ive been stuck on this question and i will give extra points but i just dont get this question

9. Option b. The two lines are perpendicular to each other

  Given:

   6x+10y = 20

   5x- 3y = 21

Consider the first line,

10 y = -6x+ 20

y = -3/5 x + 2

This is of the form y = mx+ b

where, slope =m = - 3/5

Consider the second line,

5x- 3y = 21

3y = 5x- 21

y = 5/3 x - 21

This is of the form y = mx+ b

where, slope= m = 5/3

Since the slopes of the two lines are negative reciprocals ,they are perpendicular.

10. Option a. The equation of the line  passing through (2, -9) with a slope -5 is y = - 5x + 1

Given:

slope = m= -5

point = (2,-9)

We know that ,the slope -intercept form is given by ,

y = mx+ b ---(1)

Substituting the given values in (1)

-9 = -5(2)+b

10- 9 = b

b = 1

Substituting m and b in (1)

y = -5x+1

Thus, the slope-intercept form equation of the line is y = -5x + 1

11. The  equation of the line perpendicular to y= -2x+8 and passing through the point (4,-7) is y = 1/2x- 9

Given:

line = y = -2x+8

point = (x, y)= (4, -7)

The given equation is of the form,

y = mx+ b  ---- (1)

m = -2

The line perpendicular to this line will have a negative reciprocal slope,

m = 1/2  

The new line is of the form,

y = 1/2 x+ b   ----(2)

Substituting the given point (4, -7) in (2)

- 7= 2 + b

b = - 9

Substituting b in (2)

y = 1/2x- 9 is the perpendicular line equation

12.  The  equation of the line parallel to 3x- 2y = 14 and passing through the point (-6,-11) is y = 3/2 x -2

Given:

line = 3x- 2y = 14

point = (x, y)= (-6,-11)

The slope - intercept form of the given line is ,

2y = 3x- 14

y = 3/2x - 7  

slope = m = 3/2

The line parallel to this line will have the same slope,

m = 3/2  

The new line is of the form,

y = 3/2 x+ b   ----(1)

Substituting the given point (-6, -11) in (1)

- 11= -9 + b

b = - 2

Substituting b in (1)

y = 3/2 x -2 is the parallel line equation.

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Answer:

Option 2

Step-by-step explanation:

Using point-slope form, the line passes through (3, 1).

Option 2 is the only choice that satisfes this.

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: Graph \:\: 2[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The equation is given in its point slope form :

[tex]\qquad \tt \rightarrow \:y - 1 = \dfrac{2}{3} (x - 3)[/tex]

And the general equation in point slope form is :

[tex]\qquad \tt \rightarrow \:y - y_1 = m(x - x_1)[/tex]

by comparing these two, we can get

And [tex]{ (x_1 , y_1) } [/tex] satisfies the equation, so the line (graph) of this equation should have point (3 , 1) lying on it.

And the only graph satisfying this condition is graph 2, therefore The graph 2 is the required graph.

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

Subtract 66.5 from Devon's total to find how much he has left

Answer: 5/3

Step-by-step explanation:

The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.

We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.

Answer:

yes

Step-by-step explanation:

Answer:

11, 110

Step-by-step explanation:

Constant of proportionality: Ratio of distance to time, which is 11.

Distance at 10s: Multiply time by the constant of proportionality, giving 110.

Compute the Laplace transform of [tex]f(t)=t^n[/tex], where [tex]n[/tex] is a non-negative integer.

[tex]\displaystyle L\left\{t^n\right\} = I_n = \int_0^\infty t^n e^{-st} \, dt[/tex]

Integrate by parts with

[tex]u=t^n \implies du = nt^{n-1} \, dt[/tex]

[tex]dv = e^{-st} \, dt \implies v = -\dfrac1s e^{-st}[/tex]

[tex]\displaystyle I_n = \frac ns \int_0^\infty t^{n-1} e^{-st} \, dt = \frac ns I_{n-1}[/tex]

By substitution,

[tex]\displaystyle I_n = \frac ns I_{n-1} = \frac{n(n-1)}{s^2} I_{n-2} = \cdots = \frac{n(n-1)\cdots(n-(k-1))}{s^k} I_{n-k}[/tex]

so that for [tex]k=n[/tex], we end up with

[tex]\displaystyle I_n = \frac{n(n-1)\cdots1}{s^n} I_0 = \frac{n!}{s^n} \int_0^\infty e^{-st} \, dt = \frac{n!}{s^{n+1}}[/tex]

We then have the inverse transform relation

[tex]\displaystyle L^{-1}\left\{ \frac1{s^n} \right\} = \frac{t^{n-1}}{(n-1)!}[/tex]

and so

[tex]L^{-1}\left\{ \dfrac1{s^3} + \dfrac1s \right\} = \dfrac{t^2}{2!} + \dfrac{0!}{t^0} = \boxed{\dfrac{t^2}2 + 1}[/tex]

The decimal is equal to (294117647)/(1000000000).

Hence the average rate of change, in simplest form is -10 .

What is average rate of change?

Using the coordinate points from the table  ( 4,53) ( 8, 13 )

Substitute the coordinate into the expression

Average rate of change  = y₂ - y₁/x₂ - x₁

                                         = 13 - 53/8 - 4                    

                                         = -  4 0/4 ⇒ -10

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Answer: yes, the value of x is 4 and angle HEB is 36 degrees

Step-by-step explanation:

1a. Find the value of angle CEB

Given that line segment AB and line segment EC are perpendicular you know they are right angles and therefore are equal to 90 degrees

2a.set up an equation

After noticing that angle CEB is 90 degrees you know that angle HEB+CEH=90 degrees: 13x+9x+2

3a. Solve the equation

13x+9x+2=90

22x+2=90 | combine like terms

22x=88 | subtract 2 from both sides

x=4 | divide by 22 on both sides

1b. Set up equation

Knowing x=4 and that angle HEB is 9x the equation is 9(4)

2b. Solve the equation

9(4)

36

Answer:

43°

Step-by-step explanation:

Alternate interior angle are congruent.

The line a and b from the given line diagram is parallel since <2 and <3 are corresponding angles.

An angle is the point where two lines meet or intersect. From the given line diagram, we are told that <1 and <2 are supplementary.

Since the sum of supplementary angles is 180 degrees, hence;

<1 + <3 = 180 degrees

Also <1 + <2 = 180 degrees (sum of angles on a straight line)

<1 = 180 - <3

<1 = 180 - <2

Equate

180 - <3 = 180 - <2

-<3 = -<2

<2 = <3 (corresponding angle)

Since <2 is equivalent to <3, hence the line a is parallel to b

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Based on the results of Mean and Median, we can say that Mean is larger than median in value .

Mean of n observations can be calculated using the formula

Mean = (sum of all observations)/(number of observations) .

After arranging the data in ascending or descending order , the middle value can be called as Median .

In the question ,

the set of numbers is given as 4, 5, 11, 12, 5, 38, 44

rewriting them in ascending order ,we get 4, 5, 5, 11, 12 ,38 ,44   .

the sum of all the number = 4+5+5+11+12+38+44

                                           = 119

number of observations = 7

hence the mean = 119/7 = 17

So, mean = 17

from the set of numbers 4, 5, 5, 11, 12 ,38 ,44 we can see that

the middle value of the set of numbers is 11 .

So , median = 11 .

On comparing the mean = 17  and the median = 11 ,

we can say that the mean is greater than median.

Therefore , based on the results of Mean and Median, we can say that

Mean is larger than median in value .

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Given,

f(x) = 1x + 12

expression to be in form of h

To find on the interval: [9, 9 + h]

∵ Average rate of change of f(x) on interval (a,b) is

A = f(b) - f(a) / b - a

⇒ f(9) = 1 x 9 + 12 = 21

⇒ f(9 + h) = 9 +h + 12 = 21 + h

⇒ f(b) - f(a) = 21 + h - 21 = h

⇒ (b-a) = 9 + h - 9 = h

∴ Average rate of change = h / h

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well, her husband makes "x" in salary, hmmm hers is 16% more than that, so

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{16\% of x}}{\left( \cfrac{16}{100} \right)x}\implies 0.16x[/tex]

so she really makes x + 0.16x = 1.16x, and we know their total is 72,360, so

[tex]\stackrel{husband}{x} + \stackrel{hers}{1.16x} = 72360\implies 2.16x=72360\implies x=\cfrac{72360}{2.16}\implies \boxed{x = 33500}[/tex]

The function F(20) is 50

The most common symbols for a function are the letters f, g, and h. A function's value at an element of its domain x is denoted by the notation f(x), and the numerical value obtained from the function evaluation at a specific input value is denoted by substituting that value for x. For instance, the value of f at x = 4 is denoted by the notation f(x) (4). When a function isn't given a name and is instead represented by the expression E, the value of the function at, say, x = 4 may be shown by the notation E|x=4.

Given that :f(x) = 2x + 10

f(x) = 2x + 10

F(20)= 2(20) + 10

F(20)= 40 + 10

F(20)= 50

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Answer:

Option 4

Step-by-step explanation:

Each x-value corresponds to only one y-value

Answer:

45 levels

Step-by-step explanation:

60% of 75 is 45 i think

The coordinates of a centroid of a triangle with vertices  [tex](x_1,y_1),(x_2,y_2),(x_3,y_3)[/tex]  are [tex](\frac{x_1+x_2+x_3}{3}, \frac{{y_1+y_2+y_3} }{3})[/tex].

