A train leaves the station at 6 pm traveling west at 80 mph. On a parallel track, a second train leaves the station 3 hours later traveling west at 100 mph. At what time will the second train catch up with the first?

Answer:Width = 15 units .

Step-by-step explanation:

Given  : The width of a rectangle is 4 more than half the length. If the perimeter of the rectangle is 74,

To find : what is the width.

Solution : We have given perimeter of the rectangle is 74,

Let the Length = x .

According to question :

The width of a rectangle is 4 more than half the length.

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

Perimeter = 2 length + 2 width .

Plugging the values,

74 = 2 ( x ) + 2 (4+[tex]\frac{x}{2}[/tex]).

74 = 2x + 8 + x .

Combine like terms

74 = 2x +x + 8.

74 = 3x +8.

On subtracting both sides by 8.

74 -8= 3x .

66 = 3x

On dividing both sides by 3

x = 22.

Width = Width = 4 + [tex]\frac{22}{2}[/tex].

Width = 4 +11.

Width = 15 units .

Therefore, Width = 15 units .

as you would already know, we start off to gettting any inverse of any expression by doing a quick switcheroo on the variables and then we solve for "y".

[tex]\bf y = \cfrac{x-6}{x+5}\implies \stackrel{\textit{quick switcheroo}}{x = \cfrac{y-6}{y+5}}\implies x(y+5)=y-6\implies xy+5x=y-6 \\\\\\ xy+5x+6=y\implies 5x+6=y-xy\implies 5x+6=\stackrel{\textit{common factor}}{y(1-x)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \cfrac{5x+6}{1-x}=\stackrel{f^{-1}(x)}{y}~\hfill[/tex]

Final answer:

The degree of the polynomial 5a⁶bc²+8d⁵+7e⁶f²-10g⁴h⁷ is 11, determined by the highest sum of exponents in any term of the polynomial, which is found in the term -10g⁴h⁷.

Explanation:

The degree of a polynomial is the highest exponent of its variables when it is expressed in standard form. To find the degree of the given polynomial 5a⁶bc²+8d⁵+7e⁶f²-10g⁴h⁷, we look at each term individually and sum the exponents of the variables within that term. The terms of the polynomial are:

5a⁶bc² with a degree of 6 + 1 + 2 = 9

8d⁵ with a degree of 5

7e⁶f² with a degree of 6 + 2 = 8

-10g⁴h⁷ with a degree of 4 + 7 = 11

Comparing the sums of the exponents, we see that the term -10g⁴h⁷ has the highest sum which is 11. Therefore, the degree of the given polynomial is 11.

Answer:

1/2

Step-by-step explanation:

Answer:

option c) they are parallel !!

Step-by-step explanation:

If two lines are perpendicular to the same line that is they both make 90° with the same line have difference in their angle 0° with respect to the same line , and line having difference in their angle as 0° are parallel to each other !

Answer:

[tex]\frac{1}{12} [/tex] inches per hour .

Step-by-step explanation:

Between 10 pm and 7:45 am there are 9 hours and 45 minutes i.e. [tex]9+\frac{45}{60} =\frac{39}{4}[/tex] hours

The water level in a swimming pool decreased by amount in [tex]\frac{39}{4}[/tex] hours  = [tex]\frac{13}{16}[/tex] inches

The water level in a swimming pool decreased by amount in 1 hour:

 = [tex]\frac{\frac{13}{16}}{\frac{39}{4}}[/tex] inches

 = [tex]\frac{13}{16} \times \frac{4}{39}[/tex] inches

= [tex]\frac{1}{4} \times \frac{1}{3}[/tex] inches

= [tex]\frac{1}{12} [/tex] inches

Hence  it drop by [tex]\frac{1}{12} [/tex] inches  each hour .

How much did it drop each hour is 0.08333 inches/hour

First step is to calculate the Decrease

Decrease = 13/16 inches

Decrease=0.8125 inches

Second step is to calculate the time interval

From 10 pm to  7:45 hours will be 9.45 hours

Time interval= (9 + 45/60) hours

Time interval=9.75 hours

Now let determine How much did it drop each hour

0.8125/9.75 inches/hour

=0.08333 inches/hour

Inconclusion How much did it drop each hour is 0.08333 inches/hour

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Answer:

The answer is 480

Step-by-step explanation:

Answer:

0.350 is bigger

Step-by-step explanation:

Answer:

0.305

Step-by-step explanation:

When working with decimals, it would be the smaller number that is bigger. .305 is bigger because .305 is 305 points away from 0 and .350 is 350 points away from 0!!

