answer:

whats your snap ill help

Step-by-step explanation:

Answer:

1508.6 steps

Step-by-step explanation:

one mile = 5280 feet

42 inches = 3.5 feet

5280 / 3.5 = 1508.57

Answer:

∠U = 26°

∠V = 35°

∠W = 119°

Step-by-step explanation:

Given:

∠U = (x+9)°

∠V = (2x+1)°

∠W = (7x)°

Find:

Value of each angle

Computation:

Using angle sum property

∠U + ∠V + ∠W = 180°

(x+9)° + (2x+1)° + (7x)° = 180°

10x + 10 = 180

x = 17

So,

∠U = (x+9)° = 17 + 9 = 26°

∠V = (2x+1)° = 34 + 1 = 35°

∠W = (7x)° = 7 x 17 = 119°

Answer:

(a) [tex]y = \frac{4}{x^2}[/tex]

(b) [tex]x = \frac{2}{5}[/tex]

Step-by-step explanation:

Given

Variation: Inverse proportional.

This is represented as:

[tex]y\ \alpha\ \frac{1}{x^2}[/tex]

See attachment for table

Solving (a):

First convert variation to equation

[tex]y = k\frac{1}{x^2}[/tex]

From the table:

[tex](x,y) = (1,4)[/tex]

So, we have:

[tex]4 = k * \frac{1}{1^2}[/tex]

[tex]4 = k * \frac{1}{1}[/tex]

[tex]4 = k * 1[/tex]

[tex]4 = k[/tex]

[tex]k = 4[/tex]

Substitute 4 for k in [tex]y = k\frac{1}{x^2}[/tex]

[tex]y = 4 * \frac{1}{x^2}[/tex]

[tex]y = \frac{4}{x^2}[/tex]

Solving (b): x when y = 25.

Substitute 25 for y in [tex]y = \frac{4}{x^2}[/tex]

[tex]25 = \frac{4}{x^2}[/tex]

Cross Multiply

[tex]25 * x^2 = 4[/tex]

Divide through by 25

[tex]x^2 = \frac{4}{25}[/tex]

Take positive square roots of both sides

[tex]x = \sqrt{\frac{4}{25}[/tex]

[tex]x = \frac{2}{5}[/tex]

Step-by-step explanation:

step 1. all the side length are different therefore all of the internal angles are different.

step 2. a triangle with all different angles is scalene.

step 3. all of the angles are less than 90°

step 4. a triangle with all angles less than 90° is acute.

Answer:

1. Yes

2. No

3. Yes

Step-by-step explanation:

We have three equations where x is equal to -4. We are then asked if -4 are a solution to these equations.

To solve we need to substitute the x in every equation for -4. Start :

1.

3(2(-4) - 4) = -36

3(-8 - 4) = -36

-24 - 12 = -36

Therefore -4 is a solution.

2.

5(-4) - 6(-4) - (-4) = 18

-20 + 24 + 4 = 18

4 + 4 = 18

8 ≠ 18

Therefore -4 is not a solution.

3.

5 - 2(3(-4) - 1) = 31

5 - 2(-12 - 1) = 31

5 - 2(-13) = 31

5 + 26 = 31

Therefore -4 is a solution.

Answer:

85%

Step-by-step explanation:

Answer:

85%

Step-by-step explanation:

What I would do is how much she would score if the test was a 25 question test. She would have scored 21.33. Now add this to her current score. 64+21.33 = 85.33. The rounded answer is 85.

Answer:

1) 7 x (6+y)

2)(  y x 6) + (y x 7)

3) 6(y+7)

4) (y x 6) + y^2

I hope im right !

Step-by-step explanation:

( 7 * 6 ) + ( 7 * y) ➡ 7 (6 +y)

y(6 + 7) ➡ ( y * 6 ) + ( y * 7)

( 6 * y) + ( 6 * 7) ➡ 6 ( y + 7)

y( 6 + y) ➡ ( y * 6 ) + y²

Hope it will help :)

Answer:

The answer is below

Step-by-step explanation:

Chancellor Manufacturing makes two pumps for use in household reef aquariums. The Standard pump (Model A) requires 4.5 lbs of stainless steel while the Deluxe lightweight pump (Model B) 3.0 lbs of stainless steel. There are 63 lbs of stainless steel available during this production period. The combined production of both pumps must be at least 12 pumps. There are orders for at least 6 of the lightweight Model B. Lastly, management has decided that no more than 15 Model B pumps be produced.

