Find positive integer x, if 1+2+3 +...+x=120.

Answers

Answer 1

Answer:

16

Step-by-step explanation:

Given the expression  1+2+3 +...+x=120, this means that the sum of the arithmetic sequence  1+2+3 +...+x is 120.

First we need to find the xth term of the arithmetic sequence 1+2+3 +...+x

Sum of an arithmetic seq Sx = x/2(2a+(x-1)d)

a = first term

d = common difference

x is the number of terms

from the sequence, a = 1 and d = 1

Sx = x/2(2(1)+(x-1)*1)

Sx = x/2(2+x-1)

Sx = x/2(1+x)

Sx = x²+x/2

Substitutig thid into the question to calculate x;

x²+x/2 = 120

x²+x = 240

x²+x-240 = 0

x = 1±√1²-4(-240)/2

x = 1±√961/2

x = 1±31/2

x = 1+31/2 or 1-31/2

x = 32/2 or -30/2

x = 16 or -15

Since we are to look for the positive integer of x, then x is 16


Related Questions

Drag each scenario to show whether the final result will be greater than the original value, less than the original value, or the same as the original value. Clear Check A 30% 30% increase followed by a 15% 15% decrease A $35 $35 decrease followed by a $25 $25 increase A 50% 50% decrease followed by a 100% 100% increase A 70% 70% increase followed by a 50% 50% decrease A 50% 50% increase followed by a 33 1 3 % 3313% decrease Same as the original Less than the original Greater than the original

Answers

Answer:

A) Greater than the original

B) Less than the original

C) Same as the original

D) Less than the original

E) Same as the original

Step-by-step explanation:

For all cases, let 'x' be the original value:

A) 30% increase followed by a 15% decrease

[tex]X*(1+0.3)*(1-0.15)\\1.105X[/tex]

Result is greater than the original

B) $35 decrease followed by a $25 increase

[tex]X-35+25\\X-10[/tex]

Result is less than the original

C) 50% decrease followed by a 100% increase

[tex]X*(1-0.5)*(1+1)\\1.00X[/tex]

Result is same as the original

D) 70% increase followed by a 50% decrease

[tex]X*(1+0.7)*(1-0.5)\\0.85[/tex]

Result is less than the original

E) 50% increase followed by a 33.13% decrease

[tex]X*(1+0.5)*(1-0.3313)\\1.00X[/tex]

Result is same as the original

Answer:

when the imposter is sus

Step-by-step explanation:

susssssssssssssssssssssssssssssssy now give me 5 stars and a thanks

please solve quickly

Answers

Answer:

Brainliest!

Step-by-step explanation:

100% sugar syrup = 75/30 x 100 = 250

Please help me! Ill give brainliest! The incorrect work of a student to solve an equation 2(y + 6) = 4y is shown below: Step 1: 2(y + 6) = 4y Step 2: 2y + 8 = 4y Step 3: 2y = 8 Step 4: y = 4 Which of the following explains how to correct Step 2 and shows the correct value of y? (5 points) 2 should be distributed as 2y + 12; y = 6 2 should be distributed as 2y + 12; y = 3 The equation should be y + 6 = 4y after division by 2; y = 2 The equation should be y + 6 = 4y after division by 2; y = 1

Answers

2 should be distributed as 2y + 12; y = 6

Step-by-step explanation:

The equation is...

[tex]2(y+6)=4y[/tex]

First, we need to distribute the 2 to the numbers in the parentheses. We will multiply them both by 2.

[tex]2y+12=4y[/tex]

Now we can subtract 2y from both sides. On the left it will cancel and on the right we will be left with 2y.

[tex]12=2y[/tex]

Now we can just divide and...

y = 6

3. The perimeter of a rectangle is 98 feet. Find its dimensions assuming that its length is 2 feet less than twice its width.
The width is
(Simplify your answers.)
and length is

Answers

Answer:

w = 17 fts

l = 32 fts

Step-by-step explanation:

P = 2w + 2l

l = 2w - 2

98 = 2w + 2(2w - 2)

98 = 2w + 4w - 4

98 + 4 = 6w

6w = 102

w = 17 fts

l = 2×17 - 2 = 34 - 2 = 32 fts

Please Help ASAP C: :D

Answers

Answer:

-21/10

Step-by-step explanation:

-2/5 - 4/5 + (-9/10) = -6/5 -9/10 = -12/10 -9/10 = -21/10

Answer:

-21/10

Step-by-step explanation:

Plug in 4/5 for x and simplify.

