Question 6 (Yes/No Worth 1 points) (02.01 LC) Is the following relation a function? x y 1 −2 1 −3 2 1 3 −2 Yes No

Answer:

A straight line is represented by a linear equation.

The possible equations are:

\mathbf{3y = 2x + 4}3y=2x+4 .

\mathbf{y = \frac 23x + \frac{4}{3}}y=

3

2

x+

3

4

.

\mathbf{y = \frac 23(x - 1) + 2}y=

3

2

(x−1)+2 .

\mathbf{y = \frac 23(x - 4) + 4}y=

3

2

(x−4)+4

The points are given as:

\mathbf{(x,y) = \{(1,2),(4,4)\}}(x,y)={(1,2),(4,4)}

Start by calculating the slope (m)

\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}m=

x

2

−x

1

y

2

−y

1

So, we have:

\mathbf{m = \frac{4-2}{4-1}}m=

4−1

4−2

\mathbf{m = \frac{2}{3}}m=

3

2

The equation in slope intercept form is then calculated as:

\mathbf{y = m(x - x_1) + y_1}y=m(x−x

1

)+y

1

So, we have:

\mathbf{y = \frac 23(x - 1) + 2}y=

3

2

(x−1)+2

or

\mathbf{y = \frac 23(x - 4) + 4}y=

3

2

(x−4)+4

Expand \mathbf{y = \frac 23(x - 1) + 2}y=

3

2

(x−1)+2

\mathbf{y = \frac 23x - \frac 23 + 2}y=

3

2

x−

3

2

+2

Take LCM

\mathbf{y = \frac 23x + \frac{-2 + 6}{3}}y=

3

2

x+

3

−2+6

\mathbf{y = \frac 23x + \frac{4}{3}}y=

3

2

x+

3

4

Multiply through by 3

\mathbf{3y = 2x + 4}3y=2x+4

So, the possible equations are:

\mathbf{3y = 2x + 4}3y=2x+4 .

\mathbf{y = \frac 23x + \frac{4}{3}}y=

3

2

x+

3

4

.

\mathbf{y = \frac 23(x - 1) + 2}y=

3

2

(x−1)+2 .

\mathbf{y = \frac 23(x - 4) + 4}y=

3

2

(x−4)+4

The absolute value equation representing all numbers x whose distance from 8 is 6 units will be x = {2, 14).

Based on the information given, it should be noted that the distance of x, positive or negative from 8 can be expressed as |x - 8|.

Since the distance is equal to 6, our equation will be:

|x - 8| = 6

x = 8 + 6 = 14

or

- |x - 8| = 6

-x + 8 = 6

-x = 6 - 8

-x = -2

x = 2

Therefore, the appropriate equation is x = {2, 14).

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Answer: 7. 140°  8. 60°

Step-by-step explanation:

7.

A internal angle of a convex poligon is:

[tex]\displaystyle\\x=\frac{(n-2)180^0}{n} \\\\n=9\\\\So,\\\\x=\frac{(9-2)180^0}{9} \\\\x=7*20^0\\\\x=140^0[/tex]

8.

[tex]\displaystyle\\x=\frac{(n-2)180^0}{n} \\\\n=3\\\\So,\\\\x=\frac{(3-2)180^0}{3} \\\\x=1*60^0\\\\x=60^0[/tex]

Answer:

m= 3

Step-by-step explanation:

In the slope-intercept form (y= mx +c), the coefficient of x (when the coefficient of y is 1) is the slope.

y= x +5

Slope of line= 1

Parallel lines have the same slope, hence the slope of 3y -mx +3= 0 is also equal to 1.

Let's rewrite the equation into slope-intercept form.

Keep the y term on the left-hand side, bring the others to the right.

3y= mx -3

Divide both sides by 3:

[tex]y = \frac{m}{3} x - 1[/tex]

Given that the slope is 1,

[tex] \frac{m}{3} = 1[/tex]

Multiply both sides by 3:

m= 1(3)

m= 3

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Answer:

x = 17

Step-by-step explanation:

          x² + 9 = 298

Subtract 9 from both sides,

         x² + 9 - 9 = 298 - 9

                 x²    = 289

Prime factorize 289,

                 x²   = 17*17

Take square root,

                [tex]\sf \sqrt{x^2}= \sqrt{17*17}[/tex]

                    x = 17

The value of k is 15 in the given equation f(x)=2x³ + kx - 4.

What exactly do we mean by equations?

So, the value of K:

The remainder when dividing by x-a is f(a) according to the remainder theorem:

- 18 is the remainder:

Therefore, the value of k is 15 in the given equation f(x)=2x³ + kx - 4.

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The equation to the parabola that passes through the points (0,4), (2,4) and (-2,8) is y = 6x+8.