Centroid of a triangle

For a triangle, the centroid is obtained by the intersection of its medians. The line segments of medians join vertex to the midpoint of the opposite side. All three medians meet at a single point (concurrent). The point of concurrency is known as the centroid of a triangle.

Let KLM be a triangle with the vertex coordinates [tex](x_1,y_1),(x_2,y_2),(x_3,y_3)[/tex] as K,L and M respectively.

Let the midpoints of the side LM, KL and KM are D, E, and F, respectively. The centroid of a triangle is represented as “G.”

As D is the midpoint of the side LM, we can write,

D = ((x2+x3)/2, (y2+y3)/2)

Now, we know that, G intersects AD in the ratio 2:1 , we get

Hence, using section formula we can write,

The x-coordinates of G will be:-

x = (2(x2+x3)/2 + 1.x1 )/ (2+1) =  (x2+x3+x1)/3  = (x1+x2+x3)/3

The y-coordinates of G will be :-

y =(2(y2+y3)/2 + 1.y1 )/ (2+1) =  (y2+y3+y1)/3 =  (y1+y2+y3)/3

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Answer:

54 cm

Step-by-step explanation:

A cube has six sides. The area of each face is found by squaring the length of a side. To get the total surface area of the cube, you'll multiply the area of one face by the number of faces.

a = edge

Area = 6a to the power of 2

Answer:

Not linear

Step-by-step explanation:

Can be written into the form of [tex]y=mx+b\\[/tex].

The measure of each angle is 34.1° and 55.9°

complementary angles are angles that gives 90° when added to together.

if the first angle is x and the other complementary angle is y,

then x+y=90

x= y-21.8

representing y-21.8 for x in equation x+y=90

y+ y-21.8= 90°

2y= 111.8

y= 55.9°

and x= 34.1°

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The probability of a lizard living for more than 2.5 years is 16%.

The average lifespan of a lizard is 3.1 years, with a standard deviation of 0.6 years.

Average lizard u = 3.1,

standard deviation σ = 0.6

To calculate the likelihood of a lizard living for more than 2.5 years;

p(X<2.5)

μ + aσ = 2.5

3.1 + a(0.6) = 2.5

a(0.6) = −0.6

a = −1

To calculate the probability, apply the empirical rule.

The total area = 100% (since total probability always is 1)

Area from  μ to ∞  =  p(X > μ)  = 50%

Area between  (μ−σ)  and  (μ+σ)  = 68%  

Area between  (μ−σ)  and  μ  is  p((μ−σ) < X < μ)  =34%  

Thus,

p(X< (μ−σ)) = 1 − (p((μ−σ) < X < μ) + p(X > μ))

                  = 1 − (0.34 + 0.5)

p(X< (μ−σ)) = 0.16  

Therefore, the probability that a lizard will live longer than 2.5 years 16%.

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The depreciation equation is given by

where x represents the number of years. Here, the initial value of the car corresponds to x=0, then we have

After one year, the car value corresponds to x=1, that is,

Now, let's find the depreciation percentage by means of a rule of three:

so we have

So the difference between 100% and 86% is 14% This means Nichole's car depreciate 14% each year

Answer:

Step-by-step explanation:

8(2+3)

Answer:

11

Step-by-step explanation:

A whole number is an integer greater than 0.

-76 , -34 , -57 are all negative so they are not whole numbers.

0 is too small so it also is not a whole number.

By ruling out those numbers you are left with 11 which is positive and greater than 0. Therefore, the correct answer is 11.

Answer:

0 and 11

Step-by-step explanation:

Whole numbers are set yo to be real numbers that include zero and all positive numbers while it excludes fractions, negative integers and decimals.

Therefore, from our question, 0 and 11 are whole numbers while -76, -34 and -57 are excluded because they are negative integers.

Answer:

y=4x+9

Step-by-step explanation:

y-Y1= m× x-X1

Y-1 = 4×X+2

y-1 = 4x+8

y=4x+9

Answers to your questions with explanations are below. You can ask a question, feel free. I wish you success!

This answer should be Vertical Angles.

Vertical angles are angles that are opposite of each other when two lines cross and equal each other. [tex](a^o=b^o)[/tex]

A pair of vertical angles is formed when two lines intersect each other at a single point. They are said to be linear if the angles are adjacent after the intersection of the two lines. The sum of the angles of a linear pair is always equal to [tex]180^o[/tex]. Such angles are also known as complementary or supplementary angles.

The answer is [tex]2^{nd}+4^{th}+5^{th}[/tex]

The answer is the first option. Adjacent angles. The rule is simple. If [tex]a+b=90^o[/tex] if they're adjacate angles.

The answer is the third option. Supplementary angles. The rule is simple. If [tex]a+b=180^o[/tex] if they're supplementary angles.