All categories

4 years ago

22 Evaluate the expression for a = –1 and b = 5. Show your work. 5a – 7b + b2

Mathematics

2 answers:

artcher [175]4 years ago

6 0

5*-1= -5

-5- 7b + b^2

7*5= 35

-5-35 + b^2

5*5= 25

-5- 35 +25

-5 - 35= -40

-40 + 25= -15

-15

blagie [28]4 years ago

5 0

(5x-1) - (7x5) + (5x2)
= -5 - 35 + 10
= -5 - 45
= -50

You might be interested in

Find the slope of the line that passes through the two given points. (−5,4) and (1,6)

OLga [1]

slope is 1/3

Explanation: $\text{The given points: (-5,4) and (1, 6)}$

We apply the slope formula:

$slope=m\text{ = }\frac{y_2-y_1}{x_2-x_1}$ $\begin{gathered} x_1=-5,y_1=4,x_2=1,y_2\text{ = }6 \\ m\text{ = }\frac{6\text{ - 4}}{1\text{ - (-5)}} \\ m\text{ }=\text{ }\frac{2}{1+5} \\ \end{gathered}$ $\begin{gathered} m\text{ = 2/6} \\ m\text{ = 1/3} \\ \\ \text{Hence, slope is 1/3} \end{gathered}$

5 0

1 year ago

HELP ILL GIVE BRAINLIEST what shape is the base??

stepladder [879]

Answer:

rectangle

Step-by-step explanation:

it's width is 6

it's length is 12

it couldn't be a square

6 0

3 years ago

Read 2 more answers

Find a power series for the function, centered at c, and determine the interval of convergence. f(x) = 9 3x + 2 , c = 6

san4es73 [151]

Answer:

$\frac{9}{3x + 2} = 1 - \frac{1}{3}(x - \frac{7}{3}) + \frac{1}{9}(x - \frac{7}{3})^2 - \frac{1}{27}(x - \frac{7}{3})^3 ........$

The interval of convergence is: $(-\frac{2}{3},\frac{16}{3})$

Step-by-step explanation:

Given

$f(x)= \frac{9}{3x+ 2}$

$c = 6$

The geometric series centered at c is of the form:

$\frac{a}{1 - (r - c)} = \sum\limits^{\infty}_{n=0}a(r - c)^n, |r - c| < 1.$

Where:

$a \to$ first term

$r - c \to$ common ratio

We have to write

$f(x)= \frac{9}{3x+ 2}$

In the following form:

$\frac{a}{1 - r}$

So, we have:

$f(x)= \frac{9}{3x+ 2}$

Rewrite as:

$f(x) = \frac{9}{3x - 18 + 18 +2}$

$f(x) = \frac{9}{3x - 18 + 20}$

Factorize

$f(x) = \frac{1}{\frac{1}{9}(3x + 2)}$

Open bracket

$f(x) = \frac{1}{\frac{1}{3}x + \frac{2}{9}}$

Rewrite as:

$f(x) = \frac{1}{1- 1 + \frac{1}{3}x + \frac{2}{9}}$

Collect like terms

$f(x) = \frac{1}{1 + \frac{1}{3}x + \frac{2}{9}- 1}$

Take LCM

$f(x) = \frac{1}{1 + \frac{1}{3}x + \frac{2-9}{9}}$

$f(x) = \frac{1}{1 + \frac{1}{3}x - \frac{7}{9}}$

So, we have:

$f(x) = \frac{1}{1 -(- \frac{1}{3}x + \frac{7}{9})}$

By comparison with: $\frac{a}{1 - r}$

$a = 1$

$r = -\frac{1}{3}x + \frac{7}{9}$

$r = -\frac{1}{3}(x - \frac{7}{3})$

At c = 6, we have:

$r = -\frac{1}{3}(x - \frac{7}{3}+6-6)$

Take LCM

$r = -\frac{1}{3}(x + \frac{-7+18}{3}+6-6)$

r = -\frac{1}{3}(x + \frac{11}{3}+6-6)

So, the power series becomes:

$\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}ar^n$

Substitute 1 for a

$\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}1*r^n$

$\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}r^n$

Substitute the expression for r

$\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}(-\frac{1}{3}(x - \frac{7}{3}))^n$

Expand

$\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}[(-\frac{1}{3})^n* (x - \frac{7}{3})^n]$

Further expand:

$\frac{9}{3x + 2} = 1 - \frac{1}{3}(x - \frac{7}{3}) + \frac{1}{9}(x - \frac{7}{3})^2 - \frac{1}{27}(x - \frac{7}{3})^3 ................$

The power series converges when:

$\frac{1}{3}|x - \frac{7}{3}| < 1$

Multiply both sides by 3

$|x - \frac{7}{3}|$

Expand the absolute inequality

$-3 < x - \frac{7}{3}$

Solve for x

$\frac{7}{3} -3 < x$

Take LCM

$\frac{7-9}{3} < x$

$-\frac{2}{3} < x$

The interval of convergence is: $(-\frac{2}{3},\frac{16}{3})$

6 0

3 years ago

A regular polygon inscribed in a circle can be used to derive the formula for the area of a circle. The polygon area can be expr

Marat540 [252]

Answer:

Option (D)

Step-by-step explanation:

Formula to get the area of a regular polygon in a circle will be,

Area = $n[\frac{1}{2}\times (\text{Base})\times (\text{Height})]$

= $n[\frac{1}{2}\times (\text{s})\times (\text{h})]$

Here 'n' is the number of sides.

If n increases, h approaches r so that 'rh' approaches r².

In other words, if the number of sides of the polygon gets increased, area of the polygon approaches the area of the circle.

Therefore, Option (4) will be the answer.

7 0

4 years ago

Which step could be used to solve X +3.6 equals -1.7 for x in one step

Sophie [7]

To solve any algebraic equation, we want to get x by itself. Here, x is accompanied by 3.6. So that means we have to get rid of 3.6. To get rid of 3.6, one can either subtract 3.6 from both sides or add -3.6 to each side.

8 0

3 years ago