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3 years ago

Match the correct theorem or postulate with the correct statement.

Mathematics

1 answer:

Roman55 [17]3 years ago

4 0

1. Unique line postulate

Statement: Through any two points, there is exactly one line.

2. Line intersection postulate

Statement: If two lines intersect, then their intersection is exactly one point.

3. Segment addition postulate

Statement: If A, B and C are collinear and B is between A and C, then AB + BC = AC

4. Angle Addition postulate

Statement: If R is in interior of $\angle PQS$ , then $m \angle PQR + m \angle RQS = m \angle PQS$ .

5. Linear pair theorem

Statement: If two angles form a linear pair, then the angles are supplementary.

6. Congruent Complements theorem

Statement: If two angles are complementary to the same angle, then the angles are congruent.

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A manufacturer determines that the number of toys it can sell is given by the formula

otez555 [7]

Answer:

The price where the manufacture sells the maximum number of toys is $20

Step-by-step explanation:

The given equation for that represents the number of toys the manufacturer can sell is given as follows;

T = -4·p² + 160·p - 305

Where;

p = The price of the toys in dollars

At the point where the manufacture sells the maxim number of toys on the graph of the equation T = -4·p² + 160·p - 305, which is the top of the graph, the slope = 0

Therefore, at the maximum point;

The slope = 0 = dT/dp = d(-4·p² + 160·p - 305)/dp = -8·p + 160

∴ -8·p + 160 = 0

160 = 8·p

8·p = 160

p = 160/8 = 20

The price where the manufacture sells the maximum number of toys is = p = 20 dollars

4 0

2 years ago

Harry baked a pan of brownies. He gave

Reika [66]

Harry gave away 3/6, or half of the brownies

1/6 plus 2/6 equals 3/6

4 0

2 years ago

Pls help i will mark brainliest!:) thank you!;D

pashok25 [27]

<h2>ANSWER</h2>

Here the two points given on the graph A and B

To find : The distance in between the two points we know distance in between two point on a graph 

= 

 $\sqrt{ {(x2 - x1)}^{2} } + \sqrt{ {(y2 - y1)}^{2} }$ 

The Point A = (0,0)

The point B = (3,6)

so the distance in between points A and B 

 $\sqrt{ {(0 - 0)}^{2} } + \sqrt{ {(6 - 3)}^{2} }$ 

 $\sqrt{ {3}^{2} }$ 

 $3$ 

So 3.0 is the distance

Hope it helps

7 0

2 years ago

The triangle on the grid will be translated two units left. On a coordinate plane, triangle A B C has points (negative 1, negati

nignag [31]

Answer:

Option B.

Step-by-step explanation:

The given vertices of triangle ABC are (-1, -1), (-1, -5) and (0.5, -5).

We need to find the coordinates of triangle when it is translated two units left.

So, the rule of translation is

$(x,y)\rightarrow (x-2,y)$

Using this rule, we get

$A(-1,-1)\rightarrow A'(-1-2,-1)=A'(-3,-1)$

$B(-1,-5)\rightarrow B'(-1-2,-5)=B'(-3,-5)$

$C(0.5,-5)\rightarrow C'(0.5-2,-5)=C'(-1.5,-5)$

The vertices of triangle A'B'C' are A'(-3,-1), B'(-3,-5) and C'(-1.5,-5).

Therefore, the correct option is B.

8 0

2 years ago

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Pierre Hugo is handling the estate of a prominent businesswoman. The will states that the surviving spouse is to receive one hal

umka21 [38]

Answer:

Each child will receive 0.125 (or 12.5%) of the estate.

Step-by-step explanation:

If the surviving spouse gets one half of the estate, the other half have to be divided among the four surviving children.

So its 0,5 divided among the 4 surviving children. That is 0.125 or 12.5% of the estate.

Each child will receive 0.125 of the estate.

5 0

2 years ago