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grandymaker [24]
2 years ago
8

What is the center and radius of the circle with the equation x2 + y2 = 42

Mathematics
1 answer:
MakcuM [25]2 years ago
8 0
The sender is seven hundred ajdhfkandhf
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What is the result of substituting for y in the bottom equation<br> y=x+3<br> y=x^2+2x-4
8_murik_8 [283]

The solutions are (2.1925, 5.1925) and (-3.1925, -0.1925)

<em><u>Solution:</u></em>

Given that,

y = x + 3 ------- eqn 1\\\\y = x^2 + 2x - 4  ----- eqn 2

<em><u>We have to substitute eqn 1 in eqn 2</u></em>

x + 3 = x^2 + 2x - 4

\mathrm{Switch\:sides}\\\\x^2+2x-4=x+3\\\\\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}\\\\x^2+2x-4-3=x+3-3\\\\\mathrm{Simplify}\\\\x^2+2x-7=x\\\\\mathrm{Subtract\:}x\mathrm{\:from\:both\:sides}\\\\x^2+2x-7-x=x-x\\\\\mathrm{Simplify}\\\\x^2+x-7=0

\mathrm{Solve\:with\:the\:quadratic\:formula}\\\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\mathrm{For\:}\quad a=1,\:b=1,\:c=-7\\\\x =\frac{-1\pm \sqrt{1^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}

x = \frac{-1 \pm \sqrt{ 1 + 28}}{2}\\\\x = \frac{ -1 \pm \sqrt{29}}{2}

x = \frac{ -1 \pm 5.385 }{2}\\\\We\ have\ two\ solutions\\\\x = \frac{ -1 + 5.385 }{2}\\\\x = 2.1925

Also\\\\x = \frac{ -1 - 5.385 }{2}\\\\x = -3.1925

Substitute x = 2.1925 in eqn 1

y = 2.1925 + 3

y = 5.1925

Substitute x = -3.1925 in eqn 1

y = -3.1925 + 3

y = -0.1925

Thus the solutions are (2.1925, 5.1925) and (-3.1925, -0.1925)

6 0
3 years ago
Factor completely, then place the factors in the proper location on the grid.
Lyrx [107]
4(x+5y)(x-3y)
I don't know what you mean by placing the factors on the grid
6 0
2 years ago
5 The cost of an adult's ticket into a theme park is $a.
natta225 [31]

Answer:

<u>Total Cost (in dollars) = a + c</u>

Step-by-step explanation:

<u>Algebra</u>

When mathematics quantities are generalized into letters or variables, then we are dealing with algebra.

We are said the cost of an adult's ticket into a theme park is $a and a child's ticket costs $c. Since both quantities are unknown, we must treat them as variables and use the same logic procedure to solve the problem as if they were numbers.

The total cost for an adult and a child is the sum of both individual costs, thus

Total Cost (in dollars) = a + c

4 0
3 years ago
Pls help me on this question
Maksim231197 [3]
The answer is selections 1 and 4
7 0
2 years ago
What is the distance between the points (38, 30) and (14, 20)
Brums [2.3K]
Here's a formula to slove ur problem
√(x₁-x₂) +(y₁-y₂)
=√(38-14) +(30-20)
=√24+10
=√34
6 0
2 years ago
Read 2 more answers
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