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4 years ago

Which is the solution set of the compound inequality 3.5x - 10 > -3 and 8x - 9 < 39

1 answer:

3 0

Hello! So, for the first inequality, we have to add 10 to both sides. When you do that, 3.5x > 7. Then, you have to divide both sides by 3.5. When you do that, you get x > 2. Then, for the second inequality, you have to add 9 to both sides, then you would get 8x < 48. Divide both sides by 8 and you get x < 6. The compound inequality for this question would be 2 < x < 6.

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IN A CLASS OF 60 STUDENTS, 25 PLAYS BASKETBALL, 2O PLAY VOLLEYBALL, AND 10 STUDENTS PLAY BOTH OF THEM. HOW MANY STUDENTS PLAY NE

I am Lyosha [343]

Answer:

Step-by-step explanation:

We'll compare it with the study of sets, the most noticeable operation of which is:

<u>n(A ∪ B) = n(A) + n(B) - n(A ∩ B)</u>

where,

n(A ∪ B) is the Union Set, i. e, the set that contains all the elements

n(A) is a subset of the Union Set

n(B) is another subset of the Union Set, and

n(A ∩ B) is the Intersection Set ,i.e, the set contains common elements from both A and B sets.

<h3><u>In the question:</u></h3>

n(A ∪ B) = ? (<em>the total number of students in the class who are into the above mentioned sports)</em>

Let set A contains the students who play basketball and set B, the students who play Volleyball.

n(A) = 25
n(B) = 20

10 students play both of them, i. e.,

n(A ∩ B) = 10 (<em>as 10 students have common sports - Volleyball and Basketball</em>)

<u>Using the above operation:</u>

=> n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

=> n(A ∪ B) = 25 + 20 - 10

=> n(A ∪ B) = 35

<h3><u>Final Step to the Answer:</u></h3>

<u>The total number of students in the class </u>

= students into the given sports + students who don't play any of them

Total number of students in the class is 60
Total number fo students playing basketball and volleyball is 35

The students who play neither = 60 - 35

= 25

5 0

3 years ago

Anya graphed the line (y – 2) = 3(x – 1) on the coordinate grid. What is the slope of the line

3241004551 [841]

Given a point-slope form equation, we can easily locate of the slope of the linear equation. As a review, the point-slope form can be expressed as
$(y-y_{1}) = m(x-x_{1})$

where y₁ and x₁ are the x and y-coordinates of the equation and m is the slope. Seeing that (y-2) = 3(x-1) is already in this form, we can clearly see that the slope of the equation is equal to 3.

Answer: 3

3 0

3 years ago

A slide was installed at the local swimming pool, as shown here<br> What is the length of the slide?

tresset_1 [31]

Original number 21.4709
Rounded to the nearest hundredth 21.471

6 0

3 years ago

Read 2 more answers

140 subtracted from the square of a number the result is three times the number find the negative solution

natima [27]

Answer:

$Suppose~that~the~number~is~x.\\According~to~question,\\x^2-140=3x\\or, x^2-3x-140=0\\From~the~quadratic~formula,\\x = \frac{-(-3)+\sqrt{(-3)^2-4(1)(-140)} }{2(1)} ~and ~x= \frac{-(-3)-\sqrt{(-3)^2-4(1)(-140)} }{2(1)} \\or, x = \frac{3+\sqrt{9+560} }{2}~and~x=\frac{3-\sqrt{9+569} }{2}\\or, x = \frac{3+\sqrt{569} }{2}~and~x=\frac{3-\sqrt{569} }{2}\\So,~the~required~negative~number~is~\frac{3-\sqrt{569} }{2}.$

5 0

3 years ago

Please help<br> Solve for x.

Olegator [25]

Sum of interior angles = (n-2) × 180<span> = (5-2) x 180 = 3 x 180 = 540

so
x + 90 + 107 + 144 + 138 = 540
x + 479 = 540
x = 540 - 479
x = 61</span>

5 0

4 years ago