Complete the coordinate proof of the theorem.

The slope of the line is

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

Substituting into point-slope form using the point (3,1),

[tex]\boxed{y-1=-\frac{4}{3}(x-3)}\\\\y-1=-\frac{4}{3}x+4\\\\\boxed{y=-\frac{4}{3}x+5}[/tex]

Answer: The equation of the line that passes through (6,- 3) and (3,1) is  y = [tex]\frac{-4x}{3}[/tex] +5.

Step-by-step explanation:

Point-slope formula : (y - y1) = m(x - x1)

y = y coordinate of second point

y1     = y coordinate of first point

m = slope

x = x coordinate of second point

x1     = x coordinate of first point

slope (m) = [tex]\frac{1-(-3)}{3-6}[/tex]

          m = [tex]\frac{4}{-3}[/tex] or [tex]\frac{-4}{3}[/tex]

now put values in point-slope formula  : (y - 1) = [tex]\frac{-4}{3}[/tex](x - 3)

y - 1 = [tex]\frac{-4x}{3\\}[/tex] + 4

y = [tex]\frac{-4x}{3}[/tex] +5

So the equation of the line that passes through (6,- 3) and (3,1) is y = [tex]\frac{-4x}{3}[/tex]+5.

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The number best represents the slope of the graphed line is 1/2.

We have given the two points,

(-6,-7) and (4,-2) and slope-intercept is 8 units

[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]

y = y coordinate of the second point

[tex]y_1[/tex] = y coordinate of point one

m = slope

x = x coordinate of the second point

[tex]x_{1}[/tex]= x coordinate of point one

Therefore the

[tex]slope=\frac{y_2-y_1}{x_2-x_!}[/tex]

[tex]=\frac{-2-(-7)}{4-(-6)} \\=\frac{5}{10}\\ =\frac{1}{2}[/tex]

Therefore the correct option is 1/2.

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Answer:

JN = 32

Step-by-step explanation:

Δ JMN and Δ JKL are similar ( AA postulate )

then the ratios of corresponding sides are in proportion, that is

[tex]\frac{JM}{JK}[/tex] = [tex]\frac{JN}{JL}[/tex] ( substitute values )

[tex]\frac{24}{33}[/tex] = [tex]\frac{JN}{JN+12}[/tex]

[tex]\frac{8}{11}[/tex] = [tex]\frac{JN}{JN+12}[/tex] ( cross- multiply )

11 JN  = 8(JN + 12)

11 JN = 8 JN + 96 ( subtract 8 JN from both sides )

3 JN = 96 ( divide both sides by 3 )

JN = 32

The GDP of the country for 2014 is $5.3196 × 10⁸.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

Given the Gross Domestic of a country in the first quarter of 2014 was $1.3299×10⁸. Therefore, the GDP of the country for that year will be,

GDP = 4 × (Gross Domestic for a single quarter)

         = 4 × ($1.3299×10⁸)

         = $5.3196 × 10⁸

Hence, the GDP of the country for 2014 is $5.3196 × 10⁸.

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Answer:

Step-by-step explanation:

Comment

The angle supplementary to x and 3x are equal.

Supplementary angles = 180

Solution

x + 3x = 180

4x = 180                  Divide by 4

4x/4 = 180/4

x = 45

The angle supplementary to x is 3x

3x = 3*45

3x = 135

This angle is vertically opposite y. Vertically opposite angles are equal. So  y = 135

Answer

x = 45

y = 135

Answer:

8

Step-by-step explanation:

It's 7 rows of 8 items

Answer:

11

Step-by-step explanation:

duh add 1 and 1 merge it together to get 11

that's a hard question imma go with 2 though

Step-by-step explanation:

for this problem let's let x=1 and y also =1 so x+y=2 hope this helps

[tex]x^2+72x=8\\x^2+72x+1296=1304\\(x+36)^2=1304\\x+36=\sqrt{1304} \vee x+36=-\sqrt{1304} \\x=-36+2\sqrt{326} \vee x=-36-2\sqrt{326}[/tex]

Answer:

a) quantitative - continuous

b) qualitative

c) quantitative - discrete

d) quantitative - discrete

Explanation:

A qualitative variable describes an object or its property without counting or measuring. Therefore it does not include any numbers.

