A major league baseball pitcher throws a pitch that follows these parametric equations:

x(t) = 143t
y(t) = –16t2 + 5t + 5.
Recall that the speed of the baseball at time t is

s(t)=√ [x '(t)]2 + [y ' (t)]2 ft/sec.

What is the speed of the baseball (in mph) when it passes over homeplate?

Step 1

Find the slope of the given line

Let

[tex]A(-4,4)\ B(4,-2)[/tex]

we know that

the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the values

[tex]m=\frac{-2-4}{4+4}[/tex]

[tex]m=\frac{-6}{8}[/tex]

[tex]m=-\frac{3}{4}[/tex]

Step 2

Find the slope of the line perpendicular to the given line

we know that

if two lines are perpendicular

then

the product of their slopes is equal to minus one

so

[tex]m1*m2=-1[/tex]

we have

[tex]m1=-\frac{3}{4}[/tex] ------> slope of the given line

Find the value of m2

[tex]m2=-1/m1[/tex]

substitute

[tex]m2=-1/(-3/4)[/tex]

[tex]m2=\frac{4}{3}[/tex]

Step 3

Find the equation of the line

we know that

the equation of the line into point-slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=\frac{4}{3}[/tex]

x-intercept is equal to [tex]6[/tex] --------> is the point [tex](6,0)[/tex]

substitute in the formula

[tex]y-0=\frac{4}{3}(x-6)[/tex]

[tex]y=\frac{4}{3}x-8[/tex]

therefore

the answer is the option

[tex]y=\frac{4}{3}x-8[/tex]

Answer:

y = [tex]\frac{-3x}{4}[/tex] + [tex]\frac{1}{4}[/tex].

Step-by-step explanation:

Given : Graph of slope [tex]\frac{-3}{4}[/tex] and passes through the point (–5, 4).

To find : Which is the equation of the line.

Solution : we have given that point ( -5 ,4)

By equation of line ([tex]y-y_{1}) = m (x -x_{1})[/tex]

y - 4 =  [tex]\frac{-3}{4}[/tex]( x +5).

y - 4 =  [tex]\frac{-3x}{4}[/tex] +[tex]\frac{-15}{4}[/tex].

On adding 4  both sides we get,

y = [tex]\frac{-3x}{4}[/tex] + [tex]\frac{-15}{4}+4[/tex].

y = [tex]\frac{-3x}{4}[/tex] + [tex]\frac{-15 +16}{4}[/tex].

y = [tex]\frac{-3x}{4}[/tex] + [tex]\frac{1}{4}[/tex].

Therefore, y = [tex]\frac{-3x}{4}[/tex] + [tex]\frac{1}{4}[/tex].

To express the number of miles driven, y, in terms of the number of hours driven, t, we first find the speed and then use it to formulate the equation of the line as y = 60t. However, to accurately represent the entire trip, we must include the initial 100 miles driven in 2 hours, leading to y = 60t - 20 as the final equation.

To write an equation that gives the number of miles driven, y, in terms of the number of hours driven, t, we can use the relationship between distance and travel time. Given that after two hours you had gone 100 miles and after 8 hours, you reached your destination, which is 460 miles away, we establish two points on our distance-time graph: (2, 100) and (8, 460).

Using the two points, we can find the slope of the line, which represents the speed:
Slope (speed) = (change in distance) / (change in time) = (460 - 100) miles / (8 - 2) hours = 360 miles / 6 hours = 60 miles/hour.

We can now express the equation of the line as y = mx + b, where m is the slope and b is the y-intercept. The y-intercept represents the distance at time zero, which for most driving scenarios we assume to be 0 miles. Thus, the equation becomes y = 60t. However, this equation would not accurately represent the entire trip since it doesn't account for the initial 100 miles driven in the first 2 hours.

To adjust for that, we'll introduce an offset for the initial 100 miles traveled in the first 2 hours. The y-intercept would be 100 miles less than if we had started from 0 miles at 0 hours. The corrected equation for the entire trip would be of the form y = 60t + b, where b = y - 60t and y are the miles covered in the initial 2 hours, which is 100 miles. Substituting the values, we get b = 100 - 60 x 2 which equals -20.

The final equation, accounting for the first 2 hours of travel, would therefore be: y = 60t - 20.

The equation of a line containing the point (3, –2) and having a slope of 2, is y = 2x-8

The general equation of a line in two variables of the first degree is represented as Ax + By +C = 0, A, B ≠ 0 where A, B and C are constants which belong to real numbers. When we represent the equation geometrically, we always get a straight line.

Given that a line containing the point (3, –2) and having a slope of 2, we need to find the equation of the line,

So, the general equation of a line is y = mx+c

Where, m is the slope and c is the y-intercept.

Therefore,

y = 2x+c

Now, put x = 3 and y = -2 in the equation to find the value of c,

-2 = 3(2)+c

-2 = 6+c

c = -8

Put the value of c in the equation,

y = 2x-8

Hence, the equation of a line containing the point (3, –2) and having a slope of 2, is y = 2x-8

Learn more about equation of a line, click;

https://brainly.com/question/21511618

#SPJ2

Answer:

C

Step-by-step explanation:

k is the slope of the line

The equation of the line is y = kx. Therefore, the special thing about k is that it is the slope of the line.

Using a slope intercept equation,

y = kx + b

where

Therefore, the y-intercept of the line y = kx is zero.

What is special about k is that it is the slope of the line y = kx.

learn more on equation here: https://brainly.com/question/14532490

#SPJ2

Answer:

D) 8²

Step-by-step explanation:

Evaluate each of the choices and see which one is equal to 64.

_____

It helps if appropriate mathematical symbols are used.

Jase's chickens laid more eggs.

From the information given, Jase farm has 9 chickens and each laid 3 eggs, therefore the total eggs laid will be:

= 9 × 3

= 27 eggs.

On the other hand, Ednas farm has chickens which lay a total of 23 eggs. Therefore, since 27 eggs are more than 23 eggs, Jase's chickens laid more eggs.

In conclusion, Jase's chickens laid more eggs.

Read related link on:

https://brainly.com/question/5221363

Final answer:

There is a family of normal probability distributions, each representing different populations or sets of data with varying mean and standard deviation values.

Explanation:

Yes, there is a family of normal probability distributions. The normal distribution is a continuous probability distribution that can take on different forms depending on the mean and standard deviation. The family of normal distributions is characterized by different mean and standard deviation values, which result in different shapes of the distribution curve.

For example, the standard normal distribution has a mean of 0 and a standard deviation of 1, and its curve is symmetrical around the mean. Other normal distributions may have different means and standard deviations, resulting in curves that are shifted or stretched.

Each normal distribution in the family represents a different population or set of data, and knowing the specific mean and standard deviation allows us to calculate probabilities and make statistical inferences.

Answer:

Option: B is the correct answer.

The equation of the new function g(x) on flipping the function f(x) over the x-axis is:

[tex]g(x)=-2^x[/tex]

Step-by-step explanation:

We are given a graph of the exponential function f(x) which is represented by:

[tex]f(x)=2^x[/tex]

We know that when a graph of a function is reflected or flipped over the x-axis then the the change that take place to the function is that f(x) is transformed to -f(x).

( Since on flipping the function over the x-axis the positive value of the function get changed to negative and the negative value of the function is changed to positive)

Hence, the equation for the new function is:

[tex]g(x)=-f(x)\\\\g(x)=-2^x[/tex]

The rules of the order of operations tells you to multiply and divide in order from left to right.

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.

The order of operations can be remembered by the acronym PEMDAS, which stands for: parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right. There are no parentheses in this problem, so start with exponents. Then, multiply and divide from left to right.

Hence, the rules of the order of operations tells you to multiply and divide in order from left to right.

Learn more about the multiplication here:

https://brainly.com/question/1562995.

#SPJ2

Answer:

Heres the correct answer. Hope this helps anyone who needs it!!!

Step-by-step explanation:

The polynomial function is one that involves only non-negative number powers of x, unlike a polynomial, cubic, or quartic function, and further calculation can be defined as follows:

Given:

[tex]\bold{f(x)=x^4-3x^3-23x^2+75x-50}[/tex]

To find:

Solution:

[tex]\to \bold{f(x)=x^4-3x^3-23x^2+75x-50}[/tex]

Let [tex]\bold{x=2}[/tex]

[tex]\to \bold{f(2)=2^4-3(2)^3-23(2)^2+75(2)-50}\\\\\to \bold{f(2)=16-3(8)-23(4)+75(2)-50}\\\\\to \bold{f(2)=16-24-92+150-50}\\\\\to \bold{f(2)=166-166}\\\\\to \bold{f(2)=0}\\\\[/tex]

So the factor is [tex]\bold{(x-2)}[/tex].

[tex]\to \bold{(x-5)(x-2)(x-1)(x+5)}\\\\[/tex]

Therefore, the final answer is "[tex]\bold{ f(x)=(x-5)(x-2)(x-1)(x+5)}\\\\[/tex]".

Learn more:

brainly.com/question/2511359

The exponent form of the given multiplication 5x5x5x5x5x5 is 5⁶.

Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied. Since 2 is the "base" and 5 is the "exponent,"

it can be represented as 2x2x2x2=25 for the number 32. This phrase should be understood as "two to the fifth power."

The given expression is 5x5x5x5x5x5. The exponent form of the number will be written below,

E = 5x5x5x5x5x5

E = 5⁶

Therefore, the exponent form of the given multiplication 5x5x5x5x5x5 is 5⁶.

To know more about an exponent expression follow

https://brainly.com/question/11975096

#SPJ2

Answer:

Option A is correct that is [tex]360^{\circ}[/tex]

Step-by-step explanation:

We have been given a triangle  we need to tell which one of these is a triangle below to map onto itself.

[tex]360^{\circ}[/tex] rotation is the complete rotation which eventually leads to the same figure which is given.

Option A is correct that is [tex]360^{\circ}[/tex] that will cause the triangle below to map onto itself.

The largest number which divides 149 and 101 , leaving remainder of 5 : 48

The division operation is one of the basic arithmetic operations

Common signs used are [tex] \large {\boxed {:}}} [/tex] or [tex] \large {\boxed {\slash}} [/tex]

The division is written by placing the numerator above the denominator with a horizontal line between them or use a slash with the numerator's position and the denominator is parallel

The division is actually an iterative subtraction operation (as many as the number of divisors)

Division is the opposite of multiplying

The general form of division can be stated by:

[tex] \large {\boxed {\bold {divident:divisor=quotient+remainder}} [/tex]

example:

7: 3 = 2 + 1

Division operation statement:

"7 divided by 3 equals 2 remainder 1"

A number have many factors

A common factor is a factor of two / more numbers.

Greatest common factor (GCF or HCF = Highest Common Factor) is the largest of the common factors

The largest number which divides 149 and 101 leaving remainder of 5

Division operation:

We find the value of x which is the GCF of the numbers 144 and 96

149 - 5 = 144

101 - 5 = 96

We look for GCF from factors of 144 and 96

GCF of 144 and 96 is 48

Or we can use prime factors:

144: 2⁴ X 3²

96: 2⁵ X 3

GCF = 2⁴ X 3 = 48

Highest common factor

https://brainly.com/question/128394

https://brainly.com/question/1578398

The GCF of any two even numbers

https://brainly.com/question/970482

Keywords : Greatest common factor , division, prime factors

We know that William paid his deductible that amount is the $150. 

Then William paid 20 percent of everything else. That's 20 percent of (750 minus 150), it is equal to 150.

Then the insurance company paid 80 percent of (750 minus 250), it is equal to 480.

Answer:

its is he payed 270 and insurance payed 480

Step-by-step explanation:

just simply add up the numbers to 750 and the only ones that go together are 270 + 480 = 750 hope it helps :)