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4 years ago

For g(x) = x - 11, find x when g(x) = -5.

Mathematics

1 answer:

gregori [183]4 years ago

6 0

G(x) =-16 hope this helps

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A model of a baseball diamond is a square

Ilya [14]

Okay. So let’s break this down. We can solve this problem without a picture because it is a square. Therefore, all sides are the same. There are also four sides on a square. I have two ways to solve this problem.

One:
Divide 36 by 4 to know what each side is. 36/4 is 9. Since we are running from first to third, that is two sections of the field. Half of it. We would multiply 9 by 2. We get 18.

Two:
We know that from first to third is half the field. So we can do 36/0.5. This way, get 18

Answer: 18 inches

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3 years ago

3x to the 2nd power +4y to the 2nd power x=2 y=1 z=-3

Ostrovityanka [42]

Answer:

Step-by-step explanation:

3(2)^2 + 4(1)^2

3(4) + 4

12+4= 16

7 0

3 years ago

Read 2 more answers

4. The square root of 5 less than twice a number is 7. Find the number.

vladimir1956 [14]

Answer:

3.5

Step-by-step explanation:

we can divide that

the square root of 5
less than
twice a number is 7

as you see the first one is really easy

$\sqrt{5}$

the second one is < because it points to the lower number

the third one we have

twice a number is 7

let's say x is the number

so twice x is 7

twice means 2 times

so 2 times x is 7

$2*x=7\\\\\frac{1}{2}*2x=\frac{1}{2}*7\\\\x=3.5$

so the number is 3.5

5 0

4 years ago

How do you determine the horizontal stretch of f(x)=7^x?

avanturin [10]

You look at the coefficient of x.

If the parent function is f(x) = 7^x, there is no horizontal stretch.

If the parent function is f(x) = e^x, then your function is
.. f(x) = 7^x = (e^ln(7))^x = e^(ln(7)*x)
and the horizontal compression factor is ln(7) ≈ 1.946. (The stretch factor is 1/1.946 = 0.514.)

5 0

4 years ago

- f:R → R<br> f(x + 7) = 3x - 6<br> g(2x + 1) = x2-1<br> = (f-1og)(5) = ?

Murljashka [212]

Answer:

$f^{-1}\,\circ \,g(5) = 10$

Step-by-step explanation:

Let $f(x+7) = 3\cdot x -6$ and $g(2\cdot x +1) = x^{2}-1$ , we proceed to derive $f(x)$ and $g(x)$ by algebraic means:

(i) $f(x+7) = 3\cdot x -6$

1) $f(x+7) = 3\cdot x -6$ Given

2) $f(x+7) = 3\cdot (x+0) - 6$ Modulative property

3) $f(x+7) = 3\cdot [(x+7) +(-7)]-6$ Existence of additive inverse/Associative property

4) $f(x+7) = 3\cdot (x+7) +3\cdot (-7)-6$ Distributive property

5) $f(x+7) = 3\cdot (x+7) -21-6$ $a\cdot (-b) = -a\cdot b$

6) $f(x+7) = 3\cdot (x+7) -27$ Definition of subtraction

7) $f(x) = 3\cdot x - 27$ Composition of functions/Result

(ii) $g(2\cdot x + 1) = x^{2}-1$

1) $g(2\cdot x + 1) = x^{2}-1$ Given

2) $g(2\cdot x + 1) = (x\cdot 1)^{2}-1$ Modulative property

3) $g(2\cdot x +1) = [(2\cdot x)\cdot 2^{-1}]^{2}-1$ Existence of additive inverse/Commutative and associative properties

4) $g(2\cdot x +1) = (2\cdot x)^{2}\cdot 2^{-2}-1$ $a^{c}\cdot b^{c}$ / $(a^{b})^{c} = a^{b\cdot c}$

5) $g(2\cdot x + 1) = \frac{(2\cdot x)^{2}}{4}-1$ Definitions of division and power

6) $g(2\cdot x + 1) = \frac{(2\cdot x + 0)^{2}}{4} -1$ Modulative property

7) $g(2\cdot x +1) = \frac{[(2\cdot x + 1)+(-1)]^{2}}{4} -1$ Existence of additive inverse/Associative property

8) $g(2\cdot x + 1) = \frac{(2\cdot x + 1)^{2}+2\cdot (2\cdot x + 1)\cdot (-1)+(-1)^{2}}{4} -1$ Perfect square trinomial

9) $g(2\cdot x + 1) = \frac{(2\cdot x + 1)^{2}}{4}+\frac{[2\cdot (-1)]\cdot (2\cdot x + 1)}{4} +\frac{(-1)^{2}}{4}-1$ Addition of homogeneous fractions.

10) $g(x) = \frac{x^{2}}{4}-\frac{2\cdot x}{4} + \frac{1}{4}-1$ Composition of functions/ $a\cdot (-b) = -a\cdot b$

11) $g(x) = \frac{x^{2}}{4}-\frac{x}{2}-\frac{3}{4}$ Definitions of division and subtraction/Result

Now we find the inverse of $f(x)$ :

1) $f = 3\cdot x - 27$ Given

2) $f + 27 = (3\cdot x - 27)+27$ Compatibility with addition

3) $f+ 27 = 3\cdot x +[27+(-27)]$ Definition of substraction/Commutative and associative properties

4) $f+27 = 3\cdot x$ Existence of additive inverse/Modulative property

5) $(f+27) \cdot 3^{-1} = (3\cdot 3^{-1})\cdot x$ Compatibility with multiplication/Commutative and associative properties

6) $(f+27)\cdot 3^{-1} = x$ Existence of multiplicative inverse/Modulative property

7) $f^{-1} (x) = \frac{x+27}{3}$ Symmetrical property/Notation/Result

Finally, we proceed to calculate $f^{-1}\,\circ \, g (5)$ :

1) $f^{-1} (x) = \frac{x+27}{3}$ , $g(x) = \frac{x^{2}}{4}-\frac{x}{2}-\frac{3}{4}$ Given

2) $f^{-1}\,\circ\, g(x) = \frac{\frac{x^{2}}{4}-\frac{x}{2}-\frac{3}{4}+27}{3}$ Composition of functions

3) $f^{-1}\,\circ \,g(5) = 10$ Result

3 0

3 years ago