Suppose we are given the following.
Line 1 passes through (-3, 8) and (0,4).
Line 2 passes through (4, 4) and (-4,-2).
Line 3 passes through (4, 1) and (8,4).
(a) Find the slope of each line.
Slope of Line 1-
Slope of Line 2-
Slope of Line 3-0
(b) For each pair of lines, determine whether they are parallel, perpendicular, or neither.
Line 1 and Line 2: OParallel
Line 1 and Line 3:
OParallel
Line 2 and Line 3:
OParallel
Operpendicular ONeither
Operpendicular
ONeither
OPerpendicular
Neither

The length of the missing side is 39 units

The parallelogram is a simple 2D-shaped quadrilateral with two pairs of parallel sides. In a parallelogram, the opposite sides and opposite angles are equal.

Here we have,

The length of the sides of a parallelogram is 2x+10, 5x- 20 and 4x-1

As we know parallel lines of a Parallelogram are equal

Take any two sides as equal and find the missing side

Let the sides with lengths be equal 2x+10, 5x- 20

=> 2x+10 = 5x- 20      

=> 5x - 2x = 20+ 10

=> 3x = 30

=> x = 10  

Therefore, the lengths of the 3 sides are  

2x+10 = 2(10) + 10 = 30

5x- 20 = 5(10) - 20 = 30

4x-1 = 4(10) - 1 = 40 - 1 = 39    

The length of the missing side is 39 units

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Answer:

-1/2(x - 12). Hope this helped out for you!

Answer:

-2.655 < -√4

Step-by-step explanation:

-√4 = -2

-2.655 < -2

I assume that's what the question is asking for?

Answer:

9 : 30

Step-by-step explanation:

1 PM - 1 hour = 12 PM

12 PM - 2 hours = 10 PM

10 PM - 20 minutes = 9 : 40

9 : 40 PM - 10 minutes = 9 : 30 PM

So, it is 9 : 30 PM

Answer:

=========================

The given translates as:

Use given x - intercepts to get the equation:

Use the coordinates of P to find the value of a:

The equation of this parabola is:

Answer:

[tex]\textsf{Intercept form}: \quad y=\dfrac{3}{2}(x+4)(x+10)[/tex]

[tex]\textsf{Standard form}: \quad y=\dfrac{3}{2}x^2+21x+60[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a quadratic equation}\\\\$y=a(x-p)(x-q)$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the $x$-intercepts. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]

If the x-intercepts are (-4, 0) and (-10, 0) then:

Substitute the values of p and q into the formula:

[tex]\implies y=a(x-(-4))(x-(-10))[/tex]

[tex]\implies y=a(x+4)(x+10)[/tex]

To find a, substitute the given point on the curve P (-6, -12) into the equation:

[tex]\implies -12=a(-6+4)(-6+10)[/tex]

[tex]\implies -12=a(-2)(4)[/tex]

[tex]\implies -12=-8a[/tex]

[tex]\implies a=\dfrac{-12}{-8}[/tex]

[tex]\implies a=\dfrac{3}{2}[/tex]

Substitute the found value of a into the equation:

[tex]\implies y=\dfrac{3}{2}(x+4)(x+10)[/tex]

Expand to write the equation in standard form:

[tex]\implies y=\dfrac{3}{2}(x^2+14x+40)[/tex]

[tex]\implies y=\dfrac{3}{2}x^2+21x+60[/tex]

Equation which is equivalent to the given equation 6x + 9 = 12 is given by 2x + 3 = 4.

As given in the question,

Given equation is equal to :

6x + 9 = 12

Simplify by writing each number into prime factors of the given equation 6x + 9 =12 to get the equivalent equation,

( 2 × 3 )x  + ( 3 × 3 ) = ( 2 × 2 × 3 )

3 is the common factor in all we get,

3 ( 2x + 3) = 3(4)

Divide by 3 both the side of the equation we get,

2x + 3 = 4

Therefore, equation which is equivalent to the given equation 6x + 9 = 12 is given by 2x + 3 = 4.

The complete question is:

Which equation is equivalent to the equation 6x + 9 = 12?

A. x +9=6

B. 2x + 3 = 4

C. 3x + 9 = 6

D. 6x + 12 = 9​

E. 6x = 3

F. 3 = 2x + 4

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Answer:

Step-by-step explanation:

14. y = -2/3x + 10. This is parallel to 2x -3y because they have the same slope.

15. y = -1/2x and y = -1/2x + 2. These are perpendicular because the slope is the opposite reciprocal to the slope of y = 2x + 3, which is 2.
The slopes of the lines of the 2 equations are the same. Because of that, we can state that 2 lines that are perpendicular to the same line are parallel. This can be further supported by the Perpendicular Transversal Theorem, which says the same thing.

Hope this helps!

The slope of the line is 1/5 which is positive.

From the graph:

slope:

Slope is the steepness of a line as it moves from LEFT to RIGHT. Slope is the ratio of the rise, the vertical change, to the run, the horizontal change of a line. The slope of a line is always constant (it never changes) no matter what 2 points on the line you choose.

Take any points:

(0,0) and (5,1)

slope m = y2 - y1 / x2 -x1

= 1 - 0 / 5 - 0

= 1/5

Therefore the slope of the line is 1/5 which is positive.

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The total cost for Charlie to make 40 copies of flyers is $6

Given the fact that 25 copies of flyers is costing him $3.75, we will then need to find the cost of each copy of the flyer. The figure is calculated using unit rates as follows:

25x = 3.75

    x = 3.75/25

    x = 0.15

so each copy of a flyer will cost him $0.15

To make 40 copies of flyers, Charlie will need to spend:

$0.15 × 40 = $6

So the amount of money Charlie will have to spend in order to make a copy of 40 flyers is $6

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Answer: Charlie will pay 6$.

Step-by-step explanation:

The value of x in the intersecting chords SP and PB is determined as 3.52.

The value of x is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.

arc SB =  m∠SPB

From the diagram, we have arc SB = 78⁰

m∠JNK = 78 (interior angles of intersecting secants)

23x - 3 = 78

23x = 78 + 3

23x = 81

x = 81/23

x = 3.52

Thus, the value of x in the intersecting chords SP and PB is determined as 3.52.

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The correlation between variables x and y is 0.50 . The true option is option (c) .

that's the regression coefficient is positive for given bivariata.

Correlation: Correlation is a statistical measure of how linearly two variables are related (meaning they change together at a constant rate). The

sample correlation coefficient r quantifies the strength of the relationship.

Correlation Coefficient: The Correlation Coefficient formula is used to examine the strength of the relationship between data. The formula returns a value between -1 and 1.

Here:

Pearson's correlation coefficient is denoted by "r" and is

r = (n∑xy - ∑x∑y )/√( n ∑x² - (∑x )² ) ( √ n∑y² - (∑y)²)

We have given that correlation between x and y is 0.50.

cor(x,y) = √r^2 => √r^2 = 0.50 => r ^2 = (0.50)^2

=> r^2 = 0.25 > 0 but less than 0.50 ---( 1)

Regression coefficient is the constant "b" in the regression equation that gives the change in the value of the dependent variable equal to the unit change in the independent variable.

Symbolically it can be expressed as:

bₓᵧ= r σ ₓ /σ ᵧ

where x and y are correlated

σ ₓ --> standard deviation of X

σᵧ ---> standard deviation of y

We know that standard deviations is square root value of variance of observations. we also know square root any quantity is always positive or zero.

Using the above fact about standard deviations and correlation coefficient (r) is also positive we see that bₓᵧ is postive.

Hence, Regression cofficient is positive.

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The given interval shown on the number line in inequality notation as (3, 6).

What are inequalities on a number line?

Inequalities on a number line allow us to visualise the values that are represented by an inequality.

To represent inequalities on a number line we show the range of numbers by drawing a straight line and indicating the end points with either an open circle or a closed circle.  

An open circle shows it does not include the value.

A closed circle shows it does include the value.

The left endpoint is 3. The right endpoint is 6. Both endpoints are open holes, meaning we do not include them as part of the green shaded solution region. If x is a solution, then the solution can be described as  

3 < X < 6 which converts to the interval notation (3, 6) . The curved parenthesis says "do not include the endpoint".

Note: this is not ordered pair notation (x,y).

The given interval shown on the number line in inequality notation as (3, 6).

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The vertex is (-1, 4), the domain is all real numbers, and the range is y ≤ 4.

What are the domain and range of a function?

The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.

if you use the foil method it will come out to -(x^2+2x+1)+4. then distribute the negative and simplify the equation (add the four) the equation comes out to be -x^2-2x+3.

The vertex is at -b/(2A).

The vertex is at x=2/(2*-1), which is -1. plug -1 into the original equation to find y, (y=-(-1)^2-2*(-1)+3) which is y=4. so the vertex is at (-1,4).

since the parabola opens down (negative a value) and has a maximum at 4, y is always less than or equal to 4. x is all real numbers as it goes on forever. so b is your answer.

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From the ground the length of the ladder is 15 feet.

Step-by-step explanation:

From the Pythagorean Theorem, the situation described can be expressed mathematically as:

x² +9² = (x+3)²

or,

x² + 81 = x² + 6x + 9

Now, cancelling equal terms on either side of the equation and reducing gives:

     x = 12

Since the ladder is defined to be 3 feet longer than the distance of its foot to the wall the ladder’s length must be:

       12 feet + 3 feet

        =15 feet

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0.123 < 2 > 0.1002, is the true statement after inserting symbols.

What is greater than symbol refer?

What is lesser than symbol refer?

What is equal to symbol refer?

Hence, 0.123 < 2 > 0.1002, is the true statement after inserting symbols.

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The theorem (A) CPCTC represents the given condition of the triangle.

According to the formula CPCTC, which stands for "corresponding portions of congruent triangles are congruent," if two or more triangles are congruent, their corresponding angles and sides must also be congruent.

When demonstrating the congruence of triangles or other shapes, the term CPCT is employed.

When a student is asked to demonstrate that two angles or two sides are congruent, CPCTC is frequently employed at the end of the proof or close to it.

So, in the given triangle:

The angles are bold and the lines are not bold.

This represents that it is proved first that the angles are congruent.

And through CPCTC, we are concluding that the sides of the triangles are also congruent.

Therefore, the theorem (A) CPCTC represents the given condition of the triangle.

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Answer:

4×3=12

Step-by-step explanation:

that is the answer

Answer:

(x - 2)(x² + 2x + 4) = 0

Step-by-step explanation:

x³ - 8 ← is a difference of cubes and factors in general as

a³ - b³ = (a - b)(a² + ab + b²) , then

x³ - 8

= x³ - 2³

= (x - 2)(x² + 2x + 2²) = (x - 2)(x² + 2x + 4)

Answer:

  $13

Step-by-step explanation:

You want to know how much more Rahul's investment of $1100 at 3 3/8% compounded quarterly for 8 years is worth than Caleb's investment of $1100 at 3 1/2% compounded daily for 8 years.

The amount in Rahul's account is given by ...

  A = P(1 +r/n)^(nt) . . . . . P invested at rate r compounded n times per year

  A = $1100(1 +0.03375/4)^(4·8) = $1100(1.0084375^32) ≈ $1439.33

The same formula is used for Caleb's account, but with different numbers.

  A = $1100(1 +0.0325/365)^(365·8) ≈ $1426.61

The difference in account values is ...

  Rahul's - Caleb's = $1439.33 -1426.61 = $12.72 ≈ $13

Rahul will have about $13 more in his account.

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You have a summer job that pays time and a half for overtime. That means if you work more than 40 hours in a week, your hourly wage for the extra hours is 1.5 times your rate of $12 per hour.

If you work for 47 hours you will get paid $606.

Define overtime. What does overtime pay mean?

The amount of time spent working past the regular working day is known as overtime. The word is also applied to the compensation for this period of extra time.

Employees covered by the Act must receive overtime compensation, unless they are exempt, at an overtime rate that is at least time and a half their usual rates of pay for hours worked beyond 40 in a workweek.

Solution Explained:

Given,

Normal rate = $12 per hour

Overtime rate = 1.5 times more than the normal rate per hour
                       = (15 X 12) / 10 = $18 per hour

First we will see the normal total pay for 40 hours

= 40 X 12 = $480

The overtime pay = 7 X 18 = $126

Therefore, the pay for 47 hours is = 126 + 480 = $606

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For many of the rolls die, the long run relative frequency of a number less than 3 landing face up is 1/3.

Given that,

Only two integers (1 and 2) are smaller than 3, hence their relative frequency will be 2/6=1/3.

The best way to interpret the data is thus,

For many rolls of the die, the long- run relative frequency of a number less than three landing face up is1/3.

Hence option A is correct which is for many of the rolls die, the long run relative frequency of a number less than 3 landing face up is 1/3.

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Answer:

Step-by-step explanation:

margin of error

Answer:

It should be 860

Step-by-step explanation:

if there are 215 cars and each have 4 wheels, it should be 215 x 4 = 860

The  equation that can represent the perimeter of the given rectangle is

6 + 2L = 30, option c is correct.

Given,

width of rectangle = 3 cm

length of rectangle = L

perimeter of rectangle = 30 cm

equation of perimeter of rectangle = 2 × (L + W)

By substituting the values of width and perimeter we can get the equation,

    perimeter = 2 × (L + W)

=> 30 = 2 × (L + 3)

=> 30 = 2L + 6

=> 6 + 2L = 30

Therefore, the equation of the perimeter of a rectangle is 6 + 2L = 30.

Answer: 5.9 × 10 to the power of 9

Answer:

(2⁵/x²)⁴

(32/X²)

32⁴+x⁶

1,048,576 + X⁶

Step-by-step explanation:

i don't know if this is right. this is all I know