According to the graph, what is the constant of proportionality?
(0,0) (5,3)

Answer:

a) The median AD from A to BC has a length of 6.

b) Areas of triangles ABD and ACD are the same.

Step-by-step explanation:

a) A median is a line that begin in a vertix and end at a midpoint of a side opposite to vertix. As first step the location of the point is determined:

[tex]D (x,y) = \left(\frac{x_{B}+x_{C}}{2},\frac{y_{B}+y_{C}}{2} \right)[/tex]

[tex]D(x,y) = \left(\frac{3 + 5}{2},\frac{-2 + 2}{2} \right)[/tex]

[tex]D(x,y) = (4,0)[/tex]

The length of the median AD is calculated by the Pythagorean Theorem:

[tex]AD = \sqrt{(x_{D}-x_{A})^{2}+ (y_{D}-y_{A})^{2}}[/tex]

[tex]AD = \sqrt{(4-4)^{2}+[0-(-6)]^{2}}[/tex]

[tex]AD = 6[/tex]

The median AD from A to BC has a length of 6.

b) In order to compare both areas, all lengths must be found with the help of Pythagorean Theorem:

[tex]AB = \sqrt{(x_{B}-x_{A})^{2}+ (y_{B}-y_{A})^{2}}[/tex]

[tex]AB = \sqrt{(3-4)^{2}+[-2-(-6)]^{2}}[/tex]

[tex]AB \approx 4.123[/tex]

[tex]AC = \sqrt{(x_{C}-x_{A})^{2}+ (y_{C}-y_{A})^{2}}[/tex]

[tex]AC = \sqrt{(5-4)^{2}+[2-(-6)]^{2}}[/tex]

[tex]AC \approx 4.123[/tex]

[tex]BC = \sqrt{(x_{C}-x_{B})^{2}+ (y_{C}-y_{B})^{2}}[/tex]

[tex]BC = \sqrt{(5-3)^{2}+[2-(-2)]^{2}}[/tex]

[tex]BC \approx 4.472[/tex]

[tex]BD = CD = \frac{1}{2}\cdot BC[/tex] (by the definition of median)

[tex]BD = CD = \frac{1}{2} \cdot (4.472)[/tex]

[tex]BD = CD = 2.236[/tex]

[tex]AD = 6[/tex]

The area of any triangle can be calculated in terms of their side length. Now, equations to determine the areas of triangles ABD and ACD are described below:

[tex]A_{ABD} = \sqrt{s_{ABD}\cdot (s_{ABD}-AB)\cdot (s_{ABD}-BD)\cdot (s_{ABD}-AD)}[/tex], where [tex]s_{ABD} = \frac{AB+BD+AD}{2}[/tex]

[tex]A_{ACD} = \sqrt{s_{ACD}\cdot (s_{ACD}-AC)\cdot (s_{ACD}-CD)\cdot (s_{ACD}-AD)}[/tex], where [tex]s_{ACD} = \frac{AC+CD+AD}{2}[/tex]

Finally,

[tex]s_{ABD} = \frac{4.123+2.236+6}{2}[/tex]

[tex]s_{ABD} = 6.180[/tex]

[tex]A_{ABD} = \sqrt{(6.180)\cdot (6.180-4.123)\cdot (6.180-2.236)\cdot (6.180-6)}[/tex]

[tex]A_{ABD} \approx 3.004[/tex]

[tex]s_{ACD} = \frac{4.123+2.236+6}{2}[/tex]

[tex]s_{ACD} = 6.180[/tex]

[tex]A_{ACD} = \sqrt{(6.180)\cdot (6.180-4.123)\cdot (6.180-2.236)\cdot (6.180-6)}[/tex]

[tex]A_{ACD} \approx 3.004[/tex]

Therefore, areas of triangles ABD and ACD are the same.

Answer:

Box A has 1121 buttons more than Box C

Step-by-step explanation:

4432 boxes are made in three hours

Then in six hours, we would be making double of this

The number of boxes made is 4432 * 2 = 8864 boxes

Now,

we have boxes A B C to fill

Filling box B, we have 3363 boxes left to fill A and B

Now C holds half of what A hold

so we can say the ratio of buttons in C to A is 1:2

The number of buttons in C would thus be

1/3 * 3363 = 1121

Number of buttons in A would be 2/3 * 3363 = 2 * 1121 = 2242 buttons

Now the number of buttons with which the buttons in A exceeds that in C would be 2242 -1121 = 1121 buttons

Answer:

The area of the screen is 48 square inches

Step-by-step explanation:

6x8=48

Answer:

The real answer is 10!

Step-by-step explanation:

I just did the question!

Step-by-step explanation:

θ = [tex]cos^{-1}[/tex] 17 m/27 m = 50.9°

Answer:

MAD = 2

Step-by-step explanation:

First We'll find the mean of data

Mean = [tex]\frac{20}{5}[/tex]

Mean = 4

Then, we'll find absolute deviation

=> |4-3| = 1

=> |4-2| = 2

=> |4-1| = 3

=> |4-1| = 3

=> |4-3| = 1

Now, taking the mean of these absolute deviations:

MAD = [tex]\frac{1+3+3+2+1}{5}[/tex]

MAD = [tex]\frac{10}{5}[/tex]

MAD = 2

Answer:

Mix A is the most orangey, Mix C is the least orangey

Step-by-step explanation:

Mix A largest proportion of concentrate to water

Mix C is the smallest proportion of concentrate to water

Sorry, Please rewrite it again.

Answer:

Step-by-step explanation:

4x - 6 - 5x - 1

-x - 7

the answer is d

Answer:

D . -x - 7

Step-by-step explanation:

(4x-6) - (5x+1) = 4x-6-5x-1

4x-5x-1-6

4x-5x= -x

1-6 = -7

-x - 7

Answer:

Step-by-step explanation:

I don’t know the answer

The value of x such that ∠MNQ and ∠PNR are vertical angles is 40

The given parameters are:

MNQ = 3x - 6

PNR = 114

Vertical angles are equal.

So, we have:

3x - 6 = 114

Add 6 to both sides

3x = 120

Divide both sides by 3

x = 40

Hence, the value of x is 40

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The question is incomplete:

Student Friendly Bank pays a simple interest rate of 2.5% per year. Neighborhood Bank pays a compound interest rate of 2.1% per year, compounded monthly.

Which bank will provide the largest balance if you plan to invest $10,000 for 10 years? For 20 years?

Answer:

-The bank that provides the largest balance if you plan to invest $10,000 for 10 years is Student Friendly Bank.

-The bank that provides the largest balance if you plan to invest $10,000 for 20 years is Neighborhood Bank.

Step-by-step explanation:

First, you have to calculate the balance if you invest the money in Student Friendly Bank. To do it, you have to use the simple interest formula to calculate the future value:

FV=PV(1+rt)

FV= future value

PV= present value

r= rate

t=time

-10 years:

FV= 10,000(1+(0.025*10))

FV= 10,000(1+0.25)

FV=10,000(1.25)

FV=12,500

-20 years:

FV= 10,000(1+(0.025*20))

FV= 10,000(1+0.5)

FV=10,000(1.5)

FV=15,000

Second, you have to calculate the balance if you invest the money in Student Neighborhood Bank. To do it, you have to use the compound interest formula to calculate the future value:

FV=PV(1+(r/m))^mt

FV= future value

PV= present value

r= rate

t=time

m=number compounding periods per year

-10 years:

FV=10,000*(1+(0.021/12))^12*10

FV=10,000*(1+0.00175)^120

FV=10,000*(1.00175)^120

FV=12,334.5

-20 years:

FV=10,000*(1+(0.021/12))^12*20

FV=10,000*(1+0.00175)^240

FV=10,000*(1.00175)^240

FV=15,214

According to this, the bank that provides the largest balance if you plan to invest $10,000 for 10 years is Student Friendly Bank because it will provide $12,500 and Neighborhood Bank will provide $12,334.5.

The bank that provides the largest balance if you plan to invest $10,000 for 20 years is Neighborhood Bank because it will provide $15,214 and Student Friendly Bank will provide $15,000.

Answer:

12 inches

Step-by-step explanation

The perimeter of a rectangle is the sum of each of the sides. So, it would be Perimeter= width+width+height+height. Let's make x as the width as the variable. We already know the value of the perimeter and the height. We can then substitute these values in the above equation.

So, that would be 56=x + x +16 +16

Then we would solve for x. First combine like terms.

56=2x+32

Then, subtract 32 from each side.

24=2x

Finally, divide by 2 on both sides to get the answer.

x=12

Answer:

12 inches

Step-by-step explanation:

none none none none none none none

Answer:

c

Step-by-step explanation:

t = 1

f(t) = 2000 * (3 * 1)

f(t) = 6000

-4.5

i guess this is the answer

Answer: 0.39

Step-by-step explanation:

We are required to determine the the value of f, rounded to the nearest hundredth

The value of f, rounded to the nearest hundredth is 0.39

Given function:

[tex]d(v) = \frac{2.15 {v}^{2} }{64.4f} [/tex]

Where,

d = stopping distance in feet

v = initial velocity in miles per hour

f = a constant related to friction

When

v = 40 mph

d = 138 ft

f = ?

[tex]d(v) = \frac{2.15 {v}^{2} }{64.4f} [/tex]

[tex]138= \frac{2.15 {(40)}^{2} }{64.4f} [/tex]

138(64.4f) = 2.15(1600)

8,887.2f = 3440

f = 3440 / 8,887.2

f = 0.3870735439733

Approximately to the nearest hundredth f = 0.39

Therefore, the value of f, rounded to the nearest hundredth is 0.39

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Answer:

16

Step-by-step explanation:

Multiply it by 1/3 and it equals 16

Answer:

16

Step-by-step explanation:

48/3=16

Answer:

4 and 5 are coefficients the rest are terms

Step-by-step explanation:

coefficients are the numbers not the letters

Answer:

Step-by-step explanation:

The terms are the elements of the sum:

  5b, 8c, 4p

The coefficients are the constant multipliers:

  5, 8, 4

___

In your list of items to "drag and drop", you have ...

Coefficient: 4, 5

Term: 4p, 5b, 8c

Answer:

1. equation

2. variable

3. operation

4. constants

i took this on edge so i know the answers ^-^

Answer:

Step-by-step explanation:

Graph shown in the attachment,

- Since every value of x corresponds to a distinct value of y, so the graph represents a function.

- Every input value of x of the table has a output value of y, therefore, it's a function.

- In the set of ordered pairs (5, 8) and (5, 2), input value x = 5 has two output values for y,

 y = 8 and y = 2

Therefore, it's not a function and (5, 8) should be changed to make the relation a function.

Answer:

6

Step-by-step explanation:

i did the problem and got it right

Answer:

6

Step-by-step explanation:

Answer:

0.8

Step-by-step explanation:

0.768/0.96= 0.8

0.96/1.2 =0.8

Answer:

[tex]342[/tex]

Step-by-step explanation:

The probability of heads landing is 0.43.

The probability of tails landing is 1-0.43=0.57.

Azmol throws the coin 600 times, so:

[tex]600 \times 0.57[/tex]

[tex]=342[/tex]

Answer:$35.49

Step-by-step explanation:

1. Get sales tax from the original price

8/100*45.50=$3.64

2. Get the price after the discount which is 70% of the original price

45.50*70/100 = 31.85

3. Add the sales tax to the new price to get the amount paid

31.85+3.64= $35.49

Answer:

The leftmost graph [with the points (-3,-3) and (0,3)]

Step-by-step explanation:

y+3=2(x+3)

y+3=2x+6

y=2x+3

The y-intercept is 3, meaning that the line passes through the point (0,3), and it's slope is 2, so it travels 2 units up and 1 unit over. Thus the correct graph is the top left graph, with the two points (-3,-3) and (0,3).

The graph is considered as the creation of a diagram that depicts a relationship connecting two or more items, and further discussion can be defined as follows:

Given:

[tex]\bold{y+3=2(x+3)}[/tex]

To find:

graph=?

Solution:

[tex]\bold{y+3=2(x+3)}[/tex]

Solving the given equation:

[tex]\to \bold{y+3=2(x+3)}\\\\\to \bold{y+3=2x+6}\\\\\to \bold{y=2x+6-3}\\\\\to \bold{y=2x+3}\\\\[/tex]

Please find the graph in the attached file.

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Answer:

its d i just the test

Step-by-step explanation:

StartRoot 4 Superscript 5 EndRoot expression is equivalent to (2 Superscript one-half Baseline times 2 Superscript three-fourths Baseline) squared.

Definition of equivalent

1: equal in force, amount, or value also: equal in area or volume but not superposable a square equivalent to a triangle.

2a: like in signification or import. b: having logical equivalence equivalent statements. 3: corresponding or virtually identical especially in effect or function.

The definition of equivalent is something that is essentially the same or equal to something else. An example of an equivalent is (2+2) and the number 4. Since 2+2= 4, these two things are equivalent. adjective.

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Answer:

Step-by-step explanation:

Given the nth term of a geometric sequence represented as [tex]Tn = a_1r^{n-1}[/tex]

[tex]a_1[/tex] =  first term of the sequence

n = number of terms

r = common ratio

Given [tex]a_1 = 4,096,\ r = -\frac{1}{4} , n = 5[/tex](fifth term of the sequence)

[tex]T_5 = 4,096(-\frac{1}{4} )^{5-1}\\ T_5 = 4,096(-\frac{1}{4} )^{4}\\T_5 = 4,096(\frac{1}{256} )\\T_5 = 16[/tex]

The fifth term of the geometric sequence is 16

Answer:

this is the answer for edge 2020-2021

Step-by-step explanation:

sum- -204.8

Answer:

Step-by-step explanation:

[tex]t = \frac{mu^{2} }{k} -5mg\\kt = mu^{2} -5mg\\k = \frac{mu^{2} -5mg}{t}[/tex]

To make k subject of the fomula :

Step 1 : cross multiply

Step 2 : Divide both side of the equation to isolate k

The solution of the expression for the value of k will be k = (mu² - 5mgk)/t.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The given expression is t = (mu²)/k - 5mg. The value of the expression for the value of k will be,

The value of k will be written as,

t = (mu²)/k - 5mg

k = (mu² - 5mgk)/t

Therefore, the solution of the expression for the value of k will be k = (mu² - 5mgk)/t.

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Answer:

add up all the colors

Step-by-step explanation:

Answer:

AB=5.4 units

Step-by-step explanation:

We using the theorem of intersecting tangent and secant to solve this.

By this theorem:

[tex]XY^2=XB \times AX\\9^2=15(15-XB)\\81=225-15XB\\15XB=144\\XB=9.6\\$Therefore:\\AB=AX-XB\\AB=15-9.6\\AB=5.4$ units[/tex]

Answer:

Its 9.6, the other guy got it wrong, he already got it but accidentally added a step. Its 9.6 :)

Step-by-step explanation:

trust me :).