The Bionic Woman gives Batman a 12 second
start in a 2 kilometre race. If the Bionic Woman
runs at 5 km/min, and Batman runs at 3 km/
min, who will win the race and by how many
seconds?​

Answer:

[tex] \alpha + \beta = \sqrt{2} [/tex]

[tex] \alpha \beta = \frac{1}{3} [/tex]

The quadratic equation is given by

[tex]y = {x}^{2} - ( \alpha + \beta )x + \alpha \beta [/tex]

[tex]y = {x}^{2} -x \sqrt{2} + \frac{1}{3} [/tex]

Answer:

The answer is $330.73.

Step-by-step explanation:

The answer is $330.73.

Step 1. Calculate simple interest: I = ?

Step 2. To get account balance add simple interest to the principal amount:

I + P = ?

Step 1. Calculate simple interest.

I = P * r * t

P - principal

r - rate

t - time period

We have:

P = $278.16

r = 2.1% = 2.1/100 = 0.021

t = 9

I = 278.16 * 0.021 * 9 = 52.57

Step 2. To get account balance add simple interest to the principal amount:

I + P = ?

52.57 + 278.16 = 330.73

Answer:

x- intercept at (3, 0)

y- intercept at (0, 2)

Step-by-step explanation:

x-intercept occurs at y=0.

4x +6y= 12

when y=0,

4x +6(0)= 12

4x= 12

x= 12 ÷4

x= 3

Thus, x-intercept occurs at x=3, at the point (3, 0).

y- intercept occurs at x=0.

4x +6y= 12

when x=0,

4(0) +6y= 12

6y= 12

y= 12 ÷6

y= 2

Thus, y- intercept occurs at the point (0, 2).

Answer:

x=3

Step-by-step explanation:

using the pythagorean theorem, c^2=a^2+b^2

5^2=x^2+4^2, x=3

Answer:Three is the right answer I just finished

Step-by-step explanation:

Answer:

b = √2

Step-by-step explanation:

Pythagorean Theorem: a² + b² = c²

a = Leg₁

b = Leg₂

c = Hypotenuse

Step 1: Plug in variables

3² + b² = (√11)²

Step 2: Solve

9 + b² = 11

b² = 2

b = √2

And we have our answer!

Answer: u didnt give us the full problem

Step-by-step explanation:

Answer:

its b

Step-by-step explanation:

tta be just trust me

Answer:

It's B and the length of the third side of the triangle is 9cm.

Step-by-step explanation:

One of the two equal sides  S. Both of them  2S. The third side is 2S5. The perimeter is 2S2S5 and that's 23. So 4S5 23, then 4S28, and S7. The third side is 2S5, and that's 9.

Ok so there are two ways to do this kind of pre-algebra.

I'm going to do it the way I learned it, and the way they teach you in schools.

Ok so you want the variables on one side and the constant term (normal numbers) on the other side (of the equation).

So to do that you have to bring the 6 to the right side.

17h=40+6

Except when you move it to the other side you have to change the sign in front of it.

+ → -

- → +

× → ÷

÷ → ×

In this case, there is an addition sign in front of the 6.

So + → - and the final equation is...

17h=40-6

If you want to do it the way they do it in schools, then you have to remove 6 from both sides (so it will still be equal).

17h+6=40

You have to subtract 6 from (17h+6), which would be 17h.

Then you have to subtract 6 from (40), which would be 40+(-6) or 40-6

The final equation is 17h=40-6

Ok so 40-6=34.

So 17h=34

Divide 34 by 17 or divide each side by 17.

h=34/17 or 2

♡ Hope this helped! ♡

❀ 0ranges ❀

Answer:

40-6=34.

So 17h=34

Divide 34 by 17 or divide each side by 17.

Step-by-step explanation:

Hope this helps!

For f function, we don't need to us the value of g function. So, 1-3x = 1-3.-1/3 =2

Answer : 2

f(-⅓) = 2

Step-by-step-explanation :

[tex]f(x) = 1 - 3x \\ f( \frac{ - 1}{3} ) = 1 - 3( \frac{ - 1}{3} ) \\ f( \frac{ - 1}{3} ) = 1 + \frac{3}{3} = 1 + 1 = 2[/tex]

Answer:

36 inches

Step-by-step explanation:

7 * 2 = 14

11 * 2 = 22

14 + 22 = 36

Answer: 36

Step-by-step explanation: Perimeter is the outside of a shape, so you double each number and add them since a parallelogram has 4 sides. 11+11=22. 7+7=14. 14+22=36

Step-by-step explanation:

3x2 -5x+1=0

Quadratic eq ax2 +bx+c=0

Discriminant=b2 -4ac

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

=25-12

=13>0 so 2 solutions.

Answer:

2b - 2a

Step-by-step explanation:

AB = AO + OB

     = - 2a + 2b = 2b - 2a

Answer:

28

Step-by-step explanation:

When x is equal to 4, j(x) = 28.

1. The first option is represented by a linear function, ∴ y = 50x + 150. The y intercept here is 150, as the first week is 200 dollars, not the 0th week. 200 - 50 = 150.

Given the domain here is 1 - 6 (6 weeks) we can plug in x as 1,2,3 etc and solve for y, completing the table.

Option A :

Week | 1 | 2 | 3 | 4 | 5 | 6 |

Amount Paid | 200 | 250 | 300 | 350 | 400 | 450 |

And for option b we have an exponential function. 1 + 10% = 1 + 0.1 = 1.1. Therefore we have the function ∴ y = 200( 1.1 )^x-1 that models this situation.  Remember that we have " x - 1 " as the exponent rather than x, as the first week begins with 200 dollars, not the 0th week.

That gives us the following table,

Option B :

Week | 1 | 2 | 3 | 4 | 5 | 6 |

Amount Paid | 200 | 220 | 242 | 266.2 | 292.82 | 322.102 |

2. (a) We already calculated the " iterative rules " for each sequence in the first part. For your explanation on that behalf, just include the explanation above. Rule of Option A : y = 50x + 150. Rule of Option B : [tex]y = 200( 1.1 )^{x-1}[/tex].

(b) Let's take an example week and substitute into our equations to help clarify our friend's doubt. Say week 2...

y = 50(2) + 150 = 100 + 150 = 250 ✓

y = 200( 1.1 )^2-1 = 200( 1.1 )^1 = 200( 1.1 ) = 220 ✓

3. (a) A function is an equation that represents the relation between x and y, which is exactly the purpose of the rules y = 50x + 150, and y = 200( 1.1 )^x-1.

(b) I disagree with my friend. These particular examples do have y - intercepts, but just because a rule is a function, doesn't make it have a y - intercept. There are some exceptions, such as y = 1 / x.

(c) An input such as 18.5 is meaningless, as x represents the weeks. An employer doesn't provide the payments at half weeks.

4. Let's substitute 20 as x,

y = 50 * 20 + 150 = 1,000 + 150 = $1,150

y = 200( 1.1 )^x-1 = 200( 1.1 )^20-1 = 200( 1.1 )^19 = $1,223.1818

The first payment option will provide the greatest total income.

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following instructions :

It can be deduced from part a that the final result will be twice the original number 'n'

The number 'n' multiplied by 4 = (4 * n) = 4n

10 added to 4n = 4n + 10

The result of the sum divide by 2 = (4n + 10) / 2

= 2n + 5

5 subtracted from the result of the quotient obtained : 2n +5 - 5 = 2n

Where n is the original number.

2n = twice the original number.

Answer:

infinite solutions

Step-by-step explanation:

Hello!

Since 3r - 5 is on both sides of the equation we can put any number in for r and it would still be true so the answer is infinite solutions

The answer is infinite solutions

Hope this helps!

Answer:

x = 3

Step-by-step explanation:

What you wrote, x + 8/x - 3 means [tex] x + \dfrac{8}{x} - 3 [/tex].

I assume you didn't mean that, but instead, you mean

[tex] \dfrac{x + 8}{x - 3} [/tex], so I'll use this expression in the problem.

A fraction cannot have zero in the denominator since division by zero is undefined and not allowed. The denominator of the fraction is x - 3.

We need to find which value of x makes the expression x - 3 have a value of zero. Then that is the value of x that must be excluded from the domain.

We set the denominator equal to zero, and we solve for x.

x - 3 = 0

Add 3 to both sides.

x = 3

A value of 3 used for x makes the denominator equal zero, so the real number for which the expression is undefined is

x = 3.

Answer:

26-8x

Step-by-step explanation:

factor the expression

simplify the expression

The four corners of a square are 90 degrees.

They are evenly split by the diagonal lines, so each corner is now two 45 degree angles.

The lines form triangles, which have 3 angles that need to equal 180 degrees.

Two of the angles are 45, so 45 + 45 = 90 degrees.

X = 180 -90 = 90 degrees.

Answer:

90 degrees

By 90 * 4 is 360

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

x⁵ - 8x⁴ + 22x³ - 26x² + 21x - 18 = 0

x = 2,  x = ± i,   x=3  with multiplicity 2

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

x⁴ - 5x³ + 7x² - 5x + 6 = 0

x = 2,   x=3,   x = ± i

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

-1 + 4i    =  4 + i

    i

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

x³ - 26x² + 21x - 18 = 0

x = ± 2i,   x = 3/2

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

(1 + i) (-3 - 4i)

= 1 - 7i

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

6.

(-5 + 2i) + (3 - 6i)

= -2 -4i

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

7.

x⁴ + 5x² + 4 = 0

x = ± i ,     x = ± 2i

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

8.

(7 - i) - (-5 + 6i)

= 12 - 7i

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

9.

(4 - i) (4 + i)

= 17

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

10.

(3 + 8i) (4 - 3i)

= 36 + 23i

Answer:

x² + 5x + 4

Step-by-step explanation:

(x + 1) (x + 4)

apply the FOIL method

xx + (x * 4) + (1 * x) + (1 * 4)

xx + 4x + (1 * x) + (1 * 4)  

xx + 4x + 1x + 4

x² + 5x + 4

Answer: 6 cm

Step-by-step explanation:

Given: The ratio of the areas of two similar  parallelograms is 4:9.

To find : The height of the  bigger one if the smaller is of height 4 cm.

Let h be the height of the  bigger one.

Since the areas of similar figures are proportional to the square of their corresponding sides.

Then, [tex]\dfrac{4^2}{h^2}=\dfrac{4}{9}[/tex]

[tex]\dfrac{16}{h^2}=\dfrac{4}{9}\\\\\Rightarrow\ h^2=\dfrac{9}{4}\times16\\\\\Rightarrow\ h^2=36\\\\\Rightarow\ h= 6\ cm\ \ \ \ \text{[ height cannot be negative.]}[/tex]

Hence, the height of bigger parallelogram = 6 cm

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

Explanation:

Parallel lines never cross, so we can rule out choices B, C, and D. These choices all have segments that cross or meet somehow. Segments AB and OC don't intersect, and their extended lines do not appear to intersect either.

---------

We don't really need to use a diagram for this problem even though a diagram is handy. The reason we don't need a diagram is simply look at the letters to see if there's any repeated letters.

For instance, with choice B, the letter O shows up twice. So that must mean the two segments intersect at point O. But we can't have parallel lines intersect, which allows us to rule out choice B. The other answer choices we rule out will follow the same idea.

Only AB and OC have letters that don't show up twice.

Answer:

A) AB and OC

Step-by-step explanation:

Ok, so basically, when two lines are parallel, t means they will never touch each other no matter how long they are

for example, these two l‘s are parallel

l l

in this problem, we just have to find the lines that are parallel

finsing the lines are quite easy, just look for the first letter, in this case, A, then find the other lettter, here it is B, and there is your line!

here all the lines are marked in red, whch makes finsing each line easier

proving our answer is correct...

BO and CO makes an upside down V shape ( like a roof )

CO and CD make a v Shape

and

CD and DO make an upside down L

i hope this helped!

Answer:

Let's call x as the number of friends, now, in Theatre A we have:

Price for x tickets = x*$14.50

price for 3 tubs of popcorn = 3*$5.75 = $17.25

Total price:

Pa(x) = $14.50*x + $17.25

Now, for Theatre B we have:

Price for x tickets = $13*x.

Price for 3 tubs of popcorn: = 3*$6.75 = $20.25

Total price:

Pb(x) = $13*x + $20.25.

Now, we can find the number of friends x in such case that they will pay the same in each theater by:

Pa(x) = Pb(x)

$14.50*x + $17.25 = $13*x + $20.25.

Now we solve this for x:

($14.50 - $13)*x = $20.25 - $17.25 = $3

$1.50*x = $3

x = $3/$1.50 = 2.

Then, if there are 2 friends, they will pay the same in both theatres

If there are more tha 2 friends, the cheaper place will be Theatre B, because the slope is smaller, which means that for each additional ticket the total price will increase less.

Answer:

[tex]102^\circ[/tex]

Step-by-step explanation:

Given that:

[tex]\angle 5[/tex] is a supplement of [tex]\angle 6[/tex].

m[tex]\angle 5[/tex] = 78°

To find:

m[tex]\angle 6[/tex] = ?

Solution:

First of all, let us learn about the concept of an angle being a supplement of the other angle.

[tex]\angle B[/tex] is known as supplement of [tex]\angle A[/tex], if sum of the two angles is equal to 180°.

[tex]i.e. \angle A +\angle B=180^\circ[/tex].

For example, angle made on one side by a line intersecting the other line are supplement of each other.

Here, we are given that [tex]\angle 5[/tex] is a supplement of [tex]\angle 6[/tex].

In other words:

[tex]\angle 5+\angle 6=180^\circ[/tex]

Putting value of [tex]\angle 5[/tex]:

[tex]\Rightarrow 78^\circ+\angle 6=180^\circ\\\Rightarrow \angle 6 =180^\circ-78^\circ\\\Rightarrow \bold{\angle 6 =102^\circ\\}[/tex]

So, the answer is: [tex]102^\circ[/tex]

Answer:

1.) y = 4x - 3

2.) y = -3x + 2

Step-by-step explanation:

I'm not really sure how to explain it super well, but I do know the answers

Answer:

A 53.68

Step-by-step explanation:

tan54° = BC/39

BC = tan 54° x 39

BC = 53.68

Answer:

A. 53.68

Step-by-step explanation:

Answer:

2x-y=3

Step-by-step explanation:

I just got my g mail and I went in during the middle of the class

Answer:

hi :)

Step-by-step explanation:

Answers:

Domain = [tex][-5, -2] \cup [1,5)[/tex]

Range = [tex](-4,4][/tex]

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

Explanation:

The domain is the set of allowed x value inputs. We note that the left-most point is when x = -5, and this point has a closed or filled in endpoint, so we're including this x value in the domain.

The left piece has its other endpoint at x = -2, so the interval [tex]-5 \le x \le -2[/tex] is part of the domain. We write that as [tex][-5,-2][/tex]is part of the domain's answer. The other part is [tex][1, 5)[/tex]. We include x = 1 but exclude x = 5 as there's a hole here.

Use the union symbol to glue the two intervals together and we end up with [tex][-5, -2] \cup [1,5)[/tex] as the full domain.

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

The range is the set of possible y values. The lowest point is when y = -4, but we exclude this endpoint since there's an open hole here. The highest point is when y = 4. The range is [tex]-4 < y \le 4[/tex] which we write as [tex](-4, 4][/tex]

Since there are no gaps in the range, we don't use any union symbols here. Any y value between -4 and 4 is possible, other than y = -4 itself.