5. (5 points, bonus). Find the Singular Value Decomposition of the matrix A from problem 4. Verify your answer.

Answer:

3kg = 3000 gm

Step-by-step explanation:

we use this formula

m1x (distance of m1 )= m2 x( distance of m2)

* the distance far from the triangle*

m1 =6 kg

d1 = 3m

m2 = ê (kg )

d2 = 600 cm = 6 m

m1 d1 = m2 d2

6 x 3 = ê 6

ê = 3 kg

mass = 3kg = 3000 gram

#

To make the scale balance, the weight must be added is 3000g.

"A balanced equation is an equation where both sides are equal to the same amount. The answer to the expression on the left side of the equals sign (=) should be equal to the value on the right side of the equals sign".

For the given situation,

From the diagram shown, the distance on both sides of the fulcrum (the triangle) must be the same to make the scale balance.

We know that

1 kg = 1000 g

1 m = 100 cm

Let the unknown quantity be 'x'

To write a balanced equation, units should be the same on both sides.

6 kg = 6000 g

3 m = 300 cm.

The equation is represented as

[tex]6000[/tex] × [tex]300 = x[/tex] × [tex]600[/tex]

⇒ [tex]x = \frac{(6000)(300)}{600}[/tex]

⇒ [tex]x=3000[/tex]

Hence we can conclude that to make the scale balance, the weight must be added is 3000g.

Learn more about the balance equation here

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Answer:

792/7 is the correct answer

Step-by-step explanation:

V=4/3pi r^3

=4/3×22/7×3x×3x×3x

=88×9x÷7=792/7

Answer:

B

Step-by-step explanation:

A tesselation uses 1 shape to create an image by translating it or reflecting it. The shape is translated in this scenario so they are congruent from a translation (they are in the sam orientation unlike reflections)

Answer:

26%

Step-by-step explanation:

If 1 dollar is 100%

Then 0.26 dollar is:

Answer:

(x - 3)(x + 7)

Step-by-step explanation:

x^2 + 4x - 21

=> x^2 + 7x - 3x - 21

=> x(x + 7) -3(x + 7)

=> (x + 7)(x - 3)

Answer:

[tex](x+7)(x-3)[/tex]

Step-by-step explanation:

So we want to factor the expression:

[tex]x^2+4x-21[/tex]

When factoring, we want to find two numbers that equals (a)(c) and add up to b. We can then substitute it for b.

So, we want two numbers that when multiplied equals (1)(-21)=-21 and adds up to 4.

We can use 7 and -3.

So:

[tex]x^2+4x-21\\=x^2-3x+7x-21[/tex]

Factor out an x from the first two terms, and a 7 from the third and fourth terms:

[tex]=x(x+3)+7(x-3)[/tex]

Grouping:

[tex]=(x+7)(x-3)[/tex]

And we are done :)

Answer:

(4x)¯² (4x)³ (4x)⁹ = (4x)¹⁰

Step-by-step explanation:

(4x)¯² (4x)³ (4x)⁹

The above expression can be simplified as follow:

Recall:

When we have two or more index number with same base and a multiplication sign in between them, we easily simply by adding the index number together while keeping the base constant. This is illustrated below:

a^m x a^n = a^(m + n)

Therefore,

(4x)¯² (4x)³ (4x)⁹ = (4x)^(-2 + 3 +9)

(4x)¯² (4x)³ (4x)⁹ = (4x)¹⁰

Answer: x=20.5

Step-by-step explanation:

Given

4x-17=65

Add 17 on both sides (addition property of equality)

4x-17+17=65+17

4x=82

Divide 4 on both sides (division property of equality)

4/4x=82/4

x=20.5

Hope this helps!! :)

Please let me know if you have any question

Answer:

x = 20.5

Step-by-step explanation:

4x - 17 = 65

4x = 65 + 17

x = 82 ÷ 4

x = 20.5

Hope it helps.

Answer: 5/6

Step-by-step explanation:

p - 1/6 = 2/3

    +1/6   +1/6

p = 5/6

Answer:

p = 5/6

Step-by-step explanation:

For this problem, simply take the words of the problem and convert them into an equation as such:

The difference of p and one-sixth implies --> p - 1/6

is two-thirds implies --> 2/3

So, our equation:

p - 1/6 = 2/3

Now simply solve for p, and combine the fractions.

p - 1/6 = 2/3

p - 1/6 + 1/6 = 2/3 + 1/6

p = 2/3 + 1/6

p = 4/6 + 1/6

p = 5/6

Cheers.

