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zhuklara [117]
3 years ago
10

Find the domain for the expression

Formula1" title=" \frac{2}{\sqrt{x+3}} " alt=" \frac{2}{\sqrt{x+3}} " align="absmiddle" class="latex-formula">
please explain
Mathematics
1 answer:
sashaice [31]3 years ago
3 0

Two rules come into play here:

1) We cannot divide by zero. Thux, x cannot = -3.

2) The domain of the square root function is (0, infinity). This is the dominant limiting factor.

x + 3 must be > 0. Thus, x must be > -3

The domain of this expression is (-3, infinity).

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What is the range of f(x)=4^x
Lerok [7]

Answer:

y>0

all positive real numbers

Step-by-step explanation:

the range is the output values

this will always be greater than 0

Range : y>0



7 0
3 years ago
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If (-9, 2) is on the graph of Flx), which point must be on the graph of the
dmitriy555 [2]

Answer:

(2, - 9 )

Step-by-step explanation:

Since 2 is the output when - 9 is input to f(x)

Then reversing the procedure, that is the inverse gives an output of - 9 for an input of 2.

(- 9, 2) is a point on the graph of f(x), then

(2, - 9) is a point on the graph o the inverse function f^{-1}(x)

7 0
3 years ago
Three-fourths of a number increased by one-half is equal to fourteen. Find the number.
ivanzaharov [21]

Three-fourths of a number increased by one-half

= 3/4 x + 1/2

So three-fourths of a number increased by one-half is equal to fourteen:

3/4 x + 1/2 = 14

Multiply both sides by 4

3x + 2 = 56

Subtract 2 from both sides

3x = 54

Divide both sides by 3

x = 18

Answer: The number is 18

8 0
3 years ago
Read 2 more answers
Tonya is twice kevins age
weqwewe [10]
Can you please complete your question

7 0
3 years ago
I need an answer ASAP!!! Tyyyy
patriot [66]

Part A

x = amount of money she starts with

(4/9)x = cost of the dress

(5/9)x = amount of money leftover after buying the dress

note that 4/9 and 5/9 add to 1 to represent 100% of her money

(3/4)*(5/9)x = (15/36)x = (5/12)x = amount spent on shoes

We see that she spent 5/12 of her original amount of money on shoes.

-----------------------

We can look at a more concrete example if the previous section does not make sense.

Let's multiply the denominators 9 and 4 to get 9*4 = 36. Doing this trick will mean that the later steps won't involve decimal values.

Let's say she starts off with $36

Multiply that with 4/9 to get (4/9)*36 = 16. So in this hypothetical situation, the dress costs $16 and she's left with 36-16 = 20 dollars.

Multiply that 20 by 3/4 to get (3/4)*20 = 15

In this situation, the shoes cost $15

We'll then divide the cost of the shoes (15) over the original amount of money she started with (36)

15/36 = (3*5)/(3*12) = 5/12

-----------------------

<h3>Answer:  5/12</h3>

=======================================================

Part B

From the first section in part A, we found that:

  • (4/9)x = amount of money spent on the dress
  • (5/12)x = amount of money spent on shoes

Add those two expressions

(4/9)x + (5/12)x = (16/36)x + (15/36)x = (31/36)x

This indicates that buying the dress and shoes will cost (31/36)x dollars, where x is the original amount of money Jing has to start with.

The amount left over is (5/36)x because 5/36 adds with 31/36 to get 1.

Take 1/3 of this to get:

(1/3)*(5/36)x = (5/108)x

Then set this equal to 18 and solve for x

(5/108)x = 18

5x = 18*108

5x = 1944

x = 1944/5

x = 388.80

--------------------

Let's check the answer

If she starts with 388.80 dollars, then the dress costs (4/9)*388.80 = 172.80

She's left with 388.80 - 172.80 = 216 dollars after buying the dress.

She then spends the remaining 3/4 of that on shoes. So (3/4)*216 = 162 dollars is spent on the shoes.

Jing now has 216 - 162 = 54 dollars left over.

1/3 of which is spent on the shoe bag, meaning it costs (1/3)*54 = 18 dollars

This confirms our answer.

--------------------

<h3>Answer:  $388.80</h3>
8 0
2 years ago
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