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3 years ago

Which graph shows the solution to the inequality Negative 3 x minus 7 less-than 20

Mathematics

2 answers:

Aleksandr-060686 [28]3 years ago

6 0

Answer:

A number line goes from negative 10 to positive 10. An open circle appears at negative 9. The number line is shaded from negative 9 through positive 10.

Step-by-step explanation:

we have

$-3x-7$

Solve for x

Adds 7 both sides

$-3x$

Divide by -3 both sides

Remember that

When you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol

$x> 27/(-3)\\x>-9$

The solution is the interval (-9,∞)

therefore

A number line goes from negative 10 to positive 10. An open circle appears at negative 9. The number line is shaded from negative 9 through positive 10.

Lisa [10]3 years ago

5 0

Answer:

A number line goes from negative 10 to positive 10. An open circle appears at negative 9. The number line is shaded from negative 9 through positive 10.

Step-by-step explanation:

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Find the coordinates of the circumcenter of triangle ABC with vertices A(1,4) B(1,2) and C(6,2)

Ray Of Light [21]

<span>(3.5, 3) is the circumcenter of triangle ABC. The circumcenter of a triangle is the intersection of the perpendicular bisectors of each side. All three of these perpendicular bisectors will intersect at the same point. So you have a nice self check to make sure your math is correct. Now let's calculate the equation for these bisectors. Line segment AB: Slope (4-2)/(1-1) = 2/0 = infinity. This line segment is perfectly vertical. So the bisector will be perfectly horizontal, and will pass through ((1+1)/2, (4+2)/2) = (2/2, 6/2) = (1,3). So the equation for this perpendicular bisector is y = 3. Line segment BC (2-2)/(6-1) = 0/5 = 0 This line segment is perfectly horizontal. So the bisector will be perfectly vertical, and will pass through ((1+6)/2,(2+2)/2) = (7/2, 4/2) = (3.5, 2) So the equation for this perpendicular bisector is x=3.5 So those two bisectors will intersect at point (3.5,3) which is the circumcenter of triangle ABC. Now let's do a cross check to make sure that's correct. Line segment AC Slope = (4-2)/(1-6) = 2/-5 = -2/5 The perpendicular will have slope 5/2 = 2.5. So the equation is of the form y = 2.5*x + b And will pass through the point ((1+6)/2, (4+2)/2) = (7/2, 6/2) = (3.5, 3) Plug in those coordinates and calculate b. y = 2.5x + b 3 = 2.5*3.5 + b 3 = 8.75 + b -5.75 = b So the equation for the 3rd bisector is y = 2.5x - 5.75 Now let's check if the intersection with this line against the other 2 works. Determining intersection between bisector of AC and AB y = 2.5x - 5.75 y = 3 3 = 2.5x - 5.75 8.75 = 2.5x 3.5 = x And we get the correct value. Now to check AC and BC y = 2.5x - 5.75 x = 3.5 y = 2.5*3.5 - 5.75 y = 8.75 - 5.75 y = 3 And we still get the correct intersection.</span>

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2 years ago

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The difference of 9 times a number and 2 is 67. Write an equation that can be used to find the unknown number?

pochemuha

9x - 2 = 67
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3 years ago

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If the temperature is dropping at a rate of 2° per hour how many hours will it take to drop 15°

Tju [1.3M]

Answer:

7 1/2

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2 years ago

Which statement is correctly written as a conditional statement?

bekas [8.4K]

The statement that correctly written as a conditional statement is; A number, such as 10, is a composite number because it is even. so the correct option is D.

<h3>What are natural numbers, rational numbers, integers and irrational numbers?</h3>

Natural numbers are: 1, 2, 3, ....

Integer numbers are: ...., -2, -1, 0, 1, 2, ... (so it includes positive and negative natural number, and 0 )

Rational numbers are numbers which can be written in the form of a/b

where a and b are integers.

Irrational numbers are those real numbers which are not rational numbers.

Here, Know that all natural numbers are integers, all integers are rational numbers. That means, natural numbers are not irrational.

A composite number is a number divisible by another number than 1 and the number itself.

To find example, a sum of two composite numbers, which is not a composite number, is needed.

The statement that correctly written as a conditional statement is; A number, such as 10, is a composite number because it is even.

Hence so the correct option is D.

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