The cost to produce one Standard pump is $150 and to produce one Deluxe pump is $210.

Solution:

a) Let x represent model pump A and let y represent model pump B.

Since There are 63 lbs of stainless steel available, hence:

4.5x + 3y ≤ 63

Both pumps must be at least 12 pumps. Therefore:

x + y ≤ 12

There are orders for at least 6 of the lightweight Model B:

y ≥ 6

Also,  no more than 15 Model B pumps be produced:

y ≤ 15

The cost to produce one Standard pump is $150 and to produce one Deluxe pump is $210. The cost equation is:

Minimize Cost = 150x + 210y

b)

Hence the LP formation is:

Minimize Cost = 150x + 210y

4.5x + 3y ≤ 63

x + y ≤ 12

y ≥ 6

y ≤ 15

x ≥ 0.

c) The LP problem was solved using geogebra online graphing tool.

The points that satisfy the problem are:

(0, 6), (0,12), (6, 6)

At (0,6); cost = 150(0) + 210(6) = 1260

At (0,6); cost = 150(0) + 210(12) = 2520

At (6,6); cost = 150(6) + 210(6) = 2160

Hence the minimum cost is at (0, 6)

Answer:

Minimum = 23,040

Q1 = 30315

Q2 = 31975

Q3 = 31975

Maximum = 33650

Step-by-step explanation:

Ordered data:

23040, 24050, 26520, 28730, 30170, 30460, 30930, 31300, 31860, 31920, 32030, 32320, 32340, 32590, 32700, 32720, 33020, 33190, 33280, 33650

The five number summary :

Minimum = 23,040

Lower quartile (Q1) = 1/4(n+1)th term

n = 20

Q1 = 1/4* (21)th term

Q1 = 5.25 ; (5th + 6th) term / 2

Q1 = (30170 + 30460) / 2 = 30315

Median (Q2) :

Q2 = 1/2* (21)th term

Q2 = 10.5 ; (10th + 11th) term / 2

Q2 = (31920 + 32030) / 2 = 31975

Upper Quartile (Q3) :

Q3 = 3/4* (21)th term

Q3 = 15.75 ; (15th + 16th) term / 2

Q 3 = (32700 + 32720) / 2 = 32710

Maximum : 33650

Answer:

0.125⅓×0.25½

(125/1000)⅓×(25/100)½

(5³/10³)⅓ × (5²/10²)½

5/10 × 5/10

1/2×1/2

1/4

Answer:

the last one 3(x+4) = 3x + 12

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Because the term 7x^3 is to the third power, the curve moves like x^3. This means that as x approaches infinity and -infinity, it approaches infinity and -infinity respectively. The answer is D.

Answer:

Results are below.

Step-by-step explanation:

Giving the following information:

She can either take it in five installments of $60,000 annually, starting from now; or she can take a lump-sum of $255,000 now.

First, we determine the value of the 5 installments using a 5% annual compounded rate.

We calculate the future value, and then the present value:

FV= {A*[(1+i)^n-1]}/i

A= annual payments

FV= {60,000*[(1.05^5) - 1]} / 0.05

FV= $331.537.88

PV= FV/(1+i)^n

PV= $259,768.60

At an annual rate of 5% compounded annually, she should choose the five installments instead of the $255,000.

Now, if the annual rate is 6% continuously compounded.

First, we need to calculate the effective interest rate:

r= e^i - 1

r= effective inerest rate

r= e^0.06 - 1

r= 0.0618

FV= {60,000*[(1.0618^5) - 1]} / 0.0618

FV= 339,443.23

PV= 339,443.23/1.0618^5

PV= $251,509.01

At an annual rate of 6% compounded continuously, she should choose the $255,000.

Answer:

8 times 9 or 72 devide 9 is 8

Step-by-step explanation:

that th answer

Answer:

The factors of 72 are 1,2,3,4,6,8,9,12,18,24,36,72

Step-by-step explanation:

9 is a factor of 72 because 9×8=72

Answer:

D) Yes. The five trials are independent, have only two outcomes, and have the same P(success); n = 5, r = 2, p = 1/6.

