MATHEMATICS HIGH SCHOOL

The inequality x2 + 12x + 35 ≥ 0 has two critical points and three possible intervals for solutions. Choose each set of possible test points for the three intervals.–8, –6, –4

–10, –6, 0

–6, 0, 6

–6, 0, 10

Answers

Answer 1
Answer: The answers are...

-8, -6, -4
-10, -6, 0
Answer 2
Answer:

Answer:

–8, –6, –4

-10, –6, 0

Step-by-step explanation:

a & b are the correct answers

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If 3(y-1) = y -5. y = ____________.

Answers

Answer:

-1 is the answer

Step-by-step explanation:

the question is 3(y-1)=y-5

so, we open the bracets and multiply

so it becomes 3y-3 = y-5

now, we transpose

3y-y =-5+3

2y = -2

y= -2/2 = -1

Answer:

y = -1

Step-by-step explanation:

3(y-1)=y-5\n\n3y-3=y-5\n\n3y-3+3=y-5+3\n\n3y=y-2\n\n3y-y=y-y-2\n\n2y=-2\n\n(2y=-2)/(2)\n\n\boxed{y=-1}

Hope this helps.

Find the slope of the line passing through the points ( -9, 3) and (6, 3)

Answers

Answer:

M=0

Step-by-step explanation:
You want to use the formula (y2-y1)/(x2-x1). To do this, subtract 3-3/6- -9 and that is your slope. So the slope is 0/15.

Austin plays both forward and goalie on the school soccer team. He has played forward in 4 games for every 3 games he has been the goalie this season. Pick the diagram that models the ratio in the story. If Austin has played forward in 8 games, in how many games has he been the goalie?

Answers

Answer:

Austin has been the goalie in 6 games.

Step-by-step explanation:

The diagram that models the ratio in the story is a fraction diagram.

Let's represent Austin playing forward as F and Austin being the goalie as G.

According to the story, Austin has played forward in 4 games for every 3 games he has been the goalie. This can be represented as the fraction 4/3.

Now, we know that Austin has played forward in 8 games.

To find out how many games he has been the goalie, we can set up a proportion using the ratio from the story:

4/3 = 8/x

To solve for x, we can cross-multiply:

4x = 3 * 8

4x = 24

Dividing both sides of the equation by 4, we get:

x = 6

Therefore, Austin has been the goalie in 6 games

The ratio of the number of boys to the number of girls in a school is 5:7.If there are 600 students in the school,how many girls are there?

Answers

So,

The secret to solving problems with ratios is to find the value of one unit.

5:7 = 12 units total

To find one unit, divide the total number of students by the total number of units.
600/12 = a

Simplify
50/1 = a
50 = a

The value of each unit is 50.

Now, multiply the units by the numbers in the ratio.
50(5) = b
250 = boys

50(7) = x
350 = x

There are 350 girls.
5x- number\ of\ boys\n7x-\ number\ of\ girls\n\n5x+7x=600\n12x=600\ \ \ \ | divide\ by\ 12\nx=50\n\n5x=250\n7x=350\n\nThere\ are\ 250\ boys\ and\ 350\ girls.

Describe the dimensions of two different prisms that each have a volume of 2400 cubic centimeters. Then draw each prism.

Answers

One prism with a volume of 2400 might have a rectangular base with a length of 4 and a width of 5, as well as a height of 120. 

V = l x w x h
V = 4  x 5 x 120
V = 2400

This prism would essentially look like a really tall rectangle, since the height is such a large number. I wouldn't accurately represent the units on graph paper, if I were you. Just label the sides with the numbers I gave you.

Another prism with a volume of 2400 might be a rectangular prism with a length of 8, a width of 10, and a height of 30. 

V = l x w x h
V= 8 x 10 x 30
V = 2400

This would also be a tall rectangle, although it isn't as tall. Keep in mind that l x w x h is only the volume formula for a rectangular prism. I only used rectangular prisms because they would be the easiest for this example. A triangular prism has a different volume formula.

-9x+4=-8-5x helppppp plsssss

Answers

Answer:3

Step-by-step explanation:

-9x+4=-8-5x

-4x+4=-8

-4x=-12

x=3

Answer:

Step-by-step explanation:

Add 5x so -9x+5x becomes -4x+4=-8 then subtract -4 and then -4+-8 becomes -12 and then solve for x which is -12/-4 which is 3.

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