What is the slope of the line passing through (0, 5) an d(-12, 2) ?

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The rate of change of the distance between the police car and the truck after 10 minutes is approximately 193.66 m/s

The rate of change of a function is the rate at which the output of the function is changing with regards to the input.

The velocity of the police car = 160 km/h south

The velocity of the truck = 140 km/h east

Distance of the police car from Sioux Falls = 60 km north

Distance of the truck from Sioux Falls = 50 km east

Required;

The rate at which the distance between the vehicles is changing at t = 10 minutes

Solution;

Let d represent the distance between the vehicles, we have;

d² = x² + y²

Where;

x = The distance of the truck from Sioux falls

y = The distance of the police car from Sioux Falls

Which gives;

[tex] \displaystyle{ \frac{d}{dt} d^2= \frac{d}{dt}(x^{2}) +\frac{d}{dt} (y^{2}) }[/tex]

Which gives;

[tex] \displaystyle{ 2 \cdot d \cdot \frac{d}{dt} d=2 \cdot x \cdot \frac{dx}{dt} + 2 \cdot y \cdot\frac{dy}{dt} }[/tex]

After 10 minutes, we have;

y = 60 - (10/60)×160 = 100/3

x = 50 + (10/60)×140 = 220/3

d = √((100/3)² + (220/3)²) = 20•(√146)/3

[tex] \displaystyle{ \frac{d}{dt} d=\frac{2 \cdot x \cdot \frac{dx}{dt} + 2 \cdot y \cdot\frac{dy}{dt} }{2 \cdot d }}[/tex]

Which gives;

[tex] \displaystyle{ \frac{d}{dt} d= \frac{2 \times \frac{220}{3} \times 140 + 2 \times \frac{100}{3} \times 160}{2 \times \frac{20 \times \sqrt{146}}{3}}}[/tex]

[tex] \displaystyle{ \frac{2 \times \frac{220}{3} \times 140 + 2 \times \frac{100}{3} \times 160}{2 \times \frac{20 \times \sqrt{146}}{3}}\approx 193.66}[/tex]

Therefore;

[tex] \displaystyle{ \frac{d}{dt} d \approx 193.66}[/tex]

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Explanation:

This is the LCM (lowest common multiple) of 3 and 5

3*5 = 15

Eva: 3, 6, 9, 12, 15, 18, 21, ...

Jin: 5, 10, 15, 20, 25, ...

The price of gasoline before the 15% increase is $4.75/gallon.

What is gasoline?
Petroleum-derived clear flammable liquid known as gasoline or petrol is the primary fuel for the majority of spark-ignited internal combustion engines (also known as petrol engines). It mostly comprises of organic compounds made from petroleum fractional distillation that have been improved with various additions. In the United States, refineries typically create 19 to 20 gallons of gasoline, 11 to 13 gallons of distillate fuel, the majority of which is sold as diesel fuel, and 3 to 4 gallons of jet fuel from a barrel of crude oil. The crude oil test and oil refinery processing determine the product ratio. 42 US gallons, or around 159 litres or 35 imperial gallons, is the standard measurement for the volume of an oil barrel.

How can we calculate the price before the 15% increase?

Overnight the price of gasoline increased by 15% to settle at a price of $4.90 per gallon.

15÷100+x = $4.90/gallon

0.15+x = $4.90/gallon

Therefore, x = $4.90/ gallon - 15÷100

 x = $4.90/gallon - 0.15

x = $4.75/gallon.

Hence , the price of gasoline before the 15% increase is $4.75/gallon.
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The original recipe has half of the number of strawberries She wants to use in her salad in this case we will need double the fruits of the recipe given

Bananas

4x2=8 bananas

Apples

3x2=6 apples

Pears

6x2=12 pears

Area of rectangle = Length x Width

. = 14.3 x 13.9

. = (13.9+ 0.4) x 13.9

. = 13.9^2 + 5.56

. = 13•14 +( 1.4)•8 + 5.56

. =198.77 cm2

The number of guests that were at the party is 16.

A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below. An example of a fraction is 1/2. 1 is the numerator and 2 is the denominator.

The equation that would be formed from the available information in this question is:

[tex]\frac{x}{3} + \frac{x}{4} + \frac{x}{2} = 17[/tex]

Where x represents the number of guests that are in the party.

[tex]\frac{x}{3} + \frac{x}{4} + \frac{x}{2} = 17[/tex]

Add the fractions:

[tex]\frac{3x + 4x + 6x}{12}[/tex] = 17

[tex]\frac{13x}{12}[/tex] = 17

Multiply both sides of the equation by 12

13x = 12 x 17

13x = 204

Divide both sides of the equation by 13

x = 204 / 13

x  = 15.7 ≈ 16

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The x intercept is (-7.5,0).

The y intercept is (0,5.5).

Answer:

  7/3

Step-by-step explanation:

You want the ratio 3.50 : 1.50 written as a fraction.

