A culture of bacteria has an initial population of 7100 bacteria and doubles every 2

H(x) = ax^2 +1<br> Find the value of a when h(-2) = 21.

blagie [28]

Answer:

$a = 5$

Step-by-step explanation:

Solving $h(-2) = 21$ :

$h(-2) = 21 \\ a(-2)^2 +1 = 21 \\ a(4) +1 = 21 \\ 4a +1 = 21 \\ 4a +1 -1 = 21 -1 \\ 4a = 20 \\ \frac{4a}{4} = \frac{20}{4} \\ a = 5$

4 0

2 years ago

What is the height of the triangle? 12 units 24 units 36 units 72 units.

konstantin123 [22]

Height of the triangle is the altitude of the triangle and which is drawn perpendicular from the vertex of the triangle to the opposite side. The height of the tringle is 24 units. Hence option 2 is the correct option.

<h3>Given information-</h3>

The triangle for the given problem is shown in the image below.

Form the figure the length of the each side is $16 \sqrt{3}$ units.

As all the sides are equal thus the $\Delta MNO$ is a equilateral triangle in which the height of the divides the triangle into two equal part of the length $8\sqrt{3}$ at point <em>R.</em>

<h3>Height of the triangle-</h3>

Height of the triangle is the altitude of the triangle and which is drawn perpendicular from the vertex of the triangle to the opposite side.

Now in the $\Delta MRN$ , the length of the hypotenuse is $16 \sqrt{3}$ units and the length of the base is $8\sqrt{3}$ units. Let <em>h </em>is the height of the triangle thus by the Pythagoras theorem,

$(16\sqrt{3})^2 =(8\sqrt{3})^2+h^2$

Solve for <em>h,</em>

<em />

<em /> $\begin{aligned}h^2 &=(16\sqrt{3})^2 -(8\sqrt{3})^2\\h^2 &=16\times16\times3 -8\times8\times3\\h^2 &=576\\h &=\sqrt{576}\\h &=24\\\end$ <em />

<em />

Thus the height of the tringle is 24 units. Hence option 2 is the correct option.

Learn more about the equilateral triangle here;

brainly.com/question/4268382

5 0

2 years ago

Someone please help me

Setler79 [48]

So find the area of each shape and add them.
30+30+30+30+36=156
Triangle A= 1/2xLxH
Square A= LxH

6 0

3 years ago

Given the function f(x) = 4x + 1, EXPLAIN and show how to find the average rate of change between x = 1 and x = 3.

11Alexandr11 [23.1K]

The average rate of change is calculated as the slope of the line between the two points on the graph. Since at x = 1, y = -3, and at x = 3, y = 1, these are the two points which we calculate the slope from. Using the formula

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

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

m = 4/2

m = 2

Therefore the slope, or the average rate of change, between these points is 2.

4 0

3 years ago

Read 2 more answers

Plz answer this correctly to get more points

crimeas [40]

Answer: x = 30°

Concept:

Here, we need to know the idea of an isosceles triangle and the vertical angle theorem.

An <u>isosceles triangle</u> is a triangle that has any two of its sides equal to each other. Also, the angles opposite these equal sides are equal, which is basically the base angles.

The <u>vertical angle theorem</u> states that two vertical angles formed when two lines intersect each other are always equal to each other.

Solve:

<u>Find the other base angle of the isosceles triangle.</u>

Since there are two equal sides, we know that this is an isosceles triangle.

Since the definition said that the base angles are equal, the other base angle would also be x.

<u>Find the value of x</u>

According to the vertical angle theorem, two vertical angles formed by intersection are equal.

Just as angle x and 30°, are vertical angles formed by intersection, therefore, $\boxed{x=30}$

Hope this helps!! :)

Please let me know if you have any questions

8 0

3 years ago