A string of decorative lights is 28 feet long the first light on the string is 16 inches from the plug if the lights on the string are spaced 4 inches apart how many lights are there on the string

Answers

Answer 1

Answer: 28*12=336
336-16=320
320/4=80
there are 80 lights on the string

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right triangle has an angle whose measure is 35 degrees what is the measure of the third angle in Triangle

Answers

The third angle is 55 degrees
90+35=125
125-35=55

Write and equation in standard form for a line that is (a) parallel (b) perpendicular to the line with an equation of y= 3x - 5 that passes through the point (5,8)

Answers

Answer:

(a) 3x -y = 7

(b) x +3y = 29

Step-by-step explanation:

(a) The standard form of the given line is ...

3x -y = 5

The parallel line will have a constant on the right that makes it go through (5, 8), so it will be ...

3x -y = 3(5) -(8)

3x -y = 7

(b) The perpendicular line will have coefficients for x and y swapped and one of them negated. Again, the constant is chosen to make it go through (5, 8).

x + 3y = (5) +3(8)

x + 3y = 29

I am a number between 60 and a 100 my ones digit is this then my tens digit I am a prime number the some of my digit is 8 what number am I

Answers

So a prime number and it's prime so

8_...

between 80 and 89

8_...

between 80 and 89

Graph of function f of x equals negative x squared plus 8 multiplied by x minus 15Function 2

f(x) = −x2 + 2x − 3

Function ____ has the larger maximum.
(Put 1 or 2 in the blank space)

Numerical Answers Expected!

Answers

$y=- x^(2) +8x-15$
written in vertex form, we have,
$y=-(x-4)^(2) +1$ ,
i.e. vertex = (4, 1) and maximum value at y = 1.

$y=- x^(2) +2x-3$
written in vertex form, we have,
$y=-(x-1)^(2) -2$ ,
i.e. vertex = (1, -2) and maximum value at y = -2.

Therefore, $y=- x^(2) +8x-15$ has the larger maximum.

Final answer:

To determine which function has the larger maximum, we find the vertex of each function's graph and compare the y-values. Function 1 has the larger maximum with a value of 9.25.

Explanation:

In order to determine which function has the larger maximum value, we need to find the vertex of each function's graph. The vertex of a quadratic function in the form f(x) = ax^2 + bx + c can be found using the formula x = -b / (2a). For the first function, f(x) = -x^2 + 8x - 15, a = -1, b = 8, and c = -15. Plugging these values into the formula, we get x = -8 / (2*-1) = 4.5. Substituting this value of x back into the function gives us f(4.5) = -4.5^2 + 8(4.5) - 15 = 9.25.

For the second function, f(x) = -x^2 + 2x - 3, a = -1, b = 2, and c = -3. Using the formula, we find x = -2 / (2*-1) = 1. Substituting this value back into the function gives us f(1) = -1^2 + 2(1) - 3 = -2.

Comparing the maximum values of the two functions, we see that f(x) = -x^2 + 8x - 15 (Function 1) has a larger maximum value of 9.25.

Learn more about Function maximum here:

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