The Perimeter of the park is 318 m. Determine the length of the park.


2 questions, please answer one of the 2 :)
*GRADE 9 WORK*

Answer:

a) x = 17/8

b) x = 23

c) x = -8/11.

Step-by-step explanation:

a)

-3x + 5 = 5x - 12

Add 3x to both sides:

5 = 8x - 12

Add 12 to both sides:

17 = 8x

Divide both sides by 8:

17/8 = 8x/8

x = 17/8.

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

b)

6(x-3)-4(x+2) = 20

Distribute:

6x - 18 - 4x - 8 = 20

Combine like terms:

2x - 26 = 20

Add 26 to both sides:

2x = 46

Divide both sides by 2:

x = 23.

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

c)

-2/5(x + 3) = 1/3(x - 2)

Distribute:

-2/5x - 6/5 = 1/3x - 2/3

Add 2/5x to both sides by creating a common denominator:

-6/15x - 6/5 = 5/15x - 2/3

-6/5 = 11/15x - 2/3

Add 2/3 to both sides. Create common denominator:

-18/15 = 11/15x - 10/15

-8/15 = 11/15x.

Divide both sides by 11/15:

[tex]\frac{-8}{15}* \frac{15}{11} = \frac{-8}{11} = x[/tex]

x = -8/11.

Answer:  A

Step-by-step explanation:

The standard form of a cosine equation is: y = A cos (Bx - C) + D  where

Plot the points (see graph below).

A = 28

[tex]\dfrac{1}{2}P=6\quad \rightarrow \quad P=12\\\\\\P=\dfrac{2\pi}{B}\qquad \rightarrow \qquad 12=\dfrac{2\pi}{B}\qquad \rightarrow \qquad \large\bold{B=\dfrac{\pi}{6}}[/tex]

Phase Shift = 7 = C/B

                      [tex]7=\dfrac{C}{\frac{\pi}{6}}\qquad \rightarrow \qquad \large\bold{C=\dfrac{7\pi}{6}}[/tex]

D = 49

Input the values of A, B, C, and D into the standard form of a cosine equation to get:

[tex]\large\boxed{y=28\cos \bigg(\dfrac{\pi}{6}x-\dfrac{7\pi}{6}\bigg)+49}[/tex]

Answer:

7 cm

Step-by-step explanation:

The area of a right triangle is given by

A = 1/2 bh

21 = 1/2 y* 6

21 = 3y

Divide each side by 3

21/3 = 3y/3

7 = y

The base is 7 cm

Area formula: A = bh/2

We have a height of 6, a base of y, and a area of 21.

Fill in and solve:

21 = y * 6 / 2

21 = 6y/2

21 = 3y

7 = y

Therefore, the base is 7

Best of Luck!

Answer:

y = x/3 + 10

Step-by-step explanation:

Let y be the number of minutes the flight takes

She can take off 10 minutes later than expected. She will be able to travel at  a speed three times than expected.

Let her expected speed be s, therefore, she can travel at 3s.

x = number of minutes the flight was expected to take.

In terms of distance and speed:

x = d / s ______(1)

where d = total distance traveled

The time for the flight (minus waiting time) is now the division of the distance she traveled and her speed, i.e.:

t = d / 3s

From (1):

=> t = x / 3

The time she spent waiting is 10 minutes.

Therefore, the total time that the flight takes (plus waiting time) is:

y = t + 10

=> y = x/3 + 10

Answer:

$4.18 dollars per pound

Step-by-step explanation:

We can find the price in dollars per pound by dividing the cost by the number of pounds:

14.63/3.5 = 4.18

This means the price in dollars per pound is $4.18

Answer:

1-(-3)=4

Step-by-step explanation:

To find the range you have to look at the list of numbers:

1, -2, -3, -3

Then you take the highest number, 1, and the lowest, -3, and then subtract.

1-(-3)

And once you do the math, that'll leave you with 4.

Answer:

9

Step-by-step explanation:

Given that (1, 2) is the vertex of the function represented by the table of values above, the rate of change for the interval from x = 5 to x = 6.

f(5) = 18

f(6) = ?

=>Find f(6) using the vertex form function, f(x) = a(x - h)² + k

Where, h and k are the given vertex of the function = (1, 2).

h = 1, k = 2

Thus,

f(x) = a(x - 1)² + 2

Find the value of a by using any of the points given in the table.

