Ted practices two types of swimming styles for a total of 50 minutes every day. he spends 20 minutes more practicing the breast stroke than the butterfly stroke.

Part A: write a pair of linear equations to show the relationship between the number of minutes ted practices the butterfly stroke every day (x) and the number of minutes he practices the breast stroke every day (y).

Part B: how much time does ted spend on practicing the breast stroke every day?

Part C: is it possible for ted to have spent 45 minutes practicing the butterfly stroke every day? explain your reasoning.​

9514 1404 393

Explanation:

An exterior angle is equal to the sum of the remote interior angles. Define ∠PQR = 2q, and ∠QPR = 2p. The purpose of this is to let us use a single character to represent the angle, instead of 4 characters.

The above relation tells us ...

  ∠PRS = ∠PQR +∠QPR = 2q +2p

Then ...

  ∠TRS = (1/2)∠PRS = (1/2)(2q +2p) = q +p

and

  ∠TRS = ∠TQR +∠QTR . . . . . exterior is sum of remote interior

  q +p = (1/2)(2q) +∠QTR . . . . substitute for ∠TRS and ∠TQR

  p = ∠QTR = 1/2(∠QPR) . . . . . subtract q

__

For triangle ABC, draw line DE parallel to BC through point A. Put point D on the same side of point A that point B is on the side of the median from vertex A. Then we have congruent alternate interior angles DAB and ABC, as well as EAC and ACB. The angle sum theorem tells you that ...

  ∠DAB +∠BAC +∠CAE = ∠DAE . . . . a straight angle = 180°

Substituting the congruent angles, this gives ...

  ∠ABC +∠BAC +∠ACB = 180° . . . . . the desired relation

Answer:

d) p(x)= 7x-2

Step-by-step explanation:

d) p(x) = 7x -2

Answer:

3 / 16

Step-by-step explanation:

Let The total amount = x

Fraction eaten on first day = 1/4x

Fraction left = x - 1/4x = 3/4x

Fraction of amount left eaten on second day = 3/4 of 3/4x

3/4 * 3/4x = 9/16x

Fraction left :

3/4x - 9/16x = (12x - 9x) /16 = 3/16x

Hence, fraction left = 3/16

Answer:

D. y= 0.3x2

Step-by-step explanation:

In quadratic functions, the value of a affects the wideness of the graph. The smaller the absolute value of a, the wider the graph. In these choices, 1/3 and 0.3 are the smallest. To understand which is smaller convert both to decimals; 1/3 is 0.3333 repeating. Therefore, 0.3 is slightly smaller and wider.

Answer:

m is -12/7 and b is -64/7

Step-by-step explanation:

Use rise over run (change in y / change in x) to find the slope, m:

(-4 - 8) / (-3 + 10)

= -12/7

So, m is -12/7.

Plug in this value and a point into y = mx + b, then solve for b:

y = mx + b

-4 = -12/7(-3) + b

-4 = 36/7 + b

-64/7 = b

So, m is -12/7 and b is -64/7

The linear function is given by:

[tex]y = -\frac{12}{7}x - \frac{64}{7}[/tex]

Where:

A linear function is modeled by:

[tex]y = mx + b[/tex]

In which:

In this problem, the points are (−10,8) and (−3,-4).

The slope is given by change in y divided by change in x, hence:

[tex]m = \frac{-4 - 8}{-3 - (-10)} = -\frac{12}{7}[/tex]

Hence:

[tex]y = -\frac{12}{7}x + b[/tex]

It goes through point (−3,-4), hence when [tex]x = -3, y = -4[/tex], which is used to find b.

[tex]y = -\frac{12}{7}x + b[/tex]

[tex]-4 = \frac{36}{7} + b[/tex]

[tex]b = -\frac{64}{7}[/tex]

Hence, the equation is:

[tex]y = -\frac{12}{7}x - \frac{64}{7}[/tex]

You can learn more about linear functions at https://brainly.com/question/24808124

Answer:

263.25

Step-by-step explanation:

250 x .053 (5.3%) = 13.25 tax

250 + 13.25 = 263.25 price plus sales tax

Answer:

263.25

Step-by-step explanation:

Answer:

D   2i

Step-by-step explanation:

Answer:

B. i√4

D. 2i

Step-by-step explanation:

Answer:

Area of sector is 6pi cm^2

Step-by-step explanation:

Mathematically pi radians is 180 degrees

thus pi/6 radians is 180/6 = 30 degrees

The formula for the length of an arc is;

theta/360 * 2 * pi * r

where theta in this case is 30 degrees

And the arc length is pi

so we have

30/360 * 2 * pi * r = pi

30/360 * 2 * r = 1

60r = 360

r = 360/60

r = 6 cm

Now the area of a sector is;

theta/360 * pi * r^2

30/360 * pi * 36

= 6pi cm^2

Step-by-step explanation:

