Which is the vertex of x2 + 10x = -17 (-5,-8) (5,8) (-5,8) (5,-8)

Mathematics

1 answer:

ad-work [718]3 years ago

4 0

Answer:

vertex = (- 5, - 8)

Step-by-step explanation:

Given a quadratic in standard form : ax² + bx + c = 0 : a ≠ 0

Then the x- coordinate of the vertex is

$x_{vertex}$ = - $\frac{b}{2a}$

Given x² + 10x = - 17 ( add 17 to both sides )

x² + 10x + 17 = 0 ← in standard form

with a = 1, b = 10, c = 17, then

$x_{vertex}$ = - $\frac{10}{2}$ = - 5

Substitute x = - 5 into the quadratic for the corresponding value of y

y = (- 5)² + 10(- 5) + 17 = 25 - 50 + 17 = - 8

Hence vertex = (- 5, - 8)

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Each cube in this solid figure is a unit cube. What is the volume of this solid figure?

padilas [110]

Answer:

The volume of this given solid figure is 18 cubic units.

Step-by-step explanation:

Here, given the volume of 1 small cube = 1 cubic units

Now, counting the total cubes in the given solid figure, we get

Number of cubes in base row = 10

Number of cubes in middle row = 6

Number of cubes in top most row = 2

So, the total number of cubes in the figure = 10 + 6 + 2 = 18 cubes

So, the volume of 18 cubes = 18 ( Volume of 1 small cube)

= 18 x (1 cubic units) = 18 cubic units

Hence, the volume of this given solid figure is 18 cubic units.

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3 years ago

If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalen

Alisiya [41]

The answer is 2(–4y + 13) – 3y = –29

Step 1: Express x from the second equation
Step 2: Substitute x into the first equation:

The system of equations is:
2x – 3y = –29
x + 4y = 13

Step 1:
The second equation is: x + 4y = 13
Rearrange it to get x: x = - 4y + 13

Step 2:
The first equation is: 2x – 3y = –29
The second equation is: x = - 4y + 13
Substitute x from the second equation into the first one:
2(-4y + 13) - 3y = -29

Therefore, the second choice is correct.

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3 years ago

Elena L [17]

Given:

The distance (in kilometers) Dora hiked is modeled as a function of time.

We need to determine the average rate of change in distance hiked, measured in kilometers per hour, between 8:30 am to 1:30 pm.

Average rate of change:

Let us write the time and the distance hiked in coordinates for the time 8:30 am and 1:30 pm.

Thus, the coordinates are (8.30, 4) and (1,12)

The average rate of change can be determined using the formula,

$m=\frac{y_2-y_1}{x_2-x_1}$