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1 year ago

Graph the numbers that are solutions to both inequalities.

Mathematics

1 answer:

nadya68 [22]1 year ago

3 0

Answer:

p ∈ [5 , 6)

Step-by-step explanation:

p + 6 ≥ 11

⇒ p ≥ 11 - 6

⇒ p ≥ 5

⇒ p ∈ [5 , +∞)

3p < 18

⇒ p < 18/3

⇒ p < 6

⇒ p ∈ (-∞ , 6)

Then

p the solution to both equations verify:

p ∈ (-∞ , 6) ∩ [5 , +∞)

Conclusion :

p ∈ [5 , 6)

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What is the slope of the line that passes through the points (3, -4) and (7, 4)?

Andrews [41]

The correct option is: Option (C) 2

Explanation:

The slope formula is = m = $\frac{y_2 - y_1}{x_2 - x_1}$

Insert the values in the above formula:

m = $\frac{4 - (-4)}{7 - 3} = \frac{8}{4} = 2$

Which is Option (C).

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2 years ago

One teacher wants to give each student 2/3 of a slice of pizza . If the teacher has 4 slices of pizza how many students will rec

Deffense [45]

Answer: 6 students

Step-by-step explanation:

The teacher wants to give each student 2/3 of a slice of pizza but only has 4 slices to give.

If each student gets 2/3 out of 4 slices, the number of students receiving will be:

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= 4 / 2/3

= 4 * 3/2

= 12/2

= 6 students

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2 years ago

It is important when solving an equation to perform identical operations on each side so that the equation remains equal.

Reil [10]

Answer:

true

Step-by-step explanation:

3 0

2 years ago

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How to solve the equation 8x-5=19

tiny-mole [99]

8x-5=19

+5 on each side

8x=24

Divide by 8 on each side.

X=3

8 0

2 years ago

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Suppose the lengths of two sides of a right triangle are represented by 2x and 3 (x + 1), and the longest side is 17 units. Find

densk [106]

Answer:

x=4

Step-by-step explanation:

Step 1:-

given the lengths of two sides of a right angle are represented by 2x and 3(x+1) and longest side is 17 units.

AB = 2x and BC = 3(x+1) and longest side AC= 17

by using Pythagoras theorem

$AC^2 = AB^2 + BC^2$

step 2:-

The hypotenuse is longest side is AC = 17 units

(17)^2 = 4x^2 +9(X+1)^2

on simplification, we will use formula

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

289 = 4x^2 +9(x^2+2x+1)

$13x^2 +18x-280 = 0$

finding factors 70 X 52 = 3640

$13x^2 +70x-52x-280 = 0$

$13x^2 -52x+ 70x-280 = 0$

Taking common , we get

13x(x-4)+70(x-4)=0

x-4=0 and 13x+70=0

x=4 and $13x =-70$

x=4 and $x=\frac{-70}{13}$

we can not choose negative value so x value is 4

Final answer:- x = 4

verification:-

$AC^2 = AB^2 + BC^2$

289 = 4(4)^2+9(4+1)^2

289 = 64 +9(25)

289=289

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2 years ago

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