If LN = 6x - 5, LM = x + 7, and MN = 3x + 20, find MN.
A.68
B.16
C.23
D.18

Answer:

= 8.24 × 10³

(scientific notation)

= 8.24e3

(scientific e notation)

= 8.24 × 103

(engineering notation)

(thousand; prefix kilo- (k))

= 8240

(real number)

How do you convert from scientific notation to standard form?

To change a number from scientific notation to standard form, move the decimal point to the left (if the exponent of ten is a negative number), or to the right (if the exponent is positive). You should move the point as many times as the exponent indicates.

Answer:

\(\frac{2}{\frac{1}{24} }\)

Step-by-step explanation:

2/x = 48

48x = 2

x = (2)/ (1/24)

\(\frac{2}{\frac{1}{24} }\) = 48

Answer:

-1

Step-by-step explanation:

Answer:

a. For the function:

f(x) = { sin x/3, if x ≤ π

{ x√3/2π, if x > π

I. To find lim f(x) as x approaches π from the negative side, we need to evaluate f(x) for values of x that are slightly less than π. In this case, since sin(x/3) is a continuous function, we can simply evaluate it at x = π:

lim f(x) as x approaches π- = f(π-) = sin(π/3) = √3/2

II. To find lim f(x) as x approaches π from the positive side, we need to evaluate f(x) for values of x that are slightly greater than π. In this case, we can simply evaluate the other part of the piecewise function at x = π:

lim f(x) as x approaches π+ = f(π+) = π√3/2π = √3/2

III. To find lim f(x) as x approaches π, we need to check whether the left-hand and right-hand limits are equal. In this case, since both the left- and right-hand limits exist and are equal, we have:

lim f(x) as x approaches π = √3/2

b. For the function:

f(x) = (x^2 - 36)/√(x^2 - 12x + 36)

I. To find lim f(x) as x approaches 6 from the negative side, we need to evaluate f(x) for values of x that are slightly less than 6. In this case, we can substitute x = 6 - h, where h is a positive number approaching zero, to get:

lim f(x) as x approaches 6- = lim f(6 - h) as h approaches 0

Substituting x = 6 - h into the function, we get:

f(6 - h) = [(6 - h)^2 - 36]/√[(6 - h)^2 - 12(6 - h) + 36]

= [h^2 - 12h]/√[h^2]

Simplifying the numerator and denominator separately, we get:

f(6 - h) = h(h - 12)/|h|

Since h approaches 0 from the positive side, we have:

lim f(6 - h) as h approaches 0+ = lim h(h - 12)/h as h approaches 0+ = lim (h - 12) as h approaches 0+ = -12

II. To find lim f(x) as x approaches 6 from the positive side, we need to evaluate f(x) for values of x that are slightly greater than 6. In this case, we can substitute x = 6 + h, where h is a positive number approaching zero, to get:

lim f(x) as x approaches 6+ = lim f(6 + h) as h approaches 0

Substituting x = 6 + h into the function, we get:

f(6 + h) = [(6 + h)^2 - 36]/√[(6 + h)^2 - 12(6 + h) + 36]

= [h^2 + 12h]/√[h^2]

Simplifying the numerator and denominator separately, we get:

f(6 + h) = h(h + 12)/|h|

Since h approaches 0 from the positive side, we have:

lim f(6 + h) as h approaches 0+ = lim h(h +

Step-by-step explanation:

9514 1404 393

Answer:

  (x, y) = (3, 2)

Step-by-step explanation:

These look like solution using elimination or substitution could be tedious, so we'll use the "cross multiplication" technique for solution. This requires each equation be in general form: ax+by+c = 0.

The first equation can be multiplied by 6 and 13 subtracted.

  x/2 +y/3 = 13/6

  3x +2y = 13

  3x +2y -13 = 0

The second equation can be multiplied by 28 and 10 subtracted.

  2x/7 -y/4 = 5/14

  8x -7y = 10

  8x -7y -10 = 0

Now, an array of coefficients can be constructed. The last column is the same as the first.

  \(\begin{array}{cccc}3&2&-13&3\\8&-7&-10&8\end{array}\)

Cross-multiplying adjacent columns, we can write the equation ...

  1/(3(-7)-8(2)) = x/(2(-10)-(-7)(-13)) = y/(-13(8)-(-10)(3))

  1/-37 = x/-111 = y/-74

Solving for x and y, we have ...

  x = -111/-37 = 3

  y = -74/-37 = 2

The solution is (x, y) = (3, 2).