Using (3, 6), we have the following,

6 = a(3 - 1)² + 2

6 = a(2)² + 2

6 = 4a + 2

Subtract 2 from both sides

6 - 2 = 4a

4 = 4a

Divide both sides by 4

1 = a

a = 1

Let's find f(6) using f(x) = a(x - 1)² + 2

Plug the value of a and x

f(6) = 1(6 - 1)² + 2

f(6) = 25 + 2

f(6) = 27

==>Find the rate of change/slope

f(5) = 18

f(6) = 27

Rate of change =

[tex] \frac{f(6) - f(5)}{6-5} [/tex]

[tex] \frac{27- 18}{6-5} [/tex]

[tex] \frac{9}{1} [/tex]

Rate of change = 9

Answer: 3:4

Step-by-step explanation:

Answer:

The FitnessGram Pacer Test is a multistage aerobic capacity test that progressively gets more difficult as it continues. The 20 meter pacer test will begin in 30 seconds. Line up at the start. The running speed starts slowly but gets faster each minute after you hear this signal bodeboop. A sing lap should be completed every time you hear this sound. ding Remember to run in a straight line and run as long as possible. The second time you fail to complete a lap before the sound, your test is over. The test will begin on the word start. On your mark. Get ready!… Start

Answer:

65°

Step-by-step explanation:

The missing angle is x°

tan x° = [tex]\frac{opposite }{adjacent}[/tex]

tan x° = [tex]\frac{850}{400\\}[/tex]

tan x° = 2.125

Using a calculator insert

tan^(-1)(2.125) ≈ 65°  (after rouding the the nearest unit)

Answer:

αλ and βλ

Step-by-step explanation:

if alpha beta are the roots of ax² + bx + c = 0, then:

Sum of roots = α + β = -coefficient of x / coefficient of x² = -b/a

product of roots = αβ = Constant / coefficient of x² = c/a

Let x and y be the roots of ax² + bλx + cλ² = 0

Sum of roots = x + y = -coefficient of x / coefficient of x² = -bλ/a

product of roots = xy = Constant / coefficient of x² = cλ²/a

x + y = -bλ/a = λ(α + β) = αλ + βλ

Comparing terms gives:

x = αλ and y= βλ

Therefore the roots of ax² + bλx + cλ² = 0  are αλ and βλ

Answer:

Option A and C

Step-by-step explanation:

An isosceles triangle have:

=> Two equal angles

=> Two sides with the same length

Answer:

A & C

Step-by-step explanation:

The triangle is an isosceles triangle. The two base angles are equal. Two sides of the triangle are same in length. All the angles in the triangle shown are less than 90 degrees.

Answer:

You have to multiply all the sides by 4.

B to C = 2.8*4

2.8 * 4 = 11.2

B to A = 3*4

3*4 = 12

A to C = 2.2*4

2.2*4 = 8.8

Hope this helped!

Answer: x>1/6

Step-by-step explanation:

For this problem, you solve it as if it had an equal sign.

-2(8x-4)<2x+5                        [distribute -2]

-16x+8<2x+5                           [combine like terms by adding and subtracting on both sides]

3<18x                                      [divide both sides by 18]

x>1/6

Answer:

2

Step-by-step explanation:

sec∅ is equal to 1/cos∅ or (hypotenuse over adjacent).

With that in mind:

sec∅ = 2/1

sec∅ = 2

Answer:

B. 2

Step-by-step explanation:

We need to find the value of secant for this triangle.

Remember the trigonometric functions: secant = hypotenuse / adjacent, where the hypotenuse is the longest side (2 in this case), and the adjacent is the side right next to the labelled angle but is not the hypotenuse (1 in this case).

Plugging the values into the equation yields:

sec(θ) = hypotenuse / adjacent

sec(θ) = 2 / 1 = 2

The answer is thus B.

~ an aesthetics lover

Answer:

Number common to both sides=6

Step-by-step explanation:

Average of first four numbers=5

4*5=20

Average of the last four numbers=8

4*8=32

Average of all seven numbers=6 4/7

7*6 4/7

Find the number common to both sets of four numbers

Solution

4*5=20

4*8=32

32+20=52

7 * 6 4/7

=7*46/7

=46

Number common to both sides=52-46

=6

Answer:

5/12 or 0.416667

Step-by-step explanation:

Plug in the values for x and y.

8(1/3) - 3(3/4)

Evaluate.