-2/5 - 4/5 + (-9/10)

-6/5 + (-9/10)

-21/10 or -2 1/10

I hope this helps :))

HELPPP PLEASE
50 POINTSS​

Answers

Answer:

184

Step-by-step explanation:

edmund as a 2 by 2 cube

so samuel has a cuboid twice as long

2 x 2 = 4

3 times as wide

3 x 2 = 6

and 4 times as high

2 x 4 = 8

8 x 6 x 4 = 192 small cubes

but we are trying to find how much more samuel got

so 192 - 8 = 184

Answer:

D.) 184

Step-by-step explanation:

Its kinda like solving for "X"-

Isolate "x" on one side of the algebraic equation by adding the negative number that appears on the same side of the equation as the "x." For example, in the equation "x - 5 = 12", rewrite the equation as "x = 12 + 5" and solve for "x." The solution is "x = 17." A linear algebraic equation is nice and simple, containing only constants and variables to the first degree (no exponents or fancy stuff). To solve it, simply use multiplication, division, addition, and subtraction when necessary to isolate the variable and solve for "x". Here's how you do it: 4x + 16 = 25 -3x = ____.  We have 4 ways of solving one-step equations: Adding, Substracting, multiplication and division. If we add the same number to both sides of an equation, both sides will remain equal.

*Plus i got it Right*

:D

Which of the following algebraic equations is equivalent to nVa = 7?

Answers

Answer:

first anwer is the correct one

Step-by-step explanation:

if we power to n we got

[tex](n\sqrt{a})^n = x^n[/tex]

then [tex]a = x^n[/tex]

Answer- the first answer is correct.

Tell whether the side lengths 3, 9, and 15 form a triangle. answers: No, because 9 + 3 isn’t greater than 15. Yes, because 15 + 9 is greater than 3. Yes, because the sum of any two sides is greater than 30. No, because 15 + 9 isn’t less than 3.

Answers

Answer:

The answer is no, because 9 + 3 isn't greater than 15. Remember, to form a triangle the sum of the 2 shortest sides must be greater than the longest side.

Answer:

No, because 9 + 3 isn't greater than 15.

Step-by-step explanation:

The Triangle Inequality Theorem states that the 2 shorter legs of a triangle's sum must add up to be greater than the hypotenuse or the longest side. So 3, 9, and 15 don't make a triangle.

3.
Reasons
Statements
MNOP is a parallelogram
PM || ON
N
M
Alternate Int. Zs Thm.
Given:
MNOP is a parallelogram
MN || PO
Alternate Int. Zs Thm.
Prove:
PM ON
(For this proof, use only the
definition of a parallelogram;
don't use any properties)

Answers

Answer:

[tex]\overline{PM}\cong\overline{ON}[/tex]: Reason; Corresponding parts of congruent triangles ΔOMN and ΔOMP are congruent (CPCTC)

Step-by-step explanation:

1) MNOP is a parallelogram: Reason; Given

2) [tex]\overline{PM}\left | \right |\overline{ON}[/tex]: Reason; Definition of a parallelogram

3) ∠MON ≅ ∠PMO: Reason; Alternate Int. ∠s Thm.

4) [tex]\overline{MN}\left | \right |\overline{PO}[/tex]: Reason; Definition of a parallelogram

5) ∠NMO ≅ ∠POM: Reason; Alternate Int. ∠s Thm.

6)  [tex]\overline{OM}\cong\overline{OM}[/tex]: Reason; Reflexive property

7) ΔOMN ≅ ΔOMP: Reason; Angle Angle Side (AAS) congruency theorem

8)  [tex]\overline{PM}\cong\overline{ON}[/tex]: Reason; Corresponding parts of congruent triangles are congruent (CPCTC).

Also we have;

9)  [tex]\overline{PM}\cong\overline{ON}[/tex]: Reason; Segment opposite congruent angles are congruent

Share £10 in the ratio of 2:3 ASAPP!!!!!!!!!!!!

Answers

Answer:

£4 and £6

Step-by-step explanation:

Total = £10

Ratio = 2:3

Total Parts = 2+3 = 5

Divide it by the Total

=> 10/5 = £2

Multiply it by the ratios

1) 2 * 2 = £4

2) 3 *2 = £6

Answer:

4:6

Step-by-step explanation:

2+3=5

10/5=2

3x2= 6

2x2=4

4:6

Which of the following is the solution to this system of equations?
x-y=5
2x-3y=18​

Answers

Answer:

answer:

(-3, -8)

Step-by-step explanation:

Graph the set of real numbers on a number line. {x|x> -5}
Mathematics

Answers

The answer is just -5

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

What is a number line?

A number line in elementary mathematics is a representation of a graduated straight line that serves as an abstraction for real numbers, represented by the symbol R."

It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.

The inequality is represented on the number line states that all the values of x are greater than -5.

The graph of the number line is attached with the answer below.

To know more about number lines follow

https://brainly.com/question/24644930

#SPJ2

Find all possible values of the digits Y, E, A, R if YYYY - EEE + AA - R = 1234, and different letters represent different digits. Plz help

Answers

Answer:

The values of Y, E, A, R are "2, 9, 1, 0".

Step-by-step explanation:

The given equation is:

⇒  [tex]YYYY-EEE+AA-R=1234[/tex]

Let the values,

[tex]Y=2[/tex]

[tex]E=9[/tex]

[tex]A=1[/tex]

[tex]R=0[/tex]

On substituting the estimated values in the L.H.S of the given equation, we get

⇒  [tex]2222-999+11-0[/tex]

⇒  [tex]1223+11[/tex]

⇒  [tex]1234 \ i.e., R.H.S[/tex]

So that the possible values of Y,E,A,R will be "2, 9, 1 and 0".

Please help Urgent giving brainlist!

Answers

Answer:

[tex]f=-\frac{5}{3}[/tex]

Step-by-step explanation:

[tex]-\frac{3}{4}f=\frac{5}{4}[/tex]

[tex](4)-\frac{3}{4}f=(4)\frac{5}{4}[/tex]

[tex]-3f=5[/tex]

[tex]\frac{-3f}{-3}=\frac{5}{-3}[/tex]

[tex]f=-\frac{5}{3}[/tex]

Answer:

[tex]f = - \frac{5}{3} \\ [/tex]

Step-by-step explanation:

[tex] \frac{ - 3f}{4} = \frac{5}{4} \\ cross \: \: multipication \\ - 12f = 20 \\ \frac{ - 12f}{ - 12} = \frac{20}{ - 12} \\ f = \frac{20}{ - 12} \\ f = - \frac{5}{3} [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!


Complete the statements about the system of linear
equations represented by the tables
The equation representing the left table is?

The equation representing the right table is?

The solution to the system of equations is?

Answers

Answer:

Complete the statements about the system of linear equations represented by the tables.

The equation representing the left table is

✔ y = 1.5x – 6

The equation representing the right table is

✔ y = –4x + 6.1

The solution to the system of equations is

✔ (2.2, –2.7)

The statements  about the system of linear equations represented by the tables should be described below:

Equation:The equation representing the left table is y = 1.5x – 6The equation representing the right table is y = –4x + 6.1The solution to the system of equations is (2.2, –2.7)

Find out more information about the  equation here:

https://brainly.com/question/2263981?referrer=searchResults

O perímetro de um campo retangular é de 80 metros e sua area é de 320 metros quadrados. Encontre as dimensões do campo, corrija o décimo de metro mais próximo.

Answers

Answer:

Comprimento: 28.9 m; Largura: 11.1 m

Step-by-step explanation:

P = 2(C + L) = 80

A = CL = 320

2(C + L) = 80

CL = 320

C + L = 40

CL = 320

C = 40 - L

CL = 320

(40 - L)L = 320

40L - L^2 = 320

L^2 - 40L + 320 = 0

aL^2 + bL + c = 0

[tex] L = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]

[tex] L = \dfrac{-(40) \pm \sqrt{(-40)^2 - 4(1)(320)}}{2(1)} [/tex]

[tex] L = \dfrac{40 \pm \sqrt{1600 - 1280}}{2} [/tex]

[tex] L = \dfrac{40 \pm \sqrt{320}}{2} [/tex]

[tex] L = \dfrac{40 \pm \sqrt{64 \times 5}}{2} [/tex]

[tex] L = \dfrac{40 \pm 8\sqrt{5}}{2} [/tex]

[tex] L = 20 \pm 4\sqrt{5} [/tex]

[tex] L \approx 28.9 [/tex] or [tex] L \approx 11.1 [/tex]

L = 28.9

C = 40 - L = 40 - 28.9 = 11.1

Answer: Comprimento: 28.9 m; Largura: 11.1 m

Please answer need help

Answers

Answer:

-2 3/4, -2, -1 1/2, -0.8, -1/3, 0.2

Answer:

-2 3/4

-2

-1 1/2

-0.8

-1/3

0.2

Step-by-step explanation:

you change the fractions into decimals

-1 1/2 = -1.5

0.2 = 0.2

-1/3 = -0.3

-2 = -2

-2 3/4 = -2.75

-0.8 = -0.8

then you put them in order

please meee pleasee!

Answers

Answer:

D

Step-by-step explanation:

Tenth vs Hundreth.... ten times larger

Answer:

D. 0.73

Step-by-step explanation:

In the number 0.975, 7 stands for 7 hundredths i.e. 0.07

=> Multiplying 0.07 by 10 will make it 0.7 ( 7 tenths)

=> The number with 7 tenths or 0.7 is 0.73

There are some sweets in a bag 18 of the sweets are toffees and 12are mints write down the ratio of them in the simplest form

Answers

Answer:

3:2

Step-by-step explanation:

18:12

simplest form =3:2

Answer:

3:2

Step-by-step explanation:

Divide both sides by 6

please need help I will be MARKING as BRIANILIST. thank you so much. ​​

Answers

Answer:

Option B is the correct answer.

Step-by-step explanation:

B= {- 5, - 4.5, - 3}

Number sequence

1. 2, 11, 4, 13, __, __.

2. 4, 12, 36, 108, __, __.

3. 8, 13, 18, 23, __, __.

4. 5, 10, 8, 13, 11, __, __.​

Answers

Answer:

1. 6, 15

2. 324,972

3. 28, 31

4. 16, 14

Step-by-step explanation:

Answer:

1. 6, 15

2. 324,972

3. 28, 31

4. 16, 14

Step-by-step explanation:

Solve the following system by of linear equation by guass jordan method 2x+2y+4z=18 X+3y+2z=13 3x+2y-3z=14

Answers

Answer:

[tex]x + 3y + 2z = 13 \\ 2x + 2y + 4z = 18 \\ 3x + 2y - 3z = 14 \\ \\ x = - 3y - 2z + 13 \\ 2( - 3y - 2z + 13) + 2y + 4z = 18 \\ 3( - 3y - 2z + 13) + 2y - 3z = 14 \\ y = 2 \\ z = \frac{25}{9} - \frac{7}{9} y \\ z = \frac{25}{9} - \frac{7}{9} \times 2 \\ z = \frac{11}{9} \\ x = - 3 \times 2 - 2( \frac{11}{9} ) + 13 \\ x = \frac{41}{9} \\ y = 2 \\ z = \frac{11}{9} [/tex]

please solve both. help quickly!!

Answers

Answer:

1/1000 for the 1st

1/100 for the 2nd

Step-by-step explanation:

0.1% is 0.001, which is 1/1000

1% is 0.01, which is 1/100

Answer:

0.1% = 10    1%=1/100

The axis of symmetry for the graph of the function f(x)=3x2+bx+4 is x equals three-halves. What is the value of b? −18 −9 9 18

Answers

Answer:

b = -9

Step-by-step explanation:

If we have a function with the form:

[tex]f(x)=ax^2+bx+c[/tex]

The axis of symmetry is equal to:

[tex]x = \frac{-b}{2a}[/tex]

So, for the function [tex]f(x)=3x^2+bx+4[/tex], the value of a is 3 and the value of c is 4. It means that its axis of symmetry is equal to:

[tex]x=\frac{-b}{2(3)}=\frac{-b}{6}[/tex]

Solving for b, we get that: [tex]b=-6x[/tex]

Additionally, the axis of symmetry is [tex]x=3/2[/tex], so replacing x by 3/2, we get that b is equal to:

[tex]b=-6(3/2)\\b=-9[/tex]

Answer:

b= -9

Step-by-step explanation:

I just took the quiz and got it right.

