Find the length of the midsegment of each trapezoid.

To find the distance from a point P to a plane defined by three points Q, R, and S, we can use the following formula:

distance = |(A * x + B * y + C * z + D) / √(A^2 + B^2 + C^2)|

where (A, B, C) are the coefficients of the normal vector of the plane, (x, y, z) are the coordinates of the point P, and D is the constant in the equation of the plane.

To find the coefficients of the normal vector, we can use the cross product of two vectors lying in the plane, say, QR and RS.

Let's first find the vectors QR and RS:

QR = (5 - 0, 0 - (-1), 3 - 7) = (5, 1, -4)

RS = (7 - 0, 5 - (-1), 0 - 7) = (7, 6, -7)

Next, we find the cross product of QR and RS:

cross product of QR and RS = (B, C, A) = (7, -30, 15)

So, the normal vector of the plane is (15, -30, 7).

Now we substitute the values for the coefficients and the coordinates of the point P into the formula:

distance = |(15 * 3 + (-30) * 1 + 7 * 7 + D) / √(15^2 + (-30)^2 + 7^2)|

To find the value of D, we can use any of the three points on the plane and substitute their coordinates into the equation of the plane in the form Ax + By + Cz + D = 0.

Let's use the point Q:

15 * 5 + (-30) * 0 + 7 * 3 + D = 0

Expanding and solving for D, we get:

75 + 21 + D = 0

D = -96

Finally, substituting the values back into the formula for distance, we get:

distance = |(15 * 3 + (-30) * 1 + 7 * 7 + -96) / √(15^2 + (-30)^2 + 7^2)|

distance = |(-24 + -30 + 49 - 96) / √(15^2 + (-30)^2 + 7^2)|

distance = |(-101) / √(15^2 + (-30)^2 + 7^2)|

distance = |(-101) / √(15^2 + (-30)^2 + 7^2)|

distance = |(-101) / √(225 + 900 + 49)|

distance = |(-101) / √1274|

distance = |(-101) / 35.6|

distance = 2.85

So, the distance between the point P and the plane is approximately 2.85.

Answer:

Step-by-step explanation:

1. YES

2. NO

3.NO

4. YES

1. This is because only some shoes are new not all of them.\

2. There are some new shoes so it is wrong.

3. Not all of them are new

4. Not every shoe is new because there are some old shoes.

A = {f, k, m, y}

B' = {k, x, y}

[tex]A \cup B' = \{f, ~k, ~m, ~y, ~x\}[/tex]

(every element from A and any other element that B' has that A didn't)

A' = {q, x}

B' = {k, x, y}

[tex]A \cap B' = \{x\}[/tex]

(x is the only element that both sets have)

The required description of the given piecewise linear relations is graphed, as follows:

f(x) = 1 if [-3, -1); f(x) = 2 if [-1, 1); and f(x) = 3 if [1, 3).

A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).

The graph of the piecewise linear relations is given in the question, as shown

f(x) = 1 if [-3, -1)

This the sub-function define between the interval  [-3, -1).

f(x) = 2 if [-1, 1)

This the sub-function define between the interval [-1, 1).

f(x) = 3 if [1, 3)

This the sub-function define between the interval  [1, 3).

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The given series is geometric when r equals negative three-fifths.

What is geometric series?

The geometric series refers to the total of terms with a common ratio between every pair of neighbouring terms. Geometric series can be of two different types: finite and infinite. The sequence is of the form {a, ar, ar², ar³, …….} where, a is the first term, and r is the "common ratio".

where, r = ar/a = (second term)/(first term)

Given, the series 250 – 150 + 90 – 54 + …

So, r = (-150)/250 = -3/5

or, r = 90/(-150) = -3/5

Hence, for the geometric series, r should be equal to negative three-fifths.

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The graph of the points can be seen at the end, and the relation is not a function.

The coordinate axis has two axis with numbers labeled. For any point (x, y), you need to find the value x on the horizontal axis and the value y on the vertical axis.

Then the graph of the points  ​(-7,5), (-4,-6), (-1,4), (-7,3) will be like the one at the end of the answer.

Now, is this a function?

Not, it is not, because we can see that the input -7 is being mapped into two different outputs, and a relation is a function only if each input is mapped into a single output.

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Answer:

i thinks its A im not for sure but give some money if its wrong fam bc im nice like that

Step-by-step explanation:

Answer:

It has a Unique solution.

Step-by-step explanation:

The equations are:

y=-2x+1 and y=3x-1

subtracting equation 2 from equation 3

we get,

⇒-5x+2=0

⇒5x=2

⇒x=2/5

substitute x in equation 1, then we get

⇒y=-4/5+1

⇒y=1/5

Hence the equations have a Unique solution.

