What is the equation for the line that passes through the point (-7,-7) and has a slope of 1?

Hey there!☺

\(Answer:\boxed{y=-3x+5}\)

\(Explanation:\)

Solve for y | \(9x+3y=15\)

Let's start by adding -9x to both sides of the equation:

\(9x+3y+-9x=15+-9x\\3y=-9x+15\)

Now in our second/last step, we will divide both sides by 3:

\(\frac{3y}{3}=\frac{-9x+15}{3}\\y=-3x+5\)

y=-3x+5 is your answer.

Hope this helps!☺

The required solution of the expression 9x+3y=15 for y is y = [15 - 9x] / 3.

To simply the given expression 9x+3y=15 for y.

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.

The equation is the relationship between variables and is represented as y =ax +b is an example of a polynomial equation.

Here,

9x+3y = 15
Simplification of the equation
⇒ 9x + 3y = 15
⇒ 3y = 15 - 9x

⇒ y = [15 - 9x] / 3

Thus, The required solution of the expression 9x+3y=15 for y is y = [15 - 9x] / 3.

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As per the given density function, the value of c is 0.

Density function:

Density function is an integral of the density of the variable density over a given range.

Given,

A skilled worked requires at least 10 minutes, and no more than 20 minutes, to complete a certain task. The completion time X is a continuous random variable with density function f(x) = c/x² for 10 < x < 20 and f(x) = 0 for all other values of x.

Here we need to find the value of c.

While we looking into the given question,

Least time = 10

Maximum time = 20

Density function = f(x) = c/x²

In order to find the value of c, we have to equate the function with 0, then we get,

=> c/x² = 0

=> c = 0

Therefore, the value of c is 0.

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Answer:

43/18

Step-by-step explanation:

Answer:

40 miles

Step-by-step explanation:

Since we are dealing in mph, change the minutes to hr

15 min: 15/60 = .25 hrs

3 min: 3/60 = .05 hrs

:

Let t = his normal drive time to work in hrs

then

40t = the distance to work

Write a distance equation; dist = speed * time

50(t-.25 + .05) = 40t

50(t - .20) = 40t

50t - 10 = 40t

50t - 40t = 10

10t = 10

t = 1 hr normal time to work

therefore

40(1) = 40 mi to work

:

:

Confirm this by finding the dist when he went 50 mph for 48 min (.8hrs)

50(1-.25+.05) = 50(.8) = 40 mi also

Answer:

There are two sets of numbers that meet the criteria:

1)  8 and 16, or

2) -8 and -16

Step-by-step explanation:

Let's call the two numbers A and B.

We are told:

1) A-B=8, and

2) A^2 + B^2 = 320

Rearrange 1) to solve for A:

A=8+B

Use this value of A in the second equation:

A^2 + B^2 = 320

(8+B)^2 + B^2 = 320

(64+ 16B + B^2) + B^2 = 320

2B^2 + 16B + 64 = 320

B^2 + 8B + 32 = 160

B^2 + 8B + 32 = 160

B^2 + 8B - 128 = 0

(B+16)(B-8)=0

B is either -16 or +8

Assuming B = 8

Then from A-B=8 we find that A = B+8 and A = 16

Does A^2 + B^2 = 320?

  (16)^2 + (8)^2 = 320?

  256 + 64 = 320?  YES

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

Assuming B=-16

If B=-16, then from A-B=8 we find that A = 8+(-16) and A = -8

Does A-B=8?

 -8 - (-16) = 8?  YES

Does A^2 + B^2 = 320?

 (-8)^2 + (-16)^2 = 320?

 64  + 256 = 320?  YES

Given :-

To find :-

Solution :-

Using angle sum property of a ∆ ,

Answer:

x = 12

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the given angles and equate to 180

2x + 1 + 5x + 5 + 90 = 180 , collect like terms

7x  + 96 = 180 ( subtract 96 from both sides )

7x = 84 ( divide both sides by 7 )

x = 12

Answer:

32= 2×2×2×2×2=2 power 5

Answer:

\(2^{-5}\)

Step-by-step explanation:

Using the rule of exponents

\(a^{-m}\) = \(\frac{1}{a^{m} }\)

Given

\(\frac{1}{32}\)

= \(\frac{1}{2^{5} }\)

