Pls help algebra 2 mmmmmm

KATRIN_1 [288]

Answer:

The value of x is 12 feet

Step-by-step explanation:

The shape in question is a composite shape. We can see that x is both the base of the triangle and the breadth of the rectangle.

To get the area of the shape, we will have to add the area of the rectangle to the area of the triangle.

Area of rectangle = length X breadth

Area of triangle = 1/2 base X height.

However, to calculate the area of the triangle, we need to find its height first.

The next step is to get the height of the triangle. Observing the shape properly, we can see that we can get the height by subtracting the length of the rectangle from the overall length of the shape.

Height of triangle = 16 ft - 10 ft = 6 ft

recall area = 156 square feet.

We now have most of our missing dimensions

We can now set up an equation as follows:

$(10 \times x) +0.5 \times x \times 6 = 156$

$10x +3x=156\\13x=156\\x=12 feet$

Therefore the value of x is 12 feet

8 0

4 years ago

Consider functions of the form f(x)=a^x for various values of a. In particular, choose a sequence of values of a that converges

sleet_krkn [62]

Answer:

A. As "a"⇒e, the function f(x)=aˣ tends to be its derivative.

Step-by-step explanation:

A. To show the stretched relation between the fact that "a"⇒e and the derivatives of the function, let´s differentiate f(x) without a value for "a" (leaving it as a constant):

$f(x)=a^{x}\\ f'(x)=a^xln(a)$

The process will help us to understand what is happening, at first we rewrite the function:

$f(x)=a^x\\ f(x)=e^{ln(a^x)}\\ f(x)=e^{xln(a)}\\$

And then, we use the chain rule to differentiate:

$f'(x)=e^{xln(a)}ln(a)\\ f'(x)=a^xln(a)$

Notice the only difference between f(x) and its derivative is the new factor ln(a). But we know that ln(e)=1, this tell us that as "a"⇒e, ln(a)⇒1 (because ln(x) is a continuous function in (0,∞) ) and as a consequence f'(x)⇒f(x).

In the graph that is attached it´s shown that the functions follows this inequality (the segmented lines are the derivatives):

if a<e<b, then aˣln(a) < aˣ < eˣ < bˣ < bˣln(b) (and below we explain why this happen)

Considering that ln(a) is a growing function and ln(e)=1, we have:

if a<e<b, then ln(a)< 1 <ln(b)

if a<e, then aˣln(a)<aˣ

if e<b, then bˣ<bˣln(b)

And because eˣ is defined to be the same as its derivative, the cases above results in the following

if a<e<b, then aˣ < eˣ < bˣ (because this function is also a growing function as "a" and "b" gets closer to e)

if a<e, then aˣln(a)<aˣ<eˣ ( f'(x)<f(x) )

if e<b, then eˣ<bˣ<bˣln(b) ( f(x)<f'(x) )

but as "a"⇒e, the difference between f(x) and f'(x) begin to decrease until it gets zero (when a=e)

3 0

4 years ago

if you flip a coin and roll a 6-sided die, what is the probability that you will flip a tails and roll more than a 4

Nutka1998 [239]

Answer:

12

Step-by-step explanation:

When you a coin flips there are 2 possible outcomes which are either heads, or tailer, when you roll a die there are six outcomes, one to six. Putting these together means you have a total of 2×6=12 outcomes

4 0

3 years ago

Whats is the 39th triangular number

aleksandr82 [10.1K]

Answer:

The 39th triangle number is 780

7 0

3 years ago

The sum of all digits of some number is 210. The number is always divisible by:

AlekseyPX

Answer:

2

Step-by-step explanation:

so so that you could get both halves, we had to divide by two then I got 105 +105 meaning 210 could be divided by 2

4 0

3 years ago