Two cyclists start out at the same time from points that are 395 kilometers apart and
travel toward each other. The first cyclist travels at an average speed of 40 kilometers
per hour, and the second travels at an average speed of 50 kilometers per hour After
how many hours will they be 35 kilometers apart?

Answer:

2 ^ (x - 3) ÷ 2 ^ 3(2y - 3)=2 ^ 4(x - y)

The two are common so we give it out then

x - 3 ÷ 6y - 9 =4x - 4y

x - 3 -4x - 4y = 6y -9

-3x -2y = -6

6=3x+2y

Answer:

Step-by-step explanation:

[tex]\frac{2^{x-3}}{8^{2y-3}}=16^{x-y}\\\\\frac{2^{x-3}}{(2^{3})^{2y-3}}=(2^{4})^{x-y}\\\\\frac{2^{x-3}}{2^{3*(2y-3)}}=2^{4*(x-y)}\\\\\frac{2^{x-3}}{2^{6y-9}}=2^{4x-4y}\\\\2^{x-3 -(6y-9)}=2^{4x-4y}\\\\2^{x-3-6y+9}=2^{4x-4y}\\\\2^{x-6y+6}=2^{4x-4y}[/tex]

base is same, so equate the powers

x - 6y + 6 = 4x - 4y

Subtract 'x' from both sides

-6y + 6 = 4x -x - 4y

-6y + 6 = 3x - 4y

Add '6y' to both sides

6 = 3x - 4y + 6y

6 = 3x + 2y

Hence proved

Answer:

a.

1. The rule in this sequence is (+5) every next pattern

2. 22, 27, 32, 37

3. 42

4. 12 term

5. 67

b.

1. The rule in this sequence is (-3) every next pattern

2. -7, -10, -13, -16

3. -16

4. 13 term

5. -37

Step-by-step explanation:

Answer:

I'm not sure about the answer.

a.

1. The rule in this sequence is (+5) every next pattern

2. 22, 27, 32, 37

3. 42

4. 12 term

5. 67

b.

1. The rule in this sequence is (-3) every next pattern

2. -7, -10, -13, -16

3. -16

4. 13 term

5. -37

Hope this helps you ^^

Answer:

17

Step-by-step explanation:

Look at Triangle ABC, The rays meet at line BC and they are both from the interior point A. So this means that AB=AC. This makes ABC a isosceles triangle. Using the isosceles triangle theorem, Angle B and Angle C measure is equal to each other so

[tex]50 + x + x = 180[/tex]

[tex]50 + 2x = 180[/tex]

[tex]2x = 130[/tex]

[tex]x = 65[/tex]

This means angle b and C of the triangle ABC measure is 65.

External bisector bisect a figure that it makes the original angle split into half that they are equal to each other.

This means the angle below Angle B and angle C measure is 32.5. We can find the measure of Angle B and C in triangle BOC. This is a isosceles triangle as well so

[tex]32.5 + 65 + x = 180[/tex]

[tex]98.5 + x = 180[/tex]

[tex]x = 81.5[/tex]

Angle C is 81.5 as well so

[tex]81.5 + 81.5 = 163[/tex]

Find angle o

[tex]180 - 163 = 17[/tex]

Answer:

5.56

Step-无by-step explanation:

Answer: 4 8/10m

Explanation:

Total Ribbon = 24m

Total children = 5

Ribbon each student gets = 24÷5

= 4.8

Now 4.8 = 48/10

4 8/10m is the mixed fraction

So each child will get 4 8/10m ribbon

Must click thanks and mark brainliest

If five children share 24m of ribbon equally then each children gets [tex]4\frac{4}{5}[/tex] of ribbon.

A division is a process of splitting a specific amount into equal parts.

Given that five children share 24m of ribbon equally.

We have to find the amount of ribbon each children gets.

To find this we have to divide the length of the ribbon with the number of children.

Twenty four divided by five.

24 is the dividend and five will be the divisor

24/5

Now we have to write this in mixed fraction

[tex]4\frac{4}{5}[/tex]

Hence, if five children share 24m of ribbon equally then each children gets [tex]4\frac{4}{5}[/tex] of ribbon.

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Answer:

b. 8/9

Step-by-step explanation:

step by step explanation

Answer:

A

Step-by-step explanation:

Because if you were to out each fraction into a calculator you see that b,c, and d have a never ending decimal. The only fraction that does end in option A, therefore ur answer is option a

Answer:

-1

Step-by-step explanation:

Vector a=(1,0) if visualized as a line has points (0,0) and (1,0). This means the line is horizontal and has equation y=0.

This means we are looking for a vertical line.

Instead of lambda, I'm going to use u.

So we want a+ub=(1,0)+u(1,1). to vertical. If we visualize this as a line with points (0,0) and (1+u,u). We would need u=-1 so this would be vertical.

So vectors a=(1,0) and a+ub=(1,0)+u(1,1) are perpendicular for u=-1.

So we are saying vectors (1,0) and (0,-1) are perpendicular. If you draw these, you can get a visual confirmation.

The value of λ is -1 and is perpendicular to vector a.

A vector is a number or phenomena with two distinct properties: magnitude and direction. The term can also refer to a quantity's mathematical or geometrical representation. In nature, vectors include velocity, momentum, force, electromagnetic fields, and weight.