A ratio can be written 3 ways. Any of them can be reduced to a ratio of mutually prime integers:

  3.50 : 1.50 = 3.50/1.50 = 3.50 to 1.50

Here, the fraction can be made to be a ratio of integers by multiplying both numerator and denominator by 2:

  3.50/1.50 = (2·3.50)/(2·1.50) = 7/3

The ratio 3.50:1.50 is equivalent to the fraction 7/3.

Insecticides = 14/100 x 5 = 0.7

To determine a percentage we can use the following formula:

In this case the part is equal to two, the whole is equal to 10, then we have:

Therefore, 2 is 20% of 10

We got to use the Secant-Tangent Theorem, here. It says that AC² is equal to the distance BC times the distance from C to the circumference. Let's denote the point in OC where it intercepts the circumference by D, so:

Beucase the radius is equal in all points of the circumference, OA=OB=OD, so BC = OA + OC, and CD = OC - OA. So,

we have that

the answer is the option First

perpendicular bisector

because, is perpendicular to the segment at its midpoint

The probability of selecting the integer 361 from the random generator is 0.

It should be noted that probability simply has to do with the likelihood that a particular thing will take place.

In this case, a random number generator is used to select an integer from 1 to 50 .

The probability of selecting the integer 361 from the random generator will be 0. This is because the numbers given are from 1 to 50.

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Answer: 1050 is the answer trust me i took the quiz and it was correct pls give me brainliest and friend request me ur welcome :)

Step-by-step explanation:

Given that 3x+2=17

3x=17-2

3x=15

x=15/3

x=5

so,the numbers we end up using are 17,3,15,5,2

Answer:

g(8 + x) = - 2(8 + x)

Step-by-step explanation:

substitute x = 8 + x into g(x)

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

Kevonta, this is the solution:

Time of departure : 11:49

Time of travel : 4:32

In consequence, the estimated arrival time if the train departs in the morning is:

11 + 4 = 15 hours

49 + 32 = 81 minutes

81 minutes = 1 hour + 21 minutes

4:21 pm

If the train departs at night, the estimated time of arrival is:

4:21 am

Given:

Salesman A earn = 65 per sale.

Salesman B earn = 40 per sales and 300weekly salary.

Salesman C earn = 900 weekly salary

Let "x" represent the number of sales each man

Salesman A earn is:

Salesman B earn is:

So total sales is 12 then.

S=0 For Zero week

For S=1

For s=10

Answer:

Area = 4πr²

Step-by-step explanation:

- We know that a moon revolves around its orbit as per Keplar. The moon is not a perfect sphere, so we shall take an assumption;

Assume the moon is a perfect and regular sphere

[tex]{ \tt{volume \: of \: moon = \frac{4}{3} \pi {r}^{3} }} \\ \\ { \boxed{ \tt{ \: v = \frac{4}{3} \pi {r}^{3} }}}[/tex]

- From engineering mathematics (rates of change), we know that volume is first order integral of area and area is the first order derivative of volume;

[tex]{ \tt{area = \frac{d(volume)}{dr} }} \\ \\ { \tt{volume = \int area \: dr}}[/tex]

- So, from our formular;

[tex]{ \tt{area = \frac{dv}{dr} = \frac{4}{3}\pi ( \frac{d ({r}^{3} )}{dr} ) }} \\ \\ { \tt{area = \frac{4}{3}\pi(3 {r}^{2}) }} \\ \\ { \boxed{ \rm{area = 4\pi {r}^{2} }}}[/tex]

[tex]{ \boxed{ \mathfrak{DC}}}{ \underline{ \mathfrak{ \: delta \: \delta \: creed}}} \\ [/tex]

Answer:

Domain: (-∞, ∞)

Range: (-∞, -9]

Step-by-step explanation:

The value of the expression −|a + b|/2 − c when a =1 2/3 , b=−1 , and c=−3 is 8/3

From the question, the expression is given as

−|a + b|/2 − c

Also, we have the values of the variables to be

a =1 2/3 , b=−1 , and c=−3

Rewrite a as

a = 5/3

So, we substitute a = 5/3  b=−1 , and c=−3 in −|a + b|/2 − c

This gives

−|a + b|/2 − c  = −|5/3 - 1|/2 + 3

Evaluate the difference in the expression

−|a + b|/2 − c  = −|2/3|/2 + 3

Divide

−|a + b|/2 − c  = −|1/3| + 3

Remove the absolute bracket and solve

−|a + b|/2 − c  = 8/3

Hence, the solution is −|a + b|/2 − c  = 8/3

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The required simplified value of the given expression is 8/3.

As per the given data, an expression −|a+b|/2−c is given when   a=1 2/3, b=−1, and c=−3 the value of the expression is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let the solution be x,
x = −|a+b|/2−c
Substitute value in the above equation,
x = - |1 + 2 / 3 - 1|/2 - (-3)
x = -1/3 + 3
x = -1+9 / 3
x = 8/3

Thus, the required simplified value of the given expression is 8/3.