[tex] \sqrt{ - 81} = 9i \\ \sqrt{ - 11} = i \sqrt{11} \\ \sqrt{ - 20} = i \sqrt{20} [/tex]

Answer:

Solution given:

Centre (h,k)=(-6,-2)

end points are:

A[tex]\bold{(x_{1},y_{1})=(-1,-9) \:and \:B(x_{2},y_{2})=(-11,5)}[/tex]

Now

distance between A to M is:

AM=[tex]\sqrt{(h-x_{1})²+(k-y_{1})²}[/tex]

AM=[tex]\sqrt{(-6+1)²+(-2+9)²}=8.6[/tex]units

again

distance between B to M is:

BM=[tex]\sqrt{(h-x_{2})²+(k-y_{2})²}[/tex]

BM=[tex]\sqrt{(-6+11)²+(-2-5)²}=8.6[/tex]units

again

Since AM=BM=8.6units

so

M is the centre of the circle.:Yes

Answer:

[tex]EF=6[/tex]

Step-by-step explanation:

In this problem, one is given a circle with two secants (that is a line that intersects a circle at two points). One is given certain measurements, the problem asks one to find the unknown measurements.

The product of the lengths theorem gives a ratio between the lengths in the secants. Call the part of the secant that is inside the circle (inside), and the part of the secant between the exterior of the circle and the point of intersection of the secants (outside). The sum of (inside) and (outside) make up the entire secant, call this measurement (total). Remember, there are two secants, ([tex]secant_1[/tex]) and ([tex]secant_2[/tex]) in this situation. With these naming in mind, one can state the product of the length ratio as the following:

[tex]\frac{total_1}{outside_2}=\frac{total_2}{outside_1}[/tex]

Alternatively, one can state it like the following ratio:

[tex]\frac{inside_1+ouside_1}{outside_2}=\frac{inside_2+outside_2}{outside_1}[/tex]

Apply this ratio to the given problem, substitute the lengths of the sides of the secants in and solve for the unknown.

[tex]\frac{EF+FG}{HG}=\frac{SH+HG}{FG}[/tex]

[tex]\frac{2x+4}{5}=\frac{x+5}{4}[/tex]

Cross products, multiply the numerator and denominators of opposite sides of the fraction together,

[tex]\frac{2x+4}{5}=\frac{x+5}{4}[/tex]

[tex]4(2x+4)=5(x+5)[/tex]

Simplify,

[tex]4(2x+4)=5(x+5)[/tex]

[tex]8x+16=5x+25[/tex]

Inverse operations,

[tex]8x+16=5x+25[/tex]

[tex]3x+16=25\\3x=9\\x=3[/tex]

Substitute this value into the equation given for the measure of (EF),

[tex]EF=2x\\x=3\\\\EF=2x\\=2(3)\\=6[/tex]

Answer:

Floor=2*sqrt(11)

Step-by-step explanation:

Using Pythagoras theorem, we have

Wall^2+Floor^2=(Ladder)^2

Floor^2=12^2-10^2

Floor=sqrt(44)=2*sqrt(11)

Answer:The floor is 6m

Step-by-step explanation:

In this we have to solve to find B

First we know that  A^2+B^2+C^2 and we know A is 10 and C is 12 so now we are going square both 10 and 12 which would be 100 and 144 then we subtract each other 144-100=44 and lastly we are going to get the square root of 44 which is 6.

Please give brainlist

Answer:

The correct answer 8486.

Step-by-step explanation:

Given:

Troy - P pr principle amount = 10000

rate = 9%

time = 60-22 = 38

intrest at every three months so time = t = 38*4 = 132

Nicohlas

P = x

rate = 10%

time = 60 -45 = 15

every month compounded = 15*12=180

solution:

the formula of compound intrest = P (1 + r/n)^(nt)

where n = number of counded intrests per year

puting formula for troy=

10000 (1+9/4)^132

= 294,322.96 .....1

now for nicolas

I = x(1+10/12)^180

x = 294,322.96/(1+10/12)^180

= 8486.

Answer:

12.56 m

Step-by-step explanation:

The circumference of a circle is given by

C  = 2 * pi *r

C = 2 * (3.14) * 2

C =12.56

Answer:

D.

Step-by-step explanation:

we see a1 = 6.

that is the starting value. everything else then (to generate the new sequence elements) is added to this.

so, B and C are out.

and clearly, for every new sequence element we add -3. and we do this for every sequence element except for a1. so we add -3 (n-1) times.

therefore, only D is correct.

