What is 2 to the 4 times 2 to the -7

Find the distance between the parallel lines m and n whose equations are

MA_775_DIABLO [31]

Answer:Find the distance between the parallel lines m and n whose equations are y = x + 4 and y = x - 6, respectively.

There are several ways to do this...here's one

Let (0, 4) be a point on the first line

Then.......a line with a negative reciprocal slope going through this point will have the equation :

y = -x + 4........so......we can find the intersection of this line with y = x - 6....set both equations equal

-x + 4 = x - 6 add x, 6 to both sides

10 = 2x divide both sides by 2

5 = x

So...using -x + 4, the y value at intersection = -1.......

So...we just need to find the distance from (0,4) to ( 5, -1) =

√[ (5)^2 + (4 + 1)^2 ] = 5√2 ≈ 7.07 units

Here's a pic....AB is the distance with A = (0,4) and B = (5, -1)

Step-by-step explanation:

8 0

3 years ago

Kendall had $1000 in a savings account at the beginning of the semester. She has a goal to have at least $350 in the account by

USPshnik [31]

Answer:

11 weeks

Step-by-step explanation:

First we need to check what variables we have.

Beginning Balance = $1000

Goal = $350

Withdrawal = $55 per week

Now let's declare a variable as the number of weeks.

Let x = number of weeks

1000 - 55x = 350

-55x = 350-1000

-55x = -650

Then we divide both sides by -55 to find the value of x.

x = 11.81 or 11 since we're looking for how many weeks in total

Now let's see if we still have 350 if we have a total of 11 as the value of x.

1000 - 55(11) = 350

1000 - 605 = 350

395 = 350

We can see that Kendall will have $395 compared to the $350 goal.

So Kendall can withdraw $55 a week for 11 weeks to still be within her goal of having $350 in her savings account.

6 0

3 years ago

Which expression is equivalent to 1/2x+(−7)−2 1/4x−(−2

Lynna [10]

The equivalent expression to the given expression is $\mathbf{=-(\dfrac{7}{4}x+5)}$

<h3>What is an algebraic expression?</h3>

Algebraic expressions are mathematical expressions. They usually consist of one or more variables with their coefficients and arithmetic operators such as: (division, multiplication, addition, and subtraction).

From the given expression, we are to determine an expression that is equivalent to:

$=\dfrac{1}{2}x + (-7) -2 \dfrac{1}{4}x -(-2)$

To do this, we are going to simplify the above-given expression to its lowest term since we are not given any options to choose equivalent expressions from.

By doing so, we have:

$=\dfrac{1}{2}x -7 -\dfrac{9}{4}x +2$

$=\dfrac{1}{2}x -\dfrac{9}{4}x +2 -7$

$=\dfrac{1}{2}x -\dfrac{9}{4}x -5$

$=-\dfrac{7}{4}x-5$

$\mathbf{=-(\dfrac{7}{4}x+5)}$

Learn more about solving algebraic expressions here:

brainly.com/question/4344214

#SPJ1

5 0

2 years ago

3. The annual per capita consumption of fresh bananas in the United States can be approximated by a normal distribution, with a

svlad2 [7]

Answer:

The largest annual per capita consumption of bananas in the bottom 5% of consumption is 5.465 lb

Step-by-step explanation:

Given

μ = Mean = 10.4 lb

σ = Standard deviation = 3 lb

Using a confidence level of 90%,

We'll need to first determine the z value that correspond with bottom 5% of consumption of banana

α = 5%

α = 0.05

So,

zα = z(0.05)

z(0.05) = -1.645 ----- From z table

Let x represent the largest annual per capita consumption of bananas

The relationship between x and z is

x = μ + zσ

By substitution;

x = 10.4 + (-1.645) * 3

x = 10.4 - 4.935

x = 5.465

Hence, the largest annual per capita consumption of bananas in the bottom 5% of consumption is 5.465 lb

6 0

3 years ago

Find the equation of the line that is perpendicular to the line

ddd [48]

Answer:

$y=-x+16$

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept (the value of y when x is 0)
Perpendicular lines always have slopes that are negative reciprocals (ex. 3 and -1/3, 5/6 and -6/5, etc.)

<u>1) Determine the slope (m)</u>

y=x-9

Rewrite the equation

y=1x-9

Now, we can identify clearly that the slope of the line is 1. The negative reciprocal of 1 is -1, so therefore, the slope of a perpendicular line would be -1. Plug this into $y=mx+b$ :

$y=-1x+b\\y=-x+b$