All categories

4 years ago

Find the coordinates of the midpoint of HX. H(5.5, -4.75) and X(3.75, -2.75)

Mathematics

1 answer:

MAXImum [283]4 years ago

8 0

( 4.625, - 3.75 )

the midpoint of (x₁, y₁ ) and (x₂, y₂ ) is

[ $\frac{1}{2}$ (x₁ + x₂ ), $\frac{1}{2}$ (y₁ + y₂ ) ]

here (x₁, y₁ ) = (5.5, - 4.75 ) and (x₂, y₂ ) = (3.75, - 2.75 )

[ $\frac{1}{2}$ (5.5 + 3.75 ), $\frac{1}{2}$ (- 4.75 - 2.75 ) ]

= (4.625, - 3.75 ) ← midpoint of HX

You might be interested in

Find the missing length indicated.

MA_775_DIABLO [31]

Answer:

x = 15

Step-by-step explanation:

From the above diagram, we can see that the right angled triangle has been split into two by drawing a line from the altitude.

This would really in the following ratios or proportions below

25 : x = x : 9

25/x = x/9

Cross Multiply

x² = 25 × 9

x² = 225

x = √225

x = 15

5 0

3 years ago

Consider a circle whose equation is x2 + y2 + 4x – 6y – 36 = 0. Which statements are true? Check all that apply. To begin conver

umka21 [38]

Answer:

1) False, to begin converting the equation to standard form, each side must be added by 36. 2) True, to complete the square for the x terms, add 4 to both sides, 3) True, the center of the circle is at (-2, 3), 4) False, the center of the circle is at (-2, 3), 5) False, the radius of the circle is 7 units, 6) False, the radius of the circle is 7 units.

Step-by-step explanation:

Let prove the validity of each choice:

1) To begin converting the equation to standard form, subtract 36 from both sides:

Let consider the following formula and perform the following algebraic operations:

(i) $x^{2} + y^{2} + 4\cdot x - 6\cdot y - 36 = 0$ Given

(ii) $x^{2} + 4\cdot x + y^{2} - 6\cdot y - 36 = 0$ Commutative Property

(iii) $(x^{2} + 4\cdot x + 4) - 4 + (y^{2} - 6\cdot y + 9) - 9 -36 = 0$ Modulative/Associative Property/Additive Inverse Existence

(iv) $(x+ 2)^{2} - 4 + (y - 3)^{2} - 9 - 36 = 0$ Perfect Trinomial Square

(v) $(x+2)^{2} +(y-3)^{2} = 4 + 9 + 36$ Commutative Property/Compatibility with Addition/Additive Inverse Existence/Modulative Property

(vi) $(x+2)^{2} + (y-3)^{2} = 49$ Definition of Addition/Result

False, to begin converting the equation to standard form, each side must be added by 36.

2) True, step (iii) on exercise 1) indicates that both side must be added by 4.

3) The general equation for a circle centered at (h, k) is of the form:

$(x-h)^{2}+ (y-k)^{2} = r^{2}$

Where $r$ is the radius of the circle.

By direct comparison, it is evident that circle is centered at (-2,3).

True, step (vi) on exercise 1) indicates that center of the circle is at (-2, 3).

4) False, step (vi) on exercise 1) indicates that the center of the circle is at (-2, 3), not in (4, -6).

5) After comparing both formulas, it is evident that radius of the circle is 7 units.

False, the radius of the circle is 7 units.

6) After comparing both formulas, it is evident that radius of the circle is 7 units.

False, the radius of the circle is 7 units.

5 0

3 years ago

Read 2 more answers

Can you please help me with this?

kow [346]

Answer:

257 pihff ertu job ruu 7oinc aet box took

6 0

3 years ago

If you draw a graph of the whole numbers on number line, which of the following points would not be included on the graph?

777dan777 [17]

-1 would not be included. It is an integer not a whole number.

4 0

3 years ago

5x³+8x²-7x-6

Lady_Fox [76]

Answer:

Step-by-step explanation:

Whether we divide using long division or using synthetic division, the rule is the same: If, after division, there is no remainder (i. e., the remainder is zero), the divisor binomial is a factor or the associated root is indeed a root/zero/solution.

Divide 5x³+8x²-7x-6 by (x+2) using synthetic division. Use the divisor -2 (which comes from letting x+2 = 0):

--------------------------

-2 / 5 8 -7 -6

-10 4 6

------------------------------

5 -2 -3 0 Since the remainder here is 0, we know that

-2 is a root of 5x³+8x²-7x-6 and that (x+2) is

a factor of 5x³+8x²-7x-6.

Now check out the possibility that (x+1) is a factor of 5x^3 + 8x^2 - 7x - 6:

Use -1 as the divisor in synthetic division:

--------------------------

-1 / 5 8 -7 -6

-5 -3 10

------------------------------

5 3 -10 4

Since there is a non-zero remainder (4), we can conclude that (x + 1) is NOT a factor of the given polynomial expression.

5 0

3 years ago