= \(2^{-5}\)

To create a linear model, we can use the formula for the equation of a line:

y = mx + b

where m is the slope and b is the y-intercept. We can calculate the slope using the formula:

m = (y2 - y1)/(x2 - x1)

Let's use the data from 1990 and 2005:

x1 = 1990, y1 = 210,000

x2 = 2005, y2 = 320,000

m = (320,000 - 210,000)/(2005 - 1990) = 11,000

Now we can use the point-slope form of a line to find the y-intercept:

y - y1 = m(x - x1)

y - 210,000 = 11,000(x - 1990)

y - 210,000 = 11,000x - 21,790,000

y = 11,000x - 21,580,000

So the linear model that predicts the population of Center City (y) in a given year (x) is:

y = 11,000x - 21,580,000

To find the year when the actual population of Center City was most different from the value predicted by this model, we can compare the actual population to the predicted population for each year and find the year with the largest difference.

Year | Actual Population | Predicted Population | Difference

1990 | 210,000 | 188,000 | 22,000

1995 | 240,000 | 239,000 | 1,000

2000 | 280,000 | 290,000 | 10,000

2005 | 320,000 | 341,000 | 21,000

We can see that the actual population was most different from the predicted population in 2005, with a difference of 21,000.

Answer: c (year 2000)

Step-by-step explanation:  blud above got me confused

The equation of the line that is parallel to the given line and has an x-intercept of 3 is y = 2/3x - 2

The given parameters are

Point =(0, -1) and (3, 1)

Calculate the slope using

m = (y₂ - y₁)/(x₂ - x₁)

Where m represents the slope

So, we have:

m = (1 -- 1)/(3 -0)

Evaluate

m = 2/3

Parallel lines have equal slopes

So, the slope of the other line is

m = 2/3

Linear equations are represented as:

y = mx + c

Where m represents the slope and c represents the y-intercept

So, we have

y = 2/3x + c

An x-intercept of 3 means

0 = 2/3 * 3 + c

So, we have

c = -2

Substitute c = -2 in y = 2/3x + c

y = 2/3x - 2

Hence, the equation of the line that is parallel to the given line and has an x-intercept of 3 is y = 2/3x - 2

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to minimize the time it takes to reach the island, the visitor has to run 15 km west of the tent to first get to the closest point of the shoreline to the island before swimming across to the island.

Here we have;

Location of island = 15km west

Location of tent = 2 km south of point on shoreline

Running speed of visitor = 8 km/h

Swimming speed = 1 km/h

Distance of island from tent = \(\sqrt{15^2 +2^2}\) = 15.13

Since, time = distance/speed, it will take 15.13/1 hours or 15.13 hours to swim directly to the island.

However if the visitor first runs to the closest point on the shoreline to the island, then swims across to the island, it will take;

15/8 Hr + 2/1 hr = 31/8 hours or 3.875 hours only.

Therefore, to minimize the time it takes to reach the island, the visitor has to run 15 km west of the tent to first get to the closest point of the shoreline to the island before swimming across to the island.

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Answer:

1.6666666666

Hope this helps!

Answer:

The speed of the submarine is 15.429 miles per hour.

Step-by-step explanation:

Let suppose that both ships travel at constant velocities. As we know that both travel in opposite directions, it is supposed that cruise ship moves in +x direction, whereas submarine in -x direction. Kinematic equations for each sheep are described below:

Ship

\(x_{Sh} = x_{o} + v_{Sh}\cdot t\)

Submarine

\(x_{Su} = x_{o}+v_{Su}\cdot t\)

Where:

\(x_{o}\) - Position of Diego Garcia island, measured in miles.

\(x_{Sh}\), \(x_{Su}\) - Current positions of ship and submarine, measured in miles.

\(v_{Sh}\), \(v_{Su}\) - Velocities of ship and submarine, measured in miles per hour.

\(t\) - TIme, measured in hours.