False, it is strictly greater.

Answer:

the answer is c

Step-by-step explanation:

while four dentists were asked, and three recommended it, those 4 do not speak for the thousands of dentists out there, with a larger pool it may be proven, but the 4 dentists do not speak on behalf of all dentists.

Answer:

x = 11/2 = 5.5

Step-by-step explanation:

2x-6 = 5

2x = 11

x = 11/2 = 5.5

Answer:

this is correct

Step-by-step explanation:

Step-by-step explanation:

not true but the number is wrong tho I got 14=-2

hope it help

Answer:

\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Step-by-step explanation:

Convert 1/2 + i√3/2 to rectangular form

\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)

Use DeMoivre's Theorem

\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Answer: God

Step-by-step explanation:

The reason it’s god is because god created everything so he know everything. So your answer is god

Answer:

£8 : £12

Step-by-step explanation:

2:3 means that there are 5 parts in total. Let parts be represented as p. 5p = £20, p = £4. That meant 2 parts = £8 and 3 parts = £12. Hence to share £20 in the ratio 2:3 is £8 : £12

Answer:

C. $755 i got it right

Step-by-step explanation:

If you make only the minimum payment each month, the total cost of the computer will be $755.00, which is $155 more than the original cost of the computer ($600).

percentage, a relative value indicating hundredth parts of any quantity.

To calculate the total cost of the computer if you make only the minimum payment each month, we need to use the simple interest formula:

A = P(1 + rt)

where A is the total amount paid, P is the principal or balance, r is the annual interest rate expressed as a decimal, and t is the time in years.

P = $600

r = 12.9% or 0.129 (annual interest rate)

t = 2 years

To find the monthly interest rate, we divide the annual interest rate by 12 (the number of months in a year):

Monthly interest rate = 0.129 / 12 = 0.01075

Now, we can use this monthly interest rate to calculate the minimum monthly payment:

Minimum monthly payment = 1% x P = 0.01 x $600 = $6

Therefore, the minimum monthly payment is $6.

To find the total cost of the computer over the 2-year period, we need to calculate the total amount paid (A) by making the minimum monthly payment each month:

A = P(1 + rt)

A = $600(1 + 0.01075 x 2 x 12)

A = $600(1 + 0.258)

A = $755.00

Therefore, if you make only the minimum payment each month, the total cost of the computer will be $755.00, which is $155 more than the original cost of the computer ($600).

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Answer:

Fill in the blanks with the correct verbs given below.

(croak, is ,brush, writes plays, chirp, combines, mows, are look , keeps rises ,has,

reflects leaves, walks, is)

1. Marry ...keeps rises...... to office every morning .Walking is good exercise.

2. We...brush..... our teeth after dinner. It .....makes.....them clean.

3. Salim....wakes..... for school everyday at 7:00 a.m.

4. The sun ...rises.......at 5:00 a.m. these days. The days are getting longer.

5. The tiger chirp......an endangered animal. There are only 1410 tigers left.

6. Vikram Seth.....combines........ poetry, fiction and travelogues.

7. Sania Mirza....plays..... tennis. She plays both singles and doubles.

8. Frogs....croak... ...and birds.....chirp......

9. Please ....look......for my red shirt. I cannot find it.

10. The gardener .....mows....... the loan once a week.

11. The moon ...keep rises.....the light of the sun.

12. The times of India......writes....... a national newspaper.

13. The UN headquarters.....is..... in Geneva.

14. Maya ...has........ a pet dog .Its name is Lily.

15. This book....writes..... projects and activities

Answer:

perimeter =the circumference around the semicircle

22/7×34/2

=53.43cm

area = (22/7×17^2)/2

454.14cm^2

Answer :

Step-by-step explanation :

Question :

Find the perimeter and area of the semicircle.

Given : Diameter = 14 cm

Radius = 14/2 = 7 cm

Solution :

Perimeter of semicircle = πr + d

\(\longrightarrow \: \: \dfrac{22}{7} \times 7 + 14 \\ \\ \longrightarrow \: \: 22 + 14 \\ \\ \longrightarrow \: \: 36 \: cm \\ \)

Area of semicircle = 1/2 πr²

\(\longrightarrow \: \: \dfrac{1}{2} \times \dfrac{22}{7} \times {(7)}^{2} \\ \\ \longrightarrow \: \: \frac{22}{14} \times 7 \times 7 \\ \\ \longrightarrow \: \: \frac{1078}{14} \\ \\ \longrightarrow \: \: 77 \: {cm}^{2} \\ \\ \)

Answer:

Answer: 2/1

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Line is passing through the points (2, 3) & (5, 9)

Slope = (9 - 3)/ (5 - 2) = 6/3 = 2

Slope of the line is 2.

