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postnew [5]
2 years ago
7

Which inequality is true for x = 20?

Mathematics
1 answer:
Makovka662 [10]2 years ago
8 0

The question is incomplete. Here is the complete question:

Which inequality is true for x = 20?

A. x + 30 < 3x

B. x - 5 < 2x - 35

C. x divided by 4 < x - 12

D. 2x < x + 22

Answer:

Options A, B and D.

Step-by-step explanation:

Given:

The value of 'x' is 20.

In order to find which options are correct, we need to plug in 20 for 'x' in each of the given inequalities and check which of them hold true.

Option A:

x+30

Substitute 20 for 'x' in the above inequality. This gives,

20 + 30 < 3(20)

50 < 60      

The given inequality is true as 50 is less than 60.

Option B:

x-5

Substitute 20 for 'x' in the above inequality. This gives,

20 - 5< 2(20) - 35

15 < 5

The given inequality is false as 5 is less than 15.

Option C:

\frac{x}{4}

Substitute 20 for 'x' in the above inequality. This gives,

\frac{20}{4} < 20-12

5 < 8

The given inequality is true as 5 is less than 8.

Option D:

2x

Substitute 20 for 'x' in the above inequality. This gives,

2(20) < 20+22

40 < 42

The given inequality is true as 40 is less than 42.

Therefore, the correct options are A, B and D.

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Answer:

  C.  On average, each 1 million dollar increase in salary was associated with an 8.42 point increase in winning percentage

Step-by-step explanation:

Apparently, winning percentage is plotted on the vertical axis, so the slope represents the ratio of winning percentage to salary in millions.

Then an increase in salary by 1 million is expected to be associated with an increase of 8.42 points in winning percentage.

3 0
2 years ago
Mila reads at a rate of 2 paragraphs per minute. After reading for 3 minutes, she had read a total of 6 paragraphs. This situati
stira [4]

Answer:

(3,6)

Step-by-step explanation:

Given that Mila reads at a rate of 2 paragraphs per minute. After reading for 3 minutes, she had read a total of 6 paragraphs.

This situation can be represented with a linear equation written in slope-intercept form,  as

y=2x

where 'x' represents the number of minutes and,

y represents the number of paragraphs.  

Since y intercept is 0 i.e. 0 paras in 0 minutes we have the equation as

y=2x

Since no of minutes or paragraphs cannot take negative values this line is defined only in the I quadrant where both x and y are positive

Out of the points given as follows:

(3,6) (2,3) (-3,6) or (-2,6) ,

we can remove last two since they have negative x which is impossible.

Consider  (3,6) (2,3)

Out of these only I point  (3,6) satisfies  y=2x and second point   (2,3) does not satisfy

y=2x

Hence answer is (3,6)






8 0
2 years ago
Read 2 more answers
Bart opened a credit card at a department store with an APR of 19.99% compounded monthly. What is the APY on this credit card? (
Goryan [66]

Answer:

d 1.67% thats the answer

Step-by-step explanation:

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2 years ago
The quadratic function y = –10x2 + 160x – 430 models a store’s daily profit (y) for selling a T-shirt priced at x dollars. What
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<span><span> x2-16x+48=0</span> </span>Two solutions were found :<span> x = 12 x = 4</span>

Step by step solution :<span>Step  1  :</span>Trying to factor by splitting the middle term

<span> 1.1 </span>    Factoring <span> x2-16x+48</span> 

The first term is, <span> <span>x2</span> </span> its coefficient is <span> 1 </span>.
The middle term is, <span> -16x </span> its coefficient is <span> -16 </span>.
The last term, "the constant", is <span> +48 </span>

Step-1 : Multiply the coefficient of the first term by the constant <span> <span> 1</span> • 48 = 48</span> 

Step-2 : Find two factors of  48  whose sum equals the coefficient of the middle term, which is  <span> -16 </span>.

<span><span>     -48   +   -1   =   -49</span><span>     -24   +   -2   =   -26</span><span>     -16   +   -3   =   -19</span><span>     -12   +   -4   =   -16   That's it</span></span>


Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -12  and  -4 
                     <span>x2 - 12x</span> - 4x - 48

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x-12)
              Add up the last 2 terms, pulling out common factors :
                    4 • (x-12)
Step-5 : Add up the four terms of step 4 :
                    (x-4)  •  (x-12)
             Which is the desired factorization

<span>Equation at the end of step  1  :</span> (x - 4) • (x - 12) = 0 <span>Step  2  :</span>Theory - Roots of a product :

<span> 2.1 </span>   A product of several terms equals zero.<span> 

 </span>When a product of two or more terms equals zero, then at least one of the terms must be zero.<span> 

 </span>We shall now solve each term = 0 separately<span> 

 </span>In other words, we are going to solve as many equations as there are terms in the product<span> 

 </span>Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

<span> 2.2 </span>     Solve  :    x-4 = 0<span> 

 </span>Add  4  to both sides of the equation :<span> 
 </span>                     x = 4 

Solving a Single Variable Equation :

<span> 2.3 </span>     Solve  :    x-12 = 0<span> 

 </span>Add  12  to both sides of the equation :<span> 
 </span>                     x = 12 

Supplement : Solving Quadratic Equation Directly<span>Solving <span> x2-16x+48</span>  = 0 directly </span>

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex :

<span> 3.1 </span>     Find the Vertex of   <span>y = x2-16x+48</span>

5 0
2 years ago
Read 2 more answers
The sequence of transformations that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral GHIJ i
Marina86 [1]

First transformation.

Duadrilateral ABCD has vertices with such coordinates:

  • A(15,10);
  • B(15,20);
  • C(20,15);
  • D(20,5).

Apply a rotation by 90°counterclockwise around point A to this quadrilateral, then

  • A(15,10)→A'(15,10);
  • B(15,20)→B'(5,10);
  • C(20,15)→C'(10,15);
  • D(20,5)→D'(20,15).

Second transformation.

1. A reflection across the y axis has a rule:

(x,y)→(-x,y).

Then

  • A'(15,10)→A''(-15,10);
  • B'(5,10)→B''(-5,10);
  • C'(10,15)→C''(-10,15);
  • D'(20,15)→D''(-20,15).

2. A translation 20 units down has a rule:

(x,y)→(x,y-20).

Then

  • A''(-15,10)→G(-15,-10);
  • B''(-5,10)→H(-5,-10);
  • C''(-10,15)→I(-10,-5);
  • D''(-20,15)→J(-20,-5).

Answer: first blank -B, second blank - B.

4 0
2 years ago
Read 2 more answers
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