Solve the following equation for x. Show each step.
5x + 2 = 3x + 4(2x - 1)

Answers

Answer 1

Answer:

[tex]x=1[/tex]

Step-by-step explanation:

Start with:

[tex]5x+2=3x+4(2x-1)[/tex]

Distribute the [tex]4[/tex] into [tex](2x-1)[/tex]:

[tex]5x+2=3x+8x-4[/tex]

Combine like terms:

[tex]5x+2=11x-4[/tex]

Add [tex]4[/tex] to both sides of the equation:

[tex]5x+6=11x[/tex]

Subtract [tex]5x[/tex] from both sides of the equation:

[tex]6=6x[/tex]

Divide both sides of the equation by the coefficient of [tex]x[/tex], which is [tex]6[/tex]:

[tex]1=x[/tex]

or

[tex]x=1[/tex]

Answer 2
ANSWER: x = 1

1. Distribute the 4 into (2x-1). 5x + 2 = 3x + 8x - 4.
2. Add the like terms. 5x + 2 = 11x - 4.
3. Subtract 5x on both sides. 2 = 6x - 4.
4. Add 4 on both sides. 6 = 6x
5. Divide 6 on both sides. x = 1

Related Questions

Use the following graph to estimate the rate of change of the function at x=0.6 using the points (0,0) and (1,−0.5)

Answers

Answer:

The rate of change of the function at x = 0.6 is approximately -0.72

Step-by-step explanation:

The given information from the graph are;

Points (0, 0) and (1, -0.5)

We have that the graph is that of a cubic function, therefore;

f(x) = ax³ + bx² + cx + d

At f'(x) at  (0, 0) and (1, -0.5) = 0 gives;

3ax² + 2bx + c = 0

∴ c = 0

Also

ax³ + bx² + cx + d = 0

d = 0

We have

3a(1)² + 2b(1) + 0 = 0

3·a + 2·b = 0..............(1)

a(1)³ + b(1)² + c(1) + d = -0.5

a + b + 0×(1) + 0 = -0.5

a + b = -0.5..........(2)

Multiplying equation (2) by 2 and subtracting it from equation (1) gives;

2 × (a + b = -0.5) = 2·a + 2·b = -1

3·a + 2·b - (2·a + 2·b) = 0 - (-1) = 0 + 1 = 1

a = 1

From

a + b = -0.5, we have;

1 + b = -0.5 = 0

b = -0.5 - 1 = -1.5

The equation becomes

f(x) = x³ - 1.5·x²

The rate of change of the function at x = 0.6 is therefore given as follows;

f'(x) = 3 × x² - 2 × (1.5)·x = 3·x² - 3·x

At x = 0.6, we have;

f'(0.6) = 3·(0.6)² - 3·(0.6)

f'(0.6) = 3×0.6² - 3×0.6 = -0.72

The rate of change of the function at x = 0.6 ≈ -0.72

what is the value of this expression when p=-2 and q=-1 [(p^2)(q^-3)]^-2

Answers

Answer:

Find the exact value using trigonometric identities.

Exact Form: 1/16

Decimal Form:

0.0625

Step-by-step explanation:

A pyramid has a square base with an area of 225 2. What is the perimeter of the base of the pyramid​

Answers

Answer:

60 square unit

Step-by-step explanation:

side = √225.2 = 15

perimeter = side x 4

perimeter = 15 x 4 = 60 square unit

HELP I'M GONNA FAIL​

Answers

Answer:

1/10

Step-by-step explanation:

7000/70000=1/10

1/10 would be the correct answer

what is the inverse of f(x) = -10x - 2

Answers

Answer:

f^-1(x)-(x/10)-(1/5).

Hope this helps!

Step-by-step explanation:

(See picture for explanation!)

Un volcan lanza una roca con una rapidez de 47.5 m/s con un angulo de 39.4° sobre el eje x. La roca toca el suelo a 1750 m por debajo de la altura inicial si se desprecia la resistencia del aire y considerando un valor constante de aceleracion debido a la gravedad de 9.81 m/s¨2 cual es el tiempo en completar la trayectoria

Answers

Responder: 6.1467 segundos

Explicación paso a paso:

El tiempo necesario para completar la trayectoria se conoce como tiempo de vuelo.

