A running track has two semi-circular ends with radius 27m and two straights of length 90.6m as shown.
Calculate the total distance around the track rounded to 1 DP.

Answer:

-3.662rad × 180/π = -209.8°

Step-by-step explanation:

Answer:

1 degree = .01745329 radians

1 radian = 57.2957877856 degrees

-209.8 degrees = .01745329 * -209.8 =

-3.66170024200 radians

Step-by-step explanation:

Answer:

9 years older

Step-by-step explanation:

The ratio of their ages is 8 : 5 = 8x : 5x ( x is a multiplier )

In 30 years their ages will be 8x + 30 and 5x + 30 and the ratio 6 : 5 , so

[tex]\frac{8x+30}{5x+30}[/tex] = [tex]\frac{6}{5}[/tex] ( cross- multiply )

5(8x + 30) = 6(5x + 30) ← distribute parenthesis on both sides

40x + 150 = 30x + 180 ( subtract 30x from both sides )

10x + 150 = 180 ( subtract 150 from both sides )

10x = 30 ( divide both sides by 10 )

x = 3

Then

Michell is 8x = 8 × 3 = 24 years old

Connor is 5x = 5 × 3 = 15 years old

Mitchell is 24 - 15 = 9 years older than Connor

Answer:

false

Step-by-step explanation:

this is because there is no function of an unknown in this set

Answer:

see below

Step-by-step explanation:

2^30

-------

8^9

Rewriting

8^9

2^3 ^ 9

We know a^b^c = a^(b*c)

2^(3*9) = 2^27

2^30

-------

2^27

We know a^b / a^c = a^(b-c)

2^(30-27) = 2^3

Assuming you mean 2^x

2^3 = 2^x

x=3

If you mean 2x

2^3 = 8

8 = 2x

Divide by 2

4 =x

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{2^{30}}{8^9}=2x}[/tex]

[tex]\mathsf{2^{30}}\\\mathsf{= \bf 1,073,741,824}\\\\\mathsf{8^9}\\\mathsf{= \bf 134,217,728}[/tex]

[tex]\mathsf{\rightarrow \dfrac{1,073,741,824}{134,217,728}= 2x}\\\\\\\mathsf{\dfrac{1,073,741,824}{134,217,728}= \bf 8}\\\\\\\mathsf{\rightarrow \ 8 = 2x}\\\\\\\\\large\textsf{TURN\ the\ EQUATION\ around}\\\\\\\mathsf{\rightarrow\ 2x = 8}\\\\\\\large\textsf{DIVIDE 2 to BOTH SIDES}\\\\\\\mathsf{\dfrac{2x}{2}=\dfrac{8}{2}}\\\\\\\large\textsf{CANCEL out: }\mathsf{\dfrac{2}{2}}\large\textsf{ because it gives you 1}\\\\\\\large\textsf{KEEP: }\mathsf{\dfrac{8}{2}}\large\textsf{ because it gives you the answer of x}[/tex]

[tex]\mathsf{x = \dfrac{8}{2}}\\\\\\\mathsf{x = 8\div 2}\\\\\\\mathsf{x = \bf 4}\\\\\\\\\\\boxed{\boxed{\huge\text{Therefore, your answer is: \textsf{x = 4}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

Step-by-step explanation:

[tex]\frac{sinxcos^3x-cos xsin^3x}{cos^42x-sin^42x} \\=\frac{sin x cos x(cos^2x-sin ^2 x)}{(cis^2 2x+sin^2 2x)(cos^2 2x-sin ^22x)} \\=\frac{2sin x cos x cos 2x}{2(1)(cos 4x)} \\=\frac{sin 2x cos 2x}{2 cos 4x} \\=\frac{2 sin 2x cos 2x}{4 cos 4x} \\=\frac{sin 4x}{4 cos 4x} \\=\frac{1}{4} tan 4x[/tex]

Answer:

Step-by-step explanation:

The general form of this equation is

[tex]A=Pe^{rt}[/tex] where P is the initial population, e is Euler's number (a constant), r is the rate of decay, and t is the time in years.

Therefore, filling in:

[tex]A=45000e^{-.02t[/tex]

Answer:

So the sqrt(46) is between 6 and 7

Step-by-step explanation:

sqrt(46)

5*5 = 25

6*6=36

7*7=49

So the sqrt(46) is between 6 and 7

Answer:

don't know

Step-by-step explanation:

The equation in point slope form is y - 6 = 2(x + 3)

This is from the general point slope template of [tex]y - y_1 = m(x - x_1)[/tex]

The m is the slope, which in this case is m = 2. The [tex](x_1,y_1)[/tex] is the point the line goes through. In this case, [tex]x_1 = -3 \text{ and } y_1 = 6[/tex]

If you were to solve that equation in bold for y, then you should get y = 2x+12 which is now in y = mx+b form, aka slope intercept form.

if this value 35% less than the total, we conclude that:

42,900 = 65%

1% = 660

100% = 66,000

if you want to check the value, just do 65% of 66000, which equals to 42,900

hope it helps :)

Answer:

Nicole should take 13 1/8 cups of snack mix.

