All categories

3 years ago

Help me please you don't need to show your work

Mathematics

1 answer:

marusya05 [52]3 years ago

3 0

Answer:

4.2 x 10^7

Step-by-step explanation:

4.1975 *10^7

You might be interested in

Solve 2x + 4y = -8 and 4x + 8y = 5 by elimination. Please show work on how to get the answer.

goldfiish [28.3K]

Answer:

No solution

Step-by-step explanation:

Given two equations are 2x+4y= -8 and 4x+8y= 5

These two lines are parallel They don't have a solution because they do not meet .

Multiply the first equation by 2 we get 4x+8y = -16

the other equation is 4x+8y= 5 clearly these two are parallel .

To prove by elimination method we have subtract those two equations we get 21≠0 which is not possible.

Therefore there is no solution to the given set of equation.

5 0

3 years ago

Given f(x)=x^2+2x+3 and g(x)=x+4/3 solve for f(g(x)) when x=2

Makovka662 [10]

Answer:

$\displaystyle\mathsf{f(g(2)) \:=\:\frac{187}{9}}$

Step-by-step explanation:

We are provided with the following functions:

f(x) = x² + 2x + 3

$\displaystyle\mathsf{ g(x)\:=\:x+\frac{4}{3} }$

The given problem also requires to find the Composition of Functions, f(g(x)) when x = 2.

The <u>Composition of Function</u> <em>f</em> with function <em>g</em> can be expressed as ( <em>f ° g </em>)(x) = f(g(x)). In solving for the composition of functions, we must first evaluate the <em>innermost</em> function, g(x), then use the output as an input for f(x).

<h2>Solve for f(g(x)) when x = 2:</h2><h3><u>Find g(x):</u></h3>

Starting with g(x), we will use x = 2 as an <u>input</u> value into the function:

$\displaystyle\mathsf{ g(x)\:=\:x+\frac{4}{3} }$

$\displaystyle\mathsf{ g(2)\:=\:(2)+\frac{4}{3} }$

Transform the first term, x = 2, into a fraction with a denominator of 3 to combine with 4/3:

$\displaystyle\mathsf{ g(2)\:=\:\frac{2\: \times\ 3}{3}+\frac{4}{3} }$

$\displaystyle\mathsf{ g(2)\:=\:\frac{6}{3}+\frac{4}{3}\:=\:\frac{6+4}{3}}$

$\displaystyle\mathsf{ g(2)\:=\:\frac{10}{3} }$

$\displaystyle\mathsf{Therefore,\:\: g(2)\:=\:\frac{10}{3} }$

Next, we will use $\displaystyle\mathsf{\frac{10}{3}}
$ as input for the function, f(x) = x² + 2x + 3:

f(x) = x² + 2x + 3

$\displaystyle\mathsf{f\Bigg (\frac{10}{3}\Bigg)\:=\:x^2 \:+ 2x\:+\:3}$

$\displaystyle\mathsf{f\Bigg (\frac{10}{3}\Bigg) \:=\:\Bigg (\frac{10}{3}\Bigg)^{2}\:+ 2\Bigg(\frac{10}{3}\Bigg) \:+\:3}$

Use the <u>Quotient-to-Power Rule of Exponents</u> onto the <em>leading term </em>(x²):

$\displaystyle\mathsf{Quotient-to-Power\:\:Rule:\:\: \Bigg(\frac{a}{b}\Bigg)^m\:=\:\frac{a^m}{b^m} }$

$\displaystyle\mathsf{f\Bigg (\frac{10}{3}\Bigg) \:=\:\Bigg (\frac{10\:^2}{3\:^2}\Bigg)\:+ 2\Bigg(\frac{10}{3}\Bigg) \:+\:3}$

Multiply the numerator (10) of the middle term by 2:

$\displaystyle\mathsf{f\Bigg (\frac{10}{3}\Bigg) \:=\:\Bigg (\frac{100}{9}\Bigg)\:+ \Bigg(\frac{20}{3}\Bigg) \:+\:\frac{3}{1}}$

Determine the <u>least common multiple (LCM)</u> of the denominators from the previous step: 9, 3, and 1 (which is 9).
Then, transform the denominators of 20/3 and 3/1 on the <u>right-hand side</u> of the equation into like-fractions:

$\displaystyle\mathsf{\frac{20}{3}\Rightarrow \:\frac{20\:\times\ 3}{3\:\times\ 3} =\:\frac{60}{9}}$

$\displaystyle\mathsf{\frac{3}{1}\Rightarrow \:\frac{3\:\times\ 9}{1\:\times\ 9} =\:\frac{27}{9}}$

Finally, add the three fractions on the right-hand side of the equation:

$\displaystyle\mathsf{f\Bigg (\frac{10}{3}\Bigg) \:=\:\Bigg (\frac{100}{9}\Bigg)\:+ \Bigg(\frac{60}{9}\Bigg) \:+\:\frac{27}{9}\:=\:\frac{187}{9}}$

<h2>Final Answer:</h2>

$\displaystyle\mathsf{Therefore,\:\:f(g(2)) \:=\:\frac{187}{9}.}$

<em>Keywords:</em>

Composition of functions

f o g

f (g(x))

____________________________________

Learn more about <u><em>Composition of Functions</em></u> here:

brainly.com/question/11388036

8 0

2 years ago

A line includes the points (-3, -8) and (9, 4). What is its equation in slope-intercept form?

liubo4ka [24]

Answer:

Answer is in the photo :)

Step-by-step explanation:

Hope it helped

8 0

3 years ago

The expression 1.5*1.09 models the housing costs, in thousands of dollars, for summer term t years since Chinedu applied to his

Alex777 [14]

Answer: Multiplicative rate of change in housing costs, for summer term t years since Chinedu applied to his college.

Step-by-step explanation:

Given: $1.5\times1.09^t$ models the housing costs, in thousands of dollars, for summer term t years since Chinedu applied to his college.

Since, the above expression is an exponential function. [ t is the exponent ]

The standard exponential function is given by :-

$y=Ab^x$ , A is the initial amount , b is the multiplicative rate of change with respect to time period x.

as compare to the given expression, we get b= 1.09, which is the multiplicative rate of change in the housing costs, for summer term t years since Chinedu applied to his college.

4 0

3 years ago

What is the surface area of 14cm 4cm and 6cm

daser333 [38]

The six sides would be:
2 sides of 14*4=56cm^2, 112 in total
2 sides of 4*6=24cm^2, 48 in total
2sides of 14*6=84cm^2, 168 in total
112+48+168=328cm^2

3 0

3 years ago