Step-by-step explanation:

The Number of boxes = 6

Box containing a prize = 1

Probability of success, p = box containing a price / number of boxes = 1 /6

Number of trials = 5

Probability of success on exactly 2 trials, r = 2

Hence,

P(r = 2) = nCr * p^r * (1-p)^(n-r)

n = 5 ; r = 2 ; p = 1/6

Using a binomial probability calculator :

P(r = 2) = 0.1608

Answer:

-3m+7.5=4.5m

Step-by-step explanation:

Answer:

The left graph is a positive slope (yellow box)

The middle graph has no slope (green)

The right graph has a negative slope (purple)

Step-by-step explanation:

The left graph has a positive slope because the slope increases left to right. We can see this because the line starts at the origin at zero (0, 0), and increases.

The right graph has a negative slope because the slope decreases left to right. We can see this because it starts a value greater than zero, and gradually decrease to zero.

The middle graph contains no slope because it is a straight horizontal line. If we were to calculate the slope, (rise/run) of two points, the slope is the same in every point. It is constant.

The correct answer is,

The left graph is a positive slope (yellow box)

The middle graph has no slope (green)

The right graph has a negative slope (purple)

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Here, we have.

The left graph has a positive slope because the slope increases left to right. We can see this because the line starts at the origin at zero (0, 0), and increases.

The right graph has a negative slope because the slope decreases left to right. We can see this because it starts a value greater than zero, and gradually decrease to zero.

The middle graph contains no slope because it is a straight horizontal line. If we were to calculate the slope, (rise/run) of two points, the slope is the same in every point. It is constant.

Hence, The correct answer is,

The left graph is a positive slope (yellow box)

The middle graph has no slope (green)

The right graph has a negative slope (purple)

To learn more on slope click:

https://brainly.com/question/3605446

#SPJ2

Answer:

Explanation:

-5b = 10a

-5b / -5 = 10a / -5

Answer:

Using graph for units

D=1/2(6)(9)=27 sq units

E=1/2(7)(6)=21 sq units

F=1/2(6)(8)=24 sq units

Step-by-step explanation:

Answer:

D=27 units, E=21 units, F=24 units

Step-by-step explanation:

The formula for area of a triangle is (BASE * HEIGHT)/2

For triangle D, the base is 9 units and the height is 6 units. Then you can apply the formula and do 9*6 which is 54 and then do 54/2 which is 27 units.

Similarly, the base for E is 6 units, and the height is 7 units. So you do 6*7 which is 42 and then do 42/2 which is 21 units.

Again, the base for F is 6 units, and the height is 8 units. Then again, using the formula, we can do 6*8 which is 48 and then do 48/2, which is 24 units.

Hopefully this helped!

Answer:

Step-by-step explanation:

For all Plato users.

We have to find the sum of the series has been given as.

[tex]\sum_{k=1}^{8}5(\frac{4}{3} )^{k-1}[/tex] -----(1)

If the series has been given as,

[tex]\sum_{n=1}^{k}a(r)^{n-1}[/tex] -------(2)

It's a geometric series with first term 'a' and common ratio 'r'.

Comparing both the expressions (1) and (2),

[tex]a=[/tex] 5

[tex]r=\frac{4}{3}[/tex]

Number of terms 'n' = 8

Sum of the k terms of this series is given by,

Sum = [tex]\frac{a(r^k-1)}{r-1}[/tex]

       = [tex]\frac{5[(\frac{4}{3})^8-1)]}{\frac{4}{3}-1 }[/tex]

       = [tex]\frac{5(9.98872-1)}{\frac{1}{3}}[/tex]

       = [tex]\frac{44.9436}{\frac{1}{3} }[/tex]

      = 134.83

Therefore, Option (B) is the correct option.

Learn more,

https://brainly.com/question/21087466

Answer:

Y>2x-4

B

Have a great day, hope this helps

Depreciation formula :

Amount x (1-rate)^time

125 x (1-0.005)^5

124 x 0.995^5 = 121.91

Answer: $121.91