Step-by-step explanation:

If a serving size is 7/8 and Nicole wants to take 15 serving sizes (15 7/8's), then we must multiply 7/8 by 15:

15 × 7/8

Write 15 over 1 (15 = 15/1) to make the calculations easier:

15/1 × 7/8

Multiply the numerators and denominators separately:

15 × 7 / 1 × 8

105 / 8

Instructions don't say you have to do this but I will convert this improper fraction into a mixed number:

105/8 = 13 1/8

Answer:

30

Step-by-step explanation:

Answer:

Step-by-step explanation:

B OR TRUE

Answer:

C

Step-by-step explanation:

Using exterior angle property, we have 97+4x+7=17x+13. 13x=91, x=7

Answer:

8r+8pg-pq

Step-by-step explanation:

The subtractable pg cancels out one of the 9 pg's. So 9 pg-1 pg= 8 pg

Hope this helps!

composite numbers less than 12={1,3,4,6,8,9,10}

Answer:

B

Step-by-step explanation:

|3m-2|=>1

1 <= 3m-2 or 3m-2 <= -1

3 <= 3m or 3m <= 1

1 <= m or m <= (1/3)

x ³ = 1

x ³ - 1 = 0

x ³ - 1³ = 0

Factorize the right side as a difference of cubes:

(x - 1) (x ² + x + 1) = 0

Then

x - 1 = 0   or   x ² + x + 1 = 0

The first equation yields x = 1 as a root.

For the other equation, rearrange and complete the square to get the other two roots,

x ² + x + 1/4 = -3/4

(x + 1/2)² = -3/4

x + 1/2 = ±√(-3/4) = ± i √3/2

x = -1/2 ± i √3/2

x = (-1 ± i √3)/2

Since complex roots occurs in conjugate pairs, taking the sum of these two roots eliminates the imaginary part:

(-1 + i √3)/2 + (-1 - i √3)/2 = (-1 - 1)/2 = -2/2 = -1

and adding to 1 indeed shows that the sum of roots is zero.

Answer:

(-3)

Step-by-step explanation:

follow me if you want

Step-by-step explanation:

I need help to...

I keep putting it in and no one has ever answered it and I'm struggling and getting stressed.

Step-by-step explanation:

second: (2.2,-1.4)

third: (2.2,-1.35)

Step-by-step explanation:

hope it helps✨

Answer:

B. 7y - 15

Step-by-step explanation:

Simplifying

10y + -3(y + 5) = 0

Reorder the terms:

10y + -3(5 + y) = 0

10y + (5 * -3 + y * -3) = 0

10y + (-15 + -3y) = 0

Reorder the terms:

-15 + 10y + -3y = 0

Combine like terms: 10y + -3y = 7y

-15 + 7y = 0

Solving

-15 + 7y = 0

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '15' to each side of the equation.

-15 + 15 + 7y = 0 + 15

Combine like terms: -15 + 15 = 0

0 + 7y = 0 + 15

7y = 0 + 15

Combine like terms: 0 + 15 = 15

7y = 15

Divide each side by '7'.

y = 2.142857143

Simplifying

y = 2.142857143

Answer:

b. 7y-15

Step-by-step explanation:

First, write out the expression

1. [tex]10y-3(y+5)[/tex]

To simplify the expression distribute the -3 to the terms within the paratheses.

2. [tex]10y-3y-15[/tex]

Then, combine like terms to simplify further. Since 10y and -3y are like terms they can be subtracted

3. [tex]7y-15[/tex]

This means that B is the correct answer.

Answer:

628m

Step-by-step explanation:

Given radius=100m

distance=circumference

=2pie r

=2×22/7×100

=628m

please mark me brainliest

Answer:

8% out of 175 = ( 8 ÷ 100 ) × 175 = 14

175 cm - 14 = 161 cm

...............

Answer:

1320

Step-by-step explanation:

Use the formula for sum of series, s(a) = n/2(2a + (n-1)d)

The terms increase by 6, so d is 6

a is the first term, -56

n is the terms you want to find, 33

Plug in the numbers, 33/2 (2(-56)+(32)6)

Simplify into 33(80)/2 and you get 1320

Answer: x = -3

[tex]2x+6=0\\\\2x=-6\\\\x=\frac{-6}{2} =-3[/tex]

Answer:

x= -3

Step-by-step explanation:

Solve the equation:

2x +6 = 0

We have isolate 'x'.

First subtract 6 from both sides

2x = 0-6

2x = -6

Divide each side by 2

x = -6/2

x = -3

Step-by-step explanation:

<TOS=122° [being vertically opposite angle]

Answer:

angleTOS =122°

EXPLANATION:

[ If two straight lines intersect at point O, vertically opposite angles are equal]As vertically opposite angles are equal; Hence AngleTOS=QOR=122°

Answer:

18.8

Step-by-step explanation:

Surface area=2*pi*r*(r+h)=2*pi*1*(3)=18.8