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3 years ago

Find the other endpoint of the line segment with the given endpoint and midpoint. Endpoint: (-8,8) Midpoint: (5,-3)

1 answer:

4 0

Take a look at the x-coordinates of the two given points: -8 and 5. If we depart from the left endpoint (-8,8) to the right in the direction of the midpoint (5,-3), we see that x increases by 13 as we approach the midpoint. The other endpoint is twice as far (26 units instead of 13 units) from the first one. Thus, the x-coordinate of the right endpoint is 5+13, or 18.

Take similar actions withe the y-coordinates. From y = 8 at the left endpoint, we end up at y = -3 at the midpoint, a decrease in y of 11. Decrease y again by 11 from the midpoint y-coordinate, -3, ending up with -14.

The right endpoint is thus (18, -14).

You might be interested in

A geometric sequence is shown below.

mestny [16]

Answer:

An explicit representation for the nth term of the sequence:

$f_n=-\frac{1}{2}\cdot \:4^{n-1}$

It means, option (B) should be true.

Step-by-step explanation:

Given the geometric sequence

$-\frac{1}{2},\:-2,\:-8,\:-32,...$

A geometric sequence has a constant ratio, denoted by 'r', and is defined by

$f_n=f_1\cdot r^{n-1}$

Determining the common ratios of all the adjacent terms

$\frac{-2}{-\frac{1}{2}}=4,\:\quad \frac{-8}{-2}=4,\:\quad \frac{-32}{-8}=4$

As the ratio is the same, so

r = 4

Given that f₁ = -1/2

substituting r = 4, and f₁ = -1/2 in the nth term

$f_n=f_1\cdot r^{n-1}$

$f_n=-\frac{1}{2}\cdot \:4^{n-1}$

Thus, an explicit representation for the nth term of the sequence:

$f_n=-\frac{1}{2}\cdot \:4^{n-1}$

It means, option (B) should be true.

8 0

2 years ago

Use the data table provided to calculated the values requested below. Provide all answers to three decimal places.

babymother [125]

Answer:

1) 0.700

2) 0.730

3) 0.030

4) 0.959

Step-by-step explanation:

1) proportion of support for the ban with at least one child =

$\frac{no of support atleast 1 child}{Total no of atleast 1 child\\}$

= $\frac{1739}{2485}$

= 0.700

2) proportion of support for the ban with no child =

= $\frac{no of support with no child}{Total of no child}$

= $\frac{3089}{4231}$

= 0.730

3) Difference in proportion of supporters for the ban between those with atleast one child and those with no child

= 0.700 - 0.730

= -0.03

4) Relative risk = $\frac{proportion with atleast on child}{proportion with no child}$

= $\frac{0.700}{0.730}$ = 0.959

5 0

3 years ago

In the figure, AB is parallel to CD, XY is the perpendicular bisector of AB, and E is the midpoint of XY. Prove that △AEB ≅ △DEC

Makovka662 [10]

Answer:

From top to bottom:

A, J, E, B, I, C, D, G, F, H

See below for more clarification.

Step-by-step explanation:

We are given that AB is parallel to CD, XY is the perpendicular bisector of AB, and E is the midpoint of XY. And we want to prove that ΔAEB ≅ ΔDEC.

Statements:

1) XY is perpendicular to AB.

Definition of perpendicular bisector.

2) XY ⊥ CD.

In a plane, if a transveral is perpendicular to one of the two parallel lines, then it is perpendicular to the other.

3) m∠AXE = 90°, m∠DYE = 90°.

Definition of perpendicular lines.

4) ∠AXE ≅ ∠DYE.

Right angles are congruent.

5) XE ≅ YE

Definition of a midpoint.

6) ∠A ≅ ∠D.

Alternate Interior Angles Theorem

7) ΔAEX ≅ ΔDEY

AAS Triangle Congruence*

(*∠A ≅ ∠D, ∠AXE ≅ ∠DYE, and XE ≅ YE)

8) AE ≅ DE

Corresponding parts of congruent triangles are congruent (CPCTC).

9) ∠AEB ≅ ∠DEC

Vertical Angles Theorem

10) ΔAEB ≅ ΔDEC

ASA Triangle Congruence**

(**∠A ≅ ∠D, AE ≅ DE, and ∠AEB ≅ ∠DEC)

3 0

3 years ago

Which is a factor of f(x) = 60x4 86x3 – 46x2 – 43x 8? use the rational root theorem to help you find your answer. x – 6 5x – 8 6

jolli1 [7]

Answer:

6x-1

Step-by-step explanation:

I dont know how to explain but it is correct

4 0

2 years ago

During snack time at preschool teacher divide it 4/5 of a gallon of milk evenly between two students how much milk did each stud

Ivanshal [37]

Answer:

2/5

Step-by-step explanation:

4/5 split into 2 is 2/5 or 4/10

4 0

3 years ago