A quantitative variable is one which results from counting or measuring a property of an object or situation. If the variable arises from counting, it is called discrete, and if it arises from any measurement, it is called continuous.

I assume you meant [tex]f(x)=0.5(4)^{x}[/tex]. The graph is shown below.

Answer:

width is 30, and the length 69.

Step-by-step explanation:

In order to do this, we need to do ALGOOBRAA

lets say x is equal to the width of the room

then, that means the length is (9+2x) Sooooo,

198=2x+2(9+2x)

Using the distributive property, we know that

2(9+2x)=18+4x

If you dont know what that is, then go search it up :/

so,

198=2x+18+4x

198=6x+18

180=6x

30=x

BAM

Now, we know that the width is 30, bro.

That means the length is 60+9, Which is 69.

Therefore, the width is 30, and the length 69.

Sry if im wrong btw.

The width of rectangle is 30, and the length is 69.

A rectangle is a quadrilateral. The opposite sides of a rectangle are equal and parallel to each other. The interior angle of a rectangle at each vertex is 90°. The sum of all interior angles is 360°. The diagonals bisect each other.

Here, lets say x is equal to the width of the room

then, that means the length is (9+2x) So,

              198 = 2x+2(9+2x)

Using the distributive property, we know that

                 2(9+2x)=18+4x

If you don't know what that is, then go search it up :/

so,

               198 = 2x+18+4x

                198=6x+18

                 180=6x

                  30=x

Now, we know that the width is 30,

That means the length is 60+9, Which is 69.

Thus, the width of rectangle is 30, and the length is 69.

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Answer is 1832.7

step by step

z=kx^3 / y^3

167=27k/1000

k=16700/27

k=6185.2, then

z=6185.2×4^3/6^3

z=6185.2×64/216

z=1832.7

Step-by-step explanation:

both ends are going to the same direction so the degree is even. the right side is going up so the leading coefficient is positive.

Answer:

C. 9

Step-by-step explanation:

y(x+x) +3

{x= 1 , y= 3}

Putting values..

3 (1+1) +3

= 3 (2) +3

= 6 + 3

= 9

So, the option C. 9 is the correct answer.

Answer:

LM

Step-by-step explanation:

Perpendicular slope would be   - 1 / m   =   - 1/(-5/6)   = 6/5

slope m = rise / run       line   LM   rises 6    for a run of 5      

Answer: By 8 hours, there will be 65536 bacteria in the culture.

Step-by-step explanation:

The numerical expression used for this problem is [tex]4^{8}[/tex].

You can find the value of this on a calculator. I hope this helps!! :)

If that is not the answer, then try 32 because 4*8=32.

Answer:

67.13°

Step-by-step explanation:

First separate triangles then you use Pythagoras theorem to get the third side and then apply the sine rule

Answer:

Another rational number.

Step-by-step explanation:

For example, [tex]\pi[/tex] is incorrect because It is a irrational number

you must add another rational number to 1/2 to make the sum rational.

Rational number are numbers that can be converted into a fraction.

all natural numbers, whole numbers, integers, are rational.

and all rational and irrational numbers are real numbers

The statements can be completed by using the following :

1) -2 is multiplied with (5x+8)

2)  transposing of numeral values and variable values

3) The numerical values are taken one side and added to each other

4) 30 is divided by -16

5) The numerator and denominator are cancelled to the lowest possible value

x= -15/8

Given:  -2(5x+8)=14+6x  

and steps for solving them have also been given

In the first step, -2 is multiplied with (5x+8) and we get

-10x -16 = 14 +6x

In step 2, transposing of numeral values and variable values is done and we get -16x - 16 = 14

In step 3,

The numerical values are taken one side and added to each other and we get -16x=30

In step 4, 30 is divided by -16

In step 5, they are cancelled to the lowest possible value and we get

x= -15/8

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Graphs are used to show the relationship between variables, where the variables are represented by a pair of axes.