8/3 - 9/4

32/12 - 27/12

= 5/12

Answer:

18.027

Step-by-step explanation:

7.264+3.873+6.89

18.027

Answer:

1) 245 x 20 remander2/13 = 4940

2) square root of 58 - 29 + 38

= 8.19

Step-by-step explanation:

245 x 20 remander2/13= 245* 20 2/13

245 x 20 remander2/13= 245 * 262/13

245 x 20 remander2/13= (245*262)/13

245 x 20 remander2/13 =64190/13

245 x 20 remander2/13= 4937.69

245 x 20 remander2/13 = 4940

square root of 58 - 29 + 38

= √(58-29+38)

square root of 58 - 29 + 38

= √(96-29)

square root of 58 - 29 + 38

= √(67)

square root of 58 - 29 + 38

= 8.185

square root of 58 - 29 + 38

= 8.19

Answer:

Step-by-step explanation:

Shaded area:

Area of big rectangle - Area of small rectangle

[tex] = 10 \times 12 - (10 - 5) \times (12 - 2)[/tex]

Calculate the difference

[tex] = 10 \times 12 - 5 \times 10[/tex]

Calculate the product

[tex] = 120 - 50[/tex]

Calculate the difference

[tex] = 70 \: {cm}^{2} [/tex]

Hope this helps...

Best regards!!

Answer:

y = 24

Step-by-step explanation:

5/4y-18=y/2

Multiply by 4 on all sides to get rid of the fractions

4(5/4y-18)=4*y/2

5y - 72 =2y

Subtract 5y from each side

5y-5y - 72 =2y-5y

-72 = -3y

Divide by -3

-72/-3 = -3y/-3

24 =y

Answer: x = [tex]2\frac{2}{9}[/tex]

Step-by-step explanation:

10x - 10 = x + 10

Subtract(x)

9x - 10 = 10

Add(10)

9x = 20

Divide(9)

x = [tex]2\frac{2}{9}[/tex]

Hope it helps <3

Answer:

x = 20/9

Step-by-step explanation:

10x - 10 = x + 10

Subtract x on both sides.

Add 10 on both sides.

10x - x = 10 + 10

Combine like terms.

9x = 20

Divide 9 on both sides.

x = 20/9

Answer:

f(x) = 4x - 4

Step-by-step explanation

Answer:

Vinay jumped = 49m

Step-by-step explanation:

Given:

Shubham jumped = 41m

Ashish jumped = 3m less than Shubham

Vinay jumped = 11m more than Ashish

Find:

Length of Viney's jump

Computation:

Ashish jumped = Shubham jumped - 3m

Ashish jumped = 41m - 3m  

Ashish jumped = 38m

Vinay jumped = Ashish jumped + 11m

Vinay jumped = 38m + 11m

Vinay jumped = 49m

Step-by-step explanation:

2x × 3x +(-5×1)=6x-6=o

Answer:  A: x=-3, 5

Step-by-step explanation: Use the quadratic equation or solving system method to get x=-3,5 the other questions are similar!

Answer:

A is right.  domain = {112, 120, 128, 136, 144}

Step-by-step explanation:

The range is the y-coordinate while the domain is the x-coordinate

y = x/4

x = 4y

domain = {4(28), 4(30), 4(32), 4(34), 4(36)}

= {112, 120, 128, 136, 144}

Answer:

£58,800

Step-by-step explanation:

The answer can be calculated using

FV=p(1+r/n)^nt

P=£50,000

r=2%=0.02

n=12

t=2009 to 2017=8 years

FV=p(1+r/n)^nt

=50,000(1+0.02/12)^12*8

=50,000(1+0.0017)^96

=50,000(1.0017)^96

=50,000(1.1771)

=58,855

FV=58,855

To the nearest £100=£58,800

Answer choices :

less than 0

greater than 0

exactly equal to 0

There is not enough information to answer this question.

Answer: greater than 0

Step-by-step explanation: For a normally distributed data, that is a data which is symmetrical whereby the majority of the values cluster at the center of the distribution. In general, for a normal distribution, the mean is 0 and the standard deviation is 1. Where the mean measures the average and refers to the center of the distribution and the standard deviation measures how spread out the data is.

Z - scores are used to standardize values with values above the average having z-scores greater than 0, those below average having values less than 0 and average value having a z-score of exactly 0.

Answer:

It's the first one.

hope it helps :)

Step-by-step explanation:

Answer:

x+5

Step-by-step explanation:

so first you would divide by x (which means you would multiply x+2 by -x)

x^2 + 7x + 10

-x^2 - 2x

5x + 10

then you would divide by 5 (which means you would multiply x+2 by -5)

5x + 10

5x +10

0

So then to check it you would multiply x+5 by x+2

(x+5)(x+2)

x^2 + 2x + 5x + 10

then simplify to get

x^2 + 7x + 10