MATHEMATICS HIGH SCHOOL

Solve the inequality. Show your work.
|4r + 8| ≥ 32

Answers

Answer 1

Answer:

|4r + 8| ≥ 32

4r + 8 ≥ 32 or 4r + 8 ≤ -32 inside of absolute value could be + or -

4r ≥ 24 or 4r ≤ -40 subtracted 8 from both sides

r ≥ 6 or r ≤ -10 divided both sides by 4

Graph: ←---------------- -10 6 ------------------→

Interval Notation: (-∞, -10] U [6, ∞)

Answer 2

Answer:

Okay here are the steps to solving this inequality:

First- Break down the problem into these 2 equations

4r + 8 ≥ 32 → - (4r + 8) ≥ 32

Second- Solve the 1st equation: 4r + 8 ≥ 32

r ≥ 6

Third- Solve the 2nd equation: - (4r + 8) ≥ 32

r ≤ -10

Lastly- Collect all solutions

r ≥ 6 and r ≤ -10

Answer 3

Answer:

Okay here are the steps to solving this inequality:

First- Break down the problem into these 2 equations

4r + 8 ≥ 32 → - (4r + 8) ≥ 32

Second- Solve the 1st equation: 4r + 8 ≥ 32

r ≥ 6

Third- Solve the 2nd equation: - (4r + 8) ≥ 32

r ≤ -10

Lastly- Collect all solutions

r ≥ 6 and r ≤ -10

Related Questions

Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = -1f(x) = −1/12 (x − 5)2 + 2 f(x) = 1/12 (x − 5)2 + 2 f(x) = −1/12 (x + 5)2 + 2 f(x) = 1/12 (x + 5)2 + 2
A company makes cylindrical crackers that have a cylindrical hole in the middle.
If BC= 6.5, CD= 7.8, and AD=12.2, find AB to the nearest tenth
Evaluate the expression when a=-4 and x=5.a-2x
Write a congruence statement for the pair of triangles. Name the postulate or theorem that justifies your statement.

Un topografo situado en un punto c localiza dos puntos a y b en los lados opuestos de un lago . Si el punto c esta situado a 5km de a y 8 km de b y ademas el angulo formado en el punto c es de 36 grados . Calcular el ancho del lago

Answers

The width of the lake is approximately 4.93 kilometers.

To calculate the width of the lake, you can use trigonometry. You have a triangle with one side of 5 km (from point C to point A), another side of 8 km (from point C to point B), and an included angle of 36 degrees at point C.

You can use the law of cosines to find the third side, which is the width of the lake (let's call it "x"). The law of cosines states:

$c^2 = a^2 + b^2 - 2ab * cos(C)$

Where:

c is the side you want to find (the width of the lake, in this case).

a is the side opposite to angle A (5 km).

b is the side opposite to angle B (8 km).

C is the included angle at point C (36 degrees).

So, plug in the values:

$x^2 = 5^2 + 8^2 - 2 * 5 * 8 * cos$ (36 degrees)

Now, you can solve for x:

$x^2 = 25 + 64 - 80 * cos$ (36 degrees)

$x^2 = 89 - 80 * cos$ (36 degrees)

Now, you'll need to calculate the cosine of 36 degrees, which is approximately 0.809.

$x^2 = 89 - 80 * 0.809\nx^2 = 89 - 64.72\nx^2 = 24.28$

Now, take the square root of both sides to find the width of the lake:

x ≈ √24.28

x ≈ 4.93 km

So, the width of the lake is approximately 4.93 kilometers.

for such more question on triangle

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Hi mods, I do have a link in this answer but it is a link to the spanish version of brainly since this user seems to speak spanish.

Por favor, traduzca su pregunta al inglés o encuentre la versión en español de Brainly (https://brainly.com.br/ o https://brainly.lat/.)

Estoy usando el traductor de google, lo siento por el mal español

ver diagrama adjunto abajo (el asombrosamente dibujado)

podemos formar un triangulo

Usa la ley de los cosenos del segundo apego.

Queremos encontrar el valor de c que representa el ancho del lago

En este problema, a=5, b=8, y C=36°

$c^2=a^2+b^2-2abcos(C)$

$c=√(a^2+b^2-2abcos(C))$

$c=√(5^2+8^2-2(5)(8)cos(36^o))$

$c=√(25+64-80cos(36^o))$

$c=√(89-80cos(36^o))$

c≈4.92734 km

el ancho del lago es de aproximadamente 4.93km

Ethan‘s bank account listed a balance of $328.80. He originally opened the account with a $200 deposit and a simple interest rate of 4.6% If there were no deposit or withdrawals, how long ago was the account opened

Answers

Answer:

Step-by-step explanation:

$Interest=\frac {PRT}{100}$ where P is principal amount, R is rate in percentage and T is time.

Making T the subject of the formula,

$T=\frac {Interest * 100}{PR}$

For Ethan's case, Interest=$328.8-$200=$128.8

Substituting $128.8 for interest, 4.6% for rate and $200 for P we obtain

T=(128*100)/(4.6*$200)=14

Since the rate wasn't specified whether annually or monthly, the time can be 14 years or 14 months

What numbers multiply to 6 and add up to 9

Answers

xy = 6
x + y = 9

x + y = 9
x - x + y = -x + 9
y = -x + 9

  xy = 6
  x(-x + 9) = 6
  x(-x) + x(9) = 6
-x² + 9x = 6
  -x² + 9x - 6 = 0
-1(x²) - 1(-9x) - 1(6) = 0
-1(x² - 9x + 6) = 0
-1 -1
x² - 9x + 6 = 0
x = -(-9) ± √((-9)² - 4(1)(6))
2(1)
x = 9 ± √(81 - 24)
2
x = 9 ± √(57)
2
x = 4.5 ± 0.5√(57)

x + y = 9
4.5 ± 0.5√(57) + y = 9
- (4.5 ± 0.5√(57)) - (4.5 ± 0.5√(57))
y = 4.5 ± 0.5√(57)
(x, y) = (4.5 ± 0.5√(57), 4.5 ± 0.5√(57))

The two numbers that multiply to 6 and add up to 9 are 4.5 ± 0.5√(57).

A pink crayon is made with 12 mL of red wax for every 5 mL of white wax.Which of the following wax mixtures will create the same shade of pink?

(A) 10 mL of red wax mixed wit 24 mL of white wax

(B) 48 mL of red mixed with 12 of white wax

(C) 13 mL of red mixed with 6 mL of white wax

(D) 36 mL of red mixed with 15 mL of white wax

(E) 60 mL of red mixed with 24 mL of white wax

Answers

Answer:c

Step-by-step explanation:

One recipe for cereal bars uses 5 cups of cereal and 2 1/2 cups of nuts. A different recipe uses 3 cups of cereal and 1 cup of nuts. Which recipe is more nutty?

Answers

The recipe that uses more amount of nuts is the 1st recipe, which uses 2.5 cups of nuts.

What is a fraction?

In mathematics, a fraction is represented by a specific number that designates a portion of an entire. A fraction is a piece or section of a whole, whereby a can have been any number, a particular value, or an object.

As per the information provided in the question,

Total nuts used in 1st recipe = 5/2 = 2.5 cups

Total nuts used in 2nd recipe = 1 cup

Compare the values of nuts used in both recipes.

The number of cups of nuts used in 1st recipe is greater than in the 2nd recipe.

To know more about Fraction:

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2 1/2 because it has more amount of nuts.

25 per cent of 600 is equal to 15 per cent of what number?