A parabola is a mirror-symmetrical, nearly U-shaped planar curve in mathematics. It correlates to a multitude different statistical equations that appears to be superficially distinct and yet all define the exact same arcs. A point and a line are used in one definition of a parabola. the intersection of a right circular cone with a plane parallel to an element of the cone; a plane curve produced by a point moving so that its distance from a fixed point is equivalent to its length from a dedicated line. Anything resembling a bowl (such as an antenna or microphone reflector). A parabola graph shows a quadratic function as a U-shaped curve. A parabola is one of the conic sections in mathematics and is created by the intersection of a right circle .

y= ax²+ bx +c

Always begin with the coordinates which has 0 in it

(0,4)

4=a(0)² + b(0) + c

4=c

y = ax²+ bx + 4

The next set of coordinates (2,4)

4 = a(2)² + b(2) + 8

4 = 4a + 2b + 8

-4 = 4a + 2b

The other set of coordinates(-2,8)

8 = a(-2) + 2-2b +  8

0 = 4a-2b

Add the two above equations together...

0 = 8a

0 = a

Subtract the two equations from each other...

= 0 + 4b

24 = 4b

6 = b

y = 6x+8

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If line AB and BC are intersecting at point B and ray BD bisect the angle ABC, then the value of x is 23

The line AB and BC are intersecting at point B.

Ray BD bisect the  angle ABC

∠ABD = x+8 degrees

∠ABD=∠DBC = x+8

Because the ray BD bisect the ∠ABC, so ∠ABD and ∠DBC will be equal

∠ABD+∠DBC= 4x-30 degrees

Because both are vertically opposite angles

Substitute the values in the equation

x+8 + x+8 = 4x-30

2x+16 = 4x-30

2x-4x = -30-16

-2x = -46

x = 23

Hence, if line AB and BC are intersecting at point B and ray BD bisect  the angle ABC, then the value of x is 23

The complete question is

Line AB and BC are intersecting at point B and ray BD bisect the angle ABC. What is the value of x?

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A Energy t = 54.70 min could it sustain a current.

What does energy mean according to science?

apply power  = energy/time  =  Vi

so energy  E    = vit

time t  =  E/vi

t  =  6400/(1.3* 1.5)

t  = 6400/1.95 sec

t  =  3282.05 sec

t = 54.70 min

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a. The equation of the perimeter is x + x + x + 2x + 2x = 42. Option A

b. x = 6 centimeters

c. The lengths are 6 centimeters , 6 centimeters , 6 centimeters  , 12 centimeters  and 12 centimeters respectively.

It is important to note that the formula for calculating the perimeter of a pentagon is expressed as;

Perimeter = 5a

Where: 'a' represents the length of one of its side

From the information given, we have that the perimeter of the geometrical figure is the sum of its sides.

Given the sides;

x , x , x, 2x , 2x

Now, substitute the values into the formula for perimeter

x + x + x + 2x + 2x = 42

collect like terms and add them

7x = 42

Now, make 'x' the subject of formula by dividing both sides by the coefficient of the variable 'x'

We have;

7x/7 == 42/7

x = 6 centimeters

But the length of the sides is determined by substituting the value of x as 6

x = 6 centimeters

x = 6 centimeters

x = 6 centimeters

2x = 2(6) = 12 centimeters

2x = 2(6) = 12 centimeters

Hence, the lengths are 6, 6, 6 , 12 and 12 centimeters respectively.

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Answer:

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

Equation of surface area:

Substitute and calculate:

Equation of volume:

Substitute and calculate:

The information given regarding the hair products, a styling cream and a mousse shows that it's not double bind.

The subjects in a single-blind study are not made aware of the research treatment, if any, they are receiving. In a double-blind study, the researchers and participants are both unaware of the treatment allocation.

Due to the fact that neither the participant nor the researcher are aware of who has got what therapy, double-blind trials are regarded as the most credible type of research. This is done in an effort to lessen bias and the placebo effect.

It should be noted that in this case, one group was assigned to use the styling cream for the next two weeks and the other group was assigned to use the mousse.

Both groups should have been given same product to illustrate the double bind in the experiment.

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Answer:

$14.04

Step-by-step explanation:

-21.46 + 35.50 is the same as

35.50 - 21.46 = $14.04

Answer: 14.04

Step-by-step explanation: -21.46 + 35.50 = 14.04

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{0}}} \implies \cfrac{ -4 }{ 5 } \implies - \cfrac{ 4 }{ 5 }[/tex]

Answer:

b = 64°

Step-by-step explanation:

