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3 years ago

Helpo pleasssse

Mathematics

1 answer:

Tcecarenko [31]3 years ago

5 0

Answer: The range is $\{y \in \mathbb{R}\ | \ y \le -6\}$

Explanation:

The parabola opens down, forming a "frowny face" in a way (just without the eyes). Or you can think of it as a hill or mountain. This means that the vertex (-3,-6) is at the top of that mountain. It's the highest point of that parabola.

The range is the set of all possible y values. We see that y = -6 is the largest it can get. So y = -6 or y is smaller than this. We would then write $y \le -6$ to describe all the possible y values.

Therefore, the range is $\{y \in \mathbb{R}\ | \ y \le -6\}$

This translates to "y is a real number such that y is -6 or smaller".

So the second answer you wrote is close, but you forgot the "or equal to" portion of the inequality sign.

See below for a visual example of what's going on.

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Can anyone help me with this problem??

Arlecino [84]

9514 1404 393

Answer:

(a) 4/3

(b) y -3 = 4/3(x -1)

(d) r = 5

Step-by-step explanation:

a) The slope is given by the slope formula:

m = (y2 -y1)/(x2 -x1)

m = (7 -3)/(4 -1) = 4/3

b) The radius is normal to the circle. The point-slope form of the equation for a line can be useful here:

y -k = m(x -h) . . . . . line with slope m through point (h, k)

For slope 4/3, the line through point (1, 3) will have the equation ...

y -3 = 4/3(x -1) . . . . point-slope equation of the normal

c) The tangent is perpendicular to the radius. It will have a slope that is the opposite reciprocal of the slope of the radius: -1/(4/3) = -3/4.

y -3 = -3/4(x -1) . . . . point-slope equation of the tangent

d) The radius can be found from the distance formula.

d = √((x2 -x1)² +(y2 -y1)²)

d = √((4 -1)² +(7 -3)²) = √(3² +4²) = √25 = 5

The radius of the circle is 5.

4 0

3 years ago

Use technology or a z-score table to answer the question.

Levart [38]

Answer: A:60%

Step-by-step explanation:

Since the scores for a golf tournament are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = scores for the tournament.

µ = mean score

σ = standard deviation

From the information given,

µ = 210

σ = 80

We want to find the probability percent of golfers that scored less than Ella. It is expressed as

P(x < 230)

z = (230 - 210)/80 = 0.25

Looking at the normal distribution table, the probability corresponding to the z score is 0.5987

Therefore, the percent of golfers that scored less than Ella is

0.5987 × 100 = 59.87

Approximately 60%

6 0

3 years ago

Simplify each expression.

umka21 [38]

$half\to\frac{1}{2}\\the\ sum\ of\ p\ and\ 2q\to p+2q\\increased\to"+"\\three-fourts\ q\to\frac{3}{4}q\\\\an\ expression:\\\\\frac{1}{2}(p+2q)+\frac{3}{4}q\ \ \ |use\ distributive\ property:a(b+c)=ab+ac\\\\=\frac{1}{2}(p)+\frac{1}{2}(2q)+\frac{3}{4}q=\frac{1}{2}p+q+\frac{3}{4}q=\huge\boxed{\frac{1}{2}p+1\frac{3}{4}q}$