What is the best first step to solve the inequality 5x – 3 ≥ 2?

We can express Benjamin's age with x, we can express Luca's age as y.

x-6=2y

So, if x=12

2y=6

y=3

Therfore, Lucas is 3 years old

Answer:

28/5

Step-by-step explanation:

[tex]f(x) = 5x - 3 = 25 [/tex]

[tex]5x = 25 + 3[/tex]

[tex]5x = 28[/tex]

[tex]x = \frac{28}{5} [/tex]

I think this is the answer

Step-by-step explanation:

Given the line y-1 = 1(x+2), in order to know the line that is perpendicular to the given line, we will first find the slope of the known line.

The standard form of equation of a line is expressed as y = mx+c

m is the slope

c is the intercept

Rewrite the equation given

y-1 = 1(x+2)

y-1 = x+2

y = x+2+1

y = x+3

Comparing to the standard form, the slope m = 1.

For two lines to be perpendicular, the product of their slope must be -1 i.e mM = -1

Substitute

1(M) = -1

M = -1

For us to know the line that is perpendicular to the given line, its slope must be -1.

Since none of the equation has a slope of -1, hence none of the lines are perpendicular to the line y - 1= 1(x+2).

1).  Add 27 to each side of the equation.

2). Add 72 to each side of the equation.

3). Divide each side of the equation by 12.

Answer:

x=8°

y= 96°

z= 96°

Step-by-step explanation:

Solve for z first. The whole circle is 360° so if you only count half the angles it will add up to 180°.

Solve for z:

48+36+z=180°

84+z+180°

z=96°

Now that you have z you can solve for x by using only the bottom half of the circle.

z+36+6x=180° *remember z=96

96+36+6x=180

132+6x=180

6x=48

x=8°

Now you can solve for y by either plugging x into an equation or by knowing that opposite angles are equal.

y=96°

Answer:

x=8

Step-by-step explanation:

8 times 8 equals 64

Answer:

The answer will be listed below!

Step-by-step explanation:

To graph the equation y=3/2x+2, you must know what 3/2x is and what 2 is. 2 would be your y-intercept as the 3/2x would be your slope. As you can see, look for 2 on the y axis and place a dot there. Now, take your slope and use rise/run which means up three and to the right 2. After you finish, draw a line through it and you have graphed it!

The graph of the given equation is a straight line [attached in solution]

A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.

Given is an equation, y = 3x/2+2

We need to plot its graph,

Finding the coordinates,

y = 3x/2+2

Put x = 0

y = 2

(2, 0)

Put x = -4

y = -3(4)/2+2

y = -6+2

y = -4

(-4, -4)

Plot the coordinates on a graph, and then join them, the obtained line will the graph of the given equation.

Hence, the graph of the given equation is a straight line.

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Answer: IDKDIKDIDKIKDI

Step-by-step explanation:

Answer:

15.7% decrease

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given function is,

f(x) = 5x - 3

Where f(x) represents the output values and 'x' is the variable representing the input values.

For x = -2,

f(-2) = 5(-2) - 3

     = -13

For x = -1,

f(-1) = 5(-1) - 3

     = -8

For x = 0,

f(0) = 5(0) - 3

     = -3

For x = 1,

f(1) = 5(1) - 3

    = 2

For x = 2,

f(2) = 5(2) - 3

     = 7

For x = 3,

f(3) = 5(3) - 3

     = 12

Table for the input-output values will be,

x          -2           -1           0           1             2          3

f(x)      -13          -8         -3           2            7          12

Since the values of f(x) has a common difference of [-13 - (-8) = -5] negative five, given function will be a linear function.

Answer:

2x - 10=65-x

2x+x=65+10

3x=75

x=75/3

x=25 (1.)

2x - 10

2*25-10

50-10

40 (2.)

Answer:

14

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

x+7+7=4x+2 simplify

Answer:

x = 3

Step-by-step explanation:

 (3 • (5x - 15)) -  15 • (x - 3)  = 0  

STEP

2

:

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  5x - 15  =   5 • (x - 3)  

Equation at the end of step

3

:

 15 • (x - 3) -  15 • (x - 3)  = 0  

STEP

4

:

Pulling out like terms

4.1      Pull out     15  

Pulling out like terms :

4.2      Pull out     x-3  

After pulling out, we are left with :

     15 • x-3 • ( 1  *  1 +( (-1)  *  (-1) ))

Equation at the end of step

4

:

 30 • (x - 3)  = 0  

STEP

5

:

Equations which are never true

5.1      Solve :    30   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

5.2      Solve  :    x-3 = 0  

Add  3  to both sides of the equation :  

                     x = 3

One solution was found :

x = 3

The required value of a for which the solution of the inequality is all real numbers is a > 4.

A statement of an order relationship-greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.

Now the given inequality is,

a(x + 3) < 5x + 15 - x

or, a(x + 3) < 4x + 15

Now let us solve for x first,

⇒ ax + 3a  < 4x + 15

Subtract 3a from both sides we get,

ax < 4x + 15 - 3a

Subtract 4x from both sides we get,

ax - 4x < 15 - 3a

or, (a - 4)x < 15 - 3a

Dividing both the side by (a - 4) we get,

x < (15 - 3a) / (a - 4)

Now for solutions to be real numbers,

a - 4 > 0

subtracting 4 both the side we get,

⇒ a > 4

this is the required value of a for which the solution of the inequality is all real numbers

Thus, the required value of a for which the solution of the inequality is all real numbers is a > 4.

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The linear equation plotted in the graph is y=4x-1

The slope-intercept form of a line is represented by y=mx+c where m=slope and c is the y-intercept of the line

Given here: The graph of a line that passes through the point (0,-1)

We know the slope intercept form of a line is given by

y=mx+c

Thus if the line passes through this point then

-1=m×0+c

c=-1

Again we can clearly observe that one of the points that lie on the line is (-1,3)

3=-m-1

m=4

∴ The required equation is y=4x-1

Hence, The linear equation plotted in the graph is y=4x-1

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Answer:

Exact Form:

1 /216

Step-by-step explanation:

Answer:

3/4 divided by 1/3 would equal 2 1/4 or 2.25.

Answer:

Each steak is 72/6 = 12 oz

Step-by-step explanation:

Unit rate = total ounces /  total steaks:

72 ounces / 6 steaks = 12 ounces per steak

Unit rate = 12 ounces per steak.

Answer:

f = (100 - 2h) / 5

Step-by-step explanation:

Given:

5f + 2h = 100

Solve the equation for f.

5f + 2h = 100

Subtract 2h from both sides

5f + 2h - 2h = 100 - 2h

5f = 100 - 2h

Divide both sides by 5

5f / 5 = (100 - 2h) / 5

f = (100 - 2h) / 5

If f = 1 full box

h = 1/2 box

h = 1/2 of f

h = 1/2f

Substitute h = 1/2f into

f = (100 - 2h) / 5

f = {100 - 2(1/2f)} / 5

f = (100 - 2/2f) / 5

5f = 100 - f

5f + f = 100

6f = 100

f = 100 / 6

= 16.67

f = 16.67

The required value of f is 16.67.

Given that ;

Kiran sells full box of fruit cost for each box = f = $5

And Kiran sells half box of fruit cost for each = h = $2

According to the question ;

For full box cost  + for half box cost = Total cost of his band trip

5f + 2h = 100

Solve the equation following equation for f .

5f + 2h = 100

Subtract 2h from both sides

5f + 2h - 2h = 100 - 2h

5f = 100 - 2h

Divide both sides by 5

[tex]\frac{5f}{5} = \frac{100}{5} - \frac{2h}{5}[/tex]

f = 20-2h

For full box f = 1 full box

For half box h = 1 half box

It means h = [tex]\frac{1}{2}[/tex] of f

h = [tex]\frac{1}{2}f[/tex]

Substitute the value of h  

[tex]f = \frac{(100-2h)}{5} \\f = \frac{100-2(\frac{1}{2f} )}{5}[/tex]  

[tex]f = \frac{100-f}{5}[/tex]

5f = 100 - f

5f + f = 100

6f = 100

[tex]f = \frac{100}{6}[/tex]

f = 16.67

The required value of f is 16.67.

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Step-by-step explanation:

The area of little Tommy's backyard rectangular sandbox can be represented by the given trinomial.

A = (x²-6x+8) ft²

We know that the area of a rectangle is given by :

A = L × B

[tex]LB=(x^2-6x+8) \\\\=x^2-(-4x-2x)+8\\\\=x^2+4x+2x+8\\\\=x(x+4)+2(x+4)\\\\=(x+2)(x+4)[/tex]

The length of the rectangle can be either (x+2) or (x+4).

Answer:

Step-by-step explanation:

Hope it helped you

Answer:

1. [A] More than 205

2. [B] less than 10

3. [B] less than 0.2

Step-by-step explanation:

1. The value of 25 · (8.5) is:

a. More than 205

b. Less than 205

Solve:

25 · (8.5) = 212.5

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

2. The value of (9.93) · (0.984) is:

a. More than 10

b. Less than 10

(9.93) · (0.984) = 9.77112

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

3. The value of (0.24) · (0.67) is:

a. More than 0.2

b. Less than 0.2

(0.24) · (0.67) = 0.1608

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

~lenvy~

Step-by-step explanation:

For 32:

The factors are as shown:

32 = 2*2*2*2*2

32 = 2²*2³

32 = 2²⁺³

32 = 2⁵ (Base of 2 and power of 5)

For 81:

factors

81 = 3*3*3*3

81 = 3²*3²

81 = 3²⁺²

81 = 3⁴ (Base of 3 and power of 4)

For 100:

factors

100 = 10*10

100 = 10² (Base of 10 and power of 2)

Answer:

430,000

Step-by-step explanation:

Answer: 430,000

Step-by-step explanation: hope this helps

Answer:

is -6x to the 33'd power tims 3 - 1.       3−2x33(3)−1

Step-by-step explanation:

Answer/Step-by-step explanation:

Given:

m<9 = 80°,

m<5 = 68°

Lines w and v are parallel to each other.

m<1 = m<9 (corresponding angles theorem)

m<1 = 80°

m<2 + m<1 = 180° (linear pair)

m<2 + 80° = 180° (substitution)

m<2 = 180° - 80°

m<2 = 100°

m<3 = m<1 (vertical angles are congruent)

m<3 = 80°

m<4 = m<2 (vertical angles are congruent)

m<4 = 100°

m<6 + m<5 = 180° (linear pair)

m<6 + 68° = 180° (substitution)

m<6 = 180° - 68°

m<6 = 112°

m<7 = m<5 (vertical angles)

m<7 = 68°

m<8 = m<6 (vertical angles)

m<8 = 112°

m<10 = m<2 (corresponding angles)

m<10 = 100°

m<11 = m<9 (vertical angles)

m<7 = 80°

m<12 = m<10 (vertical angles)

m<12 = 100°

m<13 = m<5 (corresponding angles)

m<13 = 68°

m<14 = m<6 (corresponding angles)

m<14 = 112°

m<15 = m<13 (vertical angles)

m<15 = 68°

m<16 = m<14 (vertical angles)

m<16 = 112°

Answer:

i thank it is 25 seconds.  

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

16.5 you have to add the divde

h(x) = -x-1

Then just substitute x =6

Then,

h(6) = (- 6-1)