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E Homework: 1-7 HW Simplify the expression. 8(5+t) - 2(t+1) 8(5 + t) - 2(t+1)=

lys-0071 [83]

Hi, I'm happy to help!

To simplify this expression, we need to first use the order of operations (Parenthesis, Exponents, Multiplication or Division (Left to Right), and Addition or Subtraction (Left to Right)), then combine like terms. (80,40,57, or 6t, 8t, 98t, or 2t²,7t²,83t²)

When a number is next to parenthesis with no sign, it means we are using multiplication. We can change this expression to look like this, by changing all the numbers next to the parenthesis with no sign, to one with a multiplication sign.

8(5+t) - 2(t+1) 8(5 + t) - 2(t+1)=

8×(5+t) - 2×(t+1)× 8×(5 + t) - 2×(t+1)=

We start with parenthesis and solve everything inside of those, but, because everything inside the parenthesis are unlike terms, we cannot combine them.

Next, We look for any exponents (x²). There are none in this equation.

We then look for multiplication or division. There is a lot of multiplication, so we start solving that from left to right.

8×(5+t) - 2×(t+1)× 8×(5 + t) - 2×(t+1)=

40+8t - 2×(t+1)× 8×(5 + t) - 2×(t+1)=

40+8t - 2×(t+1)× 8×(5 + t) - 2×(t+1)=

(40+8t) - (2t+2)× 8×(5 + t) - 2×(t+1)=

(40+8t) - (2t+2)× 8×(5 + t) - 2×(t+1)=

(40+8t) - (16t+16)×(5 + t) - 2×(t+1)=

(40+8t) - (16t+16)×(5 + t) - 2×(t+1)=

(40+8t) - (80t+16t²+80+16t) - 2×(t+1)=

(40+8t) - (80t+16t²+80+16t) - 2×(t+1)=

(40+8t) - (80t+16t²+80+16t) - (2t+2)=

(40+8t) - (80t+16t²+80+16t) - (2t+2)=

Now, before we do anything else, we need to recheck the parenthesis, now that they have changed. We can further simplify the middle parenthesis by adding together like terms.

(40+8t) - (80t+16t²+80+16t) - (2t+2)=

(40+8t) - ((80t+16t)+16t²+80) - (2t+2)=

(40+8t) - (96t+16t²+80) - (2t+2)=

(40+8t) - (96t+16t²+80) - (2t+2)=

Now, we look for addition or subtraction of like terms. We can now remove the parenthesis, since everything inside of the last two parenthesis is negative, we turn it negative, as long as we only combine the like terms.

40+8t - 96t-16t²-80 - 2t-2=

Once we find like terms, we can rearrange the expression.

(40-80-2)+8t - 96t+16t² - 2t

(-42)+8t - 96t-16t² - 2t

(-42)+8t - 96t-16t² - 2t

(-42)+(8t-96t-2t)-16t²

(-42)+(-90t)-16t²

(-42)+(-90t)-16t²

This doesn't have any like terms, so we don't alter it.

(122)+(-90t)-16t²

We can now remove the parenthesis.

122-90t-16t²

Since there are no more like terms this is the furthest we can simplify. We can then rearrange the expression to be arranged completely correct.

-16t²-90t-42

I hope this was helpful, keep learning! :D

4 0

3 years ago

Function f is an exponential function. It predicts the value of a famous painting, in thousands of dollars, as a function of the

nalin [4]

Answer:

$y=8 \cdot (\frac{5}{4})^x$

$f(x)=8 \cdot (\frac{5}{4})^x$

or

$f(x)=8 \cdot (1.25)^x$

Step-by-step explanation:

We are going to see if the exponential curve is of the form:

$y=a \cdot b^x$ , ( $b\neq 0$ ).

If you are given the $y-$ intercept, then $a$ is easy to find.

It is just the $y-$ coordinate of the $y-$ intercept is your value for $a$ .

(Why? The $y-$ intercept happens when $x=0$ . Replacing $x$ with 0 gives $y=a \cdot b^0=a \cdot 1=a$ . This says when $x=0 \text{ that} y=a$ .)

So $a=8$ .

So our function so far looks like this:

$y=8 \cdot b^x$

Now to find $b$ we need another point. We have two more points. So we will find $b$ using one of them and verify for our resulting equation works for the other.

Let's do this.

We are given $(1,10)$ is a point on our curve.

So when $x=1$ , $y=10$ .

$10=8 \cdot b^1$

$10=8 \cdot b$

Divide both sides by 8:

$\frac{10}{8}=b$

Reduce the fraction:

$\frac{5}{4}=b$

So the equation if it works out for the other point given is:

$y=8 \cdot (\frac{5}{4})^x$

Let's try it. So the last point given that we need to satisfy is $(2,12.5)$ .

This says when $x=2$ , $y=12.5$ .

Let's replace $x$ with 2 and see what we get for $y$ :

$y=8 \cdot (\frac{5}{4})^2$

$y=8 \cdot \frac{25}{16}$

$y=\frac{8}{16} \cdot 25$

$y=\frac{1}{2} \cdot 25}$

$y=\frac{25}{2}$

$y=12.5$

So we are good. We have found an equation satisfying all 3 points given.

The equation is $y=8 \cdot (\frac{5}{4})^x$ .

4 0

3 years ago

The life in hours of a battery is known to be approximately normally distributed, with standard deviation σ = 1.25 hours. A rand

Papessa [141]

Answer

The answer and procedures of the exercise are attached in the following archives.

Step-by-step explanation:

You will find the procedures, formulas or necessary explanations in the archive attached below. If you have any question ask and I will aclare your doubts kindly.

6 0

3 years ago

Find the sine r 13 12 5

Neporo4naja [7]

Answer:

9

Step-by-step explanation:

4 0

3 years ago

A pentagonal prism has a height of 9 feet, and each base edge is 3 feet. Find the volume. Round your answer to the nearest hundr

OLga [1]

Height of the pentagon = 9 ft

Edge of base = 3 ft

$area of pentagon = \frac{s^{2}n}{4 tan\left ( \frac{180}{n} \right )}$

s is the length of any side = 3

n is the number of sides = 5

tan is the tangent function calculated in degrees

$\\ \\\\area of pentagon = \frac{3^{2}(5)}{4 tan\left ( \frac{180}{5} \right )}\\\\\\area of pentagon = \frac{9(5)}{4 tan\left ( 36 \right )}\\\\area of pentagon = \frac{45}{4 ( 0.7265 )}\\\\area of pentagon = \frac{45}{2.906}\\\\area of pentagon = 15.4852$

Volume of the pentagon = area of base (height )

Volume of the pentagon = 15.4852 (9)

Volume of the pentagon = 139.366

Volume of the pentagon = 139.37 cu.ft

5 0

3 years ago

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