The Pham family and the Morgan family each used their sprinklers last summer. The water output rate for the Pham family's sprinkler was 25L per hour. The water output rate for the Morgan family's sprinkler was 35L per hour. The families used their sprinklers for a combined 65total of hours, resulting in a total water output of 1975L . How long was each sprinkler used?

Answer:

Since L.H.S = R.H.S = 0, for both [tex]y_{1} (t) = e^{t}[/tex] and [tex]y_{2} (t) = cosh(t)[/tex], y₁ and y₂ both satisfy the equation y" - y = 0 and are thus solutions to the differential equation.

Step-by-step explanation:

To check whether the given functions are solutions the given differential equation, we differentiate the functions and then insert it into the given equation.

So y" - y = 0 and  

[tex]y_{1} (t) = e^{t}\\y_{1}' (t) = e^{t}\\ y_{1}" (t) = e^{t}[/tex]

Substituting these values of y and y" into the left hand side of the equation, we have

y" - y  

[tex]y_{1}" (t) - y_{1} (t) = e^{t} - e^{t} = 0[/tex]

Since L.H.S = R.H.S

So [tex]y_{1} (t) = e^{t}[/tex] is a solution of the differential equation.

When

[tex]y_{2} (t) = cosh(t)\\ y_{2}'(t) = sinh(t) \\y_{2}"(t) = cosh(t)[/tex]

Substituting y and y" into the left hand side of the equation, we have

y" - y

[tex]y_{2}"(t) - y_{2} (t) = cosh(t) - cosh(t) = 0[/tex]

Since L.H.S = R.H.S

So, [tex]y_{2} (t) = cosh(t)[/tex] is a solution of the differential equation.

Answer:

E

Step-by-step explanation:

they all equal the same thing

hope this helps :)

Answer: [tex]x=-22.42[/tex]

Simplify both sides of the equation

[tex]-18.43=x+3.99[/tex]

Flip the equation

[tex]x+3.99=-18.43[/tex]

Subtract 3.99 from both sides

[tex]x+3.99-3.99=-18.43-3.99\\x=-22.42[/tex]

Answer:

54, 55, 56, 57, 58, and 59 are the numbers

Step-by-step explanation:

Let's pretend that the first number is [tex]n[/tex].

We know that these numbers are consecutive, meaning each number is one more than the other.

This means that

[tex]n + (n+1)+ (n+2)+ (n+3)+ (n+4)+ (n+5) = 339[/tex], since each number is consecutive.

We can combine like terms to get [tex]6n + 15 = 339[/tex].

Now let's solve for n.

[tex]6n + 15 - 15 = 339-15\\\\6n = 324\\\\n = 54[/tex]

So [tex]n=54[/tex]. This means the other 5 digits will be one more than the next.

So 54, 55, 56, 57, 58, and 59.

Hope this helped!

Answer:

a) 63°

b) 127°

Step-by-step explanation:

Complements are 90° while supplements are 180°.

So you need to find the complement of 27°. So, 90-27=63

To find the supplement, it is 180-53=127

Answer:

Your correct answer is 37

Step-by-step explanation:

Evaluate for z = 4

(10)(4)−3

(10)(4)−3

= 37

Answer:

The equation is y = (3/7)x - 7.

Step-by-step explanation:

Given that the point slope form of an equation is y = mx + b where m represents the gradient and b is the y-intercept. Then, you have to substitute the following values into the equation :

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

[tex]let \: m = \frac{3}{7} ,x = 7,y = - 4[/tex]

[tex] - 4 = \frac{3}{7} (7) + b[/tex]

[tex] - 4 = 3 + b[/tex]

[tex] - 4 - 3 = b[/tex]

[tex]b = - 7[/tex]

Answer:

3.855x 10^4

Step-by-step explanation:

Hope this helps.

Answer:

19,360

Step-by-step explanation:

1/5 is .2, or 20%.  So we multiply the number by .8 to have 80% of the original.

24,200*.8=19360

Answer:

$12.96

Step-by-step explanation:

4.5 x 2.88 = $12.96

hope this helped!

Answer:

$12.96

Step-by-step explanation

One pound of turkey is $2.88 but you need 4.5 pounds do

$2.88 x 4.5 and you should get

$12.96

Answer:

4 3/5, -14 5/5, -17 3/5

Step-by-step explanation:

Answer:

[tex]x=56[/tex]

Step-by-step explanation:

So we have the equation:

[tex]\frac{2(x+4)}{3}-8=32[/tex]

First, add 8 to both sides. The left cancels:

[tex]\frac{2(x+4)}{3}=40[/tex]

Multiply both sides by 3. The left cancels:

[tex]2(x+4)=120[/tex]

Divide both sides by 2:

[tex]x+4=60[/tex]

Subtract 4 from both sides:

[tex]x=56[/tex]

And we are done!

Answer:

167 is a prime number

Step-by-step explanation:

coz 167 is not divided by any no except 1 or itself

Answer:

No

Step-by-step explanation:

The time it takes Timothy to drive to his friends' houses is not proportional. This is because when going to the first house, he is going at 4km per minute, but when visiting the second and third houses he is no longer traveling at that speed.

In a directly proportional relationship, increasing one variable will increase another. The given relationship is not proportional.

In a directly proportional relationship, increasing one variable will increase another.

This directly proportional relationship between p and q is written as

p∝q where that middle sign is the sign of proportionality.

Inversely proportional relationship increasing one variable will decrease the other variable if both are inversely proportional.

This directly proportional relationship between p and q is written as

p∝1/q where that middle sign is the sign of proportionality.

Given that the table shows the distance and time it takes him to drive to each of his friends’ houses.

Now, to know if the time it takes Timothy to drive to his friends’ houses proportional to the distance, find the ratio of distance to time for each row. Therefore, the ratios can be written as,

R₁ = 5km / 10 min = 0.5 km per min

R₂ = 11 km / 15 min = 0.7334 km per min

R₃ = 18 km / 20 min = 0.9 km per min

Since the ratio of distance and time in different cases is different, therefore, the given relationship is not proportional.

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Answer:

yes, as long as the numbers do not go on forever.

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

Algebraic Terms:

1. Monomial - an algebraic term

2. Binomial - the sum of 2 algebraic terms

3. Trinomial - an algebraic sum in 3 terms

4. Polynomial - a function in more than 1 algebraic term

The sum of 2 binomials is not always a binomial because each of the two binomials might have different algebraic terms.

If the first binomial has 2 algebraic terms and the second binomial has 2 other algebraic terms and no single term crosses out its coefficients, the sum of both binomials will not be a binomial.

Step-by-step explanation:

-6z = 72

z = 72/(-6)

= -12

4) -12

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ - 12}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{ - 6z = 72}[/tex]

Divide both sides by -6

[tex] \dashrightarrow{ \sf{ \frac{ - 6z}{ - 6} = \frac{72}{ - 6} }}[/tex]

Calculate

[tex] \dashrightarrow{ \sf{z = - 12}}[/tex]

Hope I helped!

Best regards! :D

Answer:

£ 11.20

Step-by-step explanation:

Cost of charge per mile = 60 p

Cost of charge for 12 miles = 0.60 * 12

                                             = £7.20

Charge paid by Antoni = 4 + 7.20 = £ 11.20

Answer:

Step-by-step explanation:

-2x + 2y = -10

2x - 3y = 4

-y = -6

y = 6

2x - 18 = 4

2x = 22

x = 11

(11, 6)

Answer:

1) 11/10= 1 1/10

2)17/15= 1 2/15

3)10/10= 1

4)11/10= 1 1/10

5)9/18= 1/2

Answer:

x=5

y=0

There are a lot of different answers to. Do you have answer choices?

Answer:

3 quartars 2 nickles 4 pennnies 2 half-pennies

Step-by-step explanation:

Answer:

16,500

Step-by-step explanation:

5-1 (the bidder) = 4 divided by 66,000 = 16,500

The number of amount that bidder need to put into a kitty for the other bidders to be compensated is 52,800

5 people can claim joint ownership of an item and intend to divide it by the method of sealed bids. The winner offers a bid of $66,000

[tex]= 66,000 - (66,000 \div 5)[/tex]

= 66,000 - 13,200

= 52,800

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Answer:

669ft high

Step-by-step explanation:

642+27=669ft

The height of the mountain is 669 ft.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

For example 4 -2 = 2

A drone takes off from the base of a mountain at a height of 27 ft below sea level.

To determine the height of the mountain.

Using the arithmetic operations of addition and subtraction,

The drone then flies up 642 ft before landing at the top of the mountain.

Assume that distance below sea level is positive,

So the height of the mountain as

⇒ 642 + 27

⇒ 669 ft

Hence, the height of the mountain is 669 ft.

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Answer:

-7

Step-by-step explanation:

A constant number is a number that contains no variables like x and y. The only constant in that problem is -7.

A constant is a number which independent of anything and never changes thus the constant in the given expression 2x³ - 8x² + 3x - 7 is -7.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

As per the given expression,

2x³ - 8x² + 3x - 7

Here, x is a variable.

The constant multiplied by a variable is said to be the coefficient.

Thus, 2,-8,3 are the coefficient.

A number independent constant is -7 will be constant.

Hence "A constant is a number which is independent of anything and never changes thus the constant in the given expression 2x³ - 8x² + 3x - 7 is -7."

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Answer: its A

1. Multiply the divisor by a multiple of 10 to create an integer divisor.

2. Multiply the dividend by the same multiple of 10 as step 1.

3. Divide, and apply the rules for dividing signed numbers.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The solution set for this inequality is {x | x > 2}

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We also find the solution in a system of equations using the substitution or elimination method.

Example:

2x + 4 = 8

The solution is x = 2.

We have,

To solve the inequality:

2x - 3 > 11 - 5x

We can start by simplifying the expression on both sides:

2x - 3 > 11 - 5x

Adding 5x to both sides

7x - 3 > 11

Adding 3 to both sides

7x > 14

Dividing both sides by 7

x > 2

This means that any value of x greater than 2 will make the inequality true.

Thus,

The solution set for this inequality is {x | x > 2}

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