Consider the following inequality:2(3z - 4) > - 2z + 16Step 1 of 2: Solve the linear inequality for the given variable. Simplify and express your answer in algebraic notation.

658 text messages

Explanation:

. Since you already know that for 7$ she gets 550 text messages, we can remove the 7$ from the 39.40$ she spent for the month, which leaves 39.40 - 7 = 32.40$

. Now since we know that for each extra 30 cents she gets to send one addition text,

=> we need to figure out first how many cents there is in the amount of money left she had to pay 32.40 * 100 = 3240 cents { since 1 $ = 100 cents }

=> then we need to figure out how many text does 3,240 cents represent, since 1 text is equivalent to 30 cent it means that in 3,240 / 30 = 108 texts messages is the amount of text she got to send with 32.40$

So in total she sent 550 + 108 = 658 texts messages for 39.40$

Given:

Car uses 1.6 gallons to go 32 miles

Let's find the amount of gallons of gas the car needs to travel 420 miles.

Here, the relationship between the miles driven and the amount of gas needed is direct variation.

Since it is a direct variation, we have the variation equation when y varies directly with x:

y = kx

Where k is the constant of variation.

Hence, we have:

32 = 1.6k

Let's solve for k.

Divide both sides by 1.6:

The constant of variation is 20.

The equation that represents this situation is:

y = 20x

Therefore, to find the amount of gallons of gas needed if the car travels 420 miles, substitute 420 for y and solve for x.

420 = 20x

Divide both sides by 20:

Therefore, the car needs 21 gallons of gas

The length of the radius of the circle is √61.

Here there are two endpoints of the circle (-7,-4) and (3,8)

To find the length between the two points we have a formula:

length = [tex]\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1} )^{2} }[/tex]

So here we have

([tex]x_{1} , y_{1}[/tex]) = (-7, -4)

([tex]x_{2} , y_{2}[/tex]) = ( 3,8)

Putting the value we have,

[tex]\sqrt{(3 -(-7)^{2} + ( 8-(-4)^{2} }[/tex]

=[tex]\sqrt{10^{2} + 12^{2} }[/tex]

=[tex]\sqrt{100+ 144}[/tex]

=√244

=2√61

The diameter is 2√61

radius = diameter/2

          = 2√61/2

          = √61

Therefore the length of the radius of a circle is √61.

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1) y = 1 2) y =3 3) x = -3 4) y= -7 and y = 1

We are to answer the questions stated using the graph:

1) From the graph, when x = 0:

To understand this, check the point on the line that only lies on y

y = 1

2) f(-4) is the same as what is the value of y when x = -4

This is because f(x) = y

From the graph, when x = -4

y = 3

3) From the graph, when y =4

Trace the value of y=4 on the line to get corresponding x value:

x= -3

4) When f(x) = 0

This means what is the value of x when y = 0. This is because f(x) = y.

From the graph, we have two values of x when y = 0

y = -7

y = 1

To fill the blank spaces starting with the smaller number:

-7 and 1

Given:

The length of the arc is (1/12) x circumference of unit circle.

The objective is to find the area of the sector.

Since it is given as a unit cirle, the radius of the circle will be 1 unit.

The circumference of the circle will be,

Then, the length of the arc will be,

Now, the formula to find the area of the sector is,

On plugging the values in the above relation,

Hence, the area of the sector is 0.262 square units.

For the equation P(x)=(x+5)(x-5) and q(x)=(x+3)(x-3) the graph of the two equation never intersect each other.

It is defined as the curve which is the intersection of cone and plane. There are three major conic sections; parabola, hyperbola, and ellipse (a circle is a special type of ellipse).

The given equations are,

P(x)=(x+5)(x-5)

q(x)=(x+3)(x-3)

Parabola is defined as the graph of a quadratic function that has something bowl-shaped.

(x - h)² = 4a(y - k)

(h, k) is the vertex of the parabola:

a = √[(c-h)² + (d-k²]

(c, d) is the focus of the parabola:

The given equation represents a parabola as the equation is graphed we see that the graph of the two never intersects each other.

Thus,for the equation P(x)=(x+5)(x-5) and q(x)=(x+3)(x-3) the graph of the two equation never intersect each other.

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Answer:

30

Step-by-step explanation:

The domain and range for the relation is [-∞, ∞]  and [0,-3], and both  of them can be described by interval notation .

Since the graph given to us present a relation or a function, The domain and range of a function are the set of all the inputs and yield a function that can grant separately. The domain and range are vital viewpoints of a function. The domain takes all the conceivable input values from the set of real numbers and the range takes all the yield values of the function. In simple words, the domain is the set of all "x" values and the range is the set of all "y" values in a set of ordered sets and the requested sets are composed as in the form (x, y) or [x,y]

For the given the points are : (0,-3),(1,-3),(2,-3),(3,-3),(4,-3),(5,-3),(-1,-3)(-2,-3),(-3,-3),(-4,-3),(-5,-3)

so the domain set is ={-5,-4,-3,-2,-1,0,1,2,3,4,5}

and the range set is ={0,-3,-4,-5,-6,-7,-8}

so the domain and range is [-∞, ∞] and [0,-3]

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Given

0.216

Find

Cube root of the given number

Explanation

Cube root is the value which when multiplying by itself thrice or three times produces the original number

0.216 can be written as the product of

prime factorization of 216 and 1000

prime factorization of 216 =

1000 -

we have to find the cube root so , we make pair of three

so

hence

so , the cube root of 0.216 is 0.6

Final Answer

Therefore , The cube root of 0.216 is 0.6

According to the problem, the function f(x) represents the height of the airplane, and x is the time in seconds since the airplane was thrown.

The graph shows the zeros x = -1 and x = 4, however, the positive zero is the only one that makes sense to the problem because time can't be negative. So, the zero x = 4 means that the paper airplane will reach the water level after 4 seconds.

As we said, just the positive zero has meaning to this situation because, in real life, time is not negative.

Therefore, just one zero (x=4) has real-world meaning.

According to the zero x = 4, the paper airplane will hit the water after 4 seconds.

The control group is the group C, since they take sugar pills.

The dependent variable is the percentage of people that got fewer headaches.

The independent variables is the type of pills they gave to each of the groups.

We have the event E defined as:

E: The sum of two rolled dice is greater than or equal to 3

The event E^c is the negation of the event E. Then:

E^c: The sum of two rolled dice is smaller than 3

For two dice, the minimum sum is 2, so this is equal to the event "the sum of two rolled dice is 2". There is only one outcome:

Dice 1: 1

Dice 2: 1

Sum: 2

Then, the only possible outcome for E^c is {1, 1}

The measure of angle m∠CGE is 83°

Given,

∠AGF = 62°

∠DGB = 35°

Since, ∠DGB is vertically opposite angle of ∠CGA

Then, ∠CGA = 35°

And also,

             ∠AGF is vertically opposite angle of ∠EGB

Then, ∠EGB = 62°

Now, we know that  CD is straight line

Using angle - sum property,

Then,

      ∠CGE + ∠EGB + ∠CGA = 180°

Putting the values we get

      ∠CGE + 62° + 35° = 180°

       ∠CGE + 97° =  180°

            ∠CGE = 180° - 97°  

           ∠CGE = 83°

Hence,  ∠CGE = 83°

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Answer:

289.8.

Explanation:

Let the number = x

Then, it implies that:

Next, solve for x:

The number is 289.8 to the nearest tenth.

Explanation:

First we can see that there's a minus sign in both sides of the equation, so we can take it out:

Now we have to multiply both sides by 15:

Answer:

t = 45

The number of minutes Bob has used his phone in a month is 1024 minutes.

For the given question;

Monthly phone service paid by Bob = $29.

Additional charges = $0.06 per minute of use.

Total last month charge = $90.44.

Let number of minutes he used be 'm'.

The, the inequality forms is-

90.44 ≤ 29 + 0.06m

Simplifying,

0.06m ≥ 61.44

m ≥ 1024

Thus, the number of minutes Bob has used his phone in a month is 1024 minutes.

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Given

2x + 6y = -18

Find

x intercept and y intercept. Then use them to graph the line.

