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3 years ago

Evaluate the expression when m=5 and n=8. 4m-7 4n-3m 6m/n-3

1 answer:

3 0

4m - 7
4 * 5 - 7
20 - 7
First answer: 13
4n-3m
4*8 - 3*5
32-15
Second answer: 17
6m/n-3
6*5/8-3
30/8-3
3.75-3
Third answer: 0.75

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The graphs of three functions are shown.

satela [25.4K]

Answer:

The square root and quadratic function share a y-intercept.
The range of the square root and absolute value function are the same.

Step-by-step explanation:

Y-intercepts are the same when the curves meet the y-axis at the same point. That is true of the root and quadratic functions.

X-intercepts are the same when the curves meet the x-axis at the same point. None of these functions share an x-intercept.

The ranges of the functions are the same when they have the same vertical extent. The range of the quadratic is different from the range of the other two functions.

The absolute value and root functions have the same minimum (lower end of their range). That is the same as the maximum of the quadratic function.

The statements that match the graphs are ...

The square root and quadratic function share a y-intercept.
The range of the square root and absolute value function are the same.

7 0

3 years ago

Read 2 more answers

Jane is 5 times older than her sister. In 3 years, Jane’s sister will be 1/4 her age. Find the ages now

Korolek [52]

The present age of Jane is 45 years old and present age of her sister is 9 years old

Solution:

Let the present age of Jane be "x"

Let the present age of her sister be "y"

Jane is 5 times older than her sister

present age of Jane = 5(present age of her sister)

x = 5y ---------- eqn 1

In 3 years, Jane’s sister will be 1/4 her age

Age of sister after 3 years = 3 + y

Age of jane after 3 years = 3 + x

Age of sister after 3 years = 1/4(age of jane after 3 years)

$3 + y = \frac{1}{4}(3 + x)$

Substitute eqn 1 in above equation

$3 + y = \frac{1}{4}(3 + 5y)\\\\12 + 4y = 3 + 5y\\\\5y - 4y = 12 - 3\\\\y = 9$

Substitute y = 9 in eqn 1

x = 5(9)

x = 45

Thus present age of Jane is 45 years old and present age of her sister is 9 years old

3 0

3 years ago

What’s the answer to 4cx-b=5b when solving for x?

rusak2 [61]

Answer:

x = 3b

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

5 0

3 years ago

Write out the first four terms of the series to show how the series starts. Then find the sum of the series or show that it dive

Nostrana [21]

Answer:

The first four terms of the series are

$(9+3),(\frac97+\frac35),(\frac9{7^2}+\frac3{5^2}),(\frac9{7^3}+\frac3{5^3})$

$\sum_{n=0}^\infty \frac9{7^n}+\frac{3}{5^n}$ = 14.25

Step-by-step explanation:

We know that

Sum of convergent series is also a convergent series.

We know that,

$\sum_{k=0}^\infty a(r)^k$

If the common ratio of a sequence |r| <1 then it is a convergent series.

The sum of the series is $\sum_{k=0}^\infty a(r)^k=\frac{a}{1-r}$

Given series,

$\sum_{n=0}^\infty \frac9{7^n}+\frac{3}{5^n}$

$=(9+3)+(\frac97+\frac35)+(\frac9{7^2}+\frac3{5^2})+(\frac9{7^3}+\frac3{5^3})+.......$

The first four terms of the series are

$(9+3),(\frac97+\frac35),(\frac9{7^2}+\frac3{5^2}),(\frac9{7^3}+\frac3{5^3})$

Let

$S_n=\sum_{n=0}^\infty \frac{9}{7^n}$ and $t_n=\sum_{n=0}^\infty \frac{3}{5^n}$

Now for $S_n$ ,

$S_n=9+\frac97+\frac{9}{7^2}+\frac9{7^3}+.......$

$=\sum_{n=0}^\infty9(\frac 17)^n$

It is a geometric series.

The common ratio of $S_n$ is $\frac17$

The sum of the series

$S_n=\sum_{n=0}^\infty \frac{9}{7^n}$

$=\frac{9}{1-\frac17}$

$=\frac{9}{\frac67}$

$=\frac{9\times 7}{6}$

=10.5

Now for $t_n$

$t_n= 3+\frac35+\frac{3}{5^2}+\frac3{5^3}+.......$

$=\sum_{n=0}^\infty3(\frac 15)^n$

It is a geometric series.

The common ratio of $t_n$ is $\frac15$

The sum of the series

$t_n=\sum_{n=0}^\infty \frac{3}{5^n}$

$=\frac{3}{1-\frac15}$

$=\frac{3}{\frac45}$

$=\frac{3\times 5}{4}$

=3.75

The sum of the series is $\sum_{n=0}^\infty \frac9{7^n}+\frac{3}{5^n}$

= $S_n+t_n$

=10.5+3.75

=14.25

4 0

3 years ago

Ben drove 4,212 miles. Larry drove 3,400 miles. Ben drove at a speed of about 55 miles per hour. How many more miles does Ben dr

tekilochka [14]

Answer:

812 miles

Step-by-step explanation:

the answer is 812 miles

5 0

3 years ago