What is third triangle theorem?

Answer: To put the equation y - 4x = 17 in slope-intercept form, we need to isolate the y variable on one side of the equation and have the coefficient of x be the slope of the line and the constant term be the y-intercept.

Slope-intercept form is written as y = mx + b, where m is the slope and b is the y-intercept.

Starting with the equation y - 4x = 17, we can isolate y by adding 4x to both sides:

y - 4x + 4x = 17 + 4x

y = 4x + 17

So, the equation in slope-intercept form is y = 4x + 17, where the slope (m) is 4 and the y-intercept (b) is 17.

Step-by-step explanation:

y-4x = 17

slope intercept= y= 4x + 17

The end of the plank is sliding along the ground at a rate of approximately -0.08 m/s when it is 1.4 meters from the wall of the building. The negative sign indicates that the end of the plank is sliding in the opposite direction.

To find how fast the end of the plank is sliding along the ground, we can use related rates. Let's consider the position of the end of the plank as it moves along the ground.

Let x be the distance between the end of the plank and the wall of the building, and y be the distance between the end of the plank and the ground. We are given that dx/dt = 0.26 m/s, the rate at which the worker pulls the rope.

We can use the Pythagorean theorem to relate x and y:

x² + y² = 5²

Differentiating both sides of the equation with respect to time, we get:

2x(dx/dt) + 2y(dy/dt) = 0

At the given moment when x = 1.4 m, we can substitute this value into the equation above and solve for dy/dt, which represents the rate at which the end of the plank is sliding along the ground.

2(1.4)(0.26) + 2y(dy/dt) = 0

2(0.364) + 2y(dy/dt) = 0

0.728 + 2y(dy/dt) = 0

2y(dy/dt) = -0.728

dy/dt = -0.728 / (2y)

To find y, we can use the Pythagorean theorem:

x² + y² = 5²

(1.4)² + y² = 5²

1.96 + y² = 25

y² = 23.04

y = √23.04 ≈ 4.8 m

Substituting y = 4.8 m into the equation for dy/dt, we have:

dy/dt = -0.728 / (2 * 4.8) ≈ -0.0757 m/s

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Answer:

The answer would be 20

Step-by-step explanation:

16+4=20

Answer:

20

Step-by-step explanation:

The solution to the system of equations is x = 1 and y = 1.

To solve the system of equations using substitution, we start by solving one equation for one variable and substituting it into the other equation. Given the system of equations:

1) 4x + 3y = 7

2) 3x + 5y = 8

We can solve equation 1 for x:

4x = 7 - 3y

x = (7 - 3y)/4

Now, substitute this expression for x into equation 2:

3((7 - 3y)/4) + 5y = 8

Simplify the equation:

(21 - 9y)/4 + 5y = 8

Multiply both sides by 4 to eliminate the fraction:

21 - 9y + 20y = 32

Combine like terms:

11y = 11

Divide both sides by 11:

y = 1

Now, substitute the value of y back into equation 1 to solve for x:

4x + 3(1) = 7

4x + 3 = 7

4x = 7 - 3

4x = 4

x = 1

Therefore, the solution to the system of equations is x = 1 and y = 1.

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Answer:

24 degrees

Step-by-step explanation:

there is 180 degrees in total. You take that and subtract 156. That gives you a total of 24 degrees.

Answer:

Solving equations requires a systematic approach, attention to detail, and understanding of the underlying principles.

If you attempted the problem four times and all recorded scores were 0%, it suggests that your attempts did not yield the correct solution. To solve the equation t = r + 7kw, we need to have specific values or information about the variables involved. Without any additional details, it is not possible to provide a numerical solution.

To improve your chances of solving the equation successfully, consider the following steps:

Review the equation: Make sure you understand the structure and the relationship between the variables. In this case, t is equal to the sum of r and 7 times the product of k and w.

Check for errors: Review your calculations and ensure there are no mistakes in your algebraic manipulations. Double-check your arithmetic operations and signs.

Seek assistance: If you're having difficulty solving the equation, consider reaching out for help. Consult a teacher, tutor, or someone knowledgeable in the subject matter. They can guide you through the problem-solving process and clarify any misunderstandings.

Practice and persistence: Continue practicing similar equations to improve your problem-solving skills. Persistence and practice are key to mastering mathematical concepts.

Remember, solving equations requires a systematic approach, attention to detail, and understanding of the underlying principles. Keep practicing and seeking assistance, and you will improve your problem-solving abilities over time.

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Answer:

Solving equations requires a systematic approach, attention to detail, and understanding of the underlying principles.

