Solve:
-2(x – 4) = -8
x = 8
X = -8
X = 16
X = -16
Help please

Given:

First five consecutive positive integers.

To find:

The sum of the first 5 consecutive positive integers.

Sum of the first ​n ​consecutive whole numbers.

Solution:

First five consecutive positive integers are 1, 2, 3, 4 and 5.

Sum of these numbers is

[tex]1+2+3+4+5=15[/tex]

Therefore, the sum of the first 5 consecutive positive integers is 15.

First ​n ​consecutive whole numbers are 0, 1, 2, 3,..., (n-1). These numbers are in AP.

Here, first term is 0 and common difference is 1.

Sum of n terms of an AP is

[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]

where, a is first term and d is common difference.

Substitute a=0 and d=1 in the above formula.

[tex]S_n=\dfrac{n}{2}[2(0)+(n-1)(1)][/tex]

[tex]S_n=\dfrac{n}{2}[n-1][/tex]

Sum of first 5 consecutive positive integers is equal to the sum of first 6 consecutive whole number because in whole numbers 0 is extra number.

For n=6,

[tex]S_6=\dfrac{6}{2}[6-1][/tex]

[tex]S_6=3(5)[/tex]

[tex]S_6=15[/tex]

The sum of the first 5 consecutive positive integers is 15.

So, the sum of (n-1) consecutive positive integers is

[tex]S_n=\dfrac{n}{2}[n-1][/tex]

Answer:

A

Step-by-step explanation:

I took the test

Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

[tex]6a^{2} - 24 = 0\\6a^{2} - 24 + 24 = 0 + 24 \\6a^{2} = 24\\\frac{6a^{2}}{6} = \frac{24}{6} \\a^2 = 4\\a = \sqrt{4} \\a = +2, -2[/tex]

Answer:x=4 and y=7

Step-by-step explanation:

Answer:

6...the length is 6

This is a horizontal line!

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Answer:

81x4 = (9x^2)^2, 121a6 = (11a^3)^2, 0.09y12 = (0.3y^6)^2, 4/9b6 = (2/3b^3)^2

Step-by-step explanation:

sqrt of 81 = 9, (we do sqrt because its the inverse to exponents) x^4, x^2 * x^2 = (9x^2)^2

sqrt of 121 = 11, a^6, a^x * a^2 = a^6, x = 3, (11a^3)^2

sqrt of 0.09 = 0.3, y^12 = y^x * y^2, x=6,(0.3y^6)^2

sqrt of 4/9 = 2/3, b^x * b^2 = b^6, x = 3, (2/3b^3)^2

^ = power, * = multiplication

Answer:

[tex]9d = 36[/tex]

Step-by-step explanation:

See attachment for complete question

[tex]Length = 36ft[/tex]

[tex]n = 10[/tex]

From the question, we understand that one shrub must be at both ends.

Taking the first as a point of reference, we're left with:

[tex](n - 1) * distance = 36[/tex]

Substitute 10 for n and d for distance

[tex](10 - 1) * d = 36[/tex]

[tex]9 * d = 36[/tex]

[tex]9d = 36[/tex]

Hence:

[tex]9d = 36[/tex] answers the question

Answer:

there are 20 questions on the exam

Step-by-step explanation:

Answer:

Ben

Step-by-step explanation:

25 goodies = 20 minutes

27 goodies = 24 minutes

Let's use ratio, divide both of them by their minute

25/20 = 20/20

27/24 = 24/24

1.25 goodies = 1 minute

1.12 goodies = 1 minute

1.25 is bigger than 1.12.

Answer:Ben

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

3x − 4(2x − 5)

Distribute

3x - 8x +20

-5x +20

20 -5x

This is equal to 20 -5x

Answer:

The answer would be true.

Step-by-step explanation:

Hope this help and I took the test and got this correct! :)

Answer:

936 miles in 13 hours.

Step-by-step explanation:

if you divide 792 by 11 you get 72, which is the unit rate. You multiply that by thirteen and it is the answer 936.

Answer:

936 miles

Step-by-step explanation:

Answer:

neither

Step-by-step explanation:

Answer:

(c)

Step-by-step explanation:

If these are

Parallel, slope of both the lines is same.

Perpendicular, if they are -ve reciprocal of each other.

In y = mx + c, slope is m.

