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3 years ago

Find x, y, and z in the figure.

Mathematics

1 answer:

xz_007 [3.2K]3 years ago

4 0

Answer:

Since x + y + z = 180° and z = 90°, y + z = 90°

Thus x + y = z

Step-by-step explanation:

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Algebraic expression and identity 1)simplify the following (3a+b)3 +(3a-b)3

mylen [45]

Answer:

$(3a+b)^3+(3a-b)^3=54a^3+18ab^2$

Step-by-step explanation:

Given: $(3a+b)^3+(3a-b)^3$

Formula: $x^3+y^3=(x+y)(x^2-xy+y^2)$

$(x+y)^2=x^2+2xy+y^2$

$(x-y)^2=x^2-2xy+y^2$

$x\rightarrow 3a+b$

$y\rightarrow 3a-b$

$\Rightarrow (3a+b+3a-b)((3a+b)^2-(3a+b)(3a-b)+(3a-b)^2)$

$\Rightarrow (6a)(9a^2+b^2+6ab-9a^2+b^2+9a^2+b^2-6ab)$

$\Rightarrow (6a)(9a^2+3b^2)$

$\Rightarrow 54a^3+18ab^2$

5 0

3 years ago

Use f’( x ) = lim With h ---> 0 [f( x + h ) - f ( x )]/h to find the derivative at x for the given function. 5-x²

beks73 [17]

<h2>Answer:</h2>

The derivative of the function f(x) is:

$f'(x)=-2x$

<h2>Step-by-step explanation:</h2>

We are given a function f(x) as:

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

We have:

$f(x+h)=5-(x+h)^2\\\\i.e.\\\\f(x+h)=5-(x^2+h^2+2xh)$

( Since,

$(a+b)^2=a^2+b^2+2ab$ )

Hence, we get:

$f(x+h)=5-x^2-h^2-2xh$

Also, by using the definition of f'(x) i.e.

$f'(x)= \lim_{h \to 0} \dfrac{f(x+h)-f(x)}{h}$

Hence, on putting the value in the formula:

$f'(x)= \lim_{h \to 0} \dfrac{5-x^2-h^2-2xh-(5-x^2)}{h}\\\\\\f'(x)=\lim_{h \to 0} \dfrac{5-x^2-h^2-2xh-5+x^2}{h}\\\\i.e.\\\\f'(x)=\lim_{h \to 0} \dfrac{-h^2-2xh}{h}\\\\f'(x)=\lim_{h \to 0} \dfrac{-h^2}{h}+\dfrac{-2xh}{h}\\\\f'(x)=\lim_{h \to 0} -h-2x\\\\i.e.\ on\ putting\ the\ limit\ we\ obtain:\\\\f'(x)=-2x$

Hence, the derivative of the function f(x) is:

$f'(x)=-2x$

3 0

3 years ago

Read 2 more answers

Please help !!

nikdorinn [45]

The domain is all the numbers of which the inputs can be put. Here, we have a graph, which simplifies things. We just need to look at the x-values of the graph, or the horizontal line. The graph extends both negatively and positively. Thus since the graph extends both ways (right and left) forever, the answer would be D, or all real numbers.

5 0

3 years ago

Tim must read 2 books from a list of 7 recommended books for his summer reading program. In how many different ways can Tim choo

Marianna [84]

There are 21 ways Tim choose 2 books from the 7 recommended book

<em><u>Solution:</u></em>

Given that Tim must read 2 books from a list of 7 recommended books for his summer reading program

To find: different ways can Tim choose 2 books from the 7 recommended books

This is a combination problem

A combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected

<em><u>The formula for combinations is:</u></em>

$n C_{r}=\frac{n !}{r !(n-r) !}$

where n represents the number of items, and r represents the number of items being chosen at a time

Here we have to choose 2 books from 7 books

Therefore, n = 7 and r = 2

<em><u>Substituting values in above formula, we get</u></em>

$\begin{aligned}&7 C_{2}=\frac{7 !}{2 !(7-2) !}\\\\&7 C_{2}=\frac{7 !}{2 ! \times 5 !}\end{aligned}$

For a number n, the factorial of n can be written as,

$n !=n \times(n-1) \times(n-2) \dots \dots \times 2 \times 1$

Therefore, we get

$7 C_{2}=\frac{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 1 \times 5 \times 4 \times 3 \times 2 \times 1}\\\\7C_2 = 7 \times 3 = 21$

Thus there are 21 ways Tim choose 2 books from the 7 recommended book

7 0

3 years ago

What is the most efficient first step to isolate the variable term on one side of this equation?

stich3 [128]

Answer: subtract 5 from both sides

Explanation: get rid of the 5 before moving on to isolating the variable

3 0

3 years ago