Which system of equations is represented by the matrix below?

Step-by-step explanation:

Let the small mass be m and position on x axis be y.

A 20 kg sphere is at the origin.

Distance to 20 kg mass = y

A 10 kg sphere is at x = 20 cm

Distance to 10 kg sphere = 20 - y

We have forces between them are equal

We have gravitational force   

                    [tex]F=\frac{GMm}{r^2}[/tex]              

          Where G =  6.67 x 10⁻¹¹ N m²/kg²

                      M = Mass of body 1

                      M = Mass of body 2

                      r = Distance between them

Here we have

            [tex]\frac{G\times 20\times m}{y^2}=\frac{G\times 10\times m}{(20-y)^2}\\\\800-80y+2y^2=y^2\\\\y^2-80y+800=0\\\\y=68.28cm\texttt{ or }y=11.72cm[/tex]

So the small mass should be placed at x = 11.72 cm or x = 68.28 cm

The positions on the x-axis obtained using quadratic equation such that net gravitational force is zero are 68.28 and 11.72 cm respectively.

Recall the force of universal gravitational attraction :

Sphere 1 :

Sphere 2 :

Gravitational force ; sphere 1 :

Gravitational force ; sphere 2 :

Equate (1) and (2)

[tex] \frac{G \times 20 \times m_{2}}{d^{2}} = \frac{G \times 10 \times m_{2}}{(20 - d)^{2}} [/tex]

[tex] 20(20 - d)^{2} = 10 \times d^{2} [tex]

20(400 - 40d + d²) = 10d²

8000 - 800d + 20d² = 10d²

10d² - 800d + 8000 = 0

Divide through by 10

d² - 80d + 800 = 0

Using a quadratic equation solver :

d = 68.28 cm or d = 11.72 cm

The possible positions are 68.28 cm and 11.72 cm

Learn more :https://brainly.com/question/8882508

Answer:

Approx. 1.8 in.²

Step-by-step explanation:

Circumference of a circle (the pizza) = 2πr

Area of a circle = πr²

Set 2πr = 4.71 (because that's the length of bacon around the pizza) and solve for the radius "r". Then plug that "r" into the area equation πr² to find the area. You should get 1.8 square inches if I plugged them in correctly.

Answer:

4.08

Step-by-step explanation:

Interest I =Pnr

3 months =3/12 year = n

r = 3%

and, P = 544$

Therefore,

[tex]i = 544 \times (3 \div 100) \times (3 \div 12) \\ \: \: \: = 4.08[/tex]

Answer:

Graph of the following function is attached with the answer.

Domain : ( - ∞ , + ∞ )

Range : ( 3 , + ∞ )

Step-by-step explanation:

[tex]f(x)=\frac{1}{2}x^{2}+3[/tex]

Domain of any quadratic equation is from negative infinity to positive infinity under no restrictions.

So, Domain : ( - ∞ , + ∞ )

The Range of any function can be calculated easily if there is just one term with variable. The method to find Range by that method is explained with the example as follows:

Therefore the Range of [tex]\mathbf{f(x)\boldsymbol=\frac{1}{2}x^{2}\boldsymbol+3}[/tex] is [ 3 , + ∞ )

(NOTE : [a,b] means all the numbers between 'a' and 'b' including 'a' and 'b'.

(a,b) means all the numbers between 'a' and 'b' excluding 'a' and 'b'.

(a,b] means all the numbers between 'a' and 'b' including only 'b' not 'a'.

[a,b) means all the numbers between 'a' and 'b' including only 'a' not 'b'.

{a,b} means only 'a' and 'b'.

{a,b] or (a,b} doesn't mean anything. )

Answer:

$2,940

Step-by-step explanation:

Data provided in the question:

Cost of merchandise purchased = $40,000

Cost of merchandise returned = $3,000

Terms = 2/10, n/30

Now,

The amount that will be recorded as the purchase return

= Cost of merchandise returned - Discount on cost of merchandise

= $3,000 - ( 2% of $3,000 )

= $3,000 - ( 0.02 × $3,000 )

= $3,000 - $60

= $2,940

Answer:

Keys would have to spend $6.60 on apples for both days.

Step-by-step explanation:

Keys went to buy 5 apples and 2 oranges for $3.45 and 7 apples and 3 oranges for $4.90 .

We have to find how much money she spends on apples on both the days.

Let price of apples be x and oranges be y.

We have to make equations and solve them to find the price of oranges and apples.

5x + 2y = 3.45

7x + 3y = 4.90

Solve both these equations to find x and y.

We get x= $0.55 and y = $0.35

Key has bought 12 apples and it would cost = 12 [tex]\times[/tex] 0.55

                                           = $6.60

Multiply the parenthesis by 6:

-7x+6x-492-2(x+3)+10

Multiply the parenthesis by -2:

-7x+6x-492-2x-6+10

Calculate the sum of similar terms:

-3x-492-6+10

Calculate the sum or difference:

-3x-488

Answer: interest at the end of 6 months is $10.62

Step-by-step explanation:

The formula for simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time in years

I = interest after t years

From the information given

T = 6 months = 6/12 = 0.5 years

P = $354

R = 6%

Therefore

I = (354 × 6 × 0.5)/100

I = 1062/100

I = 10.62

Answer:

$115.67

Step-by-step explanation:

given that the markdown rate is 53%, that means that the markdown is 53% of the original price, or,

markdown = 53% of $229.99 = 0.53 x 229.99 = $121.89

sale price before tax = Original Price - Markdown

= 229.99 - 121.89

= $108.10

sales tax = 7% of sale price before tax

= 0.07 x 108.10

= $7.57

Final price =  price before tax + tax

= 108.1 + 7.57

= $115.67

Answer:

A 1.44 cm cubed

Step-by-step explanation:

Just multiply all the numbers to get the area of the block

Answer:

A 1.44 cm cubed

Step-by-step explanation:

Answer:

For 1 How does grandma have so many cookies??? For 2 if i eat 555 cookies then imma have diabetes. and for 3 there really is no way to find this out. The only way to find out how many cookies there is now it to see how much cookies there were before and you cant do that without seeing how much is in there now. Its a catch 22.

Step-by-step explanation:

Answer:

The length of the mid-segment of the trapezoid = 7

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

Step-by-step explanation:

The mid-segment of a trapezoid is the segment that connecting the midpoints of the two non-parallel sides.

As shown in the figure the two non-parallel sides are AB and CD

∴ The mid-segment of the trapezoid = [tex]\frac{BC +AD}{2}[/tex]

From the figure: BC = 8  and AD = 6

∴ The mid-segment of the trapezoid = [tex]\frac{8+6}{2} = 7[/tex]

Answer:

high glycemic carb with some protein

Step-by-step explanation:

Food like white bread made from dextrose supplement and chocolate milk that contains some protein for muscle repair.

Due to the spongelike characteristic of the muscle would make it soak up glucose from high glycemic carb.

Answer: The number of ways would be 36,036.

Step-by-step explanation:

Since we have given that

Number of white light bulbs = 5

Number of orange light bulbs = 6

Number of blue light bulbs = 2

Total number of light bulbs = 13

So, the number of distinct orders of light bulbs if two bulbs of the same color are considered identical.

[tex]N=\dfrac{n!}{r!}\\\\N=\dfrac{13!}{5!\times 6!\times 2!}\\\\N=36036[/tex]

Hence, the number of ways would be 36,036.

The number of different orders in which Raina can put the colored light bulbs into a string is 1,324, calculated using the formula of permutations with indistinguishable items.

The question is about the number of different possible arrangements, or combinations, of the colored light bulbs. Since all light bulbs of the same color are identical, this is a problem of permutations with indistinguishable items. The formula to calculate this is n!/(r1!*r2!*...*rn!), where n is the total number of items, and r1, r2,...,rn are the number of each type of identical items.

So in this case, there are 13 colored light bulbs in total (n=13), with 5 white light bulbs (r1=5), 6 orange light bulbs (r2=6), and 2 blue light bulbs (r3=2).

The total different orders of light bulbs can be found by calculating 13!/(5!*6!*2!) = 1,324 possibilities.

https://brainly.com/question/23283166

#SPJ3

Answer:

The following statements are true:

Step-by-step explanation:

Answer:

Degree of freedom = 19

Step-by-step explanation:

We are given the following information in the question:

Sample size, n = 20

For a t-test hypothesis it was claimed that the population mean is greater than 89 ​second.

1) df

Df denotes the degree of freedom.

2) Degree of freedom  = n - 1

where n is the sample size

Degree of freedom = 20 - 1 = 19

Answer:210

Step-by-step explanation:

175+70+15=210

Answer:the original price is $210

Step-by-step explanation:

Let x represent the original price of the tent. She bought it at price that is $70 off the original price. This means that $70 was taken off the original price.The amount after the discount has been removed would be

x - 70

Judy also used a coupon for an extra $15 off. This means that the amount the Judy finally paid for the tent would be

x - 70 - 15

if Judy paid $125 for the tent, it means that

x - 70 - 15 = 125

x = 125 + 70 + 15

x = $210

Answer:

Step-by-step explanation:

Set this up as a proportion.  The idea is that if we can find out the number of "no" votes based on the ratio of 5:7, then we can add the "no" votes to the number of "yes" votes to get the total number of votes.

[tex]\frac{yes}{no}:\frac{5}{7}=\frac{3710}{x}[/tex]

Cross multiply to get

5x = 25790 so

x = 5194 "no" votes.

5194 + 3710 = 8904 total votes

Answer:

Step-by-step explanation:

The slope of the line needs to be determined first:

[tex]m=\frac{-9+-5}{-12+-8}=\frac{-14}{-20}=\frac{7}{10}[/tex]

Now let's use that and one of the coordinates to write an equation in point-slope form:

[tex]y-5=\frac{7}{10}(x-8)[/tex]

and, simplifying,

[tex]y-5=\frac{7}{10}x-\frac{56}{10}[/tex]

Now let's multiply everything by 10 to get rid of the fractions:

10y - 50 = 7x - 56

and

-7x + 10 y = -6

Apparently, they do not like to lead with negatives, which is not uncommon:

7x - 10y = 6

So his model is not correct.

Answer:

Part 1) Intervals of the domain where the  graph is above the x-axis (f(x) > 0)

Part 2) location on graph where input is zero  (y-intercept)

Part 3) location on graph where output is zero  (x-intercept)

Part 4) Intervals of the domain where the  graph is below the x-axis (f(x) < 0)

Step-by-step explanation:

Verify each case

Part 1) we have

Intervals of the domain where the  graph is above the x-axis

we know that

If the graph is above the x-axis, then the value of f(x) is positive

therefore

f(x) > 0

Part 2) we have

location on graph where input is zero  

Let

x ---> the independent variable or input value

f(x) ---> the dependent variable or output value

we know that

The y-intercept is the value of f(x) (output value) when the value of x (input value) is zero

therefore

y-intercept

Part 3) we have

location on graph where output is zero  

Let

x ---> the independent variable or input value

f(x) ---> the dependent variable or output value

we know that

The x-intercept is the value of x (input value) when the value of the function f(x) (output value) is zero

therefore

x-intercept

Part 4) we have

Intervals of the domain where the  graph is below the x-axis

we know that

If the graph is below the x-axis, then the value of f(x) is negative

therefore

f(x) < 0

Answer:

Intervals of the domain where the  graph is above the x-axis (f(x) > 0)

location on graph where input is zero  (y-intercept)

location on graph where output is zero  (x-intercept)

Intervals of the domain where the  graph is below the x-axis (f(x) < 0)

Step-by-step explanation:

answer edge 2020

Explanation:

1. BF bisects ∠CBA. Given

2. ∠CBF ≅ ∠ABF. Definition of angle bisector

3. BF ≅ BF. Reflexive property

4. ∠CFB ≅ ∠AFB. Given

5. ΔCBF ≅ ∆ABF. ASA congruence postulate

6. CF ≅ FA. Corresponding parts of congruent triangles are congruent (CPCTC)

_____

Comment on the problem

It appears as though all of the congruence symbols have gone missing.

Answer:

See proof below, the converse is true

Step-by-step explanation:

Let f be a function whose domain is the set A, and X,Y be arbitrary subsets of A. One way to prove the equality of sets f(X)∩f(Y)=f(X∩Y) is, by definition, to prove the inclusions f(X)∩f(Y) ⊆ f(X∩Y)  and f(X)∩f(Y )⊇f(X∩Y).

First, let a∈f(X)∩f(Y). Then a∈f(X) and a∈f(Y) by definition of intersection. Thus, a=f(t) for some t∈X (because a is an element of the direct image of X) and a=f(s) for some s∈Y. Then a=f(t)=f(s). We know that f is 1-1, so the previous equality implies that t=s. Now, t∈X and t=s∈Y, thus t∈X∩Y. Therefore, a=f(t) for some t∈X∩Y, which means that a is an element of the direct image of X∩Y, that is, a∈f(X∩Y). This holds for all a, thus f(X)∩f(Y) ⊆ f(X∩Y).

For the second inclusion, let b∈f(X∩Y), then there exists some z∈X∩Y such that b=f(z). Since z∈X∩Y, we have that z∈X and z∈Y. Thus, b=f(z) for some z∈X, that is, b∈f(X). Similarly, b∈f(Y) because b=f(z) and z∈Y. Therefore b∈f(X)∩f(Y) for all  b∈f(X∩Y), then f(X)∩f(Y )⊇f(X∩Y). Note that this holds for any function f, as we did not use that f is 1-1.

To prove the converse, suppose that f(X)∩f(Y)=f(X∩Y)  for all  X, Y⊆ A. We will prove that f is 1-1, that is, for all a,b∈A if f(a)=f(b) then a=b.

Define the sets X:={a} and Y:={b}. Then f(X)={f(a)} and f(Y)={f(b)}. Assuming that f(a)=f(b), we obtain f(X)=f(Y). We know that f(X)∩f(Y)=f(X∩Y), which means {f(a)}=f(X∩Y). Then, there exists some s∈X∩Y such that f(s)=f(a), thus X∩Y is a non-empty set, which implies that a∈Y. But Y has only one element, b, therefore a=b which shows that f is 1-1.

Answer:

The answer to your question is letter B

Step-by-step explanation:

Process

1.- Write the equation

                                   f(x) = 2x + 1

find f(2)

2.- Substitute x for 2

                                  f(2) = 2(2) + 1

3.- Simplify

                                 f(2) = 4 + 1

                                 f(2) = 5

Answer:

5

Step-by-step explanation:

2(2) + 1 = 5

Answer:

  j = -2

Step-by-step explanation:

It usually works well to start by eliminating parentheses.

  15j +6 = 6j -12

Now you can subtract 6j from both sides to get the variable term on one side of the equation only:

  9j +6 = -12

And you can subtract 6 from both sides to get the variable term by itself:

  9j = -18

Now, dividing by the coefficient of the variable gives you the solution:

  j = -2

The solution is j = -2.

Answer:

j = -2

Step-by-step explanation:

3 (5j + 2) = 2 (3j - 6)

15j + 6 = 6j - 12

15j - 6j = - 12 - 6

9j = - 18

j = - 18/9

j = - 2

Answer:

  y^2/25 -x^2/4 = 1

Step-by-step explanation:

The equation can be written as ...

  y^2/a^2 -x^2/b^2 = 1

where the vertices are at (0, ±a) and the co-vertices are at (±b, 0). Filling in the given values (a=5, b=2) gives the equation shown above.

Answer:

12.584 N

Step-by-step explanation:

To solve this problem you need to use Hokke's law, this is a physics lar which states the force (F) you need to compress a spring for some distance (x) can be easily calculated with the equation F=kx. The constant k (the stiffness of the spring) is the value of 242 N/m and x is the distance 5.2 cm = 0.052 m. So if you multiply 242 N/m by 0.052 m you will obtain 12.584 N, which is the necessary force to compress the spring 5.2 cm. The mass of the spring is a nonrelevant data in this problem.

Answer:

Option B) and option D) are independent events. i.e. following events are independent events:

Step-by-step explanation:

Two events would be termed as Independent events if the occurrence of one event would not affect the occurrence of other event.

Let us first consider the options having independent events.

Option B) i.e. 'a coin is flipped and a spinner is spun' is treated as neither of the events is affecting the outcome of other event. For example, assuming a coin and spinner are kept isolated, the occurrence of event of a flipping coin is not affecting the outcome of the occurrence of spinner.

The same goes with the option D) i.e. 'four number cubes are rolled at the same time', as neither of the rolling is affecting the rolling of other coin.

Now, let us consider the options having dependent events

Let us suppose one ball is drawn from a bag of balls after another ball is drawn without replacement. If there is no replacement, it logically means, after every drawn event, total number of the balls are getting decreased, hence, bringing a variation among the probability after every event, as the occurrence of next event would be dealing with the remaining of the data, instead of the data that was present before the drawn of first event. Hence, the occurrence of every event depends upon the occurrence of other event, meaning the two events will keep affecting the outcome if no replacement is made before the next event.

The same logic goes with when white marbles are drawn from a bag of marbles without replacing the marbles. If there is no replacement, it logically means, after every drawn event, total number of the white marbles and marbles are getting decreased, hence, bringing a variation among the probability after every event, as the occurrence of next event would be dealing with the remaining of the data, instead of the data that was present before the drawn of first event.

So, after all the discussion, we can safely say make a conclusion that option B) and option D) are independent events. i.e. following events are independent events:

Keywords: dependent events, independent events

Learn more dependent events and independent events from brainly.com/question/8246984

learnwithBrainly

Answer:

Step-by-step explanation:

total integers=100 (1,2,3,...,98,99,100)

numbers divisible by 4 =25 (4,8,12,...,96,100)

P=25/100=1/4

Answer:

Lack of information

Step-by-step explanation:

I can't find what percent or whatever information about the flavour,so I guess you need to give more information. If you give me more information, I will try to reply in the comments.

Hope this helps!!! ;)