Solve for the variable!
1. 2x + 21 = 40
2. 4x - 12 = 3x + 9
3. 3(x -1) + 2 = 7x

Answer:27

Step-by-step explanation:

Rtf

Answer:

8695

Step-by-step explanation:

Took forever on calculator but I did it!

Answer:

8695

Step-by-step explanation:

There is a formula for adding all integers from 1 to some integer n.

[tex] 1 + 2 + 3 + ... + n = \dfrac{n(n + 1)}{2} [/tex]

In other words, to add all integers from 1 to an integer, multiply the integer by the next greater integer and divide by 2.

For example, what is

1 + 2 + 3 + 4 ?

Multiply 4 by the next integer, 5, and divide by 2.

(4 * 5)/2 = 20/2 = 10

Check: 1 + 2 + 3 + 4 = 3 + 3 + 4 = 6 + 4 = 10

We see that the formula works.

Now we need to apply that formula to this problem, but there's a little more to it.

If the problem were

1 + 2 + 3 + ... + 138 + 139, then we'd apply the formula and that would be it.

In this problem, though, we don't start the sum at 1. We start the sum at 46.

The trick here is to add all integers from 1 to 139, and then we subtract the sum of all integers from 1 to 45, so we are left with only the sum of the integers from 46 to 139.

Sum of integers from 1 to 139:

[tex] 1 + 2 + 3 + ... + 139 = \dfrac{139(139 + 1)}{2} = \dfrac{139(140)}{2} = 9730 [/tex]

Sum of integers from 1 to 45:

[tex] 1 + 2 + 3 + ... + 45 = \dfrac{45(45 + 1)}{2} = \dfrac{45(46)}{2} = 1035 [/tex]

Now we subtract the sum to 45 from the sum to 139.

46 + 47 + 48 + ... 138 + 139 = 9730 - 1035 = 8695

Answer: 8695

Answer:

431.25 approximately 431

Step-by-step explanation:

one way of calculating it would be to get the measure per one person which would be equal to 46 / 64 = 0.7 people in one square feet

then multiply 0.7 by the total distance = 431.25 approximated to 431

Answer:

Step-by-step explanation:

Given the distance of fall of the student in term of the time t expressed by the equation s(t) = −16t² + 8√t, to get the average speed of fall of the pencil after 2.8 secs, we will need to differentiate the given function first since Velocity is the change in distance of a body with respect to time i.e

V = d(s(t))/dt

s(t) = −16t² + 8t^1/2

V = -32t+1/2(8)t^(1/2 - 1)

V = -32t+4t^-1/2

The average speed of the fall Using the fact that the pencil hit the ground in exactly 2.8 seconds, will be gotten by substituting t = 2.8 into the resulting equation.

V = -32t+4(2.8)^-1/2

V = -32t+4/√2.8

V = -32+4/1.6733

V = -32+2.391

v = -29.61m/s

Hence the average speed of the fall is -29.61m/s

The  average speed of the fall is -29.61m/s

[tex]V = d(s(t))\div dt\\\\s(t) = −16t^2 + 8t^{1/2}\\\\V = -32t+1/2(8)t^{(1/2 - 1)}\\\\V = -32t+4t^{-1/2}[/tex]

Now here t = 2.8 seconds

So,

[tex]V = d(s(t))\div dt\\\\s(t) = −16t^2 + 8t^{1/2}\\\\V = -32t+1/2(8)t^{(1/2 - 1)}\\\\V = -32t+4t^-1/2[/tex]

V = -32+2.391

v = -29.61m/s

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Answer:

1. Horizontal component = -3 units

  Vertical component = -4 units

2. Horizontal component = 3 units

  Vertical component = 4 units

Step-by-step explanation:

If a vector M, starting at point A = (a, b) and ending at point B = (c, d) is given, then the vector can be resolved into x and y components as follows;

M = AB

Where;

AB = B - A

AB = (a, b) - (c, d)

AB = (a-c, b-d)

AB = (a-c)i + (b-d)k

Therefore, a-c and b-d are the x and y components of the vector M.

(1) Let the vector be M:

Starting point of M = Q = (4, 6)

Ending point of M = P = (1, 2)

So,

M = PQ

Where;

PQ = Q - P

PQ = (1,2) - (4,6)

PQ = (1-4, 2-6)  

PQ = (-3, -4)

Therefore,

M = PQ = -3i - 4j

The x and y components of M are therefore, -3 and -4 respectively.

(2) Let the vector be M:

Starting point of M = P = (1, 2)

Ending point of M = Q = (4, 6)

So,

M = PQ

Where;

PQ = Q - P

PQ = (4,6) - (1,2)

PQ = (4-1, 6-2)  

PQ = (3, 4)

Therefore,

M = PQ = 3i + 4j

The x and y components of M are therefore, 3 and 4 respectively.

Note: The x and y components are also called the horizontal and vertical components respectively.

Answer:

B is the answer..................

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Explanation:

Multiply top and bottom of the original fraction by 2

[tex]\frac{5}{16} = \frac{5*2}{16*2} = \frac{10}{32}[/tex]

Or you could go in reverse to divide each part of 10/32 by the GCF 2

[tex]\frac{10}{32} = \frac{10\div 2}{32\div 2} = \frac{5}{16}[/tex]

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Another alternative is to use your calculator to find the decimal version of each answer choice

5/32 = 0.15625

10/32 = 0.3125

1/2 = 0.5

10/16 = 0.625

And compare these results with 5/16 = 0.3125

Both 5/16 and 10/32 have the same decimal value 0.3125, which makes them equal.

Answer:

3

Step-by-step explanation:

The slope is the coefficient to the x variable.

In the equation y = 3x, this means 3 is the slope because it is the coefficient to x.

So, the slope is equal to 3.

Answer:

[tex]3[/tex] or [tex]\frac{3}{1}[/tex]

Step-by-step explanation:

Remember slope-intercept form.

[tex]y=mx+b[/tex]

~

[tex]m=slope[/tex]

[tex]b=y-intercept[/tex]

In the case of [tex]y=3x[/tex]:

[tex]m=3[/tex]

Answer:

Number of way s= N=100

The probability that it passes through  first of four servers at the third step is 0.25

Step-by-step explanation:

The total number of possible ways can be found out by multiplying the possibilities so the possibilities at the

1st stage is  5

2nd stage is 5

3rd stage is  4

4th stage is 1

So Number of way s= N= 5*5*4= 100

This can be solved by drawing a tree diagram as well.

Now the probability of finding the  that a message passes through the first of four servers at the third step.

There are five paths

And we have to find the probability of four

So 5C1*5C4/100= 0.25

The probability that it passes through  first of four servers at the third step is 0.25

Answer:

−3b /8

​  

Step-by-step explanation:

Answer:

b + 11 = 11 + b

Step-by-step explanation:

Combine like terms. Note that because you are adding for all terms, you can technically disregard the parenthesis:

3 + (b + 8) = b + 3 + 8 = b + 11

3 + (8 + b) = 3 + 8 + b = 11 + b

b + 11 = 11 + b (True).

Answer:

at least 10

Step-by-step explanation:

because i cant explain it.

Answer:

2 standard deviations above the mean is significant

Step-by-step explanation:

Answer:

75+48+x=180

x=180-123

=57degree

side length=3+3+3=9

f(3) = 4 is the answer

The idea is that y = f(x) is the output while x is the input

A point like (3,4) has x = 3 and y = 4 pair up together

Answer:

x=-8/5

Step-by-step explanation:

5x+15=7

5x=7-15

5x=-8 divide

-8/5

Answer:

I will do a random number

2/3=1 2/3

Step-by-step explanation:

And I think that is what u want

[tex]2\frac{1}{3}[/tex] is a mixed fraction and 7/3 is a improper fraction.

A fraction represents a part of a whole.

We need to write a improper fraction and a mixed number for the shaded portion of the group of figures

Fractions are three types proper, improper and mixed fraction

A proper fraction is a fraction which has its numerator value less than the denominator.

A improper fraction is a fraction which has its numerator value greater than the denominator.

A fraction represented with its quotient and remainder is a mixed fraction.

[tex]2\frac{1}{3}[/tex] is a mixed fraction

7/3 is a improper fraction.

Hence, [tex]2\frac{1}{3}[/tex] is a mixed fraction and 7/3 is a improper fraction.

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Answer:

Step-by-step explanation:

B yes their slopes are negative reciprocals

Answer:

b

Step-by-step explanation:

on edge

The value of x when f(x) = 1 is  x = 2.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.

Given:

The function,

f(x) = 3x – 5.

Solving for x when f(x) = 1,

1 = 3x - 5

3x = 6

x = 2

Therefore, the value is x = 2.

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Step-by-step explanation:

there are no different answers they are all the same

Answer:

The answer is A,B, and D

Step-by-step explanation:

Hope this helps =)

Answer:

x = -3/2

Step-by-step explanation:

Let's solve your equation step-by-step.

4(x+2(3x−7))=22x−65

Step 1: Simplify both sides of the equation.

4(x+2(3x−7))=22x−65

(4)(x)+(4)(2(3x−7))=22x+−65(Distribute)

4x+24x+−56=22x+−65

(4x+24x)+(−56)=22x−65(Combine Like Terms)

28x+−56=22x−65

28x−56=22x−65

Step 2: Subtract 22x from both sides.

28x−56−22x=22x−65−22x

6x−56=−65

Step 3: Add 56 to both sides.

6x−56+56=−65+56

6x=−9

Step 4: Divide both sides by 6.

6x = -9

6       6

x =  -3/2

In this problem, we'll need to divide the number of apples by the amount of apples in a small bag. This will leave us with the number of small bags needed for the amount of apples.

91 / 7 = 13

Therefore, Alexa and her family bought 13 small bags of apples.

Answer:

[tex] -12 [/tex]

Step-by-step explanation:

You start with 87 dollars.

[tex] 87 [/tex]

You write a check for 99 dollars.

Writing a check means taking money out of the bank.

[tex] 87 - 99 [/tex]

[tex] -12 [/tex]

She will have -12 dollars.

She is in debt for 12 dollars.

She owes the bank 12 dollars.

Answer:

A would be 13

So the full point would be (13,-3)

Answer:

Step-by-step explanation:

A). Yes. If we rotate shape I by 90° clockwise about the origin shape I will overlap shape II.

  Coordinates of one point of figure I are A(-1, 3).

  After rotation 90° clockwise,

  (x, y) → (y, -x)

  Following this rule,

  A(-1, 3) → A'(3, 1)

  It clearly states that figure I will overlap figure II.

B). No. because length of the quadrilateral I is different from the length of the quadrilateral given in figure III while width are same.

   Both are different quadrilaterals.

C). Yes. If the figure I is reflected over x-axis, we get figure III.

D). Yes. By the translation of figure I by 3 units right and 4 units down we get image figure V.

  Rule followed for the translation,

  (x, y) → (x+3, y-4)  

Answer:

A, B, and C all deal directly with the bank. While D does not deal with your bank it is a personal finance question that would NOT change your banking. So the correct answer would be D

Step-by-step explanation:

The amount of money you paid in income taxes last year.

Bank, is an institution that deals in money and its substitutes and provides other money-related services. In its role as a financial intermediary, a bank accepts deposits and makes loans.

A bank is a financial institution licensed to receive deposits and make loans. Banks may also provide financial services such as wealth management, currency exchange, and safe deposit boxes. There are several different kinds of banks including retail banks, commercial or corporate banks, and investment banks.

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Answer: B) Profit per shirt goes from $10 to $15

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Explanation:

Focus on the two points (2,0) and (3,10). The slope of the line through these points is

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

m = (10-0)/(3-2)

m = 10

Meaning the profit per shirt for this line is $10 per shirt.

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Now move onto the other line. Focus on the points (9,40) and (11,70)

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

m = (70-40)/(11-9)

m = 15

The profit per shirt has gone up to $15 per shirt

Answer:

I would personally say that his profit per shirt increases

Step-by-step explanation:

- he only made 10 after selling 7 shirts : can't be (• #1)

- they tell you that it's a profit function: so can't be (• #3)

- he spent 25 after he hit 50: can't be (• #4)

Answer:

48

Step-by-step explanation:

The Pythagorean Theorem is:

[tex]a^2+b^2=c^2[/tex]

where [tex]a[/tex] and [tex]b[/tex] are the legs of the right triangle. [tex]c[/tex] is the hypotenuse of the triangle.

In this right triangle, we know that one leg is 20 and the hypotenuse is 52. Therefore,

[tex]a=20[/tex]

[tex]c=52[/tex]

Since we don't know the other leg, we can leave it as [tex]b[/tex]. Substitute the values into the theorem.

[tex]20^2+b^2=52^2[/tex]

Evaluate the exponents first.

⇒ 20²=20*20=400

⇒ 52²= 52*52= 2704

[tex]400+b^2=2704[/tex]

Since we want to find [tex]b[/tex], we must isolate [tex]b[/tex]. First, subtract 400 from both sides of the equation.

[tex]400-400+b^2=2704-400[/tex]

[tex]b^2=2704-400[/tex]

[tex]b^2=2304[/tex]

[tex]b[/tex] is being squared. The inverse of a square is a square root. Take the square root of both sides of the equation.

[tex]\sqrt{b^2}=\sqrt{2304}[/tex]

[tex]b=\sqrt{2304}[/tex]

[tex]b=48[/tex]

The length of the other leg is 48

Answer:

[tex]-2.2[/tex]

Step-by-step explanation:

Let's simplify the expression.

[tex]1+3^2.2-5[/tex]

And the answer is

[tex]-2.2[/tex]

Hope this helps!

Answer:

14

Step-by-step explanation:

I took the test~~~~

Answer:

n = p-k-m

Step-by-step explanation:

You would just say, like k and m and 1 and 2. But instead of adding them you just bring the to the other side like

p = n+1+2

-1         -1

p-1 = n+2

-2        -2

p-1-2 = n

p-k-m-n

Answer:

C.

Step-by-step explanation:

His initial cost of the phone bill was  $25.90, which is the constant. He is charge $0.18 for each text. So you will have to add the initial bill and costs of the texts to get final cost on the phone bill, which is $30.40.

Answer:

c = 177n - 314

Step-by-step explanation:

c = 177n - 314