If you attempted the problem four times and all recorded scores were 0%, it suggests that your attempts did not yield the correct solution. To solve the equation t = r + 7kw, we need to have specific values or information about the variables involved. Without any additional details, it is not possible to provide a numerical solution.

To improve your chances of solving the equation successfully, consider the following steps:

Review the equation: Make sure you understand the structure and the relationship between the variables. In this case, t is equal to the sum of r and 7 times the product of k and w.

Check for errors: Review your calculations and ensure there are no mistakes in your algebraic manipulations. Double-check your arithmetic operations and signs.

Seek assistance: If you're having difficulty solving the equation, consider reaching out for help. Consult a teacher, tutor, or someone knowledgeable in the subject matter. They can guide you through the problem-solving process and clarify any misunderstandings.

Practice and persistence: Continue practicing similar equations to improve your problem-solving skills. Persistence and practice are key to mastering mathematical concepts.

Remember, solving equations requires a systematic approach, attention to detail, and understanding of the underlying principles. Keep practicing and seeking assistance, and you will improve your problem-solving abilities over time.

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To predict the non-violent crime rate in City 37, we can use the regression equation obtained from the researcher's analysis. The equation can be written as follows:

Non-Violent Crime Rate = Intercept + (Slope * Unemployment Rate)

Given that the slope is 27.15 and the intercept is -124.28, we can substitute the values into the equation.

For City 3, the unemployment rate is 11.4 and the non-violent crime rate is 99.8. Plugging these values into the equation, we have:

Non-Violent Crime Rate = -124.28 + (27.15 * 11.4)

Non-Violent Crime Rate = -124.28 + 309.51

Non-Violent Crime Rate = 185.23

Therefore, the predicted non-violent crime rate in City 37 would be 185.23.

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Step-by-step explanation:

-3x+4<_-23

-3x<_-23+4

-3x<_-21

Divide both sides by -3

-x<_-7

x>_7

-29>_-3x+4

3x>_29+4

3x>_33

Divide both sides by -3

×>_11

Answer:

ffuydydydodtdtstsits6z t tsktdidtsi

If the car goes to the top of spike's peak and back, the mileage of the car is 16 miles per gallon

The mileage of car in uphill = 12 miles per gallon

The mileage of car in downhill = 24  miles per gallon

The total distance traveled in up hill = 48 miles

The number of gallon of gas used = 48/12

= 4 gallon

The total distance traveled in down hill = 48 miles

The number of gallon of gas used = 48 / 24

= 2 gallon

Total distance traveled = 48 + 48

= 96 miles

Total number of gallons of gas = 4 + 2

= 6 gallon

The mileage = Total distance / The number of gallon

= 96 / 6

= 16 miles per gallon

Therefore, the mileage of the car is 16 miles per gallon

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Answer:

70

Step-by-step explanation:

ok, so since you want to find out what the profit is, first you take the times you won and multiply the amount you got for winning so 50*2=100. now that you have 100 you take the money you spent and multiply it by the number of times you played the game so 20*3=30. now that you have those you have everything you need to finish the question. you take the amount you spent per play (30) and subtract it from what you won (100). 100-30=70

Answer: The Profit is $40

Step-by-step explanation:

It costs $20 per turn so if you win you get $30

So $30+$30 = $60 (Because you won twice)

The subtract the $20 you lost $60-$20 = $40

So you earned $40!

The optimal consumption bundle (x1*, x2*) can be determined by solving the consumer's utility maximization problem subject to the budget constraint. Given the utility function u(x1, x2) = ax1 + bx2, where a > 0 and b > 0, and the budget constraint p1x1 + x2 = w, we need to find the values of x1* and x2* that maximize the utility function while satisfying the budget constraint.

To analyze the problem graphically, we can plot the budget constraint on a two-dimensional graph with x1 on the horizontal axis and x2 on the vertical axis. The slope of the budget constraint is -p1, indicating the rate at which the consumer can trade x1 for x2. The budget constraint represents all the possible combinations of x1 and x2 that the consumer can afford given their wealth (w) and the price of good 1 (p1).

By drawing indifference curves for different levels of utility, which are downward-sloping straight lines in this case due to the linear utility function, we can identify the optimal consumption bundle. In this particular case, since the utility function represents perfect substitutes, the indifference curves are parallel straight lines with a slope of -a/b. The consumer maximizes utility by choosing the consumption bundle that lies on the highest possible indifference curve and is tangent to the budget constraint.

Now, let's consider three different cases:

Case 1: When w/p1 < a/b, the consumer's wealth is not sufficient to reach the highest indifference curve. In this case, the consumer's optimal consumption bundle will be at the corner point of the budget constraint where x1 = w/p1 and x2 = 0.