Hope this helps!!!

-Unicorns110504

Answer:

depending on the car type

probs about 5-10 feet

Step-by-step explanation:

Answer:

x=-81

Step-by-step explanation:

Multiply both sides of the equation by 3 to eliminate the fraction on the left side.

[tex]-x/3(3)=27(3)[/tex]

[tex]-x=81[/tex]

Divide both sides by -1 to isolate x on the left side of the equation

[tex]-x/-1=81/-1\\x=-81\\[/tex]

Answer:

x = - 81.

Step-by-step explanation:

Given  : [tex]\frac{-x}{3} = 27[/tex].

To find : solve the equation.

Solution: We have given

[tex]\frac{-x}{3} = 27[/tex].

On multiplying both sides by 3

-x = 27*3.

On dividing both sides by -1.

x = - 81.

Therefore, x = - 81.

Answer:

-8, -5, -20.

Step-by-step explanation:

f(0) = 6(0) - 8  = -8

f(1/2) = 6(1/2) - 8 = -5

f(-2) = 6(-2) - 8 = -20.

[tex]\text{Hello there!}\\\\\text{You're plugging in the values 0, 0.5, and -2 to x}\\\\\text{Plug them into the equation:}\,\,f(x) = 6x - 8\\\\\text{Solve:}\\\\f(x) = 6(0) - 8\\\\\boxed{f(x)=-8}\\\\f(x) = 6(0.5) - 8\\\\f(x) = 3 - 8\\\\\boxed{f(x)=-5}\\\\f(x) = 6(-2) - 8\\\\f(x)=-12-8\\\\\boxed{f(x)=-20}\\\\\text{Those three solutions will be your answer}\\\\\large\boxed{\text{Answer:}\,\,-8;-5;-20}[/tex]

Answer:

1. 60 2. 200

Step-by-step explanation:

600÷10= 60

2000÷10=200

Answer:

60 and 200

Step-by-step explanation:

When divideing by 10 you can cancel the zeros from both the numertor and denominator

Answer:

The required way is shown above.

Step-by-step explanation:

Consider the provided calculation.

304 – 81 is very close to 304 – 100,

Now subtract 100 from 304 mentally, it will gives us 204

Now add 19 as we round 81 to 100.

204 + 19 = 223

So, the answer is 223.

Now write a coherent sequence of equations that correspond to your reasoning.

304 – 81  =  304 – (100 – 19)

                = (304 – 100) + 19  

                =  204 + 19  =  223

Hence, the required way is shown above.

To subtract 81 from 304 mentally, round 81 to 80, subtract from 304 to get 224, and then add 1 to compensate for the rounding, giving a final answer of 225.

To calculate 304-81 mentally, we can use the strategy of rounding and compensating. First, we can round 81 up to a number that is easier to subtract from 304, such as 80 or 100, and then we adjust the final result to account for the rounding. Here's how to think through it:

The coherent sequence of equations that correspond to this reasoning would be:

This mental math strategy involves rounding and compensation, which allows us to handle subtraction problems quickly without having to use the standard subtraction algorithm. Checking that the answer makes sense in the context of the original problem is a good practice to ensure accuracy.

Step-by-step explanation:

From the diagram,

AC = AB + BC

BC = AC - AB

BC = 54 - 25 = 29

Answer:

Step-by-step explanation:

the line for equation : x = - 3

Answer: Dimes: 11

Quarters: 48

Step-by-step explanation:

48/4= 12.00

11•0.10= 1.10

12+1.10= 13.10

For this case we have to:

x: Represents the unknown number

y: Represents the exponent of base 10

So, considering a system of equations we have:

[tex]x * 10 ^ y = 40,000\\\frac {x} {10 ^ y} = 0.000004[/tex]

From the first equation we have:

[tex]10 ^ y = \frac {40,000} {x}[/tex]

Substituting in the second equation:

[tex]\frac {x} {\frac {40,000} {x}} = 0.000004\\\frac {x ^ 2} {40,000} = 0.000004\\x ^ 2 = 40,000 * 0.000004\\x ^ 2 = 0.16\\x = \pm \sqrt {0.16}[/tex]

We choose the positive value:

[tex]x = 0.4[/tex]

So, the number is 0.4.