Step-by-step explanation:

1. Given,

Sides of the shape = 3y+9, 2y+4, y+3 and 2y+4

Therefore ,

Perimeter of the shape = Sum of all the sides

= (3y+9) + (2y+4) + (y+3) + (2y+4)

= 3y + 2y + y + 2y + 9 + 4 + 3 + 4

= 8y + 20 (Ans)

2. Given,

Side of the square = 5x - 2

Therefore,

Perimeter of the square = 4 × Sides = 4s

= 4 × (5x - 2)

= 4 × 5x + 4 × (-2)

= 20x - 8 (Ans)

Answer:

Expected value x= 35

linear transformation is defined as a + bx

here, b=4, a=1

The transformation is [tex]z=1+4x[/tex]

now, expected value, [tex]l_z=l_z(a+bx)[/tex]

[tex]=l(a)+l(bx)[/tex]

[tex]=a+b\:l\:x[/tex]

substitute the value of a=1, b=4 and l=35

[tex]l_z=1+4\times35[/tex]

[tex]=1+140[/tex]

[tex]=141[/tex]

So, the expected value of the transformed variable is 141.

OAmalOHopeO

=======================================================

Explanation:

Let's consider a set of three values such that they're all equal to 35

{35,35,35}

This rather boring set has a mean of 35 and it's hopefully very clear why this is the case. The terms "mean" and "expected value" are interchangeable.

If we multiply everything by 4, then we get the new set {140,140,140}

Then add 1 to everything and we arrive at {141,141,141}. You can quickly see that the mean here is 141.

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

You could play around with that original set of 3 values to make things more interesting. Let's say we subtract 1 from the first item and add 1 to the last item. So we could have {35,35,35} turn into {34,35,36}. You should find that the mean is still 35 here.

If we quadruple each item, then we have {34,35,36} turn into {136,140,144}

Finally, add 1 to everything to get {137,141,145}. Computing the mean of this set leads to 141.

These are just two examples you could do to help see why the answer is D) 141

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

In a more general theoretical sense, we're saying the following

Y = mX+b

E[Y] = E[m*X+b]

E[Y] = E[m*X] + E[b]

E[Y] = m*E[X] + b

where Y is the transformed variable based on the random variable X. In this case, m = 4 and b = 1. Also, E[X] = 35.

So,

E[Y] = m*E[X] + b

E[Y] = 4*35 + 1

E[Y] = 141

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

Why go through all this trouble? Well consider that you know a certain distribution is centered around 35. Then consider that you want to convert those measurements to some other unit. This conversion process is us going from variable X to variable Y. Think of it like a batch conversion of sorts.

A more real world example would be something like "we know the average temperature is 35 degrees Celsius. The question is: what is the average temperature in Fahrenheit?" The numbers would be different, but the idea still holds up.

Answer: A line parallel to one side of a triangle and intersects the other two sides divides the two sides of the triangle proportionally.

Got this straight from Edmentum

Step-by-step explanation:

Answer:

The ratio of BF to FC is proportional to the ratio of GB to AG. Similarly, the ratio of IC to BI is proportional to the ratio of HC to AH.

Step-by-step explanation:

This is the actual answer for question 7 the one above is question 8

:)

Answer: hello your question is poorly written attached below is the complete question

answer:

[tex]\sqrt{3}(cos(\frac{3\pi }{2}) + isin(\frac{3\pi }{2}))[/tex] --- ( option d )

Step-by-step explanation:

The correct option that represents a  square root of 3 as related to the question attached below is :

[tex]\sqrt{3}(cos(\frac{3\pi }{2}) + isin(\frac{3\pi }{2}))[/tex]

Answer:

D

Step-by-step explanation:

Answer:

it's 'A' I guess

Step-by-step explanation:

hope it helps

Answer:

x = 6 and x = 9

Step-by-step explanation:

16

MN is half the length of KL

MN = [tex]\frac{1}{2}[/tex] × 12 = 6

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

17

Δ LMN and Δ LJK are similar triangles, so the ratios of corresponding sides are equal, that is

[tex]\frac{LM}{LJ}[/tex] = [tex]\frac{MN}{JK}[/tex] , substitute values

[tex]\frac{x}{x+9}[/tex] = [tex]\frac{8.5}{17}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2x = x + 9 ( subtract x from both sides )

x = 9

Answer:

He is incorrect.

Step-by-step explanation:

4500 x ( 1 + 1.50%)^3

= 4500 x 1.045678

= 4705.551000

4705.551000 < 4750

Carlos is not correct, because the amount at the end of the 3 years of compounding is £4705.65 not more than £4750.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound [tex]A=P(1+\frac{r}{100})^{nt}[/tex]

Given that, Carlos invests £4500 for 3 years.

He receives compound interest of 1.5% per year.

