How high should the engineer make the hill?

Answer:

The equivalents are 1/6¹⁰ and  1/6⁸

Step-by-step explanation:

1. Let's recall the rule about the negative exponents to find the equivalents to the expressions provided:

The rule says that any number different than zero, raised to a negative power equals its reciprocal raised to the opposite positive power.

Thus, x ⁻ⁿ = 1/x ⁿ

2. Now, let's find the equivalents after following the rule:

6 ⁻ ¹⁰ = 1 ÷ 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 = 1/6 ¹⁰

6 ⁻ ⁸ = 1 ÷ 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6  = 1/6 ⁸

Answer:

4b = 8

Step-by-step explanation:

Given 12b = 24

This is written as (4 X 3)b = 24

⇒ 4b X 3 = 24

Dividing by 3 throughout, we have

4b = [tex]$ \frac{24}{3} $[/tex] = 8.

Therefore, the value of 4b is 8.

Answer:

r = 0.93

Step-by-step explanation:

The correlation coefficient gives us the "strongness" of two variables associated.

This is the value "r".

It is positive if there is strong relationship (one goes up, another goes up and vice versa)

It is negative, if one goes up and another goes down (inverse relationship)

First of all, from the scatter points, we see that as x increases, y also tend to increase. And if we were to draw a line of best fit that goes through max points, we would see the line slopes UPWARD (means as x increases, y also increase).

Thus, the value of "r" will be positive. So we can eliminate first and second choice. Now remains the other two choices

0.64

0.93

The closer the value to 1, the more that line is slopier, and less that value from 1, the line will be less "slopy".

A perfect one would be a line with slope 1, as 1 unit increase in x, the y increases 1 unit as well.

So, if we were to draw a line, we would see that it will be very close to a value of 1. The value of 0.64 can be eliminated because the points are not much "relaxed" as it should be for 0.64.

So, the correct choice is the 4th choice, r = 0.93

confused as to what you want but if you want to see the number then its 200,025

Answer:

200,025

Step-by-step explanation:

200 1000s so 200,0000 and add 25

Answer:

x=-6

Step-by-step explanation:

Follow along:

1. Distribute the -3 to those within the parenthesis.

-3x-6=12

2. Move the whole numbers to one sides, isolate the variable.

-3x=18

3. Divide both sides by -3

x=-6

Answer:

The area  of the cover for the hot tub must be:

Step-by-step explanation:

First, you must understand that since a hydromassage tub is mentioned and the diameter, it is assimilated that it is round in its upper part, which is why the formula is used to find the area of a circle:

Since the diameter is mentioned, it can be replaced in the formula:

Answer:

I believe it is 38

Step-by-step explanation:

HAVE A GOOD DAY AND GOD BLESS YOU

Answer:

We rewrite the statement correctly:

 "A linear function has an y-intercept of 12 and a slope of 3/8"

 Therefore, the linear function is:

 y = (3/8) x + 12

 We look for the linear function of the table:

 y-yo = m (x-xo)

 Where,

 m = (y2-y1) / (x2-x1)

 m = ((- 3/8) - (- 3/4)) / ((1/3) - (- 2/3))

 m = ((- 3/8) - (- 6/8)) / (3/3)

 m = ((- 3 + 6) / 8) / (1)

 m = 3/8

 (xo, yo) = (- 2/3, -3/4)

 Substituting:

 y + 3/4 = (3/8) (x + 2/3)

 y = (3/8) x + 2/8 - 3/4

 y = (3/8) x + 1/4 - 3/4

 y = (3/8) x + -2/4

 y = (3/8) x + -1/2

 The lines are:

 y = (3/8) x + 12

 y = (3/8) x + -1/2

 Answer:

 It has the same slope and a different y-intercept

Step-by-step explanation:

Answer:

B same slope but different y intercept

Step-by-step explanation:

Answer:

a. .3

b. .7

c. The car is fairly reliable because there is more people with no mechanical issues than there is people with mechanical issues

Step-by-step explanation:

Answer:

A. 3

B. .7

C. The car is fairly reliable, their is more people with no mechanical issues than their is people with mechanical issues

Step-by-step explanation:

The value of x in 984 ÷ x = 3 remainder: 84 is 300

Step-by-step explanation:

In the division problem A ÷ B = Q [tex]\frac{R}{B}[/tex], where

If A is divisible by B, then R = 0

Examples:

The rule of the dividend is ⇒dividend = (divisor × quotient) + reminder

Let us use this rule to find x

984 ÷ x = 4, remainder 84

∵ Dividend = 984

∵ Divisor = x

∵ Quotient is 3

∵ Remainder = 84

- Substitute these values in the rule of dividend above

∵ 984 = (x × 3) + 84

∴ 984 = 3x + 84

- Subtract 84 from both sides

∴ 900 = 3x

- Divide both sides by 3

∴ 300 = x

∴ The value of x = 300

The value of x in 984 ÷ x = 3 remainder: 84 is 300

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Answer:

[tex]\displaystyle 2[/tex]

Step-by-step explanation:

Starting from the y-intercept of [tex]\displaystyle [1, 1],[/tex]you do [tex]\displaystyle \frac{rise}{run}[/tex]by either moving two blocks south over one block west or two blocks north over one block east [west and south are negatives]. Doing this will give you the equation below:

[tex]\displaystyle y = 2x + 1[/tex]

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Answer:

x equals plus or minus square root of 5 minus 1

Step-by-step explanation:

we have

[tex]x^{2} +2x=4[/tex]

Divide by 2 the coefficient of the x-term

[tex]2/2=1[/tex]

squared the number

[tex]1^2=1[/tex]

Adds both sides

[tex]x^{2} +2x+1=4+1[/tex]

[tex]x^{2} +2x+1=5[/tex]

Rewrite as perfect squares

[tex](x+1)^{2}=5[/tex]

take the square root both sides

[tex]x+1=(+/-)\sqrt{5}[/tex]

[tex]x=(+/-)\sqrt{5}-1[/tex]

therefore

x equals plus or minus square root of 5 minus 1

Answer - B. x = ± [tex]\sqrt{5[/tex] - 1

Answer:

An equation is a statement that maintains the equal value of two mathematical expressions. If the statement is true for all variable values, it is called an identity. ... An equation shows the equality of two variables while an inequality shows the inequality of two variables

An equation with a variable expresses a precise equality between expressions, while an inequality with a variable represents a range of possible values expressing that one value is greater or less than another. Equations typically have a definitive set of solutions, whereas inequalities signify a continuum of solutions that satisfy the relational condition.

The difference between an equation with a variable and an inequality with a variable lies in the relationship they describe between the variables. An equation states that two expressions are equal by means of the equal sign (=), implying a specific value or set of values for the variables involved. For example, in the equation of a line y = mx + b, where x and y are the variables on the horizontal and vertical axis respectively, and b and m represent the y-intercept and the slope, we can see a direct relationship between x and y that determines the position of a point on a Cartesian plane. Conversely, an inequality such as x > y or x < 10 indicates a range of possible values rather than a single specific value, expressing a relationship where one value is either greater than or less than another value, but not equal to it.

In the context of a graph, the independent variable typically plotted on the x-axis is assumed to be the cause or input which then determines the value of the dependent variable, depicted on the y-axis. The dependent variable changes in response to the independent variable, thereby showing their relationship. This is often represented by inequalities when a range of outcomes is possible, extending beyond the linear relationship that might be depicted with an equation.

Answer:

Smaller number = 8 (x)

Larger number = 24  (y)

Step-by-step explanation:

x+y=32

7x+3y=128

Solving by Elimination

-3x-3y= -96

7x+3y=128

4x=32

4x/4=32/4

x=8

-7x-7y= -224

7x+3y=128

-4y= -96

-4y/-4= -96/-4

y=24

Check answer

x+y=32

8+24=32

7x+3y=128

7(8)=3(24)=138

56+72=128

128=128

Three other ordered pairs with θ between −360° and 360° that name the same point as (−3, 330°) are (−3, 30°), (−3, 690°), and (−3, -30°).

Given the ordered pair (−3, 330°), we can find three other ordered pairs that name the same point by adding or subtracting 360° from the given angle:

These three ordered pairs have angles between −360° and 360° and represent the same point as the given ordered pair.

Answer:

5,841 divided by 62 is 94.2

Answer:

120 50 pound bags

Step-by-step explanation:

first you see how much 50 pounds is to one ton which one 50 pound bag is equal to .025 tons

then you multiply .025 by 120 to get 3 (tons)

that shows that the answer is correct

Answer:

Step-by-step explanation:

12:32 am

Answer:

1:32 AM

Step-by-step explanation:

Arriving in Oklahoma City, the time is already 12:32 AM since it is past midnight. From Mountains to Central, time moves forward by 1 hour. 12:32 + 1 hour is 13:32 or 1:32 AM. Since the time is still past midnight, the time is AM.

Good evening ,

Answer:

Vertex (-4 , 0)

axis x = -4

It’s a parabola.

Min = 0

Step-by-step explanation:

x2 + 8x + 16 = (x + 4)².

To find the depth of the swimming pool, use the formula for the volume of a rectangular solid and substitute the given values to calculate the depth as 2.5 meters.

The depth of the Olympic-size swimming pool can be calculated using its volume, length, and width.

First, use the formula for the volume of a rectangular solid:

Volume = Length x Width x Depth

4000 = 80 x 20 x Depth

Depth = 4000 / (80 x 20) = 2.5 meters

Depth = 2.5 meters

Answer:

The graphs of the functions are both straight lines and parallel to x-axis

Step-by-step explanation:

The graph of f(x) is the line y = 16 which is parallel to x-axis.

This is because for every value of x the function f(x) only takes the value 16

Similarly the graph of g(x) is also a straight line but is characterized by y = 3/64. This line is also parallel to the x-axis.