So:

[tex]10 ^ y = \frac {40,000} {0.4}\\10 ^ y = 100,000\\y = 5[/tex]

Thus, the exponent is 5.

Answer:

Yara use 0.4 and[tex]10 ^ 5[/tex]

Answer:

0.4 and  10.5

Step-by-step explanation:

Answer:

y - 1 = 3(x - 2)

y - 1 = 3x - 6

y = 3x - 5

Answer:

The point slope form of the line is y-1=3(x-2).

Step-by-step explanation:

If a line passes through a points [tex](x_1,y_1)[/tex] with slope m, then the point slope form of the line is

[tex]y-y_1=m(x-x_1)[/tex]              .... (1)

where, m is slope.

It is given that the slope of a line is 3 and it passes through the point (2,1).

Substitute m=3, [tex]x_1=2\text{ and } y_1=1[/tex] in equation (1), to find the point slope form of the line.

[tex]y-(1)=(3)(x-(2))[/tex]

[tex]y-1=3(x-2)[/tex]

Therefore the point slope form of the line is y-1=3(x-2).

Answer:

Step-by-step explanation:

Here slope = (y2-y1)/(x2-x1)

Which comes out to be: (-4-2)/5-5 = -6/0 !!!

But we cannot divide by 0. So the slope is undefined. This is basically a vertical line. The "slope" of a vertical line. A vertical line has undefined slope because all points on the line have the same x-coordinate.

If your hw website is not accepting undefined as answer then what are the options that it provides?

Answer:

The number is 4

Step-by-step explanation:

* Lets revise some words in mathematics and how change them to

 mathematical symbols

- More than ⇒ add (+)

- Less than ⇒ subtract (-)

- Twice ⇒ Multiplied by 2 (× 2)

- Opposite of a number ⇒ change its sign (additive inverse of it)

* Now lets solve the problem

- Nine more than the opposite of a number is three less than twice

 the number

- Assume that the number is x

∴ 9 more than the opposite of x

- That means find the opposite of x and add it by 9

∵ The opposite of x is -x

∴ Nine more than the opposite of a number = -x + 9

- Three less than twice the number means 3 less than twice x

∵ The number is x

∴ Twice the number = 2 × x = 2x

∵ Three less than twice x = 2x - 3

∴ Three less than twice the number = 2x - 3

- The meaning of "is" between the two the statements is "="

∴ Nine more than the opposite of a number is three less than twice

  the number is ⇒ -x + 9 = 2x - 3

* Lets solve the equation to find x

∵ -x + 9 = 2x - 3

- add x in both sides

∴ 9 = 3x - 3

- Add 3 to both sides

∴ 12 = 3x

- Divide both sides by 3

∴ x = 4

∵ x represents the number

∴ The number is 4

* Lets check the answer

9 more than opposite 4 is 3 less than twice 4

9 + (-4) = 2 × 4 - 3

9 - 4 = 8 - 3

5 = 5

The answer is right

Answer:

1lb to $0.70, 5lb to $3.50, 10lb to $7, 15lb to $10.50

Step-by-step explanation:

Turn your ratios into fractions and place them near each other. you multiply across then divide with the remaining number.

Answer:

Expression: 1 ⇒ 18 + 63 f

Expression: 2 ⇒ 25

Step-by-step explanation:

* Lets revise at first the order of operations

- The order of these operations is:

# Parenthesis

# Exponents

# Multiplication and Division which comes first from left to right

# Addition and Subtraction which comes first from left to right

- There is a word made from the first letter of each operation

  PEMDAS to remember the order of operations

* Lets solve the problem

# Expression: 1

∵ 9(2 + 7 f)