Compare,

Slope of y=4x+1, is 4.

of 8y-16=2x is 2/8 = 1/4, which is reciprocal of 4,but not -ve.

So it is neither ll nor perpendicular.

Answer:

1/4 +1 1/10_.25 + 1.20

Step-by-step explanation:

1/4 also known as a quarter, should easily be known as .25, and .20 should be equal to 1/10 since .20x10 equals 1. that one in the equation doesn't really make a difference. (it's kinda just there¯\_(ツ)_/¯) so technically you have your answer.

Answer:

14 minutes below or 6 minutes above

Step-by-step explanation:

Let's say Sophia's time was 10 minutes WORSE

4 minutes below average- 10 minutes= 14 minutes below average

Let's say Sophia's time was ten minutes BETTER

4 minutes below average + 10 minutes= 6 minutes above average.

Hope this helps!

14 minutes below the average

6 minutes above the average

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

Let A = average running time

Jacob's time was 4 minutes under the average, so his time is A-4 minutes. Whatever A is, subtract off 4, and you'll get Jacob's time.

Sophia and Jacob have a difference of 10 minutes. If J = Jacob's time and S = sophia's time, then S-J = 10 or J-S = 10 depending on who has the larger time.

We can use absolute value to ensure that whatever we pick (S-J or J-S) will be positive. So |S-J| = 10. Recall that absolute value represents distance on a number line. Negative distance isn't possible.

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

Let's plug in J = A-4 and solve for S

|S-J| = 10

|S - ( J )| = 10

|S - (A-4)|

|S-A+4| = 10

S-A+4 = 10  or  S-A+4 = -10

S-A = 10-4  or  S-A = -10-4

S-A = 6  or  S-A = -14

S = A+6 or S = A-14

The equation S = A+6 shows Sophia is 6 minutes above the average

The equation S = A-14 shows Sophia is 14 minutes below the average

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

Let's pick some number for A that is over 14 minutes. Let's say the average running time is A = 20 minutes.

If A = 20, then Jacob's time is J = A-4 = 20-4 = 16

If the average running time is 20 minutes, then Jacob ran for 16 minutes.

If we subtract 10 from this, then J-10 = 16-10 = 6 is one possible time for Sophia. Notice how this is 14 minutes below the average (20-14 = 6)

If we add 10 to Jacob's time, then J+10 = 16+10 = 26, which is 6 minutes overage the average (20+6 = 26)

This is one numeric example, but you could use any value of A that you want as long as it's larger than 14. The reason A has to be larger than 14 is to ensure that Sophia's lower time value (A-14) is not negative. Having a time of zero is not feasible either.

Answer:

27

Step-by-step explanation:

5*6=30

6/2=3

30-3=27

[tex]5w - \dfrac{w}{x} [/tex]

w=6

w=6x=2

Let's put value of w and x

→[tex]5 \times 6 - \dfrac{6}{2} [/tex]

Step 1:

→[tex]30 - 3[/tex]

Step 2:

→[tex]\purple{27✓}[/tex]

Answer:

-72

Step-by-step explanation:

(-4)(-9)(-2)=

36(-2)=

-72

Answer:

y=1

Step-by-step explanation:

Plug in 2 for x in the original equation, this gives you y=2(2)-3. 2(2)=4 and 4-3=1 therefore y=1.

Answer:

146

Step-by-step explanation:

Since we know that this is a rhombus, we know that opposite angles must be equal to each other. This means that angle QTS is equal to angle QRS. Therefore angle QTS also equals 34.

Now, we also know that all the interior angles in a quadrilateral add up to 360. We can subtract 360-34-34=292.

Now we know that the remaining two angles S and Q need to add up to 292. We also know that they are equal because they are opposite angles. Therefore, we can solve the equation 292÷2=146. Each of these angles is 146. So the measure of angle S is 146.

The measure angle of S is 146 .

A rhombus is a special case of the parallelogram and is a quadrilateral with four equal sides. In a rhombus, the opposite sides are parallel and the opposite angles are equal. Also, all the sides of the rhombus are equal in length and the diagonals bisect each other at right angles. The rhombus is also known as a diamond.

By symmetry ;

This means that m∠QTS is equal to m∠QRS. Therefore ∠QTS is also equals 34.

We also know that The common property for all the above four-sided shapes is the sum of interior angles is always equal to 360 degrees. For a regular quadrilateral such as square, each interior angle will be equal to: 360/4 = 90 degrees.

