If in a pasture, there are 28 horses and chickens and 80 legs, how many chickens and horses are there?.

Answer:

n = -8, 7

Step-by-step explanation:

Your equation is:

\(\displaystyle{n^2+n=56}\)

Arrange the terms in the quadratic expression, ax² + bx + c:

\(\displaystyle{n^2+n-56=0}\)

Factor the expression, thus:

\(\displaystyle{\left(n+8\right)\left(n-7\right)=0}\)

This is because 8n-7n = n (middle term) and 8(-7) = -56 (last term). Then solve like a linear which results in:

\(\displaystyle{n=-8,7}\)

Hello!

\(\sf n^2 + n = 56\\\\n^2 + n - 56 = 0\\\\\\n = \dfrac{-b\±\sqrt{b^2-4ac} }{2a} \\\\\\n = \dfrac{-1\±\sqrt{1^2-4*1*(-56)} }{2*1}\\\\\\n = \dfrac{1\±15}{2} \\\\\\\boxed{\sf n = 7 ~or ~-8 }\)

Answer:

\( \huge \boxed{c = 4 \sqrt{2} }\)

Step-by-step explanation:

Since the triangle is a right angled triangle we can use Pythagoras theorem to find the missing side x

Using Pythagoras theorem we have

c² = a² + b²

where

c is the hypotenuse

So from the question we have

\( {c}^{2} = {4}^{2} + {4}^{2} \\ c = \sqrt{16 + 16} \\ c = \sqrt{32} \: \: \: \: \: \: \: \: \: \\ \\ \\ c = 4 \sqrt{2} \: \: \: \: \: \: \: \: \)

Hope this helps you

Scale ratios are used to determine the dimensions of proportional shapes

The base area of the replica is 6250 m²

The area ratio is given as:

Ratio = 1 : 10

The ratio of the original to the replica is represented as:

Ratio = Original : Replica

So, we have:

Ratio = 625 m² : Replica

By comparison, we have:

625 m² : Replica = 1 : 10

Multiply by 625 m²

625 m² : Replica = 625 m² : 6250 m²

By comparison, we have:

Replica = 6250 m²

Hence, the base area of the replica is 6250 m²

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Therefore, the 90% confidence interval for the mean height of the population of female runners is (64.77, 66.83) inches.

A confidence interval is a range of values that provides an estimate of the unknown population parameter with a certain level of confidence. The confidence level represents the percentage of times that the true population parameter will be contained within the interval, based on repeated sampling.

a) Using a t-distribution with 11 degrees of freedom (n-1), and a 90% confidence level, the t-value is 1.796.

The left boundary of the confidence interval is:

65.80 - (1.796 * (1.95 / √(12))) = 64.77 inches (rounded to two decimal places)

b) The right boundary of the confidence interval is:

65.80 + (1.796 * (1.95 / √(12))) = 66.83 inches (rounded to two decimal places)

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We need AC ≅ XZ to show that triangle ABC ≅ triangle XYZ by ASA congruence of triangle.

What is ASA congruence of triangle?

The two triangles are considered to be congruent according to the ASA rule if any two angles and the side located between the angles of one triangle are equal to the corresponding two angles and side located between the angles of the second triangle.

We are given the following:

1. ∠A ≅ ∠X

2. ∠C ≅ ∠Z

Now, in order to show the triangles as congruent by ASA congruence of triangle, we need the side which is in between both the angles.

The sides in between both the angles are AC and XZ.

Hence, we need AC ≅ XZ to show that triangle ABC ≅ triangle XYZ by ASA congruence of triangle.

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The tires and the traction control system work in tandem to ensure maximum traction and stability, minimizing the risk of traction loss and improving overall vehicle control and safety.

The two most important parts of a vehicle in preventing traction loss are the tires and the traction control system.

Tires: Tires are the primary point of contact between the vehicle and the road surface. The quality and condition of the tires greatly influence traction. Tires with good tread depth and appropriate tread pattern are essential for maintaining grip on the road. Tread depth helps to channel water, snow, or debris away from the tire, preventing hydroplaning or loss of traction. Additionally, tire pressure should be properly maintained to ensure even contact with the road. Choosing tires suitable for the specific driving conditions, such as all-season, winter, or performance tires, is crucial for optimal traction and handling.

Traction Control System: The traction control system is a vehicle safety feature that helps prevent the wheels from slipping or spinning on low-traction surfaces. It uses various sensors to monitor the speed and rotation of the wheels. If the system detects a loss of traction, it will automatically reduce engine power and apply braking force to the wheels that are slipping. By modulating power delivery and braking, the traction control system helps maintain traction and prevent wheel spin, especially in challenging conditions like slippery roads or during quick acceleration.

The tires and the traction control system work in tandem to ensure maximum traction and stability, minimizing the risk of traction loss and improving overall vehicle control and safety.

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Answer:

yea it is

Step-by-step explanation:

The Fahrenheit temperature of the can of soda, after 60 minutes, given the value of K would be 55°F.

We can use Newton's Law of Cooling formula to find the value of k:

58 = 35 + (73 - 35) x e ^ (-k x 40)

23 = 38 x e ^ (-k x 40)

23/38 = e ^ (-k x 40)

ln(23/38) = -k x 40

k = -ln(23/38) / 40 ≈ 0.010

Now that we have the value of k, we can find the temperature of the can of soda after 60 minutes (t = 60):

T = 35 + (73 - 35) x e ^ (-0.010 x 60)

T ≈ 35 + 38 x e ^ (-0.6) = 35 + 38 x 0.5488 = 54.856

The temperature of the can of soda after 60 minutes is approximately 55°F (rounded to the nearest degree).

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∂g/∂u is equal to 21u⁵cos⁴(v)sin⁴(v)(cos(v) + u³cos⁴(v)sin²(v)sin(v)).

To find the indicated derivative, we need to use the chain rule. Let's differentiate step by step:

Given:

g(u, v) = f(x(u, v), y(u, v))

f(x, y) = 7x³y³

x(u, v) = ucos(v)

y(u, v) = usin(v)

To find ∂g/∂u, we differentiate g(u, v) with respect to u while treating v as a constant:

∂g/∂u = (∂f/∂x) * (∂x/∂u) + (∂f/∂y) * (∂y/∂u)

To find ∂f/∂x, we differentiate f(x, y) with respect to x:

∂f/∂x = 21x²y³

To find ∂x/∂u, we differentiate x(u, v) with respect to u:

∂x/∂u = cos(v)

To find ∂f/∂y, we differentiate f(x, y) with respect to y:

∂f/∂y = 21x³y²

To find ∂y/∂u, we differentiate y(u, v) with respect to u:

∂y/∂u = sin(v)

Now, we can substitute these partial derivatives into the equation for ∂g/∂u:

∂g/∂u = (21x²y³) * (cos(v)) + (21x³y²) * (sin(v))

To find the simplified form, we substitute the given values of x(u, v) and y(u, v) into the equation:

x(u, v) = ucos(v) = u * cos(v)

y(u, v) = usin(v) = u * sin(v)

∂g/∂u = (21(u * cos(v))²(u * sin(v))³) * (cos(v)) + (21(u * cos(v))³(u * sin(v))²) * (sin(v))

Simplifying further, we get:

∂g/∂u = 21u⁵cos⁴(v)sin⁴(v)(cos(v) + u³cos⁴(v)sin²(v)sin(v))

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Answer:

1. -2/3

2. 5/4

3. -5/3

4. -6/5

Step-by-step explanation:

Use the slope formula for 2 points of each graph to get the answer.

Or you can just count the rise over run.

Answer:

A number that can be made by dividing two integers (an integer is a number with no fractional part). The word comes from "ratio". But π (pi) is not a rational number, it is an "Irrational Number".

Step-by-step explanation:

mark me please

Answer:

Since rational numbers are all numbers that can be written as a fraction, and includes positive numbers, negative numbers and the 0. We can conclude that since -3.4 can be written as a fraction it is a rational number.

Answer:

iam sorry

i don't know the answer

Answer:

The answer is "They are similar".

Step-by-step explanation:

They were comparable in this respect because both aspect ratios of the top triangle are one square more. The top triangle is equal to the base triangles if you remove one square away from the height and width.

Otherwise, we can say that it forms all different. The dilation factor which translates that bottom left point of shape I to form II is 2. But this does not map the other shape I vertices onto form II. There's, therefore, no dilation in form I of maps on form II.

Answer:

A. no because ratios can never be thought of as fravtions.

Answer:

26 miles

you welcomeeeeee

The critical point is (0,0). The relative maximum value is f(0,0) = 1 and there is no relative minimum value.

To find the critical point(s), we need to find where the gradient of the function is equal to zero:

∇f(x, y) = (-18x, -14y)

Setting each component equal to zero, we get:

-18x = 0 and -14y = 0

Which gives us:

x = 0 and y = 0

To classify the nature of this point using the second derivative test, we need to find the Hessian matrix:

H(f)(x,y) = | -18 0 || 0 -14 |

The determinant of the Hessian matrix is:

det(H(f)(0,0)) = (-18)(-14) = 252

Since the determinant is positive and the upper-left entry of the Hessian is negative, we can conclude that the critical point (0,0) is a relative maximum.

To find the relative extrema of the function, we can check the value of the function at the critical point and compare it to the values of the function at points near the critical point:

f(0,0) = 1

f(0.1,0.1) = 1 - 9(0.1)² - 7(0.1)² = 0.94

f(-0.1,-0.1) = 1 - 9(-0.1)² - 7(-0.1)² = 0.94

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Answer:

[see below]

Step-by-step explanation:

Rational Numbers:

Irrational Numbers:

Hope this helps.

Answer:

a = 4, b = 5

Step-by-step explanation:

we need to complete the square to get it in that form.

x^2 - 8x + 21

= x^2 - 8x + 16 + 5

= (x-4)^2 + 5

a = 4, b = 5

Answer:

0.1

Step-by-step explanation:

Just take 24/24 which is 1 and move the decimal one place to the left because there is an extra 0 on the denominator

The greatest length, in inches, that she can make from the two pieces of ribbon is 6 inches

Find the factors of 30 and 48

The greatest common factor of 30 and 48 is 6

Therefore,

Ribbon A can be cut into = 30 / 6

= 5 pieces

Ribbon B = 48/6

= 8 pieces

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Answer: 3.

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer: They played 25 games

Step-by-step explanation: If they had 15 wins and the total games they played is 60% then they lost 10 times and they played 25 games because if you divide 15 by 60 you get 0.25 so they played 25 games.

The 38th term of the sequence, rounded to the nearest thousandth, is 325.

To find the 38th term of the sequence , we observe that each term is obtained by adding 6 to the previous term. The sequence starts with 9, so we can find the 38th term by repeatedly adding 6.
Starting with 9, we add 6 to get 15 (the second term). Then, we add 6 to 15 to get 21 (the third term). We continue this pattern, adding 6 to each previous term. By repeating this process 37 times, we can find the 38th term.
Adding 6 to 21 gives us 27, then 33, 39, and so on. After performing the addition 37 times, we reach the 38th term, which is 6 times 37 plus 9 (the first term). Simplifying, we get 222 plus 9, which equals 231. Therefore, the 38th term of the sequence is 231. Rounded to the nearest thousandth, the answer is 325.

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The system of equations is.

x + y = 80

12x + 10y = 900

And the solutions are y = 30 and x = 50

Let's define the two variables:

x = number of calculators.

y = number of calendars.

With the given information we can write two equations, then the system will be:

x + y = 80

12x + 10y = 900

Now let's solve it.

We can isolate x on the first equation to get:

x = 80 - y

Replace that in the other equation to get:

12*(80 - y) + 10y = 900

-2y = 900 - 960

-2y = -60

y = -60/-2 = 30

Then x = 50

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Step-by-step explanation:

4+3n \(\geq\) 1 or -5n > 25

3n \(\geq\) -3         n > -5

n \(\geq\) -1                

Statistical process control technique that permits only 3.4 defects per million opportunities is Six Sigma.

Six Sigma is a statistical technique that emphasizes the necessity of a standardized approach to enhancing and optimizing the efficiency of the production and management processes by reducing the variation and waste within them. It concentrates on controlling a process to ensure that the results of a process are consistent and reliable by using statistical methods. The objective of the Six Sigma process is to produce 3.4 errors or defects per million opportunities. If the process is better than Six Sigma, it is considered more consistent and predictable.
Six Sigma's statistical approach to process control encompasses a range of tools and methods. Six Sigma's primary objective is to increase revenue and profits by developing and delivering high-quality products and services while eliminating defects and reducing waste.
Six Sigma aims to improve quality by detecting and reducing the reasons for variations in production processes. It accomplishes this by developing quality management practices that enable it to assess quality, establish goals, and implement best practices to achieve those goals.
In conclusion, Six Sigma is a process control approach that emphasizes statistical methods for process control and improvement. Six Sigma is used to reduce variability and eliminate waste, and its goal is to achieve 3.4 defects per million opportunities.

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Answer: The height of street sign = 15

Step-by-step explanation:

At the same time, the angle made by the light on each object is the same.

Pole and street sign both standing vertical to the ground.

So triangle made by both of them are similar

The sides of similar triangles are proportional,

\(\dfrac{\text{height of street sign}}{\text{height of pole}}=\dfrac{\text{Length of the shadow made by street sign}}{\text{Length of the shadow made by pole}}\\\\\dfrac{\text{height of street sign}}{40}=\dfrac{12}{32}\\\\\text{height of street sign}=\dfrac{12}{32}\times40=15\)

Hence, the height of street sign = 15