Find the equation of the plane which has intercepts of (4,0,0) and (0,−2,0) and no z-intercept.

Answer: Yes, the quadrilateral ABCD is a trapezoid.

Step-by-step explanation: Given that the vertices of the quadrilateral ABCD are A(–4, –5), B(–3, 0), C(0, 2), and D(5, 1).

We are to determine whether ABCD is a trapezoid or not.

We know that a trapezoid is a quadrilateral with one pair of opposite sides parallel. Also, the slopes of two parallel lines are equal.

First, we will find the slopes of the sides AB, BC, CD and DA.

We have

[tex]\textup{Step 1: The slope of AB}=\dfrac{0+5}{-3+4}=\dfrac{5}{1}=5,\\\\\textup{Step 2: The slope of BC}=\dfrac{2-0}{0+3}=\dfrac{2}{3},\\\\\textup{Step 3: The slope of CD}=\dfrac{1-2}{5-0}=-\dfrac{1}{5},\\\\\textup{Step 4: The slope of DA}=\dfrac{-5-1}{-4-5}=\dfrac{2}{3}.[/tex]

Since the slopes of the sides BC and DA are equal, so BC an DA are the parallel sides of the quadrilateral ABCD.

Thus, the quadrilateral is a trapezoid because it has a pair of opposite sides parallel.

The quadrilateral is a trapezoid because it contains two opposite sides that are parallel, the quadrilateral is called a trapezoid.

It is defined as the quadrilateral having four sides in which two sides are parallel to each other, it is a 2-dimensional geometry.

We have:

Quadrilateral ABCD with vertices A(–4, –5), B(–3, 0), C(0, 2), and D(5, 1)

To identify the quadrilateral is a trapezoid we must find the slopes of the lines AB, BC, Cd, and AD

For slope m the formula is given by:

[tex]\rm m = \frac{y_2-y_1}{x_2-x_1}[/tex]

For slope of AB:

[tex]=\rm \frac{0-(-5)}{-3-(-4)}[/tex]

[tex]=\rm \frac{0+5}{-3+4}[/tex]

= 5

For slope of BC:

[tex]=\rm \frac{2-0}{0-(-3)}[/tex]

[tex]=\rm \frac{2}{3}[/tex]

For slope of CD:

[tex]=\rm \frac{1-2}{5-0}[/tex]

= -1/5

For slope of AD:

[tex]=\rm \frac{-5-1}{-4-5}[/tex]

= 2/3

Because the slopes of the sides BC and DA are equivalent, BC and DA are the quadrilateral ABCD's parallel sides.

Thus, the quadrilateral is a trapezoid because it contains two opposite sides that are parallel, the quadrilateral is called a trapezoid.

Learn more about the trapezoid here:

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Answer:

As, there are 595 students in the school.

To find the mean number of books, read by student in the school during summer

If he will survey all the students in the school that will give the exact mean , but that will be little lengthy and tedious.

As, well as larger the number of students surveyed , the better the mean is.

But option A, is true as, select randomly few students , find the mean number of books read by them , that will be less time consuming and gives the mean of population also.

Option A:

To estimate the mean using sample,Terrance will need to randomly select students, he will survey and that represents population as well.

Apart from option A,option B is also true.

Answer:

Meters

Step-by-step explanation:

Reason:

Usually, bench length is bigger than then length of the chair and the table.

So it will be measured using meters. If we use meter it will easy to measure  and accurate because it somewhat bigger length than chair and table.

1 meter = 100 centimeters.

The standard length of a bench will 1.5 meters to 2 meters. Usually 3 to 4 people will sit on the bench.

Michael's family ate all of the sweet potato pie (8 slices) and 2 slices of the chocolate pie, making it a total of 10 slices eaten. Each pie has 8 slices, so they consumed 1 and 1/4 pies in total, which corresponds to answer choice C) 1 1/4 pie.

To find out how much pie Michael's family ate on Thanksgiving, we need to consider that the sweet potato pie had 8 slices and the chocolate pie also had 8 slices. All of the sweet potato pie was eaten, this means 8 slices of pie were consumed. From the chocolate pie, only 2 slices were eaten. To get the total number of slices eaten, we add the slices of sweet potato pie to the slices of chocolate pie that were eaten.

Total slices eaten = Slices of sweet potato pie + Slices of chocolate pie eaten
= 8 slices + 2 slices
= 10 slices

Since each pie was divided into 8 slices, we can see that the total pie eaten in terms of whole pies is:

Total pie eaten = 10 slices \/ 8 (slices per pie)
1 and 2 \/ 8
Since 2 \/ 8 can be simplified to 1 \/ 4, we get:

Total pie eaten = 1 and 1 \/ 4 pies

Therefore, the correct answer is C) 1 1 \/ 4 pie.

Answer: (-30 , 10)   Option C

In given question, some information is missing.

Complete question is :

Which ordered pair would form a proportional relationship with the point graphed below?

(–10, 30)

(30, –15)

(–30, 10)

(80, –30)

Explanation:

In graph, given point's coordinate is (60 , -20)

We need to find the proportion of the given point (60 , -20)

Proportion is number considered in comparative relation.

So,

[tex] \frac{60}{(-20)}  [/tex]

= [tex] -\frac{60}{20}  [/tex]

Divide by common factor 2 both numerator & denominator.

= [tex] -\frac{30}{10}  [/tex]

So, proportion poit's coordinate is (-30 , 10)  Option C

That's the final answer.

I hope it will help you.

The segment HJ is the secant line of the circle. Then the correct option B.

If a line intersect the circle at two point, then the line is known as a secant line.

If the line intersect at a single point on the circle, then the line is known as a tangent line.

The segment HJ is the secant line of the circle.

Then the correct option B.

More about the secant line link is given below.

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Answer:

[tex]6.36\times 10^7[/tex]  

Step-by-step explanation:

We are asked to represent 63,600,000 in scientific notation.

To express our given number in scientific notation, we need factors such that first factor is a number between 1 ans 10 and second factor will be power of 10.

[tex]63,600,000=6.36\times 10000000[/tex]  

[tex]63,600,000=6.36\times 10^7[/tex]  

Therefore, our number in scientific notation would be [tex]6.36\times 10^7[/tex].

Answer : option C

Explanation:

there will be 4 roots for the given polynomial but in graph you will see 3 points because (2,0) is repeating two times

we can see the root graphically

the points that intersect  x-axis are the roots

Here, x-axis is cut at 3 points so, these points will be the root of given polynomial.

please see the attached graph

Answer:

$546

Step-by-step explanation:

The profit from sweatshirt sales was $302.

To find the profit from sweatshirt sales, we need to find the total profit from T-shirts and sweatshirts and then calculate 1/3 of that amount. We know that the profit from T-shirt sales is $1,632 and the vendor paid the rock band $726. Let's use these numbers to calculate the profit from sweatshirt sales:

Therefore, the profit from sweatshirt sales was $302.

Answer:

(0,3)

(1,6)

(2,12)

(3,24)

(4,48)

(5,96)

(6,192)

This is a function.  For each input, there is only one y value.

Step-by-step explanation:

x = number of folds

y = thickness of paper

(0,3)

fold it once, the thickness is doubled (times 2)

Multiply the y coordinate times 2 each time you increase x by 1

(1,6)

(2,12)

(3,24)

(4,48)

(5,96)

(6,192)

This is a function.  For each input, there is only one y value.

Answer:

(0,3)

(1,6)

(2,12)

(3,24)

(4,48)

(5,96)

(6,192)

all of those are a function.

Step-by-step explanation:

A.sum of cubes is the correct answer on E.D.G.U

Good luck!

Solution:

The given equation of line is :

→  y- 5 = 43 (x -5)

= y -5 = 43 x - 43 × 5 → [Using distributive property]

= y- 5 = 43 x - 215

→ 43 x - y - 215 +5 =0

→ 43 x - y -210 =0

→ y = 43 x - 210

As the slope of line→y = m x + c is ,43.

Or , tan A = 43, where A is the angle made by line in positive direction of X axis.

And Y intercept = -210

A rotation by 360° about the origin will always carry an image onto the original figure.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

A rotation by 360° about the origin will always carry an image onto the original figure.

Find out more on transformation at: https://brainly.com/question/4289712

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