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The graph of G(x) is symmetric with respect to the y-axis. It also passes through the origin.

Since the graph of F(x) moved 4 units upward, we must add 4 to the right of the equation. Thus, the equation of F(x) is as follows.

Answer:

the answer is C

Step-by-step explanation:

25% of 150 is 37.5 so 150-37.5 is 112.5

We have the following information:

• At a sale, a sofa is being sold for ,67% of the regular price

• The sale price is $469

And we need to determine the regular price.

To find it, we can proceed as follows:

1. Let x be the regular price. Then we have:

2. Now, we have to solve for x as follows:

Therefore, in summary, the regular price is $700.

STEP - BY - STEP EXPLANATION

What to find?

Rate of change of the given function.

Given:

Step 1

State the formula for rate of change.

Step 2

Choose any two point within the given interval.

(3, 59) and (6, 44)

⇒a=3 f(a) =59

b= 6 f(b)=44

Step 3

Substitute the values into the formula and simplify.

ANSWER

Rate of change = -5

[tex] = 2(4)^{2} - (10 \div 2) \\ = 2(16) - 5 \\ = 32 - 5 \\ = 27[/tex]

THE ANSWER IS OPTION 2. 27

HOPE THIS HELPS

Answer:

Answer is 27                  

    ♬      

⚫    

a)

The oven devaluated from $1970 to $270 in 10 years.

Since each year it looses the same value, divide the change in the price over the time interval to find the rate of change of the value with respect to time.

To find the change in price, substract the initial price from the final price:

The change in price was -$1700.

Divide -1700 over 10 to find the change in the price per year:

The initial value of the oven was $1970, and each year it looses a value of $170.

Then, after x years, the value will be equal to 1970-170x.

Then, the linear equation that models the value of the oven, y, after x years of use, is:

b)

To find the value of the oven after 2.5 years, substitute x=2.5:

Then, the value of the oven after 2.5 years is $1545.

c)

To find the y-intercept, substitute x=0:

The y-intercept is the initial value of the oven when 0 years have passed.

d)

Answer: [tex]4x^{5} y^{6} \sqrt{7y}[/tex]

Step-by-step explanation:

1) Separate the radicals

sqrt(112x^10y^13) = sqrt(112)*sqrt(x^10)*sqrt(y^13)

2) For sqrt(112), rewrite it as the product of a perfect square and some other number.

sqrt(112) = sqrt(16) * sqrt(7)

= 4*sqrt(7)

3) For sqrt(x^10), rewrite it in terms of it being raised to a fraction

[tex]\sqrt[n]{x} = x^{\frac{1}{n} }[/tex]

n = 2, so x^(10/2), and when simplified you have x^5

4) For sqrt(y^13), do the same thing.

y^(13/2) = sqrt(y)*(y^6)

5)Combine everything

4x^5y^6sqrt(7y)

Answers:

Domain as an inequality:  [tex]\boldsymbol{-\infty < \text{x} < \infty}[/tex]

Domain in interval notation:  [tex]\boldsymbol{(-\infty , \infty)}[/tex]

Range as an inequality:  [tex]\boldsymbol{-3 \le \text{y} \le 3}[/tex]

Range in interval notation:  [-3, 3]

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

Explanation:

The domain is the set of allowed x inputs. This graph goes on forever in both directions, so we can plug in any real number for x. There are no restrictions to worry about.

As an inequality, we write [tex]-\infty < \text{x} < \infty[/tex] to basically say "x is between negative infinity and infinity". In other words, x is anything on the real number line.

That inequality condenses into the interval notation of [tex](-\infty , \infty)[/tex]

Always use curved parenthesis for either infinity, because we can't ever reach infinity. It's not a number on the number line but rather a concept.

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

Now onto the range.

Recall the range is the set of possible y outputs. We look at the lowest and highest points (aka min and max) to determine the boundaries for the range.

In this case, the smallest y can get is y = -3

The largest it can get is y = 3

The range is any value of y such that [tex]-3 \le \text{y} \le 3[/tex] which in word form is "any value between -3 and 3, inclusive of both endpoints".

That inequality condenses to the interval notation [-3, 3]

We use square brackets to include the endpoints as part of the range.

Answer:

[tex]\textsf{Domain}: \quad (-\infty, \infty) \quad -\infty < x < \infty[/tex]

[tex]\textsf{Range}: \quad [-3,3] \quad -3\leq y\leq 3[/tex]

Step-by-step explanation:

The domain of a function is the set of all possible input values (x-values).

The range of a function is the set of all possible output values (y-values).

Interval notation

Inequality notation

From inspection of the given graph, the function is continuous and so the domain is not restricted.

Therefore, the domain of the function is:

From inspection of the given graph, the minimum value of y is -3 and the maximum value of y is 3.  Both values are included in the range.

Therefore, the range of the function is: