1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
natima [27]
3 years ago
13

3x-7>8 and -3x ≥-36 solve the inequality

Mathematics
1 answer:
tamaranim1 [39]3 years ago
7 0

Good evening,

Answer:

x > 5

x ≤ 12

Step-by-step explanation:

Visualize as if the inequality symbols are equal signs and then solve it as you would for a normal equation, note if you divide by two negative numbers at all you then switch the sign.

On a number line, an inequality sign without the “equal to” is plotted with an open circe.

An inequality sign, with the “equal to” is plotted with a closed circle.

3x - 7> 8

Add seven on both sides, we do this because we want to eliminate the 7 from one side.

3x > 15

Divide both sides by 3, we do this because you want to get rid of the 3 from x.

x > 5

As for the second inequality.

Divide both sides by -3, as I mentioned earlier switch the side since we are dividing by two negative numbers.

x ≤ 12

For the greater than inequality x > 5, plot a open circle on 5 and draw the line going to the right.

For the less than or equal to inequality x ≤ 12, plot a closed cirlce on 12 and draw the line going to the left.

A unique trick is to graph the line based on the direction (right or left) the inequality symbol is pointing to.

You might be interested in
A triangle has an angle that measures 10°. The other two angles are in a ratio of 3:14. What
ivann1987 [24]

Step-by-step explanation:

<h3>Need to FinD :</h3>

  • We have to find the measures of other two angles of triangle.

\red{\frak{Given}} \begin{cases} & \sf{The\ measure\ of\ one\ angle\ of\ traingle\ is\ {\pmb{\sf{10^{\circ}}}}.} \\ & \sf{The\ other\ two\ angles\ are\ in\ the\ ratio\ of\ {\pmb{\sf{3\ :\ 14}}}.} \end{cases}

We know that,

  • The other two angles of triangle are in the ratio of 3 : 14. So, let us consider the other two angles of the triangle be 3x and 14x.

Angle sum property,

  • The angle sum property of triangle states that the sum of interior angles of triangle is 180°. By using this property, we'll find the other two angles of the triangle.

\rule{200}{3}

\sf \dashrightarrow {10^{\circ}\ +\ 3x\ +\ 14x\ =\ 180^{\circ}} \\ \\ \\ \sf \dashrightarrow {10^{\circ}\ +\ 17x\ =\ 180^{\circ}} \\ \\ \\ \sf \dashrightarrow {17x\ =\ 180^{\circ}\ -\ 10^{\circ}} \\ \\ \\ \sf \dashrightarrow {17x\ =\ 170^{\circ}} \\ \\ \\ \sf \dashrightarrow {x\ =\ \dfrac{\cancel{170^{\circ}}}{\cancel{17}}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{x\ =\ 10^{\circ}.}}}}_{\sf \blue {\tiny{Value\ of\ x}}}}

∴ Hence, the value of x is 10°. Now, let us find out the other two angles of the triangle.

\rule{200}{3}

Second AnglE :

  • 3x
  • 3 × 10
  • 30°

∴ Hence, the measure of the second angle of triangle is 30°. Now, let us find out the third angle of triangle.

\rule{200}{3}

Third AnglE :

  • 14x
  • 14 × 10
  • 140°

∴ Hence, the measure of the third angle of the triangle is 140°.

5 0
2 years ago
The cycle time for trucks hauling concrete to a highway construction site is uniformly distributed over the interval 40 to 75 mi
jeka57 [31]

Answer:

0.8333 = 83.33% probability that the cycle time exceeds 50 minutes if it is known that the cycle time exceeds 45 minutes

Step-by-step explanation:

A distribution is called uniform if each outcome has the same probability of happening.

The uniform distributon has two bounds, a and b, and the probability of finding a value higher than x is given by:

P(X > x) = \frac{b - x}{b - a}

Uniformly distributed over the interval 40 to 75 minutes.

This means that a = 40, b = 75

It is known that the cycle time exceeds 45 minutes

This means that we can use a = 45

What is the probability that the cycle time exceeds 50 minutes?

P(X > 50) = \frac{75 - 50}{75 - 45} = 0.8333

0.8333 = 83.33% probability that the cycle time exceeds 50 minutes if it is known that the cycle time exceeds 45 minutes

8 0
3 years ago
What is the value of y?
slega [8]

Answer:

p

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
The number of hours per week that the television is turned on is determined for each family in a sample. the mean of the data is
nikdorinn [45]
Not sure on the number listed as median ? 27.227.2? Please clarify.
5 0
3 years ago
Write 7,004,000 in scientific notation.
MAXImum [283]
<span>7,004,000 in scientific notation.
=</span>7.004 x 10^6
as 7 is the first non zero digit 
so decimal jumbed 6 numbers from right to left and exponent will be positive
option A is correct
hopr this helps
6 0
3 years ago
Other questions:
  • A rectangle is 4 cm longer than it is wide, and its area is 117 cm2 . find its dimensions.
    14·2 answers
  • A maintenance man has 12 keys on his key ring. if he tries the keys at random on a storage room door, discarding those that do n
    12·1 answer
  • Can someone please help me fill out this table
    9·1 answer
  • Define the variables and write a system of equations to represent the given situation do not solve
    11·1 answer
  • 2 times 2 and three forths
    12·1 answer
  • Dustin has a collection of quarters and pennies the total value is $4.65 there are 33 coins how many quarters and pennies does h
    11·1 answer
  • a biologist wants to determine the effect of a new fertilizer on tomato plants. what would be the control
    7·2 answers
  • Is each expression equivalent to 6 * 53? Justify your reasoning.
    13·2 answers
  • What are other ways to express 2:12
    13·1 answer
  • Please help me with this math!!
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!