What kind of sequence is this?
126, 112, 98, 84, ...

Answer:

Scientific notation: 9.79 × 10^1

Standard form: 97.9

Answer:

1/2

Step-by-step explanation:

To find the slope, we can use the slope formula

m = ( y2-y1)/(x2-x1)

   = ( 2-3)/(0-2)

   = -1/-2

  = 1/2

Answer:

Slope = 0.5

Step-by-step explanation:

Given: Line passes through (2, 3) and (0, 2)

\(\text{Slope formula} = \dfrac{\text{Rise}}{\text{Run}} = \dfrac{y_2 - y_1}{x_2 - x_1}\)

Substitute the coordinates in the formula and solve for the slope;

    \(\implies \text{Slope formula} = \dfrac{y_2 - y_1}{x_2 - x_1}\)

    \(\implies\text{Slope formula} = \dfrac{2 - 3}{0 - 2}\)

    \(\implies\text{Slope formula} = \dfrac{-1}{-2}\)

    \(\implies\text{Slope formula} = \dfrac{1}{2} = 0.5\)

Therefore, the slope of the line is 0.5.

I think its 2.5yrs

yeah thank you pls give me correct answer if I am wrong

Answer:

Step-by-step explanation:

The equation of line containing vertices (8,4) is y = 4.

Y = mx+b, where m is the slope and b is the y-intercept, is the formula for the slope-intercept form (the point where the line crosses the y-axis). Using y=mx+b to graph a line is typically simple. The standard form and the point-slope form are other formats for linear equations.

Equation of line in slope - intercept form is

y = mx + c

where m= slope

c = y - intercept

As it is given that equation of line is horizontal,

this implies

x = 0

y = m (0) + c

y = c

Now, the given coordinates are (8,4)

Slope of the equation equals 0 As the line is horizontal.

⇒ y = 0 (8) + 4

⇒ y = 4

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Answer:

45.45

Step-by-step explanation:

25 is 55% of What Number? - 25 is 55% of 45.45. 100% of 45.45 is 45.45, therefore 55 percent of 45.45 equals 25.

Answer:

x = 500/11

Step-by-step explanation:

look at the attached photo :)

Answer:

first thing, take 3 pairs of equations and in each pair, make any one variable's coefficient equal to the coefficient of the same variable in the other equation and subtract the equations.

you will get 3 different equations:  

x+y = 1

- 4x - 21z = 72

-x + 3z = -10 (simplified)

now take the value of x and y from equation 2 and 3 in terms of z and substitute x and y with those values

y = (72 + 21z)/-4

x = 3z + 10

as x + y = 1

you will get z = -4 after sloving the equation

now you have the value of one of the variables..

now we will substitute z in the equations to get the other variables

x = 3z + 10

x = 3(-4) + 10

x = -12 + 10

x = -2  

Now y:

72+21(-4)/-4

(72 - 84)/-4

-12/-4

y  = 3

so,

z = -4

x = -3

y = 3

I assume that it's brainly enough

Answer:

x= -2, z= -4

Step-by-step explanation:

-3x-2y+4z = -16

10x+10y-5z=30 ⇒ 2x+2y-z=6 ⇒ 14x+14y-7z=42

5x+7y+8z=-21 ⇒ 10x+14y+16z= -42

Add up the first one with the second:

-3x-2y+4z = -16

+

2x+2y-z=6

-------

-x+3z= -10 ⇒ x= 3z+10

Subtract the last one from the second:

14x+14y-7z=42

-

10x+14y+16z= -42

------------

Replace x with 3z+10

Answer:

x² + y² = 74

Step-by-step explanation:

given

(x - y) = 8 ( square both sides )

(x - y)² = 8² ← expand left side using FOIL

x² - 2xy + y² = 64 ← substitute xy = 5

x² - 2(5) + y² = 64

x² - 10 + y² = 64 ( add 10 to both sides )

x² + y² = 74

Answer:

\(\frac{1}{3}\)

Step-by-step explanation:

The computation is shown below:

The numbers of possible results at the time when we drawing in two tries is 9

i.e. shown below:

11, 12, 13, 21, 22, 23, 31, 32, 33

Now the probability is

\(p=\frac{\text{no. of favorable cases }}{\text{total no. of outcomes}}\\\\=\frac{3}{9}\\\\=\frac{1}{3}\)

According to the data, it can be inferred that Lin is faster than Andre because she is going at 0.3 km/min speed while he is going at 0.25 km/min speed.

To calculate who goes faster we must divide the time into the distance traveled by each character as shown below:

According to the above, the point K of each would be equal to the distance that each of them travels in one minute. As shown in the graph, after 5min (Lin) and 8min (Andre), each one reaches their respective destination located 1.5km and 2km away, respectively, taking the point (0,0) as the starting point.

The graph is attached.

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Answer:

I would identify the proportions of the corresponding sides, because that would allow you to identify whether or not the triangles are similar. You could also identify if two triangles are similar using

-SSS (side-side-side) which would tell you if all three corresponding sides are congruent

-SAS (side-angle-side) which would tell you if two sides and the angle between them are congruent

-ASA (angle-side-angle) which would tell you the two angles and the side between them are congruent

-AAS (angle-angle-side) which would tell you if two angles and a non-included side are congruent. You triangles may have all of these, or just one, but it will help you identify the similarity between triangles

All four consecutive integers will be 9, 10, 11, and 12 and can be found out by high common sense.

A pattern is a specific arrangement of numbers or any term which will follow a specific code or hint.

For example 2,4,6,8 in this, the difference between any two-term is only 2 and this will be its specific pattern.

Given that,

8 times the sum of the first and the third  =  8( 1st + 3rd)

40 greater than 10 times the fourth = 40 + 10(4th)

So,

8( 1st + 3rd) = 40 + 10(4th)

Now if we look right and side then it will come out as any number with the unit placed as 0.

So it means on the left side also the unit place must be 0.

By thinking of  1st + 3rd = 10 /20 because at 45 it will be 40 which is not equal to the right-hand side.

Now by hit and trial method, we need to guess it 20 = 9 + 11

Then

8(9 + 11) = 40 + 10(12)

One equation can never give us three unknowns hence it will be the correct way.

Hence so the four consecutive integers will be 9, 10, 11, and 12.

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I assume the given expression is

\(\sqrt x \sqrt[4]{x}\)

We can write each root as a rational power of x, then add the exponents:

\(\sqrt x \sqrt[4]{x} = x^{\frac12} x^{\frac14} = x^{\frac12 + \frac14} = x^{\frac34}\)

Then putting it back into radical form, we have

\(\sqrt x \sqrt[4]{x} = \sqrt[4]{x^3}\)

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

Work Shown:

Recall that the imaginary number i has the definition of \(i = \sqrt{-1}\)

List out the first few powers of i

I'm skipping steps when I listed out those terms, so let me know if you need to see them.

The process repeats every 4 items. This means we'll divide the exponent by 4 to look at the remainder.

Let's do that for the first exponent

12/4 = 3 remainder 0

The remainder 0 tells us that i^12 = i^0 = 1

Also,

22/4 = 5 remainder 2

The remainder 2 means i^22 = i^2 = -1

-------------------

In short:  i^12  = 1 and i^22 = -1

which means 6i^12 + 7i^22 = 6(1) + 7(-1) = -1

Answer:

378

Step-by-step explanation:

2,653 divided by 7

Answer:

Step-by-step explanation:

Required equation is:

Solution:

Answer:

3580mm²

Step-by-step explanation:

Given the area of 250mL beaker to be 38.5cm²

We need to convert the value to mm²

Using the conversion

1cm² = 100mm²

Using the equality postulate:

If 1cm² = 100mm²

35.8cm² = x mm²

Calculate x by cross multiplying

x mm² × 1 cm² = 35.8 cm² × 100mm²

x mm² = (35.8 cm² × 100mm²)/1cm²

x mm² = 3580mm²

Hence the area is square millimeters is 3580mm²

Answer:

5 rooms covered by 10/3 rolls of wire

Step-by-step explanation:

question is solved by dividing rolls used for total rooms(10/3) with rolls used for each room(2/3).

Total amount she paid to repay her loan was $17,687

Amount is the total sum  of money paid to the bank.It is basically the sum of interest and principal amount.

Principal is the sum of money taken from the bank

Interest is the sum of money charge by the bank during the period of loan repayment.

Rate of interest is the rate at which interest is charge in the principal sum

Time is the total period of the loan repayment.

Simple interest = (P x Rx T)/100

where, P=principal

           R=rate of interest

           T= time

Amount= Principal +Interest

As per question,

P=$17000

R=6.8%

I=$687

Amount=P+I

              =$17000+687

              =$17687

Therefore,Total amount she paid to repay her loan was $17,687

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Answer:

  [15-√226, 1] ∪ [29, 15+√226]

Step-by-step explanation:

You want all solutions to |x^2 - 30x - 1| + |x^2 - 30x + 29| = 30.

The equation resolves to a piecewise equation whose domains are delimited by the points where the absolute value arguments are zero.

The argument of the left absolute value function will be zero where ...

  x^2 - 30x - 1 = 0

  x = (-(-30) ±√((-30)² -4(1)(-1)))/(2(1) = 15 ± √226 ≈ {-0.0332964, 30.0332964}

The argument of the right absolute value function will be zero where ...

  x^2 -30x +29 = 0

  (x -29)(x -1) = 0

  x = {1, 29}

In this domain, both absolute value arguments are positive, so the equation is ...

  x^2 -30x -1 +x^2 -30x +29 = 30

  2x^2 -60x +28 = 30 . . . . . collect terms

  x^2 -30x -1 = 0 . . . . . . . . . write in standard form

  x = {15 -√226, 15 +√226} . . . . solutions to the equation

These solutions are not in the domain we have defined for this equation.

In this domain, the left absolute value argument is negative, and the right argument is positive, so the equation is ...

  -(x^2 -30x -1) +(x^2 -30x +29) = 30

  30 = 30

All values of x in this domain (15-√226 ≤ x ≤ 1) are in the solution set.

In this domain, both absolute value arguments are negative, so the equation is ...

  -(x^2 -30x -1) -(x^2 -30x +29) = 30

  -2x^2 +60x -58 = 0 . . . . . . write in standard form

  x^2 -30x +29 = 0 . . . . . . . divide by -2

The solutions to this are x={1, 29}, neither of which is in the domain we have defined for this equation.

In this domain, the left absolute value argument is negative and the right argument is positive. The equation resolves to the same one as for the domain 15-√226 ≤ x ≤ 1: 30 = 30. Hence, all x-values in this domain (29 ≤ x ≤ 15+√226) are part of the solution set.

In this domain, both absolute value arguments are positive, so the equation is ...

  x^2 -30x -1 = 0 . . . . . . . . . write in standard form

  x = {15 -√226, 15 +√226} . . . . solutions to the equation

These solutions are not in the domain we have defined for this equation.

In interval notation, the solution set for the equation is ...

  [15-√226, 1] ∪ [29, 15+√226]

Answer:

Option B, \(-2\)

Step-by-step explanation:

Step 1:  Substitute x with 6 and solve

\(f(x) = \frac{1}{2}x - 5\)

\(f(6) = \frac{1}{2}(6)-5\)

\(f(6) = 3 - 5\)

\(f(6) = -2\)

Answer: Option B, \(-2\)

Answer:

The  probability is  \(P[ D n R] = 0.196\)

Step-by-step explanation:

  From the question we are told that

     The number of Democrats is  \(D = 8\)

       The number of republicans is  \(R = 8\)

The  number of ways of selecting selecting two Democrats and four Republicans.

         \(N = \left {D} \atop {}} \right. C_2 * \left {R} \atop {}} \right. C_1\)

Where C represents combination

substituting values

           \(N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1\)

           \(N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8!}{(8-2)! 2!} * \frac{8! }{(8-4)! 1 !}\)

=>        \(N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8!}{(6)! 2!} * \frac{8! }{(6)! 1 !}\)

=>        \(N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8 * 7 * 6!}{(6)! 2!} * \frac{8*7 *6! }{(6)! 1 !}\)

=>        \(N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8 * 7 }{ 2*1 } * \frac{8*7 }{ 1 *1 }\)

=>      \(N = 1568\)

The total number of ways of selecting the committee of six people is  

          \(Z = \left {D+R} \atop {}} \right. C_6\)

substituting values

           \(Z = \left {8+8} \atop {}} \right. C_6\)

            \(Z= \left {16} \atop {}} \right. C_6\)

substituting values

             \(Z= \left {16} \atop {}} \right. C_6 = \frac{16! }{(16-6) ! 6!}\)

           \(Z= \left {16} \atop {}} \right. C_6 = \frac{16 *15 *14 * 13 * 12 * 11 * 10! }{10 ! 6!}\)

           \(Z= \left {16} \atop {}} \right. C_6 = \frac{16 *15 *14 * 13 * 12 * 11 }{6* 5 * 4 * 3 * 2 * 1}\)

           \(Z= \left {16} \atop {}} \right. C_6 = 8008\)

The probability of selecting two Democrats and four Republicans  is  mathematically  represented as

           \(P[ D n R] = \frac{N}{Z}\)

substituting values

           \(P[ D n R] = \frac{1568}{8008}\)

            \(P[ D n R] = 0.196\)

Answer:

∠ BDC = 29°

Step-by-step explanation:

the sides of a rhombus are congruent, so CD = ED and Δ EDC is therefore isosceles with base angles congruent , then

∠ BCD = ∠ BED = 61°

• the diagonals are perpendicular bisectors of each other , then

∠ CBD = 90°

the sum of the 3 angles in Δ BCD = 180°

∠ BDC + ∠ CBD + ∠ BCD = 180°

∠ BDC + 90° + 61° = 180°

∠ BDC + 151° = 180° ( subtract 151° from both sides )

∠ BDC = 29°

From the system of equations given

The second equation

Multiplying the equation by -4, it will give

The missing number is -8

Hence, the answer is option C

\(\text{if }x>7\text{, then }|x|>7\) is a valid argument

\(|y|>7\text{, so }y=7\) is not a valid argument

For the first argument: \(\text{if }x>7\text{, then }|x|>7\)

From the definition of absolute value function

\(|x|=x\)   if \(x\ge0\)

That is every positive number is its own absolute value. Since

\(x>7\implies x\ge0\),

we can argue that

\(x>7\implies |x|>7\)

so the first argument is valid

For the second argument: \(|y|>7\text{, so }y=7\)

From the definition of absolute value function

\(|y|:=\left \{ {y\text{ if }y\ge0}\atop{-y\text{ if }y<0} }\right\)

This means that

\(|y|>7:=\left \{ {y>7\text{ if }y\ge0}\atop{-y>7\text{ if }y<0} }\right\)

or

\(|y|>7:=\left \{ {y>7\text{ if }y\ge0}\atop{y<-7\text{ if }y<0} }\right\)

no part of the definition allow for the option \(y=7\). So the second argument is not valid.

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Answer:

Answer shown in image.. (btw we got the same chromebook)

Step-by-step explanation:

Answer:

x = 9, -15

Explanation:

The initial equation is |x + 3| = 12

It means that x + 3 = 12 or -(x + 3) = 12

Then, we can solve each equation to get:

x + 3 = 12

x + 3 - 3 = 12 - 3

x = 9

-(x + 3) = 12

- x - 3 = 12

- x - 3 + 3 = 12 + 3

- x = 15

-1(-x) = -1(15)

x = -15

Therefore, the solutions are x = 9 and x = -15