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galina1969 [7]
3 years ago
6

Which correctly solves the inequality t+18<43 Select one: a. t<25 b. t>61 c. t>25 d. t<61

Mathematics
1 answer:
Naddik [55]3 years ago
8 0

For this case we must solve the following inequality, finding the values for the variable "t":

t + 18

We subtract 18 from both sides of the inequality:

t + 18-18

Thus, the variable "t" is defined for all strict lower values than 25.

Answer:

t

Option A

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What is this can anyone help me
Solnce55 [7]

g(x) = (x - 3)² - 4

given f(x) is shifted a units horizontally to the right → f(x) → f(x - a)

If f(x) is shifted by a units horizontally left → f(x) → f(x + a)

If f(x) is shifted by b units vertically up → f(x) → f(x) + b

If f(x) is shifted by b units vertically down → f(x) → f(x) - b

The vertex (0, 0) of f(x) has shifted to (3, -4)

that is 3 units horizontally to the right and 4 units vertically down

hence g(x) = (x - 3)² - 4


4 0
4 years ago
Jeremy wants to construct an open box from an 18-inch square piece of aluminum. He plans to cut equal squares, with sides of x i
serious [3.7K]

a.

The volume of the box V = 4x³ - 72x² + 324x

Since the dimensions of the square piece of paper are 18 inches each, and we cut out a length x from each side to give a total length of 2x cut from each side. So, each dimension is L = 18 - 2x.

Since the height of the open box is x and its base is a square, the volume of the open box ix V = L²x

= (18 - 2x)²x

= (324 - 72x + 4x²)x

= 324x - 72x² + 4x³

The volume of the box V = 4x³ - 72x² + 324x

b.

The minimum value of length of the sides of the squares cut from each corner is x = 3 inches.

  • the length of the box, L = 12 inches,
  • the width of the box = 12 inches
  • and the height of the box, x = 3 inches.

Since the volume of the box is 432 cubic inches,

V = 324x - 72x² + 4x³

324x - 72x² + 4x³ = 432

4x³  - 72x² + 324x - 432 = 0

x³  - 18x² + 81x - 108 = 0

A factor of the expression is x - 3

So, x³  - 18x² + 81x - 108 ÷ x - 3 = x² - 15x + 36

So,  x³  - 18x² + 81x - 108 = (x² - 15x + 36)(x - 3) = 0

Factorizing the expression x² - 15x + 36 = 0

x² - 3x - 12x + 36 = 0

x(x - 3) - 12(x - 3) = 0

(x - 3)(x - 12) = 0

So,  x³  - 18x² + 81x - 108 = (x - 3)(x - 3)(x - 12) = 0

So, (x - 3)²(x - 12) = 0

(x - 3)² = 0 and (x - 12) = 0

x - 3 = √0 and x - 12 = 0

x - 3 = 0 and x - 12 = 0

x = 3 twice and x = 12

Since x = 3 is the minimum value, the minimum value of x = 3.

Since the length of the box, L = 18 - 2x

= 18 - 2(3)

= 18 - 6

= 12 inches

The width of the box = L = 12 inches

The height of the box = x = 3 inches.

So,

The minimum value of length of the sides of the squares cut from each corner is x = 3 inches.

  • the length of the box, L = 12 inches,
  • the width of the box = 12 inches
  • and the height of the box, x = 3 inches.

Learn more about volume of a box here:

brainly.com/question/13309609

6 0
2 years ago
Find the area of the triangle.<br> 3 cm<br> 11 cm<br> C с<br> 14.5 cm
boyakko [2]

Answer: The answer is 43.5 because when using the formula you get this result.

Step-by-step explanation: Area of triangle is base x height divided by 2. So do our base 14.5 and our height 6 and multiply them together. 14.5 x 6 = 87 / 2 = 43.5

6 0
3 years ago
A standard pair of six-sided dice is rolled. What is the probability of rolling a sum less than 7? Express your answer as a frac
zzz [600]

Answer:

0.4167 is the probability of rolling a sum less than 7.  

Step-by-step explanation:

We are given the following in the question:

Event: A standard pair of six-sided dice is rolled

A: rolling a sum less than 7

Sample space:

{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)

(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)

(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)

(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)

(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)

(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

A:

{(1,1),(1,2),(1,3),(1,4),(1,5),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(4,1),(4,2),(5,1)}

Formula:

\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}

P(A) = \dfrac{15}{36} = 0.4167

0.4167 is the probability of rolling a sum less than 7.

8 0
3 years ago
What are two other ways to name EF
chubhunter [2.5K]
Line EF and Line Segment EF
this is probs wrong, but idk bc there aren't any answer choices
4 0
3 years ago
Read 2 more answers
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