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horrorfan [7]
2 years ago
13

For the function f(x) = −2(x + 3)2 − 1, identify the vertex, domain, and range. The vertex is (3, −1), the domain is all real nu

mbers, and the range is y ≥ −1. The vertex is (3, −1), the domain is all real numbers, and the range is y ≤ −1. The vertex is (−3, −1), the domain is all real numbers, and the range is y ≤ −1. The vertex is (−3, −1), the domain is all real numbers, and the range is y ≥ −1.
Mathematics
2 answers:
monitta2 years ago
7 0

Answer:

The vertex is (−3, −1), the domain is all real numbers, and the range is y ≤ −1

Step-by-step explanation:

f(x) = −2(x + 3)^2 − 1

The vertex form is

f(x) = a ( x-h) ^2 + k  where ( h,k) is the vertex

f(x) = −2(x - -3)^2 − 1

The vertex is ( -3,-1) is the vertex

The domain is the values that x can take and x can take all real numbers

The vertex is the maximum since a is negative so the range is  all values less than -1

y ≤ −1

nalin [4]2 years ago
3 0

Answer:

The vertex is (−3, −1), the domain is all real numbers, and the range is y ≤ −1

Step-by-step explanation:

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D. 3x+(-2)=2x+4

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There is 2 red cubes of -1 so it has to be in parentheses, not combined like letter C.

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2 years ago
Which point-slope equation represents a line that passes through (3, â€"2) with a slope of negative startfraction 4 over 5 endfr
Feliz [49]

The required equation of a line is y = 9/5 (4x - 12)

Given-

The point from which the line passes through is (3,2)

The slope of the given line m is -4/5.

Equation of the line

The linear equation of a line can be represented by a set of points on a graph using the equation of the line.

The standard form of the line passing through the point x₁, y₁

The slope m is given by,

m = (y - y₁) / (x - x₁)

Put the values of points and slope in the above equation, we get,

-4/5 = (y - 2) / (x - 3)

-4/5(x - 3) = y -2

-4x/5 + 12/5 = y - 2

-1/5 (4x - 12) + 2 = y

y = 9/5 (4x - 12)

The linear equation of a line can be represented by a set of points on a graph using the equation of the line. The following equation depicts a line that crosses (3, 2) and has a slope of -4/5: y = 9/5 (4x - 12)

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5 0
1 year ago
A sample of size 60 from one population of weights had a sample average of 10.4 lb. and a sample standard deviation of 2.7 lb. A
Olegator [25]

Answer:

z=  0.278

Step-by-step explanation:

Given data

n1= 60 ; n2 = 100

mean 1= x1`= 10.4;     mean 2= x2`= 9.7

standard deviation  1= s1= 2.7 pounds ;  standard deviation 2= s2 = 1.9 lb

We formulate our null and alternate hypothesis as

H0 = x`1- x`2 = 0 and H1 = x`1- x`2 ≠ 0 ( two sided)

We set level of significance α= 0.05

the test statistic to be used under H0 is

z = x1`- x2`/ √ s₁²/n₁ + s₂²/n₂

the critical region is z > ± 1.96

Computations

z= 10.4- 9.7/ √(2.7)²/60+( 1.9)²/ 100

z= 10.4- 9.7/ √ 7.29/60 + 3.61/100

z= 0.7/√ 0.1215+ 0.0361

z=0.7 /√0.1576

z= 0.7 (0.396988)

z= 0.2778= 0.278

Since the calculated value of z does not fall in the critical region so we accept the null hypothesis H0 = x`1- x`2 = 0  at 5 % significance level. In other words we conclude that the difference between mean scores is insignificant or merely due to chance.

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3 years ago
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