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Serhud [2]
2 years ago
7

Give the steps you would use to find the solutions to the system of equations, then name the solutions. you may solve this graph

ically or algebraically
y=2x^2-6x+1
y=-x+1
Mathematics
1 answer:
balu736 [363]2 years ago
7 0

We have found one solution to the equations that the two equations intersect at the point (2.5,-1.5).

<h3>What are equations?</h3>

The equation is actually a relationship between the numbers and the variables. In this question we have two equations y=2x²-6x+1 and y=-x+1 so by equating them we can find the value of x which is the intersecting point of the two lines.

Now the solution of the equations:-

y=2x²-6x+1

y=-x+1

2x²-6x+1 = -x+1

2x²=5x

x=5/2=2.5

y=-2.5+1=-1.5

Hence the one solution to the equations that the two equations intersect at the point (2.5,-1.5).

To know more about equations follow

brainly.com/question/2972832

#SPJ1

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krek1111 [17]

First, let's declare a variable

x = # of students

Now, let's create an equation to model the problem.

x * 0.273 = 125

Divide both sides by 0.273

x = 457.8 = 458 students.

Note, I rounded to the nearest whole number.

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3 years ago
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91. Jack can read 45 pages of his book in one and a
Digiron [165]

Answer:

10 hours

Step-by-step explanation:

45 pages per 1 hour and 30 minutes,  or 60 min +30 min =90 min

90 minutes / 45 pages has to be equal to an equivalent fraction where we have 300 pages

90 minutes /45 pages = ? minutes / 300 pages , multiply both sides by 300

? minutes = 90*300/45 = 600 minutes

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3 years ago
Find the longer leg of the triangle.
Paha777 [63]

Answer:

Choice A. 3.

Step-by-step explanation:

The triangle in question is a right triangle.

  • The length of the hypotenuse (the side opposite to the right angle) is given.
  • The measure of one of the acute angle is also given.

As a result, the length of both legs can be found directly using the sine function and the cosine function.

Let \text{Opposite} denotes the length of the side opposite to the 30^{\circ} acute angle, and \text{Adjacent} be the length of the side next to this 30^{\circ} acute angle.

\displaystyle \begin{aligned}\text{Opposite} &= \text{Hypotenuse} \times \sin{30^{\circ}}\\ &=2\sqrt{3}\times \frac{1}{2} \\&= \sqrt{3}\end{aligned}.

Similarly,

\displaystyle \begin{aligned}\text{Adjacent} &= \text{Hypotenuse} \times \cos{30^{\circ}}\\ &=2\sqrt{3}\times \frac{\sqrt{3}}{2} \\&= 3\end{aligned}.

The longer leg in this case is the one adjacent to the 30^{\circ} acute angle. The answer will be 3.

There's a shortcut to the answer. Notice that \sin{30^{\circ}} < \cos{30^{\circ}}. The cosine of an acute angle is directly related to the adjacent leg. In other words, the leg adjacent to the 30^{\circ} angle will be the longer leg. There will be no need to find the length of the opposite leg.

Does this relationship \sin{\theta} < \cos{\theta} holds for all acute angles? (That is, 0^{\circ} < \theta?) It turns out that:

  • \sin{\theta} < \cos{\theta} if 0^{\circ} < \theta;
  • \sin{\theta} > \cos{\theta} if 45^{\circ} < \theta;
  • \sin{\theta} = \cos{\theta} if \theta = 45^{\circ}.

4 0
3 years ago
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If ORBIT is coded BEOVG, then how is PLANET coded? /
arlik [135]

Answer:

1. CYNARG

Step-by-step explanation:

This a example of Caesar's Cipher, in which each letter in the original word leads to a ciphered letter according to the following equation:

C = (P + o) \text{mod} 26

In which C is the index of the Ciphered letter in the alphabet, P is the index of the original letter and o is the offset.

Finding the offset:

O is coded B

O is the 15th letter in the alphabet, so P = 15.

B is the 2nd letter in the alphabet, so C = 2

C = (P + o) \text{mod} 26

2 = (15 + o) \text{mod} 26

|o = |2-15| \text{mod} 26

o = 13

So

C = (P + 13) \text{mod} 26

PLANET:

P

P is the 16th letter in the alphabet.

C = (16 + 13) \text{mod} 26 = 3

So P is coded C.

L

L is the 12th letter in the alphabet:

C = (12 + 13) \text{mod} 26 = 25

L is coded Y(25th letter in the alphabet)

A

A is the 1st letter in the alphabet

C = (1 + 13) \text{mod} 26 = 14

A is coded N

N

N is the 14th letter in the alphabet

C = (14 + 13) \text{mod} 26 = 1

N is coded A

E

E is the 5th letter in the alphabet

C = (5 + 13) \text{mod} 26 = 18

E is coded R

So the correct answer is:

1. CYNARG

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geniusboy [140]

Answer:

A square

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I'm pretty sure its a square

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