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Viktor [21]
3 years ago
9

A = {1, 3, 5, 7, 9} B = {2, 3, 5, 7} What is A ∩ B?

Mathematics
1 answer:
Oksanka [162]3 years ago
6 0

Answer:

  • It was {3,5,7}

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Match the equations representing parabolas with their directrixes. y + 8 = 3(x + 2)2 y − 14 = -(x − 3)2 y + 7.5 = 2(x + 2.5)2 y
Shkiper50 [21]

Answer:

Part 1) y+8=3(x+2)^{2} -----> y=-8.08

Part 2) y-14=-(x-3)^{2} ---->  y=14.25

Part 3) y+7.5=2(x+2.5)^{2} ---->  y=-7.625

Part 4) y-17=-(x-3)^{2} -----> y=17.25

Part 5) y+7=(x-4)^{2} ----> y=-7.25

Part 6) y-6=-(x-1)^{2} ---->  y=6.25

Step-by-step explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

y-k=\frac{1}{4p}(x-h)^{2}

where

(h,k) is the vertex

The directrix is

y=k-p

case 1) we have

y+8=3(x+2)^{2}

the vertex is the point (-2,-8)  

\frac{1}{4p}=3

p=\frac{1}{12}

The directrix is equal to

y=-8-\frac{1}{12}=-8.08

case 2) we have

y-14=-(x-3)^{2}

the vertex is the point (3,14)  

\frac{1}{4p}=-1

p=-\frac{1}{4}

The directrix is equal to

y=14+\frac{1}{4}=14.25

case 3) we have

y+7.5=2(x+2.5)^{2}

the vertex is the point (-2.5,-7.5)    

\frac{1}{4p}=2

p=\frac{1}{8}    

The directrix is equal to

y=-7.5-\frac{1}{8}=-7.625

case 4) we have

y-17=-(x-3)^{2}

the vertex is the point (3,17)      

\frac{1}{4p}=-1

p=-\frac{1}{4}    

The directrix is equal to

y=17+\frac{1}{4}=17.25

case 5) we have

y+7=(x-4)^{2}

the vertex is the point (4,-7)      

\frac{1}{4p}=1

p=\frac{1}{4}    

The directrix is equal to

y=-7-\frac{1}{4}=-7.25

case 6) we have

y-6=-(x-1)^{2}

the vertex is the point (1,6)      

\frac{1}{4p}=-1

p=-\frac{1}{4}    

The directrix is equal to

y=6+\frac{1}{4}=6.25

5 0
3 years ago
Which of the follow is a subset of the set E which contains all even integers?
Alina [70]

Answer:

The natural numbers and the whole numbers are both subsets of integers. In other words, a rational number is a number that can be written as one integer over another.

5 0
3 years ago
Sandy is getting ready for the day. She can wear either a balck or white shirt and then either pants, shorts, or a skirt. Create
gladu [14]
Black shirt and pants
Black shirt and shorts
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White shirt and pants
White shirt and shorts
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6 COMBINATIONS TOTAL
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Norris wrote the equation 7x9=63.Blake wrote the equation 7x9=9x7.Who wrote a correct equation?Explain
Karolina [17]

Answer:

Step-by-step explanation:

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3 years ago
The quotient of the sum of 2t and 2, twice the cube of s
natali 33 [55]

Answer: \frac{2t+2}{2s^3}

Step-by-step explanation:

Since you did not indicate what you need to do, I assume that you have to write an expression using the sentence given in the problem.

In order to solve this exercise, it is importat to remember the following information:

1. The quotient is the result of a division.

2. The sum is the result of an addition.

3. The word "twice" indicates a multiplicatio by 2.

4. The word "cube" indicates an exponent 3.

Then, keeping on mind the explained above and the data given in the exercise, you know that:

-The sum of 2t and 2 can be expressed as:

2t+2

- Twice the cube of s can be expressed in the following form:

2s^3

Therefore, you can dermine that "the quotient of the sum of  2t and 2 and twice the cube of s" is represented with the following expression:

\frac{2t+2}{2s^3}

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