Answer:

5x(8-1)=(5x10)-(5x4)

Answer: look at the image for the answer and explanation

Step-by-step explanation:

Following are the values of the functions -

1) f(a) = 8a - 4

2) f(a+h) = 8a+ 8h - 4

3)[tex]\frac{f (a+h)-(a) }{h}= 8[/tex]

An expression or relationship with one or more variables is called a function. Both its inputs and outputs are numerous. There is just one output per input. The function explains how the inputs and outputs are related.

To evaluate f(a), we simply substitute the value of "a" into the function:

1) f(a) = 8a - 4

To evaluate f(a+h), we substitute the value of "a+h" into the function:

2) f(a+h) = 8(a+h) - 4

f(a+h) = 8a+ 8h-4

To find the expression for [tex]\frac{f (a+h)-(a) }{h}[/tex], we divide the result by h: L(a+h)-f(a) h we can subtract f(a) from f(a+h) and then

3) [tex]\frac{f (a+h)-(a) }{h}[/tex]

[tex]= \frac{ (8a+8h-4-(8a-4)}{h} \\= \frac{8h}{h}= 8[/tex]

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Roman Rounds normally charges $18 for a large pizza.

What is the equation in one variable?

An equation in one variable is a mathematical statement that uses one variable and an equal sign to relate two expressions. The variable in the equation represents an unknown value, and the goal is often to find the value of the variable that makes the equation true.

Let's use p to represent the normal price of each large pizza charged by Roman Rounds.

Since the price of each pizza was reduced by $2 for the bulk order, the amount Mr. Mosley paid for 12 large pizzas is:

12(p - 2) = $192

We can simplify this equation by first distributing the 12 on the left side:

12p - 24 = $192

Then, we can isolate the variable p on one side of the equation by adding 24 to both sides:

12p = $216

Finally, we can solve for p by dividing both sides by 12:

p = $18

Therefore, Roman Rounds normally charges $18 for a large pizza.

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Answer:

The answer is that 1 2/3 and 3/4 common denominate is /12

Step-by-step explanation:

3 x 4 equals 12 then multiply 2 by 4 and 3 by 3 then it’s 1 8/12 and 9/12

Answer:

24 people

Step-by-step explanation:

German : 4 + (4/2) = 6

Norwegian : 4 + 4 + (4/2) = 10

Italian : 4 + 4 = 8

Add them all :

6 + 10 + 8 = 24

Answer:

the coordinate of the R' after the dilation is (-1,-0.5)

Step-by-step explanation:

Answer:

The set of all numbers less than 17 and greater than or equal to -8 can be expressed in set builder notation as:

{x | -8 <= x < 17}

Step-by-step explanation:

Set builder notation is a way of expressing a set of elements in mathematical terms. The syntax of set builder notation is {x | <condition>}, where x represents an element in the set and the condition specifies the properties that the element must satisfy to be included in the set.

In this case, the set consists of all numbers less than 17 and greater than or equal to -8. The condition for the set is -8 <= x < 17, where x is a real number. This means that x must be greater than or equal to -8 and less than 17 in order to be included in the set.

Therefore, the set of all numbers less than 17 and greater than or equal to -8 can be expressed in set builder notation as:

{x | -8 <= x < 17}.

Answer: The equation "x + y = mb" represents a linear equation in two variables, x and y. In this equation, m is a constant and b is another constant or a known value. The equation states that the sum of x and y is equal to the product of m and b.

This equation can be used to model a variety of real-world situations where two quantities are related and their sum is equal to a constant value. For example, it could represent the amount of money saved by two people, where x and y are the savings of the two people and mb is the total amount of money saved.

To solve for x and y, we can use either substitution or elimination method, or any other method for solving systems of linear equations. The values of x and y that satisfy the equation "x + y = mb" are called the solutions of the equation.

Step-by-step explanation:

The length of the arc that the tip of the pendulum travels is approximately 7 feet.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

We can use the formula for the length of an arc of a circle to find the length of the arc that the tip of the pendulum travels:

Arc length = (angle/360) x 2πr

where: angle = the central angle (in degrees or radians) that the arc subtends and r = the radius of the circle

First, we need to convert the angle from degrees and minutes to decimal degrees.

There are 60 minutes in a degree, so:

40°6' = 40 + 6/60 = 40.1 degrees

Now we can plug in the values:

Arc length = (40.1/360) x 2π(10 feet)

Arc length = 6.99 feet

Hence, the length of the arc that the tip of the pendulum travels is approximately 7 feet.

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Explanation:

Let's replace y with 0 and solve for x.

-x+6y = 2

-x+6*0 = 2

-x + 0 = 2

-x = 2

x = -2

We have x = -2 pair up with y = 0 to get the ordered pair (x,y) = (-2,0)

This is the x intercept of the graph. It's where the line crosses the x axis. You can use a tool like Desmos or GeoGebra to confirm.

Since we have infinitely many numbers to replace x or y with, we have infinitely many solution points on this line.

Each point is of the form (-2+6k, k) where k is any real number.  If k = 0, then it leads to (-2,0) found earlier.

The value equivalent to the expression is (2)√6 and option B is the correct answer.

Finding the prime factors of a given number, such as a composite number, is done through the process of prime factorization. The prime numbers are the only components in these factors. A number with just the number itself and factor 1 is said to be a prime number.

the quantities that are multiplied to produce new quantities. For instance, the factors of 15 are 3 and 5, or 3 + 5 = 15.

The given expression is √24.

Find the prime factorization of 24:

2 | 24

2 | 12

2 | 6

3 | 3

  | 1

Thus, √24 can be written as:

√24 = √(2)²(2)3

√24 = (2)√6

Hence, the value equivalent to the expression is (2)√6 and option B is the correct answer.

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Answer: the enswer is c the range is 46

Step-by-step explanation:

The maximum height the rock reaches 3.15 feet and the rock will be above the surface for 2.6 seconds

An equation is an expression that shows the relationship between two or more variables and numbers.

here, we have,

From the graph of the function h(t) = 1 + 4t - 1.86t²:

The maximum height the rock reaches 3.15 feet.

Time spent on air

= 2.38 - (-0)

= 2.38 seconds

The maximum height the rock reaches 3.15 feet and the rock will be above the surface for 2.6 seconds.

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Answer:

y = 4x + 32

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 4x ← is in slope- intercept form

with slope m = 4 and y- intercept = 0

• Parallel lines have equal slopes , then

y = 4x + c ← is the partial equation

to find c substitute (- 8, 2 ) into the partial equation

2 = 4(- 8) + c = - 32 + c ( add 32 to both sides )

34 = c

y = 4x + 32 ← in slope- intercept form

The percentage increase in Marvin's height is 4.51%

Marvin was 1.55m tall a year ago

Now her present height is 1.62m

The first step is to calculate the increase

= 1.62-1.55

= 0.07

The percentage increase can be calculated as follows

0.07/1.55 × 100

= 0.0451 × 100

= 4.51

Hence the percentage increase is 4.51%

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The percentage of R90 that will give 90c is 4%

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

1 cent = R0.04

R1 = 1/0.04

R 90 = 90/0.04 = 2,250c

x/100 × 2250 = 90

2250x = 9000

x = 9000/2250

x= 4%

therefore 4 percent of R 90 is 90c

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To find the mean (average) of a set of numbers, you add up all the numbers and then divide by the number of items in the set.

Mean = (79g + 88g + 116g + 109g + 93g) / 5

Mean = (475g) / 5

Mean = 95g

So, the mean of the set of numbers is 95g.

The value of mean of the data set is,

⇒ Mean = 97 g

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

Data set is,

79g, 88g, 116g, 109g, 93g

Now, We get;

The mean of data set is,

⇒ Mean = 79g + 88g + 116g + 109g + 93g / 5

⇒ Mean = 485g / 5

⇒ Mean = 97 g

Thus, The value of mean of the data set is,

⇒ Mean = 97 g

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The slant height of the square base pyramid is calculated as l = 17 using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

we can observe the right triangle with hypotenuse l, height = 15, and base = 8 {half the pyramid base of 16}

the slant height is calculated as follows:

l² = 15² + 8²

l² = 225 + 64

l² = 289

l = √289 {take square root of both sides}

l = 17.

Therefore, the slant height of the square base pyramid is calculated as l = 17 using the Pythagoras rule.

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The slope of the line containing (-1, 5) and (2, -4) will be negative 3.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

The points are (-1, 5) and (2, -4). Then the slope of the line is given as,

m = (5 + 4) / (- 1 - 2)

m = 9 / (-3)

m = - 3

The slope of the line containing (-1, 5) and (2, -4) will be negative 3.

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a.) The number of students that are over 145cm = 13

b.) The number of students with the height between 125 cm and 140 cm = 21 students.

C.) The number of students that were in class = 37

A frequency table is defined as a statistical tool that is used to organize the data given so that it makes it more meaningful and easier to understand.

To calculate the number of students that are over 145cm = 8+4+1 = 13 students.

To calculate the number of students that had a height

between 125 cm and 140 cm = 2+5+6+8 = 21 students.

To calculate the number of students that were in class= 3+2+5+6+8+8+4+1 = 37 students.

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