If we know that \(x_{Sh} - x_{Su} = 241\,mi\), \(v_{Sh} = 19\,\frac{mi}{h}\) and \(t = 7\,h\), then:

\(x_{Sh} - x_{Su} = (v_{Sh}-v_{Su})\cdot t\)

We clear now the velocity of submarine:

\(\frac{x_{Sh}-x_{Su}}{t} = v_{Sh}-v_{Su}\)

\(v_{Su} = v_{Sh}-\frac{x_{Sh}-x_{Su}}{t}\)

\(v_{Su} = 19\,\frac{mi}{h} -\frac{241\,mi}{7\,h}\)

\(v_{Su} = -15.429\,\frac{mi}{h}\)

Speed of the submarine is the magnitude of its velocity, which is 15.429 miles per hour.

The train will arrive at its final destination at 2:57 P.M. in the afternoon.

The total distance of the trip is 221 miles and the train travels at an average speed of 34 miles per hour. Using the formula:

time = distance / speed

We can calculate the total time it will take for the train to complete the journey without stopping at stations:

time = 221 / 34 = 6.5 hours

However, the train stops at each of ten stations for four minutes each, so the total time spent stopping is 10 x 4 = 40 minutes, or 0.67 hours. Therefore, the total time the journey will take, including the stops, is:

total time = 6.5 + 0.67 = 7.17 hours

The train departs at 7:30 A.M., so we can add 7.17 hours to this time to find the arrival time:

7:30 A.M. + 7.17 hours = 2:57 P.M.

Therefore, the train will arrive at its final destination at 2:57 P.M. in the afternoon.

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The expression can represented as,

Thus, the above expression is the required solution.

Answer:

The fraction of each used up is 1/2. All fractions of her/his pencils are equal.

Step-by-step explanation:

Ramesh had 20 pencils. After 4 months he used 10 pencils.

Therefore, Ramesh's used-up fraction is 10/20 =1/2.

Sheelu had 50 pencils. After 4 months she used 25 pencils.

Therefore, Sheelu's used-up fraction is 25/50 =1/2.

Jamaal had 80 pencils. After 4 months he used 40 pencils.

Therefore, Jamaal's used-up fraction is 40/80 =1/2.

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Answer: 88

Step-by-step explanation:

1. Add 3 and 8 together

3 + 8 = 11

2. Divide 121 by 11

121/ 11 = 11

3. Multiply the amount of paperbacks in the stack of 11 books (8) by 11

11 x 8 = 88

88 Is your answer.

If Stella walks down a flight of stairs to the basement. Then she walks back up the stairs and another flight of stairs to the second floor of her house. How far is Stella above the ground is: 12 ft.

Given:

Flight stair = 12 feet

Hence,

Let walking from down a flight of stairs to the basement = -12 f

Let  walking back up the stairs = 12Ft

Now let determine Stella height above the ground.

Height = -12 feet + 12 feet + 12 feet

Height = 12 feet

Therefore we can conclude that Stella is 12 feet above the ground.

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Answer:

i) +3

2.) 15

3.)5/8

4.)+98

5.)27

6.)17

7.) 12/17

8.)12/17

9.)+5

10.) 3.2

To solve this problem, we can use algebraic equations. Let's say that the number of weeks it takes for Ted and Carly to have the same account balance is "w".

Ted's account balance after "w" weeks can be represented by:

300 + 4w

Carly's account balance after "w" weeks can be represented by:

16w

We want to find out when their account balances will be equal, so we can set these two equations equal to each other:

300 + 4w = 16w

Simplifying this equation, we get:

300 = 12w

Dividing both sides by 12, we get:

25 = w

Therefore, it will take 25 weeks for Ted and Carly to have the same account balance.

The derivative of the function y = x(6x + 1)⁵ is: dy/dx = (6x + 1)⁵ + 30x(6x + 1)⁴

To find the derivative of the given function, we can apply the rules of differentiation. Using the product rule, we differentiate each term separately and then add them together.

For the first term x, the derivative is simply 1.

For the second term (6x + 1)⁵, we apply the chain rule. The derivative of (6x + 1)⁵ with respect to x is 5(6x + 1)⁴ multiplied by the derivative of the inner function 6x + 1, which is 6.

Multiplying these derivatives together, we get (6x + 1)⁵ * 6 = 6(6x + 1)⁵.

For the third term x(6x + 1)⁴, we again apply the product rule. The derivative of x is 1, and the derivative of (6x + 1)⁴ is 4(6x + 1)³ multiplied by the derivative of the inner function 6x + 1, which is 6.

Multiplying these derivatives together, we get x * 4(6x + 1)³ * 6 = 24x(6x + 1)³.

