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2 years ago

Which of the following is a solution to the system of two equations y = 3x – 1 and y = 2x + 3?

Mathematics

1 answer:

NeTakaya2 years ago

4 0

Point form: (4,11)
equation form: x=4 y=11

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Use only an associative property to rewrite the following expression.<br> (pk)•r=

Gennadij [26K]

Answer:

Step-by-step explanation:

(pk) * r = p * (kr)

5 0

2 years ago

In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.

konstantin123 [22]

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

$BC^2=BD\cdot AB.$

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

$x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.$

Take positive value x. You get

$AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.$

2. According to the previous theorem,

$AC^2=AD\cdot AB.$

Then

$AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

Answer: $AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

$CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D$

This means that you cannot find solutions of this equation. Then CD≠2 cm.

8 0

2 years ago

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2 doctors is what percent of 25 doctors?

Luden [163]

2 doctors is 8% of 25 total doctors.

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2 years ago

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How many meters are 345 cm equal to

Gwar [14]

There is 100 cm in 1 meter so if thats true then you must take

345/100

and that should be your answer :)

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3 years ago

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Suppose you roll not die. Find the Probability of not rolling an even number

irina [24]

I think you mean roll a die. To do this you would find the number of non-even numbers and divide that number by the total amount of numbers on the die. On a normal six-sided die these numbers would be 1,3,and 5, so your probability of not rolling an even number would be 50%

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2 years ago