For every value of x the function g(x) only takes the value 3/64

Answer:

The answer is x = 5.

Step-by-step explanation:

Given:

Δ ABC is an Isosceles triangle with AB = CA

   m∠ ABC = ( 6x + 4 )°

   m∠ BAC = 73°

   m∠ BCA = ( 8y - 7 )°

To Find:

x = ?

Solution:

Properties of an Isosceles Triangle.

Here , Δ ABC is an Isosceles triangle with AB = CA

∴  m∠ BAC = m∠ BCA

[tex]73= 8y-7\\8y=73+7\\8y=80\\y=\frac{80}{10} \\y=10[/tex]

∴      m∠ BCA = ( 8y - 7 )°

                       = 8 × 10 - 7

       m∠ BCA  = 73  Which is same as ∠ CAB

Property of a Triangle is Sum of the measures of the angle of a triangle is 180°.

[tex]\angle ACB + \angle CAB + \angle CBA = 180[/tex]

Substituting the values we get,

[tex]73 + 73 + (6x+4) = 180\\6x+4=180-146\\6x=34-4\\6x=30\\x=\frac{30}{6} \\x=5\\[/tex]

The answer is x = 5.

The rectangle can be divided into  6 ways as, 1 × 56 or 56 × 1,  2 × 28 or 28 × 2, and 4 × 14 or 14 × 4.

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel, opposite sides. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The rectangle's longer side is its length, while its shorter side is its breadth.

Given:

Darren has a piece of wood that is 7 in by 8 in

The area of the rectangle can be given by,

[tex]Area = Length\times width[/tex]

Area = 7 × 8

Area = 56

You can now divide the length and width as shown below,

Rectangle =   1 × 56 or 56 × 1

Rectangle =   2 × 28 or 28 × 2

Rectangle =   4 × 14 or 14 × 4

Therefore, the rectangle can be divided into  6 ways as   1 × 56 or 56 × 1,  2 × 28 or 28 × 2, and 4 × 14 or 14 × 4.

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How much money did he have

Answer:

His profit would be $37 of the money he got back.

Step-by-step explanation:

Answer:

Step-by-step explanation:

if y = 1/2x - 1 is the function

y = 1/2(-4) - 1

y = -2 - 1

y = -3

(-4, -3)

y = 1/2(2) -1

y = 1 - 1

y = 0

(2, 0)

y = 1/2(6) - 1

y = 3 - 1

y = 2

(6, 2)

the pictures should be in order

Answer:

[tex]\displaystyle 2 = f(6), 0 = f(2), -3 = f(-4)[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{1}{2}[6] - 1 = 3 - 1 = 2 \\ \\ \frac{1}{2}[2] = 1 - 1 = 0 \\ \\ \frac{1}{2}[-4] - 1 = -2 - 1 = -3[/tex]

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Answer:

[tex]z^2-5z+4=(z-4)(z-1)[/tex]

Step-by-step explanation:

Answer:

52

Step-by-step explanation:

2200 / 42 = 52.381

You cannot bring a section of a carton, and 53 cartons is too much

53 * 42 = 2226. This goes over the weight limit.

52 * 42 = 2184. 2184 is less than 2200, so 52 is the greatest number you can bring

By dividing the elevator's weight capacity of 2200 pounds by the weight of one 42-pound carton, we find it can carry a maximum of 52 whole cartons simultaneously without exceeding the weight limit.

To solve this problem, we can use simple mathematical analysis. We need to calculate how many 42-pound cartons can fit into an elevator that has a maximum capacity of 2200 pounds without exceeding this limit.

We start with the equation:

Therefore, the elevator can safely carry 52 cartons at once, without any people in it.

54 54 54

54 54 54

54 54 54

Answer:

√(4/5)

Step-by-step explanation:

First, let's use reflection property to find tan θ.

tan(-θ) = 1/2

-tan θ = 1/2

tan θ = -1/2

Since tan θ < 0 and sec θ > 0, θ must be in the fourth quadrant.

Now let's look at the problem we need to solve:

sin(5π/2 + θ)

Use angle sum formula:

sin(5π/2) cos θ + sin θ cos(5π/2)

Sine and cosine have periods of 2π, so:

sin(π/2) cos θ + sin θ cos(π/2)

Evaluate:

(1) cos θ + sin θ (0)

cos θ

We need to write this in terms of tan θ.  We can use Pythagorean identity:

1 + tan² θ = sec² θ

1 + tan² θ = (1 / cos θ)²

±√(1 + tan² θ) = 1 / cos θ

cos θ = ±1 / √(1 + tan² θ)

Plugging in:

cos θ = ±1 / √(1 + (-1/2)²)

cos θ = ±1 / √(1 + 1/4)

cos θ = ±1 / √(5/4)

cos θ = ±√(4/5)

Since θ is in the fourth quadrant, cos θ > 0.  So:

cos θ = √(4/5)

Or, written in proper form:

cos θ = (2√5) / 5