Finally, we add the derivatives of each term to get the derivative of the entire function: dy/dx = (6x + 1)⁵ + 30x(6x + 1)⁴.

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Complete question:

Use the rules of differentiation to find the derivative of the function y= x(6x + 1)⁵

(6x + 1)⁵ + 30x(6x + 1)⁴

(6x + 1)⁴ (36x + 1)

x-1/6

No correct answer provided.

Answer:

Step-by-step explanation:

5x + 3 = 2x - 6

3x + 3 = -6

3x = -9

x = -3

Answer:

(-4, 5)

Step-by-step explanation:

Since the pint is reflected over the y-axis, its y-coordinate remains the same.

Point (4, 5) has 4 as its x-coordinate. That is 4 units right of the y-axis. The reflection has -4 as its x-coordinate which is 4 units left of the y-axis.

Answer: (-4, 5)

4.1715 cm is the tenth-value layer. So, none of the given options (7.61 cm, 2.78 cm, 3.89 cm, 9.21 cm) matches the calculated value of the tenth-value layer.

Here, we have,

To determine the tenth-value layer, we need to find the thickness of the absorber required to reduce the intensity of the beam to one-tenth (10%) of its original value.

Given that the thickness of the absorber is 1.5 cm and 36.45% of the beam is attenuated, we can set up the following equation:

(1 - 36.45%)ⁿ = 10%

Here, 'n' represents the number of layers of absorber required to reach the tenth-value layer. Since we're looking for the thickness of the tenth-value layer, we need to solve for 'n' in the equation.

Let's calculate 'n':

(1 - 0.3645)ⁿ = 0.1

0.6355ⁿ = 0.1

Taking the natural logarithm (ln) of both sides:

n * ln(0.6355) = ln(0.1)

n = ln(0.1) / ln(0.6355)

Using a calculator, we find that n ≈ 2.781

Now, we can determine the thickness of the tenth-value layer by multiplying 'n' by the thickness of each absorber layer:

Tenth-value layer thickness = n * 1.5 cm

Tenth-value layer thickness ≈ 2.781 * 1.5 cm

Calculating this, we find that the approximate thickness of the tenth-value layer is 4.1715 cm.

Therefore, none of the given options (7.61 cm, 2.78 cm, 3.89 cm, 9.21 cm) matches the calculated value of the tenth-value layer, which is approximately 4.1715 cm.

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the radius of the circle is 30 cm when the circumference is 188.4 . The length of the boundary is its circumference.

A boy has traveled a certain distance if, after sprinting around the park once, he arrives at point "A" from point "A" in the first place. The park's circumference, which has the shape of a circle, is the length or border that it encompasses. The length of the boundary is its circumference.

calculation

Circumference=2πr

188.4=2×3.14×r

188.4=6.28×r

r= 188.4/6.28

radius=30cm

the radius of circle is 30 cm when the circumference is 188.4 .

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Triangular pyramids contain four sides, six edges, and four vertices.

What is a pyramid?

A pyramid is a structure with triangular exterior surfaces that converge to a single step at the summit, giving the form the shape of a pyramid in the geometric sense. A pyramid's base can be cooperation agreement, quadrilateral, or any polygon form. As a result, a pyramid has at least three triangular surfaces on its outside (at least four faces including the base). A typical alternative is the squares pyramid, which has a square shape and four triangular exterior surfaces. The design of a pyramid, with the majority of the weight closer to the bottom and the select at the apex, means that less material will be pushed from above. This center of mass enabled early civilizations to build sturdy massive constructions.

Triangular pyramids contain four sides, six edges, and four vertices.

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Answer:

7/3

Step-by-step explanation:

17/12+11/12

28/12

=>7/3

I took the test and I got 62

Answer: 62

Step-by-step explanation:10+10=20 15+13=28 20+14=34 34+28=62

The height of the tree and its shadow, and the height of the person and its shadow, at the same time of the day, form two similar right triangles:

Since both triangles are similar, then the corresponding sides are at the same ratio so that:

From this expression, you can determine the height of the tree, just multiply both sides of the equal sign by 5:

The height of the tree is 15 feet.

Answer:

B is the correct answer

since

a1/a2=b1/b2≠c1/c2

Answer:

I'd say nonlinear decreasing