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Rom4ik [11]
3 years ago
7

Describe the interval shown using an inequality, set notation, and interval notation. (Picture attached!) Thank you!

Mathematics
1 answer:
marta [7]3 years ago
5 0

Answer:

inequality: x > -3

Set notation: {x: x> -3}

Interval notation: [-3, ∞)

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Costs of Attendance
erastovalidia [21]

Answer:

y = 3,224x + 750

Step-by-step explanation:

Assuming the scholarship and grants are applied using the slope intercept form y=mx+b where m is the slope in this case the cost per year attending x the number of years attended and b the y intercept which in this case is the one time fee subtracting 13,774 by 10,550 gives us 3,224.

Since the one time fee is only in place once that would make it the y intercept therefore y=3,224x+750 is the correct answer

8 0
2 years ago
The school that Imani goes to is selling tickets to the annual dance competition. On the first day of the ticket sales the schoo
Tatiana [17]

Answer:

The adult and the child ticket are both 8 dollars

Step-by-step explanation:

x =adult ticket price

y = child ticket price

I will assume you forget to put that they sold 2 child tickets on the second day

7x+5y=96 and 3x+2y= 40

I will use elimination.  Multiply the first equation by 2 and the second equation by -5 to eliminate y

2(7x+5y)=96*2

14x + 10y = 192

The second equation

-5(3x+2y)= 40*-5

-15x -10y = -200

Add the equations together

14x + 10y = 192

-15x -10y = -200

------------------------

-x = -8

Multiply by -1

x = 8

Now we need to find y

3x+2y= 40

3(8) +2y = 40

24+2y = 40

Subtract 24 from each side

24-24 +2y = 40-24

2y = 16

Divide by 2

2y/2 =16/2

y =8

The adult and the child ticket are both 8 dollars


8 0
3 years ago
Point W(-6, 7) is rotated 90° clockwise. Where is W'?
MrRa [10]

Answer:

(7,6)

Step-by-step explanation:

rotate 90 degree clockwise: (x,y) -> (y,-x)

6 0
2 years ago
Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had decreased by 2%. If the rate of deca
LenaWriter [7]

The amount of radioactive material remaining after 24 hours is 92.15 kg.

<h3>Exponential function</h3>

An exponential function is in the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplier.

Let y represent the amount of the substance after t hours.

From the equation, a = 100 mg

Also, after 6 hours:

100-100*2\%=100b^6\\\\98=100b^6\\\\b=0.9966

After 24 hours:

y = 100(0.9966)²⁴ = 92.15 kg

The amount of radioactive material remaining after 24 hours is 92.15 kg.

Find out more on Exponential function at: brainly.com/question/12940982

4 0
3 years ago
Do you hypotenuse of a triangle is 1 foot more than twice the length of the shorter leg the longer leg is 7 feet longer than the
Lera25 [3.4K]

Answer:

Shorter leg: 8 units

Longer leg: 15 units

Hypotenuse: 17 units

Step-by-step explanation:

We are given h=1+2s where h is the hypotenuse and s is the length of the shorter leg.

We got this equation from reading that the "hypotenuse of a triangle is 1 foot more than twice the length of the shorter leg". I replaced the "hypotenuse of a triangle" with h, "is" with =, "1 foot more than" with 1+ and finally "twice the length of the shorter leg" with 2s.

We also have "longer leg is 7 feet longer than the shorter leg".

I'm going to replace "longer leg" with L.

I'm going to replace "is" with =.

I'm going to replace "7 feet longer than the shorter leg" with 7+s.

So we have the equation L=7+s.

So we have a right triangle since something there is a side being referred to as the hypotenuse. We can use Pythagorean Theorem to find a relation between all these sides.

So by Pythagorean Theorem, we have: s^2+L^2=h^2.

Let's make some substitutions from above:

s^2+(7+s)^2=(1+2s)^2

Let's expand the powers using:

(a+b)^2=a^2+2ab+b^2

Applying this now:

s^2+(49+2(7)s+s^2)=(1+2(1)(2s)+(2s)^2)

s^2+49+14s+s^2=1+4s+4s^2

Combine like terms on right hand side:

2s^2+49+14s=1+4s+4s^2

Subtract everything on left hand side to get 0 on that side:

0=(1-49)+(4s-14s)+(4s^2-2s^2)

Simplify:

0=(-48)+(-10s)+(2s^2)

Reorder into standard form for a quadratic:

0=2s^2-10s-48

Every term is even and therefore divisible by 2. I will divide both sides by 2:

0=s^2-5s-24

I'm going to see if this is factoroable.

We need to see if we can come up with two numbers that multiply -24 and add up to be -5.

Those numbers are -8 and 3.

So the factored form is:

0=(s-8)(s+3)

This implies that either s-8=0 os s+3=0.

The first equation can be solved by adding 8 on both sides: s=8.

The second equation can be solved by subtracting 3 on both sides: s=-3.

The only solution that makes sense for s is 8 since it can't the shorter length cannot be a negative number.

s=8

L=7+s=7+8=15

h=1+2s=1+2(8)=1+16=17

So the dimensions of the right triangle are:

Shorter leg: 8 units

Longer leg: 15 units

Hypotenuse: 17 units

6 0
3 years ago
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