The domain of the function is t ≥ 0

The greatest concentration of the medication is 5mg/L

Given that:

C(t) = [tex]\frac{-8t^2 + 56t}{t^2 +3t + 2}[/tex]

(a): The domain of the function

Because the medication concentration C(t) is a function of time (t), the domain is the possible values t can take.

t, cannot take negative values (i.e. it is not possible to have a negative time).

The least possible value of t is 0

So, the domain of the function based on the context is: t ≥ 0

(b) The greatest concentration of the medication

From the graph (see attachment), the maximum y-value is 5.

Hence, the greatest concentration of the medication is 5 mg/L

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The graph of the function is shown in the attached image.

[tex]x+y\leq 80[/tex]

[tex]7x+4y=1000[/tex]

The number of burgers = [tex]x[/tex]

the number of pizzas = [tex]y[/tex]

the cost of each burger = $[tex]7[/tex]

the cost of each pizza = $[tex]4[/tex]

not more than 80 items: [tex]x+y\leq 80[/tex]

total price =[tex]7x+4y=1000[/tex]

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Answer:

5m4n3 and 15m2n2

Step-by-step explanation:

you just have to find the 2 that each are divisible by 5m2n2, which are 5m4n3 and 15m2n2.

Answer:

KC to StL = 300

KC to Den = 600

Step-by-step explanation:

KC to StL was the base distance, so we'll call that x.

KC to Denver is twice as long, so we'll call that 2x.

If we add the together is is 900 miles total.

x + 2x = 900    Combine like terms

3x = 900          Divide by 3

x = 300

If x is 300, then 2x is 600.

Answer:

[tex]\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}[/tex]

Step-by-step explanation:

A complex number is defined as z = a + bi. Since the complex number also represents right triangle whenever forms a vector at (a,b). Hence, a = rcosθ and b = rsinθ where r is radius (sometimes is written as |z|).

Substitute a = rcosθ and b = rsinθ in which the equation be z = rcosθ + irsinθ.

Factor r-term and we finally have z = r(cosθ + isinθ). How fortunately, the polar coordinate is defined as (r, θ) coordinate and therefore we can say that r = 4 and θ = -π/4. Substitute the values in the equation.

[tex]\displaystyle \large{z=4[\cos (-\frac{\pi}{4}) + i\sin (-\frac{\pi}{4})]}[/tex]

Evaluate the values. Keep in mind that both cos(-π/4) is cos(-45°) which is √2/2 and sin(-π/4) is sin(-45°) which is -√2/2 as accorded to unit circle.

[tex]\displaystyle \large{z=4\left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2}}{2}i \right)}\\\\\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}[/tex]

Hence, the complex number that has polar coordinate of (4,-45°) is [tex]\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}[/tex]

The absolute value function that will be wider than the graph of the parent function, f(x) = |x| is (d) f(x) = 9|x|

The parent function is given as:

f(x) =|x|

A wider function would have the following equation

f(x) = k|x|

Where:

k > 0

From the list of options, we have:

f(x) = 9|x|

Hence, the absolute value function that will be wider than the graph of the parent function, f(x) = |x| is (d) f(x) = 9|x|

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Answer:

getting to the point , D.

Step-by-step explanation:

trust

Answer:

The range of the function f(x) :  is y > 0.

The correct option is (A)

Step-by-step explanation:

The definition of range is the set of all possible values that the function will give when we give in the domain as input.

Given function is :

If we draw the graph for this, then we can see that the horizontal asymptote is 0.

So,  the range is real numbers higher than 0.

Hence, the range should be y > 0.

Answer:

All real numbers greater than or equal to 2.

Step-by-step explanation:

To find the range, we look at the y values. Since all the y values never dip under 2 and also keep increasing to infinity, the range is [tex]y\geq 2[/tex].

Answer:

all real numbers greater than or equal to 2

Step-by-step explanation:

Edge