Two trains leave towns 492 miles apart at the same time and travel toward each other. One train travels 16 miles per hour slower than the other. If they meet in 3 hours, what is the rate of each train?

Answer:

d = 3√2

Step-by-step explanation:

Distance formula: [tex]d = \sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]

Answer:

On the first equation, which is (c-d)/5 - 2 = 0 Let's start by solving c.

First, you need to add 1/5d to both sides:

1/5 c + -1/5 d - 2 + 1/5 d = 0 + 1/5 d

1/5 c - 2 = 1/5 d

Next, add 2 to both sides:

1/5 c - 2 + 2 = 1/5 d + 2

1/5 c = 1/5 d + 2

Now, divide both sides by 1/5:

1/5 c/ 1/5 = 1/5 d + 2/ 1/5

c = d + 10

so, therefore, your answer is c = d + 10

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Now we are going to do the 2nd equation, which is c-6d=0 Lets solve c.

The only thing you need to do is you need to add 6d to both sides:

c − 6d + 6d = 0 + 6d

c = 6d

So, therefore, your answer is c = 6d

Answer:

2y

Step-by-step explanation:

To find the GCF ( Greatest Common factor), for an algebraic expression like the one given, all you have to do if look over the expression and circle all the terms they both share, in this case, both 4yz and 2y^2 had 2y in them, except in different forms.

If you find it difficult to recognize the similarities, divide the expressions as much as you can.

Hope this helps

Answer:

523.8 miles

Step-by-step explanation:

The drawing attached represents the question. We create a triangle with the distances from each pair of cities, and we call the distance from B to C by 'd'.

First, we need to find the angle BAC:

55° + BAC + 7° = 90°

BAC = 28°

Then, we can use the law of cosines to find the value of d:

d^2 = 470^2 + 890^2 - 2*470*890*cos(BAC)

d^2 = 470^2 + 890^2 - 2*470*890*0.8829

d^2 = 274365.86

d = 523.8 miles

Answer:

  about 11.856 time units

Step-by-step explanation:

We have to assume the equation has something to do with the path of the ball relative to the ground. Perhaps it represents height, with t representing time. The height (h) will be zero for the values of t that satisfy ...

  0 = -t^2 +10t +22

Using the quadratic formula, we can find the values of t that satisfy this equation:

  t = (-10 ±√(10² -4(-1)(22)))/(2(-1)) = (-10 ±√188)/-2 = 5±√47

The value of h is zero for t ≈ 11.856.

_____

About the quadratic formula

The quadratic formula tells you the solution to ...

  ax^2 +bx +c = 0

is given by ...

  x = (-b ±√(b^2 -4ac))/(2a)

Matching this form to the given equation, we see a=-1, b=10, c=22. The variable used in the given equation is t, instead of x.

Answer:

x=2

Step-by-step explanation

Answer:

24,53cm²

Step-by-step explanation:

rectangle area=length×width=7×3

=21cm²

circle area=1/2Π r²

=1/2×3.14×1.5×1.5

=3.5325cm²

add the two areas

21+3.53=24,53cm²

Answer:

540°

Step-by-step explanation:

The sum of all the interior angles in a pentagon with 5 sides is 540°.

Answer:

540°

Step-by-step explanation:

Using the formula for finding the sum of interior angles of polygons

(n-2)×180

Where n is no. Of sides

For pentagon (5 sides) it will be

=(5-2)×180

=(3)×180

=540

So angles of a pentagon add up to 540°

Answer:

the value of the expression is

Step-by-step explanation:

42

64^4/6

the answer is A. 16

Answer:

BXBXBXBXBXB

Step-by-step explanation:

The term without exponent is b*b*b*b*b*b,

B:  (b³)² = b⁶.

The formula for an exponential function is f (x) = aˣ, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.

Given the term (b³)²

we know a² = a*a

so (b³)² = b³*b³

and a³ = a*a*a

(b³)² = b³*b³ = b*b*b*b*b*b

so (b³)² without exponent is b*b*b*b*b*b

and we know (aⁿ)ˣ = aⁿˣ

(b³)² = b⁶

Hence term without exponent is  b*b*b*b*b*b and compared power is b⁶.

Learn more about Exponential Function;

https://brainly.com/question/14355665

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Answer:

G > 16

Step-by-step explanation:

The expression "more than" 16 gold pieces per day means that the number of gold pieces Kwame earns each day (G) must be greater than 16. In order to represent that as an inequality, we should use the greater-than sign: >.

The inequality that describes the number of gold pieces Kwame must earn per day  is G > 16.

Answer:

x=28

Step-by-step explanation:

The interior angles of a triangle must add to 180 degrees.

Therefore,

x+95+57=180

Add 95 and 57

x+152=180

We are trying to find x. In order to do this, we must get x by itself. 152 is being added to x. The opposite of addition is subtraction. So subtract 152 from both sides.

x+152-152=180-152

x=180-152

x=28

Let’s check our answer. Add all the angles together, to be sure they add to 180 degrees.

x+95+57=180

Substitute 28 for x

28+95+57=180

180=180

The equation above is true, so we know that x is equal to 28.

____________________________________

Hey!!

Solution:

X+95+57=180 (sum of angle in triangle)

or,X+152=180

or,X=180-152

X=28 degree.

The value of X is 28 degree.

Hope it helps..

Good luck on your assignment..

Stay Safe...

_____________________________________

Answer:

D. All real numbers.

Step-by-step explanation:

This expression  can have any real number assigned to x.

Answer:

The input is all real numbers

Step-by-step explanation:

The domain is the input to the function

f(x) = x^2 + 3x +5

There is no limit to what we can put in the function so

The input is all real numbers

Answer:

Option A

radius = 13 units

height = 20 units

Volume of the cylinder = πr²h

= π (13)² ×20

=3380π cu. units

The volume of the cylinder will be 3380 π cubic units. Then the correct option is A.

Let r be the radius and h be the height of the cylinder.

Then the volume of the cylinder will be

V = π r²h cubic units

The radius is 13 and height is 20.

Then the volume of the cylinder will be

V = π (13)² x 20

V = 3380 π cubic units

Then the correct option is A.

More about the volume of the cylinder link is given below.

https://brainly.com/question/12763699

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Answer:

69 hours

Step-by-step explanation:

The painter spends 3 hours working on a painting.

The sculptor spends 23 times as long as the painter.

The amount of time the sculptor spent is:

23 * 3 = 69 hours

The sculptor works for 69 hours.

Answer:

2sqrt5, 5, sqrt13, 14.5

Step-by-step explanation:

Just use vectors to calculate the change in the x and y axis during each movement and then apply the Pythagoras Theorem.

1. Answer (D). By the law of sines, we have [tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex] in any [tex]\triangle ABC.[/tex]

2. Answer (C). The law of cosines, [tex]c^2=a^2+b^2-2ab\cos C,[/tex]accepts up to three sides and an angle as an input.

3. Answer (D). Although this triangle is right, we are not given enough information to uniquely determine its sides and angles - here, we need either one more side or one more angle.

4. Answer (D). Don't get tripped up by answer choice (C) - this is just a rearrangement of the statement of the law of cosines. In choice (D), the signs of [tex]a^2[/tex] and [tex]2ab\cos C[/tex] are reversed.

5. Answer (B). By the law of sines, we have [tex]\frac{5}{\sin 40^\circ}=\frac{3}{\sin\theta}.[/tex] Solving gives [tex]\theta\approx \boxed{23^\circ},157^\circ.[/tex] Note that this is the ambiguous (SSA) case of the law of sines, where the given measures could specify one triangle, two triangles, or none at all!

6. Answer (A). Since we know all three sides and none of the angles, starting with the law of sines will not help, so we begin with the law of cosines to find one angle; from there, we can use the law of sines to find the remaining angles.

Steps:

Simplify:

5³/5⁷

= 5³/5⁷

= 5*5*5/ 5*5*5*5*5*5*5

=1/5⁴

=1/625 (Decimal: 0.0016)

Steps by Step:

5³/5⁷

=125/5⁷

=125/78125

=1/625

Answer:   =1/625       (Decimal: 0.0016)

Please mark brainliest

Hope this helps.

Answer:

Step-by-step explanation:

You can see by the markings that ST is congruent to AY, and that TA is congruent to YS. Those are 2 sides, so so far we have SS. One important thing that comes up WAY TOO OFTEN IN GEOMETRY TO IGNORE is the fact that both of those triangles share the side SA. This is called the reflexive property. The theorem for congruency between these 2 triangles is SSS.

Answer:

60%

Step-by-step explanation:

184 - 115 = 69

[tex]\frac{69}{115} =.6\\\\[/tex]

.6 × 100 = 60%

115 + 60% = 69

Answer:

Options (A), (B) and (C)

Step-by-step explanation:

In the given figure,

Length of side AD = 16 units

If this side is scaled by a factor = k

Then the length of the corresponding side will be = 16k

If 0 < k < 1,

Then length of the corresponding side will be less than 16.

[Example: If k = [tex]\frac{1}{4}[/tex]

Therefore, scaled side of the corresponding side of the quadrilateral = [tex]16\times \frac{1}{4}[/tex] = 4]

That means length of corresponding sides may be 4, 6.5 and 12.

Options (A), (B) and (C) will be the answer.

Answer:

a b and c

Step-by-step explanation:

Answer:

y=4x+2

Step-by-step explanation:

Answer:

y=4x+4

Step-by-step explanation:

move 8x to the left side than divide 2y by 8x and 4 to give u that answer. hope it helps

Answer: (2,1)

Step-by-step explanation:

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. A dilation stretches or shrinks the original figure by a Factor (in this case 1/3).

C =(6, 3)

[tex]C' = \frac{1}{3} (6, 3)=(\frac{6}{3}, \frac{3}{3} )=(2, 1)[/tex]

Answer:

9/16

Step-by-step explanation:

Total of 16 combinations:

1:2

1:3

1:4

1:5

2:2

2:3

2:4

2:5

3:2

3:3

3:4

3:5

4:2

4:3

4:4

4:5

Total is 5 or less

1:2

1:3

1:4

2:1

2:2

2:3

3:1

3:2

4:1

I got 9/16

Answer:

2,880

Step-by-step explanation:

La facturación en primas sería de 2,880

Answer:

Step-by-step explanation:

what language are you speaking what the heck

Answer:

(x - 4)(x - 2)

Step-by-step explanation:

I have attached the work to your problem.

Please see the attachment below.

I hope this helps!

Answer:

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

Step-by-step explanation:

[tex] {x}^{2} - 6x + 8 \\ {x}^{2} + 4x + 2x + 8 \\ x(x + 4) + 2(x + 4) \\ = (x + 2)(x + 4) [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!