We have,

Vector a = (1, 0) and b = (1, 1).

Here the vector is visualized as line is horizontal and has equation y=0.

Now, we have a + λb is perpendicular to vector a.

So, a + λb = (1, 0) + λ(1, 1)

                 = (1 + λ, 1)

Now, to get the vertical component we must have λ= -1.

Then, a(1, 0) and a+λb= (1,0)+ λ(1, ) are perpendicular to λ=-1.

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Answer:

136+(4n-8)=180

136+4n-8=180

4n+128=180

4n=52

n=13

Step-by-step explanation:

please mark me as brainliest

9514 1404 393

Answer:

  8

Step-by-step explanation:

The matrix being multiplied is the same in all cases, so we can "collect terms" in the usual way.

  3A +5A = (3+5)A = 8A . . . . . . where A represents the 2×2 matrix

The missing number is 8.

Answer:

Step-by-step on:ơ

Answer:

3/5=12/20 multiply by 4

4/7=16/49 a square of

25/30=5/6 divide with 5

improper fractions

9/5

21/8

10/1

5+(-18x+15)5 + (-18x +15)5

5+ (-90x +75) + (-90x + 75)

-180x +155

let's see the alternatives:

a) -2000x - 2018 -> -200x - 201,8

b) -30x - 33 -> -180x -198

c) none of the above

so, c is the right one

hope it helps :)

Answer:

ITS C

Step-by-step explanation:

Answer:

Option d

Step-by-step explanation:

-5(8x)

= -5×8×x

= -40x

Answered by GAUTHMATH

Answer: D is my guess.

Step-by-step explanation:

If you multiply those two number and subtract it by tanisha that probably is your answer if I'm  incorrect I'm sorry hopefully this helped

Answer:

irrational

Step-by-step explanation:

See the image for a Venn diagram illustrating relationships among the various subsets of real numbers.

Answer:

85 minutes

Step-by-step explanation:

425/50=8.5 10 minute increments

8.5*10= 85 minutes

Answer:

127

Step-by-step explanation:

[(-33) + 46 + 68] - (15 - 61)

(114-33)-(-46)

81+46

127

Answer:

all real numbers

Step-by-step explanation:

The domain is the numbers that the input, x, can take

We can put in any real number for x since there are no restrictions on the input

Answer:

option D is domain

Step-by-step explanation:

because no change is happen in range by keeping any real number

Answer:

x = 20

Step-by-step explanation:

[tex]16x+90=2(10x+5)\\\\16x+90=20x+10\\\\90=4x+10\\\\80=4x\\\\20=x[/tex]

Answer:

72

Step-by-step explanation:

one angle = x

other one, 4x

they're compliment,

so,

x+4x=90

or, 5x=90

or, x=18

so the angle is 4x=4×18=72

Answer:

Step-by-step explanation:

Let the angle is x.

Supplement of x:

Complement of x:

We have:

Solve for x:

Answer:

$962.00

Step-by-step explanation:

We can start from the first sentence of the word problem and work from there.

First, the employee is working for 40 hours at $18.50 per hour. This means that for each hour, the employee is gaining $18.50 . This can be represented as $18.50 * 40 = $740 for their base pay.

Next, the employee works 8 hours of overtime at 1.5 * base pay (18.50). For each hour of overtime they work, they earn 1.5 * 18.50 = $27.75 dollars. Their earnings from overtime work for the week can be represented as

8 * 27.75 = $222

Because all the employee's hours are encompassed in overtime and base pay, we can add the two together to get

740 + 222 = $962.00 for their total pay for the week

The differential equation

y''' - 5y'' + 7y' - 3y = 0

has characteristic equation

r ³ - 5r ² + 7r - 3 = (r - 3) (r - 1)² = 0

with roots at r = 3 and r = 1 (with multiplicity 2), so that the characteristic solution to the DE is

y = C₁ exp(3x) + C₂ exp(x) + C₃ x exp(x)

alright I can help!

so to find the two values of x that are roots of the equation we need to put the variables all on one side so that we can set up the quadratic formula.

3x^2+2x-5=0 (the -3x^2 becomes positive when moved across the equal sign)

now we can set up the quadratic formula. the equation is x= (-b+-(sqrt of b^2 -4ac))/ 2a

so now we just plug in our variables.

x= (-2+-(sqrt of 2^2 -4×3×-5))/ 2×3

x= (-2+-8)/6

now we just seperate the equations so that we have the two roots. and then just solve!

x= (-2-8)/6 -> x= -5/3

x= (-2+8)/6 -> x=1

hope this helps! best wishes and best of luck!!

Answer: quadrant 1

Step-by-step explanation:

the triangle will make 5 360° rotations and then one 180° rotation. we know this because 1980/360=5.5

Answer:

Step-by-step explanation:

Let the number is in the form of aabb.

We can put it as:

The number is a perfect square so it must be divisible by 11.

It is divisible by 11 if (a + b) is divisible by 11..

On the other hand, b = 0, 1, 4, 5, 6, 9 as the last digit of a perfect square.

Also, both a and b must be within (0,9) interval.

Considering the above conditions we have options:

The numbers are:

By testing we confirm only one of them is a perfect square: