Mrs.ulrich has 3 times as many markers as colored pencils.the total number of markers and colored pencils is 84.how many markers does mrs.ulrich have

The distance between the planes is increasing at a rate of approximately 252 km/hr when the southbound plane is 34 km from the airport and the westbound plane is 15 km from the airport.

Identify the relative motion: We need to find the rate of change of the distance between the planes, which is a relative motion problem.

Calculate individual velocities: Since the planes are approaching from different directions, we need to consider their velocities as vectors. The southbound plane has a southward velocity of 124 km/hr, and the westbound plane has an eastward velocity of 223 km/hr.

Apply Pythagorean theorem: At the given moment, the distance between the planes is the hypotenuse of a right triangle formed by their individual velocities. Using the Pythagorean theorem:

Distance^2 = Southbound velocity^2 + Westbound velocity^2

Distance^2 = (124 km/hr)^2 + (223 km/hr)^2

Distance ≈ 258.5 km

Differentiate distance equation: To find the rate of change of the distance, we need to differentiate the distance equation with respect to time. This gives us the relative velocity between the planes.

Calculate relative velocity: Taking the derivative of the distance equation and plugging in the individual velocities:

Rate of change of distance = (Southbound velocity * Eastward velocity) / Distance

Rate of change of distance ≈ (124 km/hr * 223 km/hr) / 258.5 km ≈ 252 km/hr

Therefore, the distance between the planes is increasing at a rate of approximately 252 km/hr when the southbound plane is 34 km from the airport and the westbound plane is 15 km from the airport.

The linear equation to model the relationship between the weight of strawberries and time can be found using the slope and y-intercept. The equation is S = 690T - 560.5. In 11 hours, the cannery can process 7109.5 pounds of strawberries.

To write a linear equation to model the relationship between the weight of strawberries S and time T, we need to determine the slope and the y-intercept. The slope represents the rate at which strawberries are processed per hour, while the y-intercept represents the initial amount of strawberries processed.

Using the given information, we can use the formula for calculating the slope (m) of a line: m = (y2 - y1) / (x2 - x1). Plugging in the values, we have: m = (2320 - 1445) / (7 - 4.5) = 690 pounds/hour.

Next, we can calculate the y-intercept (b) using the formula: b = y - mx. Plugging in the values for one of the points (1445 pounds in 4.5 hours), we have: 1445 = 690(4.5) + b. Solving for b, we get: b = -560.5 pounds.

Therefore, the linear equation to model the relationship between the weight of strawberries S and time T is: S = 690T - 560.5. To find the number of pounds of strawberries that can be processed in 11 hours, we can substitute T = 11 into the equation: S = 690(11) - 560.5 = 7109.5 pounds.

https://brainly.com/question/32634451

#SPJ2

Hello There!

61 is a prime number.

Its only factors are: 1 and 61. It has no more factors.

#HaveAnAmazingDay

Hope this helps!

[tex]GraceRosalia[/tex]

By setting up a proportion based on the concept of similar triangles, we can solve for the length of Hue's friend's shadow, which is 18 inches.

To find the length of Hue's friend's shadow, we can use the concept of similar triangles. The ratio of Hue's height to his shadow's length is the same as the ratio of his friend's height to his friend's shadow's length, assuming the sun's rays are parallel and create similar angles with respect to the ground for both individuals.

Hue's height to shadow length ratio is 56 inches to 24 inches. Let's denote the length of his friend's shadow as x inches. We can set up a proportion:

56 inches (Hue's height) / 24 inches (Hue's shadow) = 42 inches (friend's height) / x inches (friend's shadow)

Solving for x, we get: 56/24 = 42/x, which simplifies to x = (42 * 24)/56 = 18. Therefore, Hue's friend's shadow is 18 inches long.

2^2 x 3^2 is the answer... don't be rude and mark the other person bad she gave you a good explanation and fixed your question AND got the answer right... write you question correctly cause you probably just copied it and didn't fix it up!

Just do this for future questions!

You have a fractions, so the only thing you must be sure of is that the denominator is not zero.

In your case, the denominator is given by the function f(w)=3w9. You need to find out the values of w for which f(w)=0. You have
f(w)=0⇔3w9=0⇔w9=0⇔w=9√0=0

So, your only problem is w=0, and all other numbers are fine.

Your domain is thus given by the set {x∈R∣x≠0}

The domain can also be written as (−∞,0)∪(0,+∞).

Answer:

B.[tex](x-5)(x+3)[/tex]

Step-by-step explanation:

We are given that an expression

[tex]a^2-2x-15[/tex]

We have to find the binomial  factors of the given expression.

[tex]x^2-2x-15[/tex]

To find the factors of given expression we will use of  middle term splitting factor method.

The given can be written as

[tex]x^2-5x+3x-15[/tex]

[tex]x(x-5)+3(x-5)[/tex]

Taking (x-5) common

[tex](x-5)(x+3)[/tex]

Hence, the binomial factors of given expression is given by

[tex](x-5)(x+3)[/tex]

Option B is true.

Answer: True.

Step-by-step explanation:

Hi, the statement "In the normal distribution, values in the distribution being measured are close to the mean (high or low values are infrequently found)." is true.

The normal distribution is a probability function that how the values of a measure are distributed. Most of the values cluster around the mean, it’s a symmetric distribution.

Normal or Gaussian distributions Means that many variables have similar characteristics. So, middle values have higher probability or are more likely to occur, and extremely low or high values are more infrequent.