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Anastasy [175]
3 years ago
11

What is the solution of the given inequality? -4(2x+1)<_3(x-5)

Mathematics
1 answer:
soldi70 [24.7K]3 years ago
4 0

Answer:

x ≥ 1

Step-by-step explanation:

Solve the inequality by solving for x.

Solve:

-4(2x + 1) ≤ 3(x - 5)

Use the distributive property.

-8x - 4 ≤ 3(x - 5)

-8x - 4 ≤ 3x - 15

Subtract 3x from both sides.

-11x - 4 ≤ -15

Add 4 to both sides.

-11x ≤ -11

Divide both sides by -11, also flip the inequality since you're dividing by a negative number.

x ≥ 1

Your final answer would be x ≥ 1

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kakasveta [241]

1. in picture 1

2. in picture 2

Hope this helps :T

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6 0
3 years ago
X-y=6<br> 2x-3z=16<br> 2y+z=4<br><br> Solve the systems of equations.
Neko [114]

Answer:

Given System of equation:

x-y =6                                  .....,[1]

2x-3z = 16                           ......[2]  

2y+z = 4                              .......[3]

Rewrite the equation [1] as

y = x - 6                                .......[4]

Substitute the value of [4] in [3], we get

2(x-6)+z = 4

Using distributive property on LHS ( i.e,  a \cdot (b+c) =a \cdot b+ b \cdot c )

then, we have

2x - 12 +z =4

Add 12 to both sides of an equation:

2x-12+z+12=4+12

Simplify:

2x +z = 16                         .......[5]

On substituting equation [2] in [5] we get;

2x+z=2x -3z

or

z = -3z

Add 3z both sides of an equation:

z+3z = -3z+3z

4z = 0

Simplify:

z = 0

Substitute the value of z = 0 in [2] to solve for x;

2x-3(0) = 16

or

2x = 16

Divide by 2 both sides of an equation:

\frac{2x}{2} =\frac{16}{2}

Simplify:

x= 8

Substitute the value of x =8 in equation [4] to solve for y;

y = 8-6 = 2

or

y = 2

Therefore, the solution for the given system of equation is;  x = 8 , y = 2 and z =0

5 0
3 years ago
Kaira's gross pay is $4,633. Her deductions total $1,009.13. What percent of hergross pay is take-home pay?Round to the nearest
Delvig [45]

Answer:

\text{ 78\%}

Explanation:

Here, we want to get the percentage of the gross pay is the take-home pay

Mathematically, we have to divide the take-home pay by the gross pay and multiply it by 100%

Her take-home pay is the difference between her gross pay and her deductions

We have this as:

\text{ 4633 - 1009.13 = \$3,623.87}

We have this as:

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7 0
1 year ago
Given that S is the centroid of triangle MNO, find SQ.
AnnZ [28]

Answer:

|SQ|=5

Step-by-step explanation:

If S is the median, then OP is a median of triangle OMN.

This implies that:

|MP|=|NP|

3x-4=x+4

We group like terms and solve for x.

3x-x=4+4

\implies 2x=8

\implies x=4

Now we know that: MN:SQ=2:1

But MN=2x+2

This implies that:

2x+2:SQ=2:1

Put x=4

2(4)+2:SQ=2:1

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Therefore |SQ|=5

7 0
3 years ago
The following is a set of hypotheses, some information from one or more samples, and a standard error from a randomization distr
Tanya [424]

Complete Question

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Answer:

The value is  z =  -6.40

Step-by-step explanation:

Generally the standardized test statistics is mathematically represented as

     z =  \frac{\^ p  -  p }{ SE }

=>  z =  \frac{0.216  -  0.28 }{ 0.01  }

=>  z =  \frac{0.216  -  0.28 }{ 0.01  }

=>  z =  -6.40

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