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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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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

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:

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.

Answer:

C) –|x| + 3

I got the answer correct!!!

Answer:

(A) y+2=3(x-1)

Step-by-step explanation:

y-y1=m(x-x1)

y-(-2)=3(x-1)

y+2=3(x-1)

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:

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:

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:

12Pi

Step-by-step explanation:

circumference of a circle can be worked out as Pi x diameter

Diameter = 2 x radius, therefore here d = 12 and circumference = 12 Pi

The circumference of the circle is C = 12π meters

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the radius of the circle be r = 6 meters

Now , circumference of circle = 2πr

On simplifying , we get

C = 2π ( 6 )

C = 12π meters

Hence , the circumference is 12π meters

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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.

To find the product of 7 and 28 using place value and the distributive property, rewrite the product as 7(20 + 8). Distribute the 7 to both terms inside the parentheses and then add the resulting products.

To find the product of 7 and 28 using place value and the distributive property, we can rewrite the product as 7(20 + 8). This is because 28 can be decomposed into 20 + 8.

Using the distributive property, we can distribute the 7 to both terms inside the parentheses: 7(20) + 7(8).

The product of 7 and 20 is 140 and the product of 7 and 8 is 56. Therefore, the final product is 140 + 56 = 196.

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.

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.

Answer:

The valid value of x is x=-2

Step-by-step explanation:

we know that

The sum of the interior angles of any quadrilateral must be equal to 360 degrees

so

[tex](7x^{2}-24x)+100+(24-46x)+(3x^{2}+56)=360[/tex]

solve for x

Combine like terms

[tex]10x^{2}-70x+180=360[/tex]

[tex]10x^{2}-70x-180=0[/tex]

Divide by 10 both sides

[tex]x^{2}-7x-18=0[/tex]

The formula to solve a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]x^{2}-7x-18=0[/tex]

so

[tex]a=1\\b=-7\\c=-18[/tex]

substitute in the formula

[tex]x=\frac{-(-7)(+/-)\sqrt{-7^{2}-4(1)(-18)}} {2(1)}[/tex]

[tex]x=\frac{7(+/-)\sqrt{121}} {2}[/tex]

[tex]x=\frac{7(+/-)11} {2}[/tex]

[tex]x=\frac{7(+)11} {2}=9[/tex]

[tex]x=\frac{7(-)11} {2}=-2[/tex]

Remember that

The measure of the interior angle cannot be a negative number

For x=9

we have that the measure of one interior angle of quadrilateral  is

[tex]24-46x[/tex]

substitute the value of x

[tex]24-46(9)=-390\°[/tex]

therefore

The value of x=9 cannot be a solution

For x=-2

The measure of the interior angles are

[tex](7(-2)^{2}-24(-2))=76\°\\100\°\\(3(-2)^{2}+56)=68\°\\24-46(-2)=116\°[/tex]

therefore

The valid value of x is x=-2

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

Answer:

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

Step-by-step explanation:

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

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:

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

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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54 54 54

54 54 54

54 54 54

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:

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:

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

How much money did he have

Answer:

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

Step-by-step explanation:

Answer:

55/18

Step-by-step explanation:

f(x) = 2/3*12 +3

= 1/18 +3

=55/18

The value of f (12) will be;

⇒ f (12) = 11

What is substitution method?

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The function is,

⇒ f (x) = 2/3x + 3

Now,

Since, The function is,

⇒ f (x) = 2/3x + 3

Substitute x = 12 in above equation, we get;

⇒ f (x) = 2/3x + 3

⇒ f (12) = 2/3 × 12 + 3

⇒ f (12) = 2 × 4 + 3

⇒ f (12) = 11

Thus, The value of f (12) will be;

⇒ f (12) = 11

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