The linear equation we need to solve is:

$27.50*w = $309.99 - $144.99

And the solution is w = 6.

How to write and solve the equation?

We know that the cost of the gaming chair is $309.99.

To buy this, you already have saved $144.99, and save another $27.50 per week, then the amount you have after w weeks is:

f(w) = $144.99 + $27.50*w

So the linear equation we need to solve is:

$144.99 + $27.50*w = $309.99

To solve this we need to isolate w.

$144.99 + $27.50*w = $309.99

$27.50*w = $309.99 - $144.99

w = ($309.99 - $144.99)/$27.50 = 6

So they can buy the chair after 6 weeks.

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Answer:

125.5

Step-by-step explanation:

I made the shape in to 2 seperate shapes

the rectangle:8 times 10 is 80

Trapezoid: A=a+b/2(h)

3+10/2(7) is 45.5

so 80+45.5= 125.5

Answer:

x = 2

Step-by-step explanation:

8 = 6x + -2x

8 = 4x

8 = 4x

4 4

2 = x

Answer:

y=52x+b.

Step-by-step explanation:

since point (2,1) satisfies the equation.

Answer:

122°

Step-by-step explanation:

<ADC is an inscribed angle and its measure is equal to half of the arc it sees (minor arc AC)

if ADC is 61° then minor arc AC is 2 × 61 = 122

ABC is the center angle and so its measure is equal to the arc it sees which is 122°

Answer:

5

Step-by-step explanation:

(+3 + (+2))

Remove the brackets.

3 + (+2)

3 + 2

Add the numbers.

= 5

Answer:

+5 or 5

Step-by-step explanation:

(+3)+(+2)

=> According to the rule, ( + )( + ) = ( + )

So,

=> +3+2

=> +5

a) 190 kg of salt are present in the tank at time t = 15 minutes.

b) The tank holds 640 kg of salt when it is filled.

a) The quantity of brine solution injected into the tank at time t = 15 minutes is 5 gallons/minute × 15 minutes = 75 gallons.

The sum of the salt that was initially in the tank and the salt that has been added is the quantity of salt that is currently in the tank.

40 pounds of salt were initially present in the tank, and another 15 pounds had been added 2 lb./gallon × 75 gallons = 150 lb. As a result, the tank's total salt content at time t = 15 minutes is 40 + 150 = 190.

b) The entire amount of brine solution put into the tank must be determined to determine how much salt will be present when it is full. Since the tank has a 400-gallon capacity, the total quantity of brine put into it is 400 gallons - 100 gallons, or 300 gallons.

The sum of the salt that was previously in the tank and the salt that has now been added is the quantity of salt that is currently in the tank.

40 pounds of salt were already present in the tank, and the proportion which has been added is the same as 2 lb./gallon × 300 gallons = 600 lb. As a result, 40 lb + 600 lb = 640 lb of salt will be in the tank when it is full.

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The rational function graphed in this problem is defined as follows:

y = -2(x - 1)/(x² - x - 2).

The vertical asymptotes of the rational function for this problem are given as follows:

x = -1 and x = 2.

Hence the denominator of the function is given as follows:

(x + 1)(x - 2) = x² - x - 2.

The intercept of the function is given as follows:

x = 1.

Hence the numerator of the function is given as follows:

a(x - 1)

In which a is the leading coefficient.

Hence:

y = a(x - 1)/(x² - x - 2).

When x = 0, y = -1, hence the leading coefficient a is obtained as follows:

-1 = a/2

a = -2.

Thus the function is given as follows:

y = -2(x - 1)/(x² - x - 2).

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Answer:

LCD = 12

Step-by-step explanation:

The fraction of the class that is sophomores is \(35/43\).

The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.

Number of sophomores = 35

Total number of students = 43

Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)

Fraction of sophomores  \(= 35 / 43\)

Therefore, the fraction of the class that are sophomores is = \(35/43\).

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Answer: -5x^2 + 2

Step-by-step explanation: