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Bogdan [553]
3 years ago
6

1. Write the absolute value inequality in the form |x−b| c that has the solution set x<-5

Mathematics
2 answers:
NikAS [45]3 years ago
6 0

Answer:      |x - 1| > 6

Step-by-step explanation:b is the centre:

(-5 + 7)/2

2/2 = 1

b = 1

c is the distance from the centre

c = 7 - 1 = 6

Since it's an or case, > with the modulus

|x - 1| > 6

Sedbober [7]3 years ago
4 0
Answer is |x-1| > 6.
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The distributive property can be applied to which expression to factor 12x3 – 9x2 + 4x – 3?
Arturiano [62]

Answer:

(4x - 3)(3x² + 1)

Step-by-step explanation:

Given

12x³ - 9x² + 4x - 3 ( factor the first/second and third/fourth terms )

= 3x²(4x - 3) + 1(4x - 3) ← factor out (4x - 3) from each term

= (4x - 3)(3x² + 1) ← in factored form

8 0
3 years ago
A card is drawn at random out of a​ well-shuffled deck of 52 cards. Find the probability of drawing a six comma seven comma or e
Rina8888 [55]

Answer: \frac{3}{13}, or ~23.07%

Step-by-step explanation:

There are 52 cards in your average deck.

For this question, you need the numbers of the cards in the deck. There are four of each number from 2 through 10, and four aces, jacks, queens, and kings.

Considering there are four 6s, four 7s, and four 8s, there are 12 cards that fit the description.

Divide 12 by the total number of cards in the deck, 52, to get your answer.

8 0
4 years ago
10 POINTS! PLEASE HELP!! The illustration shows a compact disc tray that holds five CDs. The radius of each compact disc is 9 cm
MariettaO [177]

We can see that there are 5 CDs, each of radius 9 cm

<u>Area occupied by 1 disc:</u>

Area of a circle = πr²

Area of disc = π(9)²

Area of disc = 3.14 * 81 = 254 cm²

<u>Area occupied by 5 discs:</u>

Area occupied by 5 discs = Area occupied by 1 disc * 5

Area occupied by 5 discs = 254 * 5

Area occupied by 5 discs = 1270 cm²

3 0
3 years ago
⦁ Find the length of the third angle of a triangle given that the first two angles are 35 and 70. Show your work.
UNO [17]
180 - 70 = 110
110 - 35 = 75
The third angle is 75
3 0
3 years ago
Solve this equation for x: 2x^2 + 12x - 7 = 0
zhannawk [14.2K]

Answer:

x=0.5355 or x=-6.5355

First step is to: Isolate the constant term by adding 7 to both sides

Step-by-step explanation:

We want to solve this equation: 2x^2 + 12x - 7 = 0

On observation, the trinomial is not factorizable so we use the Completing the square method.

Step 1: Isolate the constant term by adding 7 to both sides

2x^2 + 12x - 7+7 = 0+7\\2x^2 + 12x=7

Step 2: Divide the equation all through by the coefficient of x^2 which is 2.

x^2 + 6x=\frac{7}{2}

Step 3: Divide the coefficient of x by 2, square it and add it to both sides.

Coefficient of x=6

Divided by 2=3

Square of 3=3^2

Therefore, we have:

x^2 + 6x+3^2=\frac{7}{2}+3^2

Step 4: Write the Left Hand side in the form (x+k)^2

(x+3)^2=\frac{7}{2}+3^2\\(x+3)^2=12.5\\

Step 5: Take the square root of both sides and solve for x

x+3=\pm\sqrt{12.5}\\x=-3\pm \sqrt{12.5}\\x=-3+ \sqrt{12.5}, $ or $x= -3- \sqrt{12.5}\\$x=0.5355 or x=-6.5355

6 0
3 years ago
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