Answer:

Step-by-step explanation:

Given the function  j(x) = 11.6[tex]e^x[/tex] and k(x) = [tex]ln \dfrac{x}{11.6}[/tex], to show that both equality functions are true, all we need to show is that both  j(k(x)) and k(j(x)) equal x,

For j(k(x));

j(k(x)) = j[(ln x/11.6)]

j[(ln (x/11.6)] = 11.6e^{ln (x/11.6)}

j[(ln x/11.6)] = 11.6(x/11.6) (exponential function will cancel out the natural logarithm)

j[(ln x/11.6)] = 11.6 * x/11.6

j[(ln x/11.6)] = x

Hence j[k(x)] = x

Similarly for k[j(x)];

k[j(x)] = k[11.6e^x]

k[11.6e^x] = ln (11.6e^x/11.6)

k[11.6e^x]  = ln(e^x)

exponential function will cancel out the natural logarithm leaving x

k[11.6e^x]  = x

Hence k[j(x)] = x

From the calculations above, it can be seen that j[k(x)] =  k[j(x)]  = x, this shows that the functions j(x) = 11.6[tex]e^x[/tex] and k(x) = [tex]ln \dfrac{x}{11.6}[/tex] are inverse functions.

Answer:

the answer is C

Step-by-step explanation:

I did the test and got it right

Answer:

38 minutes

Step-by-step explanation:

Volume of the first aquarium:

Volume of the second aquarium

The second aquarium is:

It will take

to fill this aquarium

Answer:

Step-by-step explanation:

Yes, it's a repeating decimal:  1.3333333....

Answer:

1 : 7

Step-by-step explanation:

Answer:

1:7

Step-by-step explanation:

5/5=1 35/5=7

Answer:

c

Step-by-step explanation:

its c

The cash received by the person who filled out this deposit is $88.79.

Option C is the correct answer.

Given,

Description                      Amount ($)

Cash, including coins.          15.00

Check 1                                 62.44

Check 2                                 27.83

Check 3                                 45.75

Subtotal                                  ??.??

Less cash received                ??.??

Total                                        62.23

We need to find the less cash received.

A deposit slip is a bank form where the customer fills in the required date such as the date, the depositor's name, the depositor's account number, and the deposit amounts.

Find the subtotal.

= Cash included coins + check 1 + check 2 + check 3

= 15.00 + 62.44 + 27.83 + 45.75

= 151.02

Find the less cash received.

We have,

Total = 62.23

Total = Subtotal - less cash received

62.23 = 151.02 - less cash received

less cash received:

= 151.02 - 62.23

= 88.79

Thus, the cash the person who filled this deposit slip received is $88.79.

Learn more about deposit slips here:

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The complete question:

Consider the following incomplete deposit slip:

Description - Amount ($)

Cash, including coins - 15.00

Check 1  - 62.44

Check 2 - 27.83

Check 3 - 45.75

Subtotal - ?? ??

Less cash received - ?? ??

Total - 62.23

How much cash did the person who filled out this deposit slip receive?

a. $381.23

b. $451.02

c. $88.79

d. $436.02

168 ÷ 14 =12

ink

...

.

...

Answer:

Let the cost the number of cartridges be x.

We have given that cost of one cartridge is 14 $/cartridge.

And we have 168 $ with us.

So, according to question we have an equation-

14x=168

x=168/14

x=12

Hence, we can buy 12 cartridges if we 168 $ and the cost of one cartridge is 14 $.

Answer:

0-3+5=2

Step-by-step explanation:

It starts in 0

The first line moves three spaces to the left so that's -3

the second line moves 5 spaces to the right so that's +5

add all up

0-3+5=2

Answer:

2

Step-by-step explanation:

1st line 0 → -3 = -3

2nd line -3  → 2 = 5

sum = 0 + (-3) + 5 = 2

Answer:

  3583 million acres

Step-by-step explanation:

If 19% is federally owned, then 81% is not.

  0.81 × 4423 million acres = 3583 million acres

that are not federally owned.

_____

This is a typo or refers to some country other than the US. The largest US state (Alaska) is about 425 million acres.

Answer:

Step-by-step explanation:

[tex]8-10=-2+k[/tex]

Switch sides

[tex]-2+k=8-10[/tex]

Subtract the  numbers : 8-10=-2

[tex]-2+k=-2[/tex]

Add 2 to both sides

[tex]-2+k+2=-2+2[/tex]

Simplify

[tex]k = 0[/tex]

Answer:

k=0

Step-by-step explanation:

Simplify  8-108−10  to  -2−2.

−2=−2+k

regroup those terms

−2=k−2

cancel -2 on both sides

0=5

switch sides k=0

i recommend using cymath free and very easy

Answer:

15

Step-by-step explanation:

-3x = -5-10

-x=-15

therefore, x=15

Answer:

I think the scale factor is 2 because 12 divided by 6 is 2.

Answer:

Parallel

Step-by-step explanation:

2x+5 slope: 2

-6x+3y=30 slope: 2

Hence the answer is parallel

Answer:

x=9

Step-by-step explanation:

If the triangles are congruent, then the angles B and E are also congruent (because they lie in the same place). Set an equation where B is equal to E:

∠[tex]B=[/tex]∠[tex]E[/tex]

Substitute values:

[tex]5x=45[/tex]

Solve for x. Divide both sides by 5:

[tex]\frac{5x}{5}=\frac{45}{5}\\\\ x=9[/tex]

So, when ΔABC≅ΔDEC, and ∠B=5x and ∠E=45°, the value of x is 9.

:Done

Answer:

I agree with the first answer

Step-by-step explanation:

basically you wrote the answer

Answer is B

Answer:

Well since u know the answer (LOL) its B

Step-by-step explanation:

U already solved it so u know how!

Answer:

Jennifer should expect a number less than 3 23 times

Step-by-step explanation:

The probability of rolling a number less than 3 on a number cube is 2/6. .

The probability of rolling a number less than 3 on a number cube is 2/6

= 1/3

Jennifer rolls a number cube 69 times

Expectations= probability*total outcome

Expectations= 1/3 * 69

Expectations= 69/3

Expectations= 23 times

Answer:

30

Step-by-step explanation:

Answer:

64 degrees

Step-by-step explanation:

complementary-angle adds up to 90 degrees.

90-26 is 64 degrees.

Answer:

p = 2

Step-by-step explanation:

17 - 2p = 2p + 5 + 2p  

- 2p - 2p - 2p = 5 - 17

- 6p = - 12

p =  -12 / -6

p = 2

Answer:

1) V = 12 π  ㏑ 3

2) [tex]\mathbf{V = \dfrac{328 \pi}{9}}[/tex]

Step-by-step explanation:

Given that:

the graphs of the equations about each given line is:

[tex]y = \dfrac{6}{x^2}, y =0 , x=1 , x=3[/tex]

Using Shell method to determine the required volume,

where;

shell radius = x;   &

height of the shell = [tex]\dfrac{6}{x^2}[/tex]

∴

Volume V = [tex]\int ^b_{x-1} \ 2 \pi ( x) ( \dfrac{6}{x^2}) \ dx[/tex]

[tex]V = \int ^3_{x-1} \ 2 \pi ( x) ( \dfrac{6}{x^2}) \ dx[/tex]

[tex]V = 12 \pi \int ^3_{x-1} \dfrac{1}{x} \ dx[/tex]

[tex]V = 12 \pi ( In \ x ) ^3_{x-1}[/tex]

V = 12 π ( ㏑ 3 - ㏑ 1)

V = 12 π ( ㏑ 3 - 0)

V = 12 π  ㏑ 3

2) Find the line y=6

Using the disk method here;

where,

Inner radius [tex]r(x) = 6 - \dfrac{6}{x^2}[/tex]

outer radius R(x) = 6

Thus, the volume of the solid is as follows:

[tex]V = \int ^3_{x-1} \begin {bmatrix} \pi (6)^2 - \pi ( 6 - \dfrac{6}{x^2})^2 \end {bmatrix} \ dx[/tex]

[tex]V = \pi (6)^2 \int ^3_{x-1} \begin {bmatrix} 1 - \pi ( 1 - \dfrac{1}{x^2})^2 \end {bmatrix} \ dx[/tex]

[tex]V = 36 \pi \int ^3_{x-1} \begin {bmatrix} 1 - ( 1 + \dfrac{1}{x^4}- \dfrac{2}{x^2}) \end {bmatrix} \ dx[/tex]

[tex]V = 36 \pi \int ^3_{x-1} \begin {bmatrix} - \dfrac{1}{x^4}+ \dfrac{2}{x^2} \end {bmatrix} \ dx[/tex]

[tex]V = 36 \pi \int ^3_{x-1} \begin {bmatrix} {-x^{-4}}+ 2x^{-2} \end {bmatrix} \ dx[/tex]

Recall that:

[tex]\int x^n dx = \dfrac{x^n +1}{n+1}[/tex]

Then:

[tex]V = 36 \pi ( -\dfrac{x^{-3}}{-3}+ \dfrac{2x^{-1}}{-1})^3_{x-1}[/tex]

[tex]V = 36 \pi ( \dfrac{1}{3x^3}- \dfrac{2}{x})^3_{x-1}[/tex]

[tex]V = 36 \pi \begin {bmatrix} ( \dfrac{1}{3(3)^3}- \dfrac{2}{3}) - ( \dfrac{1}{3(1)^3}- \dfrac{2}{1}) \end {bmatrix}[/tex]

[tex]V = 36 \pi (\dfrac{82}{81})[/tex]

[tex]\mathbf{V = \dfrac{328 \pi}{9}}[/tex]

The graph of equation for 1 and 2 is also attached in the file below.

Answer:

60,500

Step-by-step explanation:

Answer:

1) ASA

2) SSA

Step-by-step explanation:

The sine rule is used when we have; ASA, AAS or SSA cases. However, SSA is an ambiguous case which occurs when there are two sides and a given angle opposite one of these given sides. The triangles resulting from a situation like this requires a much closer look in comparison to SSS, ASA, and AAS cases. SSA may result in one triangle, two triangles, or even no triangle at all.