Tiempo de vuelo = dónde;

U es la velocidad inicial del cuerpo = 47,5 m / s

es el ángulo de lanzamiento = 39,4 °

g es la aceleración debida a la gravedad = 9,81 m / s²

Sustituyendo los parámetros dados en la fórmula anterior, tendremos;

[tex]T = \dfrac{2(47.5)sin39.4^0}{9.81} \\\\T = \dfrac{95sin39.4^0}{9.81} \\\\T = \dfrac{95*0.6347}{9.81} \\\\T = \dfrac{60.2994}{9.81} \\\\T =6.1467 secs[/tex]

El tiempo necesario para completar la trayectoria es de 6.1467 segundos.

9x9 sudoko puzzle
——————————-

Answers

I done it

I attached it

A student has a part time job in which she works 4 hour shifts. Her pay scale is $5.25 hour. How many shifts must she work to earn $220?

Answers

Answer:

Earning on one shift = 4**5.25= 21

to earn 220 she had to do 220/21= 10.48 shifts

Explanation & Process Needed

Answers

Answer:

∠ BOF = 32°

Step-by-step explanation:

Since AB is a straight line, then

∠ AOE + ∠ EOD + ∠ DOE = 180° , substitute values

90 + x + 8 + 2x - 8 = 180 , that is

3x + 90 = 180 ( subtract 90 from both sides )

3x = 90 ( divide both sides by 3 )

x = 30

Thus

∠ DOB = 2x - 8 = 2(30) - 8 = 60 - 8 = 52°

∠ COF = 4x - 24 = 4(30) - 24 = 120 - 24 = 96°

∠ AOC = ∠ DOB ( vertical angles ), thus

y = 52, then

∠ BOF = 180° - (96 + 52)° = 180° - 148° = 32° ( angles on a straight line )

What is an algebraic expression for "2 less than the product of 3 and a number x"? *

Answers

Answer:

3x-2

Step-by-step explanation:

The algebraic expression is 3x -2.

What is an algebraic expression?

Algebraic expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

What are Arithmetic operations?

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

We have to determine an algebraic expression for "2 less than the product of 3 and a number x"

Here, the product of 3 and a number x

⇒ 3x

Therefore, 2 is less than the product of 3, and a number x as

⇒ 3x -2

Hence, the algebraic expression is 3x -2.

Learn more about an algebraic expression here:

brainly.com/question/13947055

#SPJ2

A landscaping company is laying a triangular flower bed. The height of the trangle is 15ft. What lengths of the base will make the area at least 210ft squared?

Answers

Answer:

28 ft

Step-by-step explanation:

The height of the triangle = 15 ft

The least required area A = 210 ft^2

We know that the area of a triangle = 1/2bh

Where

b is the base

h is the height

Substituting, we have

210 = 1/2 x b x 15

210 = 15/2 x b

420/15 = b

b = 28 ft


A bag of candy contains 203 pieces. Each person in the room receives 10 picces of candy and there are 3 pieces of
candy left over. Write and solve an equation to find how many people were in the room.

Answers

Answer:20

Step-by-step explanation:

You take 203 and subtract 3 since you know you have 3 pieces left over you then divide 209 by 10 and get 20!!

Answer:

20 people

Step-by-step explanation:

Did it in my head

One day Freya eats 12 ice creams
in 6 hours and the second day she
eats 14 ice creams in 7 hours. How
many ice creams does Freya eat
per hour?

Answers

Answer:

she ate 2 ice creams per hour

Step-by-step explanation:

2 per hour.

12 ice creams divided by 6 hours: 12/6 =2
14 ice creams divided by 7 hours: 14/7= 2

Hope this helps!
Have a good rest of day!
Make sure you ate today

Solve by factoring x^4+6x^2-27=0

Answers

Answer:

Step-by-step explanation:

x^4+6x^2-27=0

The two factors you need to use for 27 is 9 and 3.

Since the middle term must be plus then the 9 is also plus.

(x^2 + 9)(x^2 - 3)

x^2  + 9 can't be factored in the real number system.

x^2 - 3 = 0

(x + sqrt(3))(x^2 - sqrt(3))

The full factoring answer would be

(x^2+9)(x + sqrt(3))(x^2 - sqrt(3))

round 27.68 to the nearest tenth​

Answers

Answer:

27.7

Step-by-step explanation:

For this problem, we will simply use standard rounding conventions to round the number to the nearest tenth.

If the number after the target, the hundreths place in this case, is between 0 and 4, we won't change the tenths place.  If the number is between 5 and 9, we will increment the tenths place by one.

So for our number, 27.68, 8 is between 5 and 9 so we will increment the tenths place by one for the round.

Hence, our rounded answer for the nearest tenth is 27.7.

Cheers.

Your answer is 27.7.

What is the absolute value of 2.5

Answers

☽------------❀-------------☾

Hi there!

~

The absolute value is the distance from 0 to 2.5. In this case the absolute value from 0 to |2.5| is 2.5

❀Hope this helped you!❀

☽------------❀-------------☾

The table shows the total cost, p, for renting a playroom for a birthday party with c party guests. Number of Party Guests (C) Total Cost (p), in Dollars 3 274 7 306 12 346 21 418 Which of the following equations represents the input/output table using function notation? O A. p = 8c + 250 O B. p = 258c C. f(c) = 8c + 250 O D. f(p) = 8c - 250​

Answers

Answer:

Option (A)

Step-by-step explanation:

Let the equation of the linear function representing number of party guests (c) and total cost (p) is in the form of c = mp + b

m = Slope of the line

b = y-intercept

Choose the two ordered pairs from the table (3, 274) and (7, 306).

Slope of the function 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m = [tex]\frac{306-274}{7-3}[/tex]

m = 8

Since, equation of a line passing through (x', y') and slope m is,

y - y' = m(x - x')

Therefore, equation of a line passing through (3, 274) and slope = 8,

y - 274 = 8(x - 3)

y - 274 = 8x - 24

y = 8x + 274 - 24

y = 8x + 250

Since, y = p and x = c

Therefore, p = 8c + 250 will be the equation.

Option (A) is the answer.

Answer:ok

Step-by-step explanation: the answer is A

A square sheet of paper measures 42 centimeters on each side. What is the length of the diagonal of this​ paper?

Answers

59.4cm
Use Pythagorean theorem to find the diagonal (^ means exponent)
a^2 + b^2 = c^2
42^2 + 42^2= c^2
1764+1764=c^2
3528=c^2
square root both sides
c= 59.39696962
round and you get 59.4 cm

An article was sold for Rs 30
at a loss of 24%, what would
have been sale price, had it
been sold at 17% loss.​

Answers

Answer:

Rs. 32.77

Step-by-step explanation:

At a loss of 24% sale price = Rs. 30At a loss of 17% sale price = ?

----------

Finding cost price:

Sale price = cost - loss

If cost = x:

x - 24% = 300.76x = 30x = 30/0.76x ≈ 39.48

SP at a loss of 17%:

39.48 - 17% = 39.48*0.83 ≈ 32.77

Question 3 1 pts Strawberries are on sale $7.00 for 3 pints. How much do they cost per pint?

Answers

Strawberries cost $2.33 a pint

Answer:

$2.33

Step-by-step explanation:

To find how much strawberries cost per pint, we would divide the seven dollars by 3 which will tell us how much each pint costs. Hope this helps, have a great day!

can someone please help me witch is the answer 20 points to the one who can answer first

Answers

First, let's find the slope.

Slope = (7 - (-3)) / (2 - 0) = (7 + 3) / 2 = 10 / 2 = 5

So far our equation looks like: y = 5x + b

Leta plug one of the points into our equation to find b.

-3 = 5(0) + b

Simplify.

-3 = b

The equation is: y = 5x - 3

Answer choice B is correct.


Lyle wants to build a rectangular dog pen with a length that is 12 feet more than the width. Lyle can afford no more than 560 feet of fence. Write
an inequality to show that the perimeter of the dog pen can be no more than 560 feet.
2 (12 + w) + 2w < 560
(12 + 2) + w < 560
o 2(12 + w) + 2w< 560
0 (12+w) + w < 560

Answers

Answer:

2(2W+12) < 560

Step-by-step explanation:

Perimeter of a rectangular dog pen P = 2(L+W) where;

L is the length of the dog pen

W is the width of the dog pen

If Lyle wants to build a rectangular dog pen with a length that is 12 feet more than the width, then L = W+12

If Lyle can afford no more than 560 feet of fence, this means that the perimeter cannot be more than 560feet i.e P<560

The inequality to show that the perimeter of the dog pen can be no more than 560 feet is expressed as P < 2(L+W)

Substituting the given parameters;

2([W+12]+W)<560

2(2W+12)<560

Hence the inequality to show that the perimeter of the dog pen can be no more than 560 feet is 2(2W+12)<560

4.) Solve for N
7.) Solve for F

Answers

Answer:

See Below

Step-by-step explanation:

4) t = n -r  Solve for n

Add r to both sides

t = n -r

+r     +r

t +r = n

Or  n = t+r

7) [tex]\frac{f}{g}[/tex] = h    Solve for f

Multiply both sides by g to get rid of fraction

g/1 (f/g) = h(g)

f = hg

If a triangle is an equilateral triangle, then the triangle has exactly three 60°
angles. △ABC is an equilateral triangle?

Answers

Step-by-step explanation:

In an equilateral triangle, all the three sides are equal as well as all the angles are equal. Let the angles be x.

We know that the sum of angles of a triangle is equal to 180 degrees. It means that,

x+x+x=180

3x=180

x=60°

Hence, if a triangle is an equilateral triangle, then the triangle has exactly three 60°  angles. Hence, △ABC is an equilateral triangle

the length of the rectangle is twice the breadth. the area of the rectangle is 128m2. find the length of the rectangle​

Answers

Answer:

length =16

Step-by-step explanation:

area= breadth*length

length = 2 breadth    --equation 1        

(the length of the rectangle is twice the breadth)

128m^2= breadth*2 breadth

128m^2= 2 breadth^2

breadth^2= 128/2m^2

breadth^2=64m^2

taking square root on both sides

[tex]\sqrt{breadth^2}[/tex]=[tex]\sqrt{64m^2}[/tex]

[tex]\sqrt{breadth^2}[/tex]=[tex]\sqrt{(8m)^2}[/tex]

breadth= 8m   (cancelling square root with power 2

put breadth in equation 1

length= 2*8

length= 16

CHECK:

area of rectangle = breadth * length

area= 8*16

area=128

A pitcher contains 19.25 cups of iced tea. You drink 1.25 cups of the tea each morning and 1.5 cups of the tea each evening. When will you run out of iced tea?

Answers

Answer:

Seven days

Step-by-step explanation:

From the information given, you know that you drink in a day 1.25 cups of the tea in the morning morning and 1.5 cups of the tea in the evening which is equal to:

1.25+1.5=2.75 cups a day

Now that you know the amount of cups that you drink in a day, you can divide  the amount of cups in the pitcher by the amount of cups you drink in a day:

19.25/2.75= 7

According to this, the answer is that you will run out of iced tea after seven days.

A clock is constructed using a regular polygon with 60 sides. The polygon rotates each minute, making one full revolution each hour. How much has the polygon rotated after 7 minutes?

Answers

Answer:

42

Step-by-step explanation:

D-42 on EDG.

A clock is constructed using a regular polygon with 60 sides. The polygon rotates each minute, making one full revolution each hour. The polygon has rotated 42 times after 7 minutes.

A polygon is known to be a plane figure with at least three equal sides and angles.

From the given information,

the sides of the polygon = 60 sidestime to complete a single rotation for 60 sides = 1 hour

In one full revolution, there are = 360°

To estimate the revolution completed in 1 minute, we have:

[tex]\mathbf{= \dfrac{360 \ ^ 0}{60 \ ^ 0} }[/tex]

= 6° per minute

Now, to determine how much the polygon has rotated after 7 minutes, we have:

= (6° / minute) × 7 minutes

= 42°

Therefore, we can conclude that the polygon has rotated 42° in 7 minutes,

Learn more about polygon here:

https://brainly.com/question/3491511?referrer=searchResults

How to reflect the triangle below across the line y = x.

Answers

Answer:

pre-image coordinates (x,y) imagine coordinates (y,x)

Step-by-step explanation:

bascially just switch the x and y coordinates and keep the sign :)

-7y + 3 – 12 – 2y
What is the answer

Answers

-9y-9 simplification
-9y-9=0
-9y=9
y=-1
Answer:
-9y - 9

Step by step explanation:

-7y + 3 - 12 - 2y

-7y -2y + 3 -12

= -9y - 9

resultado de
[tex](4 + 5 + 3) + 8 = [/tex]

Answers

Steps to solve:

(4 + 5 + 3) + 8

~Add everything in parenthesis

12 + 8

~Add

20

Best of Luck!

Given:

[tex] \huge \purple {\tt {(4 + 5 + 3) + 8 =? }} [/tex]

Solution:

By using parenthesis, we get

[tex] \huge \purple {\tt {12 + 8 = 20}} [/tex]

Answer:

[tex] \huge \purple {\tt {20}} [/tex]

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