Now we know that the remaining two angles S and Q need to add up to 292.

= 360 -34 -34= 292

We also know that they are equal because they are opposite angles.

Therefore, we can solve the equation,

[tex]\frac{sum of two opposite angle}{2}[/tex] = [tex]\frac{292}{2}[/tex] = 146

Each of these angles is 146.

So the measure of angle S is 146.

For the more information about properties of rhombus click the link given below.

https://brainly.com/question/4115340

Answer:

-10 + (-7)= -17

Step-by-step explanation:

Answer:

-17

Step-by-step explanation:

-10 plus -7 is -17

Answer:

120

Step-by-step explanation:

The common denominator of 24/1 and 5/6 is 6 so you multiply 24/1 by 6 which equal 144/6. Then you multiply 144/6 and 5/6 which equals 720/6. When you simplify it, it equals 120.

Answer:

.4 lbs

Step-by-step explanation:

Answer: When sales are greater than 2000 then  José's monthly earnings sre more than those of Maris.

Step-by-step explanation:

Let  x= Total sales

For José, monthly salary = $3,500

Commission percentage =  8% =0.08

Monthly earnings= Monthly salary + (Commission percentage) x (Total sales)

Monthly earnings= 3500 +0.08 x

For Maris, monthly salary = $3,900

Commission percentage =  6%

Monthly earnings= 3900 +0.06 x

When José's monthly earnings > Maris's monthly earnings

then, 3500 +0.08 x > 3900 +0.06 x

Subtract 3500 from both sides, we get

0.08 x > 400+0.06x

Subtract 0.06x from both sides, we get

0.02x>400

Divide both sides b 0.02

x> 20000

When sales are greater than 2000 then  José's monthly earnings sre more than those of Maris.

Answer:

j^6 / 18s^23

Step-by-step explanation:

You first by flipping the fraction to get rid of the negative exponents:

(j^6)/(6s^3(3s^5)^4) =

When there are exponents that are being exponentiated together, multiply them:

(j^6) / (6s^3)(3s^20) =

When there are exponents that are being multiplied, add them:

(j^6) / (18s^23)

Answer:

A

Step-by-step explanation:

cos that's the midpoint

0.2 or 2/9 in fraction form I believe.

Answer:

y = 3to6

Step-by-step explanation:

Answer:

3 ≤ y < 7

Step-by-step explanation:

≥ means greater than or equal to

≤ means less than or equal to

< means less than

> means greater than

Given y is greater than or equal to 3

y ≥ 3

y less than 7

y < 7

Joining both of them together

3 ≤ y < 7

Answer:C.

−y2−5xz+z2−x2

Step-by-step explanation:

Took the test got it right

The solution is Option C = ( -y² - 5xz + z² - x² )

What is Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

Given data ,

Expression 1 = y² - 4xz + z²

Expression 2 = x² + xz + 2y²

Let Expression 1 - Expression 2 = A

To find Expression 1 - Expression 2 = A

A = y² - 4xz + z² - ( x² + xz + 2y² )

By grouping the like terms , we get

A = ( y² - 2y² ) - ( 4xz + xz ) + z² - x²

Therefore,

A= - y² - 5xz + z² - x²

Hence , the solution is ( -y² - 5xz + z² - x² )

To learn more about quadratic equations click :
https://brainly.com/question/15739745

#SPJ2

Answer:

1 7/12

Step-by-step explanation:

The answer is 1/3+1 1/4 and if you make them common fractions it is 4/12+1 3/12=1 7/12

Answer:37/12

Step-by-step explanation:

1/3+11/4=37/12

Answer:

[tex]5+2*(7-4) =11[/tex]

Step-by-step explanation:

This expression was kind of trial and error for me seeing as I'm not really good at logic, but this is pretty basic. There are three possible places the parentheses can be placed (assuming each pair holds 2 terms);

[tex](5+2)*7-4\\5+(2*7)-4\\5+2*(7-4)[/tex]

The answer to the first expression would be 45, which is not equal to 11.

The answer to the second expression would be 15, which is also not equal to 11.

The answer to the last expression is 11, so that is the correct answer.

Hope this helped :D

- Shay

Answer:

6C2 = 15

# of ways to select two from the bag: 20C2 = 190

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P(2 red) = 15/190 = 3/38

Step-by-step explanation: