Find the value of the constant m √150 - √12m + √54 = 0​

Answer:

11 terms.

Step-by-step explanation:

We are given the arithmetic sequence:

17, 13, 9, ...

And we want to find the number of terms required such that the sum is -33.

Recall that the sum of an arithmetic series is given by:

[tex]\displaystyle S = \frac{k}{2}\left( a + x_k\right)[/tex]

Where k is the number of terms, a is the first term, and x_k is the last term.

The desired sum is -33. The first term is 17 as well. Thus:

[tex]\displaystyle (-33) = \frac{k}{2} \left( (17) +x_k\right)[/tex]

Simplify:

[tex]-66 = k(17 + x_k)[/tex]

We can write a direct formula to find the last term x_k. The direct formula of an arithmetic sequence has the form:

[tex]x_ n = a + d(n-1)[/tex]

Where a is the initial term and d is the common difference.

The initial term is 17 and the common difference is -4. Hence:

[tex]\displaystyle x_n = 17 - 4(n-1)[/tex]

Then the last term is given by:

[tex]x_k = 17 - 4(k-1)[/tex]

Substitute:

[tex]\displaystyle -66 = k\left( 17 + \left( 17 - 4(k-1)\right)\right)[/tex]

Solve for k:

[tex]\displaystyle \begin{aligned} -66 &= k(17 + (17 - 4k + 4)) \\ -66 &= k(38 -4k) \\ -66 &= -4k^2 + 38k \\ 4k^2 -38k -66 &= 0 \\ 2k^2 - 19k -33 &= 0 \\ (k-11)(2k+3) &= 0 \\ k-11&= 0 \text{ or } 2k+3 = 0 \\ \\ k &= 11 \text{ or } k = -\frac{3}{2}\end{aligned}[/tex]

Since we cannot have a negative amount of terms, we can ignore the second solution.

Therefore, the given sequence must have 11 terms such that it sums to -33.

Answer:

Here is 2 methods

Step-by-step explanation:

1) we use excel to find n=11 for lasy students

2) mathematical method

[tex]u_1=17\\u_2=13=17+(2-1)*(-4)\\u_3=9=17+(3-1)*(-4)\\\\\\\boxed{u_n=17+(n-1)*(-4)}\\\\\\\displaystyle s_n=\sum_{i=1}^nu_i\\=\sum_{i=1}^n(17+(i-1)*(-4))\\\\\\=(\sum_{i=1}^n 17) + (-4)*\sum_{i=1}^n (i) +4*\sum_{i=1}^n (1)\\\\\\=17*n+4*n-4*\frac{n*(n+1)}{2} \\\\\\=21n-2n^2-2n\\\\\\=-2n^2+19n\\\\=-33\\\\\\\Longrightarrow\ 2n^2-19n-33=0[/tex]

[tex]\Delta=19^2+4*2*33=625=25^2\\\\n=\dfrac{19-25}{4} =-1.5\ (excluded)\ or\ n=\dfrac{19+25}{4}=11\\\\[/tex]

Answer:

56000 ft

Step-by-step explanation:

4000 steps a day.

7 days in a week.

2 ft per step

so, we calculate how many steps in a week

4000 × 7 = 28000

and then we calculate the distance by saying each of these steps is 2 ft

so,

28000 × 2 = 56000 ft

as a little extra thought :

there are 5280 ft in a mile.

so, the person walks

56000 / 5280 miles = 10.61 miles

in a week.

- X + 3Y = 2  (*)

⇔X = 2 - 3Y  (1)

- Y = 2X + 3   (2)

(1),(2)⇒ Y = 2(2 - 3Y) +3

       ⇔ Y = 4 - 6Y + 3

       ⇔ Y = 1  (**)

(*),(**)⇒ X + 3×1 =2

       ⇔ X = -1

Answer:

can you translate in english,would be better...

answer maybe wrong because of the language but stil....

9x(2+6x+1)

=9x(9x)

81x..

Answer:

Not factarable, all terms must be in x. or y

Step-by-step explanation:

Answer:

[tex]{26}[/tex]

Step-by-step explanation:

[tex] \sqrt{(0 - ( - 5) ){}^{2} + (0 - 1) {}^{2} } [/tex]

[tex] = \sqrt{ {(5)}^{2} + {( - 1)}^{2} } [/tex]

[tex] = \sqrt{25 + 1} [/tex]

[tex] = \sqrt{26} [/tex]

Answered by GAUTHMATH

Answer:

26

Step-by-step explanation:

(-5, 1) (0, 0)

sqrt(5^2 + (-1^2))

sqrt(25 + 1)

sqrt(26)

So, 26 goes under the radical.

Answer:

Step-by-step explanation:

(N)0.05 + (17-N)0.1 = M; M = amount of money I have.

Or 1.7-0.05N = M.

An expression two different ways to  the amount of money is equals to

1. 5N + 10 (17 -N)  = Y cents

2. N + 2(17 - N) = Y nickels

" Amount is defined as the total of any given quantity."

According to the question,

Total number of coins = 17

Number of nickels coins = N

Number of dimes coin = 17 - N

'Y' express the amount of money

Represent amount of money in cents

1 dime = 10 cents

1 nickel = 5 cents

Expression to represents amount of money in cents,

5N + 10 (17 -N)  = Y cents

Expression to represents amount of money in nickels,

1 dime = 2 nickel

N + 2(17 - N) = Y nickels

Hence, an expression two different ways to  the amount of money is equals to

1. 5N + 10 (17 -N)  = Y cents

2. N + 2(17 - N) = Y nickels

Learn more about amount here

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9514 1404 393

Answer:

  D.  5.4

Step-by-step explanation:

The point U divides segment SP into the ratio 1 : 2. So, segment SU is 1/2 the length of segment UP.

  SU = UP/2 = 3.6/2 = 1.8

The length of PS is ...

  PS = PU +US = 3.6 +1.8

  PS = 5.4

__

Additional comment

If you were asked to find the value of x, you would discover x=1. That is not what you're asked here.

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

[tex]\sf↦ Product ~of ~numbers = 10000\\\\↦ n × 16n = 10000\\\\↦ 16n² = 10000\\\\↦ n² = \sf \dfrac{10000}{16}\\\\↦ \sf n = \sqrt{\dfrac{10000}{16}}\\\\↦ \sf n = \sqrt{\dfrac{100\:\times\:100}{4\:\times\:4}}\\\\↦ \sf n = {\cancel{\dfrac{100}{4}}}\\\\➦\pmb{\underline{\boxed{\sf{\pink{n = 25}}}}}[/tex]

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

Answer:

Step-by-step explanation:

Let the numbers be x and y.

We have:

Substitute y and solve for x:

Then y is:

The numbers are:

Answer:

8% out of 175 = ( 8 ÷ 100 ) × 175 = 14

175 cm - 14 = 161 cm

...............

Answer:

The answer is 12

Step-by-step explanation:

You see its because.

Answer:

?=12

Step-by-step explanation:

Using the Thalès's theorem:

[tex]\dfrac{6}{6+4}=\dfrac{?}{20} \\\\?*10=6*20\ (cross\ products)\\\\?=\dfrac{6*20}{10} \ dividing\ by\ 10\\\\?=12[/tex]

Answer:

2.6

Step-by-step explanation:

We'll use the Pythagoras theorem to solve this, which states that in a right angle triangle:

h^2 = a^2 + b^2

4^2 = 3^2 +b^2

16= 9 +b^2

16-9= b^2

7= b^2

(take square root in both sides)

b= 2.65

round to nearest 10th = 2.6

answer by Gauthmath

Answer:

Missing side is 2.6

3^2 + x^2 = 4^2

9 + x^2 = 16

-9            -9

x^2 = 7

([tex]\sqrt{x}[/tex])^2 = [tex]\sqrt{7}[/tex]

x = 7

Find the approximation o the square root of 7 in fractions then carry out the long division.

Or

Approx. is 2 3/5 which equals 2 6/10 which equals 2.6

Answer:

1 hour 33 minutes

Step-by-step explanation:

distance/speed= time

d =800/600

d=1.33

The aeroplane takes 1.33 hours to traverse a distance of 800 km.

Speed is the rate at which an object's position changes, measured in meters per second. For example, if an object starts at the origin, and then moves three meters in three seconds, its speed is one meter per second. The equation for speed is simple: distance divided by time

Given here: An airplane flies a distance of 800 km with an average speed of 600 km/h

Thus the time taken by the aeroplane to cover that distance is

t=800/600

t=4/3

t=1.33 hours

Hence, The aeroplane takes 1.33 hours to traverse a distance of 800 km.

Learn more about the speed of an object here:

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Answer:

(x-5)(x+2)(x+4)

Step-by-step explanation:

I just did It

Answer:

MO, NO, MN

Step-by-step explanation:

First, we can identify this triangle as a right triangle, as given by the square next to the O. Next, we know that a right angle is equal to 90 degrees, and the sum of the angles of a triangle is equal to 180 degrees.

Therefore,

∠M + ∠O + ∠N (the angles of the triangle) = 180

49 + 90 + ∠N = 180

139 + ∠N = 180

subtract both sides by 139 to isolate the variable

∠N = 41

Therefore, ∠N is 41 degrees.

In a triangle, given the angles, we know that the side opposite the smallest angle is the side with the smallest length and so on.

Our angle lengths are

41, 49, and 90 degrees in order.

Therefore, the side opposite the largest angle (90 degrees, or ∠O) is the longest side. This is MN. Similarly, ∠N is the smallest angle, and the side opposite of that (MO) is the shortest side. This leaves NO to be in the middle

Answer:

see explanation

Step-by-step explanation:

(1)

x - (9x - 10) + 11 = 12x + 3(- 2x + [tex]\frac{1}{3}[/tex] ) ← distribute parenthesis on both sides

x - 9x + 10 + 11 = 12x - 6x + 1 ← collect like terms on both sides

- 8x + 21 = 6x + 1 ( subtract 6x from both sides )

- 14x + 21 = 1 ( subtract 21 from both sides )

- 14x = - 20 ( divide both sides by - 14 )

x = [tex]\frac{-20}{-14}[/tex] = [tex]\frac{10}{7}[/tex]

(3)

- 4x - 2(8x + 1) = - (- 2x - 10) ← distribute parenthesis on both sides

- 4x - 16x - 2 = 2x + 10

- 20x - 2 = 2x + 10 ( subtract 2x from both sides )

- 22x - 2 = 10 ( add 2 to both sides )

- 22x = 12 ( divide both sides by - 22 )

x = [tex]\frac{12}{-22}[/tex] = - [tex]\frac{6}{11}[/tex]

(7)

8(2x + 9) = 56 ( divide both sides by 8 )

2x + 9 = 7 ( subtract 9 from both sides )

2x = - 2 ( divide both sides by 2 )

x = - 1

Answer:

1861÷1250

Step-by-step explanation:

This is the simplified version

Answer: x = -3

[tex]2x+6=0\\\\2x=-6\\\\x=\frac{-6}{2} =-3[/tex]

Answer:

x= -3

Step-by-step explanation:

Solve the equation:

2x +6 = 0

We have isolate 'x'.

First subtract 6 from both sides

2x = 0-6

2x = -6

Divide each side by 2

x = -6/2

x = -3

Answer:

x = 0

Step-by-step explanation:

-2(2 − 2x) = 4 − 8(1 − x)

Apply the distributive property:

−2(2 − 2x) = 4 − 8(1 − x)

(−2)(2) + (−2)(−2x) = 4 + (−8)(1) + (−8)(−x)

−4 + 4x = 4 + (−8) + 8x

Combine like terms:

4x − 4 = (8x) + (4+−8)

4x − 4 = 8x + (−4)

4x − 4 = 8x − 4

Subtract 8x from both sides:

4x − 4 − 8x = 8x − 4 − 8x

−4x − 4 = −4

Add 4 to both sides:

−4x − 4 + 4= −4 + 4

−4x = 0

Divide both sides by -4:

-4x/-4 = 0/-4

x = 0

Answer: 0

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The quotient of n and 8 is [tex]\frac{n}{8}[/tex] and 13 more than this is

[tex]\frac{n}{8}[/tex] + 13 → D

Answer:

110.5 cubic inches

Step-by-step explanation:

Base is parallelogram, so area is

A = 4.7×5 = 23.5

Height(h) is 4.7, so volume is,

V = A×h

= 23.5×4.7

= 110.45 ≈ 110.5

Answered by GAUTHMATH

Answer:

B. 7y - 15

Step-by-step explanation:

Simplifying

10y + -3(y + 5) = 0

Reorder the terms:

10y + -3(5 + y) = 0

10y + (5 * -3 + y * -3) = 0

10y + (-15 + -3y) = 0

Reorder the terms:

-15 + 10y + -3y = 0

Combine like terms: 10y + -3y = 7y

-15 + 7y = 0

Solving

-15 + 7y = 0

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '15' to each side of the equation.

-15 + 15 + 7y = 0 + 15

Combine like terms: -15 + 15 = 0

0 + 7y = 0 + 15

7y = 0 + 15

Combine like terms: 0 + 15 = 15

7y = 15

Divide each side by '7'.

y = 2.142857143

Simplifying

y = 2.142857143

Answer:

b. 7y-15

Step-by-step explanation:

First, write out the expression

1. [tex]10y-3(y+5)[/tex]

To simplify the expression distribute the -3 to the terms within the paratheses.

2. [tex]10y-3y-15[/tex]

Then, combine like terms to simplify further. Since 10y and -3y are like terms they can be subtracted

3. [tex]7y-15[/tex]

This means that B is the correct answer.

Answer:

Step-by-step explanation:

757 minutes = 12 hours 37 minutes

Answer:

-13 1/2 < -6/8

Step-by-step explanation:

*Any negative in either the numerator or denominator will make the entire fraction negative.

1/2  = .5

-13 1/2 = -13.5

-6/8 = -3/4

-3/4 = -0.75

-6/8 = -0.75

-13 1/2 = -13.5

Which means:

-13 1/2 < -6/8

Hope this helped.

Answer:

[tex] < [/tex]

Step-by-step explanation:

[tex] \frac{6}{8} [/tex]

Is close to 0 (to positive) you can use a time line to determine which is a correct answer

Answer:

(I'll leave cm out to save space and time in the answer)

the perimeter is 500, there are 5 sides. so on average a side will be 100.

that's already the important key idea.

it's indeed 100 for the third side, the second will be 10 less, the fourth 10 more (making the 2and and the 4th side 200 in sum, and therefore still 100 on average).

repeat this for the 1. and 5. side and we get:

80

90

100

110

120

Answer: -78 / 35

Step-by-step explanation:

Given

 2/5 + 3/7 + (-6/5) + (-13/7)

Combine terms that have the same denominator

= 2/5 + (-6/5) + 3/7 + (-13/7)

= -4/5 - 10/7

Convert denominator by Least Common Multiple (LCM)

= (-4 × 7) / (5 × 7) - (10 × 5) / (7 × 5)

= -28/35 - 50/35

= -78 / 35

Hope this helps!! :)

Please let me know if you have any questions

Answer:

[tex] \frac{2}{5} + \frac{3}{7} + ( - \frac{6}{5} ) + ( - \frac{13}{7} ) \\ \frac{2}{5} + \frac{3}{7} - \frac{6}{5} - \frac{13}{7} \\ ( \frac{2}{5} - \frac{6}{5} ) + ( \frac{3}{7} - \frac{13}{7} ) \\ \frac{2 - 6}{5} + \frac{3 - 13}{7} \\ \frac{ - 4}{5} + \frac{ - 10}{7} \\ \frac{ - 4}{5} - \frac{10}{7} \\ \frac{ - 28 - 50}{35} \\ \frac{ - 78}{35} \\ - \frac{78}{35} [/tex]

Answer:

x=1

Step-by-step explanation:

3x+9 = 12

Subtract 9 from each side

3x+9-9=12-9

3x = 3

Divide by 3

3x/3 = 3/3

x=1

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]x = 1[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Calculating the answer...}}\\\\3x + 9 = 12\\-------------\\\rightarrow 3x + 9 - 9 = 12 - 9\\\\\rightarrow 3x = 3\\\\\rightarrow \frac{3x=3}{3}\\\\\rightarrow \boxed{x=1}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

see below

Step-by-step explanation:

2^30

-------

8^9

Rewriting

8^9

2^3 ^ 9

We know a^b^c = a^(b*c)

2^(3*9) = 2^27

2^30

-------

2^27

We know a^b / a^c = a^(b-c)

2^(30-27) = 2^3

Assuming you mean 2^x

2^3 = 2^x

x=3

If you mean 2x

2^3 = 8

8 = 2x

Divide by 2

4 =x

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{2^{30}}{8^9}=2x}[/tex]

[tex]\mathsf{2^{30}}\\\mathsf{= \bf 1,073,741,824}\\\\\mathsf{8^9}\\\mathsf{= \bf 134,217,728}[/tex]

[tex]\mathsf{\rightarrow \dfrac{1,073,741,824}{134,217,728}= 2x}\\\\\\\mathsf{\dfrac{1,073,741,824}{134,217,728}= \bf 8}\\\\\\\mathsf{\rightarrow \ 8 = 2x}\\\\\\\\\large\textsf{TURN\ the\ EQUATION\ around}\\\\\\\mathsf{\rightarrow\ 2x = 8}\\\\\\\large\textsf{DIVIDE 2 to BOTH SIDES}\\\\\\\mathsf{\dfrac{2x}{2}=\dfrac{8}{2}}\\\\\\\large\textsf{CANCEL out: }\mathsf{\dfrac{2}{2}}\large\textsf{ because it gives you 1}\\\\\\\large\textsf{KEEP: }\mathsf{\dfrac{8}{2}}\large\textsf{ because it gives you the answer of x}[/tex]

[tex]\mathsf{x = \dfrac{8}{2}}\\\\\\\mathsf{x = 8\div 2}\\\\\\\mathsf{x = \bf 4}\\\\\\\\\\\boxed{\boxed{\huge\text{Therefore, your answer is: \textsf{x = 4}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The equation in point slope form is y - 6 = 2(x + 3)

This is from the general point slope template of [tex]y - y_1 = m(x - x_1)[/tex]

The m is the slope, which in this case is m = 2. The [tex](x_1,y_1)[/tex] is the point the line goes through. In this case, [tex]x_1 = -3 \text{ and } y_1 = 6[/tex]

If you were to solve that equation in bold for y, then you should get y = 2x+12 which is now in y = mx+b form, aka slope intercept form.