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nirvana33 [79]
2 years ago
8

Substitution method x=2y 2x+5y=4

Mathematics
1 answer:
Dvinal [7]2 years ago
6 0

Answer:

y=4/9

Step-by-step explanation:

Substitute 2y into the x

2(2y)+5y=4

4y+5y=4

9y=4

y=4/9

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Two functions are represented below. Which function has a domain that contains the domain of the other function as a
Nikitich [7]

Answer:

\\ h(x) = x-2\;contains\;the\;domain\;of\;function\;f(x) = -log(x-2)-3

Step-by-step explanation:

The domain of a function contains all possible values that it can take.

We can analyze the function:

\\ f(x) = -log(x-2)-3 [1]

And we can see that there are three functions in [1]:

h(x) = x-2 and g(x) = -log(x) - 3, and

\\ f(x) = g(h(x)) or \\ f(x) = -log(x-2)-3.

This operation is called <em>function composition</em>.<em> </em>

For every <em>x</em>, function <em>h(x)</em> can take any value, so the domain (all possible values this function can take) is \\ -\infty\;to\;\infty (all real numbers).

However, function <em>g(x)</em> is restricted to <em>positive values</em> only, since <em>log</em> function is <em>not</em> defined for <em>negative numbers</em> and 0.

Therefore, domain for <em>f(x)</em> are <em>restricted</em> to those ones that comply with the above restriction (x > 0). So, for

\\ f(x) = -log(x-2) - 3

Possible values are those which:

\\ x - 2 > 0 or \\ x > 2

In words, the domain of <em>f(x)</em> are all values greater than 2 (but not equal to 2) or all positive real values greater than 2.

Then, the function <em>f(x)</em> has a domain that is a <em>subset</em> of function <em>h(x)</em>, that is, in function <em>h(x) = </em>x - 2, <em>x</em> can takes any possible value from -(<em>infinity</em>) to <em>infinity</em>, whereas function <em>f(x)</em> can <em>only</em> takes those values greater than two (but not equal 2) to <em>infinity</em>, which makes the domain of <em>f(x)</em>  a subset of the possible values of function <em>h(x)</em>.

8 0
3 years ago
an adult elephant that is 10ft tall casts a shadow that is 15ft long. find the length of the shadow that a 8ft telephone booth c
nadya68 [22]

Answer:

The length of the shadow the telephone booth is <u>12 ft</u>.

Step-by-step explanation:

Given:

An adult elephant that is 10 ft tall casts a shadow that is 15 ft long.

The length of the telephone booth is 8 ft.

Now, to find the length of the shadow the telephone booth casts.

Let the length of the shadow the telephone booth be x.

As given, an adult elephant that is 10 ft tall casts a shadow that is 15 ft long.

So, 10 ft is equivalent to 15 ft.

Thus, 8 ft is equivalent to x.

Now, to get the length of the shadow of the booth we get cross multiplication method:

\frac{10}{15} =\frac{8}{x}

<em>By cross multiplying we get:</em>

10x=120

<em>Dividing both sides by 10 we get:</em>

x=12.

Therefore, the length of the shadow the telephone booth is 12 ft.

3 0
3 years ago
The original price of a scarf was $16. During a store-closing sale, a shopper saved $12 on the scarf. What percentage discount d
Ksivusya [100]
75%
____________________
4 0
2 years ago
Read 2 more answers
Find the volume of each of the following cubes. a. s = 7 kilometers b. s = 11 yards
nadya68 [22]

Answer:

Part 1) V=343\ km^{3}

Part 2) V=1,331\ yd^{3}

Step-by-step explanation:

we know that

The volume of a cube is equal to

V=s^{3}

where

s is the length of the cube

Part 1)

we have

s=7\ km

substitute in the formula

V=7^{3}

V=343\ km^{3}

Part 2)

we have

s=11\ yd

substitute in the formula

V=11^{3}

V=1,331\ yd^{3}


6 0
3 years ago
Read 2 more answers
Please help!!! I need this done today!!
Kryger [21]

Answer:

1) distance travelled = 75mi

time taken = 3 hrs.

speed = distance/time

= 75/3 = 25 mi/hr.

now, if time = 1.6 hrs.

Distance = speed x time

= 25 x 1.6 = 40.0 mi

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

2) earning for 8 hrs. of work = $120.

therefore, rate of earning per hr. = 120/8 = $15/hr.

so, earning in 11 hrs. = 15 x 11 = $165


8 0
3 years ago
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