Answer:
- The center (2, 2.5), radius
/ 2
Step-by-step explanation:
<u>The standard form of the equation of a circle is: </u>
- ( x - h )^2 + ( y - k )^2 = r^2, where ( h, k ) is the center and r is the radius
<u>Rewrite the given equation in the standard form:</u>
- 2x^2 + 2y^2 - 8x + 10y + 2 = 0
- x^2 - 4x + y^2 + 5y = -1
- x^2 - 4x + 2^2 + y^2 + 5y + (5/2)^2 = -1 + 4 + 25/4
- (x - 2)^2 + (y + 2.5)^2 = 37/4
<u>The center is:</u>
<u>And radius is:</u>
- <u /> / 2
From my research, the original system of equations contain the following equations:
<span>2x − y = −4
3x + 5y = 59
where obtained solution is x = 3
Among the choices, it is easier to substitute </span><span>3x + 5y = 59 with one of the choices to see if they yield the same solution set. From trial-and-error, the equation that can replace the original equation is " 13x = 39 ". Among the choices, it is the 4th choice.</span>
Answer:
x=6
Step-by-step explanation:
4x+5=6x-7
4x-6x=-7-5
-2x=-12
x=-12/-2
x=6
Answer:
Step-by-step explanation:
Hello!
X: Cholesterol level of a woman aged 30-39. (mg/dl)
This variable has an approximately normal distribution with mean μ= 190.14 mg/dl
1. You need to find the corresponding Z-value that corresponds to the top 9.3% of the distribution, i.e. is the value of the standard normal distribution that has above it 0.093 of the distribution and below it is 0.907, symbolically:
P(Z≥z₀)= 0.093
-*or*-
P(Z≤z₀)= 0.907
Since the Z-table shows accumulative probabilities P(Z<Z₁₋α) I'll work with the second expression:
P(Z≤z₀)= 0.907
Now all you have to do is look for the given probability in the body of the table and reach the margins to obtain the corresponding Z value. The first column gives you the integer and first decimal value and the first row gives you the second decimal value:
z₀= 1.323
2.
Using the Z value from 1., the mean Cholesterol level (μ= 190.14 mg/dl) and the Medical guideline that indicates that 9.3% of the women have levels above 240 mg/dl you can clear the standard deviation of the distribution from the Z-formula:
Z= (X- μ)/δ ~N(0;1)
Z= (X- μ)/δ
Z*δ= X- μ
δ=(X- μ)/Z
δ=(240-190.14)/1.323
δ= 37.687 ≅ 37.7 mg/dl
I hope it helps!
Answer:
- The next term of the sequence is represented by the point (5, –64)
Step-by-step explanation:
<u>Note:</u> <em>The first point should be (1, - 4)</em>
According to the points, the sequence is:
- t₁ = - 4, t₂ = 8, t₃ = - 16, t₄ = 32
or
We can observe it is a geometric sequence with common ratio of - 2, as:
- r = 32/ - 16 = - 16/8 = 8/ - 4 = - 2
The following term is:
- t₅ = t₄*r = 32*(- 2) = - 64
The coordinates of same term are:
As we see the correct answer choice is D.