Case 2: When w/p1 > a/b, the consumer's wealth is more than enough to reach the highest indifference curve. In this case, the consumer's optimal consumption bundle will be at the point where the budget constraint is tangent to the highest indifference curve, which will be at x1 > 0 and x2 > 0.

Case 3: When w/p1 = a/b, the consumer's wealth is exactly enough to reach the highest indifference curve. In this case, the consumer can choose any consumption bundle along the budget constraint.

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The simplified expression is\($-11p^2-8p+\frac{7}{3}$, where $a=-11$ and $b=\frac{7}{3}$.\)

To simplify the given expression, let's break it down step by step.
Step 1: Simplify the expressions inside the parentheses:
\($((5p+1)-2p\cdot4)(3)(4-1\div3)(6p-9)$$=(5p+1-8p)(3)(4-\frac{1}{3})(6p-9)$$=(-3p+1)(3)(\frac{11}{3})(6p-9)$\)
Step 2: Simplify the expression in the first set of parentheses:
\($=(-3p+1)(\frac{11}{3})(6p-9)$\\\)
Step 3: Expand the expression using the distributive property:
\($=-\frac{33}{3}p^2+11p+6p-\frac{11}{3}-18p+6$\)
Step 4: Combine like terms:
\($=-11p^2-8p+\frac{7}{3}$\\\)
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Answer:

which are the natrual numbres 12345678910 and so on..

Step-by-step explanation:

Hope it helped you

As described in the analytic geometry, the points are(1.1, -5 )

The area of algebra known as analytical geometry uses an ordered pair of numbers known as coordinates to determine the position of a point on a plane. It is utilized to model many plane objects, including points, lines, and others. The terms Coordinate geometry and Cartesian geometry are both used to refer to analytical geometry.

We have to locate the point where the line is through the x line and y line coordinates

Therefore the point is  (1.1, -5 )

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Answer:

<3 I want brainliest!!!

Step-by-step explanation:

1) 5.54 x 10^9

2) 2.5409 x 10^-5

Answer:

Nicole has 9 dimes and 19 nickels.

Answer:

0.015625

Step-by-step explanation: Its 0.015625 trust me :D

Responder:

x = 15/7

Explicação passo a passo:

Dada a equação:

7 x + 4 = 19

Subtraia 4 de ambos os lados

7x + 4 - 4 = 19 - 4

7x = 15

Divida os dois lados por 7

7x / 7 = 15/7

x = 15/7

Answer: 36.8

Step-by-step explanation:

First convert 7/19 to a decimal.

7/19 = 0.368421...

Then to convert a decimal a percent by multiplying by 100

0.3684... x 100 = 36.8

The area of the sector is A = π cm² and amplitude is a = 0.75 cm

Given data ,

The area of a sector is given by the formula:

A = (1/2) x r² x θ

where r is the radius of the sector and θ is the central angle in radians.

On simplifying , we get

A = π cm²

r = 1.5 cm

Substituting these values into the formula, we get:

π = (1/2) x (1.5)² x θ

π = (3/4) x θ

Solving for θ, we get:

θ = (4/3) x π

The amplitude of the sector is half of the radius, so:

amplitude = (1/2) x 1.5 cm = 0.75 cm

Hence , the amplitude of the sector is 0.75 cm

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The scalars c1 = 2/5, c2 = -3/5, and c3 = -8/5 satisfy the equation:

c1M1 + c2M2 + c3M3 = [ 2 3 ][ 1 2 ]

We want to find the scalars c1, c2, and c3 such that:

c1M1 + c2M2 + c3M3 = M

Substituting the given matrices:

c1[ 2 2 ] c2[ -1 1 ] c3[ 1 2 ] [ 2 3 ]

[ 1 1 ] [ 2 1 ] [ 3 1 ] [ 1 2 ]

Multiplying each scalar by its corresponding matrix:

[ 2c1 - c2 + c3 2c1 + 2c2 + 3c3 ]

[ c1 + 2c2 + 3c3 c1 + c2 + 2c3 ]

Setting the result equal to M:

[ 2c1 - c2 + c3 2c1 + 2c2 + 3c3 ] = [ 2 3 ]

[ c1 + 2c2 + 3c3 c1 + c2 + 2c3 ] [ 1 2 ]

This gives us two equations:

2c1 - c2 + c3 = 2

2c1 + 2c2 + 3c3 = 3

c1 + 2c2 + 3c3 = 1

c1 + c2 + 2c3 = 2

We can solve this system of equations using any method we prefer, such as elimination or substitution. Here, we will use elimination.

Subtracting the first equation from the second, we get:

3c2 + 4c3 = 1

Subtracting the third equation from fourth, we get:

c2 - c3 = 1

Multiplying second equation by 2, we get:

4c1 + 4c2 + 6c3 = 6

Subtracting first equation from this, we get:

5c2 + 5c3 = 4

Now we have three equations for c2 and c3:

3c2 + 4c3 = 1

c2 - c3 = 1

5c2 + 5c3 = 4

Solving for c2 and c3 using elimination, we get:

c2 = -3/5

c3 = -8/5

Substituting these values into the third equation, we get:

c1 = 2/5

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Representative fraction is a form of scale that can be used to change the size of an object to form an image. The required length is 32 inches.

A scale is a fraction of numbers that can be used to either increase or decrease the size of a given object. It is majorly referred to as representative fraction in scale drawing.

Representative fraction = \(\frac{length on drawing}{original length}\)

In the given question, we have;

12 inches = 1 feet

x inches = 30 feet

So that:

x = 30 x 12 inches

  = 360 inches

representative fraction = \(\frac{2 inches}{360 inches}\)

                             = 5.56 x \(10^{-3}\)

Thus, given that the length of the Alamo Mission is 480 feet long. Then:

480 feet = 480 x 12 inches

              = 5760 inches

So that,

the required length in inches = 5760 x 5.56 x \(10^{-3}\)

                                             = 32 inches

Therefore the expected length of the Alamo Mission is 32 inches.

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Answer:

answer is 52.5

Step-by-step explanation:

hope it helps

The best representation of the inequality y ≤ - 5/6x + 2/3 is shown in figure by red shade region.

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

The inequality is,

⇒ y ≤ - 5/6x + 2/3

Now, We can draw the graph of inequality y ≤ - 5/6x + 2/3.

Hence, The best representation of the inequality y ≤ - 5/6x + 2/3 is shown in figure by red shade region.

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The maximum vertical distance between the line y = 10x + 39 and the parabola y = x^2 for -3 ≤ x ≤ 3 is 160 units.

To find the maximum vertical distance between the line y = 10x + 39 and the parabola y = x^2 for -3 ≤ x ≤ 3, we need to determine the points on the parabola that have the maximum vertical distance from the line.

Let's start by finding the points of intersection between the line and the parabola. Setting the equations equal to each other, we have:

10x + 39 = x^2

Rearranging the equation, we get:

x^2 - 10x - 39 = 0

Solving this quadratic equation, we find that x = -3 and x = 13 are the x-coordinates of the points of intersection.

Now, let's calculate the corresponding y-values for these x-coordinates on the parabola:

For x = -3, y = (-3)^2 = 9

For x = 13, y = (13)^2 = 169

Next, we can calculate the y-values for the line at these x-coordinates:

For x = -3, y = 10(-3) + 39 = 9

For x = 13, y = 10(13) + 39 = 169

Since the y-values of the line and the parabola are the same at the points of intersection, the maximum vertical distance occurs at the point (-3, 9) and (13, 169).

The maximum vertical distance between the line and the parabola is the difference in y-coordinates at these points:

169 - 9 = 160

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Answer:

\((x-1)^2 + (y+4)^2 = 100\\\\\)

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

Work Shown:

\((x-h)^2 + (y-k)^2 = r^2\\\\(x-1)^2 + (y-(-4))^2 = 10^2\\\\(x-1)^2 + (y+4)^2 = 100\\\\\)

You could expand terms out and simplify, but I think it's more handy to leave it in this form so you can easily spot the center and radius from a glance.

The solution is, (x - 1)² + (y + 4)² = 100 , is the equation of a circle that is centered at (1,-4) with a radius of 10.

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. The perimeter around the circle is known as the circumference.

here, we have,

we know that,

the standard form of a circle equation is

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle, and r is the radius.

to get r² we simply use the given radius,

here, r = 10

so, we get,

r² = 100

now, circle that is centered at (1,-4)

so, we have,

(x - 1)² + (y + 4)² = 10²

we get, equation in standard form is therefore

(x - 1)² + (y + 4)² = 100

Hence, The solution is, (x - 1)² + (y + 4)² = 100 , is the equation of a circle that is centered at (1,-4) with a radius of 10.

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Answer:

2.

Step-by-step explanation:

The absolute value is the distance between a number and zero. The distance between −2 and 0 is 2.

Hope this helps.

Answer:

2

Step-by-step explanation:

Let's solve the equation step by step

|-2|

= 2