X divides into the line PQ in the ratio 2:3 P is (2,1) and Q is (12.5,7.5) work out the coordinates of point X

Answer:

Option B. 17.9 units²

Step-by-step explanation:

This figure consist of two figures

1). One quadrilateral

2). One semicircle

Now to get the area of total figure

= Area of triangle + area of semicircle

1). Area of quadrilateral = length × width

= √(3-1)²+(1-2)² × √(3-1)²+(1+3)² = √(4 + 1) ×√(4 + 16) = √5×2√5 = 10

2) Area of semicircle = (1/2)πr²

Radius of the circle = (1/2)√(3-1)²+(1+3)² = (1/2)√(4 + 16) = (1/2)(√20)

r = √5

Area of semicircle = (1/2).(π).(√5)² = (1/2).(3.14)(5) = 7.85

Area of the total figure = 10 + 7.85 = 17.85 ≈ 17.9 units²

Option B is the correct answer.

Answer:

salary . part time work . odd jobs.

Step-by-step explanation:

1. a(p–q)+q–p

We take out common factor

To change q - p as p - q we pull out -1

So q - p becomes -1(p - q)

a(p–q)+q–p

a(p–q) -1(p - q)

p -q is in common so we factor out p-q

(p - q) (a - 1)

2. p^2q+r^2–pqr–pr

WE change the order of terms

[tex] p^2q-pqr+r^2-pr [/tex]

We group first two terms and last two terms

[tex] (p^2q-pqr)+(r^2-pr) [/tex]

Now we factor out pq from first group and -r from second group

[tex] pq(p-r) - r(p - r) [/tex]

[tex] (p - r) (pq - r) [/tex]

To write the answer as a product of polynomials we try to factor the polynomial

a(p–q)+q–p

we can write this expression as

a(p-q)+(q-p)

from second parenthesis we can factor out -1 , so we get

a(p-q) -1(p-q)

Now it has two terms a(p-q) and -1(p-q) , from these two terms we can factor out (p-q)

So we get it

(p-q)(a-1)

So we get the polynomial as a product of two polynomials.

Second

[tex] p^2q+r^2- pqr-pr [/tex]

we can rewrite the expression as

[tex] (p^2q- pqr)+(r^2-pr) [/tex]

Now try to factor the groups

factor out "pq" as GCF from first group and "-r" as GCF from second group

[tex] pq(p- r)-r(p-r) [/tex]

Now we can factor it out for final step

[tex] (p- r)(pq-r) [/tex]

From the given information , we can make a rough figure as shown in attachment.

Now in the given triangle we can use following formula of sin to get the angle,

[tex] sin x = \frac{Perpendicular}{opposite} [/tex]

We can see from the figure that:

perpendicular = 8 and opposite =14.

Plugging the given values in the formula for sin x,

[tex] sin x = \frac{8}{14} [/tex]

sin x = 0.5714

to find x we have to find sin inverse of 0.5714 ,

x = sin⁻¹(0.5714)

x=34.8 degrees.

Answer : the angle that the telephone pole makes with the ground is 34.8 degrees. option D

Answer:

1. [tex]m\angle 1+m\angle 5=180^{\circ}[/tex] and [tex]m\angle 1+m\angle 4=180^{\circ}[/tex]; given

2. [tex]m\angle 1+m\angle5=m\angle 1+m\angle4[/tex]; substitution

3.[tex]m\angle5=m\angle4[/tex]; subtraction property of equality

4. Ray YZ is parallel to ray UV; if alternate interior angles equal , then lines are parallel.

Step-by-step explanation:

Given

[tex]m\angle1+m\angle5=180^{\circ}[/tex]

[tex]m\angle 1+m\angle4=180^{\circ}[/tex]

To prove that YZ is parallel to UV.

Proof:

1.Statement: [tex]m\angle 1+m\angle5=180^{\circ}[/tex] and [tex]m\angle1+m\angle4=180^{\circ}[/tex]

Reason; Given

2. Statement: [tex]m\angle1+m\angle5=m\angle 1+m\angle4[/tex]

Reason: By using substitution property

3.Statement: [tex]m\angle5=m\angle4[/tex]

Reason: Subtraction property of equality.

4.Statement: Ray YZ is parallel to Ray UV

Reason: If alternate interior angles equal, then lines are parallel.

The inequality that represents the number decreased by 15 is at least 4 will be equal to x - 15 ≥ 4.

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values.

Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.

As per the given data in the question,

Let the number be x.

Number is decreased by 15 which is at least equal to 4.

Then, the inequality will be,

x - 15 ≥ 4

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Final answer:

The bakery should place 6 cookies in each cellophane package to maximize the number of cookies per package and fit them evenly in both sizes of boxes. This is found by calculating the greatest common divisor (GCD) of the box sizes, which in this case is 6.

Explanation:

To solve the problem of how many cookies the bakery should place in each cellophane package to maximize the number of cookies in each package, we need to find the greatest common divisor (GCD) of the two box sizes, which are 18 cookies and 24 cookies. The GCD represents the largest number of cookies that can be evenly distributed in both box sizes without any leftovers.

Step-by-step Solution:

This way, both the smaller and the larger box sizes can be filled with equal-sized packages of cookies, and there will be no leftover cookies.

Answer:

The answer is A because

Step-by-step explanation:

1,280 in savings

160n

2

Hannah saves each week

50n parents put in savings each week

thus,

1,280 + 160n/2+ 50n

1,280 + 80n + 50n

1280 + 130n

You really have to think this one through all the way.  All the other answer choices are steps in finding the answer

Answer:

14c^2

Step-by-step explanation:

The greatest common factor is the factor between the 3 expressions that once divided by each expression, 1 becomes the only number common to all 3. Considering all the expressions as follows (broken into all the factors that make up each expression)

14c^3 = 2 × 7 × c × c

70c^4 = 2 × 5 × 7 × c × c × c × c

28c^2 = 2 × 7 × c × c

From the above, the common factors are 2, 7, c and c,the product of these

= 2 × 7 × c × c

= 14c^2

The non-congruent angle in an isosceles triangle is called the vertex angle.

What is an isosceles triangle?

An isosceles triangle is a triangle that has at least two sides of equal length.

Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.

The two angles opposite to the equal sides are congruent with each other. That means it has two congruent base angles and this is called an isosceles triangle base angle theorem.

The angle which is not congruent to the two congruent base angles is called an apex angle.

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The correct set of points that demonstrate a pre-image that has been reflected over x = -1 is A(0,-1) and A'(−2,−1).

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

To reflect a point over the line x = -1, we simply need to flip the x-coordinate of the point across the line. In other words, if a point has coordinates (x,y), its image after reflection over x = -1 will have coordinates (-x,y).

Using this rule, we can check each of the given options:

Therefore, the correct set of points is A(0,-1) and A'(−2,−1).

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