Here, amount =4500(1+1.5/100)³

= 4500(1+0.015)³

= 4500(1.015)³

= 4500×1.0457

= £4705.65

Carlos is not correct, because the amount at the end of the 3 years of compounding is £4705.65 not more than £4750.

To learn more about the compound interest visit:

https://brainly.com/question/14295570.

#SPJ2

Answer:

2520 ways

Step-by-step explanation:

Given

[tex]n = 10[/tex]

[tex]r = (2,3,5)[/tex]

Required

The number of selection

First, select 2 people from 10 in 10C2 ways.

There are 8 people, left.

Next, select 3 people from 8 in 8C3 ways.

There are 5 people left.

Lastly, select 5 from 5 in 5C5 ways

So, we have:

[tex]Total = ^{10}C_2 * ^8C_3 * ^5C_5[/tex]

Using combination formula

[tex]Total = 45 * 56 * 1[/tex]

[tex]Total = 2520[/tex]

Answer: (0;2)

3x + 2y = 4 | * (-5)

4x + 5y = 10 | * 2

-15x - 10y = -20

8x + 10y = 20

-15x - 10y + 8x + 10y = 20 - 20

x = 0

0 + 2y = 4

2y = 4

y = 2

(0; 2)

Answer:

Let a be the smaller of the two primes.

Now the middle of 2 primes is always even. So the middle number a+1 is divisible by 2.

Next the smaller of the primes when divided by 3 can have remainders 1,2.

1 is ruled out as possible remainder because then the remainder of a+2, the bigger of the primes would be (a+2) mod 3=(1+2) mod 3=3 mod 3=0,a contradiction since a prime number(except 3) when divided by 3 cannot have 0 as remainder.

So 2 is the only possible remainder of a. So the remainder of the bigger of the two primes when divided by 3 is (a+2) mod 3= (2+2) mod 3=4 mod 3=1.

This implies the middle number must have remainder (a+1)mod 3=(2+1)mod 3=3 mod 3=0. So the middle number is divisible by 3 also.

Hence a+1 is divisible by both 3 and 2 and since 2 and 3 have no common factors, so the middle number is divisible by 6

The reference angle of -200° is 20°. If you think about it, the terminal arm will be in Q2. That means that it has a reference angle of 200-180 = 20°

Answer:

3(f - 9)(f + 4)

Step-by-step explanation:

Assuming you require to factorise the expression

3f² - 15f - 108 ← factor out 3 from each term

= 3(f² - 5f - 36) ← factor the quadratic

Consider the factors 0f the constant term (- 36) which sum to give the coefficient of the f- term (- 5)

The factors are - 9 and + 4 , since

- 9 × 4 = - 36 and - 9 + 4 = - 5 , then

f² - 5f - 36 = (f- 9)(f + 4)

Then

3f² - 15f - 108 = 3(f - 9)(f + 4)

Answer:

1 + 2 + 3 + ... + 2017

sum_(n=1)^2017 n = 2035153

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

In this piece-wise function, there are three defined sections, each for a different range of x. To find an x where y is -9, we have to set all parts of it equal to -9.

-x,  x < -3

So, we can start by setting -x equal to -9 and solve for x:

-x = -9

x = 9

Our domain for this piece of the function is supposed to be x < -3. x = 9 does not fit into this range, meaning, in this range, there is no x for y = -9.

2x,   -3 ≤ x ≤ -2

We can set the value 2x equal to -9 and, again, solve for x:

2x = -9

x = -4.5

The solution x = -4.5 does not fit into the defined domain of -3 ≤ x ≤ -2, therefore it is not a solution.

-x^2,  x > -2

One last time, we can set -x^2 equal to -9 and solve for x:

-x^2 = -9

x^2 = 9

x = 3, x = -3

We are looking for a solution that fits into the domain, x > -2, x = -3 does not work, but x = 3 does.

In conclusion, the only solution where it fit the domain was x = 3

Answer:

x = 3

Step-by-step explanation:

x = - 3 in interval - 3 ≤ x ≤ - 2 then f(x) = 2x , so

f(- 3) = 2(- 3) = - 6 ≠ - 9

x = 9 in interval x > - 2 then f(x) = - x² , so

f(9) = - 9² = - 81 ≠ - 9

x = 3 in interval x > - 2 then f(x) = - x²

f(3) = - 3² = - 9

x = - 4.5 in the interval x < - 3 then f(x) = - x , so

f(- 4.5) = - (- 4.5) = 4.5

Thus

y = - 9 when x = 3

Answer:

5/3

Step-by-step explanation:

Direct variation is of the form

y = kx

where k is a constant

Using the first set of point

9 = 5k

Divide by 5

9/5 = k

The equation becomes

y = 9/5 x

Using the second set of points

3 = 9/5 x

Multiply each side by 5/9

5/9 * 3 = 9/5 *5/9x

5/3 =x