Explanation

to find the y intercept , put x = 0

2(0) + 6y = -18

6y = -18

y = -3

now , put y = 0 to find the x intercept

2x + 6(0) = -18

2x = -18

x = -9

we have two points ; (0 , -3) and (-9 , 0)

plot these points on graph to make a line

Final Answer

Hence , the x intercept is -9 and y intercept is -3. The required graph is shown above.

So,

We want to find the value in the box such that:

I wrote x instead the box.

To solve this equation, the first thing we need to do is to let the "x term" alone.

For this, we could start by multiplying both sides of the equation by 4:

Now, we could substract 1 to both sides:

And then multiply by 6:

Now, substract 2:

Therefore, the value in the box should be 1.

1) Given that you are paid every two weeks, consider that the base salary is $10 per hour. And 1.5 times for hours in excess.

2) But notice that the pay will not include overtime.

3) Thus, we can write out the following:

Note that this is the gross paycheck (no taxes).

Answer

Explanation

The best way to plot graphs, especially straight line graphs, is to use the intercepts. The intercepts are the point(s) that the graph of the function crosses or touches the x and y axis.

The equation is

y = (2/3)x - 2

when x = 0,

y = (2/3)x - 2

y = (2/3)(0) - 2

y = 0 - 2

y = -2

The first point on the graph is (0, -2)

when y = 0,

y = (2/3)x - 2

0 = (2/3)x - 2

(2x/3) = 2

Cross multiply

2x = (2) (3)

2x = 6

Divide both sides by 2

(2x/2) = (6/2)

x = 3

The second point on this graph is (3, 0)

So, the two points are (0, -2) and (3, 0)

We can then easily plot this graph by marking out those two points on the graph and connect the two points for the equation of that line.

John rode his bike 65616.8 feet on Monday which is determined by converting 20 kilometers into feet.

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

John rode his bike 20 kilometers on Monday which is given in the question.

To determine the number of feet John rides.

We have to convert  20 kilometers into feets

We know that

one kilometer = 3280.84 feet

Here 20 kilometers into feet will be:

⇒ 20 × 3280.84

Apply the multiplication operation, and we get

⇒ 65616.8 feet

Therefore, John rode his bike 65616.8 feet on Monday

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Answer:

29.7

Step-by-step explanation:

To calculate this we need to convert the percentage to a decimal and then multiply.  345% is 3.45, so our math problem is 8.6 x 3.45.  If you put that into a calculator you will get 29.67, but since the least precise number is to one decimal place (8.6), I put my answer to one decimal place as well - I rounded 29.67 to the nearest tenth.

Answer:

560

Step-by-step explanation:

If 65% were females, 35% were males.

1600(35%) = 1600(0.35) = 560

Answer:Q(2,-3)

Step-by-step explanation:

In this problem we can see that the intercept with the y axis is positive one, so we know that the answer is A) or D), now we can see that the slope is positie so the term with the x has to be positive so the correct function is:

Answer:

y+6=(3/2)(x-6)

Step-by-step explanation:

Point slope form is:  y-y1=m(x-x1)

We know:

x1= 6

y1= -6

m=3/2

The consecutive integers that are odd numbers are 17, 19 and 21.

In this problem we need to find the values of three consecutive integers that odd integers such that the following equation is satisfied:

x₁ + x₂ = 3 · x₃ - 27

Please notice that two odd numbers are consecutive when their difference is 2.

x₁ + (x₁ + 2) = 3 · (x₁ + 4) - 27

2 · x₁ + 2 = 3 · x₁ + 12 - 27

2 · x₁ + 2 = 3 · x₁ - 15

17 = x₁

x₁ = 17

Thus, the three odd integers that are consecutive are 17, 19 and 21, respectively.

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Answer:

x¹¹ • x⁹

Step-by-step explanation:

so hope it help

have a nice day

An exponential function is one in which the independent variable x appears in the exponent and has a constant a as its base. Its expression is:

With a being a positive real, a > 0, and different from 1, a ≠ 1.

When 0 < a < 1, then the exponential function is a decreasing function and when a > 1, it is an increasing function.

For example: the function

Since a = 2 > 1, the function is increasing. We have the graph below:

And the function

Since a = 0.5 < 1, the function is decreasing. Then, the graph is:

Recall that:

Therefore:

Answer: