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xeze [42]
3 years ago
7

Determine the axis of symmetry for the function f(x) = −4(x + 7)2 − 3.

Mathematics
1 answer:
spayn [35]3 years ago
6 0

Answer:

  x = -7

Step-by-step explanation:

The vertex form of this equation tells us it is a downward-opening parabola with its vertex at (-7, -3). The line of symmetry is the vertical line through the vertex: x = -7.

___

Vertex form is ...

  y = a(x -h) +k

where a is the vertical expansion factor, and (h, k) is the vertex. When a < 0, the parabola opens downward. When a > 0, it opens upward. (When a=0, the "parabola" is a horizontal line at y=k.)

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Suppose the line of best fit for some data points has a slope of 1.885. If the mean of the x-coordinates of the data points is 3
larisa86 [58]

Step-by-step Answer:

One of the properties of a least-squares regression line (line of best fit) is that the line always passes through the point (xbar, ybar).

Assuming the given "line of best fit" is a least-squares line, then we are given

a slope m=1.885 passing through (x0,y0)=(3.448,12.318).

Applying the standard point-slope formula:

(y-y0) = m (x-x0)

we get

y-12.318 = 1.885(x-3.448)

Expand and simplify,

y=1.885x -1.885*3.448 + 12.318, or

y=1.885(x) + 5.81852

(numbers to be rounded as precision dictates).

5 0
3 years ago
Read 2 more answers
The question is in the picture.
dangina [55]
<h2><u>Part A:</u></h2>

Let's denote no of seats in first row with r1 , second row with r2.....and so on.

r1=5

Since next row will have 10 additional row each time when we move to next row,

So,

r2=5+10=15

r3=15+10=25

<u>Using the terms r1,r2 and r3 , we can find explicit formula</u>

r1=5=5+0=5+0×10=5+(1-1)×10

r2=15=5+10=5+(2-1)×10

r3=25=5+20=5+(3-1)×10

<u>So for nth row,</u>

rn=5+(n-1)×10

Since 5=r1 and 10=common difference (d)

rn=r1+(n-1)d

Since 'a' is a convention term for 1st term,

<h3><u>⇒</u><u>rn=a+(n-1)d</u></h3>

which is an explicit formula to find no of seats in any given row.

<h2><u>Part B:</u></h2>

Using above explicit formula, we can calculate no of seats in 7th row,

r7=5+(7-1)×10

r7=5+(7-1)×10 =5+6×10

r7=5+(7-1)×10 =5+6×10 =65

which is the no of seats in 7th row.

8 0
3 years ago
A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past
Volgvan

Answer: We reject the null hypothesis, and we use Normal distribution for the test.

Step-by-step explanation:

Since we have given that

We claim that

Null hypothesis : H_0:\mu\geq 50000

Alternate hypothesis : H_1:\mu

There  is 5% level of significance.

\bar{X}=46800\\\\\sigma=9800\\\\n=29

So, the test statistic would be

z=\dfrac{\bar{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\\\z=\dfrac{46800-50000}{\dfrac{9800}{\sqrt{29}}}\\\\z=-1.75

Since alternate hypothesis is left tailed test.

So, p-value = P(z≤-2.31)=0.0401

And the P-value =0.0401 is less than the given level of significance i.e. 5% 0.05.

So, we reject the null hypothesis, and we use Normal distribution for the test.

4 0
3 years ago
How can one variable equations have more than one solution in some cases and no solutions in others?
yawa3891 [41]

Answer:A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line).

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
What is the simplified expression for Negative 3 (2 x minus y) + 2 y + 2 (x + y)?
Lana71 [14]

Answer:

7y - 4x

Step-by-step explanation:

-3 (2x-y)+2y+2(x+y)\\

Step 1:  Open the brackets

= -6x+3y +2y +2(x+y)\\=-6x +3y + 2y +2x + 2y

Step 2: Bring the similar variables together

=-6x +2x \ +3y + 2y + 2y

Step 3: Simplify by adding/subtracting the coefficients of the similar variables

= - 4x +7y

Step 4: Rearrange as required.

5 0
3 years ago
Read 2 more answers
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