- To simplify this expression multiply the bracket by 9

∵ 9(2 + 7 f) = 9 × 2 + 7 f × 9

∵ 9 × 2 = 18

∵ 7 f × 9 = 63 f

∴ 9(2 + 7 f) = 18 + 63 f

* Expression: 1 ⇒ 18 + 63 f

# Expression: 2

∵ 6 × 7 - 3² × 9 + 4³

- At first simplify exponent

∵ 3² = 9 and 4³ = 64

∴ 6 × 7 - 3² × 9 + 4³ = 6 × 7 - 9 × 9 + 64

- Solve the multiplication first

∵ 6 × 7 = 42

∵ 9 × 9 = 81

∴ 6 × 7 - 3² × 9 + 4³ = 42 - 81 + 64

- Solve 42 - 81 first because it comes first from left to right

∵ 42 - 81 = - 39

∴ 6 × 7 - 3² × 9 + 4³ = - 39 + 64

- Add them

∵ - 39 + 64 = 25

∴ 6 × 7 - 3² × 9 + 4³ = 25

* Expression: 2 ⇒ 25

Answer:

Step-by-step explanation:

f(x) = 10x – 4  

10x = f(x)+4

x = f(x)/10 + 2/5

the inverse is y = x/10 + 2/5

The two numbers are 3 and -5. Let's start with 3. To get three, add 4 to -1. That means, going 4 to the right on a number line. When you do so, you will end up with 3. Since adding always go up.

Let's move onto -5 now. For this, go 4 to the left. Subtracting from negative numbers will be negative numbers. Since subtracting is going down, you go down on the number line.

Therefore, 3 and -5 is the answer!

Explaining channel:

Type HWsolver-Brainly. It should pop up at the bottom with a person thumbs up.

The two numbers that are 4 units away from -1 are -5 and 3.

In math, a number line can be defined as a straight line with numbers placed at equal intervals or segments along its length.

Now the given integer is, -1.

To find the numbers that are 4 units away we need to subtract and add 4 to get the required number.

So, 4 units forward from -1 is,

-1 + 4 = 3

And 4 units backward from -1 is,

-1 - 4 = -5

So the two numbers we get are 3 and -5.

Thus, the two numbers that are 4 units away from -1 are -5 and 3.

To learn more about number line:

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#SPJ2

281.25-5.25a=2.75

step by step:

so you divide the total amount by two and you get 140.62

then you divide that by 5.25 and you get 26.78

plug that into a and you get 140.62

then you take the remainder which is 140.62 and you divide that by 2.75

which is 51.13 and that will be your number for s

and at the end you should get the remainder of 140.62

then you multiply 140.62 by 2 and you get were you started and thats how you check your answer

Select all equations that could represent the relationship between the number of

number ofstudents, s, the number of adults, a, and the dollar amount received at the game.

The equations that could represent the relationship between the number of students, s, the number of adults, a, and the dollar amount received at the game is 281.25 – 5.25a = 2.75s

let

student fee = $2.75

Adult fee = $5.25

Total income = $281.25

Number of students = s

Number of adults = a

The equation:

Total income = (student fee × Number of students) + (Adult fee × Number of adults)

A. 281.25 – 5.25a = 2.75s

True

B. a = 53.57 - 13:25

Not true

C. 281.25 -5.25s = a

Not true

D. 281.25 +2.75a = s

Not true

E. 281.25 +5.25s = a

Not true

Therefore, the equations that could represent the relationship between the number of students, s, the number of adults, a, and the dollar amount received at the game is 281.25 – 5.25a = 2.75s

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Answer:

69 and 15

Step-by-step explanation:

Second number=x

First number 4x+9

4x+9 +x = 84

5x+9=84

5x=75

x=15

15*4=60      

60+9=69

69+15=84

Answer:

[tex]\large\boxed{A=6.25\pi\ km^2\approx19.625\ km^2}[/tex]

Step-by-step explanation:

The formula of an area of a circle:

[tex]A=\pi r^2[/tex]

r - radius

We have the length of a diameter d = 5 km

We know: d = 2r. Therefor r = 5km : 2 = 2.5 km.

Substitute:

[tex]A=\pi(2.5)^2=6.25\pi\ km^2[/tex]

If you want an approximation, then

[tex]\pi\approx3.14\to A\approx(6.25)(3.14)=19.625\ km^2[/tex]

Hey!

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

Formula: A = πr²

Diameter: d / 2 = r

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

Solution:

A = (3.14)(2.5)²

A = (3.14)(6.25)

A = 19.625km.

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

Answer:

The area of the circle is 19.625km. or 6.25π km.

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

Hope This Helped! Good Luck!