(3x^3+5-3x^4) - (-5x^4+4+x^3) Express the answer in standard form. Enter your answer in the box.

Answers

Answer:

(x3 + 3x2 + 5x – 4) – (3x3 – 8x2 – 5x + 6) ... \hline -2x^3&+11x^2&+10x&-10\end{array} } x3–3x3−2x3​+3x2+8x2+11x2​+5x+5x+10x​−4–6−10​​

Step-by-step explanation:

can someone help fill in the gaps in the table and calculate an estimate for the mean

Answers

Answer:

Step-by-step explanation:

5x3= 15

8x9=72

12x11=132

14x17=138

9x17=153

15+72+132+138+153=510

510/50=10.2= mean

I WILL GIVE BRAINLIEST!!! Part A: The Sun produces 3.9 ⋅ 10^33 ergs of radiant energy per second. How many ergs of radiant energy does the Sun produce in 1.55 ⋅ 10^7 seconds? Express your answer in scientific notation and show your work. (5 points) Part B: Which is the more reasonable measurement of the distance between the tracks on a CD: 1.6 ⋅ 10−3 mm or 1.6 ⋅ 103 mm? Justify your answer. (5 points)

Answers

Answer:

Part A: This can be solved using cancellation of units: Energy produced (ergs) = (3.9 x 10^ 33 ergs/ sec)( 1.55 x 10^7 sec) = 6.045 x 10^40 ergs Part B: The grooves within a CD is very small, therefore it would be more reasonable to have a value of 1.6 x 10^-3 mm

Hope this helped you!

Step-by-step explanation:

If f(x) is defined as follows, find (a) f(-4). (b) f(O), and (c) f(1).

if x<0
f(x) = { -3
if x=0
2x+3 if x > 0
(a) f(-4)=(Simplify your answer.)
(b) f(0) = (Simplify your answer.)
(C) f(1) = (Simplify your answer.)

Answers

Answer:

f(-4)=(-4)^2=16f(0)=-3f(1)=2*1+3=5

The value of the function at x = -4, 0, and 1 will be 16, -3, and 5, respectively.

What is a function?

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The function is given below.

[tex]f(x) = \left\{\begin{matrix}x^2 & x < 0\\ - 3 & x =0\\ 2x+3 & x > 0\end{matrix}\right.[/tex]

The value of the function at x = - 4, will be

f(-4) = (-4)²

f(-4) = 16

The value of the function at x = 0, will be

f(0) = -3

The value of the function at x = 1, will be

f(1) = 2(1) + 3

f(1) = 2 + 3

f(1) = 5

The value of the function at x = -4, 0, and 1 will be 16, -3, and 5, respectively.

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ2

Simply the problem.

Answers

Answer:

C

Step-by-step explanation:

[tex]\sqrt{3}\cdot\sqrt{21}= \\\\\sqrt{3\cdot 21}= \\\\\sqrt{63}= \\\\3\sqrt{7}[/tex]

Therefore, the correct answer is choice C. Hope this helps!

Answer:

3√7

Step-by-step explanation:

√3×√21=√63

√63=√7×√9=√7 × 3

=3√7

|9t|=81 answer the equation​

Answers

Answer:

9, or -9

Step-by-step explanation:

9t=81 or -81

t=9 or -9

Answer:

[tex]t=9\\t=-9[/tex]

Step-by-step explanation:

[tex]|9t|=81[/tex]

[tex]9t=81\\9t=-81[/tex]

[tex]t=81 \div 9\\t=-81 \div 9[/tex]

[tex]t=9\\t=-9[/tex]

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