The sum of interior angles of a polygon is 180°(n - 2), where "n" is number of sides.

~~~~~~~~~~

180°(6 - 2) = 720°

114° + (b + 49°) + (2b - 25°) + 142° + (b + 39°) + (3b - 47°) = 720°

7b + (114° + 49° - 25° + 142° + 39° - 47°) = 720°

7b + 272° = 720°

7b = 448°

b = 64°

Answer:

y = 1.25x - 2.5

Step-by-step explanation:

To write the equation of a line in line in slope intercept form,

                  we can use y = mx + c

According to the question, writing the given equation in slope intercept form makes y the subject.

5x - 4y = 10

First, subtract 5x from both sides.

- 4y = 10 - 5x

Now, divide both sides by -4.

[tex]\frac{-4y}{-4}=\frac{10-5x}{-4} \\\\y = \frac{-5x}{-4}+\frac{10}{-4}\\\\y= 1.25x-2.5[/tex]

Answer: x> -99/4

Step-by-step explanation:

−2/5x −9 < 9/10

Multiply Both Sides

-4x-90<9

Move the constant to the right

-4x < 9 + 90

Calculate

-4x < 90

Divide both sides

Answer x> -99/4

The equations representing the data in the table are:

y-6 = -5/4(x+2)

y-3.5 = -1.25x

y-1 = -5/4(x-2)

The table with x and y values are:

x       |      y

-2           6

0          3.5

2             1

4          -1.5

We need to find the equation of the table in point slope form for this table by considering each point and the slope.

First two find the slope, consider two points (x₁, y₁) = (-2,6) and (x₂, y₂) = (2, 1).

Then slope, m = (y₂ - y₁)/(x₂ - x₁)

                        = (1-6)/2--2)

                        = -5/4

Now we find the point-slope form for each point (x', y') from the table.

The equation in point -slope form is y - y' = m(x-x')

y-6 = -5/4(x+2)

y-3.5 = -5/4x ⇒ y-3.5 = -1.25x

y-1 = -5/4(x-2)

y+1.5 = -5/4(x-4)

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A road is 6 degrees inclined after 4900 feet of travel. The driver's increasing in altitude is 509.6

Given that,

A road is 6 degrees inclined after 4900 feet of travel.

We have to find the driver's increasing in altitude.

In a right angle triangle,

According to the definition of a right triangle, a triangle is referred to as a right-angled triangle or simply a right triangle if one of the angles is a right angle (90°). Triangle ABC is a right triangle in the illustration, consisting of the base, altitude, and hypotenuse. The significant side of a right triangle is the hypotenuse, which is the longest side and sits in opposition to the triangle's right angle.

Sinθ=Altitude/Hypotenuse

Sinθ×Hypotenuse=Altitude

Altitude=Sin6°×4900

Altitude=0.104×4900

Altitude=509.6

Therefore, The driver's increasing in altitude is 509.6

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In this case, we're given the following information:

The mother's donation of $9 will not change no matter how many miles Isabelle has walked, so if both the mother's and grandmother's donations are equal, they must each owe 9$.

Each donor owes $9.

Step-by-step explanation:

100% = $2000

1% = 100%/100 = 2000/100 = $20

how many % are $300 ?

well, as many % as 1% fits into these $300 :

300 / 1% = 300 / 20 = 15%

15% of last semester's costs were spent on books.

Answer:

total= 2000

spent = 300

300/2000x100

= 15 %

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Answer:

B.

X>-5 and X<-1

Step-by-step explanation:

|x+3|<2

The absolute value is already isolated for, so now you make two different equations.

x+3>-2

and

x+3<2

you get x>-5 and x<-1

Answer:

Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.

Parallel lines have the same gradient so equation of line is y = -3x + c.

Substitute (1,7) into the equation to find c.

7 = -3(1) + c

c = 10

Hence equation of line is y = -3x + 10

Answer:

x =10

Step-by-step explanation:

Equation

-(2x + 5.9) +8.3 = 4+3(-x+ 2.8)             Carefully remove both sets of brackets

Solution

-2x - 5.9 + 8.3 = 4 + -3x + 8.4             Combine like terms on both sides

-2x + 2.4 = -3x + 12.4                           Add 3x to both sides

-2x+3x + 2.4 = -3x+3x + 12.4               Combine

x + 2.4 = 12.4                                        Subtract 2.4 from both sides

x + 2.4 - 2.4 = 12.4 - 2.4                       Combine

x = 10

If a researcher uses u.s. census data to examine changes in the number of individuals in each racial group across states over time, she is using stratified sampling.

Samples may be classified as:

For this problem, we have that the population is divided into groups, according to their racial group, and then parts of the sample are surveyed, hence stratified sampling is used.

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You must explicitly state that the null hypothesis is demonstrated to be true in cases where there is insufficient evidence to disprove it.

A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided observations. Using sample data, hypothesis testing is performed to judge a theory's veracity. It is sometimes referred to as just "the null," and its symbol is H₀

Even though we are unable to rule out the null hypothesis, this does not always imply that it is accurate. The reason for this is that a hypothesis test cannot tell which hypothesis is true or even which is more likely. It just evaluates whether there is sufficient evidence to disprove the null hypothesis.

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Answer:

A.) S(0) and S(6) represent the number of pairs of socks sold.

B.) S(0) = 14, S(6) = 2

C.) The domain of the function, the x-values, are all real numbers. As the domain doesn't have any imaginary number and its not infinite, as the graph shows. From (0,14) to (7,0)

Brainly pls :)

Step-by-step explanation:

B.)

S(0) = 14 - 2(0)

S(0) = 14

S(6) = 14 - 2(6)

S(6) = 2

Graph is plotted below.

A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x, y). You do the reverse to determine a point's coordinates in a coordinate system. Start at the point, then move up or down a vertical line until you reach the x-axis. Your x-coordinate is shown there. To get the y-coordinate, repeat the previous step while adhering to a horizontal line. A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

Coordinates are:

(-6,-8)

(1,--8)

(10,-8)

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