MATHEMATICS HIGH SCHOOL

Which of the following points lie in the solution set to the following system of inequalities?y < −3x + 3
y < x + 2
(1, −5)
(1, 5)
(5, 1)
(−1, 5)

Answers

Answer 1
Answer:

Answer with Step-by-step explanation:

We have to find the points which lie in the solution set of the following system of inequalities:

y < −3x + 3

y < x + 2

(1, −5)

when x=1

y < −3x + 3⇒ y<0

y < x + 2⇒ y<3

and y= -5 satisfies the above inequalities

So, it lies in the solution set

(1, 5)

when x=1

y < −3x + 3⇒ y<0

y < x + 2⇒ y<3

and y= 5 does not satisfy the above inequalities

So, it does not lie in the solution set

(5, 1)

when x=5

y < −3x + 3⇒ y< -12

y < x + 2⇒ y<7

and y= 1 does not satisfy the above inequalities

So, it does not lie in the solution set

(−1, 5)

when x= -1

y < −3x + 3⇒ y<6

y < x + 2⇒ y<1

and y= 5 does not satisfy the above inequalities

So, it does not lie in the solution set

Hence, Correct answer is:

(1,-5)
Answer 2
Answer: (1,-5) would be the answer. I used a graphing calculator to solve this. I plugged in the equation and looked at the intersection of the 2 graphs. Hope this helps.

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The slope is 3, and it passes through ( -4, -7).a. y = 6x + 5
c. y = 3x - 7
b. y = 3x + 5
d. y = 3x - 19
The slope is -7, and it passes through ( 5, -3).
a. y = -7x - 3
c. y = -14x + 32
b. y = -7x + 32
d. y = -7x - 38

Answers

The equation of the lines are b. y = 3x + 5 and b. y = -7x + 32.

What is the Equation of line in Slope Intercept form?

Equation of a line in slope intercept form is y = mx + b, where m is the slope of the line and b is the y intercept, which is the y coordinate of the point where it touches the Y axis.

Given that,

Slope = 3

And the line passes through (-4, -7).

Substituting in the slope intercept form,

-7 = (3 × -4) + c

-7 = -12 + c

c = -7 + 12

c = 5

Equation of the line is y = 3x + 5

Given slope = -7.

Line passes through (5, -3)

Substituting in the slope intercept form,

-3 = (-7 × 5) + c

-3 = -35 + c

c = -3 + 35

c = 32

Equation of the line is y = -7x + 32

Hence the equations are y = 3x + 5 and y = -7x + 32.

To learn more about Slope Intercept Form here :

brainly.com/question/29146348

#SPJ2

Answer:B

Step-by-step explanation:

9.8 < 20 – 9.8t < 20

Answers

Answer:

0 < t < 1.04 or  t ∈ (0, 1.04)

Step-by-step explanation:

Solving in steps:

  • 9.8 < 20 – 9.8t < 20                  
  • 9.8 - 20 < -9.8t < 20 - 20         ⇒ subtract 20 from all sides
  • -10.2 < -9.8t < 0                        ⇒ divide all sides by -9.8, this changes  inequality signs to reverse
  • 0< t < 10.2/9.8
  • 0 < t < 1.04 or t ∈ (0, 1.04)

Write an equivalent expression for 12^3 • 12^9 • 12^4 • 12^2

Answers

9514 1404 393

Answer:

  12^18

Step-by-step explanation:

Each exponent tells you the number of times 12 is repeated as a factor. The total number of repetitions of 12 as a factor in this product is ...

  3 +9 +4 +2 = 18

The equivalent expression is 12¹⁸.

Math Help


Explain when is a rational expression restricted.

Answers

basically, domain is all real numbers that cause an not allowed
some things that aren't allowed are dividing by zero and taking the square root of a number less than zero, restrict all values that make thos things hapen

exapmle

a/b, b can not be zero

(3+x)/(4-x)
x cannot be  4 since that would be dividing by zero


another example
√(x-3)
x cannot be less than 3 because that would make a sqrt of a negative

basiccally restrictions are not allowed becasue we don't understnad what happens when we break them

A race car moving along a circular track has a centripetal acceleration of 12 m/s. Ifthe distance between the car and the center of the track is 40 m, what is the speed
of the car?

Answers

Answer:

The speed of the car is 21.91 m/s

Step-by-step explanation:

Centripetal Acceleration

It's the acceleration experienced by an object in a uniform circular motion.

It always points toward the center of rotation and is perpendicular to the linear velocity v.

The magnitude of the centripetal acceleration is:

\displaystyle a_c=(v^2)/(r)

Where r is the radius of rotation.

The race car has a centripetal acceleration of a_c=12 m/s^2 and the radius of rotation is r=40 m.

We can calculate the speed of the car by solving the above equation for v:

v=√(a_c\cdot r)

v=√(12\cdot 40)

v=√(480)

v=21.91\ m/s

The speed of the car is 21.91 m/s

If g(x) = 4 square root of x then g(45) is

Answers

Hi,

So we have g(x) = 4√(x).  We're looking for g(45).  Think of it like this: whatever number is in the place of x in g(x), just place that number AS x.

Therefore, we have :
g(45) = 4√(45) ⇒ (4) × (√(45)) ⇒ (4)(3√(5)) = 12√(5).

-Hope this helps!
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