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3 years ago

-3(x+2)=16-x How do you solve this problem?

Mathematics

1 answer:

siniylev [52]3 years ago

8 0

Answer:

x=-11

Step-by-step explanation:

-3(x+2)=16-x

start with parenthesizes

-3*x=-3x

-3*2=-6

so you get

-3x-6=16-x

add the 6 to both sides

-3x=22-x

add x

-2x=22

divide by -2

x=-11

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Graph f(x) =-2x^+16x-30 by factoring to find the solutions, then find the coordinates of the vertex, and the axis of symmetry. I

fredd [130]

Answer:

Observe attached image

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

Axis of symmetry:

 $x =4$ 

Step-by-step explanation:

First factorize the function

$f (x) = -2x ^ 2 + 16x-30$

Take -2 as a common factor.

$-2(x ^ 2 -8x +15)$

Now factor the expression $x ^ 2 -8x +15$

You must find two numbers that when you add them, obtain the result -8 and multiplying those numbers results in 15.

These numbers are -5 and -3

Then we can factor the expression in the following way:

$f (x) = -2(x-5)(x-3)$

The quadratic function cuts the x-axis at x = 3 and at x = 5.

Now we find the coordinates of the vertex.

For a function of the form $ax ^ 2 + bx + c$ the x coordinate of its vertex is:

$x = \frac{-b}{2a}$

In the function $f (x) = -2x ^ 2 + 16x-30$

$a = -2\\b = 16\\c = 30$

Then the vertice is:

$x = \frac{-16}{2(-2)}\\\\x = 4$

The y coordinate of the symmetry axis is

$y = f (4) = -2 (4) ^ 2 +16 (4) -30\\\\y = 2$

The axis of symmetry is a vertical line that cuts the parabola in two equal halves. This axis of symmetry always passes through the vertex.

Then the axis of symmetry is the line

$x = 4$

The solutions and the vertice written as ordered pairs are:

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

6 0

3 years ago

What is the value of the expression below? (The expression is in the pic.) Brainliest!

Mkey [24]

Answer:

Step-by-step explanation:

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3 years ago

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Weekly demand for a product is normally distributed with a mean and standard deviation of 3,211 and 484 units, respectively. Wha

umka21 [38]

Answer:

The probability it is greater than or equal to 0.95 and less than or equal to 0.96

Step-by-step explanation:

In order to calculate the probability that weekly demand exceeds 4,044 we would have to calculate the z value as follows:

Z= (X-mean)/standard deviation

Z= (4044 - 3211)/484

Z=1.721

So, looking for standard normal distribution table 1.7 from row, we get values from 0.9554 till 0.9633, for column 0.02 it is 0.9573

Therefore, the probability it is greater than or equal to 0.95 and less than or equal to 0.96

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3 years ago

Carl is on the school track team. To prepare for an upcoming race, he plans to run 207 miles total over the next 31 days. Write

Mkey [24]

207 divide 31 = 6.7 miles per day
y= days
x= distance
y=6.7

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3 years ago

Ordered pair for -x+3y<-3

olga2289 [7]

Any (x, y) coordinates that fall in the red are applicable.

(5, -5)

(10, -8)

etc

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4 years ago