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2 years ago

Which represents the solution set to the inequality 5.1(3 + 2.2x) > –14.25 – 6(1.7x + 4)?

Mathematics

2 answers:

podryga [215]2 years ago

5 0

The solution set to the inequality is C) (–2.5, ∞)

<h3>Further explanation</h3>

Solving linear equation mean calculating the unknown variable from the equation.

Let the linear equation : y = mx + c

If we draw the above equation on Cartesian Coordinates , it will be a straight line with :

<em>m → gradient of the line</em>

<em>( 0 , c ) → y - intercept</em>

Gradient of the line could also be calculated from two arbitrary points on line ( x₁ , y₁ ) and ( x₂ , y₂ ) with the formula :

$\large {m = \frac{y_2 - y_1}{x_2 - x_1}$

If point ( x₁ , y₁ ) is on the line with gradient m , the equation of the line will be :

$y - y_1 = m ( x - x_1 )$

Let us tackle the problem.

Given:

$5.1(3 + 2.2x) > -14.25 - 6(1.7x + 4)$

$(5.1 \times 3) + (5.1 \times 2.2x) > -14.25 - (6 \times 1.7x + 6 \times 4)$ → distributive law of multiplication

$(15.3) + (11.22x) > -14.25 - (10.2x + 24)$

$15.3 + 11.22x > -14.25 - 10.2x - 24$

$11.22x + 10.2x > -14.25 - 15.3 - 24$ → rearrange

$21.42x > -53.55$

$x > -53.55 \div 21.42$

$x > -5/2$

$\large {\boxed {x > -2.5} }$

<h3>Learn more</h3>

Infinite Number of Solutions : brainly.com/question/5450548
System of Equations : brainly.com/question/1995493
System of Linear equations : brainly.com/question/3291576

<h3>Answer details</h3>

Grade: High School

Subject: Mathematics

Chapter: Linear Equations

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point

Nina [5.8K]2 years ago

4 0

1. Simplify the inequality $5.1(3 + 2.2x) > -14.25 - 6(1.7x + 4):$

$15.3+11.22x>-14.25-10.2x-24,\\
15.3+11.22x>-10.2x-38.75.$

2. Separate terms with x and without x in different sides:

$11.22x+10.2x>-38.75-15.3.$

3. Add similar terms:

$21.42x>-54.05.$

4. Divide by 21.42:

$x>-\dfrac{54.05}{21.42} ,\\ \\x>-2.5.$

Answer: correct choice is C.

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2 years ago

How many 4/5 cup servings are in 4/9 of a cup of yogurt

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For this question, you need to understand how to divide fractions.First we line up our fractions appropriately:
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2 years ago

Read 2 more answers

A teacher decides to purchase a new car and considers two options. Option one is the new Zoomba for $60,000 with an expected dep

kupik [55]

Answer:

She chose Option 2 which is a linear option, because it offers a smaller lose

in value compared to option 1 which is an exponential option.

The final value for option 2=$32,800

Step-by-step explanation:

Option 1

New Zoomba for 60000 with a depreciation rat of 2%per month for 3 years

Exponential equation;

y=a(1-r)^t

where;

y=future value

a=initial value=60000

r=depreciation rate=2% per month

t=time interval=12×3=36 months

Replacing;

y=60000(1-2/100)^36

y=60000(0.98)^36=28,992.79

The value after 3 years=$28,992.79

Initial value-Final value=(60000-28992.79)=$31007.21

Percentage of initial value lost=((Final value-Initial Value)/(Initial Value))×100

(31007.21/60000)×100=51.68%

Option 2

New starfish for $40,000 with a depreciation of $200 per month for 3 years

Linear equation;

y=a-bt

where;

y=Future value

a=Initial value=$40,000

b=the depreciation amount per time interval=$200 per month for 3 years

t=time interval=(3×12)=36 months

Replacing;

y=40000-(200×36)

y=32,800

Final value=y=$32,800

Initial value-Final value=(40000-32800)=$7200

Percentage of initial value lost=((Final value-Initial Value)/(Initial Value))×100

(7200/40000)×100=18%

Option 1(51.68%)>Option 2(18%) therefor Option 1 loses value at a faster rate than Option 2

She chose Option 2 which is a linear option, because it offers a smaller lose

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4 0

2 years ago

The word geometry has eight letters. three letters are chosen at random. what is the probability that two consonants and one vow

olga nikolaevna [1]

Answer:

0.536 is the required probability.

Step-by-step explanation:

We have been given the word the word "GEOMETRY"

we have to find the probability that two consonants and one vowel are chosen:

Number of consonants are: 5

Number of vowels are: 3

Hence, The required probability is: $\frac{^5C_2\cdot ^3C_1}{^8C_3}$

Using: $^nC_r=\frac{n!}{(r!)(n-r)!}$

$\frac{\frac{5!}{3!\cdot 2!}\cdot\frac{3!}{1!\cdot 2!}}{\frac{8!}{3!\cdot 5!}}$

Simplifying the above expression:

$\frac{\frac{5\cdot 4\cdot 3!}{3!\cdot 2}\cdot {\frac{3\cdot 2!}{2!}}}{\frac{8\cdot 7\cdot 6\cdot 5!}{5!\cdot 3\cdot 2}}$

Further simplification after cancelling out the common terms we get:

$\Rightarrow \frac{30}{56}=\frac{15}{28}=0.5357=0.536$

Hence, Option 1 is correct.

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2 years ago

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A parcel has a mass of 500g. Calculate its weight. (Assume the gravitational field strength is 10N/kg).

Elan Coil [88]

Answer:

The weight of the parcel is 5 N

Step-by-step explanation:

we know that

Weight can be calculated using the equation:

$W=mg$

where

W ----> weight (W) is measured in newtons (N)

m ----> mass (m) is measured in kilograms (kg)

g ----> gravitational field strength (g) is measured in newtons per kilogram (N/kg)

In this problem we have

$g=10\ N/kg$

$m=500\ g$

Remember that

$1\ kg=1,000\ g$

To convert g to kg

Divide by 1,000

$m=500\ g=500/1,000=0.5\ kg$

substitute the values in the equation

$W=(0.5)(10)=5\ N$

therefore

The weight of the parcel is 5 N

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2 years ago